regenerated "SMT_Examples" certificates after soft-timeout change + removed a few needless oracles

--- a/src/HOL/SMT_Examples/SMT_Examples.certs	Wed Oct 31 11:23:21 2012 +0100
+++ b/src/HOL/SMT_Examples/SMT_Examples.certs	Thu Nov 01 11:34:00 2012 +0100
@@ -1,13 +1,14 @@
-8c0dd63633148cae631c41716f59fedf31aaf85f 8 0
+23fa46bae38100075457f16458b7f980b6e9eaaa 8 0
+unsat
 #2 := false
 #1 := true
 #7 := (not true)
-#29 := (iff #7 false)
-#30 := [rewrite]: #29
-#28 := [asserted]: #7
-[mp #28 #30]: false
+#13 := (iff #7 false)
+#14 := [rewrite]: #13
+#9 := [asserted]: #7
+[mp #9 #14]: false
+a659f050ece3306f2b1d4dcfecadbe7f96ac25b7 14 0
 unsat
-4e759d02d4de42cc8b917c1ee399e500780bf8d9 22 0
 #2 := false
 decl f1 :: S1
 #3 := f1
@@ -17,20 +18,12 @@
 #9 := (not #8)
 #10 := (or #8 #9)
 #11 := (not #10)
-#40 := (iff #11 false)
-#1 := true
-#35 := (not true)
-#38 := (iff #35 false)
-#39 := [rewrite]: #38
-#36 := (iff #11 #35)
-#33 := (iff #10 true)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#32 := [asserted]: #11
-[mp #32 #41]: false
+#13 := [asserted]: #11
+#15 := [not-or-elim #13]: #8
+#14 := [not-or-elim #13]: #9
+[unit-resolution #14 #15]: false
+a67531da310682d5a288c23ac8f30257442b6eee 28 0
 unsat
-964f9fc947278fe63d579d7e942d63db70d69508 28 0
 #2 := false
 decl f1 :: S1
 #3 := f1
@@ -41,101 +34,141 @@
 #9 := (and #8 true)
 #10 := (iff #9 #8)
 #11 := (not #10)
-#46 := (iff #11 false)
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #11 #41)
-#39 := (iff #10 true)
-#34 := (iff #8 #8)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #10 #34)
-#33 := [rewrite]: #10
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #11
-[mp #32 #47]: false
+#30 := (iff #11 false)
+#25 := (not true)
+#28 := (iff #25 false)
+#29 := [rewrite]: #28
+#26 := (iff #11 #25)
+#23 := (iff #10 true)
+#18 := (iff #8 #8)
+#21 := (iff #18 true)
+#22 := [rewrite]: #21
+#19 := (iff #10 #18)
+#17 := [rewrite]: #10
+#20 := [monotonicity #17]: #19
+#24 := [trans #20 #22]: #23
+#27 := [monotonicity #24]: #26
+#31 := [trans #27 #29]: #30
+#13 := [asserted]: #11
+[mp #13 #31]: false
+d4525927e0ca94e2a8cd999f8854bd810a0a45a9 30 0
 unsat
-6f5c195ed8186ea009f805e2f8ea8ad3b1ee6432 41 0
 #2 := false
 decl f1 :: S1
 #3 := f1
-decl f4 :: S1
-#9 := f4
-#10 := (= f4 f1)
 decl f3 :: S1
 #7 := f3
 #8 := (= f3 f1)
+#12 := (not #8)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
 #11 := (or #8 #10)
-#64 := (iff #11 false)
-#59 := (or false false)
-#62 := (iff #59 false)
-#63 := [rewrite]: #62
-#60 := (iff #11 #59)
-#57 := (iff #10 false)
-#48 := (not #10)
-#12 := (not #8)
 #13 := (and #11 #12)
-#37 := (not #13)
-#38 := (or #37 #10)
-#41 := (not #38)
+#21 := (not #13)
+#22 := (or #21 #10)
+#25 := (not #22)
 #14 := (implies #13 #10)
 #15 := (not #14)
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#36 := [asserted]: #15
-#46 := [mp #36 #43]: #41
-#49 := [not-or-elim #46]: #48
-#58 := [iff-false #49]: #57
-#55 := (iff #8 false)
-#44 := [not-or-elim #46]: #13
-#47 := [and-elim #44]: #12
-#56 := [iff-false #47]: #55
-#61 := [monotonicity #56 #58]: #60
-#65 := [trans #61 #63]: #64
-#45 := [and-elim #44]: #11
-[mp #45 #65]: false
+#26 := (iff #15 #25)
+#23 := (iff #14 #22)
+#24 := [rewrite]: #23
+#27 := [monotonicity #24]: #26
+#17 := [asserted]: #15
+#28 := [mp #17 #27]: #25
+#29 := [not-or-elim #28]: #13
+#31 := [and-elim #29]: #12
+#32 := (not #10)
+#33 := [not-or-elim #28]: #32
+#30 := [and-elim #29]: #11
+[unit-resolution #30 #33 #31]: false
+55b7bd861df00e9621f738450037b0df80372741 84 0
 unsat
-bc6de36d6c86b416e91711bb23067cc8250ac153 33 0
 #2 := false
 decl f1 :: S1
 #3 := f1
+decl f5 :: S1
+#12 := f5
+#13 := (= f5 f1)
 decl f6 :: S1
 #14 := f6
 #15 := (= f6 f1)
-decl f5 :: S1
-#12 := f5
-#13 := (= f5 f1)
-#16 := (and #13 #15)
+#64 := (not #15)
+#63 := (not #13)
+#65 := (or #63 #64)
+#66 := (not #65)
 decl f4 :: S1
 #9 := f4
 #10 := (= f4 f1)
+#58 := (not #10)
 decl f3 :: S1
 #7 := f3
 #8 := (= f3 f1)
+#57 := (not #8)
+#59 := (or #57 #58)
+#60 := (not #59)
+#101 := [hypothesis]: #60
+#89 := (or #59 #8)
+#90 := [def-axiom]: #89
+#102 := [unit-resolution #90 #101]: #8
+#91 := (or #59 #10)
+#92 := [def-axiom]: #91
+#103 := [unit-resolution #92 #101]: #10
 #11 := (and #8 #10)
+#34 := (not #11)
+#78 := (iff #34 #59)
+#73 := (not #60)
+#76 := (iff #73 #59)
+#77 := [rewrite]: #76
+#74 := (iff #34 #73)
+#61 := (iff #11 #60)
+#62 := [rewrite]: #61
+#75 := [monotonicity #62]: #74
+#79 := [trans #75 #77]: #78
+#16 := (and #13 #15)
 #17 := (or #11 #16)
+#25 := (not #17)
+#26 := (or #25 #11 #16)
+#29 := (not #26)
 #18 := (implies #17 #17)
 #19 := (not #18)
-#48 := (iff #19 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #19 #43)
-#41 := (iff #18 true)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#40 := [asserted]: #19
-[mp #40 #49]: false
+#30 := (iff #19 #29)
+#27 := (iff #18 #26)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#21 := [asserted]: #19
+#32 := [mp #21 #31]: #29
+#35 := [not-or-elim #32]: #34
+#80 := [mp #35 #79]: #59
+#104 := [unit-resolution #80 #103 #102]: false
+#105 := [lemma #104]: #59
+#69 := (or #60 #66)
+#70 := (iff #17 #69)
+#67 := (iff #16 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #62 #68]: #70
+#33 := [not-or-elim #32]: #17
+#72 := [mp #33 #71]: #69
+#106 := [unit-resolution #72 #105]: #66
+#95 := (or #65 #13)
+#96 := [def-axiom]: #95
+#107 := [unit-resolution #96 #106]: #13
+#97 := (or #65 #15)
+#98 := [def-axiom]: #97
+#108 := [unit-resolution #98 #106]: #15
+#36 := (not #16)
+#86 := (iff #36 #65)
+#81 := (not #66)
+#84 := (iff #81 #65)
+#85 := [rewrite]: #84
+#82 := (iff #36 #81)
+#83 := [monotonicity #68]: #82
+#87 := [trans #83 #85]: #86
+#37 := [not-or-elim #32]: #36
+#88 := [mp #37 #87]: #65
+[unit-resolution #88 #108 #107]: false
+ecaaaeb4b508586ee415aaee164d7f38d7fa3191 50 0
 unsat
-e334e079d0f61721e404e4ca140ce40c317189ba 55 0
 #2 := false
 decl f1 :: S1
 #3 := f1
@@ -157,41 +190,36 @@
 #14 := (or #11 #13)
 #20 := (implies #14 #19)
 #21 := (not #20)
-#71 := (iff #21 false)
-#43 := (not #8)
-#44 := (or #43 #17)
-#47 := (or #44 #8)
-#53 := (not #14)
-#54 := (or #53 #47)
-#59 := (not #54)
-#69 := (iff #59 false)
+#50 := (iff #21 false)
 #1 := true
-#64 := (not true)
-#67 := (iff #64 false)
-#68 := [rewrite]: #67
-#65 := (iff #59 #64)
-#62 := (iff #54 true)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#70 := [trans #66 #68]: #69
-#60 := (iff #21 #59)
-#57 := (iff #20 #54)
-#50 := (implies #14 #47)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #20 #50)
-#48 := (iff #19 #47)
-#45 := (iff #18 #44)
-#46 := [rewrite]: #45
-#49 := [monotonicity #46]: #48
-#52 := [monotonicity #49]: #51
-#58 := [trans #52 #56]: #57
-#61 := [monotonicity #58]: #60
-#72 := [trans #61 #70]: #71
-#42 := [asserted]: #21
-[mp #42 #72]: false
+#45 := (not true)
+#48 := (iff #45 false)
+#49 := [rewrite]: #48
+#46 := (iff #21 #45)
+#43 := (iff #20 true)
+#38 := (implies #14 true)
+#41 := (iff #38 true)
+#42 := [rewrite]: #41
+#39 := (iff #20 #38)
+#36 := (iff #19 true)
+#27 := (not #8)
+#28 := (or #27 #15 #16)
+#31 := (or #28 #8)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #19 #31)
+#29 := (iff #18 #28)
+#30 := [rewrite]: #29
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#47 := [monotonicity #44]: #46
+#51 := [trans #47 #49]: #50
+#23 := [asserted]: #21
+[mp #23 #51]: false
+01c3def9cab437126fe354f5b2293506994546fd 60 0
 unsat
-778009f890fff5d244f6b4e04a54c69b4023bcd7 60 0
 #2 := false
 decl f1 :: S1
 #3 := f1
@@ -208,81 +236,61 @@
 #16 := (iff #15 #8)
 #17 := (iff #16 #8)
 #18 := (not #17)
-#78 := (iff #18 false)
+#62 := (iff #18 false)
 #1 := true
-#73 := (not true)
-#76 := (iff #73 false)
-#77 := [rewrite]: #76
-#74 := (iff #18 #73)
-#71 := (iff #17 true)
-#40 := (iff #9 true)
-#41 := [rewrite]: #40
-#69 := (iff #17 #9)
-#42 := (iff true #8)
-#45 := (iff #42 #8)
-#46 := [rewrite]: #45
-#66 := (iff #16 #42)
-#64 := (iff #15 true)
-#62 := (iff #15 #9)
-#59 := (iff #14 #42)
-#57 := (iff #13 true)
-#55 := (iff #13 #9)
-#52 := (iff #12 #42)
-#50 := (iff #11 true)
-#48 := (iff #11 #9)
-#43 := (iff #10 #42)
-#44 := [monotonicity #41]: #43
-#47 := [trans #44 #46]: #11
-#49 := [monotonicity #47]: #48
-#51 := [trans #49 #41]: #50
-#53 := [monotonicity #51]: #52
-#54 := [trans #53 #46]: #13
-#56 := [monotonicity #54]: #55
-#58 := [trans #56 #41]: #57
-#60 := [monotonicity #58]: #59
-#61 := [trans #60 #46]: #15
-#63 := [monotonicity #61]: #62
-#65 := [trans #63 #41]: #64
-#67 := [monotonicity #65]: #66
-#68 := [trans #67 #46]: #17
-#70 := [monotonicity #68]: #69
-#72 := [trans #70 #41]: #71
-#75 := [monotonicity #72]: #74
-#79 := [trans #75 #77]: #78
-#39 := [asserted]: #18
-[mp #39 #79]: false
+#57 := (not true)
+#60 := (iff #57 false)
+#61 := [rewrite]: #60
+#58 := (iff #18 #57)
+#55 := (iff #17 true)
+#24 := (iff #9 true)
+#25 := [rewrite]: #24
+#53 := (iff #17 #9)
+#26 := (iff true #8)
+#29 := (iff #26 #8)
+#30 := [rewrite]: #29
+#50 := (iff #16 #26)
+#48 := (iff #15 true)
+#46 := (iff #15 #9)
+#43 := (iff #14 #26)
+#41 := (iff #13 true)
+#39 := (iff #13 #9)
+#36 := (iff #12 #26)
+#34 := (iff #11 true)
+#32 := (iff #11 #9)
+#27 := (iff #10 #26)
+#28 := [monotonicity #25]: #27
+#31 := [trans #28 #30]: #11
+#33 := [monotonicity #31]: #32
+#35 := [trans #33 #25]: #34
+#37 := [monotonicity #35]: #36
+#38 := [trans #37 #30]: #13
+#40 := [monotonicity #38]: #39
+#42 := [trans #40 #25]: #41
+#44 := [monotonicity #42]: #43
+#45 := [trans #44 #30]: #15
+#47 := [monotonicity #45]: #46
+#49 := [trans #47 #25]: #48
+#51 := [monotonicity #49]: #50
+#52 := [trans #51 #30]: #17
+#54 := [monotonicity #52]: #53
+#56 := [trans #54 #25]: #55
+#59 := [monotonicity #56]: #58
+#63 := [trans #59 #61]: #62
+#20 := [asserted]: #18
+[mp #20 #63]: false
+cd163c8c9afce7b0a8a2f73345db7dfc9e0d1c10 112 0
 unsat
-1d6ace6138adeb11b9c9952f896f225452c30f9e 165 0
 #2 := false
 decl f1 :: S1
 #3 := f1
-decl f6 :: S1
-#13 := f6
-#14 := (= f6 f1)
-decl f5 :: S1
-#11 := f5
-#12 := (= f5 f1)
 decl f4 :: S1
 #9 := f4
 #10 := (= f4 f1)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#75 := (or #8 #10 #12 #14)
-#215 := (iff #75 false)
-#210 := (or false false false false)
-#213 := (iff #210 false)
-#214 := [rewrite]: #213
-#211 := (iff #75 #210)
-#167 := (iff #14 false)
-#119 := (not #14)
-#122 := (or #119 #12)
-#175 := (iff #122 #119)
-#170 := (or #119 false)
-#173 := (iff #170 #119)
-#174 := [rewrite]: #173
-#171 := (iff #122 #170)
-#168 := (iff #12 false)
+#107 := (not #10)
+decl f5 :: S1
+#11 := f5
+#12 := (= f5 f1)
 #25 := (not #12)
 decl f11 :: S1
 #43 := f11
@@ -297,59 +305,9 @@
 #48 := (and #42 #47)
 #49 := (or #12 #48)
 #50 := (not #49)
-#150 := (iff #50 #25)
-#148 := (iff #49 #12)
-#143 := (or #12 false)
-#146 := (iff #143 #12)
-#147 := [rewrite]: #146
-#144 := (iff #49 #143)
-#141 := (iff #48 false)
-#136 := (and #42 #41)
-#139 := (iff #136 false)
-#140 := [rewrite]: #139
-#137 := (iff #48 #136)
-#134 := (iff #47 #41)
-#129 := (or #41 false)
-#132 := (iff #129 #41)
-#133 := [rewrite]: #132
-#130 := (iff #47 #129)
-#126 := (iff #46 false)
-#128 := [rewrite]: #126
-#131 := [monotonicity #128]: #130
-#135 := [trans #131 #133]: #134
-#138 := [monotonicity #135]: #137
-#142 := [trans #138 #140]: #141
-#145 := [monotonicity #142]: #144
-#149 := [trans #145 #147]: #148
-#151 := [monotonicity #149]: #150
-#125 := [asserted]: #50
-#154 := [mp #125 #151]: #25
-#169 := [iff-false #154]: #168
-#172 := [monotonicity #169]: #171
-#176 := [trans #172 #174]: #175
-#37 := (or #14 false)
-#38 := (not #37)
-#39 := (or #38 #12)
-#123 := (iff #39 #122)
-#120 := (iff #38 #119)
-#116 := (iff #37 #14)
-#118 := [rewrite]: #116
-#121 := [monotonicity #118]: #120
-#124 := [monotonicity #121]: #123
-#115 := [asserted]: #39
-#127 := [mp #115 #124]: #122
-#166 := [mp #127 #176]: #119
-#177 := [iff-false #166]: #167
-#165 := (iff #10 false)
-#109 := (not #10)
-#112 := (or #109 #12)
-#183 := (iff #112 #109)
-#178 := (or #109 false)
-#181 := (iff #178 #109)
-#182 := [rewrite]: #181
-#179 := (iff #112 #178)
-#180 := [monotonicity #169]: #179
-#184 := [trans #180 #182]: #183
+#58 := [asserted]: #50
+#59 := [not-or-elim #58]: #25
+#110 := (or #107 #12)
 decl f9 :: S1
 #30 := f9
 #31 := (= f9 f1)
@@ -358,67 +316,84 @@
 #34 := (and #10 #33)
 #35 := (not #34)
 #36 := (or #35 #12)
-#113 := (iff #36 #112)
-#110 := (iff #35 #109)
-#107 := (iff #34 #10)
+#111 := (iff #36 #110)
+#108 := (iff #35 #107)
+#105 := (iff #34 #10)
 #1 := true
-#102 := (and #10 true)
-#105 := (iff #102 #10)
-#106 := [rewrite]: #105
-#103 := (iff #34 #102)
-#99 := (iff #33 true)
-#101 := [rewrite]: #99
-#104 := [monotonicity #101]: #103
-#108 := [trans #104 #106]: #107
-#111 := [monotonicity #108]: #110
-#114 := [monotonicity #111]: #113
-#98 := [asserted]: #36
-#117 := [mp #98 #114]: #112
-#164 := [mp #117 #184]: #109
-#185 := [iff-false #164]: #165
-#163 := (iff #8 false)
-#92 := (not #8)
-#95 := (or #92 #10)
-#191 := (iff #95 #92)
-#186 := (or #92 false)
-#189 := (iff #186 #92)
-#190 := [rewrite]: #189
-#187 := (iff #95 #186)
-#188 := [monotonicity #185]: #187
-#192 := [trans #188 #190]: #191
+#100 := (and #10 true)
+#103 := (iff #100 #10)
+#104 := [rewrite]: #103
+#101 := (iff #34 #100)
+#98 := (iff #33 true)
+#99 := [rewrite]: #98
+#102 := [monotonicity #99]: #101
+#106 := [trans #102 #104]: #105
+#109 := [monotonicity #106]: #108
+#112 := [monotonicity #109]: #111
+#56 := [asserted]: #36
+#113 := [mp #56 #112]: #110
+#153 := [unit-resolution #113 #59]: #107
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+decl f6 :: S1
+#13 := f6
+#14 := (= f6 f1)
+#116 := (not #14)
+#119 := (or #116 #12)
+#37 := (or #14 false)
+#38 := (not #37)
+#39 := (or #38 #12)
+#120 := (iff #39 #119)
+#117 := (iff #38 #116)
+#114 := (iff #37 #14)
+#115 := [rewrite]: #114
+#118 := [monotonicity #115]: #117
+#121 := [monotonicity #118]: #120
+#57 := [asserted]: #39
+#122 := [mp #57 #121]: #119
+#154 := [unit-resolution #122 #59]: #116
+#72 := (or #8 #10 #12 #14)
+#15 := (or #12 #14)
+#16 := (or #10 #15)
+#17 := (or #8 #16)
+#75 := (iff #17 #72)
+#66 := (or #10 #12 #14)
+#69 := (or #8 #66)
+#73 := (iff #69 #72)
+#74 := [rewrite]: #73
+#70 := (iff #17 #69)
+#67 := (iff #16 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#76 := [trans #71 #74]: #75
+#53 := [asserted]: #17
+#77 := [mp #53 #76]: #72
+#155 := [unit-resolution #77 #153 #59 #154]: #8
+#91 := (not #8)
+#94 := (or #91 #10)
 #26 := (and #12 #25)
 #27 := (or #8 #26)
 #28 := (not #27)
 #29 := (or #28 #10)
-#96 := (iff #29 #95)
-#93 := (iff #28 #92)
-#90 := (iff #27 #8)
-#85 := (or #8 false)
-#88 := (iff #85 #8)
-#89 := [rewrite]: #88
-#86 := (iff #27 #85)
-#79 := (iff #26 false)
-#84 := [rewrite]: #79
-#87 := [monotonicity #84]: #86
-#91 := [trans #87 #89]: #90
-#94 := [monotonicity #91]: #93
-#97 := [monotonicity #94]: #96
-#74 := [asserted]: #29
-#100 := [mp #74 #97]: #95
-#162 := [mp #100 #192]: #92
-#193 := [iff-false #162]: #163
-#212 := [monotonicity #193 #185 #169 #177]: #211
-#216 := [trans #212 #214]: #215
-#15 := (or #12 #14)
-#16 := (or #10 #15)
-#17 := (or #8 #16)
-#76 := (iff #17 #75)
-#77 := [rewrite]: #76
-#72 := [asserted]: #17
-#78 := [mp #72 #77]: #75
-[mp #78 #216]: false
+#95 := (iff #29 #94)
+#92 := (iff #28 #91)
+#89 := (iff #27 #8)
+#84 := (or #8 false)
+#87 := (iff #84 #8)
+#88 := [rewrite]: #87
+#85 := (iff #27 #84)
+#82 := (iff #26 false)
+#83 := [rewrite]: #82
+#86 := [monotonicity #83]: #85
+#90 := [trans #86 #88]: #89
+#93 := [monotonicity #90]: #92
+#96 := [monotonicity #93]: #95
+#55 := [asserted]: #29
+#97 := [mp #55 #96]: #94
+[unit-resolution #97 #155 #153]: false
+bda0de69751a63d54481e3e810bc744b04b03fa3 59 0
 unsat
-dd0cba0a17795cc066f8c77647c6bcb52b690616 59 0
 #2 := false
 decl f3 :: (-> S3 S2 S2)
 decl f6 :: S2
@@ -433,84 +408,55 @@
 #18 := (f4 f5 f6)
 #20 := (f3 #18 f7)
 #23 := (= #20 #22)
-#57 := (not #23)
+#41 := (not #23)
 #17 := (= f6 f6)
 #24 := (and #17 #23)
 #25 := (not #24)
-#58 := (iff #25 #57)
-#55 := (iff #24 #23)
+#42 := (iff #25 #41)
+#39 := (iff #24 #23)
 #1 := true
-#50 := (and true #23)
-#53 := (iff #50 #23)
-#54 := [rewrite]: #53
-#51 := (iff #24 #50)
-#48 := (iff #17 true)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#59 := [monotonicity #56]: #58
-#47 := [asserted]: #25
-#62 := [mp #47 #59]: #57
+#34 := (and true #23)
+#37 := (iff #34 #23)
+#38 := [rewrite]: #37
+#35 := (iff #24 #34)
+#32 := (iff #17 true)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#40 := [trans #36 #38]: #39
+#43 := [monotonicity #40]: #42
+#28 := [asserted]: #25
+#44 := [mp #28 #43]: #41
 #8 := (:var 1 S2)
 #10 := (:var 0 S2)
 #12 := (f4 f5 #10)
 #13 := (f3 #12 #8)
-#546 := (pattern #13)
+#487 := (pattern #13)
 #9 := (f4 f5 #8)
 #11 := (f3 #9 #10)
-#545 := (pattern #11)
+#486 := (pattern #11)
 #14 := (= #11 #13)
-#547 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #545 #546) #14)
+#488 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #486 #487) #14)
 #15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
-#550 := (iff #15 #547)
-#548 := (iff #14 #14)
-#549 := [refl]: #548
-#551 := [quant-intro #549]: #550
-#70 := (~ #15 #15)
-#68 := (~ #14 #14)
-#69 := [refl]: #68
-#71 := [nnf-pos #69]: #70
-#46 := [asserted]: #15
-#61 := [mp~ #46 #71]: #15
-#552 := [mp #61 #551]: #547
-#130 := (not #547)
-#216 := (or #130 #23)
-#131 := [quant-inst #16 #19]: #216
-[unit-resolution #131 #552 #62]: false
+#491 := (iff #15 #488)
+#489 := (iff #14 #14)
+#490 := [refl]: #489
+#492 := [quant-intro #490]: #491
+#66 := (~ #15 #15)
+#64 := (~ #14 #14)
+#65 := [refl]: #64
+#67 := [nnf-pos #65]: #66
+#27 := [asserted]: #15
+#68 := [mp~ #27 #67]: #15
+#493 := [mp #68 #492]: #488
+#72 := (not #488)
+#157 := (or #72 #23)
+#69 := [quant-inst #16 #19]: #157
+[unit-resolution #69 #493 #44]: false
+01921123e04538e755e19bf1587fc40380f6a26a 1573 0
 unsat
-0863329327da9e45e4d77f7bc111e467c5d58d3c 1288 0
 #2 := false
 decl f1 :: S1
 #3 := f1
-decl f9 :: S1
-#25 := f9
-#26 := (= f9 f1)
-decl f20 :: S1
-#59 := f20
-#60 := (= f20 f1)
-decl f21 :: S1
-#61 := f21
-#62 := (= f21 f1)
-#249 := (not #62)
-decl f31 :: S1
-#97 := f31
-#98 := (= f31 f1)
-decl f62 :: S1
-#207 := f62
-#208 := (= f62 f1)
-decl f58 :: S1
-#189 := f58
-#190 := (= f58 f1)
-#388 := (not #190)
-decl f47 :: S1
-#151 := f47
-#152 := (= f47 f1)
-#289 := (not #98)
-#980 := [hypothesis]: #289
-decl f46 :: S1
-#149 := f46
-#150 := (= f46 f1)
-#346 := (not #150)
 decl f48 :: S1
 #156 := f48
 #157 := (= f48 f1)
@@ -522,183 +468,20 @@
 #144 := f45
 #145 := (= f45 f1)
 #339 := (not #145)
-decl f42 :: S1
-#135 := f42
-#136 := (= f42 f1)
-#1467 := (or #136 #98)
-decl f40 :: S1
-#128 := f40
-#129 := (= f40 f1)
-#330 := (not #136)
-#1095 := [hypothesis]: #330
-decl f32 :: S1
-#99 := f32
-#100 := (= f32 f1)
-#290 := (not #100)
-decl f16 :: S1
-#46 := f16
-#47 := (= f16 f1)
-decl f17 :: S1
-#48 := f17
-#49 := (= f17 f1)
-#236 := (not #49)
-decl f28 :: S1
-#86 := f28
-#87 := (= f28 f1)
-#1450 := (or #87 #98 #136)
-decl f29 :: S1
-#90 := f29
-#91 := (= f29 f1)
-#281 := (not #91)
-#322 := (not #129)
-#277 := (not #87)
-#867 := [hypothesis]: #277
-#1427 := (or #322 #87)
-decl f51 :: S1
-#166 := f51
-#167 := (= f51 f1)
-#363 := (not #167)
-decl f54 :: S1
-#175 := f54
-#176 := (= f54 f1)
-decl f56 :: S1
-#182 := f56
-#183 := (= f56 f1)
-#380 := (not #183)
-#372 := (not #176)
-#1160 := [hypothesis]: #372
-#1189 := (or #388 #176)
-decl f18 :: S1
-#52 := f18
-#53 := (= f18 f1)
+decl f34 :: S1
+#106 := f34
+#107 := (= f34 f1)
 decl f33 :: S1
 #104 := f33
 #105 := (= f33 f1)
 #297 := (not #105)
-decl f36 :: S1
-#113 := f36
-#114 := (= f36 f1)
-#347 := (not #152)
-#1155 := [hypothesis]: #190
-#393 := (or #388 #347)
-#730 := [asserted]: #393
-#1156 := [unit-resolution #730 #1155]: #347
-#389 := (or #387 #388)
-#726 := [asserted]: #389
-#1157 := [unit-resolution #726 #1155]: #387
-#194 := (or #188 #157)
-decl f6 :: S1
-#16 := f6
-#17 := (= f6 f1)
-#579 := (or #17 #188 #157)
-#840 := (iff #579 #194)
-#835 := (or false #188 #157)
-#838 := (iff #835 #194)
-#839 := [rewrite]: #838
-#836 := (iff #579 #835)
-#759 := (iff #17 false)
-#18 := (not #17)
-#439 := [asserted]: #18
-#760 := [iff-false #439]: #759
-#837 := [monotonicity #760]: #836
-#841 := [trans #837 #839]: #840
-#195 := (or #17 #194)
-#580 := (iff #195 #579)
-#581 := [rewrite]: #580
-#568 := [asserted]: #195
-#582 := [mp #568 #581]: #579
-#842 := [mp #582 #841]: #194
-#1158 := [unit-resolution #842 #1157]: #157
 #354 := (not #157)
-#355 := (or #354 #346)
-#702 := [asserted]: #355
-#1159 := [unit-resolution #702 #1158]: #346
-decl f44 :: S1
-#142 := f44
-#143 := (= f44 f1)
-#338 := (not #143)
-decl f61 :: S1
-#203 := f61
-#204 := (= f61 f1)
-decl f60 :: S1
-#199 := f60
-#200 := (= f60 f1)
-#400 := (not #200)
 decl f37 :: S1
 #118 := f37
 #119 := (= f37 f1)
-#313 := (not #119)
-#356 := (or #354 #313)
-#703 := [asserted]: #356
-#1161 := [unit-resolution #703 #1158]: #313
-#983 := (or #400 #150 #152 #119)
-#248 := (not #60)
-decl f23 :: S1
-#68 := f23
-#69 := (= f23 f1)
-decl f34 :: S1
-#106 := f34
-#107 := (= f34 f1)
-#298 := (not #107)
-#1051 := [hypothesis]: #347
-#1052 := [hypothesis]: #346
-#306 := (not #114)
-decl f25 :: S1
-#75 := f25
-#76 := (= f25 f1)
-decl f39 :: S1
-#124 := f39
-#125 := (= f39 f1)
-#318 := (not #125)
-decl f50 :: S1
-#162 := f50
-#163 := (= f50 f1)
-decl f59 :: S1
-#196 := f59
-#197 := (= f59 f1)
-#398 := (not #197)
-#1024 := [hypothesis]: #200
-#401 := (or #400 #398)
-#736 := [asserted]: #401
-#1021 := [unit-resolution #736 #1024]: #398
-#198 := (or #197 #163)
-#573 := [asserted]: #198
-#1022 := [unit-resolution #573 #1021]: #163
-#359 := (not #163)
-#362 := (or #359 #318)
-#707 := [asserted]: #362
-#1019 := [unit-resolution #707 #1022]: #318
 decl f26 :: S1
 #80 := f26
 #81 := (= f26 f1)
-#1153 := [hypothesis]: #313
-decl f35 :: S1
-#111 := f35
-#112 := (= f35 f1)
-#305 := (not #112)
-decl f43 :: S1
-#137 := f43
-#138 := (= f43 f1)
-#331 := (not #138)
-decl f52 :: S1
-#168 := f52
-#169 := (= f52 f1)
-#364 := (not #169)
-#402 := (or #400 #364)
-#737 := [asserted]: #402
-#1020 := [unit-resolution #737 #1024]: #364
-decl f49 :: S1
-#160 := f49
-#161 := (= f49 f1)
-#358 := (not #161)
-#360 := (or #358 #359)
-#705 := [asserted]: #360
-#1017 := [unit-resolution #705 #1022]: #358
-decl f41 :: S1
-#130 := f41
-#131 := (= f41 f1)
-#323 := (not #131)
-#1126 := (or #323 #119 #125)
 #272 := (not #81)
 decl f15 :: S1
 #43 := f15
@@ -707,1089 +490,1566 @@
 #37 := f13
 #38 := (= f13 f1)
 #228 := (not #38)
-decl f11 :: S1
-#31 := f11
-#32 := (= f11 f1)
+decl f14 :: S1
+#39 := f14
+#40 := (= f14 f1)
+decl f27 :: S1
+#84 := f27
+#85 := (= f27 f1)
+decl f29 :: S1
+#90 := f29
+#91 := (= f29 f1)
+#281 := (not #91)
+decl f31 :: S1
+#97 := f31
+#98 := (= f31 f1)
+decl f36 :: S1
+#113 := f36
+#114 := (= f36 f1)
+decl f47 :: S1
+#151 := f47
+#152 := (= f47 f1)
+#347 := (not #152)
+#229 := (not #40)
+#1030 := [hypothesis]: #229
+#1766 := (or #119 #40)
+#313 := (not #119)
+#970 := [hypothesis]: #313
+decl f22 :: S1
+#66 := f22
+#67 := (= f22 f1)
+#256 := (not #67)
+decl f20 :: S1
+#59 := f20
+#60 := (= f20 f1)
+#1740 := (or #60 #40 #119)
+decl f9 :: S1
+#25 := f9
+#26 := (= f9 f1)
 #218 := (not #26)
-decl f7 :: S1
-#19 := f7
-#20 := (= f7 f1)
+#248 := (not #60)
+#919 := [hypothesis]: #248
+#1666 := (or #218 #60)
+decl f19 :: S1
+#54 := f19
+#55 := (= f19 f1)
+#241 := (not #55)
 decl f8 :: S1
 #21 := f8
 #22 := (= f8 f1)
+decl f7 :: S1
+#19 := f7
+#20 := (= f7 f1)
+#213 := (not #20)
+#1651 := [hypothesis]: #26
+#221 := (or #218 #213)
+#459 := [asserted]: #221
+#1652 := [unit-resolution #459 #1651]: #213
+#904 := (or #20 #22)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#9 := (not #8)
+#417 := [asserted]: #9
+#605 := (or #20 #22 #8)
+#23 := (or #22 #8)
+#24 := (or #20 #23)
+#606 := (iff #24 #605)
+#607 := [rewrite]: #606
+#421 := [asserted]: #24
+#608 := [mp #421 #607]: #605
+#905 := [unit-resolution #608 #417]: #904
+#1653 := [unit-resolution #905 #1652]: #22
 #214 := (not #22)
-#1154 := [hypothesis]: #318
-decl f38 :: S1
-#122 := f38
-#123 := (= f38 f1)
-#317 := (not #123)
-#1151 := [hypothesis]: #131
-#327 := (or #323 #317)
-#681 := [asserted]: #327
-#1152 := [unit-resolution #681 #1151]: #317
-#524 := (or #123 #125 #87)
-#126 := (or #125 #87)
-#127 := (or #123 #126)
-#525 := (iff #127 #524)
-#526 := [rewrite]: #525
-#513 := [asserted]: #127
-#527 := [mp #513 #526]: #524
-#1149 := [unit-resolution #527 #1152 #1154]: #87
-#280 := (or #277 #236)
-#647 := [asserted]: #280
-#1150 := [unit-resolution #647 #1149]: #236
-#783 := (or #47 #49)
+#246 := (or #241 #214)
+#475 := [asserted]: #246
+#1654 := [unit-resolution #475 #1653]: #241
+decl f21 :: S1
+#61 := f21
+#62 := (= f21 f1)
+decl f10 :: S1
+#27 := f10
+#28 := (= f10 f1)
+#219 := (not #28)
+#220 := (or #218 #219)
+#458 := [asserted]: #220
+#1655 := [unit-resolution #458 #1651]: #219
+decl f18 :: S1
+#52 := f18
+#53 := (= f18 f1)
+#240 := (not #53)
+#244 := (or #240 #214)
+#473 := [asserted]: #244
+#1656 := [unit-resolution #473 #1653]: #240
+#643 := (or #60 #62 #53 #28)
+#63 := (or #53 #28)
+#64 := (or #62 #63)
+#65 := (or #60 #64)
+#646 := (iff #65 #643)
+#637 := (or #62 #53 #28)
+#640 := (or #60 #637)
+#644 := (iff #640 #643)
+#645 := [rewrite]: #644
+#641 := (iff #65 #640)
+#638 := (iff #64 #637)
+#639 := [rewrite]: #638
+#642 := [monotonicity #639]: #641
+#647 := [trans #642 #645]: #646
+#428 := [asserted]: #65
+#648 := [mp #428 #647]: #643
+#1657 := [unit-resolution #648 #1656 #919 #1655]: #62
+#249 := (not #62)
+#296 := (or #281 #249)
+#512 := [asserted]: #296
+#1658 := [unit-resolution #512 #1657]: #281
+#276 := (not #85)
+decl f17 :: S1
+#48 := f17
+#49 := (= f17 f1)
+decl f16 :: S1
+#46 := f16
+#47 := (= f16 f1)
+#235 := (not #47)
+#247 := (or #235 #214)
+#476 := [asserted]: #247
+#1659 := [unit-resolution #476 #1653]: #235
+#915 := (or #47 #49)
 decl f4 :: S1
 #10 := f4
 #11 := (= f4 f1)
-#464 := (or #47 #49 #11)
-#786 := (iff #464 #783)
-#780 := (or #47 #49 false)
-#784 := (iff #780 #783)
-#785 := [rewrite]: #784
-#781 := (iff #464 #780)
-#755 := (iff #11 false)
 #12 := (not #11)
-#437 := [asserted]: #12
-#756 := [iff-false #437]: #755
-#782 := [monotonicity #756]: #781
-#787 := [trans #782 #785]: #786
+#418 := [asserted]: #12
+#621 := (or #47 #49 #11)
 #50 := (or #49 #11)
 #51 := (or #47 #50)
-#465 := (iff #51 #464)
-#466 := [rewrite]: #465
-#457 := [asserted]: #51
-#467 := [mp #457 #466]: #464
-#788 := [mp #467 #787]: #783
-#1147 := [unit-resolution #788 #1150]: #47
-#235 := (not #47)
-#247 := (or #235 #214)
-#623 := [asserted]: #247
-#1148 := [unit-resolution #623 #1147]: #214
-#764 := (or #20 #22)
-decl f3 :: S1
-#7 := f3
-#8 := (= f3 f1)
-#443 := (or #20 #22 #8)
-#767 := (iff #443 #764)
-#761 := (or #20 #22 false)
-#765 := (iff #761 #764)
-#766 := [rewrite]: #765
-#762 := (iff #443 #761)
-#752 := (iff #8 false)
-#9 := (not #8)
-#436 := [asserted]: #9
-#754 := [iff-false #436]: #752
-#763 := [monotonicity #754]: #762
-#768 := [trans #763 #766]: #767
-#23 := (or #22 #8)
-#24 := (or #20 #23)
-#444 := (iff #24 #443)
-#445 := [rewrite]: #444
-#440 := [asserted]: #24
-#446 := [mp #440 #445]: #443
-#769 := [mp #446 #768]: #764
-#1145 := [unit-resolution #769 #1148]: #20
-#213 := (not #20)
-#221 := (or #218 #213)
-#606 := [asserted]: #221
-#1146 := [unit-resolution #606 #1145]: #218
-decl f12 :: S1
-#33 := f12
-#34 := (= f12 f1)
-#224 := (not #34)
+#622 := (iff #51 #621)
+#623 := [rewrite]: #622
+#426 := [asserted]: #51
+#624 := [mp #426 #623]: #621
+#916 := [unit-resolution #624 #418]: #915
+#1660 := [unit-resolution #916 #1659]: #49
+#236 := (not #49)
+#279 := (or #276 #236)
+#499 := [asserted]: #279
+#1661 := [unit-resolution #499 #1660]: #276
+#1663 := (or #91 #85 #55)
 decl f30 :: S1
 #92 := f30
 #93 := (= f30 f1)
 #282 := (not #93)
-#328 := (or #323 #282)
-#682 := [asserted]: #328
-#1143 := [unit-resolution #682 #1151]: #282
-decl f27 :: S1
-#84 := f27
-#85 := (= f27 f1)
-#276 := (not #85)
-#278 := (or #276 #277)
-#645 := [asserted]: #278
-#1144 := [unit-resolution #645 #1149]: #276
-decl f19 :: S1
-#54 := f19
-#55 := (= f19 f1)
-#241 := (not #55)
-#245 := (or #241 #235)
-#621 := [asserted]: #245
-#1141 := [unit-resolution #621 #1147]: #241
-#499 := (or #91 #93 #85 #55)
-#94 := (or #85 #55)
-#95 := (or #93 #94)
-#96 := (or #91 #95)
-#500 := (iff #96 #499)
-#501 := [rewrite]: #500
-#488 := [asserted]: #96
-#502 := [mp #488 #501]: #499
-#1142 := [unit-resolution #502 #1141 #1144 #1143]: #91
-#296 := (or #281 #249)
-#659 := [asserted]: #296
-#1139 := [unit-resolution #659 #1142]: #249
-#240 := (not #53)
-#243 := (or #240 #235)
-#619 := [asserted]: #243
-#1140 := [unit-resolution #619 #1147]: #240
-decl f10 :: S1
-#27 := f10
-#28 := (= f10 f1)
-#219 := (not #28)
-#222 := (or #219 #213)
-#607 := [asserted]: #222
-#1137 := [unit-resolution #607 #1145]: #219
-#474 := (or #60 #62 #53 #28)
-#63 := (or #53 #28)
-#64 := (or #62 #63)
-#65 := (or #60 #64)
-#475 := (iff #65 #474)
-#476 := [rewrite]: #475
-#463 := [asserted]: #65
-#477 := [mp #463 #476]: #474
-#1138 := [unit-resolution #477 #1137 #1140 #1139]: #60
-#263 := (or #248 #224)
-#635 := [asserted]: #263
-#1135 := [unit-resolution #635 #1138]: #224
-#453 := (or #32 #34 #26)
-#35 := (or #34 #26)
-#36 := (or #32 #35)
-#454 := (iff #36 #453)
-#455 := [rewrite]: #454
-#442 := [asserted]: #36
-#456 := [mp #442 #455]: #453
-#1136 := [unit-resolution #456 #1135 #1146]: #32
+decl f40 :: S1
+#128 := f40
+#129 := (= f40 f1)
+#289 := (not #98)
+decl f41 :: S1
+#130 := f41
+#131 := (= f41 f1)
+decl f52 :: S1
+#168 := f52
+#169 := (= f52 f1)
+#364 := (not #169)
+decl f60 :: S1
+#199 := f60
+#200 := (= f60 f1)
+decl f61 :: S1
+#203 := f61
+#204 := (= f61 f1)
+#404 := (not #204)
+decl f56 :: S1
+#182 := f56
+#183 := (= f56 f1)
+#322 := (not #129)
+#881 := [hypothesis]: #322
+#1606 := (or #183 #129)
+decl f54 :: S1
+#175 := f54
+#176 := (= f54 f1)
+#372 := (not #176)
+decl f43 :: S1
+#137 := f43
+#138 := (= f43 f1)
+#380 := (not #183)
+#882 := [hypothesis]: #380
+#1359 := (or #387 #129 #183)
+decl f50 :: S1
+#162 := f50
+#163 := (= f50 f1)
+decl f59 :: S1
+#196 := f59
+#197 := (= f59 f1)
+#398 := (not #197)
+decl f62 :: S1
+#207 := f62
+#208 := (= f62 f1)
+decl f58 :: S1
+#189 := f58
+#190 := (= f58 f1)
+#388 := (not #190)
+#1337 := [hypothesis]: #188
+#389 := (or #387 #388)
+#579 := [asserted]: #389
+#1338 := [unit-resolution #579 #1337]: #388
+#211 := (or #208 #190)
+decl f5 :: S1
+#13 := f5
+#14 := (= f5 f1)
+#15 := (not #14)
+#419 := [asserted]: #15
+#857 := (or #14 #208 #190)
+#212 := (or #14 #211)
+#858 := (iff #212 #857)
+#859 := [rewrite]: #858
+#454 := [asserted]: #212
+#860 := [mp #454 #859]: #857
+#1339 := [unit-resolution #860 #419]: #211
+#1340 := [unit-resolution #1339 #1338]: #208
+#408 := (not #208)
+#409 := (or #408 #404)
+#595 := [asserted]: #409
+#1341 := [unit-resolution #595 #1340]: #404
+decl f53 :: S1
+#173 := f53
+#174 := (= f53 f1)
+decl f55 :: S1
+#180 := f55
+#181 := (= f55 f1)
+#379 := (not #181)
+#390 := (or #387 #379)
+#580 := [asserted]: #390
+#1342 := [unit-resolution #580 #1337]: #379
+#391 := (or #387 #347)
+#581 := [asserted]: #391
+#1343 := [unit-resolution #581 #1337]: #347
+#1335 := (or #339 #129 #181 #183 #204 #152)
+decl f39 :: S1
+#124 := f39
+#125 := (= f39 f1)
+#318 := (not #125)
+#969 := [hypothesis]: #404
+#883 := [hypothesis]: #379
+decl f25 :: S1
+#75 := f25
+#76 := (= f25 f1)
+#265 := (not #76)
+#1172 := [hypothesis]: #347
+#1304 := (or #40 #152 #204 #181 #183 #129)
+#1276 := (or #138 #152 #181 #183 #204 #129 #40)
+decl f46 :: S1
+#149 := f46
+#150 := (= f46 f1)
+#346 := (not #150)
+#1152 := (or #119 #129 #181 #183 #204)
+decl f32 :: S1
+#99 := f32
+#100 := (= f32 f1)
+#331 := (not #138)
+#400 := (not #200)
+#359 := (not #163)
+decl f28 :: S1
+#86 := f28
+#87 := (= f28 f1)
+#277 := (not #87)
+decl f11 :: S1
+#31 := f11
+#32 := (= f11 f1)
 #223 := (not #32)
-#231 := (or #228 #223)
-#612 := [asserted]: #231
-#1133 := [unit-resolution #612 #1136]: #228
-#45 := (or #44 #38)
-#452 := [asserted]: #45
-#1134 := [unit-resolution #452 #1133]: #44
 #233 := (not #44)
+#1008 := (or #233 #129 #181 #183 #204 #119)
+#371 := (not #174)
+decl f51 :: S1
+#166 := f51
+#167 := (= f51 f1)
+decl f35 :: S1
+#111 := f35
+#112 := (= f35 f1)
+#971 := [hypothesis]: #44
 #274 := (or #272 #233)
-#643 := [asserted]: #274
-#1131 := [unit-resolution #643 #1134]: #272
-#519 := (or #119 #112 #81)
+#496 := [asserted]: #274
+#972 := [unit-resolution #496 #971]: #272
+#729 := (or #119 #112 #81)
 #120 := (or #112 #81)
 #121 := (or #119 #120)
-#520 := (iff #121 #519)
-#521 := [rewrite]: #520
-#508 := [asserted]: #121
-#522 := [mp #508 #521]: #519
-#1132 := [unit-resolution #522 #1131 #1153]: #112
-decl f14 :: S1
-#39 := f14
-#40 := (= f14 f1)
-#229 := (not #40)
-#232 := (or #229 #223)
-#613 := [asserted]: #232
-#1129 := [unit-resolution #613 #1136]: #229
-decl f22 :: S1
-#66 := f22
-#67 := (= f22 f1)
-#256 := (not #67)
-#259 := (or #256 #248)
-#631 := [asserted]: #259
-#1130 := [unit-resolution #631 #1138]: #256
+#730 := (iff #121 #729)
+#731 := [rewrite]: #730
+#437 := [asserted]: #121
+#732 := [mp #437 #731]: #729
+#973 := [unit-resolution #732 #972 #970]: #112
+#305 := (not #112)
+#308 := (or #305 #297)
+#520 := [asserted]: #308
+#974 := [unit-resolution #520 #973]: #297
+#309 := (or #305 #265)
+#521 := [asserted]: #309
+#975 := [unit-resolution #521 #973]: #265
 decl f24 :: S1
 #73 := f24
 #74 := (= f24 f1)
 #264 := (not #74)
 #275 := (or #264 #233)
-#644 := [asserted]: #275
-#1127 := [unit-resolution #644 #1134]: #264
-#484 := (or #74 #76 #67 #40)
-#77 := (or #67 #40)
-#78 := (or #76 #77)
-#79 := (or #74 #78)
-#485 := (iff #79 #484)
-#486 := [rewrite]: #485
-#473 := [asserted]: #79
-#487 := [mp #473 #486]: #484
-#1128 := [unit-resolution #487 #1127 #1130 #1129]: #76
-#265 := (not #76)
-#309 := (or #305 #265)
-#668 := [asserted]: #309
-#1125 := [unit-resolution #668 #1128 #1132]: false
-#1123 := [lemma #1125]: #1126
-#1018 := [unit-resolution #1123 #1019 #1153]: #323
-#559 := (or #167 #169 #161 #131)
-#170 := (or #161 #131)
-#171 := (or #169 #170)
-#172 := (or #167 #171)
-#560 := (iff #172 #559)
-#561 := [rewrite]: #560
-#548 := [asserted]: #172
-#562 := [mp #548 #561]: #559
-#1015 := [unit-resolution #562 #1018 #1017 #1020]: #167
-#378 := (or #363 #331)
-#719 := [asserted]: #378
-#1016 := [unit-resolution #719 #1015]: #331
-#1026 := (or #305 #138 #125 #150 #152)
-#1049 := [hypothesis]: #112
-#307 := (or #305 #306)
-#666 := [asserted]: #307
-#1050 := [unit-resolution #666 #1049]: #306
-#544 := (or #150 #152 #143 #114)
-#153 := (or #143 #114)
-#154 := (or #152 #153)
-#155 := (or #150 #154)
-#545 := (iff #155 #544)
-#546 := [rewrite]: #545
-#533 := [asserted]: #155
-#547 := [mp #533 #546]: #544
-#1047 := [unit-resolution #547 #1050 #1052 #1051]: #143
-#342 := (or #338 #298)
-#692 := [asserted]: #342
-#1048 := [unit-resolution #692 #1047]: #298
-#308 := (or #305 #297)
-#667 := [asserted]: #308
-#1045 := [unit-resolution #667 #1049]: #297
-#341 := (or #338 #330)
-#691 := [asserted]: #341
-#1046 := [unit-resolution #691 #1047]: #330
-#1096 := [hypothesis]: #331
-#1063 := (or #277 #138 #136 #105 #107)
-#1083 := [hypothesis]: #87
-#1084 := [unit-resolution #647 #1083]: #236
-#1081 := [unit-resolution #788 #1084]: #47
-#1082 := [unit-resolution #623 #1081]: #214
-#1079 := [unit-resolution #769 #1082]: #20
-#1080 := [unit-resolution #607 #1079]: #219
-#1077 := [unit-resolution #619 #1081]: #240
-#1078 := [hypothesis]: #298
-#1075 := [hypothesis]: #297
-#1076 := [unit-resolution #621 #1081]: #241
-#1073 := [unit-resolution #645 #1083]: #276
-#1085 := (or #289 #85 #55 #138 #136)
-#1093 := [hypothesis]: #98
-#291 := (or #289 #290)
-#654 := [asserted]: #291
-#1094 := [unit-resolution #654 #1093]: #290
-#534 := (or #136 #138 #129 #100)
-#139 := (or #129 #100)
-#140 := (or #138 #139)
-#141 := (or #136 #140)
-#535 := (iff #141 #534)
-#536 := [rewrite]: #535
-#523 := [asserted]: #141
-#537 := [mp #523 #536]: #534
-#1091 := [unit-resolution #537 #1094 #1096 #1095]: #129
-#1092 := [hypothesis]: #241
-#1089 := [hypothesis]: #276
-#292 := (or #289 #281)
-#655 := [asserted]: #292
-#1090 := [unit-resolution #655 #1093]: #281
-#1087 := [unit-resolution #502 #1090 #1089 #1092]: #93
-#326 := (or #322 #282)
-#680 := [asserted]: #326
-#1088 := [unit-resolution #680 #1087 #1091]: false
-#1086 := [lemma #1088]: #1085
-#1074 := [unit-resolution #1086 #1073 #1076 #1096 #1095]: #289
-#509 := (or #105 #107 #98 #69)
-#108 := (or #98 #69)
-#109 := (or #107 #108)
-#110 := (or #105 #109)
-#510 := (iff #110 #509)
-#511 := [rewrite]: #510
-#498 := [asserted]: #110
-#512 := [mp #498 #511]: #509
-#1071 := [unit-resolution #512 #1074 #1075 #1078]: #69
-#257 := (not #69)
-#261 := (or #257 #248)
-#633 := [asserted]: #261
-#1072 := [unit-resolution #633 #1071]: #248
-#1069 := [unit-resolution #477 #1072 #1077 #1080]: #62
-#295 := (or #290 #249)
-#658 := [asserted]: #295
-#1070 := [unit-resolution #658 #1069]: #290
-#1067 := [unit-resolution #537 #1070 #1096 #1095]: #129
-#1068 := [unit-resolution #659 #1069]: #281
-#1065 := [unit-resolution #502 #1068 #1073 #1076]: #93
-#1066 := [unit-resolution #680 #1065 #1067]: false
-#1064 := [lemma #1066]: #1063
-#1043 := [unit-resolution #1064 #1046 #1096 #1045 #1048]: #277
-#1044 := [unit-resolution #527 #1043 #1154]: #123
-#325 := (or #322 #317)
-#679 := [asserted]: #325
-#1041 := [unit-resolution #679 #1044]: #322
-#1042 := [unit-resolution #537 #1041 #1096 #1046]: #100
-#1039 := [unit-resolution #654 #1042]: #289
-#1040 := [unit-resolution #512 #1039 #1045 #1048]: #69
-#1037 := [unit-resolution #633 #1040]: #248
-#1038 := [unit-resolution #658 #1042]: #249
-#294 := (or #290 #281)
-#657 := [asserted]: #294
-#1035 := [unit-resolution #657 #1042]: #281
-#329 := (or #317 #282)
-#683 := [asserted]: #329
-#1036 := [unit-resolution #683 #1044]: #282
-#1053 := (or #235 #62 #60)
-#1061 := [hypothesis]: #248
-#1062 := [hypothesis]: #249
-#1059 := [hypothesis]: #47
-#1060 := [unit-resolution #619 #1059]: #240
-#1057 := [unit-resolution #477 #1060 #1062 #1061]: #28
-#1058 := [unit-resolution #623 #1059]: #214
-#1055 := [unit-resolution #769 #1058]: #20
-#1056 := [unit-resolution #607 #1055 #1057]: false
-#1054 := [lemma #1056]: #1053
-#1033 := [unit-resolution #1054 #1038 #1037]: #235
-#1034 := [unit-resolution #788 #1033]: #49
-#279 := (or #276 #236)
-#646 := [asserted]: #279
-#1031 := [unit-resolution #646 #1034]: #276
-#1032 := [unit-resolution #502 #1031 #1036 #1035]: #55
-#242 := (or #240 #241)
-#618 := [asserted]: #242
-#1029 := [unit-resolution #618 #1032]: #240
-#1030 := [unit-resolution #477 #1029 #1038 #1037]: #28
-#246 := (or #241 #214)
-#622 := [asserted]: #246
-#1027 := [unit-resolution #622 #1032]: #214
-#1028 := [unit-resolution #769 #1027]: #20
-#1025 := [unit-resolution #607 #1028 #1030]: false
-#1023 := [lemma #1025]: #1026
-#1013 := [unit-resolution #1023 #1016 #1019 #1052 #1051]: #305
-#1014 := [unit-resolution #522 #1013 #1153]: #81
-#1097 := (or #272 #125 #76)
-#1124 := [hypothesis]: #81
-#1121 := [unit-resolution #643 #1124]: #233
-#1122 := [unit-resolution #452 #1121]: #38
-#1119 := [unit-resolution #612 #1122]: #223
-#273 := (or #272 #264)
-#642 := [asserted]: #273
-#1120 := [unit-resolution #642 #1124]: #264
-#1117 := [hypothesis]: #265
-#230 := (or #228 #229)
-#611 := [asserted]: #230
-#1118 := [unit-resolution #611 #1122]: #229
-#1115 := [unit-resolution #487 #1118 #1117 #1120]: #67
-#260 := (or #256 #224)
-#632 := [asserted]: #260
-#1116 := [unit-resolution #632 #1115]: #224
-#1113 := [unit-resolution #456 #1116 #1119]: #26
-#220 := (or #218 #219)
-#605 := [asserted]: #220
-#1114 := [unit-resolution #605 #1113]: #219
-#1111 := [unit-resolution #631 #1115]: #248
-#1112 := [unit-resolution #606 #1113]: #213
-#1109 := [unit-resolution #769 #1112]: #22
-#244 := (or #240 #214)
-#620 := [asserted]: #244
-#1110 := [unit-resolution #620 #1109]: #240
-#1107 := [unit-resolution #477 #1110 #1111 #1114]: #62
-#1108 := [unit-resolution #659 #1107]: #281
-#1105 := [unit-resolution #622 #1109]: #241
-#1106 := [unit-resolution #623 #1109]: #235
-#1103 := [unit-resolution #788 #1106]: #49
-#1104 := [unit-resolution #646 #1103]: #276
-#1101 := [unit-resolution #502 #1104 #1105 #1108]: #93
-#1102 := [unit-resolution #647 #1103]: #277
-#1099 := [unit-resolution #527 #1102 #1154]: #123
-#1100 := [unit-resolution #683 #1099 #1101]: false
-#1098 := [lemma #1100]: #1097
-#1011 := [unit-resolution #1098 #1014 #1019]: #76
-#311 := (or #306 #265)
-#670 := [asserted]: #311
-#1012 := [unit-resolution #670 #1011]: #306
-#1009 := [unit-resolution #547 #1012 #1052 #1051]: #143
-#1010 := [unit-resolution #692 #1009]: #298
-#312 := (or #297 #265)
-#671 := [asserted]: #312
-#1007 := [unit-resolution #671 #1011]: #297
-#1008 := [unit-resolution #691 #1009]: #330
-#1005 := [unit-resolution #1064 #1008 #1016 #1007 #1010]: #277
-#1006 := [unit-resolution #527 #1005 #1019]: #123
-#1003 := [unit-resolution #679 #1006]: #322
-#1004 := [unit-resolution #537 #1003 #1016 #1008]: #100
-#1001 := [unit-resolution #654 #1004]: #289
-#1002 := [unit-resolution #512 #1001 #1007 #1010]: #69
-#999 := [unit-resolution #633 #1002]: #248
-#1000 := [unit-resolution #658 #1004]: #249
-#997 := [unit-resolution #643 #1014]: #233
-#998 := [unit-resolution #452 #997]: #38
-#995 := [unit-resolution #612 #998]: #223
-#262 := (or #257 #224)
-#634 := [asserted]: #262
-#996 := [unit-resolution #634 #1002]: #224
-#993 := [unit-resolution #456 #996 #995]: #26
-#994 := [unit-resolution #605 #993]: #219
-#991 := [unit-resolution #477 #994 #1000 #999]: #53
-#992 := [unit-resolution #657 #1004]: #281
-#989 := [unit-resolution #683 #1006]: #282
-#990 := [unit-resolution #1054 #999 #1000]: #235
-#987 := [unit-resolution #788 #990]: #49
-#988 := [unit-resolution #646 #987]: #276
-#985 := [unit-resolution #502 #988 #989 #992]: #55
-#986 := [unit-resolution #618 #985 #991]: false
-#984 := [lemma #986]: #983
-#1162 := [unit-resolution #984 #1159 #1156 #1161]: #400
-#590 := (or #204 #200 #176)
-#205 := (or #200 #176)
-#206 := (or #204 #205)
-#591 := (iff #206 #590)
-#592 := [rewrite]: #591
-#583 := [asserted]: #206
-#593 := [mp #583 #592]: #590
-#1163 := [unit-resolution #593 #1162 #1160]: #204
-#404 := (not #204)
-#411 := (or #404 #380)
-#744 := [asserted]: #411
-#1164 := [unit-resolution #744 #1163]: #380
-decl f55 :: S1
-#180 := f55
-#181 := (= f55 f1)
-#379 := (not #181)
-#392 := (or #388 #379)
-#729 := [asserted]: #392
-#1165 := [unit-resolution #729 #1155]: #379
-decl f53 :: S1
-#173 := f53
-#174 := (= f53 f1)
-#371 := (not #174)
-#913 := (or #248 #181 #183 #150 #152 #119)
-#937 := [hypothesis]: #60
-#938 := [unit-resolution #631 #937]: #256
-#939 := (or #306 #67 #119)
-#971 := [hypothesis]: #256
-#950 := [hypothesis]: #114
-#947 := [unit-resolution #670 #950]: #265
-#948 := [unit-resolution #666 #950]: #305
-#945 := [unit-resolution #522 #948 #1153]: #81
-#946 := [unit-resolution #642 #945]: #264
-#943 := [unit-resolution #487 #946 #947 #971]: #40
-#944 := [unit-resolution #643 #945]: #233
-#941 := [unit-resolution #452 #944]: #38
-#942 := [unit-resolution #611 #941 #943]: false
-#940 := [lemma #942]: #939
-#935 := [unit-resolution #940 #938 #1153]: #306
-#936 := [unit-resolution #547 #935 #1052 #1051]: #143
-#933 := [unit-resolution #691 #936]: #330
-#934 := [unit-resolution #635 #937]: #224
-#952 := (or #223 #67 #119)
-#959 := [hypothesis]: #32
-#960 := [unit-resolution #612 #959]: #228
-#957 := [unit-resolution #452 #960]: #44
-#958 := [unit-resolution #643 #957]: #272
-#955 := [unit-resolution #522 #958 #1153]: #112
-#956 := [unit-resolution #613 #959]: #229
-#953 := [unit-resolution #644 #957]: #264
-#954 := [unit-resolution #487 #953 #956 #971]: #76
-#951 := [unit-resolution #668 #954 #955]: false
-#949 := [lemma #951]: #952
-#931 := [unit-resolution #949 #938 #1153]: #223
-#932 := [unit-resolution #456 #931 #934]: #26
-#929 := [unit-resolution #606 #932]: #213
-#930 := [unit-resolution #769 #929]: #22
-#927 := [unit-resolution #622 #930]: #241
-#928 := [unit-resolution #623 #930]: #235
-#925 := [unit-resolution #788 #928]: #49
-#926 := [unit-resolution #646 #925]: #276
-#961 := (or #297 #67 #119)
-#972 := [hypothesis]: #105
-#969 := [unit-resolution #671 #972]: #265
-#970 := [unit-resolution #667 #972]: #305
-#967 := [unit-resolution #522 #970 #1153]: #81
-#968 := [unit-resolution #642 #967]: #264
-#965 := [unit-resolution #487 #968 #969 #971]: #40
-#966 := [unit-resolution #643 #967]: #233
-#963 := [unit-resolution #452 #966]: #38
-#964 := [unit-resolution #611 #963 #965]: false
-#962 := [lemma #964]: #961
-#923 := [unit-resolution #962 #938 #1153]: #297
-#924 := [unit-resolution #633 #937]: #257
-#921 := [unit-resolution #692 #936]: #298
-#922 := [unit-resolution #512 #921 #924 #923]: #98
-#919 := [hypothesis]: #380
-#920 := [hypothesis]: #379
-#340 := (or #338 #339)
-#690 := [asserted]: #340
-#917 := [unit-resolution #690 #936]: #339
-#569 := (or #181 #183 #174 #145)
+#497 := [asserted]: #275
+#976 := [unit-resolution #497 #971]: #264
+#908 := (or #372 #74 #76 #105 #129 #181 #183)
+#879 := [hypothesis]: #176
+#377 := (or #372 #331)
+#571 := [asserted]: #377
+#880 := [unit-resolution #571 #879]: #331
+decl f42 :: S1
+#135 := f42
+#136 := (= f42 f1)
+#330 := (not #136)
+#373 := (or #371 #372)
+#567 := [asserted]: #373
+#884 := [unit-resolution #567 #879]: #371
+#823 := (or #181 #183 #174 #145)
 #184 := (or #174 #145)
 #185 := (or #183 #184)
 #186 := (or #181 #185)
-#570 := (iff #186 #569)
-#571 := [rewrite]: #570
-#558 := [asserted]: #186
-#572 := [mp #558 #571]: #569
-#918 := [unit-resolution #572 #917 #920 #919]: #174
-#375 := (or #371 #331)
-#716 := [asserted]: #375
-#915 := [unit-resolution #716 #918]: #331
-#916 := [unit-resolution #1086 #915 #922 #926 #927 #933]: false
-#914 := [lemma #916]: #913
-#1166 := [unit-resolution #914 #1165 #1164 #1159 #1156 #1161]: #248
-#753 := (or #371 #150 #152 #119 #60)
-#793 := [hypothesis]: #174
-#374 := (or #371 #363)
-#715 := [asserted]: #374
-#794 := [unit-resolution #715 #793]: #363
-#791 := [unit-resolution #716 #793]: #331
-#802 := (or #236 #119 #150 #152 #138 #60 #167)
-#881 := [hypothesis]: #363
-#819 := [hypothesis]: #49
-#820 := [unit-resolution #647 #819]: #277
-#834 := (or #322 #167 #87)
-#849 := [hypothesis]: #129
-#324 := (or #322 #323)
-#678 := [asserted]: #324
-#850 := [unit-resolution #678 #849]: #323
-#847 := [unit-resolution #679 #849]: #317
-#848 := [unit-resolution #527 #847 #867]: #125
-#361 := (or #358 #318)
-#706 := [asserted]: #361
-#845 := [unit-resolution #706 #848]: #358
-#846 := [unit-resolution #562 #845 #881 #850]: #169
-#843 := [unit-resolution #707 #848]: #359
-#844 := [unit-resolution #573 #843]: #197
-#403 := (or #398 #364)
-#738 := [asserted]: #403
-#833 := [unit-resolution #738 #844 #846]: false
-#831 := [lemma #833]: #834
-#817 := [unit-resolution #831 #820 #881]: #322
-#818 := [unit-resolution #646 #819]: #276
-#851 := (or #282 #167 #87)
-#869 := [hypothesis]: #93
-#870 := [unit-resolution #682 #869]: #323
-#868 := [unit-resolution #683 #869]: #317
-#865 := [unit-resolution #527 #868 #867]: #125
-#866 := [unit-resolution #706 #865]: #358
-#863 := [unit-resolution #562 #866 #881 #870]: #169
-#864 := [unit-resolution #707 #865]: #359
-#861 := [unit-resolution #573 #864]: #197
-#862 := [unit-resolution #738 #861 #863]: false
-#852 := [lemma #862]: #851
-#815 := [unit-resolution #852 #820 #881]: #282
-#821 := (or #55 #138 #129 #150 #152 #93 #85 #60 #119)
-#832 := [hypothesis]: #322
-#829 := [hypothesis]: #282
-#830 := [unit-resolution #502 #1092 #829 #1089]: #91
-#827 := [unit-resolution #657 #830]: #290
-#891 := (or #67 #55 #85 #138 #60 #150 #152 #119)
-#911 := [unit-resolution #940 #971 #1153]: #306
-#912 := [unit-resolution #547 #911 #1052 #1051]: #143
-#909 := [unit-resolution #691 #912]: #330
-#910 := [unit-resolution #949 #971 #1153]: #223
-#907 := [unit-resolution #962 #971 #1153]: #297
-#908 := [unit-resolution #692 #912]: #298
-#905 := [unit-resolution #1086 #909 #1096 #1089 #1092]: #289
-#906 := [unit-resolution #512 #905 #908 #907]: #69
-#903 := [unit-resolution #634 #906]: #224
-#904 := [unit-resolution #456 #903 #910]: #26
-#901 := [unit-resolution #605 #904]: #219
-#902 := [unit-resolution #606 #904]: #213
-#899 := [unit-resolution #769 #902]: #22
-#900 := [unit-resolution #620 #899]: #240
-#897 := [unit-resolution #477 #900 #1061 #901]: #62
-#898 := [unit-resolution #658 #897]: #290
-#895 := [unit-resolution #537 #898 #1096 #909]: #129
-#896 := [unit-resolution #659 #897]: #281
-#893 := [unit-resolution #502 #896 #1092 #1089]: #93
-#894 := [unit-resolution #680 #893 #895]: false
-#892 := [lemma #894]: #891
-#828 := [unit-resolution #892 #1092 #1089 #1096 #1061 #1052 #1051 #1153]: #67
+#826 := (iff #186 #823)
+#817 := (or #183 #174 #145)
+#820 := (or #181 #817)
+#824 := (iff #820 #823)
+#825 := [rewrite]: #824
+#821 := (iff #186 #820)
+#818 := (iff #185 #817)
+#819 := [rewrite]: #818
+#822 := [monotonicity #819]: #821
+#827 := [trans #822 #825]: #826
+#447 := [asserted]: #186
+#828 := [mp #447 #827]: #823
+#885 := [unit-resolution #828 #884 #883 #882]: #145
+#343 := (or #339 #330)
+#546 := [asserted]: #343
+#886 := [unit-resolution #546 #885]: #330
+#755 := (or #136 #138 #129 #100)
+#139 := (or #129 #100)
+#140 := (or #138 #139)
+#141 := (or #136 #140)
+#758 := (iff #141 #755)
+#749 := (or #138 #129 #100)
+#752 := (or #136 #749)
+#756 := (iff #752 #755)
+#757 := [rewrite]: #756
+#753 := (iff #141 #752)
+#750 := (iff #140 #749)
+#751 := [rewrite]: #750
+#754 := [monotonicity #751]: #753
+#759 := [trans #754 #757]: #758
+#440 := [asserted]: #141
+#760 := [mp #440 #759]: #755
+#887 := [unit-resolution #760 #886 #881 #880]: #100
+#290 := (not #100)
+#295 := (or #290 #249)
+#511 := [asserted]: #295
+#888 := [unit-resolution #511 #887]: #249
+decl f23 :: S1
+#68 := f23
+#69 := (= f23 f1)
+#298 := (not #107)
+#344 := (or #339 #298)
+#547 := [asserted]: #344
+#889 := [unit-resolution #547 #885]: #298
+#890 := [hypothesis]: #297
+#291 := (or #289 #290)
+#507 := [asserted]: #291
+#891 := [unit-resolution #507 #887]: #289
+#711 := (or #105 #107 #98 #69)
+#108 := (or #98 #69)
+#109 := (or #107 #108)
+#110 := (or #105 #109)
+#714 := (iff #110 #711)
+#705 := (or #107 #98 #69)
+#708 := (or #105 #705)
+#712 := (iff #708 #711)
+#713 := [rewrite]: #712
+#709 := (iff #110 #708)
+#706 := (iff #109 #705)
+#707 := [rewrite]: #706
+#710 := [monotonicity #707]: #709
+#715 := [trans #710 #713]: #714
+#435 := [asserted]: #110
+#716 := [mp #435 #715]: #711
+#892 := [unit-resolution #716 #891 #890 #889]: #69
+#257 := (not #69)
+#261 := (or #257 #248)
+#486 := [asserted]: #261
+#893 := [unit-resolution #486 #892]: #248
+decl f12 :: S1
+#33 := f12
+#34 := (= f12 f1)
+#224 := (not #34)
+#262 := (or #257 #224)
+#487 := [asserted]: #262
+#894 := [unit-resolution #487 #892]: #224
+#895 := [hypothesis]: #265
+#896 := [hypothesis]: #264
 #258 := (or #256 #257)
-#630 := [asserted]: #258
-#825 := [unit-resolution #630 #828]: #257
-#826 := [unit-resolution #655 #830]: #289
-#973 := (or #330 #69 #98 #150 #152)
-#981 := [hypothesis]: #136
-#982 := [unit-resolution #691 #981]: #338
-#979 := [unit-resolution #547 #982 #1052 #1051]: #114
-#977 := [hypothesis]: #257
-#345 := (or #330 #298)
-#695 := [asserted]: #345
-#978 := [unit-resolution #695 #981]: #298
-#975 := [unit-resolution #512 #978 #977 #980]: #105
-#310 := (or #306 #297)
-#669 := [asserted]: #310
-#976 := [unit-resolution #669 #975 #979]: false
-#974 := [lemma #976]: #973
-#823 := [unit-resolution #974 #826 #825 #1052 #1051]: #330
-#824 := [unit-resolution #537 #823 #827 #1096 #832]: false
-#822 := [lemma #824]: #821
-#816 := [unit-resolution #822 #817 #1096 #1052 #1051 #815 #818 #1061 #1153]: #55
-#813 := [unit-resolution #618 #816]: #240
-#814 := [unit-resolution #622 #816]: #214
-#811 := [unit-resolution #769 #814]: #20
-#812 := [unit-resolution #607 #811]: #219
-#809 := [unit-resolution #477 #812 #1061 #813]: #62
-#810 := [unit-resolution #658 #809]: #290
-#807 := [unit-resolution #537 #810 #1096 #817]: #136
-#808 := [unit-resolution #691 #807]: #338
-#805 := [unit-resolution #547 #808 #1052 #1051]: #114
-#293 := (or #289 #249)
-#656 := [asserted]: #293
-#806 := [unit-resolution #656 #809]: #289
-#803 := [unit-resolution #974 #807 #806 #1052 #1051]: #69
-#804 := [unit-resolution #630 #803]: #256
-#801 := [unit-resolution #940 #804 #805 #1153]: false
-#799 := [lemma #801]: #802
-#792 := [unit-resolution #799 #791 #1052 #1051 #1153 #1061 #794]: #236
-#789 := [unit-resolution #788 #792]: #47
-#790 := [unit-resolution #1054 #789 #1061]: #62
-#778 := [unit-resolution #658 #790]: #290
-#779 := [unit-resolution #656 #790]: #289
-#795 := (or #330 #119 #150 #152 #98)
-#800 := [unit-resolution #974 #981 #980 #1052 #1051]: #69
-#797 := [unit-resolution #630 #800]: #256
-#798 := [unit-resolution #940 #797 #979 #1153]: false
-#796 := [lemma #798]: #795
-#776 := [unit-resolution #796 #779 #1052 #1051 #1153]: #330
-#777 := [unit-resolution #537 #776 #791 #778]: #129
-#774 := [unit-resolution #831 #777 #794]: #87
-#775 := [unit-resolution #659 #790]: #281
-#772 := [unit-resolution #621 #789]: #241
-#773 := [unit-resolution #680 #777]: #282
-#770 := [unit-resolution #502 #773 #772 #775]: #85
-#771 := [unit-resolution #645 #770 #774]: false
-#751 := [lemma #771]: #753
-#1167 := [unit-resolution #751 #1159 #1156 #1161 #1166]: #371
-#1168 := [unit-resolution #572 #1167 #1165 #1164]: #145
-#1169 := [unit-resolution #690 #1168]: #338
-#1170 := [unit-resolution #547 #1169 #1159 #1156]: #114
-#1171 := [unit-resolution #669 #1170]: #297
-#344 := (or #339 #298)
-#694 := [asserted]: #344
-#1172 := [unit-resolution #694 #1168]: #298
-#1173 := [unit-resolution #940 #1170 #1161]: #67
-#1174 := [unit-resolution #630 #1173]: #257
-#1175 := [unit-resolution #512 #1174 #1172 #1171]: #98
-#1176 := [unit-resolution #656 #1175]: #249
-#1177 := [unit-resolution #632 #1173]: #224
-#1178 := [unit-resolution #666 #1170]: #305
-#1179 := [unit-resolution #522 #1178 #1161]: #81
-#1180 := [unit-resolution #643 #1179]: #233
-#1181 := [unit-resolution #452 #1180]: #38
-#1182 := [unit-resolution #612 #1181]: #223
-#1183 := [unit-resolution #456 #1182 #1177]: #26
-#1184 := [unit-resolution #605 #1183]: #219
-#1185 := [unit-resolution #477 #1184 #1166 #1176]: #53
-#1186 := [unit-resolution #606 #1183]: #213
-#1187 := [unit-resolution #769 #1186]: #22
-#1188 := [unit-resolution #620 #1187 #1185]: false
-#1190 := [lemma #1188]: #1189
-#1365 := [unit-resolution #1190 #1160]: #388
-#211 := (or #208 #190)
-decl f5 :: S1
-#13 := f5
-#14 := (= f5 f1)
-#600 := (or #14 #208 #190)
-#858 := (iff #600 #211)
-#853 := (or false #208 #190)
-#856 := (iff #853 #211)
-#857 := [rewrite]: #856
-#854 := (iff #600 #853)
-#757 := (iff #14 false)
-#15 := (not #14)
-#438 := [asserted]: #15
-#758 := [iff-false #438]: #757
-#855 := [monotonicity #758]: #854
-#859 := [trans #855 #857]: #858
-#212 := (or #14 #211)
-#601 := (iff #212 #600)
-#602 := [rewrite]: #601
-#589 := [asserted]: #212
-#603 := [mp #589 #602]: #600
-#860 := [mp #603 #859]: #211
-#1366 := [unit-resolution #860 #1365]: #208
-#408 := (not #208)
-#410 := (or #408 #380)
-#743 := [asserted]: #410
-#1367 := [unit-resolution #743 #1366]: #380
-#409 := (or #408 #404)
-#742 := [asserted]: #409
-#1368 := [unit-resolution #742 #1366]: #404
-#1369 := [unit-resolution #593 #1368 #1160]: #200
-#1239 := (or #119 #183 #400)
-#1224 := [unit-resolution #1123 #1153 #1019]: #323
-#1225 := [unit-resolution #562 #1224 #1017 #1020]: #167
-#1226 := [unit-resolution #715 #1225]: #371
-#1222 := (or #379 #400 #119)
-#1216 := [hypothesis]: #181
-#390 := (or #387 #379)
-#727 := [asserted]: #390
-#1217 := [unit-resolution #727 #1216]: #387
-#1218 := [unit-resolution #842 #1217]: #157
-#394 := (or #379 #347)
-#731 := [asserted]: #394
-#1219 := [unit-resolution #731 #1216]: #347
-#1220 := [unit-resolution #984 #1219 #1024 #1153]: #150
-#1221 := [unit-resolution #702 #1220 #1218]: false
-#1223 := [lemma #1221]: #1222
-#1227 := [unit-resolution #1223 #1153 #1024]: #379
-#1228 := [unit-resolution #572 #1227 #1226 #919]: #145
-#1229 := [unit-resolution #694 #1228]: #298
-#1192 := (or #297 #125 #119)
-#1191 := [unit-resolution #1098 #967 #969 #1154]: false
-#1193 := [lemma #1191]: #1192
-#1230 := [unit-resolution #1193 #1153 #1019]: #297
-#1231 := [unit-resolution #719 #1225]: #331
-#343 := (or #339 #330)
-#693 := [asserted]: #343
-#1232 := [unit-resolution #693 #1228]: #330
-#1233 := [unit-resolution #1064 #1232 #1231 #1230 #1229]: #277
-#1234 := [unit-resolution #527 #1233 #1019]: #123
-#1214 := (or #339 #138 #119 #125 #98)
-#1194 := [hypothesis]: #145
-#1195 := [unit-resolution #693 #1194]: #330
-#1196 := [unit-resolution #694 #1194]: #298
-#1197 := [unit-resolution #1193 #1153 #1154]: #297
-#1198 := [unit-resolution #1064 #1195 #1096 #1197 #1196]: #277
-#1199 := [unit-resolution #527 #1198 #1154]: #123
-#1200 := [unit-resolution #679 #1199]: #322
-#1201 := [unit-resolution #537 #1200 #1096 #1195]: #100
-#1202 := [unit-resolution #658 #1201]: #249
-#1203 := [unit-resolution #512 #1196 #1197 #980]: #69
-#1204 := [unit-resolution #633 #1203]: #248
-#1205 := [unit-resolution #634 #1203]: #224
-#1206 := [unit-resolution #630 #1203]: #256
-#1207 := [unit-resolution #949 #1206 #1153]: #223
-#1208 := [unit-resolution #456 #1207 #1205]: #26
-#1209 := [unit-resolution #605 #1208]: #219
-#1210 := [unit-resolution #477 #1209 #1204 #1202]: #53
-#1211 := [unit-resolution #606 #1208]: #213
-#1212 := [unit-resolution #769 #1211]: #22
-#1213 := [unit-resolution #620 #1212 #1210]: false
-#1215 := [lemma #1213]: #1214
-#1235 := [unit-resolution #1215 #1228 #1153 #1019 #1231]: #98
-#1236 := [unit-resolution #654 #1235]: #290
-#1237 := [unit-resolution #537 #1236 #1231 #1232]: #129
-#1238 := [unit-resolution #679 #1237 #1234]: false
-#1240 := [lemma #1238]: #1239
-#1370 := [unit-resolution #1240 #1367 #1369]: #119
-#1371 := [unit-resolution #703 #1370]: #354
-#1372 := [unit-resolution #842 #1371]: #188
-#1373 := [unit-resolution #727 #1372]: #379
-#1374 := [unit-resolution #737 #1369]: #364
-#1375 := [unit-resolution #736 #1369]: #398
-#1376 := [unit-resolution #573 #1375]: #163
-#1377 := [unit-resolution #705 #1376]: #358
-#1378 := [unit-resolution #707 #1376]: #318
-#391 := (or #387 #347)
-#728 := [asserted]: #391
-#1379 := [unit-resolution #728 #1372]: #347
+#483 := [asserted]: #258
+#897 := [unit-resolution #483 #892]: #256
+#667 := (or #74 #76 #67 #40)
+#77 := (or #67 #40)
+#78 := (or #76 #77)
+#79 := (or #74 #78)
+#670 := (iff #79 #667)
+#661 := (or #76 #67 #40)
+#664 := (or #74 #661)
+#668 := (iff #664 #667)
+#669 := [rewrite]: #668
+#665 := (iff #79 #664)
+#662 := (iff #78 #661)
+#663 := [rewrite]: #662
+#666 := [monotonicity #663]: #665
+#671 := [trans #666 #669]: #670
+#430 := [asserted]: #79
+#672 := [mp #430 #671]: #667
+#898 := [unit-resolution #672 #897 #896 #895]: #40
+#232 := (or #229 #223)
+#466 := [asserted]: #232
+#899 := [unit-resolution #466 #898]: #223
+#613 := (or #32 #34 #26)
+#35 := (or #34 #26)
+#36 := (or #32 #35)
+#614 := (iff #36 #613)
+#615 := [rewrite]: #614
+#423 := [asserted]: #36
+#616 := [mp #423 #615]: #613
+#900 := [unit-resolution #616 #899 #894]: #26
+#901 := [unit-resolution #458 #900]: #219
+#902 := [unit-resolution #648 #901 #893 #888]: #53
+#903 := [unit-resolution #459 #900]: #213
+#906 := [unit-resolution #905 #903]: #22
+#907 := [unit-resolution #473 #906 #902]: false
+#909 := [lemma #907]: #908
+#977 := [unit-resolution #909 #976 #975 #974 #881 #883 #882]: #372
+#849 := (or #204 #200 #176)
+#205 := (or #200 #176)
+#206 := (or #204 #205)
+#850 := (iff #206 #849)
+#851 := [rewrite]: #850
+#452 := [asserted]: #206
+#852 := [mp #452 #851]: #849
+#978 := [unit-resolution #852 #977 #969]: #200
+#402 := (or #400 #364)
+#590 := [asserted]: #402
+#979 := [unit-resolution #590 #978]: #364
+decl f49 :: S1
+#160 := f49
+#161 := (= f49 f1)
+#358 := (not #161)
+#401 := (or #400 #398)
+#589 := [asserted]: #401
+#980 := [unit-resolution #589 #978]: #398
+#198 := (or #197 #163)
+#450 := [asserted]: #198
+#981 := [unit-resolution #450 #980]: #163
+#360 := (or #358 #359)
+#558 := [asserted]: #360
+#982 := [unit-resolution #558 #981]: #358
+#323 := (not #131)
+decl f38 :: S1
+#122 := f38
+#123 := (= f38 f1)
+#362 := (or #359 #318)
+#560 := [asserted]: #362
+#983 := [unit-resolution #560 #981]: #318
+#946 := (or #256 #105 #129 #181 #183 #161 #169 #125)
+#931 := [hypothesis]: #364
+#932 := [hypothesis]: #358
+#910 := [hypothesis]: #318
+#933 := [hypothesis]: #67
+#259 := (or #256 #248)
+#484 := [asserted]: #259
+#934 := [unit-resolution #484 #933]: #248
+#929 := (or #323 #60 #125)
+#317 := (not #123)
+#911 := [hypothesis]: #131
+#327 := (or #323 #317)
+#534 := [asserted]: #327
+#912 := [unit-resolution #534 #911]: #317
+#733 := (or #123 #125 #87)
+#126 := (or #125 #87)
+#127 := (or #123 #126)
+#734 := (iff #127 #733)
+#735 := [rewrite]: #734
+#438 := [asserted]: #127
+#736 := [mp #438 #735]: #733
+#913 := [unit-resolution #736 #912 #910]: #87
+#280 := (or #277 #236)
+#500 := [asserted]: #280
+#914 := [unit-resolution #500 #913]: #236
+#917 := [unit-resolution #916 #914]: #47
+#243 := (or #240 #235)
+#472 := [asserted]: #243
+#918 := [unit-resolution #472 #917]: #240
+#328 := (or #323 #282)
+#535 := [asserted]: #328
+#920 := [unit-resolution #535 #911]: #282
+#278 := (or #276 #277)
+#498 := [asserted]: #278
+#921 := [unit-resolution #498 #913]: #276
+#245 := (or #241 #235)
+#474 := [asserted]: #245
+#922 := [unit-resolution #474 #917]: #241
+#687 := (or #91 #93 #85 #55)
+#94 := (or #85 #55)
+#95 := (or #93 #94)
+#96 := (or #91 #95)
+#690 := (iff #96 #687)
+#681 := (or #93 #85 #55)
+#684 := (or #91 #681)
+#688 := (iff #684 #687)
+#689 := [rewrite]: #688
+#685 := (iff #96 #684)
+#682 := (iff #95 #681)
+#683 := [rewrite]: #682
+#686 := [monotonicity #683]: #685
+#691 := [trans #686 #689]: #690
+#433 := [asserted]: #96
+#692 := [mp #433 #691]: #687
+#923 := [unit-resolution #692 #922 #921 #920]: #91
+#924 := [unit-resolution #512 #923]: #249
+#925 := [unit-resolution #476 #917]: #214
+#926 := [unit-resolution #905 #925]: #20
+#222 := (or #219 #213)
+#460 := [asserted]: #222
+#927 := [unit-resolution #460 #926]: #219
+#928 := [unit-resolution #648 #927 #924 #919 #918]: false
+#930 := [lemma #928]: #929
+#935 := [unit-resolution #930 #934 #910]: #323
+#799 := (or #167 #169 #161 #131)
+#170 := (or #161 #131)
+#171 := (or #169 #170)
+#172 := (or #167 #171)
+#802 := (iff #172 #799)
+#793 := (or #169 #161 #131)
+#796 := (or #167 #793)
+#800 := (iff #796 #799)
+#801 := [rewrite]: #800
+#797 := (iff #172 #796)
+#794 := (iff #171 #793)
+#795 := [rewrite]: #794
+#798 := [monotonicity #795]: #797
+#803 := [trans #798 #801]: #802
+#445 := [asserted]: #172
+#804 := [mp #445 #803]: #799
+#936 := [unit-resolution #804 #935 #932 #931]: #167
+#363 := (not #167)
+#378 := (or #363 #331)
+#572 := [asserted]: #378
+#937 := [unit-resolution #572 #936]: #331
+#374 := (or #371 #363)
+#568 := [asserted]: #374
+#938 := [unit-resolution #568 #936]: #371
+#939 := [unit-resolution #828 #938 #883 #882]: #145
+#940 := [unit-resolution #546 #939]: #330
+#941 := [unit-resolution #760 #940 #881 #937]: #100
+#942 := [unit-resolution #483 #933]: #257
+#943 := [unit-resolution #547 #939]: #298
+#944 := [unit-resolution #716 #943 #890 #942]: #98
+#945 := [unit-resolution #507 #944 #941]: false
+#947 := [lemma #945]: #946
+#984 := [unit-resolution #947 #974 #881 #883 #882 #982 #979 #983]: #256
+#985 := [unit-resolution #672 #984 #976 #975]: #40
+#986 := [unit-resolution #466 #985]: #223
+#967 := (or #60 #32 #105 #129 #181 #183 #161 #169 #125)
+#948 := [unit-resolution #930 #919 #910]: #323
+#949 := [unit-resolution #804 #948 #932 #931]: #167
+#950 := [unit-resolution #572 #949]: #331
+#951 := [unit-resolution #568 #949]: #371
+#952 := [unit-resolution #828 #951 #883 #882]: #145
+#953 := [unit-resolution #546 #952]: #330
+#954 := [unit-resolution #760 #953 #881 #950]: #100
+#955 := [unit-resolution #511 #954]: #249
+#956 := [hypothesis]: #223
+#957 := [unit-resolution #547 #952]: #298
+#958 := [unit-resolution #507 #954]: #289
+#959 := [unit-resolution #716 #958 #890 #957]: #69
+#960 := [unit-resolution #487 #959]: #224
+#961 := [unit-resolution #616 #960 #956]: #26
+#962 := [unit-resolution #458 #961]: #219
+#963 := [unit-resolution #648 #962 #919 #955]: #53
+#964 := [unit-resolution #459 #961]: #213
+#965 := [unit-resolution #905 #964]: #22
+#966 := [unit-resolution #473 #965 #963]: false
+#968 := [lemma #966]: #967
+#987 := [unit-resolution #968 #986 #974 #881 #883 #882 #982 #979 #983]: #60
+#263 := (or #248 #224)
+#488 := [asserted]: #263
+#988 := [unit-resolution #488 #987]: #224
+#989 := [unit-resolution #616 #988 #986]: #26
+#990 := [unit-resolution #459 #989]: #213
+#991 := [unit-resolution #905 #990]: #22
+#992 := [unit-resolution #476 #991]: #235
+#993 := [unit-resolution #916 #992]: #49
+#994 := [unit-resolution #500 #993]: #277
+#995 := [unit-resolution #736 #994 #983]: #123
+#996 := [unit-resolution #534 #995]: #323
+#997 := [unit-resolution #804 #996 #982 #979]: #167
+#998 := [unit-resolution #568 #997]: #371
+#999 := [unit-resolution #828 #998 #883 #882]: #145
+#1000 := [unit-resolution #572 #997]: #331
+#1001 := [unit-resolution #499 #993]: #276
+#1002 := [unit-resolution #475 #991]: #241
+#329 := (or #317 #282)
+#536 := [asserted]: #329
+#1003 := [unit-resolution #536 #995]: #282
+#1004 := [unit-resolution #692 #1003 #1002 #1001]: #91
+#294 := (or #290 #281)
+#510 := [asserted]: #294
+#1005 := [unit-resolution #510 #1004]: #290
+#1006 := [unit-resolution #760 #1005 #881 #1000]: #136
+#1007 := [unit-resolution #546 #1006 #999]: false
+#1009 := [lemma #1007]: #1008
+#1072 := [unit-resolution #1009 #970 #883 #882 #969 #881]: #233
+#45 := (or #44 #38)
+#425 := [asserted]: #45
+#1073 := [unit-resolution #425 #1072]: #38
+#231 := (or #228 #223)
+#465 := [asserted]: #231
+#1075 := [unit-resolution #465 #1073]: #223
+#1100 := (or #60 #119 #129 #181 #183 #204)
+#230 := (or #228 #229)
+#464 := [asserted]: #230
+#1074 := [unit-resolution #464 #1073]: #229
+#1086 := (or #125 #129 #119 #60 #181 #183 #204)
+#1023 := [unit-resolution #930 #910 #919]: #323
+#1020 := (or #371 #131 #204)
+#1010 := [hypothesis]: #174
+#1011 := [unit-resolution #567 #1010]: #372
+#1012 := [unit-resolution #852 #1011 #969]: #200
+#1013 := [unit-resolution #589 #1012]: #398
+#1014 := [unit-resolution #450 #1013]: #163
+#1015 := [unit-resolution #568 #1010]: #363
+#1016 := [hypothesis]: #323
+#1017 := [unit-resolution #590 #1012]: #364
+#1018 := [unit-resolution #804 #1017 #1016 #1015]: #161
+#1019 := [unit-resolution #558 #1018 #1014]: false
+#1021 := [lemma #1019]: #1020
+#1069 := [unit-resolution #1021 #1023 #969]: #371
+#1070 := [unit-resolution #828 #1069 #883 #882]: #145
+#1071 := [unit-resolution #546 #1070]: #330
+#1076 := [unit-resolution #547 #1070]: #298
+#1067 := (or #290 #60 #32 #119 #107 #40)
+#1057 := [hypothesis]: #100
+#1058 := [unit-resolution #511 #1057]: #249
+#1045 := [hypothesis]: #298
+#1059 := [unit-resolution #507 #1057]: #289
+#1055 := (or #224 #40 #119 #107 #98)
+#1044 := [hypothesis]: #289
+#1046 := [hypothesis]: #34
+#1047 := [unit-resolution #487 #1046]: #257
+#1048 := [unit-resolution #716 #1047 #1045 #1044]: #105
+#1049 := [unit-resolution #520 #1048]: #305
+#1050 := [unit-resolution #732 #1049 #970]: #81
+#260 := (or #256 #224)
+#485 := [asserted]: #260
+#1051 := [unit-resolution #485 #1046]: #256
+#312 := (or #297 #265)
+#524 := [asserted]: #312
+#1052 := [unit-resolution #524 #1048]: #265
+#1053 := [unit-resolution #672 #1052 #1030 #1051]: #74
+#273 := (or #272 #264)
+#495 := [asserted]: #273
+#1054 := [unit-resolution #495 #1053 #1050]: false
+#1056 := [lemma #1054]: #1055
+#1060 := [unit-resolution #1056 #1059 #970 #1045 #1030]: #224
+#1061 := [unit-resolution #616 #1060 #956]: #26
+#1062 := [unit-resolution #458 #1061]: #219
+#1063 := [unit-resolution #648 #1062 #919 #1058]: #53
+#1064 := [unit-resolution #459 #1061]: #213
+#1065 := [unit-resolution #905 #1064]: #22
+#1066 := [unit-resolution #473 #1065 #1063]: false
+#1068 := [lemma #1066]: #1067
+#1077 := [unit-resolution #1068 #1076 #1075 #970 #919 #1074]: #290
+#1078 := [unit-resolution #760 #1077 #881 #1071]: #138
+#1079 := [unit-resolution #571 #1078]: #372
+#1080 := [unit-resolution #852 #1079 #969]: #200
+#1081 := [unit-resolution #589 #1080]: #398
+#1082 := [unit-resolution #450 #1081]: #163
+#1083 := [unit-resolution #590 #1080]: #364
+#1042 := (or #161 #60 #32 #40 #129 #136 #119 #169 #181 #183 #125)
+#1022 := [hypothesis]: #330
+#1024 := [unit-resolution #804 #932 #1023 #931]: #167
+#1025 := [unit-resolution #572 #1024]: #331
+#1026 := [unit-resolution #760 #1025 #881 #1022]: #100
+#1027 := [unit-resolution #511 #1026]: #249
+#1028 := [unit-resolution #968 #932 #956 #881 #883 #882 #919 #931 #910]: #105
+#1029 := [unit-resolution #524 #1028]: #265
+#1031 := [unit-resolution #520 #1028]: #305
+#1032 := [unit-resolution #732 #1031 #970]: #81
+#1033 := [unit-resolution #495 #1032]: #264
+#1034 := [unit-resolution #672 #1033 #1030 #1029]: #67
+#1035 := [unit-resolution #485 #1034]: #224
+#1036 := [unit-resolution #616 #1035 #956]: #26
+#1037 := [unit-resolution #458 #1036]: #219
+#1038 := [unit-resolution #648 #1037 #919 #1027]: #53
+#1039 := [unit-resolution #459 #1036]: #213
+#1040 := [unit-resolution #905 #1039]: #22
+#1041 := [unit-resolution #473 #1040 #1038]: false
+#1043 := [lemma #1041]: #1042
+#1084 := [unit-resolution #1043 #1083 #1075 #1074 #881 #1071 #970 #919 #883 #882 #910]: #161
+#1085 := [unit-resolution #558 #1084 #1082]: false
+#1087 := [lemma #1085]: #1086
+#1088 := [unit-resolution #1087 #919 #970 #881 #883 #882 #969]: #125
+#1089 := [unit-resolution #560 #1088]: #359
+#1090 := [unit-resolution #450 #1089]: #197
+#1091 := [unit-resolution #589 #1090]: #400
+#1092 := [unit-resolution #852 #1091 #969]: #176
+#1093 := [unit-resolution #567 #1092]: #371
+#1094 := [unit-resolution #828 #1093 #883 #882]: #145
+#1095 := [unit-resolution #547 #1094]: #298
+#1096 := [unit-resolution #571 #1092]: #331
+#1097 := [unit-resolution #546 #1094]: #330
+#1098 := [unit-resolution #760 #1097 #881 #1096]: #100
+#1099 := [unit-resolution #1068 #1098 #1095 #1075 #970 #919 #1074]: false
+#1101 := [lemma #1099]: #1100
+#1125 := [unit-resolution #1101 #970 #881 #883 #882 #969]: #60
+#1126 := [unit-resolution #488 #1125]: #224
+#1127 := [unit-resolution #616 #1126 #1075]: #26
+#1128 := [unit-resolution #459 #1127]: #213
+#1129 := [unit-resolution #905 #1128]: #22
+#1130 := [unit-resolution #476 #1129]: #235
+#1131 := [unit-resolution #916 #1130]: #49
+#1132 := [unit-resolution #500 #1131]: #277
+#1133 := [unit-resolution #475 #1129]: #241
+#1134 := [unit-resolution #499 #1131]: #276
+#1135 := [unit-resolution #484 #1125]: #256
+#1109 := (or #297 #40 #67 #119)
+#1102 := [hypothesis]: #105
+#1103 := [unit-resolution #520 #1102]: #305
+#1104 := [unit-resolution #732 #1103 #970]: #81
+#1105 := [hypothesis]: #256
+#1106 := [unit-resolution #524 #1102]: #265
+#1107 := [unit-resolution #672 #1106 #1030 #1105]: #74
+#1108 := [unit-resolution #495 #1107 #1104]: false
+#1110 := [lemma #1108]: #1109
+#1136 := [unit-resolution #1110 #1074 #1135 #970]: #297
+#1137 := [unit-resolution #486 #1125]: #257
+#1123 := (or #317 #69 #105 #181 #183 #85 #55 #204)
+#1111 := [hypothesis]: #257
+#1112 := [hypothesis]: #241
+#1113 := [hypothesis]: #276
+#1114 := [hypothesis]: #123
+#1115 := [unit-resolution #536 #1114]: #282
+#1116 := [unit-resolution #692 #1115 #1113 #1112]: #91
+#292 := (or #289 #281)
+#508 := [asserted]: #292
+#1117 := [unit-resolution #508 #1116]: #289
+#1118 := [unit-resolution #534 #1114]: #323
+#1119 := [unit-resolution #1021 #1118 #969]: #371
+#1120 := [unit-resolution #828 #1119 #883 #882]: #145
+#1121 := [unit-resolution #547 #1120]: #298
+#1122 := [unit-resolution #716 #1121 #1117 #1111 #890]: false
+#1124 := [lemma #1122]: #1123
+#1138 := [unit-resolution #1124 #1137 #1136 #883 #882 #1134 #1133 #969]: #317
+#1139 := [unit-resolution #736 #1138 #1132]: #125
+#1140 := [unit-resolution #560 #1139]: #359
+#1141 := [unit-resolution #450 #1140]: #197
+#1142 := [unit-resolution #589 #1141]: #400
+#1143 := [unit-resolution #852 #1142 #969]: #176
+#1144 := [unit-resolution #571 #1143]: #331
+#1145 := [unit-resolution #567 #1143]: #371
+#1146 := [unit-resolution #828 #1145 #883 #882]: #145
+#1147 := [unit-resolution #546 #1146]: #330
+#1148 := [unit-resolution #760 #1147 #881 #1144]: #100
+#1149 := [unit-resolution #547 #1146]: #298
+#1150 := [unit-resolution #716 #1149 #1137 #1136]: #98
+#1151 := [unit-resolution #507 #1150 #1148]: false
+#1153 := [lemma #1151]: #1152
+#1195 := [unit-resolution #1153 #883 #881 #882 #969]: #119
 #357 := (or #346 #313)
-#704 := [asserted]: #357
-#1380 := [unit-resolution #704 #1370]: #346
-#1351 := (or #98 #125 #161 #169 #181 #183 #150 #152)
-#1258 := [hypothesis]: #364
-#1259 := [hypothesis]: #358
-#1332 := (or #136 #150 #152 #181 #183 #125 #161 #169 #98)
-#1317 := (or #129 #125 #136 #161 #169 #181 #183 #150 #152 #98)
-#1297 := (or #105 #125 #98 #161 #169 #181 #183 #129 #136)
-#1276 := (or #290 #125 #161 #169 #181 #183 #98 #105)
-#1256 := [hypothesis]: #100
-#1257 := [unit-resolution #657 #1256]: #281
-#1260 := [unit-resolution #658 #1256]: #249
-#1254 := (or #60 #62 #91 #125)
-#1241 := [hypothesis]: #281
-#1242 := [unit-resolution #1054 #1061 #1062]: #235
-#1243 := [unit-resolution #788 #1242]: #49
-#1244 := [unit-resolution #646 #1243]: #276
-#1245 := [unit-resolution #647 #1243]: #277
-#1246 := [unit-resolution #527 #1245 #1154]: #123
-#1247 := [unit-resolution #683 #1246]: #282
-#1248 := [unit-resolution #502 #1247 #1244 #1241]: #55
-#1249 := [unit-resolution #618 #1248]: #240
-#1250 := [unit-resolution #477 #1249 #1061 #1062]: #28
-#1251 := [unit-resolution #622 #1248]: #214
-#1252 := [unit-resolution #769 #1251]: #20
-#1253 := [unit-resolution #607 #1252 #1250]: false
-#1255 := [lemma #1253]: #1254
-#1261 := [unit-resolution #1255 #1260 #1257 #1154]: #60
-#1262 := [unit-resolution #633 #1261]: #257
-#1263 := [unit-resolution #512 #1262 #980 #1075]: #107
-#1264 := [unit-resolution #694 #1263]: #339
-#1265 := [unit-resolution #572 #1264 #920 #919]: #174
-#1266 := [unit-resolution #715 #1265]: #363
-#1267 := [unit-resolution #562 #1266 #1259 #1258]: #131
-#1268 := [unit-resolution #682 #1267]: #282
-#1269 := [unit-resolution #681 #1267]: #317
-#1270 := [unit-resolution #527 #1269 #1154]: #87
-#1271 := [unit-resolution #645 #1270]: #276
-#1272 := [unit-resolution #502 #1271 #1268 #1257]: #55
-#1273 := [unit-resolution #647 #1270]: #236
-#1274 := [unit-resolution #788 #1273]: #47
-#1275 := [unit-resolution #621 #1274 #1272]: false
+#557 := [asserted]: #357
+#1196 := [unit-resolution #557 #1195]: #346
+decl f44 :: S1
+#142 := f44
+#143 := (= f44 f1)
+#338 := (not #143)
+#1207 := (or #60 #204 #181 #183 #40 #129 #152)
+#1165 := (or #331 #60 #204)
+#1154 := [hypothesis]: #138
+#1155 := [unit-resolution #571 #1154]: #372
+#1156 := [unit-resolution #852 #1155 #969]: #200
+#1157 := [unit-resolution #589 #1156]: #398
+#1158 := [unit-resolution #450 #1157]: #163
+#1159 := [unit-resolution #560 #1158]: #318
+#1160 := [unit-resolution #590 #1156]: #364
+#1161 := [unit-resolution #572 #1154]: #363
+#1162 := [unit-resolution #558 #1158]: #358
+#1163 := [unit-resolution #804 #1162 #1161 #1160]: #131
+#1164 := [unit-resolution #930 #1163 #1159 #919]: false
+#1166 := [lemma #1164]: #1165
+#1197 := [unit-resolution #1166 #919 #969]: #331
+#1193 := (or #339 #60 #40 #129 #138 #150 #152)
+#1167 := [hypothesis]: #331
+#1168 := [hypothesis]: #145
+#1169 := [unit-resolution #546 #1168]: #330
+#1170 := [unit-resolution #760 #1169 #881 #1167]: #100
+#1171 := [unit-resolution #511 #1170]: #249
+#1173 := [hypothesis]: #346
+#340 := (or #338 #339)
+#543 := [asserted]: #340
+#1174 := [unit-resolution #543 #1168]: #338
+#779 := (or #150 #152 #143 #114)
+#153 := (or #143 #114)
+#154 := (or #152 #153)
+#155 := (or #150 #154)
+#782 := (iff #155 #779)
+#773 := (or #152 #143 #114)
+#776 := (or #150 #773)
+#780 := (iff #776 #779)
+#781 := [rewrite]: #780
+#777 := (iff #155 #776)
+#774 := (iff #154 #773)
+#775 := [rewrite]: #774
+#778 := [monotonicity #775]: #777
+#783 := [trans #778 #781]: #782
+#442 := [asserted]: #155
+#784 := [mp #442 #783]: #779
+#1175 := [unit-resolution #784 #1174 #1173 #1172]: #114
+#306 := (not #114)
+#310 := (or #306 #297)
+#522 := [asserted]: #310
+#1176 := [unit-resolution #522 #1175]: #297
+#1177 := [unit-resolution #547 #1168]: #298
+#1178 := [unit-resolution #507 #1170]: #289
+#1179 := [unit-resolution #716 #1178 #1177 #1176]: #69
+#1180 := [unit-resolution #487 #1179]: #224
+#311 := (or #306 #265)
+#523 := [asserted]: #311
+#1181 := [unit-resolution #523 #1175]: #265
+#1182 := [unit-resolution #483 #1179]: #256
+#1183 := [unit-resolution #672 #1182 #1030 #1181]: #74
+#1184 := [unit-resolution #497 #1183]: #233
+#1185 := [unit-resolution #425 #1184]: #38
+#1186 := [unit-resolution #465 #1185]: #223
+#1187 := [unit-resolution #616 #1186 #1180]: #26
+#1188 := [unit-resolution #458 #1187]: #219
+#1189 := [unit-resolution #648 #1188 #919 #1171]: #53
+#1190 := [unit-resolution #459 #1187]: #213
+#1191 := [unit-resolution #905 #1190]: #22
+#1192 := [unit-resolution #473 #1191 #1189]: false
+#1194 := [lemma #1192]: #1193
+#1198 := [unit-resolution #1194 #919 #1030 #881 #1197 #1196 #1172]: #339
+#1199 := [unit-resolution #828 #1198 #883 #882]: #174
+#1200 := [unit-resolution #567 #1199]: #372
+#1201 := [unit-resolution #852 #1200 #969]: #200
+#1202 := [unit-resolution #589 #1201]: #398
+#1203 := [unit-resolution #1021 #1199 #969]: #131
+#1204 := [unit-resolution #930 #1203 #919]: #125
+#1205 := [unit-resolution #560 #1204]: #359
+#1206 := [unit-resolution #450 #1205 #1202]: false
+#1208 := [lemma #1206]: #1207
+#1261 := [unit-resolution #1208 #1030 #883 #882 #969 #881 #1172]: #60
+#1262 := [unit-resolution #486 #1261]: #257
+#1218 := (or #281 #69 #150 #152 #129 #138)
+#1209 := [hypothesis]: #91
+#1210 := [unit-resolution #510 #1209]: #290
+#1211 := [unit-resolution #760 #1210 #881 #1167]: #136
+#341 := (or #338 #330)
+#544 := [asserted]: #341
+#1212 := [unit-resolution #544 #1211]: #338
+#1213 := [unit-resolution #784 #1212 #1173 #1172]: #114
+#1214 := [unit-resolution #508 #1209]: #289
+#345 := (or #330 #298)
+#548 := [asserted]: #345
+#1215 := [unit-resolution #548 #1211]: #298
+#1216 := [unit-resolution #716 #1215 #1111 #1214]: #105
+#1217 := [unit-resolution #522 #1216 #1213]: false
+#1219 := [lemma #1217]: #1218
+#1263 := [unit-resolution #1219 #1167 #1196 #1172 #881 #1262]: #281
+#1259 := (or #371 #91 #204)
+#1249 := [unit-resolution #1021 #1010 #969]: #131
+#1250 := [unit-resolution #535 #1249]: #282
+#1236 := [hypothesis]: #281
+#1251 := [unit-resolution #534 #1249]: #317
+#1252 := [unit-resolution #560 #1014]: #318
+#1253 := [unit-resolution #736 #1252 #1251]: #87
+#1254 := [unit-resolution #498 #1253]: #276
+#1255 := [unit-resolution #692 #1254 #1236 #1250]: #55
+#1256 := [unit-resolution #500 #1253]: #236
+#1257 := [unit-resolution #916 #1256]: #47
+#1258 := [unit-resolution #474 #1257 #1255]: false
+#1260 := [lemma #1258]: #1259
+#1264 := [unit-resolution #1260 #1263 #969]: #371
+#1265 := [unit-resolution #828 #1264 #883 #882]: #145
+#1266 := [unit-resolution #543 #1265]: #338
+#1267 := [unit-resolution #784 #1266 #1196 #1172]: #114
+#1268 := [unit-resolution #484 #1261]: #256
+#1269 := [unit-resolution #488 #1261]: #224
+#1247 := (or #330 #91 #34 #204 #40 #67 #181 #183 #150 #152)
+#1220 := [hypothesis]: #224
+#1221 := [hypothesis]: #136
+#1222 := [unit-resolution #544 #1221]: #338
+#1223 := [unit-resolution #784 #1222 #1173 #1172]: #114
+#1224 := [unit-resolution #523 #1223]: #265
+#1225 := [unit-resolution #672 #1224 #1030 #1105]: #74
+#1226 := [unit-resolution #497 #1225]: #233
+#1227 := [unit-resolution #425 #1226]: #38
+#1228 := [unit-resolution #465 #1227]: #223
+#1229 := [unit-resolution #616 #1228 #1220]: #26
+#1230 := [unit-resolution #459 #1229]: #213
+#1231 := [unit-resolution #905 #1230]: #22
+#1232 := [unit-resolution #546 #1221]: #339
+#1233 := [unit-resolution #828 #1232 #883 #882]: #174
+#1234 := [unit-resolution #1021 #1233 #969]: #131
+#1235 := [unit-resolution #535 #1234]: #282
+#1237 := [unit-resolution #534 #1234]: #317
+#1238 := [unit-resolution #567 #1233]: #372
+#1239 := [unit-resolution #852 #1238 #969]: #200
+#1240 := [unit-resolution #589 #1239]: #398
+#1241 := [unit-resolution #450 #1240]: #163
+#1242 := [unit-resolution #560 #1241]: #318
+#1243 := [unit-resolution #736 #1242 #1237]: #87
+#1244 := [unit-resolution #498 #1243]: #276
+#1245 := [unit-resolution #692 #1244 #1236 #1235]: #55
+#1246 := [unit-resolution #475 #1245 #1231]: false
+#1248 := [lemma #1246]: #1247
+#1270 := [unit-resolution #1248 #1263 #1269 #969 #1030 #1268 #883 #882 #1196 #1172]: #330
+#1271 := [unit-resolution #760 #1270 #881 #1167]: #100
+#1272 := [unit-resolution #507 #1271]: #289
+#1273 := [unit-resolution #547 #1265]: #298
+#1274 := [unit-resolution #716 #1273 #1262 #1272]: #105
+#1275 := [unit-resolution #522 #1274 #1267]: false
 #1277 := [lemma #1275]: #1276
-#1278 := [unit-resolution #1277 #1075 #1259 #1258 #920 #919 #980 #1154]: #290
-#1279 := [unit-resolution #537 #1278 #832 #1095]: #138
-#1280 := [unit-resolution #716 #1279]: #371
-#1281 := [unit-resolution #572 #1280 #920 #919]: #145
-#1282 := [unit-resolution #694 #1281]: #298
-#1283 := [unit-resolution #512 #1282 #980 #1075]: #69
-#1284 := [unit-resolution #633 #1283]: #248
-#1285 := [unit-resolution #719 #1279]: #363
-#1286 := [unit-resolution #562 #1285 #1259 #1258]: #131
-#1287 := [unit-resolution #681 #1286]: #317
-#1288 := [unit-resolution #527 #1287 #1154]: #87
-#1289 := [unit-resolution #647 #1288]: #236
-#1290 := [unit-resolution #788 #1289]: #47
-#1291 := [unit-resolution #1054 #1290 #1284]: #62
-#1292 := [unit-resolution #645 #1288]: #276
-#1293 := [unit-resolution #682 #1286]: #282
-#1294 := [unit-resolution #621 #1290]: #241
-#1295 := [unit-resolution #502 #1294 #1293 #1292]: #91
-#1296 := [unit-resolution #659 #1295 #1291]: false
-#1298 := [lemma #1296]: #1297
-#1299 := [unit-resolution #1298 #832 #980 #1259 #1258 #920 #919 #1154 #1095]: #105
-#1300 := [unit-resolution #669 #1299]: #306
-#1301 := [unit-resolution #547 #1300 #1052 #1051]: #143
-#1302 := [unit-resolution #690 #1301]: #339
-#1303 := [unit-resolution #572 #1302 #920 #919]: #174
-#1304 := [unit-resolution #716 #1303]: #331
-#1305 := [unit-resolution #537 #1304 #832 #1095]: #100
-#1306 := [unit-resolution #657 #1305]: #281
-#1307 := [unit-resolution #715 #1303]: #363
-#1308 := [unit-resolution #562 #1307 #1259 #1258]: #131
-#1309 := [unit-resolution #682 #1308]: #282
-#1310 := [unit-resolution #681 #1308]: #317
-#1311 := [unit-resolution #527 #1310 #1154]: #87
-#1312 := [unit-resolution #645 #1311]: #276
-#1313 := [unit-resolution #502 #1312 #1309 #1306]: #55
-#1314 := [unit-resolution #647 #1311]: #236
-#1315 := [unit-resolution #788 #1314]: #47
-#1316 := [unit-resolution #621 #1315 #1313]: false
-#1318 := [lemma #1316]: #1317
-#1319 := [unit-resolution #1318 #1095 #1154 #1259 #1258 #920 #919 #1052 #1051 #980]: #129
-#1320 := [unit-resolution #678 #1319]: #323
-#1321 := [unit-resolution #562 #1320 #1259 #1258]: #167
-#1322 := [unit-resolution #715 #1321]: #371
-#1323 := [unit-resolution #572 #1322 #920 #919]: #145
-#1324 := [unit-resolution #690 #1323]: #338
-#1325 := [unit-resolution #547 #1324 #1052 #1051]: #114
-#1326 := [unit-resolution #679 #1319]: #317
-#1327 := [unit-resolution #527 #1326 #1154]: #87
-#335 := (or #331 #322)
-#687 := [asserted]: #335
-#1328 := [unit-resolution #687 #1319]: #331
-#1329 := [unit-resolution #694 #1323]: #298
-#1330 := [unit-resolution #1064 #1329 #1095 #1328 #1327]: #105
-#1331 := [unit-resolution #669 #1330 #1325]: false
-#1333 := [lemma #1331]: #1332
-#1334 := [unit-resolution #1333 #980 #1051 #920 #919 #1154 #1259 #1258 #1052]: #136
-#1335 := [unit-resolution #974 #1334 #980 #1052 #1051]: #69
-#1336 := [unit-resolution #633 #1335]: #248
-#1337 := [unit-resolution #693 #1334]: #339
-#1338 := [unit-resolution #572 #1337 #920 #919]: #174
-#1339 := [unit-resolution #715 #1338]: #363
-#1340 := [unit-resolution #562 #1339 #1259 #1258]: #131
-#1341 := [unit-resolution #681 #1340]: #317
-#1342 := [unit-resolution #527 #1341 #1154]: #87
-#1343 := [unit-resolution #647 #1342]: #236
-#1344 := [unit-resolution #788 #1343]: #47
-#1345 := [unit-resolution #1054 #1344 #1336]: #62
-#1346 := [unit-resolution #645 #1342]: #276
-#1347 := [unit-resolution #682 #1340]: #282
-#1348 := [unit-resolution #621 #1344]: #241
-#1349 := [unit-resolution #502 #1348 #1347 #1346]: #91
-#1350 := [unit-resolution #659 #1349 #1345]: false
-#1352 := [lemma #1350]: #1351
-#1381 := [unit-resolution #1352 #1378 #1377 #1374 #1373 #1367 #1380 #1379]: #98
-#1382 := [unit-resolution #654 #1381]: #290
-#1363 := (or #317 #100 #181 #183 #161 #169)
-#1353 := [hypothesis]: #123
-#1354 := [unit-resolution #681 #1353]: #323
-#1355 := [unit-resolution #562 #1354 #1259 #1258]: #167
-#1356 := [unit-resolution #715 #1355]: #371
-#1357 := [unit-resolution #572 #1356 #920 #919]: #145
-#1358 := [unit-resolution #679 #1353]: #322
-#1359 := [hypothesis]: #290
-#1360 := [unit-resolution #719 #1355]: #331
-#1361 := [unit-resolution #537 #1360 #1359 #1358]: #136
-#1362 := [unit-resolution #693 #1361 #1357]: false
-#1364 := [lemma #1362]: #1363
-#1383 := [unit-resolution #1364 #1382 #1373 #1367 #1377 #1374]: #317
-#1384 := [unit-resolution #527 #1383 #1378]: #87
-#1385 := [unit-resolution #645 #1384]: #276
-#1386 := [unit-resolution #655 #1381]: #281
-#1387 := [unit-resolution #647 #1384]: #236
-#1388 := [unit-resolution #788 #1387]: #47
-#1389 := [unit-resolution #621 #1388]: #241
-#1390 := [unit-resolution #502 #1389 #1386 #1385]: #93
-#1391 := [unit-resolution #682 #1390]: #323
-#1392 := [unit-resolution #562 #1391 #1377 #1374]: #167
-#1393 := [unit-resolution #715 #1392]: #371
-#1394 := [unit-resolution #572 #1393 #1373 #1367]: #145
-#1395 := [unit-resolution #680 #1390]: #322
-#1396 := [unit-resolution #719 #1392]: #331
-#1397 := [unit-resolution #537 #1396 #1382 #1395]: #136
-#1398 := [unit-resolution #693 #1397 #1394]: false
-#1399 := [lemma #1398]: #176
-#376 := (or #372 #363)
-#717 := [asserted]: #376
-#1426 := [unit-resolution #717 #1399]: #363
-#1428 := [unit-resolution #831 #1426]: #1427
-#1429 := [unit-resolution #1428 #867]: #322
-#1431 := (or #136 #129 #100)
-#377 := (or #372 #331)
-#718 := [asserted]: #377
-#1430 := [unit-resolution #718 #1399]: #331
-#1432 := [unit-resolution #537 #1430]: #1431
-#1433 := [unit-resolution #1432 #1429 #1095]: #100
-#1434 := [unit-resolution #657 #1433]: #281
-#1435 := (or #282 #87)
-#1436 := [unit-resolution #852 #1426]: #1435
-#1437 := [unit-resolution #1436 #867]: #282
-#1419 := (or #214 #93 #91)
-#1413 := [hypothesis]: #22
-#1414 := [unit-resolution #622 #1413]: #241
-#1415 := [unit-resolution #502 #1414 #829 #1241]: #85
-#1416 := [unit-resolution #623 #1413]: #235
-#1417 := [unit-resolution #788 #1416]: #49
-#1418 := [unit-resolution #646 #1417 #1415]: false
-#1420 := [lemma #1418]: #1419
-#1438 := [unit-resolution #1420 #1437 #1434]: #214
-#1439 := [unit-resolution #769 #1438]: #20
-#1440 := [unit-resolution #607 #1439]: #219
-#1441 := [unit-resolution #658 #1433]: #249
-#1442 := [unit-resolution #606 #1439]: #218
-#1424 := (or #248 #26 #98)
-#1421 := [hypothesis]: #218
-#1411 := (or #223 #98 #69 #67)
-#1400 := [unit-resolution #949 #959 #971]: #119
-#1401 := [unit-resolution #703 #1400]: #354
-#1402 := [unit-resolution #842 #1401]: #188
-#1403 := [unit-resolution #728 #1402]: #347
-#1404 := [unit-resolution #704 #1400]: #346
-#1405 := [unit-resolution #487 #953 #971 #956]: #76
-#1406 := [unit-resolution #670 #1405]: #306
-#1407 := [unit-resolution #547 #1406 #1404 #1403]: #143
-#1408 := [unit-resolution #671 #1405]: #297
-#1409 := [unit-resolution #512 #1408 #980 #977]: #107
-#1410 := [unit-resolution #692 #1409 #1407]: false
-#1412 := [lemma #1410]: #1411
-#1422 := [unit-resolution #1412 #924 #980 #938]: #223
-#1423 := [unit-resolution #456 #1422 #934 #1421]: false
-#1425 := [lemma #1423]: #1424
-#1443 := [unit-resolution #1425 #1442 #980]: #248
-#1444 := [unit-resolution #477 #1443 #1441 #1440]: #53
-#1445 := [unit-resolution #618 #1444]: #241
-#1446 := [unit-resolution #1054 #1443 #1441]: #235
-#1447 := [unit-resolution #788 #1446]: #49
-#1448 := [unit-resolution #646 #1447]: #276
-#1449 := [unit-resolution #502 #1448 #1445 #1437 #1434]: false
-#1451 := [lemma #1449]: #1450
-#1452 := [unit-resolution #1451 #1095 #980]: #87
-#1453 := [unit-resolution #647 #1452]: #236
-#1454 := [unit-resolution #788 #1453]: #47
-#1455 := [unit-resolution #623 #1454]: #214
-#1456 := [unit-resolution #769 #1455]: #20
-#1457 := [unit-resolution #606 #1456]: #218
-#1458 := [unit-resolution #1425 #1457 #980]: #248
-#1459 := [unit-resolution #1054 #1458 #1454]: #62
-#1460 := [unit-resolution #658 #1459]: #290
-#1461 := [unit-resolution #1432 #1460 #1095]: #129
-#1462 := [unit-resolution #621 #1454]: #241
-#1463 := [unit-resolution #645 #1452]: #276
-#1464 := [unit-resolution #659 #1459]: #281
-#1465 := [unit-resolution #502 #1464 #1463 #1462]: #93
-#1466 := [unit-resolution #680 #1465 #1461]: false
-#1468 := [lemma #1466]: #1467
-#1481 := [unit-resolution #1468 #980]: #136
-#1482 := [unit-resolution #693 #1481]: #339
-#1479 := (or #387 #145)
-#1469 := [hypothesis]: #188
-#1470 := [unit-resolution #726 #1469]: #388
-#1471 := [unit-resolution #860 #1470]: #208
-#1472 := [hypothesis]: #339
-#1473 := [unit-resolution #727 #1469]: #379
-#1475 := (or #181 #183 #145)
-#373 := (or #371 #372)
-#714 := [asserted]: #373
-#1474 := [unit-resolution #714 #1399]: #371
-#1476 := [unit-resolution #572 #1474]: #1475
-#1477 := [unit-resolution #1476 #1473 #1472]: #183
-#1478 := [unit-resolution #743 #1477 #1471]: false
-#1480 := [lemma #1478]: #1479
-#1483 := [unit-resolution #1480 #1482]: #387
-#1484 := [unit-resolution #842 #1483]: #157
-#1485 := [unit-resolution #702 #1484]: #346
-#1486 := [unit-resolution #703 #1484]: #313
-#1487 := [unit-resolution #796 #1486 #1481 #1485 #980]: #152
-#1488 := [unit-resolution #730 #1487]: #388
-#1489 := [unit-resolution #860 #1488]: #208
-#1490 := [unit-resolution #731 #1487]: #379
-#1491 := [unit-resolution #1476 #1490 #1482]: #183
-#1492 := [unit-resolution #743 #1491 #1489]: false
-#1493 := [lemma #1492]: #98
-#1515 := [unit-resolution #656 #1493]: #249
-#1511 := [unit-resolution #655 #1493]: #281
-#1512 := [unit-resolution #1420 #829 #1511]: #214
-#1513 := [unit-resolution #769 #1512]: #20
-#1514 := [unit-resolution #607 #1513]: #219
-#1516 := [unit-resolution #606 #1513]: #218
-#1509 := (or #248 #26)
-#1494 := [unit-resolution #654 #1493]: #290
-#1495 := [unit-resolution #1432 #1095 #1494]: #129
-#300 := (or #297 #289)
-#661 := [asserted]: #300
-#1496 := [unit-resolution #661 #1493]: #297
-#302 := (or #298 #289)
-#663 := [asserted]: #302
-#1497 := [unit-resolution #663 #1493]: #298
-#1498 := (or #277 #136 #105 #107)
-#1499 := [unit-resolution #1064 #1430]: #1498
-#1500 := [unit-resolution #1499 #1095 #1497 #1496]: #277
-#1501 := [unit-resolution #1428 #1500 #1495]: false
-#1502 := [lemma #1501]: #136
-#1503 := [unit-resolution #693 #1502]: #339
-#1504 := [unit-resolution #1480 #1503]: #387
-#1505 := [unit-resolution #842 #1504]: #157
-#1506 := [unit-resolution #703 #1505]: #313
-#1507 := [unit-resolution #949 #938 #1506]: #223
-#1508 := [unit-resolution #456 #1507 #934 #1421]: false
-#1510 := [lemma #1508]: #1509
-#1517 := [unit-resolution #1510 #1516]: #248
-#1518 := [unit-resolution #477 #1517 #1515 #1514]: #53
-#1519 := [unit-resolution #618 #1518]: #241
-#1520 := [unit-resolution #1054 #1517 #1515]: #235
-#1521 := [unit-resolution #788 #1520]: #49
-#1522 := [unit-resolution #646 #1521]: #276
-#1523 := [unit-resolution #502 #1522 #1519 #1511 #829]: false
-#1524 := [lemma #1523]: #93
-#1525 := [unit-resolution #1436 #1524]: #87
-#321 := (or #318 #277)
-#677 := [asserted]: #321
-#1526 := [unit-resolution #677 #1525]: #318
-#1527 := [unit-resolution #1255 #1526 #1511 #1515]: #60
-#1528 := [unit-resolution #1510 #1527]: #26
-#1529 := [unit-resolution #647 #1525]: #236
-#1530 := [unit-resolution #788 #1529]: #47
-#1531 := [unit-resolution #623 #1530]: #214
-#1532 := [unit-resolution #769 #1531]: #20
-[unit-resolution #606 #1532 #1528]: false
+#1278 := [unit-resolution #1277 #1030 #883 #882 #969 #881 #1172]: #138
+#1279 := [unit-resolution #571 #1278]: #372
+#1280 := [unit-resolution #852 #1279 #969]: #200
+#1281 := [unit-resolution #590 #1280]: #364
+#1282 := [unit-resolution #572 #1278]: #363
+#1283 := [unit-resolution #589 #1280]: #398
+#1284 := [unit-resolution #450 #1283]: #163
+#1285 := [unit-resolution #558 #1284]: #358
+#1286 := [unit-resolution #804 #1285 #1282 #1281]: #131
+#1287 := [unit-resolution #535 #1286]: #282
+#375 := (or #371 #331)
+#569 := [asserted]: #375
+#1288 := [unit-resolution #569 #1278]: #371
+#1289 := [unit-resolution #828 #1288 #883 #882]: #145
+#1290 := [unit-resolution #547 #1289]: #298
+#1291 := [unit-resolution #543 #1289]: #338
+#1292 := [unit-resolution #784 #1291 #1196 #1172]: #114
+#1293 := [unit-resolution #522 #1292]: #297
+#1294 := [unit-resolution #716 #1293 #1262 #1290]: #98
+#1295 := [unit-resolution #508 #1294]: #281
+#1296 := [unit-resolution #560 #1284]: #318
+#1297 := [unit-resolution #534 #1286]: #317
+#1298 := [unit-resolution #736 #1297 #1296]: #87
+#1299 := [unit-resolution #498 #1298]: #276
+#1300 := [unit-resolution #692 #1299 #1295 #1287]: #55
+#1301 := [unit-resolution #500 #1298]: #236
+#1302 := [unit-resolution #916 #1301]: #47
+#1303 := [unit-resolution #474 #1302 #1300]: false
+#1305 := [lemma #1303]: #1304
+#1306 := [unit-resolution #1305 #1172 #969 #883 #882 #881]: #40
+#270 := (or #265 #229)
+#493 := [asserted]: #270
+#1307 := [unit-resolution #493 #1306]: #265
+#268 := (or #264 #229)
+#491 := [asserted]: #268
+#1308 := [unit-resolution #491 #1306]: #264
+#1309 := [unit-resolution #784 #1174 #1196 #1172]: #114
+#1310 := [unit-resolution #522 #1309]: #297
+#1311 := [unit-resolution #909 #1310 #1308 #1307 #881 #883 #882]: #372
+#1312 := [unit-resolution #852 #1311 #969]: #200
+#1313 := [unit-resolution #589 #1312]: #398
+#1314 := [unit-resolution #450 #1313]: #163
+#1315 := [unit-resolution #560 #1314]: #318
+#1316 := [unit-resolution #590 #1312]: #364
+#1317 := [unit-resolution #558 #1314]: #358
+#1318 := [unit-resolution #466 #1306]: #223
+#1319 := [unit-resolution #968 #1315 #1317 #881 #883 #882 #1316 #1310 #1318]: #60
+#1320 := [unit-resolution #486 #1319]: #257
+#1321 := [unit-resolution #716 #1320 #1310 #1177]: #98
+#1322 := [unit-resolution #507 #1321]: #290
+#1323 := [unit-resolution #760 #1322 #881 #1169]: #138
+#1324 := [unit-resolution #572 #1323]: #363
+#1325 := [unit-resolution #804 #1324 #1317 #1316]: #131
+#1326 := [unit-resolution #534 #1325]: #317
+#1327 := [unit-resolution #488 #1319]: #224
+#1328 := [unit-resolution #616 #1327 #1318]: #26
+#1329 := [unit-resolution #459 #1328]: #213
+#1330 := [unit-resolution #905 #1329]: #22
+#1331 := [unit-resolution #476 #1330]: #235
+#1332 := [unit-resolution #916 #1331]: #49
+#1333 := [unit-resolution #500 #1332]: #277
+#1334 := [unit-resolution #736 #1333 #1326 #1315]: false
+#1336 := [lemma #1334]: #1335
+#1344 := [unit-resolution #1336 #1342 #881 #882 #1341 #1343]: #339
+#1345 := [unit-resolution #828 #1344 #1342 #882]: #174
+#1346 := [unit-resolution #567 #1345]: #372
+#1347 := [unit-resolution #852 #1346 #1341]: #200
+#1348 := [unit-resolution #589 #1347]: #398
+#1349 := [unit-resolution #450 #1348]: #163
+#1350 := [unit-resolution #1021 #1345 #1341]: #131
+#1351 := [unit-resolution #569 #1345]: #331
+#1352 := [unit-resolution #1153 #1342 #881 #882 #1341]: #119
+#1353 := [unit-resolution #557 #1352]: #346
+#1354 := [unit-resolution #1260 #1345 #1341]: #91
+#1355 := [unit-resolution #1219 #1354 #1353 #1343 #881 #1351]: #69
+#1356 := [unit-resolution #486 #1355]: #248
+#1357 := [unit-resolution #930 #1356 #1350]: #125
+#1358 := [unit-resolution #560 #1357 #1349]: false
+#1360 := [lemma #1358]: #1359
+#1496 := [unit-resolution #1360 #882 #881]: #387
+#194 := (or #188 #157)
+decl f6 :: S1
+#16 := f6
+#17 := (= f6 f1)
+#18 := (not #17)
+#420 := [asserted]: #18
+#841 := (or #17 #188 #157)
+#195 := (or #17 #194)
+#842 := (iff #195 #841)
+#843 := [rewrite]: #842
+#449 := [asserted]: #195
+#844 := [mp #449 #843]: #841
+#1497 := [unit-resolution #844 #420]: #194
+#1498 := [unit-resolution #1497 #1496]: #157
+#356 := (or #354 #313)
+#556 := [asserted]: #356
+#1499 := [unit-resolution #556 #1498]: #313
+#355 := (or #354 #346)
+#555 := [asserted]: #355
+#1564 := [unit-resolution #555 #1498]: #346
+#1503 := (or #347 #129 #183)
+#1493 := [hypothesis]: #152
+#393 := (or #388 #347)
+#583 := [asserted]: #393
+#1494 := [unit-resolution #583 #1493]: #388
+#1495 := [unit-resolution #1339 #1494]: #208
+#394 := (or #379 #347)
+#584 := [asserted]: #394
+#1500 := [unit-resolution #584 #1493]: #379
+#1501 := [unit-resolution #1153 #1500 #881 #882 #1499]: #204
+#1502 := [unit-resolution #595 #1501 #1495]: false
+#1504 := [lemma #1502]: #1503
+#1565 := [unit-resolution #1504 #882 #881]: #347
+#1491 := (or #152 #129 #138 #150 #119)
+#1476 := (or #40 #129 #138 #150 #152 #119)
+#1455 := (or #60 #129 #138 #150 #152 #119)
+#1431 := (or #40 #119 #150 #152 #129 #138 #60)
+#1382 := (or #289 #60 #40 #119 #150 #152 #129 #138)
+#1361 := [hypothesis]: #98
+#293 := (or #289 #249)
+#509 := [asserted]: #293
+#1362 := [unit-resolution #509 #1361]: #249
+#1363 := [unit-resolution #507 #1361]: #290
+#1364 := [unit-resolution #760 #1363 #881 #1167]: #136
+#1365 := [unit-resolution #544 #1364]: #338
+#1366 := [unit-resolution #784 #1365 #1173 #1172]: #114
+#307 := (or #305 #306)
+#519 := [asserted]: #307
+#1367 := [unit-resolution #519 #1366]: #305
+#1368 := [unit-resolution #732 #1367 #970]: #81
+#1369 := [unit-resolution #496 #1368]: #233
+#1370 := [unit-resolution #425 #1369]: #38
+#1371 := [unit-resolution #465 #1370]: #223
+#1372 := [unit-resolution #523 #1366]: #265
+#1373 := [unit-resolution #495 #1368]: #264
+#1374 := [unit-resolution #672 #1373 #1030 #1372]: #67
+#1375 := [unit-resolution #485 #1374]: #224
+#1376 := [unit-resolution #616 #1375 #1371]: #26
+#1377 := [unit-resolution #458 #1376]: #219
+#1378 := [unit-resolution #648 #1377 #919 #1362]: #53
+#1379 := [unit-resolution #459 #1376]: #213
+#1380 := [unit-resolution #905 #1379]: #22
+#1381 := [unit-resolution #473 #1380 #1378]: false
+#1383 := [lemma #1381]: #1382
+#1417 := [unit-resolution #1383 #1030 #919 #970 #1173 #1172 #881 #1167]: #289
+#1415 := (or #290 #60 #40 #119 #150 #152 #98)
+#1395 := (or #107 #40 #98 #119 #60 #290)
+#1384 := [unit-resolution #1068 #1045 #970 #919 #1057 #1030]: #32
+#1385 := [unit-resolution #465 #1384]: #228
+#1386 := [unit-resolution #425 #1385]: #44
+#1387 := [unit-resolution #496 #1386]: #272
+#1388 := [unit-resolution #732 #1387 #970]: #112
+#1389 := [unit-resolution #520 #1388]: #297
+#1390 := [unit-resolution #716 #1389 #1044 #1045]: #69
+#1391 := [unit-resolution #497 #1386]: #264
+#1392 := [unit-resolution #521 #1388]: #265
+#1393 := [unit-resolution #672 #1392 #1030 #1391]: #67
+#1394 := [unit-resolution #483 #1393 #1390]: false
+#1396 := [lemma #1394]: #1395
+#1397 := [unit-resolution #1396 #1057 #1044 #970 #919 #1030]: #107
+#342 := (or #338 #298)
+#545 := [asserted]: #342
+#1398 := [unit-resolution #545 #1397]: #338
+#1399 := [unit-resolution #784 #1398 #1173 #1172]: #114
+#1400 := [unit-resolution #523 #1399]: #265
+#1401 := [unit-resolution #519 #1399]: #305
+#1402 := [unit-resolution #732 #1401 #970]: #81
+#1403 := [unit-resolution #495 #1402]: #264
+#1404 := [unit-resolution #672 #1403 #1030 #1400]: #67
+#1405 := [unit-resolution #485 #1404]: #224
+#1406 := [unit-resolution #496 #1402]: #233
+#1407 := [unit-resolution #425 #1406]: #38
+#1408 := [unit-resolution #465 #1407]: #223
+#1409 := [unit-resolution #616 #1408 #1405]: #26
+#1410 := [unit-resolution #458 #1409]: #219
+#1411 := [unit-resolution #648 #1410 #919 #1058]: #53
+#1412 := [unit-resolution #459 #1409]: #213
+#1413 := [unit-resolution #905 #1412]: #22
+#1414 := [unit-resolution #473 #1413 #1411]: false
+#1416 := [lemma #1414]: #1415
+#1418 := [unit-resolution #1416 #1030 #919 #970 #1173 #1172 #1417]: #290
+#1419 := [unit-resolution #760 #1418 #881 #1167]: #136
+#1420 := [unit-resolution #544 #1419]: #338
+#1421 := [unit-resolution #784 #1420 #1173 #1172]: #114
+#1422 := [unit-resolution #523 #1421]: #265
+#1423 := [unit-resolution #519 #1421]: #305
+#1424 := [unit-resolution #732 #1423 #970]: #81
+#1425 := [unit-resolution #495 #1424]: #264
+#1426 := [unit-resolution #548 #1419]: #298
+#1427 := [unit-resolution #522 #1421]: #297
+#1428 := [unit-resolution #716 #1427 #1417 #1426]: #69
+#1429 := [unit-resolution #483 #1428]: #256
+#1430 := [unit-resolution #672 #1429 #1425 #1030 #1422]: false
+#1432 := [lemma #1430]: #1431
+#1433 := [unit-resolution #1432 #919 #1173 #1172 #881 #1167 #970]: #40
+#1434 := [unit-resolution #464 #1433]: #228
+#1435 := [unit-resolution #425 #1434]: #44
+#1436 := [unit-resolution #496 #1435]: #272
+#1437 := [unit-resolution #732 #1436 #970]: #112
+#1438 := [unit-resolution #519 #1437]: #306
+#1439 := [unit-resolution #784 #1438 #1173 #1172]: #143
+#1440 := [unit-resolution #544 #1439]: #330
+#1441 := [unit-resolution #760 #1440 #881 #1167]: #100
+#1442 := [unit-resolution #511 #1441]: #249
+#1443 := [unit-resolution #466 #1433]: #223
+#1444 := [unit-resolution #545 #1439]: #298
+#1445 := [unit-resolution #520 #1437]: #297
+#1446 := [unit-resolution #507 #1441]: #289
+#1447 := [unit-resolution #716 #1446 #1445 #1444]: #69
+#1448 := [unit-resolution #487 #1447]: #224
+#1449 := [unit-resolution #616 #1448 #1443]: #26
+#1450 := [unit-resolution #458 #1449]: #219
+#1451 := [unit-resolution #648 #1450 #919 #1442]: #53
+#1452 := [unit-resolution #459 #1449]: #213
+#1453 := [unit-resolution #905 #1452]: #22
+#1454 := [unit-resolution #473 #1453 #1451]: false
+#1456 := [lemma #1454]: #1455
+#1465 := [unit-resolution #1456 #1172 #1167 #1173 #881 #970]: #60
+#1466 := [unit-resolution #484 #1465]: #256
+#1463 := (or #306 #67 #40 #119)
+#1457 := [hypothesis]: #114
+#1458 := [unit-resolution #519 #1457]: #305
+#1459 := [unit-resolution #732 #1458 #970]: #81
+#1460 := [unit-resolution #523 #1457]: #265
+#1461 := [unit-resolution #672 #1460 #1105 #1030]: #74
+#1462 := [unit-resolution #495 #1461 #1459]: false
+#1464 := [lemma #1462]: #1463
+#1467 := [unit-resolution #1464 #1030 #1466 #970]: #306
+#1468 := [unit-resolution #784 #1467 #1173 #1172]: #143
+#1469 := [unit-resolution #544 #1468]: #330
+#1470 := [unit-resolution #760 #1469 #881 #1167]: #100
+#1471 := [unit-resolution #1110 #1030 #970 #1466]: #297
+#1472 := [unit-resolution #486 #1465]: #257
+#1473 := [unit-resolution #545 #1468]: #298
+#1474 := [unit-resolution #716 #1473 #1472 #1471]: #98
+#1475 := [unit-resolution #507 #1474 #1470]: false
+#1477 := [lemma #1475]: #1476
+#1478 := [unit-resolution #1477 #1172 #1167 #1173 #881 #970]: #40
+#1479 := [unit-resolution #464 #1478]: #228
+#1480 := [unit-resolution #425 #1479]: #44
+#1481 := [unit-resolution #496 #1480]: #272
+#1482 := [unit-resolution #732 #1481 #970]: #112
+#1483 := [unit-resolution #519 #1482]: #306
+#1484 := [unit-resolution #784 #1483 #1173 #1172]: #143
+#1485 := [unit-resolution #544 #1484]: #330
+#1486 := [unit-resolution #760 #1485 #881 #1167]: #100
+#1487 := [unit-resolution #520 #1482]: #297
+#1488 := [unit-resolution #545 #1484]: #298
+#1489 := [unit-resolution #716 #1488 #1472 #1487]: #98
+#1490 := [unit-resolution #507 #1489 #1486]: false
+#1492 := [lemma #1490]: #1491
+#1566 := [unit-resolution #1492 #1565 #881 #1564 #1499]: #138
+#1567 := [unit-resolution #571 #1566]: #372
+#1568 := [unit-resolution #569 #1566]: #371
+#1562 := (or #40 #183 #150 #152 #119 #331)
+#1505 := [unit-resolution #569 #1154]: #371
+#1531 := (or #60 #119 #40 #150 #152 #183 #331)
+#1506 := [unit-resolution #1166 #919 #1154]: #204
+#1507 := [unit-resolution #595 #1506]: #408
+#1508 := [unit-resolution #1339 #1507]: #190
+#392 := (or #388 #379)
+#582 := [asserted]: #392
+#1509 := [unit-resolution #582 #1508]: #379
+#1510 := [unit-resolution #828 #1509 #1505 #882]: #145
+#1511 := [unit-resolution #543 #1510]: #338
+#1512 := [unit-resolution #784 #1511 #1173 #1172]: #114
+#1513 := [unit-resolution #522 #1512]: #297
+#1514 := [unit-resolution #547 #1510]: #298
+#1515 := [unit-resolution #1464 #1512 #1030 #970]: #67
+#1516 := [unit-resolution #483 #1515]: #257
+#1517 := [unit-resolution #716 #1516 #1514 #1513]: #98
+#1518 := [unit-resolution #509 #1517]: #249
+#1519 := [unit-resolution #485 #1515]: #224
+#1520 := [unit-resolution #519 #1512]: #305
+#1521 := [unit-resolution #732 #1520 #970]: #81
+#1522 := [unit-resolution #496 #1521]: #233
+#1523 := [unit-resolution #425 #1522]: #38
+#1524 := [unit-resolution #465 #1523]: #223
+#1525 := [unit-resolution #616 #1524 #1519]: #26
+#1526 := [unit-resolution #458 #1525]: #219
+#1527 := [unit-resolution #648 #1526 #919 #1518]: #53
+#1528 := [unit-resolution #459 #1525]: #213
+#1529 := [unit-resolution #905 #1528]: #22
+#1530 := [unit-resolution #473 #1529 #1527]: false
+#1532 := [lemma #1530]: #1531
+#1533 := [unit-resolution #1532 #1030 #970 #1173 #1172 #882 #1154]: #60
+#1534 := [unit-resolution #484 #1533]: #256
+#1535 := [unit-resolution #1464 #1534 #1030 #970]: #306
+#1536 := [unit-resolution #784 #1535 #1173 #1172]: #143
+#1537 := [unit-resolution #543 #1536]: #339
+#1538 := [unit-resolution #828 #1537 #1505 #882]: #181
+#1539 := [unit-resolution #582 #1538]: #388
+#1540 := [unit-resolution #1339 #1539]: #208
+#1541 := [unit-resolution #595 #1540]: #404
+#1542 := [unit-resolution #852 #1541 #1155]: #200
+#1543 := [unit-resolution #590 #1542]: #364
+#1544 := [unit-resolution #589 #1542]: #398
+#1545 := [unit-resolution #450 #1544]: #163
+#1546 := [unit-resolution #558 #1545]: #358
+#1547 := [unit-resolution #804 #1546 #1161 #1543]: #131
+#1548 := [unit-resolution #535 #1547]: #282
+#1549 := [unit-resolution #1110 #1534 #970 #1030]: #297
+#1550 := [unit-resolution #486 #1533]: #257
+#1551 := [unit-resolution #545 #1536]: #298
+#1552 := [unit-resolution #716 #1551 #1550 #1549]: #98
+#1553 := [unit-resolution #508 #1552]: #281
+#1554 := [unit-resolution #560 #1545]: #318
+#1555 := [unit-resolution #534 #1547]: #317
+#1556 := [unit-resolution #736 #1555 #1554]: #87
+#1557 := [unit-resolution #498 #1556]: #276
+#1558 := [unit-resolution #692 #1557 #1553 #1548]: #55
+#1559 := [unit-resolution #500 #1556]: #236
+#1560 := [unit-resolution #916 #1559]: #47
+#1561 := [unit-resolution #474 #1560 #1558]: false
+#1563 := [lemma #1561]: #1562
+#1569 := [unit-resolution #1563 #882 #1564 #1565 #1499 #1566]: #40
+#1570 := [unit-resolution #464 #1569]: #228
+#1571 := [unit-resolution #425 #1570]: #44
+#1572 := [unit-resolution #496 #1571]: #272
+#1573 := [unit-resolution #732 #1572 #1499]: #112
+#1574 := [unit-resolution #519 #1573]: #306
+#1575 := [unit-resolution #784 #1574 #1564 #1565]: #143
+#1576 := [unit-resolution #543 #1575]: #339
+#1577 := [unit-resolution #828 #1576 #1568 #882]: #181
+#1578 := [unit-resolution #582 #1577]: #388
+#1579 := [unit-resolution #1339 #1578]: #208
+#1580 := [unit-resolution #595 #1579]: #404
+#1581 := [unit-resolution #852 #1580 #1567]: #200
+#1582 := [unit-resolution #590 #1581]: #364
+#1583 := [unit-resolution #572 #1566]: #363
+#1584 := [unit-resolution #589 #1581]: #398
+#1585 := [unit-resolution #450 #1584]: #163
+#1586 := [unit-resolution #558 #1585]: #358
+#1587 := [unit-resolution #804 #1586 #1583 #1582]: #131
+#1588 := [unit-resolution #535 #1587]: #282
+#1589 := [unit-resolution #520 #1573]: #297
+#1590 := [unit-resolution #545 #1575]: #298
+#1591 := [unit-resolution #1166 #1580 #1566]: #60
+#1592 := [unit-resolution #486 #1591]: #257
+#1593 := [unit-resolution #716 #1592 #1590 #1589]: #98
+#1594 := [unit-resolution #508 #1593]: #281
+#1595 := [unit-resolution #466 #1569]: #223
+#1596 := [unit-resolution #488 #1591]: #224
+#1597 := [unit-resolution #616 #1596 #1595]: #26
+#1598 := [unit-resolution #459 #1597]: #213
+#1599 := [unit-resolution #905 #1598]: #22
+#1600 := [unit-resolution #475 #1599]: #241
+#1601 := [unit-resolution #692 #1600 #1594 #1588]: #85
+#1602 := [unit-resolution #560 #1585]: #318
+#1603 := [unit-resolution #534 #1587]: #317
+#1604 := [unit-resolution #736 #1603 #1602]: #87
+#1605 := [unit-resolution #498 #1604 #1601]: false
+#1607 := [lemma #1605]: #1606
+#1608 := [unit-resolution #1607 #881]: #183
+#411 := (or #404 #380)
+#597 := [asserted]: #411
+#1609 := [unit-resolution #597 #1608]: #404
+#410 := (or #408 #380)
+#596 := [asserted]: #410
+#1610 := [unit-resolution #596 #1608]: #408
+#1611 := [unit-resolution #1339 #1610]: #190
+#1612 := [unit-resolution #579 #1611]: #387
+#1613 := [unit-resolution #1497 #1612]: #157
+#1614 := [unit-resolution #556 #1613]: #313
+#1615 := [unit-resolution #583 #1611]: #347
+#1616 := [unit-resolution #555 #1613]: #346
+#1617 := [unit-resolution #1492 #1616 #881 #1615 #1614]: #138
+#1618 := [unit-resolution #571 #1617]: #372
+#1619 := [unit-resolution #852 #1618 #1609]: #200
+#1620 := [unit-resolution #590 #1619]: #364
+#1621 := [unit-resolution #572 #1617]: #363
+#1622 := [unit-resolution #589 #1619]: #398
+#1623 := [unit-resolution #450 #1622]: #163
+#1624 := [unit-resolution #558 #1623]: #358
+#1625 := [unit-resolution #804 #1624 #1621 #1620]: #131
+#1626 := [unit-resolution #535 #1625]: #282
+#1627 := [unit-resolution #560 #1623]: #318
+#1628 := [unit-resolution #534 #1625]: #317
+#1629 := [unit-resolution #736 #1628 #1627]: #87
+#1630 := [unit-resolution #498 #1629]: #276
+#1631 := [unit-resolution #500 #1629]: #236
+#1632 := [unit-resolution #916 #1631]: #47
+#1633 := [unit-resolution #474 #1632]: #241
+#1634 := [unit-resolution #692 #1633 #1630 #1626]: #91
+#1635 := [unit-resolution #508 #1634]: #289
+#1636 := [unit-resolution #1166 #1617 #1609]: #60
+#1637 := [unit-resolution #486 #1636]: #257
+#1638 := [unit-resolution #484 #1636]: #256
+#1639 := [unit-resolution #488 #1636]: #224
+#1640 := [unit-resolution #476 #1632]: #214
+#1641 := [unit-resolution #905 #1640]: #20
+#1642 := [unit-resolution #459 #1641]: #218
+#1643 := [unit-resolution #616 #1642 #1639]: #32
+#1644 := [unit-resolution #466 #1643]: #229
+#1645 := [unit-resolution #1110 #1644 #1614 #1638]: #297
+#1646 := [unit-resolution #716 #1645 #1637 #1635]: #107
+#1647 := [unit-resolution #1464 #1644 #1638 #1614]: #306
+#1648 := [unit-resolution #784 #1647 #1616 #1615]: #143
+#1649 := [unit-resolution #545 #1648 #1646]: false
+#1650 := [lemma #1649]: #129
+#326 := (or #322 #282)
+#533 := [asserted]: #326
+#1662 := [unit-resolution #533 #1650]: #282
+#1664 := [unit-resolution #692 #1662]: #1663
+#1665 := [unit-resolution #1664 #1661 #1658 #1654]: false
+#1667 := [lemma #1665]: #1666
+#1725 := [unit-resolution #1667 #919]: #218
+#1689 := (or #306 #26 #119 #40)
+#1668 := [hypothesis]: #218
+#1683 := [unit-resolution #1464 #1457 #1030 #970]: #67
+#1684 := [unit-resolution #485 #1683]: #224
+#1685 := [unit-resolution #616 #1684 #1668]: #32
+#1686 := [unit-resolution #496 #1459]: #233
+#1687 := [unit-resolution #425 #1686]: #38
+#1688 := [unit-resolution #465 #1687 #1685]: false
+#1690 := [lemma #1688]: #1689
+#1726 := [unit-resolution #1690 #1725 #970 #1030]: #306
+#1715 := (or #298 #114)
+#1700 := [hypothesis]: #107
+#1701 := [unit-resolution #545 #1700]: #338
+#1702 := [hypothesis]: #306
+#1703 := [unit-resolution #547 #1700]: #339
+#1698 := (or #387 #145)
+#1691 := [hypothesis]: #339
+#1692 := [unit-resolution #596 #1340]: #380
+#1694 := (or #371 #204)
+#324 := (or #322 #323)
+#531 := [asserted]: #324
+#1693 := [unit-resolution #531 #1650]: #323
+#1695 := [unit-resolution #1021 #1693]: #1694
+#1696 := [unit-resolution #1695 #1341]: #371
+#1697 := [unit-resolution #828 #1696 #1692 #1691 #1342]: false
+#1699 := [lemma #1697]: #1698
+#1704 := [unit-resolution #1699 #1703]: #387
+#1705 := [unit-resolution #1497 #1704]: #157
+#1706 := [unit-resolution #555 #1705]: #346
+#1707 := [unit-resolution #784 #1706 #1702 #1701]: #152
+#1708 := [unit-resolution #584 #1707]: #379
+#1709 := [unit-resolution #583 #1707]: #388
+#1710 := [unit-resolution #1339 #1709]: #208
+#1711 := [unit-resolution #596 #1710]: #380
+#1712 := [unit-resolution #595 #1710]: #404
+#1713 := [unit-resolution #1695 #1712]: #371
+#1714 := [unit-resolution #828 #1713 #1711 #1703 #1708]: false
+#1716 := [lemma #1714]: #1715
+#1727 := [unit-resolution #1716 #1726]: #298
+#1681 := (or #107 #40 #98 #119 #26)
+#1669 := [unit-resolution #1056 #1045 #970 #1030 #1044]: #224
+#1670 := [unit-resolution #616 #1669 #1668]: #32
+#1671 := [unit-resolution #465 #1670]: #228
+#1672 := [unit-resolution #425 #1671]: #44
+#1673 := [unit-resolution #496 #1672]: #272
+#1674 := [unit-resolution #732 #1673 #970]: #112
+#1675 := [unit-resolution #520 #1674]: #297
+#1676 := [unit-resolution #716 #1675 #1045 #1044]: #69
+#1677 := [unit-resolution #497 #1672]: #264
+#1678 := [unit-resolution #521 #1674]: #265
+#1679 := [unit-resolution #672 #1678 #1030 #1677]: #67
+#1680 := [unit-resolution #483 #1679 #1676]: false
+#1682 := [lemma #1680]: #1681
+#1728 := [unit-resolution #1682 #1727 #1030 #970 #1725]: #98
+#1729 := [unit-resolution #508 #1728]: #281
+#1730 := [unit-resolution #509 #1728]: #249
+#1723 := (or #240 #91)
+#1717 := [hypothesis]: #53
+#242 := (or #240 #241)
+#471 := [asserted]: #242
+#1718 := [unit-resolution #471 #1717]: #241
+#1719 := [unit-resolution #1664 #1718 #1236]: #85
+#1720 := [unit-resolution #472 #1717]: #235
+#1721 := [unit-resolution #916 #1720]: #49
+#1722 := [unit-resolution #499 #1721 #1719]: false
+#1724 := [lemma #1722]: #1723
+#1731 := [unit-resolution #1724 #1729]: #240
+#1732 := [unit-resolution #648 #1731 #919 #1730]: #28
+#1733 := [unit-resolution #460 #1732]: #213
+#1734 := [unit-resolution #905 #1733]: #22
+#1735 := [unit-resolution #475 #1734]: #241
+#1736 := [unit-resolution #1664 #1735 #1729]: #85
+#1737 := [unit-resolution #476 #1734]: #235
+#1738 := [unit-resolution #916 #1737]: #49
+#1739 := [unit-resolution #499 #1738 #1736]: false
+#1741 := [lemma #1739]: #1740
+#1742 := [unit-resolution #1741 #970 #1030]: #60
+#1743 := [unit-resolution #484 #1742]: #256
+#1748 := [unit-resolution #1110 #1743 #1030 #970]: #297
+#1749 := [unit-resolution #486 #1742]: #257
+#1750 := [unit-resolution #1464 #1743 #1030 #970]: #306
+#1751 := [unit-resolution #1716 #1750]: #298
+#1752 := [unit-resolution #716 #1751 #1749 #1748]: #98
+#1753 := [unit-resolution #508 #1752]: #281
+#1754 := [unit-resolution #488 #1742]: #224
+#1746 := (or #233 #40 #119)
+#1744 := [unit-resolution #672 #976 #1030 #1743]: #76
+#1745 := [unit-resolution #521 #1744 #973]: false
+#1747 := [lemma #1745]: #1746
+#1755 := [unit-resolution #1747 #970 #1030]: #233
+#1756 := [unit-resolution #425 #1755]: #38
+#1757 := [unit-resolution #465 #1756]: #223
+#1758 := [unit-resolution #616 #1757 #1754]: #26
+#1759 := [unit-resolution #459 #1758]: #213
+#1760 := [unit-resolution #905 #1759]: #22
+#1761 := [unit-resolution #475 #1760]: #241
+#1762 := [unit-resolution #1664 #1761 #1753]: #85
+#1763 := [unit-resolution #476 #1760]: #235
+#1764 := [unit-resolution #916 #1763]: #49
+#1765 := [unit-resolution #499 #1764 #1762]: false
+#1767 := [lemma #1765]: #1766
+#1768 := [unit-resolution #1767 #1030]: #119
+#1769 := [unit-resolution #556 #1768]: #354
+#1770 := [unit-resolution #1497 #1769]: #188
+#1771 := [unit-resolution #581 #1770]: #347
+#1772 := [unit-resolution #557 #1768]: #346
+#1773 := [unit-resolution #1699 #1770]: #145
+#1774 := [unit-resolution #543 #1773]: #338
+#1775 := [unit-resolution #784 #1774 #1772 #1771]: #114
+#1787 := [unit-resolution #522 #1775]: #297
+#1788 := [unit-resolution #547 #1773]: #298
+#1802 := (or #60 #40)
+#1785 := (or #257 #26 #40)
+#1776 := [unit-resolution #523 #1775]: #265
+#1777 := [hypothesis]: #69
+#1778 := [unit-resolution #483 #1777]: #256
+#1779 := [unit-resolution #672 #1778 #1030 #1776]: #74
+#1780 := [unit-resolution #497 #1779]: #233
+#1781 := [unit-resolution #487 #1777]: #224
+#1782 := [unit-resolution #616 #1781 #1668]: #32
+#1783 := [unit-resolution #465 #1782]: #228
+#1784 := [unit-resolution #425 #1783 #1780]: false
+#1786 := [lemma #1784]: #1785
+#1789 := [unit-resolution #1786 #1725 #1030]: #257
+#1790 := [unit-resolution #716 #1789 #1788 #1787]: #98
+#1791 := [unit-resolution #508 #1790]: #281
+#1792 := [unit-resolution #509 #1790]: #249
+#1793 := [unit-resolution #1724 #1791]: #240
+#1794 := [unit-resolution #648 #1793 #919 #1792]: #28
+#1795 := [unit-resolution #460 #1794]: #213
+#1796 := [unit-resolution #905 #1795]: #22
+#1797 := [unit-resolution #475 #1796]: #241
+#1798 := [unit-resolution #1664 #1797 #1791]: #85
+#1799 := [unit-resolution #476 #1796]: #235
+#1800 := [unit-resolution #916 #1799]: #49
+#1801 := [unit-resolution #499 #1800 #1798]: false
+#1803 := [lemma #1801]: #1802
+#1804 := [unit-resolution #1803 #1030]: #60
+#1805 := [unit-resolution #486 #1804]: #257
+#1806 := [unit-resolution #716 #1805 #1788 #1787]: #98
+#1807 := [unit-resolution #508 #1806]: #281
+#1808 := [unit-resolution #488 #1804]: #224
+#1809 := [unit-resolution #484 #1804]: #256
+#1810 := [unit-resolution #672 #1809 #1030 #1776]: #74
+#1811 := [unit-resolution #497 #1810]: #233
+#1812 := [unit-resolution #425 #1811]: #38
+#1813 := [unit-resolution #465 #1812]: #223
+#1814 := [unit-resolution #616 #1813 #1808]: #26
+#1815 := [unit-resolution #459 #1814]: #213
+#1816 := [unit-resolution #905 #1815]: #22
+#1817 := [unit-resolution #475 #1816]: #241
+#1818 := [unit-resolution #1664 #1817 #1807]: #85
+#1819 := [unit-resolution #476 #1816]: #235
+#1820 := [unit-resolution #916 #1819]: #49
+#1821 := [unit-resolution #499 #1820 #1818]: false
+#1822 := [lemma #1821]: #40
+#1855 := [unit-resolution #464 #1822]: #228
+#1856 := [unit-resolution #425 #1855]: #44
+#1857 := [unit-resolution #496 #1856]: #272
+#1858 := [unit-resolution #732 #1103 #1857]: #119
+#1859 := [unit-resolution #556 #1858]: #354
+#1860 := [unit-resolution #1497 #1859]: #188
+#1861 := [unit-resolution #1699 #1860]: #145
+#1862 := [unit-resolution #557 #1858]: #346
+#1863 := [unit-resolution #522 #1102]: #306
+#1864 := [unit-resolution #581 #1860]: #347
+#1865 := [unit-resolution #784 #1864 #1863 #1862]: #143
+#1866 := [unit-resolution #543 #1865 #1861]: false
+#1867 := [lemma #1866]: #297
+#1853 := (or #105 #107)
+#1838 := (or #60 #107 #105)
+#1823 := [unit-resolution #466 #1822]: #223
+#1824 := [unit-resolution #616 #1725 #1823]: #34
+#1825 := [unit-resolution #487 #1824]: #257
+#1826 := [unit-resolution #716 #1825 #1045 #890]: #98
+#1827 := [unit-resolution #508 #1826]: #281
+#1828 := [unit-resolution #509 #1826]: #249
+#1829 := [unit-resolution #1724 #1827]: #240
+#1830 := [unit-resolution #648 #1829 #919 #1828]: #28
+#1831 := [unit-resolution #460 #1830]: #213
+#1832 := [unit-resolution #905 #1831]: #22
+#1833 := [unit-resolution #475 #1832]: #241
+#1834 := [unit-resolution #1664 #1833 #1827]: #85
+#1835 := [unit-resolution #476 #1832]: #235
+#1836 := [unit-resolution #916 #1835]: #49
+#1837 := [unit-resolution #499 #1836 #1834]: false
+#1839 := [lemma #1837]: #1838
+#1840 := [unit-resolution #1839 #890 #1045]: #60
+#1841 := [unit-resolution #486 #1840]: #257
+#1842 := [unit-resolution #716 #1841 #1045 #890]: #98
+#1843 := [unit-resolution #508 #1842]: #281
+#1844 := [unit-resolution #488 #1840]: #224
+#1845 := [unit-resolution #616 #1844 #1823]: #26
+#1846 := [unit-resolution #459 #1845]: #213
+#1847 := [unit-resolution #905 #1846]: #22
+#1848 := [unit-resolution #475 #1847]: #241
+#1849 := [unit-resolution #1664 #1848 #1843]: #85
+#1850 := [unit-resolution #476 #1847]: #235
+#1851 := [unit-resolution #916 #1850]: #49
+#1852 := [unit-resolution #499 #1851 #1849]: false
+#1854 := [lemma #1852]: #1853
+#1868 := [unit-resolution #1854 #1867]: #107
+#1869 := [unit-resolution #547 #1868]: #339
+#1870 := [unit-resolution #1699 #1869]: #387
+#1871 := [unit-resolution #1497 #1870]: #157
+#1872 := [unit-resolution #1716 #1868]: #114
+#1873 := [unit-resolution #519 #1872]: #305
+#1874 := [unit-resolution #732 #1873 #1857]: #119
+[unit-resolution #556 #1874 #1871]: false
+4981f4ce905ff5bd45aa1d26b0e079fee17e6b28 67 0
 unsat
-0020560a0c4fa3058b0174abbbe01bb65cb5b25a 67 0
 #2 := false
 decl f1 :: S1
 #3 := f1
 decl f3 :: (-> Int S1)
 decl ?v0!0 :: Int
-#55 := ?v0!0
-#56 := (f3 ?v0!0)
-#57 := (= #56 f1)
-#58 := (not #57)
+#53 := ?v0!0
+#54 := (f3 ?v0!0)
+#55 := (= #54 f1)
+#56 := (not #55)
 decl ?v1!1 :: Int
 #66 := ?v1!1
 #67 := (f3 ?v1!1)
 #68 := (= #67 f1)
-#69 := (or #57 #68)
+#69 := (or #55 #68)
 #70 := (not #69)
-#86 := (and #57 #70)
-#63 := (not #58)
-#76 := (and #63 #70)
-#87 := (iff #76 #86)
-#84 := (iff #63 #57)
-#85 := [rewrite]: #84
-#88 := [monotonicity #85]: #87
+#84 := (and #55 #70)
+#63 := (not #56)
+#74 := (and #63 #70)
+#85 := (iff #74 #84)
+#82 := (iff #63 #55)
+#83 := [rewrite]: #82
+#86 := [monotonicity #83]: #85
 #7 := (:var 0 Int)
 #8 := (f3 #7)
 #9 := (= #8 f1)
@@ -1798,44 +2058,44 @@
 #12 := (= #11 f1)
 #13 := (or #12 #9)
 #14 := (forall (vars (?v1 Int)) #13)
-#39 := (not #9)
-#40 := (or #39 #14)
-#43 := (forall (vars (?v0 Int)) #40)
-#46 := (not #43)
-#79 := (~ #46 #76)
-#50 := (or #57 #9)
-#52 := (forall (vars (?v1 Int)) #50)
-#59 := (or #58 #52)
+#23 := (not #9)
+#24 := (or #23 #14)
+#27 := (forall (vars (?v0 Int)) #24)
+#30 := (not #27)
+#77 := (~ #30 #74)
+#57 := (or #55 #9)
+#58 := (forall (vars (?v1 Int)) #57)
+#59 := (or #56 #58)
 #60 := (not #59)
-#77 := (~ #60 #76)
-#71 := (not #52)
+#75 := (~ #60 #74)
+#71 := (not #58)
 #72 := (~ #71 #70)
 #73 := [sk]: #72
 #64 := (~ #63 #63)
 #65 := [refl]: #64
-#78 := [nnf-neg #65 #73]: #77
-#61 := (~ #46 #60)
+#76 := [nnf-neg #65 #73]: #75
+#61 := (~ #30 #60)
 #62 := [sk]: #61
-#80 := [trans #62 #78]: #79
+#78 := [trans #62 #76]: #77
 #15 := (implies #9 #14)
 #16 := (forall (vars (?v0 Int)) #15)
 #17 := (not #16)
-#47 := (iff #17 #46)
-#44 := (iff #16 #43)
-#41 := (iff #15 #40)
-#42 := [rewrite]: #41
-#45 := [quant-intro #42]: #44
-#48 := [monotonicity #45]: #47
-#38 := [asserted]: #17
-#51 := [mp #38 #48]: #46
-#81 := [mp~ #51 #80]: #76
-#82 := [mp #81 #88]: #86
-#89 := [and-elim #82]: #70
-#90 := [not-or-elim #89]: #58
-#83 := [and-elim #82]: #57
-[unit-resolution #83 #90]: false
+#31 := (iff #17 #30)
+#28 := (iff #16 #27)
+#25 := (iff #15 #24)
+#26 := [rewrite]: #25
+#29 := [quant-intro #26]: #28
+#32 := [monotonicity #29]: #31
+#19 := [asserted]: #17
+#33 := [mp #19 #32]: #30
+#79 := [mp~ #33 #78]: #74
+#80 := [mp #79 #86]: #84
+#87 := [and-elim #80]: #70
+#88 := [not-or-elim #87]: #56
+#81 := [and-elim #80]: #55
+[unit-resolution #81 #88]: false
+4467e2bf3cf901d999549d9b67e78dac1d5ecf0f 117 0
 unsat
-71f21c0a5d88cb94f60cf796ba4f0c3c95e6bff5 117 0
 #2 := false
 decl f3 :: (-> S3 S2 S1)
 #10 := (:var 0 S2)
@@ -1846,120 +2106,120 @@
 #7 := f5
 #17 := (f4 f5 f6)
 #18 := (f3 #17 #10)
-#573 := (pattern #18)
+#512 := (pattern #18)
 decl f1 :: S1
 #3 := f1
 #19 := (= #18 f1)
-#76 := (not #19)
-#574 := (forall (vars (?v0 S2)) (:pat #573) #76)
+#57 := (not #19)
+#513 := (forall (vars (?v0 S2)) (:pat #512) #57)
 decl f7 :: S2
 #21 := f7
 #22 := (f3 #17 f7)
 #23 := (= #22 f1)
-#150 := (= f6 f1)
-#151 := (iff #23 #150)
+#86 := (= f6 f1)
+#87 := (iff #23 #86)
 #8 := (:var 1 S1)
 #9 := (f4 f5 #8)
 #11 := (f3 #9 #10)
-#566 := (pattern #11)
+#505 := (pattern #11)
 #13 := (= #8 f1)
 #12 := (= #11 f1)
 #14 := (iff #12 #13)
-#567 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #566) #14)
+#506 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #505) #14)
 #15 := (forall (vars (?v0 S1) (?v1 S2)) #14)
-#570 := (iff #15 #567)
-#568 := (iff #14 #14)
-#569 := [refl]: #568
-#571 := [quant-intro #569]: #570
-#62 := (~ #15 #15)
+#509 := (iff #15 #506)
+#507 := (iff #14 #14)
+#508 := [refl]: #507
+#510 := [quant-intro #508]: #509
+#58 := (~ #15 #15)
 #60 := (~ #14 #14)
 #61 := [refl]: #60
-#63 := [nnf-pos #61]: #62
-#46 := [asserted]: #15
-#53 := [mp~ #46 #63]: #15
-#572 := [mp #53 #571]: #567
-#152 := (not #567)
-#228 := (or #152 #151)
-#561 := [quant-inst #16 #21]: #228
-#237 := [unit-resolution #561 #572]: #151
+#59 := [nnf-pos #61]: #58
+#27 := [asserted]: #15
+#56 := [mp~ #27 #59]: #15
+#511 := [mp #56 #510]: #506
+#90 := (not #506)
+#167 := (or #90 #87)
+#500 := [quant-inst #16 #21]: #167
+#176 := [unit-resolution #500 #511]: #87
 decl ?v0!0 :: S2
-#66 := ?v0!0
-#67 := (f3 #17 ?v0!0)
-#68 := (= #67 f1)
-#236 := (iff #68 #150)
-#238 := (or #152 #236)
-#229 := [quant-inst #16 #66]: #238
-#227 := [unit-resolution #229 #572]: #236
-#240 := (not #236)
-#199 := (or #240 #150)
-#55 := (not #23)
-#215 := [hypothesis]: #55
-#83 := (or #68 #23)
-#79 := (forall (vars (?v0 S2)) #76)
-#82 := (or #79 #55)
-#84 := (and #83 #82)
+#67 := ?v0!0
+#68 := (f3 #17 ?v0!0)
+#69 := (= #68 f1)
+#175 := (iff #69 #86)
+#177 := (or #90 #175)
+#168 := [quant-inst #16 #67]: #177
+#166 := [unit-resolution #168 #511]: #175
+#179 := (not #175)
+#138 := (or #179 #86)
+#77 := (not #23)
+#154 := [hypothesis]: #77
+#81 := (or #69 #23)
+#64 := (forall (vars (?v0 S2)) #57)
+#80 := (or #64 #77)
+#82 := (and #81 #80)
 #20 := (exists (vars (?v0 S2)) #19)
-#48 := (not #20)
-#49 := (iff #48 #23)
-#85 := (~ #49 #84)
-#57 := (~ #23 #23)
-#65 := [refl]: #57
-#64 := (~ #55 #55)
-#56 := [refl]: #64
-#80 := (~ #48 #79)
-#77 := (~ #76 #76)
-#78 := [refl]: #77
-#81 := [nnf-neg #78]: #80
-#73 := (not #48)
-#74 := (~ #73 #68)
-#69 := (~ #20 #68)
-#70 := [sk]: #69
-#75 := [nnf-neg #70]: #74
-#86 := [nnf-pos #75 #81 #56 #65]: #85
+#32 := (not #20)
+#33 := (iff #32 #23)
+#83 := (~ #33 #82)
+#78 := (~ #77 #77)
+#79 := [refl]: #78
+#75 := (~ #23 #23)
+#76 := [refl]: #75
+#72 := (not #32)
+#73 := (~ #72 #69)
+#70 := (~ #20 #69)
+#71 := [sk]: #70
+#74 := [nnf-neg #71]: #73
+#65 := (~ #32 #64)
+#62 := (~ #57 #57)
+#63 := [refl]: #62
+#66 := [nnf-neg #63]: #65
+#84 := [nnf-pos #66 #74 #76 #79]: #83
 #24 := (iff #20 #23)
 #25 := (not #24)
-#50 := (iff #25 #49)
-#51 := [rewrite]: #50
-#47 := [asserted]: #25
-#54 := [mp #47 #51]: #49
-#87 := [mp~ #54 #86]: #84
-#90 := [and-elim #87]: #83
-#557 := [unit-resolution #90 #215]: #68
-#243 := (not #68)
-#222 := (or #240 #243 #150)
-#558 := [def-axiom]: #222
-#541 := [unit-resolution #558 #557]: #199
-#203 := [unit-resolution #541 #227]: #150
-#241 := (not #150)
-#562 := (not #151)
-#204 := (or #562 #241)
-#563 := (or #562 #23 #241)
-#564 := [def-axiom]: #563
-#205 := [unit-resolution #564 #215]: #204
-#206 := [unit-resolution #205 #203 #237]: false
-#543 := [lemma #206]: #23
-#579 := (or #574 #55)
-#580 := (iff #82 #579)
-#577 := (iff #79 #574)
-#575 := (iff #76 #76)
-#576 := [refl]: #575
-#578 := [quant-intro #576]: #577
-#581 := [monotonicity #578]: #580
-#91 := [and-elim #87]: #82
-#582 := [mp #91 #581]: #579
-#242 := [unit-resolution #582 #543]: #574
-#555 := (not #574)
-#214 := (or #555 #55)
-#219 := [quant-inst #21]: #214
-[unit-resolution #219 #543 #242]: false
+#34 := (iff #25 #33)
+#35 := [rewrite]: #34
+#28 := [asserted]: #25
+#36 := [mp #28 #35]: #33
+#85 := [mp~ #36 #84]: #82
+#88 := [and-elim #85]: #81
+#496 := [unit-resolution #88 #154]: #69
+#182 := (not #69)
+#161 := (or #179 #182 #86)
+#497 := [def-axiom]: #161
+#480 := [unit-resolution #497 #496]: #138
+#142 := [unit-resolution #480 #166]: #86
+#180 := (not #86)
+#501 := (not #87)
+#143 := (or #501 #180)
+#502 := (or #501 #23 #180)
+#503 := [def-axiom]: #502
+#144 := [unit-resolution #503 #154]: #143
+#145 := [unit-resolution #144 #142 #176]: false
+#482 := [lemma #145]: #23
+#518 := (or #513 #77)
+#519 := (iff #80 #518)
+#516 := (iff #64 #513)
+#514 := (iff #57 #57)
+#515 := [refl]: #514
+#517 := [quant-intro #515]: #516
+#520 := [monotonicity #517]: #519
+#89 := [and-elim #85]: #80
+#521 := [mp #89 #520]: #518
+#181 := [unit-resolution #521 #482]: #513
+#494 := (not #513)
+#153 := (or #494 #77)
+#158 := [quant-inst #21]: #153
+[unit-resolution #158 #482 #181]: false
+03b722cb2eea463c8897e294f3d4d3f3f1ac4061 117 0
 unsat
-ae3e0f78fcdef723f102d089b42d97f098766d9e 117 0
 #2 := false
 decl f1 :: S1
 #3 := f1
 decl f7 :: S1
 #25 := f7
-#206 := (= f7 f1)
+#140 := (= f7 f1)
 decl f3 :: (-> S3 S2 S1)
 decl f6 :: S2
 #20 := f6
@@ -1969,109 +2229,109 @@
 #26 := (f4 f5 f7)
 #30 := (f3 #26 f6)
 #31 := (= #30 f1)
-#292 := (iff #31 #206)
+#229 := (iff #31 #140)
 #10 := (:var 0 S2)
 #8 := (:var 1 S1)
 #9 := (f4 f5 #8)
 #11 := (f3 #9 #10)
-#622 := (pattern #11)
+#559 := (pattern #11)
 #13 := (= #8 f1)
 #12 := (= #11 f1)
 #14 := (iff #12 #13)
-#623 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #622) #14)
+#560 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #559) #14)
 #15 := (forall (vars (?v0 S1) (?v1 S2)) #14)
-#626 := (iff #15 #623)
-#624 := (iff #14 #14)
-#625 := [refl]: #624
-#627 := [quant-intro #625]: #626
-#73 := (~ #15 #15)
-#71 := (~ #14 #14)
-#72 := [refl]: #71
-#74 := [nnf-pos #72]: #73
-#54 := [asserted]: #15
-#62 := [mp~ #54 #74]: #15
-#628 := [mp #62 #627]: #623
-#295 := (not #623)
-#611 := (or #295 #292)
-#270 := [quant-inst #25 #20]: #611
-#297 := [unit-resolution #270 #628]: #292
+#563 := (iff #15 #560)
+#561 := (iff #14 #14)
+#562 := [refl]: #561
+#564 := [quant-intro #562]: #563
+#71 := (~ #15 #15)
+#67 := (~ #14 #14)
+#68 := [refl]: #67
+#72 := [nnf-pos #68]: #71
+#35 := [asserted]: #15
+#65 := [mp~ #35 #72]: #15
+#565 := [mp #65 #564]: #560
+#232 := (not #560)
+#548 := (or #232 #229)
+#207 := [quant-inst #25 #20]: #548
+#234 := [unit-resolution #207 #565]: #229
 decl ?v0!3 :: S2
-#120 := ?v0!3
-#123 := (f3 #26 ?v0!3)
-#124 := (= #123 f1)
-#296 := (iff #124 #206)
-#299 := (or #295 #296)
-#278 := [quant-inst #25 #120]: #299
-#298 := [unit-resolution #278 #628]: #296
-#614 := (not #296)
-#599 := (or #614 #206)
-#108 := (not #31)
+#121 := ?v0!3
+#122 := (f3 #26 ?v0!3)
+#123 := (= #122 f1)
+#233 := (iff #123 #140)
+#236 := (or #232 #233)
+#215 := [quant-inst #25 #121]: #236
+#235 := [unit-resolution #215 #565]: #233
+#551 := (not #233)
+#536 := (or #551 #140)
+#131 := (not #31)
 #27 := (f3 #26 #10)
-#654 := (pattern #27)
+#591 := (pattern #27)
 #28 := (= #27 f1)
-#132 := (not #28)
-#655 := (forall (vars (?v0 S2)) (:pat #654) #132)
-#207 := [hypothesis]: #31
-#660 := (or #655 #108)
-#135 := (forall (vars (?v0 S2)) #132)
-#138 := (or #135 #108)
-#661 := (iff #138 #660)
-#658 := (iff #135 #655)
-#656 := (iff #132 #132)
-#657 := [refl]: #656
-#659 := [quant-intro #657]: #658
-#662 := [monotonicity #659]: #661
-#139 := (or #124 #31)
-#140 := (and #139 #138)
+#113 := (not #28)
+#592 := (forall (vars (?v0 S2)) (:pat #591) #113)
+#141 := [hypothesis]: #31
+#597 := (or #592 #131)
+#118 := (forall (vars (?v0 S2)) #113)
+#134 := (or #118 #131)
+#598 := (iff #134 #597)
+#595 := (iff #118 #592)
+#593 := (iff #113 #113)
+#594 := [refl]: #593
+#596 := [quant-intro #594]: #595
+#599 := [monotonicity #596]: #598
+#135 := (or #123 #31)
+#136 := (and #135 #134)
 #29 := (exists (vars (?v0 S2)) #28)
-#57 := (not #29)
-#58 := (iff #57 #31)
-#141 := (~ #58 #140)
-#81 := (~ #31 #31)
-#119 := [refl]: #81
-#109 := (~ #108 #108)
-#80 := [refl]: #109
-#136 := (~ #57 #135)
-#133 := (~ #132 #132)
-#134 := [refl]: #133
-#137 := [nnf-neg #134]: #136
-#129 := (not #57)
-#130 := (~ #129 #124)
-#125 := (~ #29 #124)
-#126 := [sk]: #125
-#131 := [nnf-neg #126]: #130
-#142 := [nnf-pos #131 #137 #80 #119]: #141
+#41 := (not #29)
+#42 := (iff #41 #31)
+#137 := (~ #42 #136)
+#132 := (~ #131 #131)
+#133 := [refl]: #132
+#129 := (~ #31 #31)
+#130 := [refl]: #129
+#126 := (not #41)
+#127 := (~ #126 #123)
+#124 := (~ #29 #123)
+#125 := [sk]: #124
+#128 := [nnf-neg #125]: #127
+#119 := (~ #41 #118)
+#114 := (~ #113 #113)
+#117 := [refl]: #114
+#120 := [nnf-neg #117]: #119
+#138 := [nnf-pos #120 #128 #130 #133]: #137
 #32 := (iff #29 #31)
 #33 := (not #32)
-#59 := (iff #33 #58)
-#60 := [rewrite]: #59
-#56 := [asserted]: #33
-#63 := [mp #56 #60]: #58
-#143 := [mp~ #63 #142]: #140
-#147 := [and-elim #143]: #138
-#663 := [mp #147 #662]: #660
-#293 := [unit-resolution #663 #207]: #655
-#610 := (not #655)
-#283 := (or #610 #108)
-#284 := [quant-inst #20]: #283
-#617 := [unit-resolution #284 #207 #293]: false
-#618 := [lemma #617]: #108
-#146 := [and-elim #143]: #139
-#262 := [unit-resolution #146 #618]: #124
-#208 := (not #124)
-#294 := (or #614 #208 #206)
-#285 := [def-axiom]: #294
-#600 := [unit-resolution #285 #262]: #599
-#601 := [unit-resolution #600 #298]: #206
-#616 := (not #206)
-#275 := (not #292)
-#602 := (or #275 #616)
-#612 := (or #275 #31 #616)
-#271 := [def-axiom]: #612
-#603 := [unit-resolution #271 #618]: #602
-[unit-resolution #603 #601 #297]: false
+#43 := (iff #33 #42)
+#44 := [rewrite]: #43
+#37 := [asserted]: #33
+#45 := [mp #37 #44]: #42
+#139 := [mp~ #45 #138]: #136
+#143 := [and-elim #139]: #134
+#600 := [mp #143 #599]: #597
+#230 := [unit-resolution #600 #141]: #592
+#547 := (not #592)
+#220 := (or #547 #131)
+#221 := [quant-inst #20]: #220
+#554 := [unit-resolution #221 #141 #230]: false
+#555 := [lemma #554]: #131
+#142 := [and-elim #139]: #135
+#199 := [unit-resolution #142 #555]: #123
+#144 := (not #123)
+#231 := (or #551 #144 #140)
+#222 := [def-axiom]: #231
+#537 := [unit-resolution #222 #199]: #536
+#538 := [unit-resolution #537 #235]: #140
+#553 := (not #140)
+#212 := (not #229)
+#539 := (or #212 #553)
+#549 := (or #212 #31 #553)
+#208 := [def-axiom]: #549
+#540 := [unit-resolution #208 #555]: #539
+[unit-resolution #540 #538 #234]: false
+d52a85a56d8c1a29429987c40f8741cebe859405 61 0
 unsat
-5dc6f25776aabe70ad45ce325942b3a138a1974d 61 0
 #2 := false
 decl f1 :: S1
 #3 := f1
@@ -2084,92 +2344,92 @@
 #18 := f5
 #19 := (f3 f5)
 #20 := (= #19 f1)
-#45 := (not #9)
-#46 := (or #45 #20)
-#49 := (not #46)
+#29 := (not #9)
+#30 := (or #29 #20)
+#33 := (not #30)
 #21 := (implies #9 #20)
 #22 := (not #21)
-#50 := (iff #22 #49)
-#47 := (iff #21 #46)
-#48 := [rewrite]: #47
-#51 := [monotonicity #48]: #50
-#44 := [asserted]: #22
-#54 := [mp #44 #51]: #49
-#52 := [not-or-elim #54]: #9
+#34 := (iff #22 #33)
+#31 := (iff #21 #30)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#25 := [asserted]: #22
+#36 := [mp #25 #35]: #33
+#37 := [not-or-elim #36]: #9
 #10 := (:var 0 S2)
 #11 := (f3 #10)
-#550 := (pattern #11)
+#491 := (pattern #11)
 #12 := (= #11 f1)
 #15 := (not #12)
-#551 := (forall (vars (?v0 S2)) (:pat #550) #15)
+#492 := (forall (vars (?v0 S2)) (:pat #491) #15)
 #16 := (forall (vars (?v0 S2)) #15)
-#554 := (iff #16 #551)
-#552 := (iff #15 #15)
-#553 := [refl]: #552
-#555 := [quant-intro #553]: #554
+#495 := (iff #16 #492)
+#493 := (iff #15 #15)
+#494 := [refl]: #493
+#496 := [quant-intro #494]: #495
 #13 := (exists (vars (?v0 S2)) #12)
 #14 := (not #13)
-#60 := (~ #14 #16)
-#63 := (~ #15 #15)
-#64 := [refl]: #63
-#72 := [nnf-neg #64]: #60
+#71 := (~ #14 #16)
+#59 := (~ #15 #15)
+#60 := [refl]: #59
+#72 := [nnf-neg #60]: #71
 #17 := (if #9 #14 #16)
-#70 := (iff #17 #14)
+#68 := (iff #17 #14)
 #1 := true
 #65 := (if true #14 #16)
-#68 := (iff #65 #14)
-#69 := [rewrite]: #68
+#62 := (iff #65 #14)
+#67 := [rewrite]: #62
 #66 := (iff #17 #65)
-#61 := (iff #9 true)
-#62 := [iff-true #52]: #61
-#67 := [monotonicity #62]: #66
-#71 := [trans #67 #69]: #70
-#43 := [asserted]: #17
-#59 := [mp #43 #71]: #14
-#57 := [mp~ #59 #72]: #16
-#556 := [mp #57 #555]: #551
-#135 := (not #551)
-#221 := (or #135 #45)
-#136 := [quant-inst #7]: #221
-[unit-resolution #136 #556 #52]: false
+#63 := (iff #9 true)
+#64 := [iff-true #37]: #63
+#61 := [monotonicity #64]: #66
+#69 := [trans #61 #67]: #68
+#24 := [asserted]: #17
+#70 := [mp #24 #69]: #14
+#73 := [mp~ #70 #72]: #16
+#497 := [mp #73 #496]: #492
+#75 := (not #492)
+#162 := (or #75 #29)
+#76 := [quant-inst #7]: #162
+[unit-resolution #76 #497 #37]: false
+4ee0a4e3f4c5dbd20f1be18c405a836de5af68d2 17 0
 unsat
-29e0fbcf1b3262888237e1fa476aa8a7425443c7 17 0
 #2 := false
 #7 := 3::Int
 #8 := (= 3::Int 3::Int)
 #9 := (not #8)
-#38 := (iff #9 false)
+#23 := (iff #9 false)
 #1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #9 #33)
-#31 := (iff #8 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#30 := [asserted]: #9
-[mp #30 #39]: false
+#18 := (not true)
+#21 := (iff #18 false)
+#22 := [rewrite]: #21
+#19 := (iff #9 #18)
+#16 := (iff #8 true)
+#17 := [rewrite]: #16
+#20 := [monotonicity #17]: #19
+#24 := [trans #20 #22]: #23
+#11 := [asserted]: #9
+[mp #11 #24]: false
+8eb471f821b833f83e55527f320dd341eddcf700 17 0
 unsat
-065da226a83f89ade06131ac7b676aff1d33184f 17 0
 #2 := false
 #7 := 3::Real
 #8 := (= 3::Real 3::Real)
 #9 := (not #8)
-#38 := (iff #9 false)
+#23 := (iff #9 false)
 #1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #9 #33)
-#31 := (iff #8 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#30 := [asserted]: #9
-[mp #30 #39]: false
+#18 := (not true)
+#21 := (iff #18 false)
+#22 := [rewrite]: #21
+#19 := (iff #9 #18)
+#16 := (iff #8 true)
+#17 := [rewrite]: #16
+#20 := [monotonicity #17]: #19
+#24 := [trans #20 #22]: #23
+#11 := [asserted]: #9
+[mp #11 #24]: false
+c53677498fbbc0279d49e170ecebacd85ec37066 26 0
 unsat
-52cd464fc4027157f69df0b8cc3229ae55ad2079 26 0
 #2 := false
 #10 := 4::Int
 #8 := 1::Int
@@ -2177,26 +2437,26 @@
 #9 := (+ 3::Int 1::Int)
 #11 := (= #9 4::Int)
 #12 := (not #11)
-#47 := (iff #12 false)
+#32 := (iff #12 false)
 #1 := true
-#42 := (not true)
-#45 := (iff #42 false)
-#46 := [rewrite]: #45
-#43 := (iff #12 #42)
-#40 := (iff #11 true)
-#35 := (= 4::Int 4::Int)
-#38 := (iff #35 true)
-#39 := [rewrite]: #38
-#36 := (iff #11 #35)
-#34 := [rewrite]: #11
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#33 := [asserted]: #12
-[mp #33 #48]: false
+#27 := (not true)
+#30 := (iff #27 false)
+#31 := [rewrite]: #30
+#28 := (iff #12 #27)
+#25 := (iff #11 true)
+#19 := (= 4::Int 4::Int)
+#23 := (iff #19 true)
+#24 := [rewrite]: #23
+#20 := (iff #11 #19)
+#18 := [rewrite]: #11
+#21 := [monotonicity #18]: #20
+#26 := [trans #21 #24]: #25
+#29 := [monotonicity #26]: #28
+#33 := [trans #29 #31]: #32
+#14 := [asserted]: #12
+[mp #14 #33]: false
+7e6f4869abf700172472e795c9b4c6c255ad1fbe 37 0
 unsat
-28b6536c2d4f9dc75412d00f15231ed2ee58fe03 41 0
 #2 := false
 decl f3 :: Int
 #7 := f3
@@ -2210,35 +2470,31 @@
 #11 := (+ f3 #10)
 #14 := (= #11 #13)
 #15 := (not #14)
-#59 := (iff #15 false)
+#40 := (iff #15 false)
 #1 := true
-#54 := (not true)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #15 #54)
-#52 := (iff #14 true)
-#47 := (= #11 #11)
-#50 := (iff #47 true)
-#51 := [rewrite]: #50
-#48 := (iff #14 #47)
-#45 := (= #13 #11)
-#37 := (+ f3 f5)
-#40 := (+ f4 #37)
-#43 := (= #40 #11)
-#44 := [rewrite]: #43
-#41 := (= #13 #40)
-#38 := (= #12 #37)
+#35 := (not true)
+#38 := (iff #35 false)
 #39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#36 := [asserted]: #15
-[mp #36 #60]: false
+#36 := (iff #15 #35)
+#33 := (iff #14 true)
+#24 := (+ f4 f5 f3)
+#21 := (+ f3 f4 f5)
+#27 := (= #21 #24)
+#31 := (iff #27 true)
+#32 := [rewrite]: #31
+#28 := (iff #14 #27)
+#25 := (= #13 #24)
+#26 := [rewrite]: #25
+#22 := (= #11 #21)
+#23 := [rewrite]: #22
+#29 := [monotonicity #23 #26]: #28
+#34 := [trans #29 #32]: #33
+#37 := [monotonicity #34]: #36
+#41 := [trans #37 #39]: #40
+#17 := [asserted]: #15
+[mp #17 #41]: false
+a824144d3163a12246d06059fe9af86abcf7fb10 48 0
 unsat
-8450cf6a350ba6ec26331e50c3fd5d8f999ad9a0 35 0
 #2 := false
 #8 := 3::Int
 #9 := 8::Int
@@ -2247,34 +2503,46 @@
 #7 := 5::Int
 #12 := (< 5::Int #11)
 #13 := (not #12)
-#58 := (iff #13 false)
+#54 := (iff #13 false)
 #1 := true
-#53 := (not true)
-#56 := (iff #53 false)
-#57 := [rewrite]: #56
-#54 := (iff #13 #53)
-#51 := (iff #12 true)
-#46 := (< 5::Int 8::Int)
-#49 := (iff #46 true)
-#50 := [rewrite]: #49
-#47 := (iff #12 #46)
-#44 := (= #11 8::Int)
-#39 := (if true 8::Int 3::Int)
-#42 := (= #39 8::Int)
-#43 := [rewrite]: #42
-#40 := (= #11 #39)
-#37 := (iff #10 true)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#45 := [trans #41 #43]: #44
-#48 := [monotonicity #45]: #47
-#52 := [trans #48 #50]: #51
-#55 := [monotonicity #52]: #54
-#59 := [trans #55 #57]: #58
-#34 := [asserted]: #13
-[mp #34 #59]: false
-unsat
-6afccd7c6734a9f80c327ff8b0bab36d43ee827b 216 0
+#49 := (not true)
+#52 := (iff #49 false)
+#53 := [rewrite]: #52
+#50 := (iff #13 #49)
+#47 := (iff #12 true)
+#32 := (<= 8::Int 5::Int)
+#33 := (not #32)
+#45 := (iff #33 true)
+#40 := (not false)
+#43 := (iff #40 true)
+#44 := [rewrite]: #43
+#41 := (iff #33 #40)
+#38 := (iff #32 false)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#36 := (iff #12 #33)
+#29 := (< 5::Int 8::Int)
+#34 := (iff #29 #33)
+#35 := [rewrite]: #34
+#30 := (iff #12 #29)
+#27 := (= #11 8::Int)
+#22 := (if true 8::Int 3::Int)
+#25 := (= #22 8::Int)
+#26 := [rewrite]: #25
+#23 := (= #11 #22)
+#20 := (iff #10 true)
+#21 := [rewrite]: #20
+#24 := [monotonicity #21]: #23
+#28 := [trans #24 #26]: #27
+#31 := [monotonicity #28]: #30
+#37 := [trans #31 #35]: #36
+#48 := [trans #37 #46]: #47
+#51 := [monotonicity #48]: #50
+#55 := [trans #51 #53]: #54
+#15 := [asserted]: #13
+[mp #15 #55]: false
+8b049c9c7421dfc8c62639e17338cbd84ff8a029 216 0
 #2 := false
 #10 := 0::Real
 decl f4 :: Real
@@ -2491,7 +2759,7 @@
 #240 := [unit-resolution #189 #239]: #155
 [th-lemma arith farkas -1 -1 1 1 #240 #217 #127 #238]: false
 unsat
-c722596cfa285e209992f7087932c1ec15fd226b 42 0
+2130c0a211865d32db21d0798ef35056b373441f 42 0
 #2 := false
 decl f3 :: (-> S1 S2)
 decl f1 :: S1
@@ -2534,7 +2802,7 @@
 #35 := [asserted]: #14
 [mp #35 #61]: false
 unsat
-4d8a8a08b49cb28d987bdc1bcdbb3a144907bf45 49 0
+962a57e270a873c5fccc9aa943c37c86be9989bb 49 0
 #2 := false
 #12 := 1::Int
 decl f3 :: Int
@@ -2584,7 +2852,7 @@
 #36 := [asserted]: #15
 [mp #36 #70]: false
 unsat
-8bd98db330c82b711ec70353229651c63b6517b9 63 0
+2afccb348df223d2e9a13eda20d89b37612cbef1 63 0
 #2 := false
 #14 := 0::Int
 decl f4 :: Int
@@ -2648,7 +2916,7 @@
 #83 := [mp #59 #82]: #70
 [mp #83 #95]: false
 unsat
-e799a1569bcb7c90a4ec458d9136d7c6af5e039d 35 0
+b910449e10d880c681c7024f160f5239d3b9f56e 35 0
 #2 := false
 #9 := 5::Int
 #7 := 2::Int
@@ -2684,7 +2952,7 @@
 #33 := [asserted]: #12
 [mp #33 #57]: false
 unsat
-94bbb14edc8e8a8aac37f1ba3711bbb03b5ccb30 45 0
+31cab35b749e92f0f69d54060a3adf77628fdcc3 45 0
 #2 := false
 #14 := 4::Real
 decl f4 :: Real
@@ -2730,7 +2998,7 @@
 #67 := [mp #43 #66]: #58
 [th-lemma arith farkas 7 3/2 1 #67 #54 #45]: false
 unsat
-4588f343772c15f1f661bad429073998929c6598 59 0
+70d100587a22b3aac8b6223ca69d10fc4232fd77 59 0
 #2 := false
 #19 := (not false)
 decl f4 :: Int
@@ -2790,181 +3058,7 @@
 #41 := [asserted]: #21
 [mp #41 #78]: false
 unsat
-78003574b5d95d4c28641909502b0f435784ad24 104 0
-#2 := false
-decl f1 :: S1
-#3 := f1
-decl f2 :: S1
-#4 := f2
-#8 := 3::Int
-decl f3 :: Int
-#7 := f3
-#49 := (>= f3 3::Int)
-#54 := (if #49 f2 f1)
-#76 := (= f1 #54)
-#61 := (if #49 f1 f2)
-#71 := (= f1 #61)
-#118 := (iff #71 #76)
-#116 := (iff #76 #71)
-#64 := (= #54 #61)
-#11 := (<= 3::Int f3)
-#12 := (if #11 f1 f2)
-#9 := (< f3 3::Int)
-#10 := (if #9 f1 f2)
-#13 := (distinct #10 #12)
-#14 := (not #13)
-#67 := (iff #14 #64)
-#36 := (= #10 #12)
-#65 := (iff #36 #64)
-#62 := (= #12 #61)
-#59 := (iff #11 #49)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#57 := (= #10 #54)
-#47 := (not #49)
-#51 := (if #47 f1 f2)
-#55 := (= #51 #54)
-#56 := [rewrite]: #55
-#52 := (= #10 #51)
-#48 := (iff #9 #47)
-#50 := [rewrite]: #48
-#53 := [monotonicity #50]: #52
-#58 := [trans #53 #56]: #57
-#66 := [monotonicity #58 #63]: #65
-#45 := (iff #14 #36)
-#37 := (not #36)
-#40 := (not #37)
-#43 := (iff #40 #36)
-#44 := [rewrite]: #43
-#41 := (iff #14 #40)
-#38 := (iff #13 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#68 := [trans #46 #66]: #67
-#35 := [asserted]: #14
-#69 := [mp #35 #68]: #64
-#117 := [monotonicity #69]: #116
-#119 := [symm #117]: #118
-#112 := (not #76)
-#5 := (= f1 f2)
-#72 := (= f2 #61)
-#108 := (iff #72 #5)
-#106 := (iff #5 #72)
-#101 := (= #61 f2)
-#104 := (iff #101 #72)
-#105 := [commutativity]: #104
-#102 := (iff #5 #101)
-#99 := [hypothesis]: #76
-#100 := [trans #99 #69]: #71
-#103 := [monotonicity #100]: #102
-#107 := [trans #103 #105]: #106
-#109 := [symm #107]: #108
-#75 := (= f2 #54)
-#87 := (iff #75 #72)
-#88 := [monotonicity #69]: #87
-#89 := (iff #72 #75)
-#90 := [symm #88]: #89
-#83 := (not #75)
-#84 := [hypothesis]: #83
-#77 := (or #47 #75)
-#78 := [def-axiom]: #77
-#85 := [unit-resolution #78 #84]: #47
-#81 := (or #49 #72)
-#82 := [def-axiom]: #81
-#86 := [unit-resolution #82 #85]: #72
-#91 := [mp #86 #90]: #75
-#92 := [unit-resolution #84 #91]: false
-#93 := [lemma #92]: #75
-#96 := [mp #93 #88]: #72
-#94 := (not #72)
-#95 := [hypothesis]: #94
-#97 := [unit-resolution #95 #96]: false
-#98 := [lemma #97]: #72
-#110 := [mp #98 #109]: #5
-#6 := (not #5)
-#34 := [asserted]: #6
-#111 := [unit-resolution #34 #110]: false
-#113 := [lemma #111]: #112
-#73 := (or #49 #76)
-#74 := [def-axiom]: #73
-#114 := [unit-resolution #74 #113]: #49
-#79 := (or #47 #71)
-#80 := [def-axiom]: #79
-#115 := [unit-resolution #80 #114]: #71
-#120 := [mp #115 #119]: #76
-[unit-resolution #113 #120]: false
-unsat
-5d7df2dbd3da6509a839adcbe280f54ee342d7d8 68 0
-#2 := false
-#7 := 0::Int
-decl f3 :: Int
-#8 := f3
-#10 := 2::Int
-#36 := (* 2::Int f3)
-#58 := (= #36 0::Int)
-#59 := (not #58)
-#62 := (= f3 0::Int)
-#63 := (not #62)
-#60 := (= f3 #36)
-#61 := (not #60)
-#56 := (and #61 #63 #59)
-#69 := (not #56)
-#46 := (distinct f3 #36 0::Int)
-#49 := (not #46)
-#12 := (- f3 f3)
-#11 := (* f3 2::Int)
-#13 := (distinct f3 #11 #12)
-#14 := (not #13)
-#50 := (iff #14 #49)
-#47 := (iff #13 #46)
-#44 := (= #12 0::Int)
-#45 := [rewrite]: #44
-#42 := (= #11 #36)
-#43 := [rewrite]: #42
-#48 := [monotonicity #43 #45]: #47
-#51 := [monotonicity #48]: #50
-#35 := [asserted]: #14
-#54 := [mp #35 #51]: #49
-#80 := (or #46 #69)
-#81 := [def-axiom]: #80
-#82 := [unit-resolution #81 #54]: #69
-#67 := (<= #36 0::Int)
-#83 := (not #67)
-#37 := (<= f3 0::Int)
-#38 := (not #37)
-#9 := (< 0::Int f3)
-#39 := (iff #9 #38)
-#40 := [rewrite]: #39
-#34 := [asserted]: #9
-#41 := [mp #34 #40]: #38
-#84 := (or #83 #37)
-#85 := [th-lemma arith assign-bounds 2]: #84
-#86 := [unit-resolution #85 #41]: #83
-#87 := (or #59 #67)
-#88 := [th-lemma arith triangle-eq]: #87
-#89 := [unit-resolution #88 #86]: #59
-#57 := -1::Int
-#53 := (* -1::Int #36)
-#55 := (+ f3 #53)
-#65 := (>= #55 0::Int)
-#90 := (not #65)
-#91 := (or #90 #37)
-#92 := [th-lemma arith assign-bounds 1]: #91
-#93 := [unit-resolution #92 #41]: #90
-#94 := (or #61 #65)
-#95 := [th-lemma arith triangle-eq]: #94
-#96 := [unit-resolution #95 #93]: #61
-#100 := (or #56 #60 #58)
-#97 := (or #63 #37)
-#98 := [th-lemma arith triangle-eq]: #97
-#99 := [unit-resolution #98 #41]: #63
-#76 := (or #56 #60 #62 #58)
-#77 := [def-axiom]: #76
-#101 := [unit-resolution #77 #99]: #100
-[unit-resolution #101 #96 #89 #82]: false
-unsat
-adcd90d27a640d65adf92b737298d76a88dcb2d7 439 0
+b1114e42b528a3f3368f02584a60d74e21ce36f3 439 0
 #2 := false
 decl f4 :: Int
 #8 := f4
@@ -3404,7 +3498,7 @@
 #497 := [unit-resolution #456 #496 #490]: #20
 [unit-resolution #497 #501]: false
 unsat
-c461f417e01961729e64bc338da8fe68ac7ad70e 2215 0
+85045dafb5b814ffc5cbcd5ff6b6686db0c031a5 2215 0
 #2 := false
 decl f12 :: Int
 #52 := f12
@@ -5620,7 +5714,7 @@
 #2264 := [unit-resolution #1544 #2263 #2262]: #65
 [unit-resolution #658 #2264 #2259]: false
 unsat
-ebb9b9eba458556c3c96e64ab347c2dd794296aa 52 0
+c69d5d4255e8606842bc591eb455581408ecf173 52 0
 #2 := false
 #11 := 1::Real
 decl f3 :: Real
@@ -5673,7 +5767,7 @@
 #37 := [asserted]: #16
 [mp #37 #73]: false
 unsat
-7284d3250d19a32079c86839237365aa695997b1 341 0
+831d28afa9cf941930d32bdaa862b9ddf2a718a5 341 0
 #2 := false
 #24 := 0::Int
 decl f3 :: Int
@@ -6015,7 +6109,7 @@
 #652 := [unit-resolution #646 #666]: #755
 [unit-resolution #652 #650 #649]: false
 unsat
-cf5adef89e3e53946521876e9bc33cdee144fbaf 343 0
+939e3758e2e10d03fb65ec30390e9e486d20dc8e 343 0
 #2 := false
 #23 := 0::Int
 decl f3 :: Int
@@ -6359,7 +6453,7 @@
 #635 := [unit-resolution #634 #645]: #750
 [unit-resolution #635 #630 #629]: false
 unsat
-cfa8a4e8b0964986b89eaf37e6038032e9b8b0d6 101 0
+74ff14110bbb0018e1d9b2bb1ca338d7d58b9ba7 101 0
 #2 := false
 #8 := 0::Real
 decl f3 :: Real
@@ -6461,7 +6555,7 @@
 #122 := [th-lemma arith triangle-eq]: #121
 [unit-resolution #122 #118 #111 #45]: false
 unsat
-0e941ae848fda6bf9dfac1fd97560c61c65c1f6a 916 0
+5d74029d261367c40f523c70d0425e39aa05656a 916 0
 #2 := false
 #22 := 1::Int
 decl f3 :: (-> S2 Int Int)
@@ -7378,7 +7472,7 @@
 #1665 := [unit-resolution #1640 #1664 #1654 #1663]: #1266
 [unit-resolution #1468 #1665 #1662]: false
 unsat
-c04d38458726eb1b2cafd52bd3881d6f8160666f 24 0
+708c54fa92a38587409efdd16c74ec37e20e2b24 24 0
 #2 := false
 #7 := (exists (vars (?v0 Int)) false)
 #8 := (not #7)
@@ -7403,7 +7497,7 @@
 #30 := [asserted]: #9
 [mp #30 #46]: false
 unsat
-b7e68d81e2b1e168216a793b1d4c3fb61e54a4fa 24 0
+fc6d81b59098b37bdb85891cea739cff88a4cdb6 24 0
 #2 := false
 #7 := (exists (vars (?v0 Real)) false)
 #8 := (not #7)
@@ -7428,13 +7522,13 @@
 #30 := [asserted]: #9
 [mp #30 #46]: false
 unsat
-091ba9e3776453f72e577cca020359bfc2bbb1a8 1 0
+0af127c441080d9be87ef936c6f900945a11800e 1 0
 unsat
-6b48d925e625c5baa918d61afc02b3d6fa4e46f8 1 0
+39442bd44c6b81734dce64f48a2e8cfe6d7ef53b 1 0
 unsat
-7b03d36f70c1cb511c7ddbbd8c6bb360b0e823ac 1 0
+92a9cdc5e3be1caf16415f275672ba72e11bb4d1 1 0
 unsat
-770827669678f8e68bf300baf101a56cec1c8d6b 54 0
+75d80d6072d013ed3e949f6837066b1429f3d619 54 0
 #2 := false
 #11 := 1::Int
 #8 := 0::Int
@@ -7489,7 +7583,7 @@
 #136 := [trans #134 #72]: #135
 [mp #136 #138]: false
 unsat
-2d33526ae6f55fa8bf28af8a491289a10023ebc3 82 0
+92fd6555d299024a17bfc17027870ad0919243ff 82 0
 #2 := false
 #8 := (:var 0 Int)
 #10 := 0::Int
@@ -7572,7 +7666,7 @@
 #37 := [asserted]: #17
 [mp #37 #103]: false
 unsat
-faa0ca9568a00467876bf060199376e2ca905359 78 0
+46de1bc1af5e350ddd1b0ad779cbf855c1a471a1 78 0
 #2 := false
 #8 := (:var 0 Int)
 #10 := 2::Int
@@ -7651,7 +7745,7 @@
 #39 := [asserted]: #18
 [mp #39 #99]: false
 unsat
-05a0d5d1100f50948c093c944115de9816b9e0d9 56 0
+b862ad22dd9ecdb24d22ad71d0b47057aeade516 56 0
 #2 := false
 #12 := (:var 0 Int)
 #7 := 2::Int
@@ -7708,7 +7802,7 @@
 #38 := [asserted]: #17
 [mp #38 #78]: false
 unsat
-cb31e6f6a1ecdcd5cb5be0830fe96dcd6a225db2 89 0
+d22de288e1e6fa553e6f3d0d9c4c72eaac8ba9f7 89 0
 #2 := false
 #7 := 2::Int
 decl ?v0!1 :: Int
@@ -7798,7 +7892,7 @@
 #174 := [unit-resolution #172 #84]: #173
 [unit-resolution #174 #111 #110]: false
 unsat
-14c5d2b27aee290cf4e7c2c280797baa69660461 89 0
+bbb79358278efd2f50b5374712065c2bd5509427 89 0
 #2 := false
 #7 := 0::Int
 decl ?v0!0 :: Int
@@ -7888,7 +7982,8 @@
 #178 := [unit-resolution #165 #97]: #177
 [unit-resolution #178 #176 #173]: false
 unsat
-74ffecf155cc435ac1a2bcfe873a84647e4ce6b1 83 2
+f8d6fcfb2c146004937d3e2687f80fb7b9e71e08 84 0
+WARNING: failed to find a pattern for quantifier (quantifier id: k!10)
 #2 := false
 #8 := 0::Int
 #7 := (:var 0 Int)
@@ -7972,9 +8067,8 @@
 #63 := [mp~ #61 #70]: #56
 [unit-resolution #63 #529]: false
 unsat
+98ea18bb7ed4825aeaf82772b27a9684cb2bed9f 165 0
 WARNING: failed to find a pattern for quantifier (quantifier id: k!10)
-
-8602f0cbb8a6b885b19d4424fa42859ac2937970 164 2
 #2 := false
 #7 := 0::Int
 #8 := (:var 0 Int)
@@ -8139,9 +8233,7 @@
 #563 := [unit-resolution #136 #574]: #62
 [unit-resolution #563 #570]: false
 unsat
-WARNING: failed to find a pattern for quantifier (quantifier id: k!10)
-
-2f9041ab2507988941f04b373596319a25dbff04 63 0
+41a9dc7919d6df65f060b1b899094fbf1d9ad6ba 63 0
 #2 := false
 #15 := 1::Int
 #12 := (:var 1 Int)
@@ -8205,7 +8297,7 @@
 #40 := [asserted]: #19
 [mp #40 #87]: false
 unsat
-e7e4f914c64da4bb9f5ff1d016939e644d6e9497 101 0
+6912c1751294e15845c5073be78e1e9aebf84cf9 101 0
 #2 := false
 #7 := 0::Int
 decl ?v1!1 :: Int
@@ -8307,7 +8399,7 @@
 #125 := [and-elim #108]: #88
 [th-lemma arith farkas 1 1 1 #125 #124 #126]: false
 unsat
-68c837c3dabb51cfb3fa72be140feeef8d58aa35 99 0
+602658d510491230a33b4d0db4cf9ef889fff5d2 99 0
 #2 := false
 #39 := -1::Int
 decl ?v1!1 :: Int
@@ -8407,7 +8499,7 @@
 #180 := [unit-resolution #179 #118]: #107
 [unit-resolution #180 #120]: false
 unsat
-111e0e11b10e3dfb46a207e5da98c171ac0c63ad 143 0
+985c93e0a5f1ce8a2da959ba74511df9451610ad 143 0
 #2 := false
 #10 := 0::Int
 #8 := (:var 0 Int)
@@ -8551,7 +8643,8 @@
 #160 := [mp #128 #159]: #155
 [mp #160 #183]: false
 unsat
-f97f94cdf9ea1da48e107362c172b39f4b82d4a8 66 2
+63d20accf8ad42641c987f5442607c5721cb43fb 67 0
+ERROR: line 11 column 83: invalid pattern.
 #2 := false
 decl f3 :: Int
 #8 := f3
@@ -8618,9 +8711,7 @@
 #37 := [asserted]: #16
 [mp #37 #86]: false
 unsat
-ERROR: line 11 column 83: invalid pattern.
-
-1953a39a3cc38daf2fde4846aa1d5cbc2ff95785 54 0
+1cfe9564946e052422f3734e258f62595f0a9412 54 0
 #2 := false
 #10 := 1::Int
 decl ?v1!0 :: Int
@@ -8675,9 +8766,9 @@
 #139 := [unit-resolution #138 #78]: #62
 [unit-resolution #139 #79]: false
 unsat
-8f616b17d0807409dc26bfdf9593c5fcd06fb7e7 1 0
+c22c22b3ba012feae782c7385953ed357b59b45c 1 0
 unsat
-3eb9cf11ee8774c9212c37c265e7552f3b8f24a9 75 0
+341447bcaf93988f0b7d6678a14d4c50e4db9b7f 75 0
 #2 := false
 #9 := 1::Int
 decl f5 :: Int
@@ -8753,7 +8844,7 @@
 #40 := [asserted]: #19
 [mp #40 #94]: false
 unsat
-741a564e40e4b6610d1d47bdab19a223e004482a 62 0
+d5d80b9320d4c205de1be4e0283a62bbca18eb64 62 0
 #2 := false
 decl f4 :: Real
 #9 := f4
@@ -8816,7 +8907,7 @@
 #40 := [asserted]: #19
 [mp #40 #82]: false
 unsat
-06d1bd5308956fb019ef1c09bf97c6326d872fd6 141 0
+e45dae900e2e0eeb849f9514267495ab98a945b1 141 0
 #2 := false
 decl f6 :: Int
 #12 := f6
@@ -8958,7 +9049,7 @@
 #53 := [asserted]: #32
 [mp #53 #158]: false
 unsat
-d578ad7e6589d737d5b50614f48a1b12ef69c636 37 0
+7e345b8256329432a24c0098659af0d0da3f8b9c 37 0
 #2 := false
 #10 := 0::Int
 decl f3 :: Int
@@ -8996,7 +9087,7 @@
 #53 := [not-or-elim #52]: #11
 [th-lemma arith farkas 1 1 1 #53 #57 #55]: false
 unsat
-33e2bdae82fc59f778e5db15565f1c50c2c2fee4 225 0
+173dcd56c4eb3955c1a0afe5894b9f20d665d5a4 225 0
 #2 := false
 #24 := 0::Int
 decl f5 :: (-> S4 S3 Int)
@@ -9222,7 +9313,7 @@
 #527 := [unit-resolution #526 #425]: #550
 [th-lemma arith gcd-test -1/2 -1/2 -1/2 -1/2 #529 #527 #515 #524]: false
 unsat
-d558048bb276c46209081d2fdff3fd787837bb57 55 0
+10b9b3d3225e279927703a7138fa37357bc1a2b4 55 0
 #2 := false
 #74 := 4::Int
 decl f3 :: (-> S2 S3 Int)
@@ -9278,7 +9369,7 @@
 #301 := [unit-resolution #216 #88]: #76
 [unit-resolution #301 #89]: false
 unsat
-8932fefe7cf3366bddd35470f58d0b1fde78bc6e 270 0
+83084ab04d727810863c900d9684257895074106 270 0
 #2 := false
 #7 := 0::Int
 decl f3 :: (-> S2 S3 Int)
@@ -9549,7 +9640,7 @@
 #90 := [mp #57 #89]: #77
 [th-lemma arith farkas -1 -1 1 #90 #519 #518]: false
 unsat
-68d347fdf181bb23634330d38e10cbe4fff1953a 269 0
+0c91cb6bf3bcb8a10a4871e9ec475b571f03d883 269 0
 #2 := false
 #7 := 0::Int
 decl f3 :: (-> S2 S3 Int)
@@ -9819,382 +9910,7 @@
 #580 := [unit-resolution #596 #594]: #654
 [th-lemma arith farkas 1 -1 -1 1 #600 #119 #580 #609]: false
 unsat
-9bd1c4986d286e4e0abfd70c7740b5ad11395fe6 374 0
-#2 := false
-decl f5 :: (-> S4 S3 Int)
-decl f3 :: (-> S2 Int S3)
-decl f7 :: S3
-#9 := f7
-decl f6 :: S4
-#8 := f6
-#10 := (f5 f6 f7)
-#11 := 1::Int
-#60 := (+ 1::Int #10)
-decl f4 :: S2
-#7 := f4
-#63 := (f3 f4 #60)
-#622 := (f5 f6 #63)
-#14 := 2::Int
-#66 := (* 2::Int #10)
-#16 := 3::Int
-#72 := (+ 3::Int #66)
-#77 := (f3 f4 #72)
-#588 := (f5 f6 #77)
-#399 := (= #588 #622)
-#387 := (= #622 #588)
-#217 := (= #63 #77)
-#28 := 0::Int
-#82 := (f3 f4 0::Int)
-#304 := (= #77 #82)
-#295 := (not #304)
-#573 := (= #588 0::Int)
-#566 := (f5 f6 #82)
-#563 := (= #566 0::Int)
-#29 := (:var 0 Int)
-#31 := (f3 f4 #29)
-#639 := (pattern #31)
-#32 := (f5 f6 #31)
-#33 := (= #32 #29)
-#103 := (>= #29 0::Int)
-#104 := (not #103)
-#107 := (or #104 #33)
-#640 := (forall (vars (?v0 Int)) (:pat #639) #107)
-#110 := (forall (vars (?v0 Int)) #107)
-#643 := (iff #110 #640)
-#641 := (iff #107 #107)
-#642 := [refl]: #641
-#644 := [quant-intro #642]: #643
-#147 := (~ #110 #110)
-#146 := (~ #107 #107)
-#143 := [refl]: #146
-#148 := [nnf-pos #143]: #147
-#30 := (<= 0::Int #29)
-#34 := (implies #30 #33)
-#35 := (forall (vars (?v0 Int)) #34)
-#113 := (iff #35 #110)
-#94 := (not #30)
-#95 := (or #94 #33)
-#98 := (forall (vars (?v0 Int)) #95)
-#111 := (iff #98 #110)
-#108 := (iff #95 #107)
-#105 := (iff #94 #104)
-#101 := (iff #30 #103)
-#102 := [rewrite]: #101
-#106 := [monotonicity #102]: #105
-#109 := [monotonicity #106]: #108
-#112 := [quant-intro #109]: #111
-#99 := (iff #35 #98)
-#96 := (iff #34 #95)
-#97 := [rewrite]: #96
-#100 := [quant-intro #97]: #99
-#114 := [trans #100 #112]: #113
-#92 := [asserted]: #35
-#115 := [mp #92 #114]: #110
-#144 := [mp~ #115 #148]: #110
-#645 := [mp #144 #644]: #640
-#615 := (not #640)
-#537 := (or #615 #563)
-#472 := (>= 0::Int 0::Int)
-#473 := (not #472)
-#567 := (or #473 #563)
-#538 := (or #615 #567)
-#541 := (iff #538 #537)
-#543 := (iff #537 #537)
-#539 := [rewrite]: #543
-#546 := (iff #567 #563)
-#560 := (or false #563)
-#551 := (iff #560 #563)
-#552 := [rewrite]: #551
-#549 := (iff #567 #560)
-#559 := (iff #473 false)
-#1 := true
-#548 := (not true)
-#557 := (iff #548 false)
-#558 := [rewrite]: #557
-#545 := (iff #473 #548)
-#554 := (iff #472 true)
-#556 := [rewrite]: #554
-#547 := [monotonicity #556]: #545
-#555 := [trans #547 #558]: #559
-#550 := [monotonicity #555]: #549
-#553 := [trans #550 #552]: #546
-#542 := [monotonicity #553]: #541
-#544 := [trans #542 #539]: #541
-#540 := [quant-inst #28]: #538
-#530 := [mp #540 #544]: #537
-#443 := [unit-resolution #530 #645]: #563
-#447 := (= #588 #566)
-#444 := [hypothesis]: #304
-#432 := [monotonicity #444]: #447
-#448 := [trans #432 #443]: #573
-#439 := (not #573)
-#470 := (<= #588 0::Int)
-#430 := (not #470)
-#628 := -1::Int
-#265 := (>= #10 -1::Int)
-#519 := (>= #10 0::Int)
-#480 := (= #10 0::Int)
-#629 := (f3 f4 #10)
-#520 := (f5 f6 #629)
-#521 := (= #520 0::Int)
-#374 := (not #519)
-#485 := [hypothesis]: #374
-#522 := (or #519 #521)
-#37 := (= #32 0::Int)
-#133 := (or #103 #37)
-#646 := (forall (vars (?v0 Int)) (:pat #639) #133)
-#136 := (forall (vars (?v0 Int)) #133)
-#649 := (iff #136 #646)
-#647 := (iff #133 #133)
-#648 := [refl]: #647
-#650 := [quant-intro #648]: #649
-#149 := (~ #136 #136)
-#157 := (~ #133 #133)
-#158 := [refl]: #157
-#150 := [nnf-pos #158]: #149
-#36 := (< #29 0::Int)
-#38 := (implies #36 #37)
-#39 := (forall (vars (?v0 Int)) #38)
-#139 := (iff #39 #136)
-#117 := (not #36)
-#118 := (or #117 #37)
-#121 := (forall (vars (?v0 Int)) #118)
-#137 := (iff #121 #136)
-#134 := (iff #118 #133)
-#131 := (iff #117 #103)
-#126 := (not #104)
-#129 := (iff #126 #103)
-#130 := [rewrite]: #129
-#127 := (iff #117 #126)
-#124 := (iff #36 #104)
-#125 := [rewrite]: #124
-#128 := [monotonicity #125]: #127
-#132 := [trans #128 #130]: #131
-#135 := [monotonicity #132]: #134
-#138 := [quant-intro #135]: #137
-#122 := (iff #39 #121)
-#119 := (iff #38 #118)
-#120 := [rewrite]: #119
-#123 := [quant-intro #120]: #122
-#140 := [trans #123 #138]: #139
-#116 := [asserted]: #39
-#141 := [mp #116 #140]: #136
-#159 := [mp~ #141 #150]: #136
-#651 := [mp #159 #650]: #646
-#599 := (not #646)
-#525 := (or #599 #519 #521)
-#526 := (or #599 #522)
-#528 := (iff #526 #525)
-#518 := [rewrite]: #528
-#527 := [quant-inst #10]: #526
-#529 := [mp #527 #518]: #525
-#486 := [unit-resolution #529 #651]: #522
-#487 := [unit-resolution #486 #485]: #521
-#490 := (= #10 #520)
-#488 := (= f7 #629)
-#630 := (= #629 f7)
-#23 := (:var 0 S3)
-#24 := (f5 f6 #23)
-#632 := (pattern #24)
-#25 := (f3 f4 #24)
-#26 := (= #25 #23)
-#633 := (forall (vars (?v0 S3)) (:pat #632) #26)
-#27 := (forall (vars (?v0 S3)) #26)
-#636 := (iff #27 #633)
-#634 := (iff #26 #26)
-#635 := [refl]: #634
-#637 := [quant-intro #635]: #636
-#155 := (~ #27 #27)
-#153 := (~ #26 #26)
-#154 := [refl]: #153
-#156 := [nnf-pos #154]: #155
-#91 := [asserted]: #27
-#145 := [mp~ #91 #156]: #27
-#638 := [mp #145 #637]: #633
-#621 := (not #633)
-#280 := (or #621 #630)
-#285 := [quant-inst #9]: #280
-#492 := [unit-resolution #285 #638]: #630
-#489 := [symm #492]: #488
-#493 := [monotonicity #489]: #490
-#494 := [trans #493 #487]: #480
-#495 := (not #480)
-#491 := (or #495 #519)
-#496 := [th-lemma arith triangle-eq]: #491
-#476 := [unit-resolution #496 #485 #494]: false
-#422 := [lemma #476]: #519
-#418 := (or #374 #265)
-#449 := [th-lemma arith farkas 1 1]: #418
-#474 := [unit-resolution #449 #422]: #265
-#434 := -3::Int
-#435 := (* -1::Int #588)
-#577 := (+ #66 #435)
-#572 := (<= #577 -3::Int)
-#578 := (= #577 -3::Int)
-#270 := (not #265)
-#579 := (or #270 #578)
-#575 := (or #615 #270 #578)
-#589 := (= #588 #72)
-#598 := (>= #72 0::Int)
-#587 := (not #598)
-#584 := (or #587 #589)
-#581 := (or #615 #584)
-#568 := (iff #581 #575)
-#576 := (or #615 #579)
-#414 := (iff #576 #575)
-#415 := [rewrite]: #414
-#583 := (iff #581 #576)
-#580 := (iff #584 #579)
-#592 := (iff #589 #578)
-#433 := [rewrite]: #592
-#591 := (iff #587 #270)
-#585 := (iff #598 #265)
-#590 := [rewrite]: #585
-#586 := [monotonicity #590]: #591
-#574 := [monotonicity #586 #433]: #580
-#412 := [monotonicity #574]: #583
-#569 := [trans #412 #415]: #568
-#582 := [quant-inst #72]: #581
-#571 := [mp #582 #569]: #575
-#511 := [unit-resolution #571 #645]: #579
-#454 := [unit-resolution #511 #474]: #578
-#513 := (not #578)
-#514 := (or #513 #572)
-#509 := [th-lemma arith triangle-eq]: #514
-#475 := [unit-resolution #509 #454]: #572
-#431 := (not #572)
-#436 := (or #430 #431 #270)
-#437 := [th-lemma arith assign-bounds 1 2]: #436
-#438 := [unit-resolution #437 #475 #474]: #430
-#440 := (or #439 #470)
-#441 := [th-lemma arith triangle-eq]: #440
-#442 := [unit-resolution #441 #438]: #439
-#409 := [unit-resolution #442 #448]: false
-#410 := [lemma #409]: #295
-#218 := (= #63 #82)
-#303 := (not #218)
-#224 := (= #622 0::Int)
-#401 := (= #622 #566)
-#429 := [hypothesis]: #218
-#402 := [monotonicity #429]: #401
-#404 := [trans #402 #443]: #224
-#426 := (not #224)
-#597 := (<= #622 0::Int)
-#420 := (not #597)
-#611 := (* -1::Int #622)
-#612 := (+ #10 #611)
-#330 := (<= #612 -1::Int)
-#610 := (= #612 -1::Int)
-#608 := (or #270 #610)
-#617 := (or #615 #270 #610)
-#281 := (= #622 #60)
-#625 := (>= #60 0::Int)
-#631 := (not #625)
-#623 := (or #631 #281)
-#256 := (or #615 #623)
-#313 := (iff #256 #617)
-#618 := (or #615 #608)
-#605 := (iff #618 #617)
-#606 := [rewrite]: #605
-#616 := (iff #256 #618)
-#614 := (iff #623 #608)
-#609 := (iff #281 #610)
-#613 := [rewrite]: #609
-#271 := (iff #631 #270)
-#607 := (iff #625 #265)
-#269 := [rewrite]: #607
-#272 := [monotonicity #269]: #271
-#251 := [monotonicity #272 #613]: #614
-#619 := [monotonicity #251]: #616
-#328 := [trans #619 #606]: #313
-#257 := [quant-inst #60]: #256
-#329 := [mp #257 #328]: #617
-#501 := [unit-resolution #329 #645]: #608
-#445 := [unit-resolution #501 #474]: #610
-#498 := (not #610)
-#446 := (or #498 #330)
-#417 := [th-lemma arith triangle-eq]: #446
-#419 := [unit-resolution #417 #445]: #330
-#421 := (not #330)
-#423 := (or #420 #421 #374)
-#424 := [th-lemma arith assign-bounds 1 -1]: #423
-#425 := [unit-resolution #424 #419 #422]: #420
-#427 := (or #426 #597)
-#428 := [th-lemma arith triangle-eq]: #427
-#411 := [unit-resolution #428 #425]: #426
-#405 := [unit-resolution #411 #404]: false
-#406 := [lemma #405]: #303
-#407 := (or #217 #218 #304)
-#302 := (not #217)
-#306 := (and #302 #303 #295)
-#307 := (not #306)
-#85 := (distinct #63 #77 #82)
-#88 := (not #85)
-#19 := (- #10 #10)
-#20 := (f3 f4 #19)
-#15 := (* #10 2::Int)
-#17 := (+ #15 3::Int)
-#18 := (f3 f4 #17)
-#12 := (+ #10 1::Int)
-#13 := (f3 f4 #12)
-#21 := (distinct #13 #18 #20)
-#22 := (not #21)
-#89 := (iff #22 #88)
-#86 := (iff #21 #85)
-#83 := (= #20 #82)
-#80 := (= #19 0::Int)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#78 := (= #18 #77)
-#75 := (= #17 #72)
-#69 := (+ #66 3::Int)
-#73 := (= #69 #72)
-#74 := [rewrite]: #73
-#70 := (= #17 #69)
-#67 := (= #15 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#76 := [trans #71 #74]: #75
-#79 := [monotonicity #76]: #78
-#64 := (= #13 #63)
-#61 := (= #12 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#87 := [monotonicity #65 #79 #84]: #86
-#90 := [monotonicity #87]: #89
-#59 := [asserted]: #22
-#93 := [mp #59 #90]: #88
-#294 := (or #85 #307)
-#627 := [def-axiom]: #294
-#248 := [unit-resolution #627 #93]: #307
-#282 := (or #306 #217 #218 #304)
-#413 := [def-axiom]: #282
-#403 := [unit-resolution #413 #248]: #407
-#408 := [unit-resolution #403 #406 #410]: #217
-#390 := [monotonicity #408]: #387
-#394 := [symm #390]: #399
-#524 := (+ #588 #611)
-#507 := (<= #524 0::Int)
-#500 := (not #507)
-#506 := (or #270 #500)
-#510 := [hypothesis]: #265
-#512 := [unit-resolution #511 #510]: #578
-#515 := [unit-resolution #509 #512]: #572
-#331 := (>= #612 -1::Int)
-#497 := [unit-resolution #501 #510]: #610
-#499 := (or #498 #331)
-#502 := [th-lemma arith triangle-eq]: #499
-#503 := [unit-resolution #502 #497]: #331
-#504 := [hypothesis]: #507
-#505 := [th-lemma arith farkas -1 1 -1 1 #504 #503 #515 #510]: false
-#479 := [lemma #505]: #506
-#396 := [unit-resolution #479 #474]: #500
-#397 := (not #399)
-#395 := (or #397 #507)
-#398 := [th-lemma arith triangle-eq]: #395
-[unit-resolution #398 #396 #394]: false
-unsat
-b95d641e1affb872027fbe667ba2ad4475fc0039 147 0
+883f0bd08ff2fcce6dafab7dcff61923fd895e14 147 0
 #2 := false
 #10 := 0::Int
 decl f7 :: Int
@@ -10342,7 +10058,8 @@
 #338 := [unit-resolution #616 #618]: #641
 [th-lemma arith farkas 1 1 1 #338 #262 #629]: false
 unsat
-05afc7fcdcf1433af94de36ed38785db528a50f6 430 2
+0f3d54ed51fa30b450e38c23afe57212bbebc6dd 431 0
+WARNING: For problems containing quantifiers, the model finding capabilities of Z3 work better when the formula does not contain nested quantifiers. You can use PULL_NESTED_QUANTIFIERS=true to eliminate nested quantifiers.
 #2 := false
 #446 := -1::Int
 decl f4 :: (-> S3 S2 Int)
@@ -10773,9 +10490,7 @@
 #150 := [not-or-elim #147]: #149
 [th-lemma arith farkas -4 1 1 #150 #622 #575]: false
 unsat
-WARNING: For problems containing quantifiers, the model finding capabilities of Z3 work better when the formula does not contain nested quantifiers. You can use PULL_NESTED_QUANTIFIERS=true to eliminate nested quantifiers.
-
-8bbf55cbd9308f9edfe0203d9100aace31ed1b8b 58 0
+fd4d98b0eed13792693ae0a8136c6836082ab811 58 0
 #2 := false
 decl f8 :: S2
 #18 := f8
@@ -10834,7 +10549,7 @@
 #55 := [not-or-elim #54]: #53
 [unit-resolution #55 #214]: false
 unsat
-995e3c8bb1366c3ddfd69a100721f0bf4e72ec56 106 0
+54ed94e7408ff82930a92d4010c74312402c8de2 106 0
 #2 := false
 decl f11 :: (-> S9 S5 S3)
 decl f16 :: S5
@@ -10941,7 +10656,7 @@
 #80 := [not-or-elim #77]: #79
 [unit-resolution #80 #217]: false
 unsat
-29cfa5c687980cc2eca5b8b3a0340a9f66137754 113 0
+a973ebe0ddefe8f57f45047d94130cd1cb03b18f 113 0
 #2 := false
 decl f3 :: (-> S2 S3 S4)
 decl f8 :: S3
@@ -11055,7 +10770,7 @@
 #87 := [not-or-elim #84]: #86
 [unit-resolution #87 #529]: false
 unsat
-10c4eb4ff6b9f0c880cfc3af0cd433a1ff110114 74 0
+bb72677b6383b269d7de6046448ed8d87d1bc4ef 74 0
 #2 := false
 decl f1 :: S1
 #3 := f1
@@ -11130,121 +10845,114 @@
 #80 := [mp #69 #79]: #77
 [mp #80 #82]: false
 unsat
-8821f61b34007b1fd5b5c2b393b7f6276c9650d7 113 0
+53946fb2c677a4b873691332b928354017b0ad0e 106 0
 #2 := false
-decl f7 :: (-> S5 Int S3)
-decl f9 :: (-> Int Int)
-decl f10 :: Int
-#20 := f10
-#21 := (f9 f10)
-#22 := (f9 #21)
-decl f8 :: S5
-#19 := f8
-#23 := (f7 f8 #22)
+decl f7 :: S3
+#19 := f7
 decl f5 :: (-> S4 S3 S3)
 decl f6 :: S4
 #14 := f6
-#24 := (f5 f6 #23)
-#25 := (= #24 #23)
-#78 := (not #25)
+#20 := (f5 f6 f7)
+#21 := (= #20 f7)
+#74 := (not #21)
 decl f1 :: S1
 #3 := f1
 decl f3 :: (-> S2 S1 S1)
 decl f4 :: S2
 #7 := f4
-#26 := (f3 f4 f1)
-#27 := (= #26 f1)
-#79 := (not #27)
-#562 := [hypothesis]: #79
+#22 := (f3 f4 f1)
+#23 := (= #22 f1)
+#75 := (not #23)
+#558 := [hypothesis]: #75
 #8 := (:var 0 S1)
 #9 := (f3 f4 #8)
-#566 := (pattern #9)
+#562 := (pattern #9)
 #11 := (= #8 f1)
 #10 := (= #9 f1)
 #12 := (iff #10 #11)
-#567 := (forall (vars (?v0 S1)) (:pat #566) #12)
+#563 := (forall (vars (?v0 S1)) (:pat #562) #12)
 #13 := (forall (vars (?v0 S1)) #12)
-#570 := (iff #13 #567)
-#568 := (iff #12 #12)
-#569 := [refl]: #568
-#571 := [quant-intro #569]: #570
-#74 := (~ #13 #13)
-#72 := (~ #12 #12)
-#73 := [refl]: #72
-#75 := [nnf-pos #73]: #74
-#51 := [asserted]: #13
-#63 := [mp~ #51 #75]: #13
-#572 := [mp #63 #571]: #567
-#243 := (not #567)
-#222 := (or #243 #27)
-#150 := (= f1 f1)
-#151 := (iff #27 #150)
-#558 := (or #243 #151)
-#216 := (iff #558 #222)
-#554 := (iff #222 #222)
-#227 := [rewrite]: #554
-#242 := (iff #151 #27)
+#566 := (iff #13 #563)
+#564 := (iff #12 #12)
+#565 := [refl]: #564
+#567 := [quant-intro #565]: #566
+#70 := (~ #13 #13)
+#68 := (~ #12 #12)
+#69 := [refl]: #68
+#71 := [nnf-pos #69]: #70
+#47 := [asserted]: #13
+#59 := [mp~ #47 #71]: #13
+#568 := [mp #59 #567]: #563
+#239 := (not #563)
+#218 := (or #239 #23)
+#146 := (= f1 f1)
+#147 := (iff #23 #146)
+#554 := (or #239 #147)
+#212 := (iff #554 #218)
+#550 := (iff #218 #218)
+#223 := [rewrite]: #550
+#238 := (iff #147 #23)
 #1 := true
-#28 := (iff #27 true)
-#54 := (iff #28 #27)
-#55 := [rewrite]: #54
-#240 := (iff #151 #28)
-#236 := (iff #150 true)
-#229 := [rewrite]: #236
-#241 := [monotonicity #229]: #240
-#239 := [trans #241 #55]: #242
-#347 := [monotonicity #239]: #216
-#228 := [trans #347 #227]: #216
-#560 := [quant-inst #3]: #558
-#561 := [mp #560 #228]: #222
-#563 := [unit-resolution #561 #572 #562]: false
-#564 := [lemma #563]: #27
-#68 := (or #78 #79)
-#56 := (and #25 #27)
-#59 := (not #56)
-#85 := (iff #59 #68)
-#69 := (not #68)
-#80 := (not #69)
-#83 := (iff #80 #68)
-#84 := [rewrite]: #83
-#81 := (iff #59 #80)
-#70 := (iff #56 #69)
-#71 := [rewrite]: #70
-#82 := [monotonicity #71]: #81
-#86 := [trans #82 #84]: #85
-#29 := (and #25 #28)
-#30 := (not #29)
-#60 := (iff #30 #59)
-#57 := (iff #29 #56)
-#58 := [monotonicity #55]: #57
-#61 := [monotonicity #58]: #60
-#53 := [asserted]: #30
-#64 := [mp #53 #61]: #59
-#87 := [mp #64 #86]: #68
-#559 := [unit-resolution #87 #564]: #78
+#24 := (iff #23 true)
+#50 := (iff #24 #23)
+#51 := [rewrite]: #50
+#236 := (iff #147 #24)
+#232 := (iff #146 true)
+#225 := [rewrite]: #232
+#237 := [monotonicity #225]: #236
+#235 := [trans #237 #51]: #238
+#343 := [monotonicity #235]: #212
+#224 := [trans #343 #223]: #212
+#556 := [quant-inst #3]: #554
+#557 := [mp #556 #224]: #218
+#559 := [unit-resolution #557 #568 #558]: false
+#560 := [lemma #559]: #23
+#64 := (or #74 #75)
+#52 := (and #21 #23)
+#55 := (not #52)
+#81 := (iff #55 #64)
+#65 := (not #64)
+#76 := (not #65)
+#79 := (iff #76 #64)
+#80 := [rewrite]: #79
+#77 := (iff #55 #76)
+#66 := (iff #52 #65)
+#67 := [rewrite]: #66
+#78 := [monotonicity #67]: #77
+#82 := [trans #78 #80]: #81
+#25 := (and #21 #24)
+#26 := (not #25)
+#56 := (iff #26 #55)
+#53 := (iff #25 #52)
+#54 := [monotonicity #51]: #53
+#57 := [monotonicity #54]: #56
+#49 := [asserted]: #26
+#60 := [mp #49 #57]: #55
+#83 := [mp #60 #82]: #64
+#555 := [unit-resolution #83 #560]: #74
 #15 := (:var 0 S3)
 #16 := (f5 f6 #15)
-#573 := (pattern #16)
+#569 := (pattern #16)
 #17 := (= #16 #15)
-#574 := (forall (vars (?v0 S3)) (:pat #573) #17)
+#570 := (forall (vars (?v0 S3)) (:pat #569) #17)
 #18 := (forall (vars (?v0 S3)) #17)
-#577 := (iff #18 #574)
-#575 := (iff #17 #17)
-#576 := [refl]: #575
-#578 := [quant-intro #576]: #577
-#66 := (~ #18 #18)
-#65 := (~ #17 #17)
-#76 := [refl]: #65
-#67 := [nnf-pos #76]: #66
-#52 := [asserted]: #18
-#77 := [mp~ #52 #67]: #18
-#579 := [mp #77 #578]: #574
-#555 := (not #574)
-#214 := (or #555 #25)
-#219 := [quant-inst #23]: #214
-[unit-resolution #219 #579 #559]: false
+#573 := (iff #18 #570)
+#571 := (iff #17 #17)
+#572 := [refl]: #571
+#574 := [quant-intro #572]: #573
+#62 := (~ #18 #18)
+#61 := (~ #17 #17)
+#72 := [refl]: #61
+#63 := [nnf-pos #72]: #62
+#48 := [asserted]: #18
+#73 := [mp~ #48 #63]: #18
+#575 := [mp #73 #574]: #570
+#551 := (not #570)
+#210 := (or #551 #21)
+#215 := [quant-inst #19]: #210
+[unit-resolution #215 #575 #555]: false
 unsat
-c2e9404480cb814492148c359fbbbb3b0e606571 29 0
+b9731ef54c4e3499fb2c009710dd563fdc4be6ee 29 0
 #2 := false
 #1 := true
 decl f1 :: S1
@@ -11274,7 +10982,7 @@
 #36 := [asserted]: #15
 [mp #36 #45]: false
 unsat
-343488aeda93da0c02f8ac1558cbc54ab37a2bb9 29 0
+c1459ffeaaac12de208e5b699c20294611368ff4 29 0
 #2 := false
 #1 := true
 decl f1 :: S1
@@ -11304,7 +11012,7 @@
 #36 := [asserted]: #15
 [mp #36 #45]: false
 unsat
-46a14fd6aa65cfd8a30d4b0b44a855a19c19f288 8 0
+bf2cd5b03536b5bd0602eda620854302cd150049 8 0
 #2 := false
 #1 := true
 #23 := (not true)
@@ -11313,7 +11021,7 @@
 #46 := [asserted]: #23
 [mp #46 #48]: false
 unsat
-ad406fc43130e24f380abadc1fc8a246fab490af 113 0
+89bfa27ccdaa7dcf714e523cef143bce280239ad 113 0
 #2 := false
 decl f1 :: S1
 #3 := f1
@@ -11427,7 +11135,7 @@
 #71 := [not-or-elim #70]: #69
 [unit-resolution #71 #525]: false
 unsat
-a5a23002374b3531b57fc274b72111cc0f0bdd3e 424 0
+273bebb141dbf0be0689bc04e07d9801bbd88484 424 0
 #2 := false
 decl f9 :: (-> S6 S7 S7)
 decl f12 :: S7
@@ -11852,7 +11560,7 @@
 #145 := [asserted]: #91
 [unit-resolution #145 #373]: false
 unsat
-b18aa009c5b54d915c2c9feecd9762a9bb0c27b5 24 0
+8ed6ae59787ef073a0f2ee12e54e0a9e18c847b1 24 0
 #2 := false
 decl f1 :: S1
 #3 := f1
@@ -11877,7 +11585,7 @@
 #34 := [asserted]: #13
 [mp #34 #43]: false
 unsat
-6484c4415dc032ed762d879b9df0ebba83c1370d 344 0
+0a480e932cf9544226aa308a652a130c00794519 344 0
 #2 := false
 decl f7 :: (-> S5 Int S2)
 #28 := 6::Int
@@ -12222,9 +11930,9 @@
 #107 := [asserted]: #31
 [unit-resolution #107 #388]: false
 unsat
-f954792d8be81671314fd3cce76fa4be3cd4ee23 1 0
+e9a200a4c01396af8a28649e89651e82c566aea6 1 0
 unsat
-6fc5c498589f75255cd22f4154985bdeb92fa551 95 0
+a1b617e98026794f4fabc7b88d3c7c6545b77aeb 95 0
 #2 := false
 decl f1 :: S1
 #3 := f1
@@ -12320,7 +12028,7 @@
 #312 := [mp #310 #308]: #298
 [unit-resolution #312 #641 #138 #139 #140]: false
 unsat
-e776ea3cea49bcb73b17ecdacf5c2db068ae9e28 59 0
+faeea2438f581c39182be7618ceac231cf77a00a 59 0
 #2 := false
 decl f1 :: S1
 #3 := f1
@@ -12380,7 +12088,7 @@
 #339 := [quant-inst #70]: #338
 [unit-resolution #339 #673 #163]: false
 unsat
-2e1ce9e1ff9cb725a3a169498ce8fc405a17724f 394 0
+ed7e0385c3012dbbfdc71724063f8cbb116b4c06 394 0
 #2 := false
 decl f3 :: (-> S2 S3 S4)
 decl f5 :: (-> S1 S3)
@@ -12775,110 +12483,3 @@
 #247 := [asserted]: #123
 [unit-resolution #247 #633]: false
 unsat
-477e29453df08396d997096a4fc4a8771c735880 106 0
-#2 := false
-decl f7 :: S3
-#19 := f7
-decl f5 :: (-> S4 S3 S3)
-decl f6 :: S4
-#14 := f6
-#20 := (f5 f6 f7)
-#21 := (= #20 f7)
-#74 := (not #21)
-decl f1 :: S1
-#3 := f1
-decl f3 :: (-> S2 S1 S1)
-decl f4 :: S2
-#7 := f4
-#22 := (f3 f4 f1)
-#23 := (= #22 f1)
-#75 := (not #23)
-#558 := [hypothesis]: #75
-#8 := (:var 0 S1)
-#9 := (f3 f4 #8)
-#562 := (pattern #9)
-#11 := (= #8 f1)
-#10 := (= #9 f1)
-#12 := (iff #10 #11)
-#563 := (forall (vars (?v0 S1)) (:pat #562) #12)
-#13 := (forall (vars (?v0 S1)) #12)
-#566 := (iff #13 #563)
-#564 := (iff #12 #12)
-#565 := [refl]: #564
-#567 := [quant-intro #565]: #566
-#70 := (~ #13 #13)
-#68 := (~ #12 #12)
-#69 := [refl]: #68
-#71 := [nnf-pos #69]: #70
-#47 := [asserted]: #13
-#59 := [mp~ #47 #71]: #13
-#568 := [mp #59 #567]: #563
-#239 := (not #563)
-#218 := (or #239 #23)
-#146 := (= f1 f1)
-#147 := (iff #23 #146)
-#554 := (or #239 #147)
-#212 := (iff #554 #218)
-#550 := (iff #218 #218)
-#223 := [rewrite]: #550
-#238 := (iff #147 #23)
-#1 := true
-#24 := (iff #23 true)
-#50 := (iff #24 #23)
-#51 := [rewrite]: #50
-#236 := (iff #147 #24)
-#232 := (iff #146 true)
-#225 := [rewrite]: #232
-#237 := [monotonicity #225]: #236
-#235 := [trans #237 #51]: #238
-#343 := [monotonicity #235]: #212
-#224 := [trans #343 #223]: #212
-#556 := [quant-inst #3]: #554
-#557 := [mp #556 #224]: #218
-#559 := [unit-resolution #557 #568 #558]: false
-#560 := [lemma #559]: #23
-#64 := (or #74 #75)
-#52 := (and #21 #23)
-#55 := (not #52)
-#81 := (iff #55 #64)
-#65 := (not #64)
-#76 := (not #65)
-#79 := (iff #76 #64)
-#80 := [rewrite]: #79
-#77 := (iff #55 #76)
-#66 := (iff #52 #65)
-#67 := [rewrite]: #66
-#78 := [monotonicity #67]: #77
-#82 := [trans #78 #80]: #81
-#25 := (and #21 #24)
-#26 := (not #25)
-#56 := (iff #26 #55)
-#53 := (iff #25 #52)
-#54 := [monotonicity #51]: #53
-#57 := [monotonicity #54]: #56
-#49 := [asserted]: #26
-#60 := [mp #49 #57]: #55
-#83 := [mp #60 #82]: #64
-#555 := [unit-resolution #83 #560]: #74
-#15 := (:var 0 S3)
-#16 := (f5 f6 #15)
-#569 := (pattern #16)
-#17 := (= #16 #15)
-#570 := (forall (vars (?v0 S3)) (:pat #569) #17)
-#18 := (forall (vars (?v0 S3)) #17)
-#573 := (iff #18 #570)
-#571 := (iff #17 #17)
-#572 := [refl]: #571
-#574 := [quant-intro #572]: #573
-#62 := (~ #18 #18)
-#61 := (~ #17 #17)
-#72 := [refl]: #61
-#63 := [nnf-pos #72]: #62
-#48 := [asserted]: #18
-#73 := [mp~ #48 #63]: #18
-#575 := [mp #73 #574]: #570
-#551 := (not #570)
-#210 := (or #551 #21)
-#215 := [quant-inst #19]: #210
-[unit-resolution #215 #575 #555]: false
-unsat

--- a/src/HOL/SMT_Examples/SMT_Tests.certs	Wed Oct 31 11:23:21 2012 +0100
+++ b/src/HOL/SMT_Examples/SMT_Tests.certs	Thu Nov 01 11:34:00 2012 +0100
@@ -1,8801 +1,2418 @@
-8c0dd63633148cae631c41716f59fedf31aaf85f 8 0
-#2 := false
-#1 := true
-#8 := (not true)
-#29 := (iff #8 false)
+23fa46bae38100075457f16458b7f980b6e9eaaa 8 0
+#2 := false
+#1 := true
+#7 := (not true)
+#29 := (iff #7 false)
 #30 := [rewrite]: #29
-#28 := [asserted]: #8
+#28 := [asserted]: #7
 [mp #28 #30]: false
 unsat
-0e95eca2e0e7caa31aef537bbf293f83696bbe8a 16 0
-#2 := false
-#8 := (not false)
-#9 := (not #8)
-#37 := (iff #9 false)
[phone]e05a82038d4f69182ea74d5c78a71f 16 0
+#2 := false
+#7 := (not false)
+#8 := (not #7)
+#37 := (iff #8 false)
 #1 := true
 #32 := (not true)
 #35 := (iff #32 false)
 #36 := [rewrite]: #35
-#33 := (iff #9 #32)
-#30 := (iff #8 true)
+#33 := (iff #8 #32)
+#30 := (iff #7 true)
 #31 := [rewrite]: #30
 #34 := [monotonicity #31]: #33
 #38 := [trans #34 #36]: #37
-#29 := [asserted]: #9
+#29 := [asserted]: #8
 [mp #29 #38]: false
 unsat
-bbd400f7a6b516cc913f7b22468b7a0f5ab6d4ef 21 0
-#2 := false
-#1 := true
-#8 := (not true)
+cf32c4bf044ef30ccaadb4c2a904bc42cc810589 21 0
+#2 := false
+#1 := true
+#7 := (not true)
+#8 := (not #7)
 #9 := (not #8)
-#10 := (not #9)
-#42 := (iff #10 false)
-#31 := (iff #8 false)
+#42 := (iff #9 false)
+#31 := (iff #7 false)
 #32 := [rewrite]: #31
-#40 := (iff #10 #8)
-#38 := (iff #9 true)
+#40 := (iff #9 #7)
+#38 := (iff #8 true)
 #33 := (not false)
 #36 := (iff #33 true)
 #37 := [rewrite]: #36
-#34 := (iff #9 #33)
+#34 := (iff #8 #33)
 #35 := [monotonicity #32]: #34
 #39 := [trans #35 #37]: #38
 #41 := [monotonicity #39]: #40
 #43 := [trans #41 #32]: #42
-#30 := [asserted]: #10
+#30 := [asserted]: #9
 [mp #30 #43]: false
 unsat
-218e23551f716b340d470b13088877ee41ffeabf 16 0
-#2 := false
-#1 := true
-#8 := (and true true)
-#9 := (not #8)
-#37 := (iff #9 false)
+1ca76146d8caa3873d987c8f2b2b61e67bf99885 16 0
+#2 := false
+#1 := true
+#7 := (and true true)
+#8 := (not #7)
+#37 := (iff #8 false)
 #32 := (not true)
 #35 := (iff #32 false)
 #36 := [rewrite]: #35
-#33 := (iff #9 #32)
-#30 := (iff #8 true)
+#33 := (iff #8 #32)
+#30 := (iff #7 true)
 #31 := [rewrite]: #30
 #34 := [monotonicity #31]: #33
 #38 := [trans #34 #36]: #37
-#29 := [asserted]: #9
+#29 := [asserted]: #8
 [mp #29 #38]: false
 unsat
-4820ba699dfc46472702e8103b5f713f524239e1 16 0
-#2 := false
-#1 := true
-#8 := (or true false)
-#9 := (not #8)
-#37 := (iff #9 false)
+6fe44a8c791d15e051ebac6bd54712b11019176f 16 0
+#2 := false
+#1 := true
+#7 := (or true false)
+#8 := (not #7)
+#37 := (iff #8 false)
 #32 := (not true)
 #35 := (iff #32 false)
 #36 := [rewrite]: #35
-#33 := (iff #9 #32)
-#30 := (iff #8 true)
+#33 := (iff #8 #32)
+#30 := (iff #7 true)
 #31 := [rewrite]: #30
 #34 := [monotonicity #31]: #33
 #38 := [trans #34 #36]: #37
-#29 := [asserted]: #9
+#29 := [asserted]: #8
 [mp #29 #38]: false
 unsat
-ee9714cb019befa9d851be80ac36f38d43541012 16 0
-#2 := false
-#1 := true
-#8 := (implies false true)
-#9 := (not #8)
-#37 := (iff #9 false)
+cd5b6483316374c04155ccdcb2bd4ec732d555bc 16 0
+#2 := false
+#1 := true
+#7 := (implies false true)
+#8 := (not #7)
+#37 := (iff #8 false)
 #32 := (not true)
 #35 := (iff #32 false)
 #36 := [rewrite]: #35
-#33 := (iff #9 #32)
-#30 := (iff #8 true)
+#33 := (iff #8 #32)
+#30 := (iff #7 true)
 #31 := [rewrite]: #30
 #34 := [monotonicity #31]: #33
 #38 := [trans #34 #36]: #37
-#29 := [asserted]: #9
+#29 := [asserted]: #8
 [mp #29 #38]: false
 unsat
-7869b66c1f04020ccc620174a1f0451e995f1abd 24 0
-#2 := false
-#1 := true
-#8 := (iff false true)
+1d8b1fcc54699acf56c2f7bd752c247e433581cb 24 0
+#2 := false
+#1 := true
+#7 := (iff false true)
+#8 := (not #7)
 #9 := (not #8)
-#10 := (not #9)
-#45 := (iff #10 false)
+#45 := (iff #9 false)
 #40 := (not true)
 #43 := (iff #40 false)
 #44 := [rewrite]: #43
-#41 := (iff #10 #40)
-#38 := (iff #9 true)
+#41 := (iff #9 #40)
+#38 := (iff #8 true)
 #33 := (not false)
 #36 := (iff #33 true)
 #37 := [rewrite]: #36
-#34 := (iff #9 #33)
-#31 := (iff #8 false)
+#34 := (iff #8 #33)
+#31 := (iff #7 false)
 #32 := [rewrite]: #31
 #35 := [monotonicity #32]: #34
 #39 := [trans #35 #37]: #38
 #42 := [monotonicity #39]: #41
 #46 := [trans #42 #44]: #45
-#30 := [asserted]: #10
+#30 := [asserted]: #9
 [mp #30 #46]: false
 unsat
-4e759d02d4de42cc8b917c1ee399e500780bf8d9 33 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#10 := (not #9)
-#11 := (or #9 #10)
-#12 := (not #11)
-#51 := (iff #12 false)
-#1 := true
-#46 := (not true)
-#49 := (iff #46 false)
-#50 := [rewrite]: #49
-#47 := (iff #12 #46)
-#44 := (iff #11 true)
-#33 := (= f1 f3)
-#36 := (not #33)
-#39 := (or #33 #36)
-#42 := (iff #39 true)
-#43 := [rewrite]: #42
-#40 := (iff #11 #39)
-#37 := (iff #10 #36)
-#34 := (iff #9 #33)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#41 := [monotonicity #35 #38]: #40
-#45 := [trans #41 #43]: #44
-#48 := [monotonicity #45]: #47
-#52 := [trans #48 #50]: #51
-#32 := [asserted]: #12
-[mp #32 #52]: false
-unsat
-6f508687a1b8d851ff54bda8c3b55201243d9664 41 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#10 := (not #9)
-#11 := (and #9 #10)
-#12 := (not #11)
-#13 := (not #12)
-#59 := (iff #13 false)
-#1 := true
-#54 := (not true)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #13 #54)
-#52 := (iff #12 true)
-#47 := (not false)
-#50 := (iff #47 true)
-#51 := [rewrite]: #50
-#48 := (iff #12 #47)
-#45 := (iff #11 false)
-#34 := (= f1 f3)
-#37 := (not #34)
-#40 := (and #34 #37)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 #37)
-#35 := (iff #9 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#42 := [monotonicity #36 #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#33 := [asserted]: #13
-[mp #33 #60]: false
-unsat
-a570d829481d812db472649896375ed3e544b2a0 65 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#12 := (and false #9)
-#13 := (or #12 #9)
-#11 := (not #9)
-#14 := (or #11 #13)
-#1 := true
-#10 := (and true #9)
-#15 := (or #10 #14)
-#16 := (not #15)
-#83 := (iff #16 false)
-#78 := (not true)
-#81 := (iff #78 false)
-#82 := [rewrite]: #81
-#79 := (iff #16 #78)
-#76 := (iff #15 true)
-#37 := (= f1 f3)
-#71 := (or #37 true)
-#74 := (iff #71 true)
-#75 := [rewrite]: #74
-#72 := (iff #15 #71)
-#69 := (iff #14 true)
-#47 := (not #37)
-#64 := (or #47 #37)
-#67 := (iff #64 true)
-#68 := [rewrite]: #67
-#65 := (iff #14 #64)
-#62 := (iff #13 #37)
-#57 := (or false #37)
-#60 := (iff #57 #37)
-#61 := [rewrite]: #60
-#58 := (iff #13 #57)
-#38 := (iff #9 #37)
-#39 := [rewrite]: #38
-#55 := (iff #12 false)
-#50 := (and false #37)
-#53 := (iff #50 false)
-#54 := [rewrite]: #53
-#51 := (iff #12 #50)
-#52 := [monotonicity #39]: #51
-#56 := [trans #52 #54]: #55
-#59 := [monotonicity #56 #39]: #58
-#63 := [trans #59 #61]: #62
-#48 := (iff #11 #47)
-#49 := [monotonicity #39]: #48
-#66 := [monotonicity #49 #63]: #65
-#70 := [trans #66 #68]: #69
-#45 := (iff #10 #37)
-#40 := (and true #37)
-#43 := (iff #40 #37)
-#44 := [rewrite]: #43
-#41 := (iff #10 #40)
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#73 := [monotonicity #46 #70]: #72
-#77 := [trans #73 #75]: #76
-#80 := [monotonicity #77]: #79
-#84 := [trans #80 #82]: #83
-#36 := [asserted]: #16
-[mp #36 #84]: false
-unsat
-4cee40af08d20a91303cc3118e83d7eca7872920 29 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#10 := (implies #9 #9)
-#11 := (not #10)
-#47 := (iff #11 false)
-#1 := true
-#42 := (not true)
-#45 := (iff #42 false)
-#46 := [rewrite]: #45
-#43 := (iff #11 #42)
-#40 := (iff #10 true)
-#32 := (= f1 f3)
-#35 := (implies #32 #32)
-#38 := (iff #35 true)
-#39 := [rewrite]: #38
-#36 := (iff #10 #35)
-#33 := (iff #9 #32)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34 #34]: #36
-#41 := [trans #37 #39]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#31 := [asserted]: #11
-[mp #31 #48]: false
-unsat
-0fe45fcdabd9bb3a2f80916a3d449a773092c058 41 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#10 := (not #9)
-#11 := (and #9 #10)
-#12 := (implies #11 false)
-#13 := (not #12)
-#59 := (iff #13 false)
-#1 := true
-#54 := (not true)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #13 #54)
-#52 := (iff #12 true)
-#47 := (implies false false)
-#50 := (iff #47 true)
-#51 := [rewrite]: #50
-#48 := (iff #12 #47)
-#45 := (iff #11 false)
-#34 := (= f1 f3)
-#37 := (not #34)
-#40 := (and #34 #37)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 #37)
-#35 := (iff #9 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#42 := [monotonicity #36 #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#33 := [asserted]: #13
-[mp #33 #60]: false
-unsat
-d63aa12ea1f62e0c634eee23e682ed847e82572d 47 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#13 := (and #11 #9)
-#12 := (and #9 #11)
-#14 := (implies #12 #13)
-#15 := (not #14)
-#64 := (iff #15 false)
-#1 := true
-#59 := (not true)
-#62 := (iff #59 false)
-#63 := [rewrite]: #62
-#60 := (iff #15 #59)
-#57 := (iff #14 true)
-#39 := (= f1 f4)
-#36 := (= f1 f3)
-#42 := (and #36 #39)
-#52 := (implies #42 #42)
-#55 := (iff #52 true)
-#56 := [rewrite]: #55
-#53 := (iff #14 #52)
-#50 := (iff #13 #42)
-#45 := (and #39 #36)
-#48 := (iff #45 #42)
-#49 := [rewrite]: #48
-#46 := (iff #13 #45)
-#37 := (iff #9 #36)
-#38 := [rewrite]: #37
-#40 := (iff #11 #39)
-#41 := [rewrite]: #40
-#47 := [monotonicity #41 #38]: #46
-#51 := [trans #47 #49]: #50
-#43 := (iff #12 #42)
-#44 := [monotonicity #38 #41]: #43
-#54 := [monotonicity #44 #51]: #53
-#58 := [trans #54 #56]: #57
-#61 := [monotonicity #58]: #60
-#65 := [trans #61 #63]: #64
-#35 := [asserted]: #15
-[mp #35 #65]: false
-unsat
-ac9f8dfae9db87406db77382935caeb1212c8720 47 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#13 := (or #11 #9)
-#12 := (or #9 #11)
-#14 := (implies #12 #13)
-#15 := (not #14)
-#64 := (iff #15 false)
-#1 := true
-#59 := (not true)
-#62 := (iff #59 false)
-#63 := [rewrite]: #62
-#60 := (iff #15 #59)
-#57 := (iff #14 true)
-#39 := (= f1 f4)
-#36 := (= f1 f3)
-#42 := (or #36 #39)
-#52 := (implies #42 #42)
-#55 := (iff #52 true)
-#56 := [rewrite]: #55
-#53 := (iff #14 #52)
-#50 := (iff #13 #42)
-#45 := (or #39 #36)
-#48 := (iff #45 #42)
-#49 := [rewrite]: #48
-#46 := (iff #13 #45)
-#37 := (iff #9 #36)
-#38 := [rewrite]: #37
-#40 := (iff #11 #39)
-#41 := [rewrite]: #40
-#47 := [monotonicity #41 #38]: #46
-#51 := [trans #47 #49]: #50
-#43 := (iff #12 #42)
-#44 := [monotonicity #38 #41]: #43
-#54 := [monotonicity #44 #51]: #53
-#58 := [trans #54 #56]: #57
-#61 := [monotonicity #58]: #60
-#65 := [trans #61 #63]: #64
-#35 := [asserted]: #15
-[mp #35 #65]: false
-unsat
-3ca7c9c03f9ec0a6bb70ba63fef8fe4be3fc1124 55 0
-#2 := false
-decl f3 :: S1
-#8 := f3
-decl f1 :: S1
-#4 := f1
-#36 := (= f1 f3)
-#79 := (iff #36 false)
-#69 := (not #36)
-decl f4 :: S1
-#10 := f4
-#39 := (= f1 f4)
-#42 := (and #36 #39)
-#51 := (not #42)
-#60 := (or #36 #39 #51)
-#63 := (not #60)
-#11 := (= f4 f1)
-#9 := (= f3 f1)
-#13 := (or #9 #11)
-#12 := (and #9 #11)
-#14 := (implies #12 #13)
-#15 := (not #14)
-#66 := (iff #15 #63)
-#45 := (or #36 #39)
-#52 := (or #51 #45)
-#57 := (not #52)
-#64 := (iff #57 #63)
-#61 := (iff #52 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#58 := (iff #15 #57)
-#55 := (iff #14 #52)
-#48 := (implies #42 #45)
-#53 := (iff #48 #52)
-#54 := [rewrite]: #53
-#49 := (iff #14 #48)
-#46 := (iff #13 #45)
-#40 := (iff #11 #39)
-#41 := [rewrite]: #40
-#37 := (iff #9 #36)
-#38 := [rewrite]: #37
-#47 := [monotonicity #38 #41]: #46
-#43 := (iff #12 #42)
-#44 := [monotonicity #38 #41]: #43
-#50 := [monotonicity #44 #47]: #49
-#56 := [trans #50 #54]: #55
-#59 := [monotonicity #56]: #58
-#67 := [trans #59 #65]: #66
-#35 := [asserted]: #15
-#68 := [mp #35 #67]: #63
-#70 := [not-or-elim #68]: #69
-#80 := [iff-false #70]: #79
-#73 := [not-or-elim #68]: #42
-#74 := [and-elim #73]: #36
-[mp #74 #80]: false
-unsat
-520e744f261e775610c6856eddf3b7e384835c22 55 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#14 := (not #9)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#12 := (or #9 #11)
-#13 := (not #12)
-#15 := (implies #13 #14)
-#16 := (not #15)
-#72 := (iff #16 false)
-#40 := (= f1 f4)
-#37 := (= f1 f3)
-#43 := (or #37 #40)
-#49 := (not #37)
-#55 := (or #49 #43)
-#60 := (not #55)
-#70 := (iff #60 false)
-#1 := true
-#65 := (not true)
-#68 := (iff #65 false)
-#69 := [rewrite]: #68
-#66 := (iff #60 #65)
-#63 := (iff #55 true)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#71 := [trans #67 #69]: #70
-#61 := (iff #16 #60)
-#58 := (iff #15 #55)
-#46 := (not #43)
-#52 := (implies #46 #49)
-#56 := (iff #52 #55)
-#57 := [rewrite]: #56
-#53 := (iff #15 #52)
-#50 := (iff #14 #49)
-#38 := (iff #9 #37)
-#39 := [rewrite]: #38
-#51 := [monotonicity #39]: #50
-#47 := (iff #13 #46)
-#44 := (iff #12 #43)
-#41 := (iff #11 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #39 #42]: #44
-#48 := [monotonicity #45]: #47
-#54 := [monotonicity #48 #51]: #53
-#59 := [trans #54 #57]: #58
-#62 := [monotonicity #59]: #61
-#73 := [trans #62 #71]: #72
-#36 := [asserted]: #16
-[mp #36 #73]: false
-unsat
-a4cd863a4afcd8896c4557ed1f94e6b2e251460c 55 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#14 := (not #11)
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#12 := (or #9 #11)
-#13 := (not #12)
-#15 := (implies #13 #14)
-#16 := (not #15)
-#72 := (iff #16 false)
-#40 := (= f1 f4)
-#37 := (= f1 f3)
-#43 := (or #37 #40)
-#49 := (not #40)
-#55 := (or #49 #43)
-#60 := (not #55)
-#70 := (iff #60 false)
-#1 := true
-#65 := (not true)
-#68 := (iff #65 false)
-#69 := [rewrite]: #68
-#66 := (iff #60 #65)
-#63 := (iff #55 true)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#71 := [trans #67 #69]: #70
-#61 := (iff #16 #60)
-#58 := (iff #15 #55)
-#46 := (not #43)
-#52 := (implies #46 #49)
-#56 := (iff #52 #55)
-#57 := [rewrite]: #56
-#53 := (iff #15 #52)
-#50 := (iff #14 #49)
-#41 := (iff #11 #40)
-#42 := [rewrite]: #41
-#51 := [monotonicity #42]: #50
-#47 := (iff #13 #46)
-#44 := (iff #12 #43)
-#38 := (iff #9 #37)
-#39 := [rewrite]: #38
-#45 := [monotonicity #39 #42]: #44
-#48 := [monotonicity #45]: #47
-#54 := [monotonicity #48 #51]: #53
-#59 := [trans #54 #57]: #58
-#62 := [monotonicity #59]: #61
-#73 := [trans #62 #71]: #72
-#36 := [asserted]: #16
-[mp #36 #73]: false
-unsat
-971edb4251c21bd89bd88e455c303075d8fa8060 49 0
-#2 := false
-decl f3 :: S1
-#8 := f3
-decl f1 :: S1
-#4 := f1
-#37 := (= f1 f3)
-#71 := (iff #37 false)
-#40 := (not #37)
-decl f4 :: S1
-#11 := f4
-#43 := (= f1 f4)
-#46 := (and #37 #43)
-#49 := (not #46)
-#55 := (or #37 #49)
-#60 := (not #55)
-#12 := (= f4 f1)
-#9 := (= f3 f1)
-#13 := (and #9 #12)
-#14 := (not #13)
-#10 := (not #9)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#61 := (iff #16 #60)
-#58 := (iff #15 #55)
-#52 := (implies #40 #49)
-#56 := (iff #52 #55)
-#57 := [rewrite]: #56
-#53 := (iff #15 #52)
-#50 := (iff #14 #49)
-#47 := (iff #13 #46)
-#44 := (iff #12 #43)
-#45 := [rewrite]: #44
-#38 := (iff #9 #37)
-#39 := [rewrite]: #38
-#48 := [monotonicity #39 #45]: #47
-#51 := [monotonicity #48]: #50
-#41 := (iff #10 #40)
-#42 := [monotonicity #39]: #41
-#54 := [monotonicity #42 #51]: #53
-#59 := [trans #54 #57]: #58
-#62 := [monotonicity #59]: #61
-#36 := [asserted]: #16
-#65 := [mp #36 #62]: #60
-#63 := [not-or-elim #65]: #40
-#72 := [iff-false #63]: #71
-#64 := [not-or-elim #65]: #46
-#66 := [and-elim #64]: #37
-[mp #66 #72]: false
-unsat
-f2ade1ff188c65975bec097c4372f4c2c6bf872d 54 0
-#2 := false
-decl f3 :: S1
-#8 := f3
-decl f1 :: S1
-#4 := f1
-#37 := (= f1 f3)
-#76 := (iff #37 false)
-#40 := (not #37)
-decl f4 :: S1
-#11 := f4
-#43 := (= f1 f4)
-#49 := (and #37 #43)
-#54 := (not #49)
-#60 := (or #37 #54)
-#65 := (not #60)
-#9 := (= f3 f1)
-#12 := (= f4 f1)
-#13 := (and #12 #9)
-#14 := (not #13)
-#10 := (not #9)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#66 := (iff #16 #65)
-#63 := (iff #15 #60)
-#57 := (implies #40 #54)
-#61 := (iff #57 #60)
-#62 := [rewrite]: #61
-#58 := (iff #15 #57)
-#55 := (iff #14 #54)
-#52 := (iff #13 #49)
-#46 := (and #43 #37)
-#50 := (iff #46 #49)
-#51 := [rewrite]: #50
-#47 := (iff #13 #46)
-#38 := (iff #9 #37)
-#39 := [rewrite]: #38
-#44 := (iff #12 #43)
-#45 := [rewrite]: #44
-#48 := [monotonicity #45 #39]: #47
-#53 := [trans #48 #51]: #52
-#56 := [monotonicity #53]: #55
-#41 := (iff #10 #40)
-#42 := [monotonicity #39]: #41
-#59 := [monotonicity #42 #56]: #58
-#64 := [trans #59 #62]: #63
-#67 := [monotonicity #64]: #66
-#36 := [asserted]: #16
-#70 := [mp #36 #67]: #65
-#68 := [not-or-elim #70]: #40
-#77 := [iff-false #68]: #76
-#69 := [not-or-elim #70]: #49
-#71 := [and-elim #69]: #37
-[mp #71 #77]: false
-unsat
-682534b0f67b638e243f2eb512302b970aa41e32 60 0
-#2 := false
-decl f4 :: S1
-#10 := f4
-decl f1 :: S1
-#4 := f1
-#42 := (= f1 f4)
-#51 := (not #42)
-decl f3 :: S1
-#8 := f3
-#39 := (= f1 f3)
-#48 := (not #39)
-#54 := (or #48 #51)
-#45 := (and #39 #42)
-#67 := (iff #45 #54)
-#72 := (iff #67 false)
-#57 := (not #54)
-#78 := (iff #57 #54)
-#75 := (iff #78 false)
-#76 := [rewrite]: #75
-#79 := (iff #67 #78)
-#60 := (iff #45 #57)
-#77 := [rewrite]: #60
-#80 := [monotonicity #77]: #79
-#74 := [trans #80 #76]: #72
-#11 := (= f4 f1)
-#14 := (not #11)
-#9 := (= f3 f1)
-#13 := (not #9)
-#15 := (or #13 #14)
-#16 := (not #15)
-#12 := (and #9 #11)
-#17 := (iff #12 #16)
-#18 := (not #17)
-#69 := (iff #18 #67)
-#63 := (not #60)
-#66 := (iff #63 #67)
-#68 := [rewrite]: #66
-#64 := (iff #18 #63)
-#61 := (iff #17 #60)
-#58 := (iff #16 #57)
-#55 := (iff #15 #54)
-#52 := (iff #14 #51)
-#43 := (iff #11 #42)
-#44 := [rewrite]: #43
-#53 := [monotonicity #44]: #52
-#49 := (iff #13 #48)
-#40 := (iff #9 #39)
-#41 := [rewrite]: #40
-#50 := [monotonicity #41]: #49
-#56 := [monotonicity #50 #53]: #55
-#59 := [monotonicity #56]: #58
-#46 := (iff #12 #45)
-#47 := [monotonicity #41 #44]: #46
-#62 := [monotonicity #47 #59]: #61
-#65 := [monotonicity #62]: #64
-#70 := [trans #65 #68]: #69
-#38 := [asserted]: #18
-#73 := [mp #38 #70]: #67
-[mp #73 #74]: false
-unsat
-18c084b69ef057902c4f565daffb9414815edad2 79 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f5 :: S1
-#13 := f5
-#14 := (= f5 f1)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#16 := (and #11 #14)
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#17 := (and #9 #16)
-#12 := (and #9 #11)
-#15 := (and #12 #14)
-#18 := (implies #15 #17)
-#19 := (not #18)
-#95 := (iff #19 false)
-#49 := (= f1 f5)
-#43 := (= f1 f4)
-#55 := (and #43 #49)
-#40 := (= f1 f3)
-#58 := (and #40 #55)
-#46 := (and #40 #43)
-#52 := (and #46 #49)
-#64 := (not #52)
-#65 := (or #64 #58)
-#70 := (not #65)
-#93 := (iff #70 false)
-#1 := true
-#88 := (not true)
-#91 := (iff #88 false)
-#92 := [rewrite]: #91
-#89 := (iff #70 #88)
-#86 := (iff #65 true)
-#73 := (and #40 #43 #49)
-#76 := (not #73)
-#81 := (or #76 #73)
-#84 := (iff #81 true)
-#85 := [rewrite]: #84
-#82 := (iff #65 #81)
-#79 := (iff #58 #73)
-#80 := [rewrite]: #79
-#77 := (iff #64 #76)
-#74 := (iff #52 #73)
-#75 := [rewrite]: #74
-#78 := [monotonicity #75]: #77
-#83 := [monotonicity #78 #80]: #82
-#87 := [trans #83 #85]: #86
-#90 := [monotonicity #87]: #89
-#94 := [trans #90 #92]: #93
-#71 := (iff #19 #70)
-#68 := (iff #18 #65)
-#61 := (implies #52 #58)
-#66 := (iff #61 #65)
-#67 := [rewrite]: #66
-#62 := (iff #18 #61)
-#59 := (iff #17 #58)
-#56 := (iff #16 #55)
-#50 := (iff #14 #49)
-#51 := [rewrite]: #50
-#44 := (iff #11 #43)
-#45 := [rewrite]: #44
-#57 := [monotonicity #45 #51]: #56
-#41 := (iff #9 #40)
-#42 := [rewrite]: #41
-#60 := [monotonicity #42 #57]: #59
-#53 := (iff #15 #52)
-#47 := (iff #12 #46)
-#48 := [monotonicity #42 #45]: #47
-#54 := [monotonicity #48 #51]: #53
-#63 := [monotonicity #54 #60]: #62
-#69 := [trans #63 #67]: #68
-#72 := [monotonicity #69]: #71
-#96 := [trans #72 #94]: #95
-#39 := [asserted]: #19
-[mp #39 #96]: false
-unsat
-b35caa01ace8f0712871ad8d5740788301cd45cb 94 0
-#2 := false
-decl f5 :: S1
-#13 := f5
-decl f1 :: S1
-#4 := f1
-#49 := (= f1 f5)
-decl f4 :: S1
-#10 := f4
-#43 := (= f1 f4)
-decl f3 :: S1
-#8 := f3
-#40 := (= f1 f3)
-#73 := (or #40 #43 #49)
-#114 := (iff #73 false)
-#109 := (or false false false)
-#112 := (iff #109 false)
-#113 := [rewrite]: #112
-#110 := (iff #73 #109)
-#107 := (iff #49 false)
-#97 := (not #49)
-#76 := (not #73)
-#82 := (or #40 #43 #49 #76)
-#87 := (not #82)
-#14 := (= f5 f1)
-#11 := (= f4 f1)
-#16 := (or #11 #14)
-#9 := (= f3 f1)
-#17 := (or #9 #16)
-#12 := (or #9 #11)
-#15 := (or #12 #14)
-#18 := (implies #15 #17)
-#19 := (not #18)
-#90 := (iff #19 #87)
-#55 := (or #43 #49)
-#58 := (or #40 #55)
-#46 := (or #40 #43)
-#52 := (or #46 #49)
-#64 := (not #52)
-#65 := (or #64 #58)
-#70 := (not #65)
-#88 := (iff #70 #87)
-#85 := (iff #65 #82)
-#79 := (or #76 #58)
-#83 := (iff #79 #82)
-#84 := [rewrite]: #83
-#80 := (iff #65 #79)
-#77 := (iff #64 #76)
-#74 := (iff #52 #73)
-#75 := [rewrite]: #74
-#78 := [monotonicity #75]: #77
-#81 := [monotonicity #78]: #80
-#86 := [trans #81 #84]: #85
-#89 := [monotonicity #86]: #88
-#71 := (iff #19 #70)
-#68 := (iff #18 #65)
-#61 := (implies #52 #58)
-#66 := (iff #61 #65)
-#67 := [rewrite]: #66
-#62 := (iff #18 #61)
-#59 := (iff #17 #58)
-#56 := (iff #16 #55)
-#50 := (iff #14 #49)
-#51 := [rewrite]: #50
-#44 := (iff #11 #43)
-#45 := [rewrite]: #44
-#57 := [monotonicity #45 #51]: #56
-#41 := (iff #9 #40)
-#42 := [rewrite]: #41
-#60 := [monotonicity #42 #57]: #59
-#53 := (iff #15 #52)
-#47 := (iff #12 #46)
-#48 := [monotonicity #42 #45]: #47
-#54 := [monotonicity #48 #51]: #53
-#63 := [monotonicity #54 #60]: #62
-#69 := [trans #63 #67]: #68
-#72 := [monotonicity #69]: #71
-#91 := [trans #72 #89]: #90
-#39 := [asserted]: #19
-#92 := [mp #39 #91]: #87
-#98 := [not-or-elim #92]: #97
-#108 := [iff-false #98]: #107
-#105 := (iff #43 false)
-#95 := (not #43)
-#96 := [not-or-elim #92]: #95
-#106 := [iff-false #96]: #105
-#103 := (iff #40 false)
-#93 := (not #40)
-#94 := [not-or-elim #92]: #93
-#104 := [iff-false #94]: #103
-#111 := [monotonicity #104 #106 #108]: #110
-#115 := [trans #111 #113]: #114
-#99 := [not-or-elim #92]: #73
-[mp #99 #115]: false
-unsat
-644cc5c7eac6cad9197e62e1430e0caf631242de 114 0
-#2 := false
-decl f5 :: S1
-#13 := f5
-decl f1 :: S1
-#4 := f1
-#50 := (= f1 f5)
-decl f3 :: S1
-#8 := f3
-#41 := (= f1 f3)
-#56 := (or #41 #50)
-decl f4 :: S1
-#10 := f4
-#44 := (= f1 f4)
-#89 := (not #44)
-#88 := (not #41)
-#90 := (or #88 #89)
-#91 := (not #90)
-#119 := (not #50)
-#130 := [hypothesis]: #50
-#120 := (or #56 #119)
-#121 := [def-axiom]: #120
-#131 := [unit-resolution #121 #130]: #56
-#59 := (or #44 #50)
-#126 := (or #59 #119)
-#127 := [def-axiom]: #126
-#132 := [unit-resolution #127 #130]: #59
-#98 := (not #59)
-#97 := (not #56)
-#99 := (or #97 #98)
-#62 := (and #56 #59)
-#78 := (not #62)
-#108 := (iff #78 #99)
-#100 := (not #99)
-#103 := (not #100)
-#106 := (iff #103 #99)
-#107 := [rewrite]: #106
-#104 := (iff #78 #103)
-#101 := (iff #62 #100)
-#102 := [rewrite]: #101
-#105 := [monotonicity #102]: #104
-#109 := [trans #105 #107]: #108
-#47 := (and #41 #44)
-#53 := (or #47 #50)
-#68 := (not #53)
-#69 := (or #68 #62)
-#74 := (not #69)
-#14 := (= f5 f1)
-#11 := (= f4 f1)
-#17 := (or #11 #14)
-#9 := (= f3 f1)
-#16 := (or #9 #14)
-#18 := (and #16 #17)
-#12 := (and #9 #11)
-#15 := (or #12 #14)
-#19 := (implies #15 #18)
-#20 := (not #19)
-#75 := (iff #20 #74)
-#72 := (iff #19 #69)
-#65 := (implies #53 #62)
-#70 := (iff #65 #69)
-#71 := [rewrite]: #70
-#66 := (iff #19 #65)
-#63 := (iff #18 #62)
-#60 := (iff #17 #59)
-#51 := (iff #14 #50)
-#52 := [rewrite]: #51
-#45 := (iff #11 #44)
-#46 := [rewrite]: #45
-#61 := [monotonicity #46 #52]: #60
-#57 := (iff #16 #56)
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#58 := [monotonicity #43 #52]: #57
-#64 := [monotonicity #58 #61]: #63
-#54 := (iff #15 #53)
-#48 := (iff #12 #47)
-#49 := [monotonicity #43 #46]: #48
-#55 := [monotonicity #49 #52]: #54
-#67 := [monotonicity #55 #64]: #66
-#73 := [trans #67 #71]: #72
-#76 := [monotonicity #73]: #75
-#40 := [asserted]: #20
-#79 := [mp #40 #76]: #74
-#80 := [not-or-elim #79]: #78
-#110 := [mp #80 #109]: #99
-#133 := [unit-resolution #110 #132 #131]: false
-#134 := [lemma #133]: #119
-#83 := (or #50 #91)
-#94 := (iff #53 #83)
-#84 := (or #91 #50)
-#92 := (iff #84 #83)
-#93 := [rewrite]: #92
-#85 := (iff #53 #84)
-#86 := (iff #47 #91)
-#87 := [rewrite]: #86
-#82 := [monotonicity #87]: #85
-#95 := [trans #82 #93]: #94
-#77 := [not-or-elim #79]: #53
-#96 := [mp #77 #95]: #83
-#135 := [unit-resolution #96 #134]: #91
-#111 := (or #90 #41)
-#112 := [def-axiom]: #111
-#136 := [unit-resolution #112 #135]: #41
-#117 := (or #56 #88)
-#118 := [def-axiom]: #117
-#137 := [unit-resolution #118 #136]: #56
-#113 := (or #90 #44)
-#114 := [def-axiom]: #113
-#138 := [unit-resolution #114 #135]: #44
-#124 := (or #59 #89)
-#125 := [def-axiom]: #124
-#139 := [unit-resolution #125 #138]: #59
-[unit-resolution #110 #139 #137]: false
-unsat
-93bc0888dce281b8a619c094f485437218f003bd 121 0
-#2 := false
-decl f5 :: S1
-#13 := f5
-decl f1 :: S1
-#4 := f1
-#50 := (= f1 f5)
-decl f3 :: S1
-#8 := f3
-#41 := (= f1 f3)
-#64 := (and #41 #50)
-#101 := (not #64)
-#140 := (iff #101 false)
-#1 := true
-#135 := (not true)
-#138 := (iff #135 false)
-#139 := [rewrite]: #138
-#136 := (iff #101 #135)
-#133 := (iff #64 true)
-#128 := (and true true)
-#131 := (iff #128 true)
-#132 := [rewrite]: #131
-#129 := (iff #64 #128)
-#126 := (iff #50 true)
-decl f4 :: S1
-#10 := f4
-#44 := (= f1 f4)
-#56 := (or #44 #50)
-#123 := (iff #56 #50)
-#118 := (or false #50)
-#121 := (iff #118 #50)
-#122 := [rewrite]: #121
-#119 := (iff #56 #118)
-#106 := (iff #44 false)
-#96 := (not #44)
-#47 := (or #41 #44)
-#61 := (and #47 #56)
-#78 := (not #61)
-#87 := (or #44 #78 #64)
-#90 := (not #87)
-#11 := (= f4 f1)
-#14 := (= f5 f1)
-#9 := (= f3 f1)
-#17 := (and #9 #14)
-#18 := (or #17 #11)
-#15 := (or #14 #11)
-#12 := (or #9 #11)
-#16 := (and #12 #15)
-#19 := (implies #16 #18)
-#20 := (not #19)
-#93 := (iff #20 #90)
-#70 := (or #44 #64)
-#79 := (or #78 #70)
-#84 := (not #79)
-#91 := (iff #84 #90)
-#88 := (iff #79 #87)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#85 := (iff #20 #84)
-#82 := (iff #19 #79)
-#75 := (implies #61 #70)
-#80 := (iff #75 #79)
-#81 := [rewrite]: #80
-#76 := (iff #19 #75)
-#73 := (iff #18 #70)
-#67 := (or #64 #44)
-#71 := (iff #67 #70)
-#72 := [rewrite]: #71
-#68 := (iff #18 #67)
-#45 := (iff #11 #44)
-#46 := [rewrite]: #45
-#65 := (iff #17 #64)
-#51 := (iff #14 #50)
-#52 := [rewrite]: #51
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#66 := [monotonicity #43 #52]: #65
-#69 := [monotonicity #66 #46]: #68
-#74 := [trans #69 #72]: #73
-#62 := (iff #16 #61)
-#59 := (iff #15 #56)
-#53 := (or #50 #44)
-#57 := (iff #53 #56)
-#58 := [rewrite]: #57
-#54 := (iff #15 #53)
-#55 := [monotonicity #52 #46]: #54
-#60 := [trans #55 #58]: #59
-#48 := (iff #12 #47)
-#49 := [monotonicity #43 #46]: #48
-#63 := [monotonicity #49 #60]: #62
-#77 := [monotonicity #63 #74]: #76
-#83 := [trans #77 #81]: #82
-#86 := [monotonicity #83]: #85
-#94 := [trans #86 #92]: #93
-#40 := [asserted]: #20
-#95 := [mp #40 #94]: #90
-#97 := [not-or-elim #95]: #96
-#107 := [iff-false #97]: #106
-#120 := [monotonicity #107]: #119
-#124 := [trans #120 #122]: #123
-#98 := [not-or-elim #95]: #61
-#100 := [and-elim #98]: #56
-#125 := [mp #100 #124]: #50
-#127 := [iff-true #125]: #126
-#116 := (iff #41 true)
-#113 := (iff #47 #41)
-#108 := (or #41 false)
-#111 := (iff #108 #41)
-#112 := [rewrite]: #111
-#109 := (iff #47 #108)
-#110 := [monotonicity #107]: #109
-#114 := [trans #110 #112]: #113
-#99 := [and-elim #98]: #47
-#115 := [mp #99 #114]: #41
-#117 := [iff-true #115]: #116
-#130 := [monotonicity #117 #127]: #129
-#134 := [trans #130 #132]: #133
-#137 := [monotonicity #134]: #136
-#141 := [trans #137 #139]: #140
-#102 := [not-or-elim #95]: #101
-[mp #102 #141]: false
-unsat
-25b40c8c6dac4ff528a28853107efdd6966efb87 110 0
-#2 := false
-decl f4 :: S1
-#10 := f4
-decl f1 :: S1
-#4 := f1
-#44 := (= f1 f4)
-decl f3 :: S1
-#8 := f3
-#41 := (= f1 f3)
-#47 := (or #41 #44)
-#131 := (iff #47 false)
-#126 := (or false false)
-#129 := (iff #126 false)
-#130 := [rewrite]: #129
-#127 := (iff #47 #126)
-#124 := (iff #44 false)
-#120 := (not #44)
-decl f5 :: S1
-#13 := f5
-#50 := (= f1 f5)
-#59 := (and #44 #50)
-#91 := (not #59)
-#121 := (iff #91 #120)
-#118 := (iff #59 #44)
-#1 := true
-#113 := (and #44 true)
-#116 := (iff #113 #44)
-#117 := [rewrite]: #116
-#114 := (iff #59 #113)
-#98 := (iff #50 true)
-#53 := (and #47 #50)
-#56 := (and #41 #50)
-#68 := (not #53)
-#77 := (or #68 #56 #59)
-#80 := (not #77)
-#14 := (= f5 f1)
-#11 := (= f4 f1)
-#17 := (and #11 #14)
-#9 := (= f3 f1)
-#16 := (and #9 #14)
-#18 := (or #16 #17)
-#12 := (or #9 #11)
-#15 := (and #12 #14)
-#19 := (implies #15 #18)
-#20 := (not #19)
-#83 := (iff #20 #80)
-#62 := (or #56 #59)
-#69 := (or #68 #62)
-#74 := (not #69)
-#81 := (iff #74 #80)
-#78 := (iff #69 #77)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#75 := (iff #20 #74)
-#72 := (iff #19 #69)
-#65 := (implies #53 #62)
-#70 := (iff #65 #69)
-#71 := [rewrite]: #70
-#66 := (iff #19 #65)
-#63 := (iff #18 #62)
-#60 := (iff #17 #59)
-#51 := (iff #14 #50)
-#52 := [rewrite]: #51
-#45 := (iff #11 #44)
-#46 := [rewrite]: #45
-#61 := [monotonicity #46 #52]: #60
-#57 := (iff #16 #56)
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#58 := [monotonicity #43 #52]: #57
-#64 := [monotonicity #58 #61]: #63
-#54 := (iff #15 #53)
-#48 := (iff #12 #47)
-#49 := [monotonicity #43 #46]: #48
-#55 := [monotonicity #49 #52]: #54
-#67 := [monotonicity #55 #64]: #66
-#73 := [trans #67 #71]: #72
-#76 := [monotonicity #73]: #75
-#84 := [trans #76 #82]: #83
-#40 := [asserted]: #20
-#85 := [mp #40 #84]: #80
-#86 := [not-or-elim #85]: #53
-#88 := [and-elim #86]: #50
-#99 := [iff-true #88]: #98
-#115 := [monotonicity #99]: #114
-#119 := [trans #115 #117]: #118
-#122 := [monotonicity #119]: #121
-#92 := [not-or-elim #85]: #91
-#123 := [mp #92 #122]: #120
-#125 := [iff-false #123]: #124
-#111 := (iff #41 false)
-#107 := (not #41)
-#89 := (not #56)
-#108 := (iff #89 #107)
-#105 := (iff #56 #41)
-#100 := (and #41 true)
-#103 := (iff #100 #41)
-#104 := [rewrite]: #103
-#101 := (iff #56 #100)
-#102 := [monotonicity #99]: #101
-#106 := [trans #102 #104]: #105
-#109 := [monotonicity #106]: #108
-#90 := [not-or-elim #85]: #89
-#110 := [mp #90 #109]: #107
-#112 := [iff-false #110]: #111
-#128 := [monotonicity #112 #125]: #127
-#132 := [trans #128 #130]: #131
-#87 := [and-elim #86]: #47
-[mp #87 #132]: false
-unsat
-3be7256d2b13897c8029d9190e000fab6c7cea0c 127 0
-#2 := false
-decl f5 :: S1
-#13 := f5
-decl f1 :: S1
-#4 := f1
-#50 := (= f1 f5)
-#94 := (not #50)
-decl f4 :: S1
-#10 := f4
-#44 := (= f1 f4)
-#99 := (not #44)
-#95 := (or #99 #94)
-#92 := (not #95)
-decl f3 :: S1
-#8 := f3
-#41 := (= f1 f3)
-#98 := (not #41)
-#100 := (or #98 #99)
-#101 := (not #100)
-#143 := [hypothesis]: #101
-#133 := (or #100 #44)
-#134 := [def-axiom]: #133
-#144 := [unit-resolution #134 #143]: #44
-#64 := (or #41 #50)
-#131 := (or #100 #41)
-#132 := [def-axiom]: #131
-#145 := [unit-resolution #132 #143]: #41
-#137 := (or #64 #98)
-#138 := [def-axiom]: #137
-#146 := [unit-resolution #138 #145]: #64
-#112 := (not #64)
-#113 := (or #99 #112)
-#70 := (and #44 #64)
-#88 := (not #70)
-#122 := (iff #88 #113)
-#114 := (not #113)
-#117 := (not #114)
-#120 := (iff #117 #113)
-#121 := [rewrite]: #120
-#118 := (iff #88 #117)
-#115 := (iff #70 #114)
-#116 := [rewrite]: #115
-#119 := [monotonicity #116]: #118
-#123 := [trans #119 #121]: #122
-#56 := (and #44 #50)
-#47 := (and #41 #44)
-#61 := (or #47 #56)
-#78 := (not #61)
-#79 := (or #78 #70)
-#84 := (not #79)
-#11 := (= f4 f1)
-#14 := (= f5 f1)
-#9 := (= f3 f1)
-#17 := (or #9 #14)
-#18 := (and #17 #11)
-#15 := (and #14 #11)
-#12 := (and #9 #11)
-#16 := (or #12 #15)
-#19 := (implies #16 #18)
-#20 := (not #19)
-#85 := (iff #20 #84)
-#82 := (iff #19 #79)
-#75 := (implies #61 #70)
-#80 := (iff #75 #79)
-#81 := [rewrite]: #80
-#76 := (iff #19 #75)
-#73 := (iff #18 #70)
-#67 := (and #64 #44)
-#71 := (iff #67 #70)
-#72 := [rewrite]: #71
-#68 := (iff #18 #67)
-#45 := (iff #11 #44)
-#46 := [rewrite]: #45
-#65 := (iff #17 #64)
-#51 := (iff #14 #50)
-#52 := [rewrite]: #51
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#66 := [monotonicity #43 #52]: #65
-#69 := [monotonicity #66 #46]: #68
-#74 := [trans #69 #72]: #73
-#62 := (iff #16 #61)
-#59 := (iff #15 #56)
-#53 := (and #50 #44)
-#57 := (iff #53 #56)
-#58 := [rewrite]: #57
-#54 := (iff #15 #53)
-#55 := [monotonicity #52 #46]: #54
-#60 := [trans #55 #58]: #59
-#48 := (iff #12 #47)
-#49 := [monotonicity #43 #46]: #48
-#63 := [monotonicity #49 #60]: #62
-#77 := [monotonicity #63 #74]: #76
-#83 := [trans #77 #81]: #82
-#86 := [monotonicity #83]: #85
-#40 := [asserted]: #20
-#89 := [mp #40 #86]: #84
-#90 := [not-or-elim #89]: #88
-#124 := [mp #90 #123]: #113
-#147 := [unit-resolution #124 #146 #144]: false
-#148 := [lemma #147]: #100
-#106 := (or #92 #101)
-#109 := (iff #61 #106)
-#103 := (or #101 #92)
-#107 := (iff #103 #106)
-#108 := [rewrite]: #107
-#104 := (iff #61 #103)
-#93 := (iff #56 #92)
-#102 := [rewrite]: #93
-#96 := (iff #47 #101)
-#97 := [rewrite]: #96
-#105 := [monotonicity #97 #102]: #104
-#110 := [trans #105 #108]: #109
-#87 := [not-or-elim #89]: #61
-#111 := [mp #87 #110]: #106
-#149 := [unit-resolution #111 #148]: #92
-#127 := (or #95 #50)
-#128 := [def-axiom]: #127
-#150 := [unit-resolution #128 #149]: #50
-#125 := (or #95 #44)
-#126 := [def-axiom]: #125
-#151 := [unit-resolution #126 #149]: #44
-#152 := [unit-resolution #124 #151]: #112
-#139 := (or #64 #94)
-#140 := [def-axiom]: #139
-[unit-resolution #140 #152 #150]: false
-unsat
-e4d3d98d52d5e02451d4a933a7ae69eccde69dc7 66 0
-#2 := false
-decl f3 :: S1
-#8 := f3
-decl f1 :: S1
-#4 := f1
-#36 := (= f1 f3)
-decl f4 :: S1
-#10 := f4
-#39 := (= f1 f4)
-#45 := (not #36)
-#46 := (or #45 #39)
-#54 := (not #46)
-#55 := (or #36 #54)
-#85 := (iff #55 #54)
-#80 := (or false #54)
-#83 := (iff #80 #54)
-#84 := [rewrite]: #83
-#81 := (iff #55 #80)
-#78 := (iff #36 false)
-#63 := (not #55)
-#64 := (or #36 #63)
-#69 := (not #64)
-#9 := (= f3 f1)
-#11 := (= f4 f1)
-#12 := (implies #9 #11)
-#13 := (implies #12 #9)
-#14 := (implies #13 #9)
-#15 := (not #14)
-#70 := (iff #15 #69)
-#67 := (iff #14 #64)
-#60 := (implies #55 #36)
-#65 := (iff #60 #64)
-#66 := [rewrite]: #65
-#61 := (iff #14 #60)
-#37 := (iff #9 #36)
-#38 := [rewrite]: #37
-#58 := (iff #13 #55)
-#51 := (implies #46 #36)
-#56 := (iff #51 #55)
-#57 := [rewrite]: #56
-#52 := (iff #13 #51)
-#49 := (iff #12 #46)
-#42 := (implies #36 #39)
-#47 := (iff #42 #46)
-#48 := [rewrite]: #47
-#43 := (iff #12 #42)
-#40 := (iff #11 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #38 #41]: #43
-#50 := [trans #44 #48]: #49
-#53 := [monotonicity #50 #38]: #52
-#59 := [trans #53 #57]: #58
-#62 := [monotonicity #59 #38]: #61
-#68 := [trans #62 #66]: #67
-#71 := [monotonicity #68]: #70
-#35 := [asserted]: #15
-#74 := [mp #35 #71]: #69
-#72 := [not-or-elim #74]: #45
-#79 := [iff-false #72]: #78
-#82 := [monotonicity #79]: #81
-#86 := [trans #82 #84]: #85
-#73 := [not-or-elim #74]: #55
-#87 := [mp #73 #86]: #54
-#76 := [not-or-elim #87]: #36
-[unit-resolution #72 #76]: false
-unsat
-19c46603d78602c88e567210d895a32ffee713db 157 0
-#2 := false
-decl f5 :: S1
-#13 := f5
-decl f1 :: S1
-#4 := f1
-#56 := (= f1 f5)
-#62 := (not #56)
-decl f4 :: S1
-#10 := f4
-#44 := (= f1 f4)
-#63 := (or #44 #62)
-#102 := (not #63)
-decl f3 :: S1
-#8 := f3
-#41 := (= f1 f3)
-#50 := (not #41)
-#51 := (or #50 #44)
-#120 := (not #44)
-#101 := (not #51)
-#155 := [hypothesis]: #101
-#130 := (or #51 #120)
-#131 := [def-axiom]: #130
-#156 := [unit-resolution #131 #155]: #120
-#71 := (or #41 #56)
-#128 := (or #51 #41)
-#129 := [def-axiom]: #128
-#157 := [unit-resolution #129 #155]: #41
-#114 := (or #71 #50)
-#115 := [def-axiom]: #114
-#158 := [unit-resolution #115 #157]: #71
-#77 := (not #71)
-#78 := (or #44 #77)
-#103 := (or #101 #102)
-#140 := (or #103 #51)
-#141 := [def-axiom]: #140
-#159 := [unit-resolution #141 #155]: #103
-#104 := (not #103)
-#149 := (or #78 #104)
-#110 := (iff #78 #103)
-#68 := (and #51 #63)
-#89 := (not #68)
-#90 := (iff #78 #89)
-#111 := (iff #90 #110)
-#108 := (iff #89 #103)
-#96 := (not #104)
-#106 := (iff #96 #103)
-#107 := [rewrite]: #106
-#98 := (iff #89 #96)
-#99 := (iff #68 #104)
-#100 := [rewrite]: #99
-#105 := [monotonicity #100]: #98
-#109 := [trans #105 #107]: #108
-#112 := [monotonicity #109]: #111
-#11 := (= f4 f1)
-#14 := (= f5 f1)
-#9 := (= f3 f1)
-#17 := (or #9 #14)
-#18 := (implies #17 #11)
-#15 := (implies #14 #11)
-#12 := (implies #9 #11)
-#16 := (and #12 #15)
-#19 := (iff #16 #18)
-#20 := (not #19)
-#93 := (iff #20 #90)
-#83 := (iff #68 #78)
-#86 := (not #83)
-#91 := (iff #86 #90)
-#92 := [rewrite]: #91
-#87 := (iff #20 #86)
-#84 := (iff #19 #83)
-#81 := (iff #18 #78)
-#74 := (implies #71 #44)
-#79 := (iff #74 #78)
-#80 := [rewrite]: #79
-#75 := (iff #18 #74)
-#45 := (iff #11 #44)
-#46 := [rewrite]: #45
-#72 := (iff #17 #71)
-#57 := (iff #14 #56)
-#58 := [rewrite]: #57
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#73 := [monotonicity #43 #58]: #72
-#76 := [monotonicity #73 #46]: #75
-#82 := [trans #76 #80]: #81
-#69 := (iff #16 #68)
-#66 := (iff #15 #63)
-#59 := (implies #56 #44)
-#64 := (iff #59 #63)
-#65 := [rewrite]: #64
-#60 := (iff #15 #59)
-#61 := [monotonicity #58 #46]: #60
-#67 := [trans #61 #65]: #66
-#54 := (iff #12 #51)
-#47 := (implies #41 #44)
-#52 := (iff #47 #51)
-#53 := [rewrite]: #52
-#48 := (iff #12 #47)
-#49 := [monotonicity #43 #46]: #48
-#55 := [trans #49 #53]: #54
-#70 := [monotonicity #55 #67]: #69
-#85 := [monotonicity #70 #82]: #84
-#88 := [monotonicity #85]: #87
-#94 := [trans #88 #92]: #93
-#40 := [asserted]: #20
-#97 := [mp #40 #94]: #90
-#113 := [mp #97 #112]: #110
-#146 := (not #110)
-#147 := (or #78 #104 #146)
-#148 := [def-axiom]: #147
-#150 := [unit-resolution #148 #113]: #149
-#160 := [unit-resolution #150 #159]: #78
-#125 := (not #78)
-#126 := (or #125 #44 #77)
-#127 := [def-axiom]: #126
-#161 := [unit-resolution #127 #160 #158 #156]: false
-#162 := [lemma #161]: #51
-#163 := [hypothesis]: #125
-#121 := (or #78 #120)
-#122 := [def-axiom]: #121
-#164 := [unit-resolution #122 #163]: #120
-#165 := [unit-resolution #150 #163]: #104
-#142 := (or #103 #63)
-#143 := [def-axiom]: #142
-#166 := [unit-resolution #143 #165]: #63
-#123 := (or #78 #71)
-#124 := [def-axiom]: #123
-#167 := [unit-resolution #124 #163]: #71
-#132 := (or #101 #50 #44)
-#133 := [def-axiom]: #132
-#168 := [unit-resolution #133 #164 #162]: #50
-#118 := (or #77 #41 #56)
-#119 := [def-axiom]: #118
-#169 := [unit-resolution #119 #168 #167]: #56
-#138 := (or #102 #44 #62)
-#139 := [def-axiom]: #138
-#170 := [unit-resolution #139 #169 #166 #164]: false
-#171 := [lemma #170]: #78
-#153 := (or #125 #103)
-#151 := (or #125 #103 #146)
-#152 := [def-axiom]: #151
-#154 := [unit-resolution #152 #113]: #153
-#172 := [unit-resolution #154 #171]: #103
-#144 := (or #104 #101 #102)
-#145 := [def-axiom]: #144
-#173 := [unit-resolution #145 #172 #162]: #102
-#136 := (or #63 #56)
-#137 := [def-axiom]: #136
-#174 := [unit-resolution #137 #173]: #56
-#134 := (or #63 #120)
-#135 := [def-axiom]: #134
-#175 := [unit-resolution #135 #173]: #120
-#176 := [unit-resolution #127 #175 #171]: #77
-#116 := (or #71 #62)
-#117 := [def-axiom]: #116
-[unit-resolution #117 #176 #174]: false
-unsat
-9ca0ea6fd7baaf9ab5e21ea28520ab880b00ee9a 114 0
-#2 := false
-decl f5 :: S1
-#13 := f5
-decl f1 :: S1
-#4 := f1
-#49 := (= f1 f5)
-decl f4 :: S1
-#10 := f4
-#43 := (= f1 f4)
-#64 := (not #43)
-decl f3 :: S1
-#8 := f3
-#40 := (= f1 f3)
-#73 := (not #40)
-#91 := (or #73 #64 #49)
-#46 := (and #40 #43)
-#55 := (not #46)
-#56 := (or #55 #49)
-#85 := (not #56)
-#97 := (iff #85 #91)
-#132 := (iff #97 false)
-#124 := (not #91)
-#127 := (iff #124 #91)
-#130 := (iff #127 false)
-#131 := [rewrite]: #130
-#128 := (iff #97 #127)
-#125 := (iff #85 #124)
-#122 := (iff #56 #91)
-#110 := (or #73 #64)
-#117 := (or #110 #49)
-#120 := (iff #117 #91)
-#121 := [rewrite]: #120
-#118 := (iff #56 #117)
-#115 := (iff #55 #110)
-#111 := (not #110)
-#108 := (not #111)
-#107 := (iff #108 #110)
-#114 := [rewrite]: #107
-#109 := (iff #55 #108)
-#112 := (iff #46 #111)
-#113 := [rewrite]: #112
-#106 := [monotonicity #113]: #109
-#116 := [trans #106 #114]: #115
-#119 := [monotonicity #116]: #118
-#123 := [trans #119 #121]: #122
-#126 := [monotonicity #123]: #125
-#129 := [monotonicity #126]: #128
-#133 := [trans #129 #131]: #132
-#14 := (= f5 f1)
-#11 := (= f4 f1)
-#16 := (implies #11 #14)
-#9 := (= f3 f1)
-#17 := (implies #9 #16)
-#12 := (and #9 #11)
-#15 := (implies #12 #14)
-#18 := (iff #15 #17)
-#19 := (not #18)
-#102 := (iff #19 #97)
-#65 := (or #64 #49)
-#74 := (or #73 #65)
-#86 := (iff #74 #85)
-#100 := (iff #86 #97)
-#94 := (iff #91 #85)
-#98 := (iff #94 #97)
-#99 := [rewrite]: #98
-#95 := (iff #86 #94)
-#92 := (iff #74 #91)
-#93 := [rewrite]: #92
-#96 := [monotonicity #93]: #95
-#101 := [trans #96 #99]: #100
-#89 := (iff #19 #86)
-#79 := (iff #56 #74)
-#82 := (not #79)
-#87 := (iff #82 #86)
-#88 := [rewrite]: #87
-#83 := (iff #19 #82)
-#80 := (iff #18 #79)
-#77 := (iff #17 #74)
-#70 := (implies #40 #65)
-#75 := (iff #70 #74)
-#76 := [rewrite]: #75
-#71 := (iff #17 #70)
-#68 := (iff #16 #65)
-#61 := (implies #43 #49)
-#66 := (iff #61 #65)
-#67 := [rewrite]: #66
-#62 := (iff #16 #61)
-#50 := (iff #14 #49)
-#51 := [rewrite]: #50
-#44 := (iff #11 #43)
-#45 := [rewrite]: #44
-#63 := [monotonicity #45 #51]: #62
-#69 := [trans #63 #67]: #68
-#41 := (iff #9 #40)
-#42 := [rewrite]: #41
-#72 := [monotonicity #42 #69]: #71
-#78 := [trans #72 #76]: #77
-#59 := (iff #15 #56)
-#52 := (implies #46 #49)
-#57 := (iff #52 #56)
-#58 := [rewrite]: #57
-#53 := (iff #15 #52)
-#47 := (iff #12 #46)
-#48 := [monotonicity #42 #45]: #47
-#54 := [monotonicity #48 #51]: #53
-#60 := [trans #54 #58]: #59
-#81 := [monotonicity #60 #78]: #80
-#84 := [monotonicity #81]: #83
-#90 := [trans #84 #88]: #89
-#103 := [trans #90 #101]: #102
-#39 := [asserted]: #19
-#104 := [mp #39 #103]: #97
-[mp #104 #133]: false
-unsat
-04315913425b7fdaa9756cb775e4e6e81e279b08 198 0
-#2 := false
-decl f5 :: S1
-#14 := f5
-decl f1 :: S1
-#4 := f1
-#68 := (= f1 f5)
-decl f3 :: S1
-#8 := f3
-#44 := (= f1 f3)
-#89 := (and #44 #68)
-#95 := (not #89)
-decl f4 :: S1
-#10 := f4
-#47 := (= f1 f4)
-#96 := (or #47 #95)
-#217 := (iff #96 false)
-#212 := (or false false)
-#215 := (iff #212 false)
-#216 := [rewrite]: #215
-#213 := (iff #96 #212)
-#210 := (iff #95 false)
-#1 := true
-#205 := (not true)
-#208 := (iff #205 false)
-#209 := [rewrite]: #208
-#206 := (iff #95 #205)
-#203 := (iff #89 true)
-#198 := (and true true)
-#201 := (iff #198 true)
-#202 := [rewrite]: #201
-#199 := (iff #89 #198)
-#196 := (iff #68 true)
-#74 := (not #68)
-#75 := (or #47 #74)
-#83 := (not #75)
-#84 := (or #47 #83)
-#193 := (iff #84 #68)
-#188 := (or false #68)
-#191 := (iff #188 #68)
-#192 := [rewrite]: #191
-#189 := (iff #84 #188)
-#186 := (iff #83 #68)
-#181 := (not #74)
-#184 := (iff #181 #68)
-#185 := [rewrite]: #184
-#182 := (iff #83 #181)
-#179 := (iff #75 #74)
-#174 := (or false #74)
-#177 := (iff #174 #74)
-#178 := [rewrite]: #177
-#175 := (iff #75 #174)
-#148 := (iff #47 false)
-#140 := (not #47)
-#104 := (not #96)
-#113 := (not #84)
-#53 := (not #44)
-#54 := (or #53 #47)
-#62 := (not #54)
-#63 := (or #47 #62)
-#122 := (not #63)
-#131 := (or #47 #122 #113 #104)
-#134 := (not #131)
-#11 := (= f4 f1)
-#15 := (= f5 f1)
-#9 := (= f3 f1)
-#18 := (and #9 #15)
-#19 := (implies #18 #11)
-#20 := (implies #19 #11)
-#16 := (implies #15 #11)
-#17 := (implies #16 #11)
-#21 := (implies #17 #20)
-#12 := (implies #9 #11)
-#13 := (implies #12 #11)
-#22 := (implies #13 #21)
-#23 := (not #22)
-#137 := (iff #23 #134)
-#105 := (or #47 #104)
-#114 := (or #113 #105)
-#123 := (or #122 #114)
-#128 := (not #123)
-#135 := (iff #128 #134)
-#132 := (iff #123 #131)
-#133 := [rewrite]: #132
-#136 := [monotonicity #133]: #135
-#129 := (iff #23 #128)
-#126 := (iff #22 #123)
-#119 := (implies #63 #114)
-#124 := (iff #119 #123)
-#125 := [rewrite]: #124
-#120 := (iff #22 #119)
-#117 := (iff #21 #114)
-#110 := (implies #84 #105)
-#115 := (iff #110 #114)
-#116 := [rewrite]: #115
-#111 := (iff #21 #110)
-#108 := (iff #20 #105)
-#101 := (implies #96 #47)
-#106 := (iff #101 #105)
-#107 := [rewrite]: #106
-#102 := (iff #20 #101)
-#48 := (iff #11 #47)
-#49 := [rewrite]: #48
-#99 := (iff #19 #96)
-#92 := (implies #89 #47)
-#97 := (iff #92 #96)
-#98 := [rewrite]: #97
-#93 := (iff #19 #92)
-#90 := (iff #18 #89)
-#69 := (iff #15 #68)
-#70 := [rewrite]: #69
-#45 := (iff #9 #44)
-#46 := [rewrite]: #45
-#91 := [monotonicity #46 #70]: #90
-#94 := [monotonicity #91 #49]: #93
-#100 := [trans #94 #98]: #99
-#103 := [monotonicity #100 #49]: #102
-#109 := [trans #103 #107]: #108
-#87 := (iff #17 #84)
-#80 := (implies #75 #47)
-#85 := (iff #80 #84)
-#86 := [rewrite]: #85
-#81 := (iff #17 #80)
-#78 := (iff #16 #75)
-#71 := (implies #68 #47)
-#76 := (iff #71 #75)
-#77 := [rewrite]: #76
-#72 := (iff #16 #71)
-#73 := [monotonicity #70 #49]: #72
-#79 := [trans #73 #77]: #78
-#82 := [monotonicity #79 #49]: #81
-#88 := [trans #82 #86]: #87
-#112 := [monotonicity #88 #109]: #111
-#118 := [trans #112 #116]: #117
-#66 := (iff #13 #63)
-#59 := (implies #54 #47)
-#64 := (iff #59 #63)
-#65 := [rewrite]: #64
-#60 := (iff #13 #59)
-#57 := (iff #12 #54)
-#50 := (implies #44 #47)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #12 #50)
-#52 := [monotonicity #46 #49]: #51
-#58 := [trans #52 #56]: #57
-#61 := [monotonicity #58 #49]: #60
-#67 := [trans #61 #65]: #66
-#121 := [monotonicity #67 #118]: #120
-#127 := [trans #121 #125]: #126
-#130 := [monotonicity #127]: #129
-#138 := [trans #130 #136]: #137
-#43 := [asserted]: #23
-#139 := [mp #43 #138]: #134
-#141 := [not-or-elim #139]: #140
-#149 := [iff-false #141]: #148
-#176 := [monotonicity #149]: #175
-#180 := [trans #176 #178]: #179
-#183 := [monotonicity #180]: #182
-#187 := [trans #183 #185]: #186
-#190 := [monotonicity #149 #187]: #189
-#194 := [trans #190 #192]: #193
-#143 := [not-or-elim #139]: #84
-#195 := [mp #143 #194]: #68
-#197 := [iff-true #195]: #196
-#172 := (iff #44 true)
-#169 := (iff #63 #44)
-#164 := (or false #44)
-#167 := (iff #164 #44)
-#168 := [rewrite]: #167
-#165 := (iff #63 #164)
-#162 := (iff #62 #44)
-#157 := (not #53)
-#160 := (iff #157 #44)
-#161 := [rewrite]: #160
-#158 := (iff #62 #157)
-#155 := (iff #54 #53)
-#150 := (or #53 false)
-#153 := (iff #150 #53)
-#154 := [rewrite]: #153
-#151 := (iff #54 #150)
-#152 := [monotonicity #149]: #151
-#156 := [trans #152 #154]: #155
-#159 := [monotonicity #156]: #158
-#163 := [trans #159 #161]: #162
-#166 := [monotonicity #149 #163]: #165
-#170 := [trans #166 #168]: #169
-#142 := [not-or-elim #139]: #63
-#171 := [mp #142 #170]: #44
-#173 := [iff-true #171]: #172
-#200 := [monotonicity #173 #197]: #199
-#204 := [trans #200 #202]: #203
-#207 := [monotonicity #204]: #206
-#211 := [trans #207 #209]: #210
-#214 := [monotonicity #149 #211]: #213
-#218 := [trans #214 #216]: #217
-#144 := [not-or-elim #139]: #96
-[mp #144 #218]: false
-unsat
-a3110cebbaf91f1580f58fbd5e9552fa7ad95997 134 0
-#2 := false
-decl f5 :: S1
-#14 := f5
-decl f1 :: S1
-#4 := f1
-#62 := (= f1 f5)
+a659f050ece3306f2b1d4dcfecadbe7f96ac25b7 22 0
+#2 := false
+decl f1 :: S1
+#3 := f1
 decl f3 :: S1
-#8 := f3
-#44 := (= f1 f3)
-#77 := (and #44 #62)
-#83 := (not #77)
-decl f4 :: S1
-#10 := f4
-#47 := (= f1 f4)
-#84 := (or #47 #83)
-#153 := (iff #84 false)
-#148 := (or false false)
-#151 := (iff #148 false)
-#152 := [rewrite]: #151
-#149 := (iff #84 #148)
-#146 := (iff #83 false)
-#1 := true
-#141 := (not true)
-#144 := (iff #141 false)
-#145 := [rewrite]: #144
-#142 := (iff #83 #141)
-#139 := (iff #77 true)
-#134 := (and true true)
-#137 := (iff #134 true)
-#138 := [rewrite]: #137
-#135 := (iff #77 #134)
-#132 := (iff #62 true)
-#89 := (not #84)
-#68 := (not #62)
-#53 := (not #44)
-#111 := (or #53 #47 #68 #89)
-#114 := (not #111)
-#11 := (= f4 f1)
-#15 := (= f5 f1)
-#9 := (= f3 f1)
-#18 := (and #9 #15)
-#19 := (implies #18 #11)
-#20 := (not #19)
-#16 := (implies #15 #11)
-#17 := (not #16)
-#21 := (implies #17 #20)
-#12 := (implies #9 #11)
-#13 := (not #12)
-#22 := (implies #13 #21)
-#23 := (not #22)
-#117 := (iff #23 #114)
-#69 := (or #47 #68)
-#95 := (or #69 #89)
-#54 := (or #53 #47)
-#103 := (or #54 #95)
-#108 := (not #103)
-#115 := (iff #108 #114)
-#112 := (iff #103 #111)
-#113 := [rewrite]: #112
-#116 := [monotonicity #113]: #115
-#109 := (iff #23 #108)
-#106 := (iff #22 #103)
-#59 := (not #54)
-#100 := (implies #59 #95)
-#104 := (iff #100 #103)
-#105 := [rewrite]: #104
-#101 := (iff #22 #100)
-#98 := (iff #21 #95)
-#74 := (not #69)
-#92 := (implies #74 #89)
-#96 := (iff #92 #95)
-#97 := [rewrite]: #96
-#93 := (iff #21 #92)
-#90 := (iff #20 #89)
-#87 := (iff #19 #84)
-#80 := (implies #77 #47)
-#85 := (iff #80 #84)
-#86 := [rewrite]: #85
-#81 := (iff #19 #80)
-#48 := (iff #11 #47)
-#49 := [rewrite]: #48
-#78 := (iff #18 #77)
-#63 := (iff #15 #62)
-#64 := [rewrite]: #63
-#45 := (iff #9 #44)
-#46 := [rewrite]: #45
-#79 := [monotonicity #46 #64]: #78
-#82 := [monotonicity #79 #49]: #81
-#88 := [trans #82 #86]: #87
-#91 := [monotonicity #88]: #90
-#75 := (iff #17 #74)
-#72 := (iff #16 #69)
-#65 := (implies #62 #47)
-#70 := (iff #65 #69)
-#71 := [rewrite]: #70
-#66 := (iff #16 #65)
-#67 := [monotonicity #64 #49]: #66
-#73 := [trans #67 #71]: #72
-#76 := [monotonicity #73]: #75
-#94 := [monotonicity #76 #91]: #93
-#99 := [trans #94 #97]: #98
-#60 := (iff #13 #59)
-#57 := (iff #12 #54)
-#50 := (implies #44 #47)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #12 #50)
-#52 := [monotonicity #46 #49]: #51
-#58 := [trans #52 #56]: #57
-#61 := [monotonicity #58]: #60
-#102 := [monotonicity #61 #99]: #101
-#107 := [trans #102 #105]: #106
-#110 := [monotonicity #107]: #109
-#118 := [trans #110 #116]: #117
-#43 := [asserted]: #23
-#119 := [mp #43 #118]: #114
-#123 := [not-or-elim #119]: #62
-#133 := [iff-true #123]: #132
-#128 := (iff #44 true)
-#120 := [not-or-elim #119]: #44
-#129 := [iff-true #120]: #128
-#136 := [monotonicity #129 #133]: #135
-#140 := [trans #136 #138]: #139
-#143 := [monotonicity #140]: #142
-#147 := [trans #143 #145]: #146
-#130 := (iff #47 false)
-#121 := (not #47)
-#122 := [not-or-elim #119]: #121
-#131 := [iff-false #122]: #130
-#150 := [monotonicity #131 #147]: #149
-#154 := [trans #150 #152]: #153
-#124 := [not-or-elim #119]: #84
-[mp #124 #154]: false
-unsat
-d522bffbdc6af87260d2b830a506e89f66c0f6c5 162 0
-#2 := false
-decl f5 :: S1
-#12 := f5
-decl f1 :: S1
-#4 := f1
-#47 := (= f1 f5)
-decl f3 :: S1
-#8 := f3
-#41 := (= f1 f3)
-#56 := (not #41)
-#73 := (or #56 #47)
-#100 := (not #73)
-decl f4 :: S1
-#10 := f4
-#44 := (= f1 f4)
-#65 := (or #56 #44)
-#99 := (not #65)
-#101 := (or #99 #100)
-#96 := (not #47)
-#94 := (not #44)
-#103 := (or #94 #96)
-#104 := (not #103)
-#107 := (or #56 #104)
-#110 := (not #107)
-#102 := (not #101)
-#161 := [hypothesis]: #102
-#155 := (or #101 #110)
-#116 := (iff #101 #107)
-#50 := (and #44 #47)
-#57 := (or #56 #50)
-#87 := (not #57)
-#78 := (and #65 #73)
-#88 := (iff #78 #87)
-#119 := (iff #88 #116)
-#113 := (iff #102 #110)
-#117 := (iff #113 #116)
-#118 := [rewrite]: #117
-#114 := (iff #88 #113)
-#111 := (iff #87 #110)
-#108 := (iff #57 #107)
-#105 := (iff #50 #104)
-#106 := [rewrite]: #105
-#109 := [monotonicity #106]: #108
-#112 := [monotonicity #109]: #111
-#97 := (iff #78 #102)
-#98 := [rewrite]: #97
-#115 := [monotonicity #98 #112]: #114
-#120 := [trans #115 #118]: #119
-#13 := (= f5 f1)
-#9 := (= f3 f1)
-#17 := (implies #9 #13)
-#11 := (= f4 f1)
-#16 := (implies #9 #11)
-#18 := (and #16 #17)
-#14 := (and #11 #13)
-#15 := (implies #9 #14)
-#19 := (iff #15 #18)
-#20 := (not #19)
-#91 := (iff #20 #88)
-#81 := (iff #57 #78)
-#84 := (not #81)
-#89 := (iff #84 #88)
-#90 := [rewrite]: #89
-#85 := (iff #20 #84)
-#82 := (iff #19 #81)
-#79 := (iff #18 #78)
-#76 := (iff #17 #73)
-#70 := (implies #41 #47)
-#74 := (iff #70 #73)
-#75 := [rewrite]: #74
-#71 := (iff #17 #70)
-#48 := (iff #13 #47)
-#49 := [rewrite]: #48
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#72 := [monotonicity #43 #49]: #71
-#77 := [trans #72 #75]: #76
-#68 := (iff #16 #65)
-#62 := (implies #41 #44)
-#66 := (iff #62 #65)
-#67 := [rewrite]: #66
-#63 := (iff #16 #62)
-#45 := (iff #11 #44)
-#46 := [rewrite]: #45
-#64 := [monotonicity #43 #46]: #63
-#69 := [trans #64 #67]: #68
-#80 := [monotonicity #69 #77]: #79
-#60 := (iff #15 #57)
-#53 := (implies #41 #50)
-#58 := (iff #53 #57)
-#59 := [rewrite]: #58
-#54 := (iff #15 #53)
-#51 := (iff #14 #50)
-#52 := [monotonicity #46 #49]: #51
-#55 := [monotonicity #43 #52]: #54
-#61 := [trans #55 #59]: #60
-#83 := [monotonicity #61 #80]: #82
-#86 := [monotonicity #83]: #85
-#92 := [trans #86 #90]: #91
-#40 := [asserted]: #20
-#95 := [mp #40 #92]: #88
-#121 := [mp #95 #120]: #116
-#152 := (not #116)
-#153 := (or #101 #110 #152)
-#154 := [def-axiom]: #153
-#156 := [unit-resolution #154 #121]: #155
-#162 := [unit-resolution #156 #161]: #110
-#148 := (or #107 #103)
-#149 := [def-axiom]: #148
-#163 := [unit-resolution #149 #162]: #103
-#134 := (or #101 #65)
-#135 := [def-axiom]: #134
-#164 := [unit-resolution #135 #161]: #65
-#146 := (or #107 #41)
-#147 := [def-axiom]: #146
-#165 := [unit-resolution #147 #162]: #41
-#126 := (or #99 #56 #44)
-#127 := [def-axiom]: #126
-#166 := [unit-resolution #127 #165 #164]: #44
-#136 := (or #101 #73)
-#137 := [def-axiom]: #136
-#167 := [unit-resolution #137 #161]: #73
-#132 := (or #100 #56 #47)
-#133 := [def-axiom]: #132
-#168 := [unit-resolution #133 #165 #167]: #47
-#144 := (or #104 #94 #96)
-#145 := [def-axiom]: #144
-#169 := [unit-resolution #145 #168 #166 #163]: false
-#170 := [lemma #169]: #101
-#159 := (or #102 #107)
-#157 := (or #102 #107 #152)
-#158 := [def-axiom]: #157
-#160 := [unit-resolution #158 #121]: #159
-#176 := [unit-resolution #160 #170]: #107
-#171 := [hypothesis]: #56
-#122 := (or #65 #41)
-#123 := [def-axiom]: #122
-#172 := [unit-resolution #123 #171]: #65
-#128 := (or #73 #41)
-#129 := [def-axiom]: #128
-#173 := [unit-resolution #129 #171]: #73
-#138 := (or #102 #99 #100)
-#139 := [def-axiom]: #138
-#174 := [unit-resolution #139 #173 #172 #170]: false
-#175 := [lemma #174]: #41
-#150 := (or #110 #56 #104)
-#151 := [def-axiom]: #150
-#177 := [unit-resolution #151 #175 #176]: #104
-#140 := (or #103 #44)
-#141 := [def-axiom]: #140
-#178 := [unit-resolution #141 #177]: #44
-#124 := (or #65 #94)
-#125 := [def-axiom]: #124
-#179 := [unit-resolution #125 #178]: #65
-#142 := (or #103 #47)
-#143 := [def-axiom]: #142
-#180 := [unit-resolution #143 #177]: #47
-#130 := (or #73 #96)
-#131 := [def-axiom]: #130
-#181 := [unit-resolution #131 #180]: #73
-[unit-resolution #139 #181 #179 #170]: false
-unsat
-f29fbcc0ceaf6bd7f24274c3de5b8c954ec638b1 54 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#12 := (implies #11 #9)
-#13 := (implies #9 #12)
-#14 := (not #13)
-#71 := (iff #14 false)
-#38 := (= f1 f4)
-#44 := (not #38)
-#35 := (= f1 f3)
-#45 := (or #35 #44)
-#53 := (not #35)
-#54 := (or #53 #45)
-#59 := (not #54)
-#69 := (iff #59 false)
-#1 := true
-#64 := (not true)
-#67 := (iff #64 false)
-#68 := [rewrite]: #67
-#65 := (iff #59 #64)
-#62 := (iff #54 true)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#70 := [trans #66 #68]: #69
-#60 := (iff #14 #59)
-#57 := (iff #13 #54)
-#50 := (implies #35 #45)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #13 #50)
-#48 := (iff #12 #45)
-#41 := (implies #38 #35)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #12 #41)
-#36 := (iff #9 #35)
-#37 := [rewrite]: #36
-#39 := (iff #11 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40 #37]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #37 #49]: #51
-#58 := [trans #52 #56]: #57
-#61 := [monotonicity #58]: #60
-#72 := [trans #61 #70]: #71
-#34 := [asserted]: #14
-[mp #34 #72]: false
-unsat
-d58edad648d31ef919b96bbaf6580f1a23405517 144 0
-#2 := false
-decl f5 :: S1
-#12 := f5
-decl f1 :: S1
-#4 := f1
-#47 := (= f1 f5)
-decl f4 :: S1
-#10 := f4
-#44 := (= f1 f4)
-#53 := (not #44)
-decl f3 :: S1
-#8 := f3
-#41 := (= f1 f3)
-#62 := (not #41)
-#105 := (or #62 #53 #47)
-#163 := (iff #105 false)
-#158 := (or false false false)
-#161 := (iff #158 false)
-#162 := [rewrite]: #161
-#159 := (iff #105 #158)
-#135 := (iff #47 false)
-#126 := (not #47)
-#108 := (not #105)
-#71 := (or #62 #44)
-#87 := (not #71)
-#114 := (or #62 #47 #87 #108)
-#119 := (not #114)
-#13 := (= f5 f1)
-#9 := (= f3 f1)
-#17 := (implies #9 #13)
-#11 := (= f4 f1)
-#16 := (implies #9 #11)
-#18 := (implies #16 #17)
-#14 := (implies #11 #13)
-#15 := (implies #9 #14)
-#19 := (implies #15 #18)
-#20 := (not #19)
-#122 := (iff #20 #119)
-#79 := (or #62 #47)
-#88 := (or #87 #79)
-#54 := (or #53 #47)
-#63 := (or #62 #54)
-#96 := (not #63)
-#97 := (or #96 #88)
-#102 := (not #97)
-#120 := (iff #102 #119)
-#117 := (iff #97 #114)
-#111 := (or #108 #88)
-#115 := (iff #111 #114)
-#116 := [rewrite]: #115
-#112 := (iff #97 #111)
-#109 := (iff #96 #108)
-#106 := (iff #63 #105)
-#107 := [rewrite]: #106
-#110 := [monotonicity #107]: #109
-#113 := [monotonicity #110]: #112
-#118 := [trans #113 #116]: #117
-#121 := [monotonicity #118]: #120
-#103 := (iff #20 #102)
-#100 := (iff #19 #97)
-#93 := (implies #63 #88)
-#98 := (iff #93 #97)
-#99 := [rewrite]: #98
-#94 := (iff #19 #93)
-#91 := (iff #18 #88)
-#84 := (implies #71 #79)
-#89 := (iff #84 #88)
-#90 := [rewrite]: #89
-#85 := (iff #18 #84)
-#82 := (iff #17 #79)
-#76 := (implies #41 #47)
-#80 := (iff #76 #79)
-#81 := [rewrite]: #80
-#77 := (iff #17 #76)
-#48 := (iff #13 #47)
-#49 := [rewrite]: #48
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#78 := [monotonicity #43 #49]: #77
-#83 := [trans #78 #81]: #82
-#74 := (iff #16 #71)
-#68 := (implies #41 #44)
-#72 := (iff #68 #71)
-#73 := [rewrite]: #72
-#69 := (iff #16 #68)
-#45 := (iff #11 #44)
-#46 := [rewrite]: #45
-#70 := [monotonicity #43 #46]: #69
-#75 := [trans #70 #73]: #74
-#86 := [monotonicity #75 #83]: #85
-#92 := [trans #86 #90]: #91
-#66 := (iff #15 #63)
-#59 := (implies #41 #54)
-#64 := (iff #59 #63)
-#65 := [rewrite]: #64
-#60 := (iff #15 #59)
-#57 := (iff #14 #54)
-#50 := (implies #44 #47)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #14 #50)
-#52 := [monotonicity #46 #49]: #51
-#58 := [trans #52 #56]: #57
-#61 := [monotonicity #43 #58]: #60
-#67 := [trans #61 #65]: #66
-#95 := [monotonicity #67 #92]: #94
-#101 := [trans #95 #99]: #100
-#104 := [monotonicity #101]: #103
-#123 := [trans #104 #121]: #122
-#40 := [asserted]: #20
-#124 := [mp #40 #123]: #119
-#127 := [not-or-elim #124]: #126
-#136 := [iff-false #127]: #135
-#156 := (iff #53 false)
-#1 := true
-#137 := (not true)
-#140 := (iff #137 false)
-#141 := [rewrite]: #140
-#154 := (iff #53 #137)
-#152 := (iff #44 true)
-#149 := (iff #71 #44)
-#144 := (or false #44)
-#147 := (iff #144 #44)
-#148 := [rewrite]: #147
-#145 := (iff #71 #144)
-#142 := (iff #62 false)
-#138 := (iff #62 #137)
-#133 := (iff #41 true)
-#125 := [not-or-elim #124]: #41
-#134 := [iff-true #125]: #133
-#139 := [monotonicity #134]: #138
-#143 := [trans #139 #141]: #142
-#146 := [monotonicity #143]: #145
-#150 := [trans #146 #148]: #149
-#128 := [not-or-elim #124]: #71
-#151 := [mp #128 #150]: #44
-#153 := [iff-true #151]: #152
-#155 := [monotonicity #153]: #154
-#157 := [trans #155 #141]: #156
-#160 := [monotonicity #143 #157 #136]: #159
-#164 := [trans #160 #162]: #163
-#129 := [not-or-elim #124]: #105
-[mp #129 #164]: false
-unsat
-00d66332779f959f5155f96744316681d812ae6d 121 0
-#2 := false
-decl f5 :: S1
-#13 := f5
-decl f1 :: S1
-#4 := f1
-#56 := (= f1 f5)
-decl f4 :: S1
-#10 := f4
-#44 := (= f1 f4)
-decl f3 :: S1
-#8 := f3
-#41 := (= f1 f3)
-#50 := (not #41)
-#93 := (or #50 #44 #56)
-#140 := (iff #93 false)
-#135 := (or false false false)
-#138 := (iff #135 false)
-#139 := [rewrite]: #138
-#136 := (iff #93 #135)
-#126 := (iff #56 false)
-#116 := (not #56)
-#96 := (not #93)
-#102 := (or #50 #44 #56 #96)
-#107 := (not #102)
-#14 := (= f5 f1)
-#11 := (= f4 f1)
-#17 := (or #11 #14)
-#9 := (= f3 f1)
-#18 := (implies #9 #17)
-#15 := (implies #9 #14)
-#12 := (implies #9 #11)
-#16 := (or #12 #15)
-#19 := (implies #16 #18)
-#20 := (not #19)
-#110 := (iff #20 #107)
-#70 := (or #44 #56)
-#76 := (or #50 #70)
-#62 := (or #50 #56)
-#51 := (or #50 #44)
-#67 := (or #51 #62)
-#84 := (not #67)
-#85 := (or #84 #76)
-#90 := (not #85)
-#108 := (iff #90 #107)
-#105 := (iff #85 #102)
-#99 := (or #96 #76)
-#103 := (iff #99 #102)
-#104 := [rewrite]: #103
-#100 := (iff #85 #99)
-#97 := (iff #84 #96)
-#94 := (iff #67 #93)
-#95 := [rewrite]: #94
-#98 := [monotonicity #95]: #97
-#101 := [monotonicity #98]: #100
-#106 := [trans #101 #104]: #105
-#109 := [monotonicity #106]: #108
-#91 := (iff #20 #90)
-#88 := (iff #19 #85)
-#81 := (implies #67 #76)
-#86 := (iff #81 #85)
-#87 := [rewrite]: #86
-#82 := (iff #19 #81)
-#79 := (iff #18 #76)
-#73 := (implies #41 #70)
-#77 := (iff #73 #76)
-#78 := [rewrite]: #77
-#74 := (iff #18 #73)
-#71 := (iff #17 #70)
-#57 := (iff #14 #56)
-#58 := [rewrite]: #57
-#45 := (iff #11 #44)
-#46 := [rewrite]: #45
-#72 := [monotonicity #46 #58]: #71
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#75 := [monotonicity #43 #72]: #74
-#80 := [trans #75 #78]: #79
-#68 := (iff #16 #67)
-#65 := (iff #15 #62)
-#59 := (implies #41 #56)
-#63 := (iff #59 #62)
-#64 := [rewrite]: #63
-#60 := (iff #15 #59)
-#61 := [monotonicity #43 #58]: #60
-#66 := [trans #61 #64]: #65
-#54 := (iff #12 #51)
-#47 := (implies #41 #44)
-#52 := (iff #47 #51)
-#53 := [rewrite]: #52
-#48 := (iff #12 #47)
-#49 := [monotonicity #43 #46]: #48
-#55 := [trans #49 #53]: #54
-#69 := [monotonicity #55 #66]: #68
-#83 := [monotonicity #69 #80]: #82
-#89 := [trans #83 #87]: #88
-#92 := [monotonicity #89]: #91
-#111 := [trans #92 #109]: #110
-#40 := [asserted]: #20
-#112 := [mp #40 #111]: #107
-#117 := [not-or-elim #112]: #116
-#127 := [iff-false #117]: #126
-#124 := (iff #44 false)
-#114 := (not #44)
-#115 := [not-or-elim #112]: #114
-#125 := [iff-false #115]: #124
-#133 := (iff #50 false)
-#1 := true
-#128 := (not true)
-#131 := (iff #128 false)
-#132 := [rewrite]: #131
-#129 := (iff #50 #128)
-#122 := (iff #41 true)
-#113 := [not-or-elim #112]: #41
-#123 := [iff-true #113]: #122
-#130 := [monotonicity #123]: #129
-#134 := [trans #130 #132]: #133
-#137 := [monotonicity #134 #125 #127]: #136
-#141 := [trans #137 #139]: #140
-#118 := [not-or-elim #112]: #93
-[mp #118 #141]: false
-unsat
-e8da757bab2c8873de4c9abb00d9ba6b32efbf76 123 0
-#2 := false
-decl f4 :: S1
-#10 := f4
-decl f1 :: S1
-#4 := f1
-#41 := (= f1 f4)
-decl f3 :: S1
-#8 := f3
-#38 := (= f1 f3)
-#47 := (not #38)
-#48 := (or #47 #41)
-#56 := (not #48)
-#57 := (or #38 #56)
-#65 := (not #57)
-#66 := (or #38 #65)
-#74 := (not #66)
-#75 := (or #41 #74)
-#143 := (iff #75 false)
-#138 := (or false false)
-#141 := (iff #138 false)
-#142 := [rewrite]: #141
-#139 := (iff #75 #138)
-#136 := (iff #74 false)
-#1 := true
-#131 := (not true)
-#134 := (iff #131 false)
-#135 := [rewrite]: #134
-#132 := (iff #74 #131)
-#129 := (iff #66 true)
-#124 := (or #38 #47)
-#127 := (iff #124 true)
-#128 := [rewrite]: #127
-#125 := (iff #66 #124)
-#122 := (iff #65 #47)
-#120 := (iff #57 #38)
-#115 := (or #38 #38)
-#118 := (iff #115 #38)
-#119 := [rewrite]: #118
-#116 := (iff #57 #115)
-#113 := (iff #56 #38)
-#108 := (not #47)
-#111 := (iff #108 #38)
-#112 := [rewrite]: #111
-#109 := (iff #56 #108)
-#106 := (iff #48 #47)
-#101 := (or #47 false)
-#104 := (iff #101 #47)
-#105 := [rewrite]: #104
-#102 := (iff #48 #101)
-#99 := (iff #41 false)
-#92 := (not #41)
-#83 := (not #75)
-#84 := (or #41 #83)
-#89 := (not #84)
-#11 := (= f4 f1)
-#9 := (= f3 f1)
-#12 := (implies #9 #11)
-#13 := (implies #12 #9)
-#14 := (implies #13 #9)
-#15 := (implies #14 #11)
-#16 := (implies #15 #11)
-#17 := (not #16)
-#90 := (iff #17 #89)
-#87 := (iff #16 #84)
-#80 := (implies #75 #41)
-#85 := (iff #80 #84)
-#86 := [rewrite]: #85
-#81 := (iff #16 #80)
-#42 := (iff #11 #41)
-#43 := [rewrite]: #42
-#78 := (iff #15 #75)
-#71 := (implies #66 #41)
-#76 := (iff #71 #75)
-#77 := [rewrite]: #76
-#72 := (iff #15 #71)
-#69 := (iff #14 #66)
-#62 := (implies #57 #38)
-#67 := (iff #62 #66)
-#68 := [rewrite]: #67
-#63 := (iff #14 #62)
-#39 := (iff #9 #38)
-#40 := [rewrite]: #39
-#60 := (iff #13 #57)
-#53 := (implies #48 #38)
-#58 := (iff #53 #57)
-#59 := [rewrite]: #58
-#54 := (iff #13 #53)
-#51 := (iff #12 #48)
-#44 := (implies #38 #41)
-#49 := (iff #44 #48)
-#50 := [rewrite]: #49
-#45 := (iff #12 #44)
-#46 := [monotonicity #40 #43]: #45
-#52 := [trans #46 #50]: #51
-#55 := [monotonicity #52 #40]: #54
-#61 := [trans #55 #59]: #60
-#64 := [monotonicity #61 #40]: #63
-#70 := [trans #64 #68]: #69
-#73 := [monotonicity #70 #43]: #72
-#79 := [trans #73 #77]: #78
-#82 := [monotonicity #79 #43]: #81
-#88 := [trans #82 #86]: #87
-#91 := [monotonicity #88]: #90
-#37 := [asserted]: #17
-#94 := [mp #37 #91]: #89
-#93 := [not-or-elim #94]: #92
-#100 := [iff-false #93]: #99
-#103 := [monotonicity #100]: #102
-#107 := [trans #103 #105]: #106
-#110 := [monotonicity #107]: #109
-#114 := [trans #110 #112]: #113
-#117 := [monotonicity #114]: #116
-#121 := [trans #117 #119]: #120
-#123 := [monotonicity #121]: #122
-#126 := [monotonicity #123]: #125
-#130 := [trans #126 #128]: #129
-#133 := [monotonicity #130]: #132
-#137 := [trans #133 #135]: #136
-#140 := [monotonicity #100 #137]: #139
-#144 := [trans #140 #142]: #143
-#95 := [not-or-elim #94]: #75
-[mp #95 #144]: false
-unsat
-e9d35c7bb1cf28b044ff39158dac0d3feace74d2 60 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#14 := (not #9)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#13 := (not #11)
-#15 := (implies #13 #14)
-#12 := (implies #9 #11)
-#16 := (implies #12 #15)
-#17 := (not #16)
-#77 := (iff #17 false)
-#1 := true
-#72 := (not true)
-#75 := (iff #72 false)
-#76 := [rewrite]: #75
-#73 := (iff #17 #72)
-#70 := (iff #16 true)
-#41 := (= f1 f4)
-#38 := (= f1 f3)
-#47 := (not #38)
-#48 := (or #47 #41)
-#65 := (implies #48 #48)
-#68 := (iff #65 true)
-#69 := [rewrite]: #68
-#66 := (iff #16 #65)
-#63 := (iff #15 #48)
-#53 := (not #41)
-#58 := (implies #53 #47)
-#61 := (iff #58 #48)
-#62 := [rewrite]: #61
-#59 := (iff #15 #58)
-#56 := (iff #14 #47)
-#39 := (iff #9 #38)
-#40 := [rewrite]: #39
-#57 := [monotonicity #40]: #56
-#54 := (iff #13 #53)
-#42 := (iff #11 #41)
-#43 := [rewrite]: #42
-#55 := [monotonicity #43]: #54
-#60 := [monotonicity #55 #57]: #59
-#64 := [trans #60 #62]: #63
-#51 := (iff #12 #48)
-#44 := (implies #38 #41)
-#49 := (iff #44 #48)
-#50 := [rewrite]: #49
-#45 := (iff #12 #44)
-#46 := [monotonicity #40 #43]: #45
-#52 := [trans #46 #50]: #51
-#67 := [monotonicity #52 #64]: #66
-#71 := [trans #67 #69]: #70
-#74 := [monotonicity #71]: #73
-#78 := [trans #74 #76]: #77
-#37 := [asserted]: #17
-[mp #37 #78]: false
-unsat
-ff95a56cf58e4b621d6e82e0aebf8b86faaedf39 121 0
-#2 := false
-decl f5 :: S1
-#12 := f5
-decl f1 :: S1
-#4 := f1
-#47 := (= f1 f5)
-decl f4 :: S1
-#10 := f4
-#44 := (= f1 f4)
-decl f3 :: S1
-#8 := f3
-#41 := (= f1 f3)
-#56 := (not #41)
-#93 := (or #56 #44 #47)
-#140 := (iff #93 false)
-#135 := (or false false false)
-#138 := (iff #135 false)
-#139 := [rewrite]: #138
-#136 := (iff #93 #135)
-#126 := (iff #47 false)
-#116 := (not #47)
-#96 := (not #93)
-#102 := (or #56 #44 #47 #96)
-#107 := (not #102)
-#13 := (= f5 f1)
-#9 := (= f3 f1)
-#17 := (implies #9 #13)
-#11 := (= f4 f1)
-#16 := (implies #9 #11)
-#18 := (or #16 #17)
-#14 := (or #11 #13)
-#15 := (implies #9 #14)
-#19 := (implies #15 #18)
-#20 := (not #19)
-#110 := (iff #20 #107)
-#73 := (or #56 #47)
-#65 := (or #56 #44)
-#78 := (or #65 #73)
-#50 := (or #44 #47)
-#57 := (or #56 #50)
-#84 := (not #57)
-#85 := (or #84 #78)
-#90 := (not #85)
-#108 := (iff #90 #107)
-#105 := (iff #85 #102)
-#99 := (or #96 #78)
-#103 := (iff #99 #102)
-#104 := [rewrite]: #103
-#100 := (iff #85 #99)
-#97 := (iff #84 #96)
-#94 := (iff #57 #93)
-#95 := [rewrite]: #94
-#98 := [monotonicity #95]: #97
-#101 := [monotonicity #98]: #100
-#106 := [trans #101 #104]: #105
-#109 := [monotonicity #106]: #108
-#91 := (iff #20 #90)
-#88 := (iff #19 #85)
-#81 := (implies #57 #78)
-#86 := (iff #81 #85)
-#87 := [rewrite]: #86
-#82 := (iff #19 #81)
-#79 := (iff #18 #78)
-#76 := (iff #17 #73)
-#70 := (implies #41 #47)
-#74 := (iff #70 #73)
-#75 := [rewrite]: #74
-#71 := (iff #17 #70)
-#48 := (iff #13 #47)
-#49 := [rewrite]: #48
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#72 := [monotonicity #43 #49]: #71
-#77 := [trans #72 #75]: #76
-#68 := (iff #16 #65)
-#62 := (implies #41 #44)
-#66 := (iff #62 #65)
-#67 := [rewrite]: #66
-#63 := (iff #16 #62)
-#45 := (iff #11 #44)
-#46 := [rewrite]: #45
-#64 := [monotonicity #43 #46]: #63
-#69 := [trans #64 #67]: #68
-#80 := [monotonicity #69 #77]: #79
-#60 := (iff #15 #57)
-#53 := (implies #41 #50)
-#58 := (iff #53 #57)
-#59 := [rewrite]: #58
-#54 := (iff #15 #53)
-#51 := (iff #14 #50)
-#52 := [monotonicity #46 #49]: #51
-#55 := [monotonicity #43 #52]: #54
-#61 := [trans #55 #59]: #60
-#83 := [monotonicity #61 #80]: #82
-#89 := [trans #83 #87]: #88
-#92 := [monotonicity #89]: #91
-#111 := [trans #92 #109]: #110
-#40 := [asserted]: #20
-#112 := [mp #40 #111]: #107
-#117 := [not-or-elim #112]: #116
-#127 := [iff-false #117]: #126
-#124 := (iff #44 false)
-#114 := (not #44)
-#115 := [not-or-elim #112]: #114
-#125 := [iff-false #115]: #124
-#133 := (iff #56 false)
-#1 := true
-#128 := (not true)
-#131 := (iff #128 false)
-#132 := [rewrite]: #131
-#129 := (iff #56 #128)
-#122 := (iff #41 true)
-#113 := [not-or-elim #112]: #41
-#123 := [iff-true #113]: #122
-#130 := [monotonicity #123]: #129
-#134 := [trans #130 #132]: #133
-#137 := [monotonicity #134 #125 #127]: #136
-#141 := [trans #137 #139]: #140
-#118 := [not-or-elim #112]: #93
-[mp #118 #141]: false
-unsat
-47f13964ba3dfd91ee45da107e4d79352a28a5c5 84 0
-#2 := false
-decl f4 :: S1
-#10 := f4
-decl f1 :: S1
-#4 := f1
-#41 := (= f1 f4)
-#56 := (not #41)
-#100 := [hypothesis]: #56
+#7 := f3
+#8 := (= f3 f1)
+#9 := (not #8)
+#10 := (or #8 #9)
+#11 := (not #10)
+#40 := (iff #11 false)
+#1 := true
+#35 := (not true)
+#38 := (iff #35 false)
+#39 := [rewrite]: #38
+#36 := (iff #11 #35)
+#33 := (iff #10 true)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#41 := [trans #37 #39]: #40
+#32 := [asserted]: #11
+[mp #32 #41]: false
+unsat
+075ccbca5ef8abd85cfaedf1a7322d296271c46f 30 0
+#2 := false
+decl f1 :: S1
+#3 := f1
 decl f3 :: S1
-#8 := f3
-#38 := (= f1 f3)
-#47 := (not #38)
-#48 := (or #47 #41)
-#57 := (or #38 #56)
-#62 := (and #48 #57)
-#65 := (iff #38 #41)
-#71 := (not #62)
-#72 := (or #71 #65)
-#77 := (not #72)
-#11 := (= f4 f1)
-#9 := (= f3 f1)
-#15 := (iff #9 #11)
-#13 := (implies #11 #9)
-#12 := (implies #9 #11)
-#14 := (and #12 #13)
-#16 := (implies #14 #15)
-#17 := (not #16)
-#78 := (iff #17 #77)
-#75 := (iff #16 #72)
-#68 := (implies #62 #65)
-#73 := (iff #68 #72)
-#74 := [rewrite]: #73
-#69 := (iff #16 #68)
-#66 := (iff #15 #65)
-#42 := (iff #11 #41)
-#43 := [rewrite]: #42
-#39 := (iff #9 #38)
-#40 := [rewrite]: #39
-#67 := [monotonicity #40 #43]: #66
-#63 := (iff #14 #62)
-#60 := (iff #13 #57)
-#53 := (implies #41 #38)
-#58 := (iff #53 #57)
-#59 := [rewrite]: #58
-#54 := (iff #13 #53)
-#55 := [monotonicity #43 #40]: #54
-#61 := [trans #55 #59]: #60
-#51 := (iff #12 #48)
-#44 := (implies #38 #41)
-#49 := (iff #44 #48)
-#50 := [rewrite]: #49
-#45 := (iff #12 #44)
-#46 := [monotonicity #40 #43]: #45
-#52 := [trans #46 #50]: #51
-#64 := [monotonicity #52 #61]: #63
-#70 := [monotonicity #64 #67]: #69
-#76 := [trans #70 #74]: #75
-#79 := [monotonicity #76]: #78
-#37 := [asserted]: #17
-#82 := [mp #37 #79]: #77
-#80 := [not-or-elim #82]: #62
-#81 := [and-elim #80]: #48
-#101 := [unit-resolution #81 #100]: #47
-#92 := (or #41 #38)
-#93 := (iff #41 #47)
-#84 := (not #65)
-#94 := (iff #84 #93)
-#95 := [rewrite]: #94
-#85 := [not-or-elim #82]: #84
-#96 := [mp #85 #95]: #93
-#97 := (not #93)
-#98 := (or #41 #38 #97)
-#91 := [def-axiom]: #98
-#89 := [unit-resolution #91 #96]: #92
-#102 := [unit-resolution #89 #101 #100]: false
-#103 := [lemma #102]: #41
-#83 := [and-elim #80]: #57
-#104 := [unit-resolution #83 #103]: #38
-#88 := (or #56 #47)
-#90 := (or #56 #47 #97)
-#87 := [def-axiom]: #90
-#99 := [unit-resolution #87 #96]: #88
-[unit-resolution #99 #104 #103]: false
-unsat
-67d0291df830bf23c2458b5c5d9ab7a1b7326290 47 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#13 := (iff #11 #9)
-#12 := (iff #9 #11)
-#14 := (iff #12 #13)
-#15 := (not #14)
-#64 := (iff #15 false)
-#1 := true
-#59 := (not true)
-#62 := (iff #59 false)
-#63 := [rewrite]: #62
-#60 := (iff #15 #59)
-#57 := (iff #14 true)
-#39 := (= f1 f4)
-#36 := (= f1 f3)
-#42 := (iff #36 #39)
-#52 := (iff #42 #42)
-#55 := (iff #52 true)
-#56 := [rewrite]: #55
-#53 := (iff #14 #52)
-#50 := (iff #13 #42)
-#45 := (iff #39 #36)
-#48 := (iff #45 #42)
-#49 := [rewrite]: #48
-#46 := (iff #13 #45)
-#37 := (iff #9 #36)
-#38 := [rewrite]: #37
-#40 := (iff #11 #39)
-#41 := [rewrite]: #40
-#47 := [monotonicity #41 #38]: #46
-#51 := [trans #47 #49]: #50
-#43 := (iff #12 #42)
-#44 := [monotonicity #38 #41]: #43
-#54 := [monotonicity #44 #51]: #53
-#58 := [trans #54 #56]: #57
-#61 := [monotonicity #58]: #60
-#65 := [trans #61 #63]: #64
-#35 := [asserted]: #15
-[mp #35 #65]: false
-unsat
-6d227e1b0585e5b365b0d07f07d7c5708cbc3115 41 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#10 := (not #9)
-#11 := (iff #9 #10)
+#7 := f3
+#8 := (= f3 f1)
+#9 := (not #8)
+#10 := (and #8 #9)
+#11 := (not #10)
 #12 := (not #11)
-#13 := (not #12)
-#59 := (iff #13 false)
-#1 := true
-#54 := (not true)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #13 #54)
-#52 := (iff #12 true)
-#47 := (not false)
-#50 := (iff #47 true)
-#51 := [rewrite]: #50
-#48 := (iff #12 #47)
-#45 := (iff #11 false)
-#34 := (= f1 f3)
-#37 := (not #34)
-#40 := (iff #34 #37)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 #37)
-#35 := (iff #9 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#42 := [monotonicity #36 #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#33 := [asserted]: #13
-[mp #33 #60]: false
-unsat
-183781528451fe65de60bc2d2e22c1d75fff00de 60 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#14 := (not #9)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#13 := (not #11)
-#15 := (implies #13 #14)
-#12 := (implies #9 #11)
-#16 := (iff #12 #15)
-#17 := (not #16)
-#77 := (iff #17 false)
-#1 := true
-#72 := (not true)
-#75 := (iff #72 false)
-#76 := [rewrite]: #75
-#73 := (iff #17 #72)
-#70 := (iff #16 true)
-#41 := (= f1 f4)
-#38 := (= f1 f3)
-#47 := (not #38)
-#48 := (or #47 #41)
-#65 := (iff #48 #48)
-#68 := (iff #65 true)
-#69 := [rewrite]: #68
-#66 := (iff #16 #65)
-#63 := (iff #15 #48)
-#53 := (not #41)
-#58 := (implies #53 #47)
-#61 := (iff #58 #48)
-#62 := [rewrite]: #61
-#59 := (iff #15 #58)
-#56 := (iff #14 #47)
-#39 := (iff #9 #38)
-#40 := [rewrite]: #39
-#57 := [monotonicity #40]: #56
-#54 := (iff #13 #53)
-#42 := (iff #11 #41)
-#43 := [rewrite]: #42
-#55 := [monotonicity #43]: #54
-#60 := [monotonicity #55 #57]: #59
-#64 := [trans #60 #62]: #63
-#51 := (iff #12 #48)
-#44 := (implies #38 #41)
-#49 := (iff #44 #48)
-#50 := [rewrite]: #49
-#45 := (iff #12 #44)
-#46 := [monotonicity #40 #43]: #45
-#52 := [trans #46 #50]: #51
-#67 := [monotonicity #52 #64]: #66
-#71 := [trans #67 #69]: #70
-#74 := [monotonicity #71]: #73
-#78 := [trans #74 #76]: #77
-#37 := [asserted]: #17
-[mp #37 #78]: false
-unsat
-8a2f295cb26eb802daa0916270c630d0aae6a230 72 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#10 := (iff #9 #9)
-#11 := (iff #9 #10)
-#12 := (iff #9 #11)
-#13 := (iff #9 #12)
-#14 := (iff #9 #13)
-#15 := (iff #9 #14)
-#16 := (iff #9 #15)
-#17 := (iff #9 #16)
-#18 := (iff #9 #17)
-#19 := (not #18)
-#90 := (iff #19 false)
-#1 := true
-#85 := (not true)
-#88 := (iff #85 false)
-#89 := [rewrite]: #88
-#86 := (iff #19 #85)
-#83 := (iff #18 true)
-#40 := (= f1 f3)
-#43 := (iff #40 #40)
-#46 := (iff #43 true)
-#47 := [rewrite]: #46
-#81 := (iff #18 #43)
-#79 := (iff #17 #40)
-#50 := (iff #40 true)
-#53 := (iff #50 #40)
-#54 := [rewrite]: #53
-#77 := (iff #17 #50)
-#75 := (iff #16 true)
-#73 := (iff #16 #43)
-#71 := (iff #15 #40)
-#69 := (iff #15 #50)
-#67 := (iff #14 true)
-#65 := (iff #14 #43)
-#63 := (iff #13 #40)
-#61 := (iff #13 #50)
-#59 := (iff #12 true)
-#57 := (iff #12 #43)
-#55 := (iff #11 #40)
-#51 := (iff #11 #50)
-#48 := (iff #10 true)
-#44 := (iff #10 #43)
-#41 := (iff #9 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42 #42]: #44
-#49 := [trans #45 #47]: #48
-#52 := [monotonicity #42 #49]: #51
-#56 := [trans #52 #54]: #55
-#58 := [monotonicity #42 #56]: #57
-#60 := [trans #58 #47]: #59
-#62 := [monotonicity #42 #60]: #61
-#64 := [trans #62 #54]: #63
-#66 := [monotonicity #42 #64]: #65
-#68 := [trans #66 #47]: #67
-#70 := [monotonicity #42 #68]: #69
-#72 := [trans #70 #54]: #71
-#74 := [monotonicity #42 #72]: #73
-#76 := [trans #74 #47]: #75
-#78 := [monotonicity #42 #76]: #77
-#80 := [trans #78 #54]: #79
-#82 := [monotonicity #42 #80]: #81
-#84 := [trans #82 #47]: #83
-#87 := [monotonicity #84]: #86
-#91 := [trans #87 #89]: #90
-#39 := [asserted]: #19
-[mp #39 #91]: false
-unsat
-1c44d521ac456bc35b48a603c12488d178412b54 151 0
-#2 := false
-decl f4 :: S1
-#10 := f4
-decl f1 :: S1
-#4 := f1
-#44 := (= f1 f4)
-decl f5 :: S1
-#12 := f5
-#47 := (= f1 f5)
-decl f3 :: S1
-#8 := f3
-#41 := (= f1 f3)
-#50 := (ite #41 #44 #47)
-#67 := (or #41 #47)
-#94 := (not #67)
-#56 := (not #41)
-#57 := (or #56 #44)
-#93 := (not #57)
-#95 := (or #93 #94)
-#96 := (not #95)
-#153 := [hypothesis]: #96
-#133 := (or #95 #67)
-#134 := [def-axiom]: #133
-#154 := [unit-resolution #134 #153]: #67
-#81 := (not #50)
-#144 := (or #81 #95)
-#103 := (iff #50 #95)
-#72 := (and #57 #67)
-#82 := (iff #72 #81)
-#106 := (iff #82 #103)
-#98 := (iff #95 #50)
-#104 := (iff #98 #103)
-#105 := [rewrite]: #104
-#101 := (iff #82 #98)
-#88 := (iff #96 #81)
-#99 := (iff #88 #98)
-#100 := [rewrite]: #99
-#90 := (iff #82 #88)
-#91 := (iff #72 #96)
-#92 := [rewrite]: #91
-#97 := [monotonicity #92]: #90
-#102 := [trans #97 #100]: #101
-#107 := [trans #102 #105]: #106
-#13 := (= f5 f1)
-#9 := (= f3 f1)
-#16 := (not #9)
-#17 := (implies #16 #13)
-#11 := (= f4 f1)
-#15 := (implies #9 #11)
-#18 := (and #15 #17)
-#14 := (ite #9 #11 #13)
-#19 := (iff #14 #18)
-#20 := (not #19)
-#85 := (iff #20 #82)
-#75 := (iff #50 #72)
-#78 := (not #75)
-#83 := (iff #78 #82)
-#84 := [rewrite]: #83
-#79 := (iff #20 #78)
-#76 := (iff #19 #75)
-#73 := (iff #18 #72)
-#70 := (iff #17 #67)
-#64 := (implies #56 #47)
-#68 := (iff #64 #67)
-#69 := [rewrite]: #68
-#65 := (iff #17 #64)
-#48 := (iff #13 #47)
-#49 := [rewrite]: #48
-#62 := (iff #16 #56)
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#63 := [monotonicity #43]: #62
-#66 := [monotonicity #63 #49]: #65
-#71 := [trans #66 #69]: #70
-#60 := (iff #15 #57)
-#53 := (implies #41 #44)
-#58 := (iff #53 #57)
-#59 := [rewrite]: #58
-#54 := (iff #15 #53)
-#45 := (iff #11 #44)
-#46 := [rewrite]: #45
-#55 := [monotonicity #43 #46]: #54
-#61 := [trans #55 #59]: #60
-#74 := [monotonicity #61 #71]: #73
-#51 := (iff #14 #50)
-#52 := [monotonicity #43 #46 #49]: #51
-#77 := [monotonicity #52 #74]: #76
-#80 := [monotonicity #77]: #79
-#86 := [trans #80 #84]: #85
-#40 := [asserted]: #20
-#89 := [mp #40 #86]: #82
-#108 := [mp #89 #107]: #103
-#137 := (not #103)
-#142 := (or #81 #95 #137)
-#143 := [def-axiom]: #142
-#145 := [unit-resolution #143 #108]: #144
-#155 := [unit-resolution #145 #153]: #81
-#131 := (or #95 #57)
-#132 := [def-axiom]: #131
-#156 := [unit-resolution #132 #153]: #57
-#151 := (or #56 #93 #50)
-#146 := [hypothesis]: #57
-#147 := [hypothesis]: #41
-#113 := (not #44)
-#148 := [hypothesis]: #81
-#114 := (or #50 #56 #113)
-#115 := [def-axiom]: #114
-#149 := [unit-resolution #115 #147 #148]: #113
-#123 := (or #93 #56 #44)
-#124 := [def-axiom]: #123
-#150 := [unit-resolution #124 #149 #147 #146]: false
-#152 := [lemma #150]: #151
-#157 := [unit-resolution #152 #156 #155]: #56
-#116 := (not #47)
-#117 := (or #50 #41 #116)
-#118 := [def-axiom]: #117
-#158 := [unit-resolution #118 #157 #155]: #116
-#129 := (or #94 #41 #47)
-#130 := [def-axiom]: #129
-#159 := [unit-resolution #130 #158 #157 #154]: false
-#160 := [lemma #159]: #95
-#140 := (or #50 #96)
-#138 := (or #50 #96 #137)
-#139 := [def-axiom]: #138
-#141 := [unit-resolution #139 #108]: #140
-#163 := [unit-resolution #141 #160]: #50
-#161 := [hypothesis]: #56
-#119 := (or #57 #41)
-#120 := [def-axiom]: #119
-#162 := [unit-resolution #120 #161]: #57
-#111 := (or #81 #41 #47)
-#112 := [def-axiom]: #111
-#164 := [unit-resolution #112 #161 #163]: #47
-#127 := (or #67 #116)
-#128 := [def-axiom]: #127
-#165 := [unit-resolution #128 #164]: #67
-#135 := (or #96 #93 #94)
-#136 := [def-axiom]: #135
-#166 := [unit-resolution #136 #165 #162 #160]: false
-#167 := [lemma #166]: #41
-#109 := (or #81 #56 #44)
-#110 := [def-axiom]: #109
-#168 := [unit-resolution #110 #167 #163]: #44
-#125 := (or #67 #56)
-#126 := [def-axiom]: #125
-#169 := [unit-resolution #126 #167]: #67
-#170 := [unit-resolution #136 #169 #160]: #93
-#121 := (or #57 #113)
-#122 := [def-axiom]: #121
-[unit-resolution #122 #170 #168]: false
-unsat
-643b93e1a561bfd028bc3792417378d161ef2e8a 66 0
-#2 := false
-decl f3 :: S1
-#8 := f3
-decl f1 :: S1
-#4 := f1
-#36 := (= f1 f3)
-#54 := (not #36)
-#90 := [hypothesis]: #36
-decl f4 :: S1
-#10 := f4
-#39 := (= f1 f4)
-#45 := (not #39)
-#46 := (or #36 #45)
-#72 := (or #46 #54)
-#73 := [def-axiom]: #72
-#91 := [unit-resolution #73 #90]: #46
-#70 := (not #46)
-#92 := (or #54 #70)
-#55 := (or #54 #39)
-#60 := (ite #36 #46 #55)
-#63 := (not #60)
-#11 := (= f4 f1)
-#9 := (= f3 f1)
-#13 := (implies #9 #11)
-#12 := (implies #11 #9)
-#14 := (ite #9 #12 #13)
-#15 := (not #14)
-#64 := (iff #15 #63)
-#61 := (iff #14 #60)
-#58 := (iff #13 #55)
-#51 := (implies #36 #39)
-#56 := (iff #51 #55)
-#57 := [rewrite]: #56
-#52 := (iff #13 #51)
-#40 := (iff #11 #39)
-#41 := [rewrite]: #40
-#37 := (iff #9 #36)
-#38 := [rewrite]: #37
-#53 := [monotonicity #38 #41]: #52
-#59 := [trans #53 #57]: #58
-#49 := (iff #12 #46)
-#42 := (implies #39 #36)
-#47 := (iff #42 #46)
-#48 := [rewrite]: #47
-#43 := (iff #12 #42)
-#44 := [monotonicity #41 #38]: #43
-#50 := [trans #44 #48]: #49
-#62 := [monotonicity #38 #50 #59]: #61
-#65 := [monotonicity #62]: #64
-#35 := [asserted]: #15
-#68 := [mp #35 #65]: #63
-#86 := (or #60 #54 #70)
-#87 := [def-axiom]: #86
-#93 := [unit-resolution #87 #68]: #92
-#94 := [unit-resolution #93 #91 #90]: false
-#95 := [lemma #94]: #54
-#69 := (or #55 #36)
-#76 := [def-axiom]: #69
-#96 := [unit-resolution #76 #95]: #55
-#79 := (not #55)
-#97 := (or #36 #79)
-#88 := (or #60 #36 #79)
-#89 := [def-axiom]: #88
-#98 := [unit-resolution #89 #68]: #97
-[unit-resolution #98 #96 #95]: false
-unsat
-8a97d35ae3bf1f06142ca3c295d9a54474a4bbad 67 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f6 :: S1
-#15 := f6
-#16 := (= f6 f1)
-decl f5 :: S1
-#13 := f5
-#14 := (= f5 f1)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#18 := (ite #11 #14 #16)
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#19 := (ite #9 #14 #18)
-#12 := (or #9 #11)
-#17 := (ite #12 #14 #16)
-#20 := (iff #17 #19)
-#21 := (not #20)
-#82 := (iff #21 false)
-#1 := true
-#77 := (not true)
-#80 := (iff #77 false)
-#81 := [rewrite]: #80
-#78 := (iff #21 #77)
-#75 := (iff #20 true)
-#54 := (= f1 f6)
-#51 := (= f1 f5)
-#45 := (= f1 f4)
-#42 := (= f1 f3)
-#48 := (or #42 #45)
-#57 := (ite #48 #51 #54)
-#70 := (iff #57 #57)
-#73 := (iff #70 true)
-#74 := [rewrite]: #73
-#71 := (iff #20 #70)
-#68 := (iff #19 #57)
-#60 := (ite #45 #51 #54)
-#63 := (ite #42 #51 #60)
-#66 := (iff #63 #57)
-#67 := [rewrite]: #66
-#64 := (iff #19 #63)
-#61 := (iff #18 #60)
-#55 := (iff #16 #54)
-#56 := [rewrite]: #55
-#52 := (iff #14 #51)
-#53 := [rewrite]: #52
-#46 := (iff #11 #45)
-#47 := [rewrite]: #46
-#62 := [monotonicity #47 #53 #56]: #61
-#43 := (iff #9 #42)
-#44 := [rewrite]: #43
-#65 := [monotonicity #44 #53 #62]: #64
-#69 := [trans #65 #67]: #68
-#58 := (iff #17 #57)
-#49 := (iff #12 #48)
-#50 := [monotonicity #44 #47]: #49
-#59 := [monotonicity #50 #53 #56]: #58
-#72 := [monotonicity #59 #69]: #71
-#76 := [trans #72 #74]: #75
-#79 := [monotonicity #76]: #78
-#83 := [trans #79 #81]: #82
-#41 := [asserted]: #21
-[mp #41 #83]: false
-unsat
-d57ccd1bb5c7d6c6ba7796601f6907fb7769428b 67 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f6 :: S1
-#15 := f6
-#16 := (= f6 f1)
-decl f5 :: S1
-#13 := f5
-#14 := (= f5 f1)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#18 := (ite #11 #14 #16)
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#19 := (ite #9 #18 #16)
-#12 := (and #9 #11)
-#17 := (ite #12 #14 #16)
-#20 := (iff #17 #19)
-#21 := (not #20)
-#82 := (iff #21 false)
-#1 := true
-#77 := (not true)
-#80 := (iff #77 false)
-#81 := [rewrite]: #80
-#78 := (iff #21 #77)
-#75 := (iff #20 true)
-#54 := (= f1 f6)
-#51 := (= f1 f5)
-#45 := (= f1 f4)
-#42 := (= f1 f3)
-#48 := (and #42 #45)
-#57 := (ite #48 #51 #54)
-#70 := (iff #57 #57)
-#73 := (iff #70 true)
-#74 := [rewrite]: #73
-#71 := (iff #20 #70)
-#68 := (iff #19 #57)
-#60 := (ite #45 #51 #54)
-#63 := (ite #42 #60 #54)
-#66 := (iff #63 #57)
-#67 := [rewrite]: #66
-#64 := (iff #19 #63)
-#55 := (iff #16 #54)
-#56 := [rewrite]: #55
-#61 := (iff #18 #60)
-#52 := (iff #14 #51)
-#53 := [rewrite]: #52
-#46 := (iff #11 #45)
-#47 := [rewrite]: #46
-#62 := [monotonicity #47 #53 #56]: #61
-#43 := (iff #9 #42)
-#44 := [rewrite]: #43
-#65 := [monotonicity #44 #62 #56]: #64
-#69 := [trans #65 #67]: #68
-#58 := (iff #17 #57)
-#49 := (iff #12 #48)
-#50 := [monotonicity #44 #47]: #49
-#59 := [monotonicity #50 #53 #56]: #58
-#72 := [monotonicity #59 #69]: #71
-#76 := [trans #72 #74]: #75
-#79 := [monotonicity #76]: #78
-#83 := [trans #79 #81]: #82
-#41 := [asserted]: #21
-[mp #41 #83]: false
-unsat
-cc825ea9100726025c75fca6a38c4c3107dd3158 181 0
-#2 := false
-decl f6 :: S1
-#14 := f6
-decl f1 :: S1
-#4 := f1
-#53 := (= f1 f6)
-decl f5 :: S1
-#12 := f5
-#50 := (= f1 f5)
-decl f4 :: S1
-#10 := f4
-#47 := (= f1 f4)
-#56 := (ite #47 #50 #53)
-decl f3 :: S1
-#8 := f3
-#44 := (= f1 f3)
-#62 := (not #44)
-#63 := (or #62 #56)
-#101 := (not #63)
-#176 := [hypothesis]: #101
-#151 := (or #63 #44)
-#152 := [def-axiom]: #151
-#177 := [unit-resolution #152 #176]: #44
-#87 := (or #62 #53)
-#79 := (or #62 #50)
-#71 := (or #62 #47)
-#92 := (ite #71 #79 #87)
-#160 := (or #92 #63)
-#102 := (iff #92 #101)
-#15 := (= f6 f1)
-#9 := (= f3 f1)
-#20 := (implies #9 #15)
-#13 := (= f5 f1)
-#19 := (implies #9 #13)
-#11 := (= f4 f1)
-#18 := (implies #9 #11)
-#21 := (ite #18 #19 #20)
-#16 := (ite #11 #13 #15)
-#17 := (implies #9 #16)
-#22 := (iff #17 #21)
-#23 := (not #22)
-#105 := (iff #23 #102)
-#95 := (iff #63 #92)
-#98 := (not #95)
-#103 := (iff #98 #102)
-#104 := [rewrite]: #103
-#99 := (iff #23 #98)
-#96 := (iff #22 #95)
-#93 := (iff #21 #92)
-#90 := (iff #20 #87)
-#84 := (implies #44 #53)
-#88 := (iff #84 #87)
-#89 := [rewrite]: #88
-#85 := (iff #20 #84)
-#54 := (iff #15 #53)
-#55 := [rewrite]: #54
-#45 := (iff #9 #44)
-#46 := [rewrite]: #45
-#86 := [monotonicity #46 #55]: #85
-#91 := [trans #86 #89]: #90
-#82 := (iff #19 #79)
-#76 := (implies #44 #50)
-#80 := (iff #76 #79)
-#81 := [rewrite]: #80
-#77 := (iff #19 #76)
-#51 := (iff #13 #50)
-#52 := [rewrite]: #51
-#78 := [monotonicity #46 #52]: #77
-#83 := [trans #78 #81]: #82
-#74 := (iff #18 #71)
-#68 := (implies #44 #47)
-#72 := (iff #68 #71)
-#73 := [rewrite]: #72
-#69 := (iff #18 #68)
-#48 := (iff #11 #47)
-#49 := [rewrite]: #48
-#70 := [monotonicity #46 #49]: #69
-#75 := [trans #70 #73]: #74
-#94 := [monotonicity #75 #83 #91]: #93
-#66 := (iff #17 #63)
-#59 := (implies #44 #56)
-#64 := (iff #59 #63)
-#65 := [rewrite]: #64
-#60 := (iff #17 #59)
-#57 := (iff #16 #56)
-#58 := [monotonicity #49 #52 #55]: #57
-#61 := [monotonicity #46 #58]: #60
-#67 := [trans #61 #65]: #66
-#97 := [monotonicity #67 #94]: #96
-#100 := [monotonicity #97]: #99
-#106 := [trans #100 #104]: #105
-#43 := [asserted]: #23
-#109 := [mp #43 #106]: #102
-#157 := (not #102)
-#158 := (or #92 #63 #157)
-#159 := [def-axiom]: #158
-#161 := [unit-resolution #159 #109]: #160
-#178 := [unit-resolution #161 #176]: #92
-#112 := (not #71)
-#142 := (not #56)
-#153 := (or #63 #142)
-#154 := [def-axiom]: #153
-#179 := [unit-resolution #154 #176]: #142
-#133 := (not #92)
-#174 := (or #112 #56 #62 #133)
-#166 := [hypothesis]: #142
-#167 := [hypothesis]: #44
-#168 := [hypothesis]: #71
-#108 := (or #112 #62 #47)
-#110 := [def-axiom]: #108
-#169 := [unit-resolution #110 #168 #167]: #47
-#170 := [hypothesis]: #92
-#134 := (or #133 #112 #79)
-#135 := [def-axiom]: #134
-#171 := [unit-resolution #135 #168 #170]: #79
-#122 := (not #79)
-#123 := (or #122 #62 #50)
-#124 := [def-axiom]: #123
-#172 := [unit-resolution #124 #171 #167]: #50
-#119 := (not #50)
-#115 := (not #47)
-#147 := (or #56 #115 #119)
-#148 := [def-axiom]: #147
-#173 := [unit-resolution #148 #172 #169 #166]: false
-#175 := [lemma #173]: #174
-#180 := [unit-resolution #175 #179 #177 #178]: #112
-#136 := (or #133 #71 #87)
-#137 := [def-axiom]: #136
-#181 := [unit-resolution #137 #180 #178]: #87
-#127 := (not #53)
-#116 := (or #71 #115)
-#111 := [def-axiom]: #116
-#182 := [unit-resolution #111 #180]: #115
-#149 := (or #56 #47 #127)
-#150 := [def-axiom]: #149
-#183 := [unit-resolution #150 #182 #179]: #127
-#130 := (not #87)
-#131 := (or #130 #62 #53)
-#132 := [def-axiom]: #131
-#184 := [unit-resolution #132 #183 #181 #177]: false
-#185 := [lemma #184]: #63
-#164 := (or #133 #101)
-#162 := (or #133 #101 #157)
-#163 := [def-axiom]: #162
-#165 := [unit-resolution #163 #109]: #164
-#186 := [unit-resolution #165 #185]: #133
-#187 := [hypothesis]: #62
-#113 := (or #71 #44)
-#114 := [def-axiom]: #113
-#188 := [unit-resolution #114 #187]: #71
-#117 := (or #79 #44)
-#118 := [def-axiom]: #117
-#189 := [unit-resolution #118 #187]: #79
-#138 := (or #92 #112 #122)
-#139 := [def-axiom]: #138
-#190 := [unit-resolution #139 #189 #188 #186]: false
-#191 := [lemma #190]: #44
-#155 := (or #101 #62 #56)
-#156 := [def-axiom]: #155
-#194 := [unit-resolution #156 #191 #185]: #56
-#192 := [hypothesis]: #112
-#140 := (or #92 #71 #130)
-#141 := [def-axiom]: #140
-#193 := [unit-resolution #141 #192 #186]: #130
-#195 := [unit-resolution #111 #192]: #115
-#145 := (or #142 #47 #53)
-#146 := [def-axiom]: #145
-#196 := [unit-resolution #146 #195 #194]: #53
-#128 := (or #87 #127)
-#129 := [def-axiom]: #128
-#197 := [unit-resolution #129 #196 #193]: false
-#198 := [lemma #197]: #71
-#199 := [unit-resolution #110 #198 #191]: #47
-#200 := [unit-resolution #139 #198 #186]: #122
-#120 := (or #79 #119)
-#121 := [def-axiom]: #120
-#201 := [unit-resolution #121 #200]: #119
-#143 := (or #142 #115 #50)
-#144 := [def-axiom]: #143
-[unit-resolution #144 #201 #199 #194]: false
-unsat
-7ec9b76ddbd0690a0ae0e84f7aac32369b67562e 33 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#10 := (not #9)
-#11 := (ite #9 #9 #10)
-#12 := (not #11)
-#51 := (iff #12 false)
-#1 := true
-#46 := (not true)
-#49 := (iff #46 false)
-#50 := [rewrite]: #49
-#47 := (iff #12 #46)
-#44 := (iff #11 true)
-#33 := (= f1 f3)
-#36 := (not #33)
-#39 := (ite #33 #33 #36)
-#42 := (iff #39 true)
-#43 := [rewrite]: #42
-#40 := (iff #11 #39)
-#37 := (iff #10 #36)
-#34 := (iff #9 #33)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#41 := [monotonicity #35 #35 #38]: #40
-#45 := [trans #41 #43]: #44
-#48 := [monotonicity #45]: #47
-#52 := [trans #48 #50]: #51
-#32 := [asserted]: #12
-[mp #32 #52]: false
-unsat
-9a59901175f7c3f42e5be82db6a8df07aaf0199e 33 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#10 := (not #9)
-#11 := (ite #10 #10 #9)
-#12 := (not #11)
-#51 := (iff #12 false)
-#1 := true
-#46 := (not true)
-#49 := (iff #46 false)
-#50 := [rewrite]: #49
-#47 := (iff #12 #46)
-#44 := (iff #11 true)
-#33 := (= f1 f3)
-#36 := (not #33)
-#39 := (ite #36 #36 #33)
-#42 := (iff #39 true)
-#43 := [rewrite]: #42
-#40 := (iff #11 #39)
-#34 := (iff #9 #33)
-#35 := [rewrite]: #34
-#37 := (iff #10 #36)
-#38 := [monotonicity #35]: #37
-#41 := [monotonicity #38 #38 #35]: #40
-#45 := [trans #41 #43]: #44
-#48 := [monotonicity #45]: #47
-#52 := [trans #48 #50]: #51
-#32 := [asserted]: #12
-[mp #32 #52]: false
-unsat
-6758e928b7c8973f924b8c2c252430960344c442 18 0
-#2 := false
-decl f3 :: S2
-#8 := f3
-#9 := (= f3 f3)
-#10 := (not #9)
-#38 := (iff #10 false)
-#1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#31 := (iff #9 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#30 := [asserted]: #10
-[mp #30 #39]: false
-unsat
-5cd924cc739389c12253492d422dfc6ac2f6d405 29 0
-#2 := false
-decl f3 :: S2
-#8 := f3
-decl f4 :: S2
-#9 := f4
-#11 := (= f4 f3)
-#10 := (= f3 f4)
-#12 := (implies #10 #11)
-#13 := (not #12)
-#48 := (iff #13 false)
+#48 := (iff #12 false)
 #1 := true
 #43 := (not true)
 #46 := (iff #43 false)
 #47 := [rewrite]: #46
-#44 := (iff #13 #43)
-#41 := (iff #12 true)
-#36 := (implies #10 #10)
+#44 := (iff #12 #43)
+#41 := (iff #11 true)
+#36 := (not false)
 #39 := (iff #36 true)
 #40 := [rewrite]: #39
-#37 := (iff #12 #36)
-#34 := (iff #11 #10)
+#37 := (iff #11 #36)
+#34 := (iff #10 false)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#33 := [asserted]: #12
+[mp #33 #49]: false
+unsat
+aa0273c12559afb5fd359c235b02afbc8f3cc399 49 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#11 := (and false #8)
+#12 := (or #11 #8)
+#10 := (not #8)
+#13 := (or #10 #12)
+#1 := true
+#9 := (and true #8)
+#14 := (or #9 #13)
+#15 := (not #14)
+#67 := (iff #15 false)
+#62 := (not true)
+#65 := (iff #62 false)
+#66 := [rewrite]: #65
+#63 := (iff #15 #62)
+#60 := (iff #14 true)
+#55 := (or #8 true)
+#58 := (iff #55 true)
+#59 := [rewrite]: #58
+#56 := (iff #14 #55)
+#53 := (iff #13 true)
+#48 := (or #10 #8)
+#51 := (iff #48 true)
+#52 := [rewrite]: #51
+#49 := (iff #13 #48)
+#46 := (iff #12 #8)
+#41 := (or false #8)
+#44 := (iff #41 #8)
+#45 := [rewrite]: #44
+#42 := (iff #12 #41)
+#39 := (iff #11 false)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#50 := [monotonicity #47]: #49
+#54 := [trans #50 #52]: #53
+#37 := (iff #9 #8)
+#38 := [rewrite]: #37
+#57 := [monotonicity #38 #54]: #56
+#61 := [trans #57 #59]: #60
+#64 := [monotonicity #61]: #63
+#68 := [trans #64 #66]: #67
+#36 := [asserted]: #15
+[mp #36 #68]: false
+unsat
+22c928dddd46280815470bda1451161b824f3f34 21 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#9 := (implies #8 #8)
+#10 := (not #9)
+#39 := (iff #10 false)
+#1 := true
+#34 := (not true)
+#37 := (iff #34 false)
+#38 := [rewrite]: #37
+#35 := (iff #10 #34)
+#32 := (iff #9 true)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#40 := [trans #36 #38]: #39
+#31 := [asserted]: #10
+[mp #31 #40]: false
+unsat
+eb161eaf2af208e84d9da7d647585602865b89ac 30 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#9 := (not #8)
+#10 := (and #8 #9)
+#11 := (implies #10 false)
+#12 := (not #11)
+#48 := (iff #12 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (iff #11 true)
+#36 := (implies false false)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #11 #36)
+#34 := (iff #10 false)
 #35 := [rewrite]: #34
 #38 := [monotonicity #35]: #37
 #42 := [trans #38 #40]: #41
 #45 := [monotonicity #42]: #44
 #49 := [trans #45 #47]: #48
-#33 := [asserted]: #13
+#33 := [asserted]: #12
 [mp #33 #49]: false
 unsat
-e82612aca334f7d47bdb5a90fdc8f5dfc017ae67 34 0
-#2 := false
-decl f5 :: S2
-#11 := f5
-decl f3 :: S2
-#8 := f3
-#14 := (= f3 f5)
-decl f4 :: S2
+b2602e0e3e3911fa8042ad9ddbc6f102e48e88f7 48 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#12 := (and #10 #8)
+#47 := (not #12)
+#68 := (iff #47 false)
+#1 := true
+#63 := (not true)
+#66 := (iff #63 false)
+#67 := [rewrite]: #66
+#64 := (iff #47 #63)
+#61 := (iff #12 true)
+#56 := (and true true)
+#59 := (iff #56 true)
+#60 := [rewrite]: #59
+#57 := (iff #12 #56)
+#52 := (iff #8 true)
+#11 := (and #8 #10)
+#36 := (not #11)
+#37 := (or #36 #12)
+#40 := (not #37)
+#13 := (implies #11 #12)
+#14 := (not #13)
+#41 := (iff #14 #40)
+#38 := (iff #13 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#35 := [asserted]: #14
+#45 := [mp #35 #42]: #40
+#43 := [not-or-elim #45]: #11
+#44 := [and-elim #43]: #8
+#53 := [iff-true #44]: #52
+#54 := (iff #10 true)
+#46 := [and-elim #43]: #10
+#55 := [iff-true #46]: #54
+#58 := [monotonicity #55 #53]: #57
+#62 := [trans #58 #60]: #61
+#65 := [monotonicity #62]: #64
+#69 := [trans #65 #67]: #68
+#48 := [not-or-elim #45]: #47
+[mp #48 #69]: false
+unsat
+467aa750a0af9865e5bc1b47f63cfc13f031554b 48 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#11 := (or #8 #10)
+#71 := (iff #11 false)
+#66 := (or false false)
+#69 := (iff #66 false)
+#70 := [rewrite]: #69
+#67 := (iff #11 #66)
+#62 := (iff #10 false)
+#53 := (not #10)
+#36 := (not #11)
+#43 := (or #36 #10 #8)
+#46 := (not #43)
+#12 := (or #10 #8)
+#13 := (implies #11 #12)
+#14 := (not #13)
+#49 := (iff #14 #46)
+#37 := (or #36 #12)
+#40 := (not #37)
+#47 := (iff #40 #46)
+#44 := (iff #37 #43)
+#45 := [rewrite]: #44
+#48 := [monotonicity #45]: #47
+#41 := (iff #14 #40)
+#38 := (iff #13 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#50 := [trans #42 #48]: #49
+#35 := [asserted]: #14
+#51 := [mp #35 #50]: #46
+#54 := [not-or-elim #51]: #53
+#63 := [iff-false #54]: #62
+#64 := (iff #8 false)
+#55 := (not #8)
+#56 := [not-or-elim #51]: #55
+#65 := [iff-false #56]: #64
+#68 := [monotonicity #65 #63]: #67
+#72 := [trans #68 #70]: #71
+#52 := [not-or-elim #51]: #11
+[mp #52 #72]: false
+unsat
+ff06b47195393e825a3f80a82c50109ac3e8bd12 46 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#55 := (not #8)
+#71 := (iff #55 false)
+#1 := true
+#66 := (not true)
+#69 := (iff #66 false)
+#70 := [rewrite]: #69
+#67 := (iff #55 #66)
+#62 := (iff #8 true)
+decl f4 :: S1
 #9 := f4
-#12 := (= f4 f5)
-#61 := (iff #12 #14)
-#59 := (iff #14 #12)
-#10 := (= f3 f4)
-#13 := (and #10 #12)
-#37 := (not #13)
-#38 := (or #37 #14)
-#41 := (not #38)
-#15 := (implies #13 #14)
-#16 := (not #15)
-#42 := (iff #16 #41)
-#39 := (iff #15 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#36 := [asserted]: #16
-#46 := [mp #36 #43]: #41
-#44 := [not-or-elim #46]: #13
-#45 := [and-elim #44]: #10
-#60 := [monotonicity #45]: #59
-#62 := [symm #60]: #61
-#47 := [and-elim #44]: #12
-#57 := [mp #47 #62]: #14
-#48 := (not #14)
-#49 := [not-or-elim #46]: #48
-[unit-resolution #49 #57]: false
-unsat
-450aaafd6173c5e6036fdec198da2898811d4211 27 0
-#2 := false
-decl f5 :: (-> S2 S2)
-decl f4 :: S2
+#10 := (= f4 f1)
+#11 := (and #8 #10)
+#36 := (not #11)
+#43 := (or #36 #8 #10)
+#46 := (not #43)
+#12 := (or #8 #10)
+#13 := (implies #11 #12)
+#14 := (not #13)
+#49 := (iff #14 #46)
+#37 := (or #36 #12)
+#40 := (not #37)
+#47 := (iff #40 #46)
+#44 := (iff #37 #43)
+#45 := [rewrite]: #44
+#48 := [monotonicity #45]: #47
+#41 := (iff #14 #40)
+#38 := (iff #13 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#50 := [trans #42 #48]: #49
+#35 := [asserted]: #14
+#51 := [mp #35 #50]: #46
+#52 := [not-or-elim #51]: #11
+#53 := [and-elim #52]: #8
+#63 := [iff-true #53]: #62
+#68 := [monotonicity #63]: #67
+#72 := [trans #68 #70]: #71
+#56 := [not-or-elim #51]: #55
+[mp #56 #72]: false
+unsat
+a9e6ae903779155c6cefbf205c225628953e624e 35 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#13 := (not #8)
+decl f4 :: S1
 #9 := f4
-#12 := (f5 f4)
-decl f3 :: S2
-#8 := f3
-#11 := (f5 f3)
-#13 := (= #11 #12)
-#10 := (= f3 f4)
-#36 := (not #10)
-#37 := (or #36 #13)
+#10 := (= f4 f1)
+#11 := (or #8 #10)
+#12 := (not #11)
+#14 := (implies #12 #13)
+#15 := (not #14)
+#52 := (iff #15 false)
+#37 := (or #11 #13)
 #40 := (not #37)
-#14 := (implies #10 #13)
+#50 := (iff #40 false)
+#1 := true
+#45 := (not true)
+#48 := (iff #45 false)
+#49 := [rewrite]: #48
+#46 := (iff #40 #45)
+#43 := (iff #37 true)
+#44 := [rewrite]: #43
+#47 := [monotonicity #44]: #46
+#51 := [trans #47 #49]: #50
+#41 := (iff #15 #40)
+#38 := (iff #14 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#53 := [trans #42 #51]: #52
+#36 := [asserted]: #15
+[mp #36 #53]: false
+unsat
+fb622d34475687ad69de4f4faf6a2f3bed3d41ba 35 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#13 := (not #10)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#11 := (or #8 #10)
+#12 := (not #11)
+#14 := (implies #12 #13)
+#15 := (not #14)
+#52 := (iff #15 false)
+#37 := (or #11 #13)
+#40 := (not #37)
+#50 := (iff #40 false)
+#1 := true
+#45 := (not true)
+#48 := (iff #45 false)
+#49 := [rewrite]: #48
+#46 := (iff #40 #45)
+#43 := (iff #37 true)
+#44 := [rewrite]: #43
+#47 := [monotonicity #44]: #46
+#51 := [trans #47 #49]: #50
+#41 := (iff #15 #40)
+#38 := (iff #14 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#53 := [trans #42 #51]: #52
+#36 := [asserted]: #15
+[mp #36 #53]: false
+unsat
+53094a0b951afe51834bc943782c2a61c91fc254 29 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#51 := (iff #8 false)
+#9 := (not #8)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#12 := (and #8 #11)
+#13 := (not #12)
+#37 := (or #8 #13)
+#40 := (not #37)
+#14 := (implies #9 #13)
 #15 := (not #14)
 #41 := (iff #15 #40)
 #38 := (iff #14 #37)
 #39 := [rewrite]: #38
 #42 := [monotonicity #39]: #41
-#35 := [asserted]: #15
-#45 := [mp #35 #42]: #40
-#43 := [not-or-elim #45]: #10
-#54 := [monotonicity #43]: #13
-#44 := (not #13)
-#46 := [not-or-elim #45]: #44
-[unit-resolution #46 #54]: false
-unsat
-268885483340f29776e2c235da393d33273743e0 31 0
-#2 := false
-decl f5 :: (-> S2 S2 S3)
-decl f3 :: S2
-#8 := f3
-decl f4 :: S2
-#9 := f4
-#12 := (f5 f4 f3)
-#11 := (f5 f3 f4)
-#13 := (= #11 #12)
-#56 := (= #12 #11)
-#10 := (= f3 f4)
-#36 := (not #10)
-#37 := (or #36 #13)
+#36 := [asserted]: #15
+#45 := [mp #36 #42]: #40
+#43 := [not-or-elim #45]: #9
+#52 := [iff-false #43]: #51
+#44 := [not-or-elim #45]: #12
+#46 := [and-elim #44]: #8
+[mp #46 #52]: false
+unsat
+380c58b7f01c4eb6d1f5b709fb3a647172217808 29 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#51 := (iff #8 false)
+#9 := (not #8)
+decl f4 :: S1
+#10 := f4
+#11 := (= f4 f1)
+#12 := (and #11 #8)
+#13 := (not #12)
+#37 := (or #8 #13)
 #40 := (not #37)
-#14 := (implies #10 #13)
+#14 := (implies #9 #13)
 #15 := (not #14)
 #41 := (iff #15 #40)
 #38 := (iff #14 #37)
 #39 := [rewrite]: #38
 #42 := [monotonicity #39]: #41
-#35 := [asserted]: #15
-#45 := [mp #35 #42]: #40
-#43 := [not-or-elim #45]: #10
-#54 := (= f4 f3)
-#55 := [symm #43]: #54
-#57 := [monotonicity #55 #43]: #56
-#52 := [symm #57]: #13
-#44 := (not #13)
-#46 := [not-or-elim #45]: #44
-[unit-resolution #46 #52]: false
-unsat
-b23fdcb8ecc896d99515b950a22874e320c73a5e 63 0
-#2 := false
-decl f3 :: (-> S2 S2)
-decl f4 :: S2
-#8 := f4
-#9 := (f3 f4)
-#49 := (= f4 #9)
-#10 := (f3 #9)
-#12 := (f3 #10)
-#81 := (= #12 #9)
-#79 := (= #9 #12)
-#40 := (= f4 #10)
-#13 := (f3 #12)
-#14 := (f3 #13)
-#43 := (= f4 #14)
-#46 := (and #40 #43)
-#55 := (not #46)
-#56 := (or #55 #49)
+#36 := [asserted]: #15
+#45 := [mp #36 #42]: #40
+#43 := [not-or-elim #45]: #9
+#52 := [iff-false #43]: #51
+#44 := [not-or-elim #45]: #12
+#47 := [and-elim #44]: #8
+[mp #47 #52]: false
+unsat
+bfe8aa961b370c267ecd388cc5b7c835a7cfadff 31 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#13 := (not #10)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#12 := (not #8)
+#14 := (or #12 #13)
+#11 := (and #8 #10)
+#40 := (iff #11 #14)
+#43 := (iff #40 false)
+#15 := (not #14)
+#49 := (iff #15 #14)
+#46 := (iff #49 false)
+#47 := [rewrite]: #46
+#50 := (iff #40 #49)
+#16 := (iff #11 #15)
+#48 := [rewrite]: #16
+#51 := [monotonicity #48]: #50
+#45 := [trans #51 #47]: #43
+#17 := (not #16)
+#39 := (iff #17 #40)
+#41 := [rewrite]: #39
+#38 := [asserted]: #17
+#44 := [mp #38 #41]: #40
+[mp #44 #45]: false
+unsat
+f98cd324a1d939c466a676264b34fe6330962e34 53 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f5 :: S1
+#12 := f5
+#13 := (= f5 f1)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#15 := (and #10 #13)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#16 := (and #8 #15)
+#11 := (and #8 #10)
+#14 := (and #11 #13)
+#17 := (implies #14 #16)
+#18 := (not #17)
+#69 := (iff #18 false)
+#40 := (not #14)
+#41 := (or #40 #16)
+#44 := (not #41)
+#67 := (iff #44 false)
+#1 := true
+#62 := (not true)
+#65 := (iff #62 false)
+#66 := [rewrite]: #65
+#63 := (iff #44 #62)
+#60 := (iff #41 true)
+#47 := (and #8 #10 #13)
+#50 := (not #47)
+#55 := (or #50 #47)
+#58 := (iff #55 true)
+#59 := [rewrite]: #58
+#56 := (iff #41 #55)
+#53 := (iff #16 #47)
+#54 := [rewrite]: #53
+#51 := (iff #40 #50)
+#48 := (iff #14 #47)
+#49 := [rewrite]: #48
+#52 := [monotonicity #49]: #51
+#57 := [monotonicity #52 #54]: #56
+#61 := [trans #57 #59]: #60
+#64 := [monotonicity #61]: #63
+#68 := [trans #64 #66]: #67
+#45 := (iff #18 #44)
+#42 := (iff #17 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#70 := [trans #46 #68]: #69
+#39 := [asserted]: #18
+[mp #39 #70]: false
+unsat
+8a92c826e93199f25eaea9a9d8eb4b750d4ce618 68 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f5 :: S1
+#12 := f5
+#13 := (= f5 f1)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#47 := (or #8 #10 #13)
+#90 := (iff #47 false)
+#85 := (or false false false)
+#88 := (iff #85 false)
+#89 := [rewrite]: #88
+#86 := (iff #47 #85)
+#83 := (iff #13 false)
+#72 := (not #13)
+#50 := (not #47)
+#56 := (or #50 #8 #10 #13)
 #61 := (not #56)
-#17 := (= #9 f4)
-#15 := (= #14 f4)
-#11 := (= #10 f4)
-#16 := (and #11 #15)
-#18 := (implies #16 #17)
+#15 := (or #10 #13)
+#16 := (or #8 #15)
+#11 := (or #8 #10)
+#14 := (or #11 #13)
+#17 := (implies #14 #16)
+#18 := (not #17)
+#64 := (iff #18 #61)
+#40 := (not #14)
+#41 := (or #40 #16)
+#44 := (not #41)
+#62 := (iff #44 #61)
+#59 := (iff #41 #56)
+#53 := (or #50 #16)
+#57 := (iff #53 #56)
+#58 := [rewrite]: #57
+#54 := (iff #41 #53)
+#51 := (iff #40 #50)
+#48 := (iff #14 #47)
+#49 := [rewrite]: #48
+#52 := [monotonicity #49]: #51
+#55 := [monotonicity #52]: #54
+#60 := [trans #55 #58]: #59
+#63 := [monotonicity #60]: #62
+#45 := (iff #18 #44)
+#42 := (iff #17 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#65 := [trans #46 #63]: #64
+#39 := [asserted]: #18
+#66 := [mp #39 #65]: #61
+#73 := [not-or-elim #66]: #72
+#84 := [iff-false #73]: #83
+#81 := (iff #10 false)
+#70 := (not #10)
+#71 := [not-or-elim #66]: #70
+#82 := [iff-false #71]: #81
+#79 := (iff #8 false)
+#68 := (not #8)
+#69 := [not-or-elim #66]: #68
+#80 := [iff-false #69]: #79
+#87 := [monotonicity #80 #82 #84]: #86
+#91 := [trans #87 #89]: #90
+#67 := [not-or-elim #66]: #47
+[mp #67 #91]: false
+unsat
+fc4b5f359a07a487172052f71a085a338dacb4ab 80 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f5 :: S1
+#12 := f5
+#13 := (= f5 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#15 := (or #8 #13)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#60 := (not #10)
+#59 := (not #8)
+#61 := (or #59 #60)
+#62 := (not #61)
+#85 := (not #13)
+#96 := [hypothesis]: #13
+#86 := (or #15 #85)
+#87 := [def-axiom]: #86
+#97 := [unit-resolution #87 #96]: #15
+#16 := (or #10 #13)
+#92 := (or #16 #85)
+#93 := [def-axiom]: #92
+#98 := [unit-resolution #93 #96]: #16
+#64 := (not #16)
+#63 := (not #15)
+#65 := (or #63 #64)
+#17 := (and #15 #16)
+#49 := (not #17)
+#74 := (iff #49 #65)
+#66 := (not #65)
+#69 := (not #66)
+#72 := (iff #69 #65)
+#73 := [rewrite]: #72
+#70 := (iff #49 #69)
+#67 := (iff #17 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#75 := [trans #71 #73]: #74
+#11 := (and #8 #10)
+#14 := (or #11 #13)
+#41 := (not #14)
+#42 := (or #41 #17)
+#45 := (not #42)
+#18 := (implies #14 #17)
 #19 := (not #18)
-#62 := (iff #19 #61)
-#59 := (iff #18 #56)
-#52 := (implies #46 #49)
-#57 := (iff #52 #56)
+#46 := (iff #19 #45)
+#43 := (iff #18 #42)
+#44 := [rewrite]: #43
+#47 := [monotonicity #44]: #46
+#40 := [asserted]: #19
+#50 := [mp #40 #47]: #45
+#51 := [not-or-elim #50]: #49
+#76 := [mp #51 #75]: #65
+#99 := [unit-resolution #76 #98 #97]: false
+#100 := [lemma #99]: #85
+#55 := (or #62 #13)
+#56 := (iff #14 #55)
+#57 := (iff #11 #62)
 #58 := [rewrite]: #57
-#53 := (iff #18 #52)
-#50 := (iff #17 #49)
-#51 := [rewrite]: #50
-#47 := (iff #16 #46)
-#44 := (iff #15 #43)
-#45 := [rewrite]: #44
-#41 := (iff #11 #40)
-#42 := [rewrite]: #41
-#48 := [monotonicity #42 #45]: #47
-#54 := [monotonicity #48 #51]: #53
-#60 := [trans #54 #58]: #59
-#63 := [monotonicity #60]: #62
-#39 := [asserted]: #19
-#66 := [mp #39 #63]: #61
-#64 := [not-or-elim #66]: #46
-#65 := [and-elim #64]: #40
-#80 := [monotonicity #65]: #79
-#82 := [symm #80]: #81
-#84 := (= f4 #12)
-#72 := (= #14 #12)
-#73 := (= #12 #14)
-#75 := (= #10 #13)
-#77 := (= #13 #10)
-#78 := [monotonicity #82]: #77
-#76 := [symm #78]: #75
-#74 := [monotonicity #76]: #73
-#83 := [symm #74]: #72
-#67 := [and-elim #64]: #43
-#85 := [trans #67 #83]: #84
-#86 := [trans #85 #82]: #49
-#68 := (not #49)
-#69 := [not-or-elim #66]: #68
-[unit-resolution #69 #86]: false
-unsat
-bdf634420f64829e899fdad55dc280602f81f222 176 0
-#2 := false
-decl f5 :: S2
-#11 := f5
-decl f4 :: S2
-#10 := f4
+#53 := [monotonicity #58]: #56
+#48 := [not-or-elim #50]: #14
+#54 := [mp #48 #53]: #55
+#101 := [unit-resolution #54 #100]: #62
+#77 := (or #61 #8)
+#78 := [def-axiom]: #77
+#102 := [unit-resolution #78 #101]: #8
+#83 := (or #15 #59)
+#84 := [def-axiom]: #83
+#103 := [unit-resolution #84 #102]: #15
+#79 := (or #61 #10)
+#80 := [def-axiom]: #79
+#104 := [unit-resolution #80 #101]: #10
+#90 := (or #16 #60)
+#91 := [def-axiom]: #90
+#105 := [unit-resolution #91 #104]: #16
+[unit-resolution #76 #105 #103]: false
+unsat
+a7b9e3e37b2bf7cfdd0c93de11378292f7f169f7 82 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f5 :: S1
+#12 := f5
+#13 := (= f5 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#16 := (and #8 #13)
+#60 := (not #16)
+#101 := (iff #60 false)
+#1 := true
+#71 := (not true)
+#99 := (iff #71 false)
+#100 := [rewrite]: #99
+#72 := (iff #60 #71)
+#96 := (iff #16 true)
+#91 := (and true true)
+#94 := (iff #91 true)
+#95 := [rewrite]: #94
+#92 := (iff #16 #91)
+#70 := (iff #13 true)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#14 := (or #13 #10)
+#80 := (iff #14 #13)
+#75 := (or #13 false)
+#78 := (iff #75 #13)
+#79 := [rewrite]: #78
+#76 := (iff #14 #75)
+#73 := (iff #10 false)
+#62 := (not #10)
+#11 := (or #8 #10)
+#15 := (and #11 #14)
+#41 := (not #15)
+#48 := (or #41 #16 #10)
+#51 := (not #48)
+#17 := (or #16 #10)
+#18 := (implies #15 #17)
+#19 := (not #18)
+#54 := (iff #19 #51)
+#42 := (or #41 #17)
+#45 := (not #42)
+#52 := (iff #45 #51)
+#49 := (iff #42 #48)
+#50 := [rewrite]: #49
+#53 := [monotonicity #50]: #52
+#46 := (iff #19 #45)
+#43 := (iff #18 #42)
+#44 := [rewrite]: #43
+#47 := [monotonicity #44]: #46
+#55 := [trans #47 #53]: #54
+#40 := [asserted]: #19
+#56 := [mp #40 #55]: #51
+#63 := [not-or-elim #56]: #62
+#74 := [iff-false #63]: #73
+#77 := [monotonicity #74]: #76
+#81 := [trans #77 #79]: #80
+#57 := [not-or-elim #56]: #15
+#59 := [and-elim #57]: #14
+#69 := [mp #59 #81]: #13
+#82 := [iff-true #69]: #70
+#68 := (iff #8 true)
+#88 := (iff #11 #8)
+#83 := (or #8 false)
+#86 := (iff #83 #8)
+#87 := [rewrite]: #86
+#84 := (iff #11 #83)
+#85 := [monotonicity #74]: #84
+#89 := [trans #85 #87]: #88
+#58 := [and-elim #57]: #11
+#67 := [mp #58 #89]: #8
+#90 := [iff-true #67]: #68
+#93 := [monotonicity #90 #82]: #92
+#97 := [trans #93 #95]: #96
+#98 := [monotonicity #97]: #72
+#102 := [trans #98 #100]: #101
+#61 := [not-or-elim #56]: #60
+[mp #61 #102]: false
+unsat
+fbfd7f42f20fd17af6ee42b17ec7a0dc3c529924 81 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#11 := (or #8 #10)
+#102 := (iff #11 false)
+#97 := (or false false)
+#100 := (iff #97 false)
+#101 := [rewrite]: #100
+#98 := (iff #11 #97)
+#95 := (iff #10 false)
+#91 := (not #10)
+decl f5 :: S1
+#12 := f5
+#13 := (= f5 f1)
+#16 := (and #10 #13)
+#62 := (not #16)
+#92 := (iff #62 #91)
+#89 := (iff #16 #10)
+#1 := true
+#84 := (and #10 true)
+#87 := (iff #84 #10)
+#88 := [rewrite]: #87
+#85 := (iff #16 #84)
+#69 := (iff #13 true)
+#14 := (and #11 #13)
+#15 := (and #8 #13)
+#41 := (not #14)
+#48 := (or #41 #15 #16)
+#51 := (not #48)
+#17 := (or #15 #16)
+#18 := (implies #14 #17)
+#19 := (not #18)
+#54 := (iff #19 #51)
+#42 := (or #41 #17)
+#45 := (not #42)
+#52 := (iff #45 #51)
+#49 := (iff #42 #48)
+#50 := [rewrite]: #49
+#53 := [monotonicity #50]: #52
+#46 := (iff #19 #45)
+#43 := (iff #18 #42)
+#44 := [rewrite]: #43
+#47 := [monotonicity #44]: #46
+#55 := [trans #47 #53]: #54
+#40 := [asserted]: #19
+#56 := [mp #40 #55]: #51
+#57 := [not-or-elim #56]: #14
+#59 := [and-elim #57]: #13
+#70 := [iff-true #59]: #69
+#86 := [monotonicity #70]: #85
+#90 := [trans #86 #88]: #89
+#93 := [monotonicity #90]: #92
+#63 := [not-or-elim #56]: #62
+#94 := [mp #63 #93]: #91
+#96 := [iff-false #94]: #95
+#82 := (iff #8 false)
+#78 := (not #8)
+#60 := (not #15)
+#79 := (iff #60 #78)
+#76 := (iff #15 #8)
+#71 := (and #8 true)
+#74 := (iff #71 #8)
+#75 := [rewrite]: #74
+#72 := (iff #15 #71)
+#73 := [monotonicity #70]: #72
+#77 := [trans #73 #75]: #76
+#80 := [monotonicity #77]: #79
+#61 := [not-or-elim #56]: #60
+#81 := [mp #61 #80]: #78
+#83 := [iff-false #81]: #82
+#99 := [monotonicity #83 #96]: #98
+#103 := [trans #99 #101]: #102
+#58 := [and-elim #57]: #11
+[mp #58 #103]: false
+unsat
+e8a50c44ee4032088b7ba718bb04f0f679fca9de 83 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#60 := (not #10)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#59 := (not #8)
+#61 := (or #59 #60)
+decl f5 :: S1
+#12 := f5
+#13 := (= f5 f1)
+#16 := (or #8 #13)
+#68 := (not #16)
+#99 := [hypothesis]: #60
+#83 := (or #61 #10)
+#84 := [def-axiom]: #83
+#100 := [unit-resolution #84 #99]: #61
+#55 := (not #13)
+#56 := (or #55 #60)
+#89 := (or #56 #10)
+#90 := [def-axiom]: #89
+#101 := [unit-resolution #90 #99]: #56
+#53 := (not #56)
+#62 := (not #61)
+#64 := (or #62 #53)
+#14 := (and #13 #10)
+#11 := (and #8 #10)
+#15 := (or #11 #14)
+#65 := (iff #15 #64)
+#54 := (iff #14 #53)
+#63 := [rewrite]: #54
+#57 := (iff #11 #62)
+#58 := [rewrite]: #57
+#66 := [monotonicity #58 #63]: #65
+#17 := (and #16 #10)
+#41 := (not #15)
+#42 := (or #41 #17)
+#45 := (not #42)
+#18 := (implies #15 #17)
+#19 := (not #18)
+#46 := (iff #19 #45)
+#43 := (iff #18 #42)
+#44 := [rewrite]: #43
+#47 := [monotonicity #44]: #46
+#40 := [asserted]: #19
+#50 := [mp #40 #47]: #45
+#48 := [not-or-elim #50]: #15
+#67 := [mp #48 #66]: #64
+#102 := [unit-resolution #67 #101 #100]: false
+#103 := [lemma #102]: #10
+#69 := (or #68 #60)
+#49 := (not #17)
+#78 := (iff #49 #69)
+#70 := (not #69)
+#73 := (not #70)
+#76 := (iff #73 #69)
+#77 := [rewrite]: #76
+#74 := (iff #49 #73)
+#71 := (iff #17 #70)
+#72 := [rewrite]: #71
+#75 := [monotonicity #72]: #74
+#79 := [trans #75 #77]: #78
+#51 := [not-or-elim #50]: #49
+#80 := [mp #51 #79]: #69
+#104 := [unit-resolution #80 #103]: #68
+#93 := (or #16 #59)
+#94 := [def-axiom]: #93
+#105 := [unit-resolution #94 #104]: #59
+#81 := (or #61 #8)
+#82 := [def-axiom]: #81
+#106 := [unit-resolution #82 #105]: #61
+#95 := (or #16 #55)
+#96 := [def-axiom]: #95
+#107 := [unit-resolution #96 #104]: #55
+#87 := (or #56 #13)
+#88 := [def-axiom]: #87
+#108 := [unit-resolution #88 #107]: #56
+[unit-resolution #67 #108 #106]: false
+unsat
+7e6dd7d516e726860ffc428f31cde1cf481b2e62 55 0
+#2 := false
+decl f1 :: S1
+#3 := f1
 decl f3 :: S1
-#8 := f3
-decl f1 :: S1
-#4 := f1
-#43 := (= f1 f3)
-#46 := (ite #43 f4 f5)
-decl f6 :: S2
-#13 := f6
-#52 := (= f6 #46)
-#114 := (= f5 #46)
-#60 := (not #43)
-#15 := (= f4 f6)
-#172 := (iff #52 #15)
-#170 := (iff #15 #52)
-#49 := (= #46 f6)
-#53 := (iff #49 #52)
-#169 := [commutativity]: #53
-#167 := (iff #15 #49)
-#113 := (= f4 #46)
-#161 := [hypothesis]: #43
-#115 := (or #60 #113)
-#116 := [def-axiom]: #115
-#166 := [unit-resolution #116 #161]: #113
-#168 := [monotonicity #166]: #167
-#171 := [trans #168 #169]: #170
-#173 := [symm #171]: #172
-#18 := (= f5 f6)
-#71 := (or #18 #43)
-#98 := (not #71)
-#61 := (or #15 #60)
-#97 := (not #61)
-#99 := (or #97 #98)
-#178 := (or #99 #60)
-#119 := (not #15)
-#85 := (not #52)
-#174 := (iff #85 #119)
-#175 := [monotonicity #173]: #174
-#100 := (not #99)
-#162 := [hypothesis]: #100
-#146 := (or #85 #99)
-#107 := (iff #52 #99)
-#76 := (and #61 #71)
-#86 := (iff #76 #85)
-#110 := (iff #86 #107)
-#102 := (iff #99 #52)
-#108 := (iff #102 #107)
-#109 := [rewrite]: #108
-#105 := (iff #86 #102)
-#92 := (iff #100 #85)
-#103 := (iff #92 #102)
+#7 := f3
+#8 := (= f3 f1)
+#36 := (not #8)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#37 := (or #36 #10)
+#43 := (not #37)
+#44 := (or #43 #8)
+#52 := (not #44)
+#53 := (or #52 #8)
+#58 := (not #53)
+#11 := (implies #8 #10)
+#12 := (implies #11 #8)
+#13 := (implies #12 #8)
+#14 := (not #13)
+#59 := (iff #14 #58)
+#56 := (iff #13 #53)
+#49 := (implies #44 #8)
+#54 := (iff #49 #53)
+#55 := [rewrite]: #54
+#50 := (iff #13 #49)
+#47 := (iff #12 #44)
+#40 := (implies #37 #8)
+#45 := (iff #40 #44)
+#46 := [rewrite]: #45
+#41 := (iff #12 #40)
+#38 := (iff #11 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#48 := [trans #42 #46]: #47
+#51 := [monotonicity #48]: #50
+#57 := [trans #51 #55]: #56
+#60 := [monotonicity #57]: #59
+#35 := [asserted]: #14
+#63 := [mp #35 #60]: #58
+#62 := [not-or-elim #63]: #36
+#76 := (iff #44 #43)
+#71 := (or #43 false)
+#74 := (iff #71 #43)
+#75 := [rewrite]: #74
+#72 := (iff #44 #71)
+#69 := (iff #8 false)
+#70 := [iff-false #62]: #69
+#73 := [monotonicity #70]: #72
+#77 := [trans #73 #75]: #76
+#61 := [not-or-elim #63]: #44
+#67 := [mp #61 #77]: #43
+#65 := [not-or-elim #67]: #8
+[unit-resolution #65 #62]: false
+unsat
+a3a59727086c9b1cf17547c43bc0b367753da6a2 129 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+decl f5 :: S1
+#12 := f5
+#13 := (= f5 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#16 := (or #8 #13)
+#52 := (not #16)
+#53 := (or #52 #10)
+#45 := (not #13)
+#46 := (or #45 #10)
+#75 := (not #46)
+#41 := (not #8)
+#42 := (or #41 #10)
+#74 := (not #42)
+#76 := (or #74 #75)
+#116 := (not #53)
+#77 := (not #76)
+#128 := [hypothesis]: #77
+#122 := (or #76 #116)
+#83 := (iff #76 #53)
+#49 := (and #42 #46)
+#62 := (not #49)
+#63 := (iff #62 #53)
+#84 := (iff #63 #83)
+#81 := (iff #62 #76)
+#69 := (not #77)
+#79 := (iff #69 #76)
+#80 := [rewrite]: #79
+#71 := (iff #62 #69)
+#72 := (iff #49 #77)
+#73 := [rewrite]: #72
+#78 := [monotonicity #73]: #71
+#82 := [trans #78 #80]: #81
+#85 := [monotonicity #82]: #84
+#17 := (implies #16 #10)
+#14 := (implies #13 #10)
+#11 := (implies #8 #10)
+#15 := (and #11 #14)
+#18 := (iff #15 #17)
+#19 := (not #18)
+#66 := (iff #19 #63)
+#56 := (iff #49 #53)
+#59 := (not #56)
+#64 := (iff #59 #63)
+#65 := [rewrite]: #64
+#60 := (iff #19 #59)
+#57 := (iff #18 #56)
+#54 := (iff #17 #53)
+#55 := [rewrite]: #54
+#50 := (iff #15 #49)
+#47 := (iff #14 #46)
+#48 := [rewrite]: #47
+#43 := (iff #11 #42)
+#44 := [rewrite]: #43
+#51 := [monotonicity #44 #48]: #50
+#58 := [monotonicity #51 #55]: #57
+#61 := [monotonicity #58]: #60
+#67 := [trans #61 #65]: #66
+#40 := [asserted]: #19
+#70 := [mp #40 #67]: #63
+#86 := [mp #70 #85]: #83
+#119 := (not #83)
+#120 := (or #76 #116 #119)
+#121 := [def-axiom]: #120
+#123 := [unit-resolution #121 #86]: #122
+#129 := [unit-resolution #123 #128]: #116
+#112 := (or #53 #16)
+#113 := [def-axiom]: #112
+#130 := [unit-resolution #113 #129]: #16
+#100 := (or #76 #42)
+#101 := [def-axiom]: #100
+#131 := [unit-resolution #101 #128]: #42
+#89 := (not #10)
+#114 := (or #53 #89)
+#115 := [def-axiom]: #114
+#132 := [unit-resolution #115 #129]: #89
+#92 := (or #74 #41 #10)
+#93 := [def-axiom]: #92
+#133 := [unit-resolution #93 #132 #131]: #41
+#102 := (or #76 #46)
+#103 := [def-axiom]: #102
+#134 := [unit-resolution #103 #128]: #46
+#98 := (or #75 #45 #10)
+#99 := [def-axiom]: #98
+#135 := [unit-resolution #99 #132 #134]: #45
+#110 := (or #52 #8 #13)
+#111 := [def-axiom]: #110
+#136 := [unit-resolution #111 #135 #133 #130]: false
+#137 := [lemma #136]: #76
+#126 := (or #77 #53)
+#124 := (or #77 #53 #119)
+#125 := [def-axiom]: #124
+#127 := [unit-resolution #125 #86]: #126
+#138 := [unit-resolution #127 #137]: #53
+#139 := [hypothesis]: #74
+#90 := (or #42 #89)
+#91 := [def-axiom]: #90
+#140 := [unit-resolution #91 #139]: #89
+#87 := (or #42 #8)
+#88 := [def-axiom]: #87
+#141 := [unit-resolution #88 #139]: #8
+#106 := (or #16 #41)
+#107 := [def-axiom]: #106
+#142 := [unit-resolution #107 #141]: #16
+#117 := (or #116 #52 #10)
+#118 := [def-axiom]: #117
+#143 := [unit-resolution #118 #142 #140 #138]: false
+#144 := [lemma #143]: #42
+#104 := (or #77 #74 #75)
+#105 := [def-axiom]: #104
+#145 := [unit-resolution #105 #144 #137]: #75
+#96 := (or #46 #89)
+#97 := [def-axiom]: #96
+#146 := [unit-resolution #97 #145]: #89
+#94 := (or #46 #13)
+#95 := [def-axiom]: #94
+#147 := [unit-resolution #95 #145]: #13
+#108 := (or #16 #45)
+#109 := [def-axiom]: #108
+#148 := [unit-resolution #109 #147]: #16
+[unit-resolution #118 #148 #146 #138]: false
+unsat
+286bd8b6cdfa66f845900e18ef113ce800adfe6f 87 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f5 :: S1
+#12 := f5
+#13 := (= f5 f1)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#44 := (not #10)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#51 := (not #8)
+#69 := (or #51 #44 #13)
+#11 := (and #8 #10)
+#40 := (not #11)
+#41 := (or #40 #13)
+#63 := (not #41)
+#72 := (iff #63 #69)
+#105 := (iff #72 false)
+#97 := (not #69)
+#100 := (iff #97 #69)
+#103 := (iff #100 false)
 #104 := [rewrite]: #103
-#94 := (iff #86 #92)
-#95 := (iff #76 #100)
-#96 := [rewrite]: #95
-#101 := [monotonicity #96]: #94
-#106 := [trans #101 #104]: #105
-#111 := [trans #106 #109]: #110
-#9 := (= f3 f1)
-#17 := (not #9)
-#19 := (implies #17 #18)
-#16 := (implies #9 #15)
-#20 := (and #16 #19)
-#12 := (ite #9 f4 f5)
-#14 := (= #12 f6)
-#21 := (iff #14 #20)
+#101 := (iff #72 #100)
+#98 := (iff #63 #97)
+#95 := (iff #41 #69)
+#83 := (or #51 #44)
+#90 := (or #83 #13)
+#93 := (iff #90 #69)
+#94 := [rewrite]: #93
+#91 := (iff #41 #90)
+#88 := (iff #40 #83)
+#84 := (not #83)
+#81 := (not #84)
+#80 := (iff #81 #83)
+#87 := [rewrite]: #80
+#82 := (iff #40 #81)
+#85 := (iff #11 #84)
+#86 := [rewrite]: #85
+#79 := [monotonicity #86]: #82
+#89 := [trans #79 #87]: #88
+#92 := [monotonicity #89]: #91
+#96 := [trans #92 #94]: #95
+#99 := [monotonicity #96]: #98
+#102 := [monotonicity #99]: #101
+#106 := [trans #102 #104]: #105
+#15 := (implies #10 #13)
+#16 := (implies #8 #15)
+#14 := (implies #11 #13)
+#17 := (iff #14 #16)
+#18 := (not #17)
+#75 := (iff #18 #72)
+#45 := (or #44 #13)
+#52 := (or #51 #45)
+#64 := (iff #63 #52)
+#73 := (iff #64 #72)
+#70 := (iff #52 #69)
+#71 := [rewrite]: #70
+#74 := [monotonicity #71]: #73
+#67 := (iff #18 #64)
+#57 := (iff #41 #52)
+#60 := (not #57)
+#65 := (iff #60 #64)
+#66 := [rewrite]: #65
+#61 := (iff #18 #60)
+#58 := (iff #17 #57)
+#55 := (iff #16 #52)
+#48 := (implies #8 #45)
+#53 := (iff #48 #52)
+#54 := [rewrite]: #53
+#49 := (iff #16 #48)
+#46 := (iff #15 #45)
+#47 := [rewrite]: #46
+#50 := [monotonicity #47]: #49
+#56 := [trans #50 #54]: #55
+#42 := (iff #14 #41)
+#43 := [rewrite]: #42
+#59 := [monotonicity #43 #56]: #58
+#62 := [monotonicity #59]: #61
+#68 := [trans #62 #66]: #67
+#76 := [trans #68 #74]: #75
+#39 := [asserted]: #18
+#77 := [mp #39 #76]: #72
+[mp #77 #106]: false
+unsat
+161dd0114051200a7ffcef5c767f1dd1f3eb1d26 172 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f5 :: S1
+#13 := f5
+#14 := (= f5 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#17 := (and #8 #14)
+#70 := (not #17)
+#191 := (iff #70 false)
+#1 := true
+#126 := (not true)
+#189 := (iff #126 false)
+#190 := [rewrite]: #189
+#136 := (iff #70 #126)
+#186 := (iff #17 true)
+#181 := (and true true)
+#184 := (iff #181 true)
+#185 := [rewrite]: #184
+#182 := (iff #17 #181)
+#124 := (iff #14 true)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#57 := (not #14)
+#58 := (or #57 #10)
+#64 := (not #58)
+#65 := (or #64 #10)
+#156 := (iff #65 #14)
+#151 := (or #14 false)
+#154 := (iff #151 #14)
+#155 := [rewrite]: #154
+#152 := (iff #65 #151)
+#127 := (iff #10 false)
+#116 := (not #10)
+#71 := (or #70 #10)
+#77 := (not #71)
+#86 := (not #65)
+#44 := (not #8)
+#45 := (or #44 #10)
+#51 := (not #45)
+#52 := (or #51 #10)
+#95 := (not #52)
+#104 := (or #95 #86 #77 #10)
+#107 := (not #104)
+#18 := (implies #17 #10)
+#19 := (implies #18 #10)
+#15 := (implies #14 #10)
+#16 := (implies #15 #10)
+#20 := (implies #16 #19)
+#11 := (implies #8 #10)
+#12 := (implies #11 #10)
+#21 := (implies #12 #20)
 #22 := (not #21)
-#89 := (iff #22 #86)
-#79 := (iff #52 #76)
-#82 := (not #79)
-#87 := (iff #82 #86)
-#88 := [rewrite]: #87
-#83 := (iff #22 #82)
-#80 := (iff #21 #79)
-#77 := (iff #20 #76)
-#74 := (iff #19 #71)
-#68 := (implies #60 #18)
-#72 := (iff #68 #71)
+#110 := (iff #22 #107)
+#78 := (or #77 #10)
+#87 := (or #86 #78)
+#96 := (or #95 #87)
+#101 := (not #96)
+#108 := (iff #101 #107)
+#105 := (iff #96 #104)
+#106 := [rewrite]: #105
+#109 := [monotonicity #106]: #108
+#102 := (iff #22 #101)
+#99 := (iff #21 #96)
+#92 := (implies #52 #87)
+#97 := (iff #92 #96)
+#98 := [rewrite]: #97
+#93 := (iff #21 #92)
+#90 := (iff #20 #87)
+#83 := (implies #65 #78)
+#88 := (iff #83 #87)
+#89 := [rewrite]: #88
+#84 := (iff #20 #83)
+#81 := (iff #19 #78)
+#74 := (implies #71 #10)
+#79 := (iff #74 #78)
+#80 := [rewrite]: #79
+#75 := (iff #19 #74)
+#72 := (iff #18 #71)
 #73 := [rewrite]: #72
-#69 := (iff #19 #68)
-#66 := (iff #17 #60)
-#44 := (iff #9 #43)
-#45 := [rewrite]: #44
-#67 := [monotonicity #45]: #66
-#70 := [monotonicity #67]: #69
-#75 := [trans #70 #73]: #74
-#64 := (iff #16 #61)
-#57 := (implies #43 #15)
+#76 := [monotonicity #73]: #75
+#82 := [trans #76 #80]: #81
+#68 := (iff #16 #65)
+#61 := (implies #58 #10)
+#66 := (iff #61 #65)
+#67 := [rewrite]: #66
+#62 := (iff #16 #61)
+#59 := (iff #15 #58)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#69 := [trans #63 #67]: #68
+#85 := [monotonicity #69 #82]: #84
+#91 := [trans #85 #89]: #90
+#55 := (iff #12 #52)
+#48 := (implies #45 #10)
+#53 := (iff #48 #52)
+#54 := [rewrite]: #53
+#49 := (iff #12 #48)
+#46 := (iff #11 #45)
+#47 := [rewrite]: #46
+#50 := [monotonicity #47]: #49
+#56 := [trans #50 #54]: #55
+#94 := [monotonicity #56 #91]: #93
+#100 := [trans #94 #98]: #99
+#103 := [monotonicity #100]: #102
+#111 := [trans #103 #109]: #110
+#43 := [asserted]: #22
+#112 := [mp #43 #111]: #107
+#117 := [not-or-elim #112]: #116
+#128 := [iff-false #117]: #127
+#149 := (iff #64 #14)
+#144 := (not #57)
+#147 := (iff #144 #14)
+#148 := [rewrite]: #147
+#145 := (iff #64 #144)
+#142 := (iff #58 #57)
+#137 := (or #57 false)
+#140 := (iff #137 #57)
+#141 := [rewrite]: #140
+#138 := (iff #58 #137)
+#139 := [monotonicity #128]: #138
+#143 := [trans #139 #141]: #142
+#146 := [monotonicity #143]: #145
+#150 := [trans #146 #148]: #149
+#153 := [monotonicity #150 #128]: #152
+#157 := [trans #153 #155]: #156
+#114 := [not-or-elim #112]: #65
+#123 := [mp #114 #157]: #14
+#158 := [iff-true #123]: #124
+#122 := (iff #8 true)
+#178 := (iff #52 #8)
+#173 := (or #8 false)
+#176 := (iff #173 #8)
+#177 := [rewrite]: #176
+#174 := (iff #52 #173)
+#171 := (iff #51 #8)
+#166 := (not #44)
+#169 := (iff #166 #8)
+#170 := [rewrite]: #169
+#167 := (iff #51 #166)
+#164 := (iff #45 #44)
+#159 := (or #44 false)
+#162 := (iff #159 #44)
+#163 := [rewrite]: #162
+#160 := (iff #45 #159)
+#161 := [monotonicity #128]: #160
+#165 := [trans #161 #163]: #164
+#168 := [monotonicity #165]: #167
+#172 := [trans #168 #170]: #171
+#175 := [monotonicity #172 #128]: #174
+#179 := [trans #175 #177]: #178
+#113 := [not-or-elim #112]: #52
+#121 := [mp #113 #179]: #8
+#180 := [iff-true #121]: #122
+#183 := [monotonicity #180 #158]: #182
+#187 := [trans #183 #185]: #186
+#188 := [monotonicity #187]: #136
+#192 := [trans #188 #190]: #191
+#134 := (iff #71 #70)
+#129 := (or #70 false)
+#132 := (iff #129 #70)
+#133 := [rewrite]: #132
+#130 := (iff #71 #129)
+#131 := [monotonicity #128]: #130
+#135 := [trans #131 #133]: #134
+#115 := [not-or-elim #112]: #71
+#125 := [mp #115 #135]: #70
+[mp #125 #192]: false
+unsat
+4b04cbf4156c7db75a1cf1b753251a6923a9c62d 107 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+decl f5 :: S1
+#13 := f5
+#14 := (= f5 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#17 := (and #8 #14)
+#58 := (not #17)
+#59 := (or #58 #10)
+#126 := (iff #59 false)
+#121 := (or false false)
+#124 := (iff #121 false)
+#125 := [rewrite]: #124
+#122 := (iff #59 #121)
+#105 := (iff #10 false)
+#95 := (not #10)
+#62 := (not #59)
+#51 := (not #14)
+#44 := (not #8)
+#84 := (or #44 #51 #10 #62)
+#87 := (not #84)
+#18 := (implies #17 #10)
+#19 := (not #18)
+#15 := (implies #14 #10)
+#16 := (not #15)
+#20 := (implies #16 #19)
+#11 := (implies #8 #10)
+#12 := (not #11)
+#21 := (implies #12 #20)
+#22 := (not #21)
+#90 := (iff #22 #87)
+#52 := (or #51 #10)
+#68 := (or #52 #62)
+#45 := (or #44 #10)
+#76 := (or #45 #68)
+#81 := (not #76)
+#88 := (iff #81 #87)
+#85 := (iff #76 #84)
+#86 := [rewrite]: #85
+#89 := [monotonicity #86]: #88
+#82 := (iff #22 #81)
+#79 := (iff #21 #76)
+#48 := (not #45)
+#73 := (implies #48 #68)
+#77 := (iff #73 #76)
+#78 := [rewrite]: #77
+#74 := (iff #21 #73)
+#71 := (iff #20 #68)
+#55 := (not #52)
+#65 := (implies #55 #62)
+#69 := (iff #65 #68)
+#70 := [rewrite]: #69
+#66 := (iff #20 #65)
+#63 := (iff #19 #62)
+#60 := (iff #18 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#56 := (iff #16 #55)
+#53 := (iff #15 #52)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#67 := [monotonicity #57 #64]: #66
+#72 := [trans #67 #70]: #71
+#49 := (iff #12 #48)
+#46 := (iff #11 #45)
+#47 := [rewrite]: #46
+#50 := [monotonicity #47]: #49
+#75 := [monotonicity #50 #72]: #74
+#80 := [trans #75 #78]: #79
+#83 := [monotonicity #80]: #82
+#91 := [trans #83 #89]: #90
+#43 := [asserted]: #22
+#92 := [mp #43 #91]: #87
+#96 := [not-or-elim #92]: #95
+#106 := [iff-false #96]: #105
+#119 := (iff #58 false)
+#1 := true
+#114 := (not true)
+#117 := (iff #114 false)
+#118 := [rewrite]: #117
+#115 := (iff #58 #114)
+#112 := (iff #17 true)
+#107 := (and true true)
+#110 := (iff #107 true)
+#111 := [rewrite]: #110
+#108 := (iff #17 #107)
+#103 := (iff #14 true)
+#94 := [not-or-elim #92]: #14
+#104 := [iff-true #94]: #103
+#101 := (iff #8 true)
+#93 := [not-or-elim #92]: #8
+#102 := [iff-true #93]: #101
+#109 := [monotonicity #102 #104]: #108
+#113 := [trans #109 #111]: #112
+#116 := [monotonicity #113]: #115
+#120 := [trans #116 #118]: #119
+#123 := [monotonicity #120 #106]: #122
+#127 := [trans #123 #125]: #126
+#97 := [not-or-elim #92]: #59
+[mp #97 #127]: false
+unsat
+4ede140945dac021e73f57bd5aabbe283e3ec513 136 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f5 :: S1
+#11 := f5
+#12 := (= f5 f1)
+#73 := (not #12)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#41 := (not #8)
+#48 := (or #41 #12)
+#81 := (not #48)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#45 := (or #41 #10)
+#80 := (not #45)
+#134 := [hypothesis]: #80
+#107 := (or #45 #8)
+#108 := [def-axiom]: #107
+#135 := [unit-resolution #108 #134]: #8
+#72 := (not #10)
+#74 := (or #72 #73)
+#109 := (or #45 #72)
+#110 := [def-axiom]: #109
+#136 := [unit-resolution #110 #134]: #72
+#95 := (or #74 #10)
+#96 := [def-axiom]: #95
+#137 := [unit-resolution #96 #136]: #74
+#75 := (not #74)
+#67 := (or #41 #75)
+#82 := (or #80 #81)
+#119 := (or #82 #45)
+#120 := [def-axiom]: #119
+#138 := [unit-resolution #120 #134]: #82
+#83 := (not #82)
+#128 := (or #67 #83)
+#89 := (iff #67 #82)
+#51 := (and #45 #48)
+#13 := (and #10 #12)
+#42 := (or #41 #13)
+#60 := (not #42)
+#61 := (iff #60 #51)
+#92 := (iff #61 #89)
+#77 := (not #67)
+#86 := (iff #77 #83)
+#90 := (iff #86 #89)
+#91 := [rewrite]: #90
+#87 := (iff #61 #86)
+#84 := (iff #51 #83)
+#85 := [rewrite]: #84
+#78 := (iff #60 #77)
+#69 := (iff #42 #67)
+#70 := (iff #13 #75)
+#71 := [rewrite]: #70
+#76 := [monotonicity #71]: #69
+#79 := [monotonicity #76]: #78
+#88 := [monotonicity #79 #85]: #87
+#93 := [trans #88 #91]: #92
+#16 := (implies #8 #12)
+#15 := (implies #8 #10)
+#17 := (and #15 #16)
+#14 := (implies #8 #13)
+#18 := (iff #14 #17)
+#19 := (not #18)
+#64 := (iff #19 #61)
+#54 := (iff #42 #51)
+#57 := (not #54)
 #62 := (iff #57 #61)
 #63 := [rewrite]: #62
-#58 := (iff #16 #57)
-#59 := [monotonicity #45]: #58
+#58 := (iff #19 #57)
+#55 := (iff #18 #54)
+#52 := (iff #17 #51)
+#49 := (iff #16 #48)
+#50 := [rewrite]: #49
+#46 := (iff #15 #45)
+#47 := [rewrite]: #46
+#53 := [monotonicity #47 #50]: #52
+#43 := (iff #14 #42)
+#44 := [rewrite]: #43
+#56 := [monotonicity #44 #53]: #55
+#59 := [monotonicity #56]: #58
 #65 := [trans #59 #63]: #64
-#78 := [monotonicity #65 #75]: #77
-#55 := (iff #14 #52)
-#54 := [rewrite]: #53
-#50 := (iff #14 #49)
-#47 := (= #12 #46)
-#48 := [monotonicity #45]: #47
-#51 := [monotonicity #48]: #50
-#56 := [trans #51 #54]: #55
-#81 := [monotonicity #56 #78]: #80
-#84 := [monotonicity #81]: #83
-#90 := [trans #84 #88]: #89
-#42 := [asserted]: #22
-#93 := [mp #42 #90]: #86
-#112 := [mp #93 #111]: #107
-#139 := (not #107)
-#144 := (or #85 #99 #139)
-#145 := [def-axiom]: #144
-#147 := [unit-resolution #145 #112]: #146
-#165 := [unit-resolution #147 #162]: #85
-#176 := [mp #165 #175]: #119
-#133 := (or #99 #61)
-#134 := [def-axiom]: #133
-#163 := [unit-resolution #134 #162]: #61
-#124 := (or #97 #15 #60)
-#125 := [def-axiom]: #124
-#164 := [unit-resolution #125 #163 #161]: #15
-#177 := [unit-resolution #164 #176]: false
-#179 := [lemma #177]: #178
-#180 := [unit-resolution #179 #161]: #99
-#142 := (or #52 #100)
-#140 := (or #52 #100 #139)
-#141 := [def-axiom]: #140
-#143 := [unit-resolution #141 #112]: #142
-#183 := [unit-resolution #143 #180]: #52
-#184 := [mp #183 #173]: #15
-#156 := (iff #114 #18)
-#154 := (iff #18 #114)
-#148 := [hypothesis]: #98
-#135 := (or #99 #71)
-#136 := [def-axiom]: #135
-#152 := [unit-resolution #136 #148]: #99
-#153 := [unit-resolution #143 #152]: #52
-#155 := [monotonicity #153]: #154
-#157 := [symm #155]: #156
-#129 := (or #71 #60)
-#130 := [def-axiom]: #129
-#150 := [unit-resolution #130 #148]: #60
-#117 := (or #43 #114)
+#40 := [asserted]: #19
+#68 := [mp #40 #65]: #61
+#94 := [mp #68 #93]: #89
+#125 := (not #89)
+#126 := (or #67 #83 #125)
+#127 := [def-axiom]: #126
+#129 := [unit-resolution #127 #94]: #128
+#139 := [unit-resolution #129 #138]: #67
+#105 := (or #77 #41 #75)
+#106 := [def-axiom]: #105
+#140 := [unit-resolution #106 #139 #137 #135]: false
+#141 := [lemma #140]: #45
+#142 := [hypothesis]: #77
+#101 := (or #67 #8)
+#102 := [def-axiom]: #101
+#143 := [unit-resolution #102 #142]: #8
+#144 := [unit-resolution #129 #142]: #83
+#121 := (or #82 #48)
+#122 := [def-axiom]: #121
+#145 := [unit-resolution #122 #144]: #48
+#103 := (or #67 #74)
+#104 := [def-axiom]: #103
+#146 := [unit-resolution #104 #142]: #74
+#111 := (or #80 #41 #10)
+#112 := [def-axiom]: #111
+#147 := [unit-resolution #112 #143 #141]: #10
+#99 := (or #75 #72 #73)
+#100 := [def-axiom]: #99
+#148 := [unit-resolution #100 #147 #146]: #73
+#117 := (or #81 #41 #12)
 #118 := [def-axiom]: #117
-#151 := [unit-resolution #118 #150]: #114
-#158 := [mp #151 #157]: #18
-#126 := (not #18)
-#127 := (or #71 #126)
-#128 := [def-axiom]: #127
-#149 := [unit-resolution #128 #148]: #126
-#159 := [unit-resolution #149 #158]: false
-#160 := [lemma #159]: #71
-#137 := (or #100 #97 #98)
-#138 := [def-axiom]: #137
-#181 := [unit-resolution #138 #180 #160]: #97
-#120 := (or #61 #119)
-#121 := [def-axiom]: #120
-#182 := [unit-resolution #121 #181]: #119
-#185 := [unit-resolution #182 #184]: false
-#186 := [lemma #185]: #60
-#190 := [unit-resolution #118 #186]: #114
-#192 := (= f6 f5)
-#131 := (or #98 #18 #43)
-#132 := [def-axiom]: #131
-#191 := [unit-resolution #132 #186 #160]: #18
-#193 := [symm #191]: #192
-#194 := [trans #193 #190]: #52
-#122 := (or #61 #43)
-#123 := [def-axiom]: #122
-#187 := [unit-resolution #123 #186]: #61
-#188 := [unit-resolution #138 #187 #160]: #100
-#189 := [unit-resolution #147 #188]: #85
-[unit-resolution #189 #194]: false
-unsat
-7caf561e8dba712e3313b4433e2a7d62033d4cc1 36 0
-#2 := false
-decl f5 :: S2
-#10 := f5
-decl f3 :: S2
-#8 := f3
-#12 := (= f3 f5)
+#149 := [unit-resolution #118 #148 #145 #143]: false
+#150 := [lemma #149]: #67
+#132 := (or #77 #82)
+#130 := (or #77 #82 #125)
+#131 := [def-axiom]: #130
+#133 := [unit-resolution #131 #94]: #132
+#151 := [unit-resolution #133 #150]: #82
+#123 := (or #83 #80 #81)
+#124 := [def-axiom]: #123
+#152 := [unit-resolution #124 #151 #141]: #81
+#115 := (or #48 #73)
+#116 := [def-axiom]: #115
+#153 := [unit-resolution #116 #152]: #73
+#113 := (or #48 #8)
+#114 := [def-axiom]: #113
+#154 := [unit-resolution #114 #152]: #8
+#155 := [unit-resolution #106 #154 #150]: #75
+#97 := (or #74 #12)
+#98 := [def-axiom]: #97
+[unit-resolution #98 #155 #153]: false
+unsat
+a1bd5a7826fb084e07c1ba646f5039bc9faf9bf8 43 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#11 := (implies #10 #8)
+#12 := (implies #8 #11)
 #13 := (not #12)
-decl f4 :: S2
+#60 := (iff #13 false)
+#35 := (not #10)
+#36 := (or #35 #8)
+#42 := (not #8)
+#43 := (or #42 #36)
+#48 := (not #43)
+#58 := (iff #48 false)
+#1 := true
+#53 := (not true)
+#56 := (iff #53 false)
+#57 := [rewrite]: #56
+#54 := (iff #48 #53)
+#51 := (iff #43 true)
+#52 := [rewrite]: #51
+#55 := [monotonicity #52]: #54
+#59 := [trans #55 #57]: #58
+#49 := (iff #13 #48)
+#46 := (iff #12 #43)
+#39 := (implies #8 #36)
+#44 := (iff #39 #43)
+#45 := [rewrite]: #44
+#40 := (iff #12 #39)
+#37 := (iff #11 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#47 := [trans #41 #45]: #46
+#50 := [monotonicity #47]: #49
+#61 := [trans #50 #59]: #60
+#34 := [asserted]: #13
+[mp #34 #61]: false
+unsat
+3050918d31c36048af6e7954efb4023260756a72 120 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f5 :: S1
+#11 := f5
+#12 := (= f5 f1)
+decl f4 :: S1
 #9 := f4
-#11 := (distinct f3 f4 f5)
-#36 := (not #11)
-#37 := (or #36 #13)
-#40 := (not #37)
-#14 := (implies #11 #13)
-#15 := (not #14)
-#41 := (iff #15 #40)
-#38 := (iff #14 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#35 := [asserted]: #15
-#45 := [mp #35 #42]: #40
-#44 := [not-or-elim #45]: #12
-#55 := (= f4 f5)
-#56 := (not #55)
-#53 := (= f3 f4)
-#54 := (not #53)
-#51 := (and #54 #13 #56)
-#43 := [not-or-elim #45]: #11
-#61 := (or #36 #51)
-#62 := [def-axiom]: #61
-#65 := [unit-resolution #62 #43]: #51
-#52 := (not #51)
-#47 := (or #52 #13)
-#48 := [def-axiom]: #47
-[unit-resolution #48 #65 #44]: false
-unsat
-5d166c0e6b2d72dafe17b5b5de7117e70ffd077f 77 0
-#2 := false
-decl f4 :: S2
+#10 := (= f4 f1)
+#41 := (not #10)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#48 := (not #8)
+#81 := (or #48 #41 #12)
+#141 := (iff #81 false)
+#136 := (or false false false)
+#139 := (iff #136 false)
+#140 := [rewrite]: #139
+#137 := (iff #81 #136)
+#115 := (iff #12 false)
+#104 := (not #12)
+#54 := (or #48 #10)
+#63 := (not #54)
+#84 := (not #81)
+#90 := (or #84 #63 #48 #12)
+#95 := (not #90)
+#16 := (implies #8 #12)
+#15 := (implies #8 #10)
+#17 := (implies #15 #16)
+#13 := (implies #10 #12)
+#14 := (implies #8 #13)
+#18 := (implies #14 #17)
+#19 := (not #18)
+#98 := (iff #19 #95)
+#57 := (or #48 #12)
+#64 := (or #63 #57)
+#42 := (or #41 #12)
+#49 := (or #48 #42)
+#72 := (not #49)
+#73 := (or #72 #64)
+#78 := (not #73)
+#96 := (iff #78 #95)
+#93 := (iff #73 #90)
+#87 := (or #84 #64)
+#91 := (iff #87 #90)
+#92 := [rewrite]: #91
+#88 := (iff #73 #87)
+#85 := (iff #72 #84)
+#82 := (iff #49 #81)
+#83 := [rewrite]: #82
+#86 := [monotonicity #83]: #85
+#89 := [monotonicity #86]: #88
+#94 := [trans #89 #92]: #93
+#97 := [monotonicity #94]: #96
+#79 := (iff #19 #78)
+#76 := (iff #18 #73)
+#69 := (implies #49 #64)
+#74 := (iff #69 #73)
+#75 := [rewrite]: #74
+#70 := (iff #18 #69)
+#67 := (iff #17 #64)
+#60 := (implies #54 #57)
+#65 := (iff #60 #64)
+#66 := [rewrite]: #65
+#61 := (iff #17 #60)
+#58 := (iff #16 #57)
+#59 := [rewrite]: #58
+#55 := (iff #15 #54)
+#56 := [rewrite]: #55
+#62 := [monotonicity #56 #59]: #61
+#68 := [trans #62 #66]: #67
+#52 := (iff #14 #49)
+#45 := (implies #8 #42)
+#50 := (iff #45 #49)
+#51 := [rewrite]: #50
+#46 := (iff #14 #45)
+#43 := (iff #13 #42)
+#44 := [rewrite]: #43
+#47 := [monotonicity #44]: #46
+#53 := [trans #47 #51]: #52
+#71 := [monotonicity #53 #68]: #70
+#77 := [trans #71 #75]: #76
+#80 := [monotonicity #77]: #79
+#99 := [trans #80 #97]: #98
+#40 := [asserted]: #19
+#100 := [mp #40 #99]: #95
+#105 := [not-or-elim #100]: #104
+#116 := [iff-false #105]: #115
+#134 := (iff #41 false)
+#1 := true
+#117 := (not true)
+#120 := (iff #117 false)
+#121 := [rewrite]: #120
+#132 := (iff #41 #117)
+#112 := (iff #10 true)
+#129 := (iff #54 #10)
+#124 := (or false #10)
+#127 := (iff #124 #10)
+#128 := [rewrite]: #127
+#125 := (iff #54 #124)
+#122 := (iff #48 false)
+#118 := (iff #48 #117)
+#113 := (iff #8 true)
+#103 := [not-or-elim #100]: #8
+#114 := [iff-true #103]: #113
+#119 := [monotonicity #114]: #118
+#123 := [trans #119 #121]: #122
+#126 := [monotonicity #123]: #125
+#130 := [trans #126 #128]: #129
+#102 := [not-or-elim #100]: #54
+#111 := [mp #102 #130]: #10
+#131 := [iff-true #111]: #112
+#133 := [monotonicity #131]: #132
+#135 := [trans #133 #121]: #134
+#138 := [monotonicity #123 #135 #116]: #137
+#142 := [trans #138 #140]: #141
+#101 := [not-or-elim #100]: #81
+[mp #101 #142]: false
+unsat
+419cf0503137091c5bc92af96aa593cffd70f2cf 94 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f5 :: S1
+#12 := f5
+#13 := (= f5 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#41 := (not #8)
+decl f4 :: S1
 #9 := f4
-decl f3 :: S2
-#8 := f3
-#84 := (= f3 f4)
-decl f6 :: S2
-#12 := f6
-#39 := (= f4 f6)
-#103 := (iff #39 #84)
-#101 := (iff #84 #39)
-#13 := (= f6 f4)
-#40 := (iff #13 #39)
-#100 := [commutativity]: #40
-#98 := (iff #84 #13)
-#14 := (= f3 f6)
+#10 := (= f4 f1)
+#66 := (or #10 #41 #13)
+#115 := (iff #66 false)
+#110 := (or false false false)
+#113 := (iff #110 false)
+#114 := [rewrite]: #113
+#111 := (iff #66 #110)
+#101 := (iff #13 false)
+#90 := (not #13)
+#69 := (not #66)
+#75 := (or #69 #41 #10 #13)
+#80 := (not #75)
+#16 := (or #10 #13)
+#17 := (implies #8 #16)
+#14 := (implies #8 #13)
+#11 := (implies #8 #10)
+#15 := (or #11 #14)
+#18 := (implies #15 #17)
+#19 := (not #18)
+#83 := (iff #19 #80)
+#51 := (or #41 #16)
+#45 := (or #41 #13)
+#42 := (or #41 #10)
+#48 := (or #42 #45)
+#57 := (not #48)
+#58 := (or #57 #51)
+#63 := (not #58)
+#81 := (iff #63 #80)
+#78 := (iff #58 #75)
+#72 := (or #69 #51)
+#76 := (iff #72 #75)
+#77 := [rewrite]: #76
+#73 := (iff #58 #72)
+#70 := (iff #57 #69)
+#67 := (iff #48 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#74 := [monotonicity #71]: #73
+#79 := [trans #74 #77]: #78
+#82 := [monotonicity #79]: #81
+#64 := (iff #19 #63)
+#61 := (iff #18 #58)
+#54 := (implies #48 #51)
+#59 := (iff #54 #58)
+#60 := [rewrite]: #59
+#55 := (iff #18 #54)
+#52 := (iff #17 #51)
+#53 := [rewrite]: #52
+#49 := (iff #15 #48)
+#46 := (iff #14 #45)
+#47 := [rewrite]: #46
+#43 := (iff #11 #42)
+#44 := [rewrite]: #43
+#50 := [monotonicity #44 #47]: #49
+#56 := [monotonicity #50 #53]: #55
+#62 := [trans #56 #60]: #61
+#65 := [monotonicity #62]: #64
+#84 := [trans #65 #82]: #83
+#40 := [asserted]: #19
+#85 := [mp #40 #84]: #80
+#91 := [not-or-elim #85]: #90
+#102 := [iff-false #91]: #101
+#108 := (iff #41 false)
+#1 := true
+#103 := (not true)
+#106 := (iff #103 false)
+#107 := [rewrite]: #106
+#104 := (iff #41 #103)
+#97 := (iff #8 true)
+#87 := [not-or-elim #85]: #8
+#98 := [iff-true #87]: #97
+#105 := [monotonicity #98]: #104
+#109 := [trans #105 #107]: #108
+#99 := (iff #10 false)
+#88 := (not #10)
+#89 := [not-or-elim #85]: #88
+#100 := [iff-false #89]: #99
+#112 := [monotonicity #100 #109 #102]: #111
+#116 := [trans #112 #114]: #115
+#86 := [not-or-elim #85]: #66
+[mp #86 #116]: false
+unsat
+2da11420e5b99236635a72b7c77f978d01d57534 112 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#38 := (not #8)
+#39 := (or #38 #10)
 #45 := (not #39)
-#15 := (not #14)
-decl f5 :: S2
-#10 := f5
-#11 := (distinct f3 f4 f5)
-#54 := (not #11)
-#63 := (or #54 #15 #45)
-#66 := (not #63)
-#16 := (implies #13 #15)
-#17 := (implies #11 #16)
-#18 := (not #17)
-#69 := (iff #18 #66)
-#46 := (or #15 #45)
-#55 := (or #54 #46)
-#60 := (not #55)
-#67 := (iff #60 #66)
-#64 := (iff #55 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#61 := (iff #18 #60)
-#58 := (iff #17 #55)
-#51 := (implies #11 #46)
+#46 := (or #45 #8)
+#54 := (not #46)
+#55 := (or #54 #8)
+#63 := (not #55)
+#64 := (or #63 #10)
+#134 := (iff #64 false)
+#129 := (or false false)
+#132 := (iff #129 false)
+#133 := [rewrite]: #132
+#130 := (iff #64 #129)
+#90 := (iff #10 false)
+#82 := (not #10)
+#72 := (not #64)
+#73 := (or #72 #10)
+#78 := (not #73)
+#11 := (implies #8 #10)
+#12 := (implies #11 #8)
+#13 := (implies #12 #8)
+#14 := (implies #13 #10)
+#15 := (implies #14 #10)
+#16 := (not #15)
+#79 := (iff #16 #78)
+#76 := (iff #15 #73)
+#69 := (implies #64 #10)
+#74 := (iff #69 #73)
+#75 := [rewrite]: #74
+#70 := (iff #15 #69)
+#67 := (iff #14 #64)
+#60 := (implies #55 #10)
+#65 := (iff #60 #64)
+#66 := [rewrite]: #65
+#61 := (iff #14 #60)
+#58 := (iff #13 #55)
+#51 := (implies #46 #8)
 #56 := (iff #51 #55)
 #57 := [rewrite]: #56
-#52 := (iff #17 #51)
-#49 := (iff #16 #46)
-#42 := (implies #39 #15)
+#52 := (iff #13 #51)
+#49 := (iff #12 #46)
+#42 := (implies #39 #8)
 #47 := (iff #42 #46)
 #48 := [rewrite]: #47
-#43 := (iff #16 #42)
+#43 := (iff #12 #42)
+#40 := (iff #11 #39)
 #41 := [rewrite]: #40
 #44 := [monotonicity #41]: #43
 #50 := [trans #44 #48]: #49
 #53 := [monotonicity #50]: #52
 #59 := [trans #53 #57]: #58
 #62 := [monotonicity #59]: #61
-#70 := [trans #62 #68]: #69
-#38 := [asserted]: #18
-#71 := [mp #38 #70]: #66
-#73 := [not-or-elim #71]: #14
-#99 := [monotonicity #73]: #98
-#102 := [trans #99 #100]: #101
-#104 := [symm #102]: #103
-#74 := [not-or-elim #71]: #39
-#105 := [mp #74 #104]: #84
-#85 := (not #84)
-#82 := (= f4 f5)
-#83 := (not #82)
-#86 := (= f3 f5)
-#87 := (not #86)
-#80 := (and #85 #87 #83)
-#72 := [not-or-elim #71]: #11
-#92 := (or #54 #80)
-#93 := [def-axiom]: #92
-#96 := [unit-resolution #93 #72]: #80
-#81 := (not #80)
-#78 := (or #81 #85)
-#79 := [def-axiom]: #78
-#97 := [unit-resolution #79 #96]: #85
-[unit-resolution #97 #105]: false
-unsat
-533428288e5c80da242f85265bdf0f4abb151e65 28 0
-#2 := false
-decl f4 :: S2
-#9 := f4
-decl f3 :: S2
-#8 := f3
-#10 := (distinct f3 f4 f3 f4)
-#11 := (not #10)
-#12 := (not #11)
-#47 := (iff #12 false)
-#1 := true
-#42 := (not true)
-#45 := (iff #42 false)
-#46 := [rewrite]: #45
-#43 := (iff #12 #42)
-#40 := (iff #11 true)
-#35 := (not false)
-#38 := (iff #35 true)
-#39 := [rewrite]: #38
-#36 := (iff #11 #35)
-#33 := (iff #10 false)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#32 := [asserted]: #12
-[mp #32 #48]: false
-unsat
-017c0a2408f982087afab8f6a30c931842322a6a 38 0
-#2 := false
-decl f4 :: S2
-#9 := f4
-decl f3 :: S2
-#8 := f3
-#11 := (distinct f3 f4)
-#12 := (not #11)
-#10 := (= f3 f4)
-#13 := (implies #10 #12)
-#14 := (not #13)
-#57 := (iff #14 false)
-#1 := true
-#52 := (not true)
-#55 := (iff #52 false)
-#56 := [rewrite]: #55
-#53 := (iff #14 #52)
-#50 := (iff #13 true)
-#45 := (implies #10 #10)
-#48 := (iff #45 true)
-#49 := [rewrite]: #48
-#46 := (iff #13 #45)
-#43 := (iff #12 #10)
-#35 := (not #10)
-#38 := (not #35)
-#41 := (iff #38 #10)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#47 := [monotonicity #44]: #46
-#51 := [trans #47 #49]: #50
-#54 := [monotonicity #51]: #53
-#58 := [trans #54 #56]: #57
-#34 := [asserted]: #14
-[mp #34 #58]: false
-unsat
-3d691d698b1a15f8a77e4e6f63eb68946744774b 40 0
-#2 := false
-decl f5 :: S2
-#11 := f5
-decl f4 :: S2
-#9 := f4
-decl f3 :: S2
-#8 := f3
-#14 := (distinct f3 f4 f5)
-#15 := (not #14)
-#12 := (= f3 f5)
-#10 := (= f3 f4)
-#13 := (and #10 #12)
-#38 := (not #13)
-#39 := (or #38 #15)
-#42 := (not #39)
-#16 := (implies #13 #15)
-#17 := (not #16)
-#43 := (iff #17 #42)
-#40 := (iff #16 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#37 := [asserted]: #17
-#47 := [mp #37 #44]: #42
-#49 := [not-or-elim #47]: #14
-#61 := (= f4 f5)
-#62 := (not #61)
-#60 := (not #12)
-#59 := (not #10)
-#57 := (and #59 #60 #62)
-#58 := (not #57)
-#45 := [not-or-elim #47]: #13
-#46 := [and-elim #45]: #10
-#55 := (or #58 #59)
-#56 := [def-axiom]: #55
-#69 := [unit-resolution #56 #46]: #58
-#65 := (or #15 #57)
-#66 := [def-axiom]: #65
-#70 := [unit-resolution #66 #69]: #15
-[unit-resolution #70 #49]: false
-unsat
-91ca794ae2ea70dac95d2e0e4e034ae7338238ca 33 0
-#2 := false
-decl f3 :: S2
-#8 := f3
-decl f5 :: S2
-#10 := f5
-decl f4 :: S2
-#9 := f4
-decl f6 :: S2
-#11 := f6
-#13 := (distinct f6 f4 f5 f3)
-#12 := (distinct f3 f4 f5 f6)
-#14 := (implies #12 #13)
-#15 := (not #14)
-#50 := (iff #15 false)
-#1 := true
-#45 := (not true)
-#48 := (iff #45 false)
-#49 := [rewrite]: #48
-#46 := (iff #15 #45)
-#43 := (iff #14 true)
-#38 := (implies #12 #12)
-#41 := (iff #38 true)
-#42 := [rewrite]: #41
-#39 := (iff #14 #38)
-#36 := (iff #13 #12)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#47 := [monotonicity #44]: #46
-#51 := [trans #47 #49]: #50
-#35 := [asserted]: #15
-[mp #35 #51]: false
-unsat
-213abf865430cd165dad7b08270c63f2d0321573 91 0
-#2 := false
-decl f5 :: S2
-#10 := f5
-decl f4 :: S2
+#68 := [trans #62 #66]: #67
+#71 := [monotonicity #68]: #70
+#77 := [trans #71 #75]: #76
+#80 := [monotonicity #77]: #79
+#37 := [asserted]: #16
+#83 := [mp #37 #80]: #78
+#84 := [not-or-elim #83]: #82
+#91 := [iff-false #84]: #90
+#127 := (iff #63 false)
+#1 := true
+#122 := (not true)
+#125 := (iff #122 false)
+#126 := [rewrite]: #125
+#123 := (iff #63 #122)
+#120 := (iff #55 true)
+#115 := (or #38 #8)
+#118 := (iff #115 true)
+#119 := [rewrite]: #118
+#116 := (iff #55 #115)
+#113 := (iff #54 #38)
+#111 := (iff #46 #8)
+#106 := (or #8 #8)
+#109 := (iff #106 #8)
+#110 := [rewrite]: #109
+#107 := (iff #46 #106)
+#104 := (iff #45 #8)
+#99 := (not #38)
+#102 := (iff #99 #8)
+#103 := [rewrite]: #102
+#100 := (iff #45 #99)
+#97 := (iff #39 #38)
+#92 := (or #38 false)
+#95 := (iff #92 #38)
+#96 := [rewrite]: #95
+#93 := (iff #39 #92)
+#94 := [monotonicity #91]: #93
+#98 := [trans #94 #96]: #97
+#101 := [monotonicity #98]: #100
+#105 := [trans #101 #103]: #104
+#108 := [monotonicity #105]: #107
+#112 := [trans #108 #110]: #111
+#114 := [monotonicity #112]: #113
+#117 := [monotonicity #114]: #116
+#121 := [trans #117 #119]: #120
+#124 := [monotonicity #121]: #123
+#128 := [trans #124 #126]: #127
+#131 := [monotonicity #128 #91]: #130
+#135 := [trans #131 #133]: #134
+#81 := [not-or-elim #83]: #64
+[mp #81 #135]: false
+unsat
+05cf053531ebb482bce7d481dd6a6d959ba6e021 67 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: S1
 #9 := f4
-decl f3 :: S2
-#8 := f3
-#13 := (distinct f3 f4 f5)
-#70 := (= f4 f5)
-#71 := (not #70)
-#66 := (= f3 f5)
-#67 := (not #66)
-#64 := (= f3 f4)
-#65 := (not #64)
-#96 := (and #65 #67 #71)
-decl f6 :: S2
-#11 := f6
-#74 := (= f5 f6)
-#75 := (not #74)
-#72 := (= f4 f6)
-#73 := (not #72)
-#68 := (= f3 f6)
-#69 := (not #68)
-#76 := (and #65 #67 #69 #71 #73 #75)
-#12 := (distinct f3 f4 f5 f6)
-#14 := (distinct f4 f5 f6)
-#15 := (and #13 #14)
-#38 := (not #12)
-#39 := (or #38 #15)
-#42 := (not #39)
-#16 := (implies #12 #15)
-#17 := (not #16)
-#43 := (iff #17 #42)
-#40 := (iff #16 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#37 := [asserted]: #17
-#47 := [mp #37 #44]: #42
-#45 := [not-or-elim #47]: #12
-#92 := (or #38 #76)
-#93 := [def-axiom]: #92
-#124 := [unit-resolution #93 #45]: #76
-#77 := (not #76)
-#78 := (or #77 #65)
-#79 := [def-axiom]: #78
-#125 := [unit-resolution #79 #124]: #65
-#84 := (or #77 #71)
-#85 := [def-axiom]: #84
-#126 := [unit-resolution #85 #124]: #71
-#80 := (or #77 #67)
-#81 := [def-axiom]: #80
-#127 := [unit-resolution #81 #124]: #67
-#104 := (or #96 #64 #66 #70)
-#105 := [def-axiom]: #104
-#128 := [unit-resolution #105 #127 #126 #125]: #96
-#97 := (not #96)
-#108 := (or #13 #97)
-#109 := [def-axiom]: #108
-#129 := [unit-resolution #109 #128]: #13
-#110 := (and #71 #73 #75)
-#88 := (or #77 #75)
-#89 := [def-axiom]: #88
-#130 := [unit-resolution #89 #124]: #75
-#86 := (or #77 #73)
-#87 := [def-axiom]: #86
-#131 := [unit-resolution #87 #124]: #73
-#118 := (or #110 #70 #72 #74)
-#119 := [def-axiom]: #118
-#132 := [unit-resolution #119 #131 #130 #126]: #110
-#111 := (not #110)
-#122 := (or #14 #111)
-#123 := [def-axiom]: #122
-#133 := [unit-resolution #123 #132]: #14
-#57 := (not #14)
-#56 := (not #13)
-#58 := (or #56 #57)
-#46 := (not #15)
-#61 := (iff #46 #58)
-#59 := (not #58)
-#52 := (not #59)
-#51 := (iff #52 #58)
-#60 := [rewrite]: #51
-#53 := (iff #46 #52)
-#54 := (iff #15 #59)
-#55 := [rewrite]: #54
-#50 := [monotonicity #55]: #53
-#62 := [trans #50 #60]: #61
-#48 := [not-or-elim #47]: #46
-#63 := [mp #48 #62]: #58
-[unit-resolution #63 #133 #129]: false
-unsat
-f1809e8489f94ca6f5ab262d227412571fae6063 25 0
-#2 := false
-#8 := (:var 0 S2)
-#9 := (= #8 #8)
-#10 := (forall (vars (?v0 S2)) #9)
-#11 := (not #10)
-#46 := (iff #11 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #11 #41)
-#39 := (iff #10 true)
-#34 := (forall (vars (?v0 S2)) true)
-#37 := (iff #34 true)
-#38 := [elim-unused]: #37
-#35 := (iff #10 #34)
-#32 := (iff #9 true)
-#33 := [rewrite]: #32
-#36 := [quant-intro #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#31 := [asserted]: #11
-[mp #31 #47]: false
-unsat
-d955ec6b7cfeeee07c53113d44b234b0343ba998 34 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: (-> S2 S1)
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#10 := (= #9 f1)
-#11 := (forall (vars (?v0 S2)) #10)
-#12 := (iff #11 #11)
-#13 := (not #12)
-#52 := (iff #13 false)
-#1 := true
-#47 := (not true)
-#50 := (iff #47 false)
-#51 := [rewrite]: #50
-#48 := (iff #13 #47)
-#45 := (iff #12 true)
-#34 := (= f1 #9)
-#37 := (forall (vars (?v0 S2)) #34)
-#40 := (iff #37 #37)
-#43 := (iff #40 true)
-#44 := [rewrite]: #43
-#41 := (iff #12 #40)
-#38 := (iff #11 #37)
-#35 := (iff #10 #34)
-#36 := [rewrite]: #35
-#39 := [quant-intro #36]: #38
-#42 := [monotonicity #39 #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#33 := [asserted]: #13
-[mp #33 #53]: false
-unsat
-ac9cb8d0afa0ef87b47bcfca90097c8127bbb5a7 95 0
-#2 := false
-decl f3 :: (-> S2 S1)
-decl ?v0!0 :: S2
-#77 := ?v0!0
-#78 := (f3 ?v0!0)
-decl f1 :: S1
-#4 := f1
-#79 := (= f1 #78)
-#74 := (not #79)
-decl ?v1!1 :: S2
-#88 := ?v1!1
-#89 := (f3 ?v1!1)
-#90 := (= f1 #89)
-#108 := (or #79 #90)
-#111 := (not #108)
-#114 := (and #79 #111)
-#91 := (or #90 #79)
-#92 := (not #91)
-#85 := (not #74)
-#98 := (and #85 #92)
-#115 := (iff #98 #114)
-#112 := (iff #92 #111)
-#109 := (iff #91 #108)
-#110 := [rewrite]: #109
-#113 := [monotonicity #110]: #112
-#106 := (iff #85 #79)
-#107 := [rewrite]: #106
-#116 := [monotonicity #107 #113]: #115
-#11 := (:var 1 S2)
-#12 := (f3 #11)
-#42 := (= f1 #12)
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#39 := (= f1 #9)
-#48 := (or #39 #42)
-#53 := (forall (vars (?v1 S2)) #48)
-#59 := (not #39)
-#60 := (or #59 #53)
-#65 := (forall (vars (?v0 S2)) #60)
-#68 := (not #65)
-#101 := (~ #68 #98)
-#80 := (or #39 #79)
-#72 := (forall (vars (?v1 S2)) #80)
-#81 := (or #74 #72)
-#82 := (not #81)
-#99 := (~ #82 #98)
-#93 := (not #72)
-#94 := (~ #93 #92)
-#95 := [sk]: #94
-#86 := (~ #85 #85)
-#87 := [refl]: #86
-#100 := [nnf-neg #87 #95]: #99
-#83 := (~ #68 #82)
-#84 := [sk]: #83
-#102 := [trans #84 #100]: #101
-#10 := (= #9 f1)
-#13 := (= #12 f1)
-#14 := (or #13 #10)
-#15 := (forall (vars (?v1 S2)) #14)
-#16 := (implies #10 #15)
-#17 := (forall (vars (?v0 S2)) #16)
-#18 := (not #17)
-#69 := (iff #18 #68)
-#66 := (iff #17 #65)
-#63 := (iff #16 #60)
-#56 := (implies #39 #53)
-#61 := (iff #56 #60)
-#62 := [rewrite]: #61
-#57 := (iff #16 #56)
-#54 := (iff #15 #53)
-#51 := (iff #14 #48)
-#45 := (or #42 #39)
-#49 := (iff #45 #48)
+#10 := (= f4 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#13 := (not #8)
+#38 := (or #13 #10)
+#89 := (iff #38 false)
+#84 := (or false false)
+#87 := (iff #84 false)
+#88 := [rewrite]: #87
+#85 := (iff #38 #84)
+#73 := (iff #10 false)
+#12 := (not #10)
+#47 := (not #38)
+#56 := (or #47 #10 #13)
+#59 := (not #56)
+#14 := (implies #12 #13)
+#11 := (implies #8 #10)
+#15 := (implies #11 #14)
+#16 := (not #15)
+#62 := (iff #16 #59)
+#41 := (or #10 #13)
+#48 := (or #47 #41)
+#53 := (not #48)
+#60 := (iff #53 #59)
+#57 := (iff #48 #56)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#54 := (iff #16 #53)
+#51 := (iff #15 #48)
+#44 := (implies #38 #41)
+#49 := (iff #44 #48)
 #50 := [rewrite]: #49
-#46 := (iff #14 #45)
-#40 := (iff #10 #39)
-#41 := [rewrite]: #40
-#43 := (iff #13 #42)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44 #41]: #46
-#52 := [trans #47 #50]: #51
-#55 := [quant-intro #52]: #54
-#58 := [monotonicity #41 #55]: #57
-#64 := [trans #58 #62]: #63
-#67 := [quant-intro #64]: #66
-#70 := [monotonicity #67]: #69
-#38 := [asserted]: #18
-#73 := [mp #38 #70]: #68
-#103 := [mp~ #73 #102]: #98
-#104 := [mp #103 #116]: #114
-#117 := [and-elim #104]: #111
-#118 := [not-or-elim #117]: #74
-#105 := [and-elim #104]: #79
-[unit-resolution #105 #118]: false
-unsat
-049ea7d2d96c9794ec9b3845824fa548d49c024b 296 0
-#2 := false
-decl f3 :: (-> S2 S1)
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#664 := (pattern #9)
-decl f1 :: S1
-#4 := f1
-#40 := (= f1 #9)
-#671 := (forall (vars (?v0 S2)) (:pat #664) #40)
-decl f4 :: (-> S2 S1)
-#11 := (f4 #8)
-#665 := (pattern #11)
-#43 := (= f1 #11)
-#679 := (forall (vars (?v0 S2)) (:pat #665) #43)
-#684 := (not #679)
-#676 := (not #671)
-#687 := (or #676 #684)
-#690 := (not #687)
-#173 := (not #43)
-#172 := (not #40)
-#174 := (or #172 #173)
-#175 := (not #174)
-#666 := (forall (vars (?v0 S2)) (:pat #664 #665) #175)
-#445 := (not #666)
-decl ?v0!1 :: S2
-#95 := ?v0!1
-#633 := (f4 ?v0!1)
-#634 := (= f1 #633)
-#356 := (not #634)
-#96 := (f3 ?v0!1)
-#97 := (= f1 #96)
-#98 := (not #97)
-#357 := (or #98 #356)
-decl ?v0!2 :: S2
-#104 := ?v0!2
-#105 := (f4 ?v0!2)
-#106 := (= f1 #105)
-#326 := (f3 ?v0!2)
-#337 := (= f1 #326)
-#338 := (not #337)
-#107 := (not #106)
-#336 := (or #107 #338)
-#656 := (not #336)
-#639 := [hypothesis]: #666
-#301 := (or #656 #445)
-#296 := [hypothesis]: #336
-#652 := (or #445 #656)
-#266 := (or #338 #107)
-#339 := (not #266)
-#324 := (or #445 #339)
-#659 := (iff #324 #652)
-#661 := (iff #652 #652)
-#662 := [rewrite]: #661
-#658 := (iff #339 #656)
-#340 := (iff #266 #336)
-#319 := [rewrite]: #340
-#313 := [monotonicity #319]: #658
-#660 := [monotonicity #313]: #659
-#657 := [trans #660 #662]: #659
-#325 := [quant-inst #104]: #324
-#663 := [mp #325 #657]: #652
-#300 := [unit-resolution #663 #639 #296]: false
-#302 := [lemma #300]: #301
-#635 := [unit-resolution #302 #639]: #656
-#653 := (or #336 #106)
-#311 := [def-axiom]: #653
-#632 := [unit-resolution #311 #635]: #106
-decl ?v0!0 :: S2
-#84 := ?v0!0
-#85 := (f4 ?v0!0)
-#86 := (= f1 #85)
-#87 := (f3 ?v0!0)
-#88 := (= f1 #87)
-#103 := (not #88)
-#102 := (not #86)
-#93 := (or #102 #103)
-#94 := (not #93)
-#363 := (or #94 #445)
-#362 := [hypothesis]: #93
-#640 := (or #445 #94)
-#303 := (or #103 #102)
-#641 := (not #303)
-#646 := (or #445 #641)
-#647 := (iff #646 #640)
-#287 := (iff #640 #640)
-#288 := [rewrite]: #287
-#644 := (iff #641 #94)
-#642 := (iff #303 #93)
-#643 := [rewrite]: #642
-#645 := [monotonicity #643]: #644
-#649 := [monotonicity #645]: #647
-#650 := [trans #649 #288]: #647
-#282 := [quant-inst #84]: #646
-#648 := [mp #282 #650]: #640
-#348 := [unit-resolution #648 #639 #362]: false
-#254 := [lemma #348]: #363
-#625 := [unit-resolution #254 #639]: #94
-#651 := (or #93 #86)
-#637 := [def-axiom]: #651
-#629 := [unit-resolution #637 #625]: #86
-#638 := (or #93 #88)
-#344 := [def-axiom]: #638
-#626 := [unit-resolution #344 #625]: #88
-#166 := (or #102 #103 #98 #107)
-#135 := (and #86 #88)
-#138 := (not #135)
-#144 := (or #98 #107 #138)
-#169 := (iff #144 #166)
-#163 := (or #98 #107 #93)
-#167 := (iff #163 #166)
-#168 := [rewrite]: #167
-#164 := (iff #144 #163)
-#161 := (iff #138 #93)
-#156 := (not #94)
-#159 := (iff #156 #93)
-#160 := [rewrite]: #159
-#157 := (iff #138 #156)
-#111 := (iff #135 #94)
-#112 := [rewrite]: #111
-#158 := [monotonicity #112]: #157
-#162 := [trans #158 #160]: #161
-#165 := [monotonicity #162]: #164
-#170 := [trans #165 #168]: #169
-#55 := (forall (vars (?v0 S2)) #43)
-#52 := (forall (vars (?v0 S2)) #40)
-#58 := (and #52 #55)
-#46 := (and #40 #43)
-#49 := (forall (vars (?v0 S2)) #46)
-#149 := (or #49 #58)
-#152 := (and #144 #149)
-#127 := (or #58 #49)
-#89 := (and #88 #86)
-#90 := (not #89)
-#113 := (or #98 #107)
-#128 := (or #113 #90)
-#129 := (and #128 #127)
-#153 := (iff #129 #152)
-#150 := (iff #127 #149)
-#151 := [rewrite]: #150
-#147 := (iff #128 #144)
-#141 := (or #113 #138)
-#145 := (iff #141 #144)
-#146 := [rewrite]: #145
-#142 := (iff #128 #141)
-#139 := (iff #90 #138)
-#136 := (iff #89 #135)
-#137 := [rewrite]: #136
-#140 := [monotonicity #137]: #139
-#143 := [monotonicity #140]: #142
-#148 := [trans #143 #146]: #147
-#154 := [monotonicity #148 #151]: #153
-#67 := (not #49)
-#68 := (iff #58 #67)
-#130 := (~ #68 #129)
-#91 := (~ #67 #90)
-#92 := [sk]: #91
-#74 := (not #67)
-#76 := (~ #74 #49)
-#81 := (~ #49 #49)
-#79 := (~ #46 #46)
-#80 := [refl]: #79
-#82 := [nnf-pos #80]: #81
-#83 := [nnf-neg #82]: #76
-#125 := (~ #58 #58)
-#123 := (~ #55 #55)
-#121 := (~ #43 #43)
-#122 := [refl]: #121
-#124 := [nnf-pos #122]: #123
-#119 := (~ #52 #52)
-#117 := (~ #40 #40)
-#118 := [refl]: #117
-#120 := [nnf-pos #118]: #119
-#126 := [monotonicity #120 #124]: #125
-#114 := (not #58)
-#115 := (~ #114 #113)
-#108 := (not #55)
-#109 := (~ #108 #107)
-#110 := [sk]: #109
-#99 := (not #52)
-#100 := (~ #99 #98)
-#101 := [sk]: #100
-#116 := [nnf-neg #101 #110]: #115
-#131 := [nnf-pos #116 #126 #83 #92]: #130
-#12 := (= #11 f1)
-#16 := (forall (vars (?v0 S2)) #12)
-#10 := (= #9 f1)
-#15 := (forall (vars (?v0 S2)) #10)
-#17 := (and #15 #16)
-#13 := (and #10 #12)
-#14 := (forall (vars (?v0 S2)) #13)
-#18 := (iff #14 #17)
+#45 := (iff #15 #44)
+#42 := (iff #14 #41)
+#43 := [rewrite]: #42
+#39 := (iff #11 #38)
+#40 := [rewrite]: #39
+#46 := [monotonicity #40 #43]: #45
+#52 := [trans #46 #50]: #51
+#55 := [monotonicity #52]: #54
+#63 := [trans #55 #61]: #62
+#37 := [asserted]: #16
+#64 := [mp #37 #63]: #59
+#66 := [not-or-elim #64]: #12
+#74 := [iff-false #66]: #73
+#82 := (iff #13 false)
+#1 := true
+#77 := (not true)
+#80 := (iff #77 false)
+#81 := [rewrite]: #80
+#78 := (iff #13 #77)
+#75 := (iff #8 true)
+#67 := [not-or-elim #64]: #8
+#76 := [iff-true #67]: #75
+#79 := [monotonicity #76]: #78
+#83 := [trans #79 #81]: #82
+#86 := [monotonicity #83 #74]: #85
+#90 := [trans #86 #88]: #89
+#65 := [not-or-elim #64]: #38
+[mp #65 #90]: false
+unsat
+ffac54a02f0c200516a317aa5c330cf1c35aa36e 94 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f5 :: S1
+#11 := f5
+#12 := (= f5 f1)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#41 := (not #8)
+#66 := (or #41 #10 #12)
+#115 := (iff #66 false)
+#110 := (or false false false)
+#113 := (iff #110 false)
+#114 := [rewrite]: #113
+#111 := (iff #66 #110)
+#101 := (iff #12 false)
+#90 := (not #12)
+#69 := (not #66)
+#75 := (or #69 #10 #41 #12)
+#80 := (not #75)
+#16 := (implies #8 #12)
+#15 := (implies #8 #10)
+#17 := (or #15 #16)
+#13 := (or #10 #12)
+#14 := (implies #8 #13)
+#18 := (implies #14 #17)
 #19 := (not #18)
-#71 := (iff #19 #68)
-#61 := (iff #49 #58)
-#64 := (not #61)
-#69 := (iff #64 #68)
-#70 := [rewrite]: #69
-#65 := (iff #19 #64)
-#62 := (iff #18 #61)
-#59 := (iff #17 #58)
-#56 := (iff #16 #55)
-#44 := (iff #12 #43)
-#45 := [rewrite]: #44
-#57 := [quant-intro #45]: #56
-#53 := (iff #15 #52)
-#41 := (iff #10 #40)
-#42 := [rewrite]: #41
-#54 := [quant-intro #42]: #53
-#60 := [monotonicity #54 #57]: #59
-#50 := (iff #14 #49)
-#47 := (iff #13 #46)
-#48 := [monotonicity #42 #45]: #47
-#51 := [quant-intro #48]: #50
-#63 := [monotonicity #51 #60]: #62
-#66 := [monotonicity #63]: #65
-#72 := [trans #66 #70]: #71
-#39 := [asserted]: #19
-#75 := [mp #39 #72]: #68
-#132 := [mp~ #75 #131]: #129
-#133 := [mp #132 #154]: #152
-#134 := [and-elim #133]: #144
-#171 := [mp #134 #170]: #166
-#630 := [unit-resolution #171 #626 #629 #632]: #98
-#346 := (or #357 #97)
-#347 := [def-axiom]: #346
-#619 := [unit-resolution #347 #630]: #357
-#631 := (not #357)
-#636 := (or #445 #631)
-#345 := [quant-inst #95]: #636
-#620 := [unit-resolution #345 #639 #619]: false
-#621 := [lemma #620]: #445
-#693 := (or #666 #690)
-#181 := (or #99 #108)
-#182 := (not #181)
-#178 := (forall (vars (?v0 S2)) #175)
-#185 := (or #178 #182)
-#694 := (iff #185 #693)
-#691 := (iff #182 #690)
-#688 := (iff #181 #687)
-#685 := (iff #108 #684)
-#682 := (iff #55 #679)
-#680 := (iff #43 #43)
-#681 := [refl]: #680
-#683 := [quant-intro #681]: #682
-#686 := [monotonicity #683]: #685
-#677 := (iff #99 #676)
-#674 := (iff #52 #671)
-#672 := (iff #40 #40)
-#673 := [refl]: #672
-#675 := [quant-intro #673]: #674
-#678 := [monotonicity #675]: #677
-#689 := [monotonicity #678 #686]: #688
-#692 := [monotonicity #689]: #691
-#669 := (iff #178 #666)
-#667 := (iff #175 #175)
-#668 := [refl]: #667
-#670 := [quant-intro #668]: #669
-#695 := [monotonicity #670 #692]: #694
-#186 := (iff #149 #185)
-#183 := (iff #58 #182)
-#184 := [rewrite]: #183
-#179 := (iff #49 #178)
-#176 := (iff #46 #175)
-#177 := [rewrite]: #176
-#180 := [quant-intro #177]: #179
-#187 := [monotonicity #180 #184]: #186
-#155 := [and-elim #133]: #149
-#188 := [mp #155 #187]: #185
-#696 := [mp #188 #695]: #693
-#349 := [unit-resolution #696 #621]: #690
-#246 := (or #687 #671)
-#333 := [def-axiom]: #246
-#627 := [unit-resolution #333 #349]: #671
-#247 := (or #687 #679)
-#334 := [def-axiom]: #247
-#623 := [unit-resolution #334 #349]: #679
-#618 := [hypothesis]: #102
-#624 := (or #684 #86)
-#465 := [quant-inst #84]: #624
-#466 := [unit-resolution #465 #618 #623]: false
-#467 := [lemma #466]: #86
-#616 := [hypothesis]: #98
-#628 := (or #676 #97)
-#341 := [quant-inst #95]: #628
-#617 := [unit-resolution #341 #616 #627]: false
-#622 := [lemma #617]: #97
-#609 := [hypothesis]: #107
-#611 := (or #684 #106)
-#612 := [quant-inst #104]: #611
-#610 := [unit-resolution #612 #609 #623]: false
-#606 := [lemma #610]: #106
-#607 := [unit-resolution #171 #606 #622 #467]: #103
-#614 := (or #676 #88)
-#608 := [quant-inst #84]: #614
-[unit-resolution #608 #607 #627]: false
-unsat
-3b618dd5f7cad6fec6bf71ac0425349f4d47cb2a 204 0
-#2 := false
-decl f3 :: (-> S2 S1)
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#624 := (pattern #9)
-decl f4 :: S1
-#12 := f4
-decl f1 :: S1
-#4 := f1
-#45 := (= f1 f4)
-#39 := (= f1 #9)
-#51 := (or #39 #45)
-#630 := (forall (vars (?v0 S2)) (:pat #624) #51)
-#93 := (not #45)
-decl ?v0!0 :: S2
-#84 := ?v0!0
-#85 := (f3 ?v0!0)
-#86 := (= f1 #85)
-#91 := (or #45 #86)
-#279 := [hypothesis]: #45
-#206 := (or #91 #93)
-#293 := [def-axiom]: #206
-#616 := [unit-resolution #293 #279]: #91
-decl ?v0!1 :: S2
-#99 := ?v0!1
-#100 := (f3 ?v0!1)
-#101 := (= f1 #100)
-#121 := (or #45 #101)
-#286 := (or #121 #93)
-#297 := [def-axiom]: #286
-#618 := [unit-resolution #297 #279]: #121
-#124 := (not #121)
-#92 := (not #91)
-#143 := (or #92 #124)
-#87 := (not #86)
-#127 := (and #93 #87)
-#130 := (or #124 #127)
-#146 := (iff #130 #143)
-#140 := (or #124 #92)
-#144 := (iff #140 #143)
-#145 := [rewrite]: #144
-#141 := (iff #130 #140)
-#107 := (iff #127 #92)
-#108 := [rewrite]: #107
-#142 := [monotonicity #108]: #141
-#147 := [trans #142 #145]: #146
-#54 := (forall (vars (?v0 S2)) #51)
-#42 := (forall (vars (?v0 S2)) #39)
-#133 := (or #42 #45 #54)
-#136 := (and #130 #133)
-#48 := (or #42 #45)
-#113 := (or #54 #48)
-#96 := (and #87 #93)
-#102 := (or #101 #45)
-#103 := (not #102)
-#114 := (or #103 #96)
-#115 := (and #114 #113)
-#137 := (iff #115 #136)
-#134 := (iff #113 #133)
-#135 := [rewrite]: #134
-#131 := (iff #114 #130)
-#128 := (iff #96 #127)
-#129 := [rewrite]: #128
-#125 := (iff #103 #124)
-#122 := (iff #102 #121)
-#123 := [rewrite]: #122
-#126 := [monotonicity #123]: #125
-#132 := [monotonicity #126 #129]: #131
-#138 := [monotonicity #132 #135]: #137
-#63 := (not #48)
-#64 := (iff #54 #63)
-#116 := (~ #64 #115)
-#97 := (~ #63 #96)
-#94 := (~ #93 #93)
-#95 := [refl]: #94
-#88 := (not #42)
-#89 := (~ #88 #87)
-#90 := [sk]: #89
-#98 := [nnf-neg #90 #95]: #97
-#81 := (not #63)
-#82 := (~ #81 #48)
-#79 := (~ #48 #48)
-#70 := (~ #45 #45)
-#72 := [refl]: #70
-#77 := (~ #42 #42)
-#75 := (~ #39 #39)
-#76 := [refl]: #75
-#78 := [nnf-pos #76]: #77
-#80 := [monotonicity #78 #72]: #79
-#83 := [nnf-neg #80]: #82
-#111 := (~ #54 #54)
-#109 := (~ #51 #51)
-#110 := [refl]: #109
-#112 := [nnf-pos #110]: #111
-#104 := (not #54)
-#105 := (~ #104 #103)
-#106 := [sk]: #105
-#117 := [nnf-pos #106 #112 #83 #98]: #116
-#13 := (= f4 f1)
-#10 := (= #9 f1)
-#15 := (or #10 #13)
-#16 := (forall (vars (?v0 S2)) #15)
-#11 := (forall (vars (?v0 S2)) #10)
-#14 := (or #11 #13)
-#17 := (iff #14 #16)
-#18 := (not #17)
-#67 := (iff #18 #64)
-#57 := (iff #48 #54)
-#60 := (not #57)
-#65 := (iff #60 #64)
-#66 := [rewrite]: #65
-#61 := (iff #18 #60)
-#58 := (iff #17 #57)
-#55 := (iff #16 #54)
-#52 := (iff #15 #51)
-#46 := (iff #13 #45)
-#47 := [rewrite]: #46
-#40 := (iff #10 #39)
-#41 := [rewrite]: #40
-#53 := [monotonicity #41 #47]: #52
-#56 := [quant-intro #53]: #55
-#49 := (iff #14 #48)
-#43 := (iff #11 #42)
-#44 := [quant-intro #41]: #43
-#50 := [monotonicity #44 #47]: #49
-#59 := [monotonicity #50 #56]: #58
-#62 := [monotonicity #59]: #61
-#68 := [trans #62 #66]: #67
-#38 := [asserted]: #18
-#71 := [mp #38 #68]: #64
-#118 := [mp~ #71 #117]: #115
-#119 := [mp #118 #138]: #136
-#120 := [and-elim #119]: #130
-#148 := [mp #120 #147]: #143
-#273 := [unit-resolution #148 #618 #616]: false
-#405 := [lemma #273]: #93
-#625 := (forall (vars (?v0 S2)) (:pat #624) #39)
-#262 := (not #625)
-#604 := [hypothesis]: #625
-#612 := (not #630)
-#298 := (not #101)
-#272 := [hypothesis]: #298
-#256 := (or #612 #101)
-#614 := [hypothesis]: #630
-#284 := (or #612 #45 #101)
-#285 := (or #612 #102)
-#613 := (iff #285 #284)
-#620 := (or #612 #121)
-#617 := (iff #620 #284)
-#623 := [rewrite]: #617
-#621 := (iff #285 #620)
-#622 := [monotonicity #123]: #621
-#271 := [trans #622 #623]: #613
-#619 := [quant-inst #99]: #285
-#276 := [mp #619 #271]: #284
-#615 := [unit-resolution #276 #405 #272 #614]: false
-#599 := [lemma #615]: #256
-#260 := [unit-resolution #599 #272]: #612
-#635 := (or #625 #45 #630)
-#636 := (iff #133 #635)
-#633 := (iff #54 #630)
-#631 := (iff #51 #51)
-#632 := [refl]: #631
-#634 := [quant-intro #632]: #633
-#628 := (iff #42 #625)
-#626 := (iff #39 #39)
-#627 := [refl]: #626
-#629 := [quant-intro #627]: #628
-#637 := [monotonicity #629 #634]: #636
-#139 := [and-elim #119]: #133
-#638 := [mp #139 #637]: #635
-#261 := [unit-resolution #638 #260 #405]: #625
-#263 := (or #262 #101)
-#601 := [quant-inst #99]: #263
-#602 := [unit-resolution #601 #272 #261]: false
-#603 := [lemma #602]: #101
-#226 := (or #121 #298)
-#299 := [def-axiom]: #226
-#605 := [unit-resolution #299 #603]: #121
-#242 := [unit-resolution #148 #605]: #92
-#207 := (or #91 #87)
-#294 := [def-axiom]: #207
-#607 := [unit-resolution #294 #242]: #87
-#600 := (or #262 #86)
-#606 := [quant-inst #84]: #600
-#609 := [unit-resolution #606 #607 #604]: false
-#247 := [lemma #609]: #262
-#594 := [unit-resolution #638 #247 #405]: #630
-#611 := (or #612 #45 #86)
-#248 := (or #86 #45)
-#597 := (or #612 #248)
-#323 := (iff #597 #611)
-#304 := (or #612 #91)
-#322 := (iff #304 #611)
-#308 := [rewrite]: #322
-#320 := (iff #597 #304)
-#610 := (iff #248 #91)
-#608 := [rewrite]: #610
-#321 := [monotonicity #608]: #320
-#214 := [trans #321 #308]: #323
-#598 := [quant-inst #84]: #597
-#593 := [mp #598 #214]: #611
-[unit-resolution #593 #405 #607 #594]: false
-unsat
-d3ac39bb1c7a6d7418172a244d9e337158e1130d 249 0
-#2 := false
-decl f3 :: (-> S2 S1)
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#650 := (pattern #9)
-decl f1 :: S1
-#4 := f1
-#39 := (= f1 #9)
-#651 := (forall (vars (?v0 S2)) (:pat #650) #39)
-decl f4 :: S1
-#12 := f4
-#45 := (= f1 f4)
-#93 := (not #45)
-#656 := (not #651)
-#659 := (or #656 #93)
-#662 := (not #659)
-#163 := (not #39)
-#164 := (or #163 #93)
-#165 := (not #164)
-#665 := (forall (vars (?v0 S2)) (:pat #650) #165)
-#310 := (not #665)
-decl ?v0!1 :: S2
-#99 := ?v0!1
-#100 := (f3 ?v0!1)
-#101 := (= f1 #100)
-#91 := (not #101)
-#92 := (or #93 #91)
-decl ?v0!0 :: S2
-#84 := ?v0!0
-#85 := (f3 ?v0!0)
-#86 := (= f1 #85)
-#87 := (not #86)
-#305 := (or #93 #87)
-#323 := [hypothesis]: #87
-#298 := (or #305 #86)
-#641 := [def-axiom]: #298
-#286 := [unit-resolution #641 #323]: #305
-#324 := (or #656 #86)
-#312 := [hypothesis]: #651
-#252 := [quant-inst #84]: #324
-#325 := [unit-resolution #252 #323 #312]: false
-#322 := [lemma #325]: #324
-#287 := [unit-resolution #322 #323]: #656
-#232 := (or #659 #651)
-#319 := [def-axiom]: #232
-#288 := [unit-resolution #319 #287]: #659
-#670 := (or #662 #665)
-#168 := (forall (vars (?v0 S2)) #165)
-#42 := (forall (vars (?v0 S2)) #39)
-#88 := (not #42)
-#159 := (or #88 #93)
-#160 := (not #159)
-#171 := (or #160 #168)
-#671 := (iff #171 #670)
-#668 := (iff #168 #665)
-#666 := (iff #165 #165)
-#667 := [refl]: #666
-#669 := [quant-intro #667]: #668
-#663 := (iff #160 #662)
-#660 := (iff #159 #659)
-#657 := (iff #88 #656)
-#654 := (iff #42 #651)
-#652 := (iff #39 #39)
-#653 := [refl]: #652
-#655 := [quant-intro #653]: #654
-#658 := [monotonicity #655]: #657
-#661 := [monotonicity #658]: #660
-#664 := [monotonicity #661]: #663
-#672 := [monotonicity #664 #669]: #671
-#51 := (and #39 #45)
-#54 := (forall (vars (?v0 S2)) #51)
-#48 := (and #42 #45)
-#135 := (or #48 #54)
-#172 := (iff #135 #171)
-#169 := (iff #54 #168)
-#166 := (iff #51 #165)
-#167 := [rewrite]: #166
-#170 := [quant-intro #167]: #169
-#161 := (iff #48 #160)
-#162 := [rewrite]: #161
-#173 := [monotonicity #162 #170]: #172
-#121 := (and #45 #101)
-#124 := (not #121)
-#130 := (or #93 #87 #124)
-#138 := (and #130 #135)
-#113 := (or #54 #48)
-#96 := (or #87 #93)
-#102 := (and #101 #45)
-#103 := (not #102)
-#114 := (or #103 #96)
-#115 := (and #114 #113)
-#139 := (iff #115 #138)
-#136 := (iff #113 #135)
-#137 := [rewrite]: #136
-#133 := (iff #114 #130)
-#127 := (or #124 #96)
-#131 := (iff #127 #130)
-#132 := [rewrite]: #131
-#128 := (iff #114 #127)
-#125 := (iff #103 #124)
-#122 := (iff #102 #121)
-#123 := [rewrite]: #122
-#126 := [monotonicity #123]: #125
-#129 := [monotonicity #126]: #128
-#134 := [trans #129 #132]: #133
-#140 := [monotonicity #134 #137]: #139
-#63 := (not #48)
-#64 := (iff #54 #63)
-#116 := (~ #64 #115)
-#97 := (~ #63 #96)
-#94 := (~ #93 #93)
-#95 := [refl]: #94
-#89 := (~ #88 #87)
-#90 := [sk]: #89
-#98 := [nnf-neg #90 #95]: #97
-#81 := (not #63)
-#82 := (~ #81 #48)
-#79 := (~ #48 #48)
-#70 := (~ #45 #45)
-#72 := [refl]: #70
-#77 := (~ #42 #42)
-#75 := (~ #39 #39)
-#76 := [refl]: #75
-#78 := [nnf-pos #76]: #77
-#80 := [monotonicity #78 #72]: #79
-#83 := [nnf-neg #80]: #82
-#111 := (~ #54 #54)
-#109 := (~ #51 #51)
-#110 := [refl]: #109
-#112 := [nnf-pos #110]: #111
-#104 := (not #54)
-#105 := (~ #104 #103)
-#106 := [sk]: #105
-#117 := [nnf-pos #106 #112 #83 #98]: #116
-#13 := (= f4 f1)
-#10 := (= #9 f1)
-#15 := (and #10 #13)
-#16 := (forall (vars (?v0 S2)) #15)
-#11 := (forall (vars (?v0 S2)) #10)
-#14 := (and #11 #13)
-#17 := (iff #14 #16)
-#18 := (not #17)
-#67 := (iff #18 #64)
-#57 := (iff #48 #54)
-#60 := (not #57)
-#65 := (iff #60 #64)
-#66 := [rewrite]: #65
-#61 := (iff #18 #60)
-#58 := (iff #17 #57)
-#55 := (iff #16 #54)
-#52 := (iff #15 #51)
-#46 := (iff #13 #45)
-#47 := [rewrite]: #46
-#40 := (iff #10 #39)
-#41 := [rewrite]: #40
-#53 := [monotonicity #41 #47]: #52
-#56 := [quant-intro #53]: #55
-#49 := (iff #14 #48)
-#43 := (iff #11 #42)
-#44 := [quant-intro #41]: #43
-#50 := [monotonicity #44 #47]: #49
-#59 := [monotonicity #50 #56]: #58
-#62 := [monotonicity #59]: #61
-#68 := [trans #62 #66]: #67
-#38 := [asserted]: #18
-#71 := [mp #38 #68]: #64
-#118 := [mp~ #71 #117]: #115
-#119 := [mp #118 #140]: #138
-#141 := [and-elim #119]: #135
-#174 := [mp #141 #173]: #171
-#673 := [mp #174 #672]: #670
-#289 := [unit-resolution #673 #288]: #665
-#299 := (not #305)
-#311 := (or #310 #299)
-#326 := (not #96)
-#645 := (or #310 #326)
-#647 := (iff #645 #311)
-#643 := (iff #311 #311)
-#649 := [rewrite]: #643
-#431 := (iff #326 #299)
-#642 := (iff #96 #305)
-#644 := [rewrite]: #642
-#638 := [monotonicity #644]: #431
-#648 := [monotonicity #638]: #647
-#639 := [trans #648 #649]: #647
-#646 := [quant-inst #84]: #645
-#297 := [mp #646 #639]: #311
-#627 := [unit-resolution #297 #289 #286]: false
-#628 := [lemma #627]: #86
-#107 := (not #92)
-#619 := [hypothesis]: #107
-#634 := (or #92 #45)
-#637 := [def-axiom]: #634
-#620 := [unit-resolution #637 #619]: #45
-#623 := (or #92 #101)
-#624 := [def-axiom]: #623
-#342 := [unit-resolution #624 #619]: #101
-#153 := (or #93 #87 #91)
-#156 := (iff #130 #153)
-#150 := (or #93 #87 #92)
-#154 := (iff #150 #153)
-#155 := [rewrite]: #154
-#151 := (iff #130 #150)
-#148 := (iff #124 #92)
-#143 := (not #107)
-#146 := (iff #143 #92)
-#147 := [rewrite]: #146
-#144 := (iff #124 #143)
-#108 := (iff #121 #107)
-#142 := [rewrite]: #108
-#145 := [monotonicity #142]: #144
-#149 := [trans #145 #147]: #148
-#152 := [monotonicity #149]: #151
-#157 := [trans #152 #155]: #156
-#120 := [and-elim #119]: #130
-#158 := [mp #120 #157]: #153
-#343 := [unit-resolution #158 #342 #620 #628]: false
-#617 := [lemma #343]: #92
-#349 := (or #107 #310)
-#347 := [hypothesis]: #92
-#348 := [hypothesis]: #665
-#631 := (or #310 #107)
-#302 := (or #91 #93)
-#640 := (not #302)
-#626 := (or #310 #640)
-#268 := (iff #626 #631)
-#635 := (iff #631 #631)
-#273 := [rewrite]: #635
-#629 := (iff #640 #107)
-#282 := (iff #302 #92)
-#625 := [rewrite]: #282
-#630 := [monotonicity #625]: #629
-#633 := [monotonicity #630]: #268
-#274 := [trans #633 #273]: #268
-#632 := [quant-inst #99]: #626
-#636 := [mp #632 #274]: #631
-#334 := [unit-resolution #636 #348 #347]: false
-#240 := [lemma #334]: #349
-#621 := [unit-resolution #240 #617]: #310
-#618 := [unit-resolution #673 #621]: #662
-#332 := [unit-resolution #319 #618]: #651
-#233 := (or #659 #45)
-#320 := [def-axiom]: #233
-#333 := [unit-resolution #320 #618]: #45
-#335 := [unit-resolution #158 #333 #628]: #91
-#622 := (or #656 #101)
-#331 := [quant-inst #99]: #622
-[unit-resolution #331 #335 #332]: false
-unsat
-44bf7cfb85eb1c4e00dce5a88ea0a349e1b59c09 49 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: (-> S2 S2 S1)
-#9 := (:var 0 S2)
-#13 := (:var 1 S2)
-#14 := (f3 #13 #9)
-#15 := (= #14 f1)
-#16 := (forall (vars (?v0 S2) (?v1 S2)) #15)
-#8 := (:var 2 S2)
-#10 := (f3 #8 #9)
-#11 := (= #10 f1)
-#12 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #11)
-#17 := (iff #12 #16)
-#18 := (not #17)
-#67 := (iff #18 false)
-#1 := true
-#62 := (not true)
-#65 := (iff #62 false)
-#66 := [rewrite]: #65
-#63 := (iff #18 #62)
-#60 := (iff #17 true)
-#45 := (= f1 #14)
-#46 := (forall (vars (?v0 S2) (?v2 S2)) #45)
-#55 := (iff #46 #46)
-#58 := (iff #55 true)
-#59 := [rewrite]: #58
-#56 := (iff #17 #55)
-#53 := (iff #16 #46)
-#51 := (iff #15 #45)
-#52 := [rewrite]: #51
-#54 := [quant-intro #52]: #53
-#49 := (iff #12 #46)
-#39 := (= f1 #10)
-#42 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #39)
-#47 := (iff #42 #46)
-#48 := [elim-unused]: #47
-#43 := (iff #12 #42)
-#40 := (iff #11 #39)
-#41 := [rewrite]: #40
-#44 := [quant-intro #41]: #43
-#50 := [trans #44 #48]: #49
-#57 := [monotonicity #50 #54]: #56
-#61 := [trans #57 #59]: #60
-#64 := [monotonicity #61]: #63
-#68 := [trans #64 #66]: #67
-#38 := [asserted]: #18
-[mp #38 #68]: false
-unsat
-07180efbff5a77042937fc4dee6db649992c0567 136 0
-#2 := false
-decl f3 :: (-> S2 S2 S1)
-decl f4 :: S2
-#16 := f4
-decl f5 :: S2
-#20 := f5
-#175 := (f3 f5 f4)
-decl f1 :: S1
-#4 := f1
-#262 := (= f1 #175)
-#176 := (not #262)
-#21 := (f3 f4 f5)
-#70 := (= f1 #21)
-#105 := (not #70)
-#9 := (:var 0 S2)
-#17 := (f3 #9 f4)
-#64 := (= f1 #17)
-#67 := (forall (vars (?v0 S2)) #64)
-#76 := (not #67)
-#8 := (:var 1 S2)
-#12 := (f3 #9 #8)
-#49 := (= f1 #12)
-#10 := (f3 #8 #9)
-#46 := (= f1 #10)
-#55 := (not #46)
-#56 := (or #55 #49)
-#61 := (forall (vars (?v0 S2) (?v1 S2)) #56)
-#85 := (not #61)
-#94 := (or #85 #76 #70)
-#97 := (not #94)
-#22 := (= #21 f1)
-#18 := (= #17 f1)
-#19 := (forall (vars (?v0 S2)) #18)
-#23 := (implies #19 #22)
-#13 := (= #12 f1)
-#11 := (= #10 f1)
-#14 := (implies #11 #13)
-#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
-#24 := (implies #15 #23)
-#25 := (not #24)
-#100 := (iff #25 #97)
-#77 := (or #76 #70)
-#86 := (or #85 #77)
-#91 := (not #86)
-#98 := (iff #91 #97)
-#95 := (iff #86 #94)
-#96 := [rewrite]: #95
-#99 := [monotonicity #96]: #98
-#92 := (iff #25 #91)
-#89 := (iff #24 #86)
-#82 := (implies #61 #77)
-#87 := (iff #82 #86)
-#88 := [rewrite]: #87
-#83 := (iff #24 #82)
-#80 := (iff #23 #77)
-#73 := (implies #67 #70)
-#78 := (iff #73 #77)
-#79 := [rewrite]: #78
-#74 := (iff #23 #73)
-#71 := (iff #22 #70)
-#72 := [rewrite]: #71
-#68 := (iff #19 #67)
-#65 := (iff #18 #64)
-#66 := [rewrite]: #65
-#69 := [quant-intro #66]: #68
-#75 := [monotonicity #69 #72]: #74
-#81 := [trans #75 #79]: #80
-#62 := (iff #15 #61)
-#59 := (iff #14 #56)
-#52 := (implies #46 #49)
-#57 := (iff #52 #56)
-#58 := [rewrite]: #57
-#53 := (iff #14 #52)
-#50 := (iff #13 #49)
-#51 := [rewrite]: #50
-#47 := (iff #11 #46)
-#48 := [rewrite]: #47
-#54 := [monotonicity #48 #51]: #53
-#60 := [trans #54 #58]: #59
-#63 := [quant-intro #60]: #62
-#84 := [monotonicity #63 #81]: #83
-#90 := [trans #84 #88]: #89
-#93 := [monotonicity #90]: #92
-#101 := [trans #93 #99]: #100
-#45 := [asserted]: #25
-#102 := [mp #45 #101]: #97
-#106 := [not-or-elim #102]: #105
-#594 := (pattern #12)
-#593 := (pattern #10)
-#595 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #593 #594) #56)
-#598 := (iff #61 #595)
-#596 := (iff #56 #56)
-#597 := [refl]: #596
-#599 := [quant-intro #597]: #598
-#118 := (~ #61 #61)
-#116 := (~ #56 #56)
-#117 := [refl]: #116
-#119 := [nnf-pos #117]: #118
-#103 := [not-or-elim #102]: #61
-#108 := [mp~ #103 #119]: #61
-#600 := [mp #108 #599]: #595
-#266 := (not #595)
-#267 := (or #266 #70 #176)
-#263 := (or #176 #70)
-#195 := (or #266 #263)
-#242 := (iff #195 #267)
-#177 := (or #70 #176)
-#265 := (or #266 #177)
-#585 := (iff #265 #267)
-#587 := [rewrite]: #585
-#269 := (iff #195 #265)
-#264 := (iff #263 #177)
-#255 := [rewrite]: #264
-#248 := [monotonicity #255]: #269
-#374 := [trans #248 #587]: #242
-#268 := [quant-inst #20 #16]: #195
-#581 := [mp #268 #374]: #267
-#253 := [unit-resolution #581 #600 #106]: #176
-#601 := (pattern #17)
-#602 := (forall (vars (?v0 S2)) (:pat #601) #64)
-#605 := (iff #67 #602)
-#603 := (iff #64 #64)
-#604 := [refl]: #603
-#606 := [quant-intro #604]: #605
-#110 := (~ #67 #67)
-#109 := (~ #64 #64)
-#120 := [refl]: #109
-#111 := [nnf-pos #120]: #110
-#104 := [not-or-elim #102]: #67
-#121 := [mp~ #104 #111]: #67
-#607 := [mp #121 #606]: #602
-#588 := (not #602)
-#589 := (or #588 #262)
-#590 := [quant-inst #20]: #589
-[unit-resolution #590 #607 #253]: false
-unsat
-1b292cde8b432d2890e3f7c5bd6fc59df5914e46 126 0
-#2 := false
-decl f3 :: (-> S2 S1)
-decl f4 :: (-> S3 S2 S2)
-decl f6 :: S2
-#17 := f6
-decl f5 :: S3
-#11 := f5
-#21 := (f4 f5 f6)
-#22 := (f4 f5 #21)
-#158 := (f3 #22)
-decl f1 :: S1
-#4 := f1
-#245 := (= f1 #158)
-#156 := (f3 #21)
-#243 := (= f1 #156)
-#18 := (f3 f6)
-#66 := (= f1 #18)
-#8 := (:var 0 S2)
-#12 := (f4 f5 #8)
-#13 := (f3 #12)
-#51 := (= f1 #13)
-#9 := (f3 #8)
-#48 := (= f1 #9)
-#57 := (not #48)
+#83 := (iff #19 #80)
+#48 := (or #41 #12)
+#45 := (or #41 #10)
+#51 := (or #45 #48)
+#42 := (or #41 #13)
+#57 := (not #42)
 #58 := (or #57 #51)
-#63 := (forall (vars (?v0 S2)) #58)
-#69 := (and #63 #66)
-#23 := (f4 f5 #22)
-#24 := (f3 #23)
-#72 := (= f1 #24)
-#78 := (not #69)
-#79 := (or #78 #72)
-#84 := (not #79)
-#25 := (= #24 f1)
-#19 := (= #18 f1)
-#14 := (= #13 f1)
-#10 := (= #9 f1)
-#15 := (implies #10 #14)
-#16 := (forall (vars (?v0 S2)) #15)
-#20 := (and #16 #19)
-#26 := (implies #20 #25)
-#27 := (not #26)
-#85 := (iff #27 #84)
-#82 := (iff #26 #79)
-#75 := (implies #69 #72)
-#80 := (iff #75 #79)
-#81 := [rewrite]: #80
-#76 := (iff #26 #75)
-#73 := (iff #25 #72)
-#74 := [rewrite]: #73
-#70 := (iff #20 #69)
-#67 := (iff #19 #66)
+#63 := (not #58)
+#81 := (iff #63 #80)
+#78 := (iff #58 #75)
+#72 := (or #69 #51)
+#76 := (iff #72 #75)
+#77 := [rewrite]: #76
+#73 := (iff #58 #72)
+#70 := (iff #57 #69)
+#67 := (iff #42 #66)
 #68 := [rewrite]: #67
-#64 := (iff #16 #63)
-#61 := (iff #15 #58)
-#54 := (implies #48 #51)
+#71 := [monotonicity #68]: #70
+#74 := [monotonicity #71]: #73
+#79 := [trans #74 #77]: #78
+#82 := [monotonicity #79]: #81
+#64 := (iff #19 #63)
+#61 := (iff #18 #58)
+#54 := (implies #42 #51)
 #59 := (iff #54 #58)
 #60 := [rewrite]: #59
-#55 := (iff #15 #54)
-#52 := (iff #14 #51)
-#53 := [rewrite]: #52
-#49 := (iff #10 #48)
+#55 := (iff #18 #54)
+#52 := (iff #17 #51)
+#49 := (iff #16 #48)
 #50 := [rewrite]: #49
-#56 := [monotonicity #50 #53]: #55
-#62 := [trans #56 #60]: #61
-#65 := [quant-intro #62]: #64
-#71 := [monotonicity #65 #68]: #70
-#77 := [monotonicity #71 #74]: #76
-#83 := [trans #77 #81]: #82
-#86 := [monotonicity #83]: #85
-#47 := [asserted]: #27
-#89 := [mp #47 #86]: #84
-#87 := [not-or-elim #89]: #69
-#90 := [and-elim #87]: #66
-#574 := (pattern #12)
-#575 := (forall (vars (?v0 S2)) (:pat #574) #58)
-#578 := (iff #63 #575)
-#576 := (iff #58 #58)
-#577 := [refl]: #576
-#579 := [quant-intro #577]: #578
-#104 := (~ #63 #63)
-#102 := (~ #58 #58)
-#103 := [refl]: #102
-#105 := [nnf-pos #103]: #104
-#88 := [and-elim #87]: #63
-#94 := [mp~ #88 #105]: #63
-#580 := [mp #94 #579]: #575
-#157 := (not #66)
-#236 := (not #575)
-#247 := (or #236 #157 #243)
-#244 := (or #157 #243)
-#248 := (or #236 #244)
-#249 := (iff #248 #247)
-#246 := [rewrite]: #249
-#176 := [quant-inst #17]: #248
-#250 := [mp #176 #246]: #247
-#212 := [unit-resolution #250 #580 #90]: #243
-#229 := (not #243)
-#355 := (or #236 #229 #245)
-#566 := (or #229 #245)
-#562 := (or #236 #566)
-#235 := (iff #562 #355)
-#569 := [rewrite]: #235
-#234 := [quant-inst #21]: #562
-#570 := [mp #234 #569]: #355
-#213 := [unit-resolution #570 #580 #212]: #245
-#91 := (not #72)
-#92 := [not-or-elim #89]: #91
-#568 := (not #245)
-#573 := (or #236 #72 #568)
-#223 := (or #568 #72)
-#563 := (or #236 #223)
-#549 := (iff #563 #573)
-#571 := (or #72 #568)
-#226 := (or #236 #571)
-#565 := (iff #226 #573)
-#206 := [rewrite]: #565
-#564 := (iff #563 #226)
-#572 := (iff #223 #571)
-#567 := [rewrite]: #572
-#222 := [monotonicity #567]: #564
-#210 := [trans #222 #206]: #549
-#221 := [quant-inst #22]: #563
-#211 := [mp #221 #210]: #573
-[unit-resolution #211 #580 #92 #213]: false
-unsat
-13b01358656727e1edb81fc16730f2ee5b483b3e 64 0
-#2 := false
-decl f3 :: (-> S2 S2 S3)
-decl f4 :: S2
-#14 := f4
-decl f5 :: S2
-#16 := f5
-#18 := (f3 f5 f4)
-#17 := (f3 f4 f5)
-#19 := (= #17 #18)
-#65 := (not #19)
-#8 := (:var 1 S2)
-#9 := (:var 0 S2)
-#11 := (f3 #9 #8)
-#10 := (f3 #8 #9)
-#12 := (= #10 #11)
-#13 := (forall (vars (?v0 S2) (?v1 S2)) #12)
-#55 := (not #13)
-#56 := (or #55 #19)
-#61 := (not #56)
-#15 := (= f4 f4)
-#20 := (and #15 #19)
-#21 := (implies #13 #20)
-#22 := (not #21)
-#62 := (iff #22 #61)
-#59 := (iff #21 #56)
-#52 := (implies #13 #19)
-#57 := (iff #52 #56)
-#58 := [rewrite]: #57
-#53 := (iff #21 #52)
-#50 := (iff #20 #19)
-#1 := true
-#45 := (and true #19)
-#48 := (iff #45 #19)
-#49 := [rewrite]: #48
-#46 := (iff #20 #45)
-#43 := (iff #15 true)
+#46 := (iff #15 #45)
+#47 := [rewrite]: #46
+#53 := [monotonicity #47 #50]: #52
+#43 := (iff #14 #42)
 #44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#51 := [trans #47 #49]: #50
-#54 := [monotonicity #51]: #53
-#60 := [trans #54 #58]: #59
-#63 := [monotonicity #60]: #62
-#42 := [asserted]: #22
-#66 := [mp #42 #63]: #61
-#67 := [not-or-elim #66]: #65
-#550 := (pattern #11)
-#549 := (pattern #10)
-#551 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #549 #550) #12)
-#554 := (iff #13 #551)
-#552 := (iff #12 #12)
-#553 := [refl]: #552
-#555 := [quant-intro #553]: #554
-#77 := (~ #13 #13)
-#75 := (~ #12 #12)
-#76 := [refl]: #75
-#78 := [nnf-pos #76]: #77
-#64 := [not-or-elim #66]: #13
-#69 := [mp~ #64 #78]: #13
-#556 := [mp #69 #555]: #551
-#132 := (not #551)
-#219 := (or #132 #19)
-#133 := [quant-inst #14 #16]: #219
-[unit-resolution #133 #556 #67]: false
-unsat
-8729e6c9d45ca3f4162f872a23bbd60b4b1c3963 250 0
-#2 := false
-decl f3 :: (-> S2 S1)
-decl f7 :: S2
-#22 := f7
-#25 := (f3 f7)
-decl f1 :: S1
-#4 := f1
-#97 := (= f1 #25)
-#286 := (not #97)
-decl f4 :: (-> S2 S1)
-#8 := (:var 0 S2)
-#11 := (f4 #8)
-#705 := (pattern #11)
-#9 := (f3 #8)
-#704 := (pattern #9)
-#60 := (= f1 #11)
-#57 := (= f1 #9)
-#66 := (not #57)
-#67 := (or #66 #60)
-#706 := (forall (vars (?v0 S2)) (:pat #704 #705) #67)
-#72 := (forall (vars (?v0 S2)) #67)
-#709 := (iff #72 #706)
-#707 := (iff #67 #67)
-#708 := [refl]: #707
-#710 := [quant-intro #708]: #709
-#190 := (~ #72 #72)
-#204 := (~ #67 #67)
-#205 := [refl]: #204
-#191 := [nnf-pos #205]: #190
-decl f6 :: (-> S2 S1)
-#23 := (f6 f7)
-#94 := (= f1 #23)
-#81 := (not #60)
-#89 := (and #66 #81)
-#106 := (not #89)
-#139 := (or #106 #94 #97)
-#142 := (forall (vars (?v0 S2)) #139)
-decl f5 :: S2
-#15 := f5
-#16 := (f4 f5)
-#75 := (= f1 #16)
-#78 := (not #75)
-#151 := (and #72 #78 #142)
-#156 := (not #151)
-#32 := (f4 f7)
-#121 := (= f1 #32)
-#162 := (or #94 #121 #156)
-#167 := (not #162)
-#33 := (= #32 f1)
-#24 := (= #23 f1)
-#34 := (or #24 #33)
-#26 := (= #25 f1)
-#27 := (or #24 #26)
-#10 := (= #9 f1)
-#20 := (not #10)
-#12 := (= #11 f1)
-#19 := (not #12)
-#21 := (and #19 #20)
-#28 := (implies #21 #27)
-#29 := (forall (vars (?v0 S2)) #28)
-#17 := (= #16 f1)
-#18 := (not #17)
-#30 := (and #18 #29)
-#13 := (implies #10 #12)
-#14 := (forall (vars (?v0 S2)) #13)
-#31 := (and #14 #30)
-#35 := (implies #31 #34)
-#36 := (not #35)
-#170 := (iff #36 #167)
-#124 := (or #94 #121)
-#100 := (or #94 #97)
-#107 := (or #106 #100)
-#112 := (forall (vars (?v0 S2)) #107)
-#115 := (and #78 #112)
-#118 := (and #72 #115)
-#130 := (not #118)
-#131 := (or #130 #124)
-#136 := (not #131)
-#168 := (iff #136 #167)
-#165 := (iff #131 #162)
-#159 := (or #156 #124)
-#163 := (iff #159 #162)
-#164 := [rewrite]: #163
-#160 := (iff #131 #159)
-#157 := (iff #130 #156)
-#154 := (iff #118 #151)
-#145 := (and #78 #142)
-#148 := (and #72 #145)
-#152 := (iff #148 #151)
-#153 := [rewrite]: #152
-#149 := (iff #118 #148)
-#146 := (iff #115 #145)
-#143 := (iff #112 #142)
-#140 := (iff #107 #139)
-#141 := [rewrite]: #140
-#144 := [quant-intro #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [monotonicity #147]: #149
-#155 := [trans #150 #153]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#166 := [trans #161 #164]: #165
-#169 := [monotonicity #166]: #168
-#137 := (iff #36 #136)
-#134 := (iff #35 #131)
-#127 := (implies #118 #124)
-#132 := (iff #127 #131)
-#133 := [rewrite]: #132
-#128 := (iff #35 #127)
-#125 := (iff #34 #124)
-#122 := (iff #33 #121)
-#123 := [rewrite]: #122
-#95 := (iff #24 #94)
-#96 := [rewrite]: #95
-#126 := [monotonicity #96 #123]: #125
-#119 := (iff #31 #118)
-#116 := (iff #30 #115)
-#113 := (iff #29 #112)
-#110 := (iff #28 #107)
-#103 := (implies #89 #100)
-#108 := (iff #103 #107)
-#109 := [rewrite]: #108
-#104 := (iff #28 #103)
-#101 := (iff #27 #100)
-#98 := (iff #26 #97)
-#99 := [rewrite]: #98
-#102 := [monotonicity #96 #99]: #101
-#92 := (iff #21 #89)
-#86 := (and #81 #66)
-#90 := (iff #86 #89)
-#91 := [rewrite]: #90
-#87 := (iff #21 #86)
-#84 := (iff #20 #66)
-#58 := (iff #10 #57)
-#59 := [rewrite]: #58
-#85 := [monotonicity #59]: #84
-#82 := (iff #19 #81)
-#61 := (iff #12 #60)
-#62 := [rewrite]: #61
-#83 := [monotonicity #62]: #82
-#88 := [monotonicity #83 #85]: #87
-#93 := [trans #88 #91]: #92
-#105 := [monotonicity #93 #102]: #104
-#111 := [trans #105 #109]: #110
-#114 := [quant-intro #111]: #113
-#79 := (iff #18 #78)
-#76 := (iff #17 #75)
-#77 := [rewrite]: #76
-#80 := [monotonicity #77]: #79
-#117 := [monotonicity #80 #114]: #116
-#73 := (iff #14 #72)
-#70 := (iff #13 #67)
-#63 := (implies #57 #60)
-#68 := (iff #63 #67)
-#69 := [rewrite]: #68
-#64 := (iff #13 #63)
-#65 := [monotonicity #59 #62]: #64
-#71 := [trans #65 #69]: #70
-#74 := [quant-intro #71]: #73
-#120 := [monotonicity #74 #117]: #119
-#129 := [monotonicity #120 #126]: #128
-#135 := [trans #129 #133]: #134
-#138 := [monotonicity #135]: #137
-#171 := [trans #138 #169]: #170
-#56 := [asserted]: #36
-#172 := [mp #56 #171]: #167
-#177 := [not-or-elim #172]: #151
-#178 := [and-elim #177]: #72
-#188 := [mp~ #178 #191]: #72
-#711 := [mp #188 #710]: #706
-#175 := (not #121)
-#176 := [not-or-elim #172]: #175
-#288 := (not #706)
-#375 := (or #288 #286 #121)
-#373 := (or #286 #121)
-#366 := (or #288 #373)
-#378 := (iff #366 #375)
-#306 := [rewrite]: #378
-#377 := [quant-inst #22]: #366
-#379 := [mp #377 #306]: #375
-#401 := [unit-resolution #379 #176 #711]: #286
-#220 := (or #57 #60 #97)
-#712 := (forall (vars (?v0 S2)) (:pat #704 #705) #220)
-#225 := (forall (vars (?v0 S2)) #220)
-#715 := (iff #225 #712)
-#713 := (iff #220 #220)
-#714 := [refl]: #713
-#716 := [quant-intro #714]: #715
-#195 := (or #106 #97)
-#200 := (forall (vars (?v0 S2)) #195)
-#226 := (iff #200 #225)
-#223 := (iff #195 #220)
-#206 := (or #57 #60)
-#217 := (or #206 #97)
-#221 := (iff #217 #220)
-#222 := [rewrite]: #221
-#218 := (iff #195 #217)
-#215 := (iff #106 #206)
-#207 := (not #206)
-#210 := (not #207)
-#213 := (iff #210 #206)
-#214 := [rewrite]: #213
-#211 := (iff #106 #210)
-#208 := (iff #89 #207)
-#209 := [rewrite]: #208
-#212 := [monotonicity #209]: #211
-#216 := [trans #212 #214]: #215
-#219 := [monotonicity #216]: #218
-#224 := [trans #219 #222]: #223
-#227 := [quant-intro #224]: #226
-#187 := (~ #200 #200)
-#189 := (~ #195 #195)
-#186 := [refl]: #189
-#182 := [nnf-pos #186]: #187
-#201 := (iff #142 #200)
-#198 := (iff #139 #195)
-#192 := (or #106 false #97)
-#196 := (iff #192 #195)
-#197 := [rewrite]: #196
-#193 := (iff #139 #192)
-#184 := (iff #94 false)
-#173 := (not #94)
-#174 := [not-or-elim #172]: #173
-#185 := [iff-false #174]: #184
-#194 := [monotonicity #185]: #193
-#199 := [trans #194 #197]: #198
-#202 := [quant-intro #199]: #201
-#180 := [and-elim #177]: #142
-#203 := [mp #180 #202]: #200
-#183 := [mp~ #203 #182]: #200
-#228 := [mp #183 #227]: #225
-#717 := [mp #228 #716]: #712
-#359 := (not #712)
-#696 := (or #359 #97 #121)
-#287 := (or #97 #121 #97)
-#698 := (or #359 #287)
-#700 := (iff #698 #696)
-#374 := (or #97 #121)
-#485 := (or #359 #374)
-#365 := (iff #485 #696)
-#699 := [rewrite]: #365
-#692 := (iff #698 #485)
-#376 := (iff #287 #374)
-#380 := [rewrite]: #376
-#364 := [monotonicity #380]: #692
-#701 := [trans #364 #699]: #700
-#353 := [quant-inst #22]: #698
-#702 := [mp #353 #701]: #696
-[unit-resolution #702 #176 #717 #401]: false
-unsat
-b2586fe221d4519a3bc11715a6afc923e5ff0b19 25 0
-#2 := false
-#8 := (:var 0 S2)
-#9 := (= #8 #8)
-#10 := (exists (vars (?v0 S2)) #9)
-#11 := (not #10)
-#46 := (iff #11 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #11 #41)
-#39 := (iff #10 true)
-#34 := (exists (vars (?v0 S2)) true)
-#37 := (iff #34 true)
-#38 := [elim-unused]: #37
-#35 := (iff #10 #34)
-#32 := (iff #9 true)
-#33 := [rewrite]: #32
-#36 := [quant-intro #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#31 := [asserted]: #11
-[mp #31 #47]: false
-unsat
-0b9b80c026d042a35c3971f59d4c9cc24f2e1be5 34 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: (-> S2 S1)
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#10 := (= #9 f1)
-#11 := (exists (vars (?v0 S2)) #10)
-#12 := (iff #11 #11)
-#13 := (not #12)
-#52 := (iff #13 false)
-#1 := true
-#47 := (not true)
-#50 := (iff #47 false)
-#51 := [rewrite]: #50
-#48 := (iff #13 #47)
-#45 := (iff #12 true)
-#34 := (= f1 #9)
-#37 := (exists (vars (?v0 S2)) #34)
-#40 := (iff #37 #37)
-#43 := (iff #40 true)
-#44 := [rewrite]: #43
-#41 := (iff #12 #40)
-#38 := (iff #11 #37)
-#35 := (iff #10 #34)
-#36 := [rewrite]: #35
-#39 := [quant-intro #36]: #38
-#42 := [monotonicity #39 #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#33 := [asserted]: #13
-[mp #33 #53]: false
-unsat
-2ad5bfe4ae1a537e6115da5fac3d5e5fd857b08d 263 0
-#2 := false
-decl f3 :: (-> S2 S1)
-decl ?v0!1 :: S2
-#114 := ?v0!1
-#115 := (f3 ?v0!1)
-decl f1 :: S1
-#4 := f1
-#116 := (= f1 #115)
-decl f4 :: (-> S2 S1)
-decl ?v0!2 :: S2
-#121 := ?v0!2
-#122 := (f4 ?v0!2)
-#123 := (= f1 #122)
-#602 := (not #123)
-#595 := [hypothesis]: #123
-#8 := (:var 0 S2)
-#11 := (f4 #8)
-#642 := (pattern #11)
-#43 := (= f1 #11)
-#103 := (not #43)
-#643 := (forall (vars (?v0 S2)) (:pat #642) #103)
-#648 := (not #643)
-#9 := (f3 #8)
-#633 := (pattern #9)
-#40 := (= f1 #9)
-#96 := (not #40)
-#634 := (forall (vars (?v0 S2)) (:pat #633) #96)
-#639 := (not #634)
-#651 := (or #639 #648)
-#654 := (not #651)
-#46 := (or #40 #43)
-#90 := (not #46)
-#657 := (forall (vars (?v0 S2)) (:pat #633 #642) #90)
-#282 := (not #657)
-decl ?v0!0 :: S2
-#79 := ?v0!0
-#80 := (f4 ?v0!0)
-#81 := (= f1 #80)
-#82 := (f3 ?v0!0)
-#74 := (= f1 #82)
-#76 := (or #74 #81)
-#265 := (not #116)
-#628 := (f4 ?v0!1)
-#629 := (= f1 #628)
-#630 := (or #116 #629)
-#631 := (not #630)
-#623 := [hypothesis]: #657
-#613 := (or #631 #282)
-#626 := [hypothesis]: #630
-#281 := (or #282 #631)
-#624 := [quant-inst #114]: #281
-#612 := [unit-resolution #624 #623 #626]: false
-#614 := [lemma #612]: #613
-#596 := [unit-resolution #614 #623]: #631
-#608 := (or #630 #265)
-#269 := [def-axiom]: #608
-#597 := [unit-resolution #269 #596]: #265
-#295 := (not #74)
-#306 := [hypothesis]: #74
-#293 := (or #76 #295)
-#294 := [def-axiom]: #293
-#625 := [unit-resolution #294 #306]: #76
-#235 := (or #639 #295)
-#307 := [hypothesis]: #634
-#308 := [quant-inst #79]: #235
-#305 := [unit-resolution #308 #307 #306]: false
-#309 := [lemma #305]: #235
-#627 := [unit-resolution #309 #306]: #639
-#215 := (or #651 #634)
-#302 := [def-axiom]: #215
-#632 := [unit-resolution #302 #627]: #651
-#662 := (or #654 #657)
-#93 := (forall (vars (?v0 S2)) #90)
-#106 := (forall (vars (?v0 S2)) #103)
-#120 := (not #106)
-#99 := (forall (vars (?v0 S2)) #96)
-#119 := (not #99)
-#85 := (or #119 #120)
-#86 := (not #85)
-#152 := (or #86 #93)
-#663 := (iff #152 #662)
-#660 := (iff #93 #657)
-#658 := (iff #90 #90)
-#659 := [refl]: #658
-#661 := [quant-intro #659]: #660
-#655 := (iff #86 #654)
-#652 := (iff #85 #651)
-#649 := (iff #120 #648)
-#646 := (iff #106 #643)
-#644 := (iff #103 #103)
-#645 := [refl]: #644
-#647 := [quant-intro #645]: #646
-#650 := [monotonicity #647]: #649
-#640 := (iff #119 #639)
-#637 := (iff #99 #634)
-#635 := (iff #96 #96)
-#636 := [refl]: #635
-#638 := [quant-intro #636]: #637
-#641 := [monotonicity #638]: #640
-#653 := [monotonicity #641 #650]: #652
-#656 := [monotonicity #653]: #655
-#664 := [monotonicity #656 #661]: #663
-#110 := (and #99 #106)
-#139 := (or #93 #110)
-#155 := (iff #139 #152)
-#149 := (or #93 #86)
-#153 := (iff #149 #152)
-#154 := [rewrite]: #153
-#150 := (iff #139 #149)
-#126 := (iff #110 #86)
-#127 := [rewrite]: #126
-#151 := [monotonicity #127]: #150
-#156 := [trans #151 #154]: #155
-#142 := (or #74 #81 #116 #123)
-#145 := (and #139 #142)
-#128 := (or #116 #123)
-#131 := (or #128 #76)
-#132 := (or #110 #93)
-#133 := (and #132 #131)
-#146 := (iff #133 #145)
-#143 := (iff #131 #142)
-#144 := [rewrite]: #143
-#140 := (iff #132 #139)
-#141 := [rewrite]: #140
-#147 := [monotonicity #141 #144]: #146
-#49 := (exists (vars (?v0 S2)) #46)
-#67 := (not #49)
-#55 := (exists (vars (?v0 S2)) #43)
-#52 := (exists (vars (?v0 S2)) #40)
-#58 := (or #52 #55)
-#68 := (iff #58 #67)
-#134 := (~ #68 #133)
-#94 := (~ #67 #93)
-#91 := (~ #90 #90)
-#92 := [refl]: #91
-#95 := [nnf-neg #92]: #94
-#87 := (not #67)
-#88 := (~ #87 #76)
-#83 := (~ #49 #76)
-#84 := [sk]: #83
-#89 := [nnf-neg #84]: #88
-#129 := (~ #58 #128)
-#124 := (~ #55 #123)
-#125 := [sk]: #124
-#117 := (~ #52 #116)
-#118 := [sk]: #117
-#130 := [monotonicity #118 #125]: #129
-#111 := (not #58)
-#112 := (~ #111 #110)
-#107 := (not #55)
-#108 := (~ #107 #106)
-#104 := (~ #103 #103)
-#105 := [refl]: #104
-#109 := [nnf-neg #105]: #108
-#100 := (not #52)
-#101 := (~ #100 #99)
-#97 := (~ #96 #96)
-#98 := [refl]: #97
-#102 := [nnf-neg #98]: #101
-#113 := [nnf-neg #102 #109]: #112
-#135 := [nnf-pos #113 #130 #89 #95]: #134
-#12 := (= #11 f1)
-#16 := (exists (vars (?v0 S2)) #12)
-#10 := (= #9 f1)
-#15 := (exists (vars (?v0 S2)) #10)
-#17 := (or #15 #16)
-#13 := (or #10 #12)
-#14 := (exists (vars (?v0 S2)) #13)
-#18 := (iff #14 #17)
-#19 := (not #18)
-#71 := (iff #19 #68)
-#61 := (iff #49 #58)
-#64 := (not #61)
-#69 := (iff #64 #68)
-#70 := [rewrite]: #69
-#65 := (iff #19 #64)
-#62 := (iff #18 #61)
-#59 := (iff #17 #58)
-#56 := (iff #16 #55)
+#56 := [monotonicity #44 #53]: #55
+#62 := [trans #56 #60]: #61
+#65 := [monotonicity #62]: #64
+#84 := [trans #65 #82]: #83
+#40 := [asserted]: #19
+#85 := [mp #40 #84]: #80
+#91 := [not-or-elim #85]: #90
+#102 := [iff-false #91]: #101
+#97 := (iff #10 false)
+#87 := (not #10)
+#88 := [not-or-elim #85]: #87
+#98 := [iff-false #88]: #97
+#108 := (iff #41 false)
+#1 := true
+#103 := (not true)
+#106 := (iff #103 false)
+#107 := [rewrite]: #106
+#104 := (iff #41 #103)
+#99 := (iff #8 true)
+#89 := [not-or-elim #85]: #8
+#100 := [iff-true #89]: #99
+#105 := [monotonicity #100]: #104
+#109 := [trans #105 #107]: #108
+#112 := [monotonicity #109 #98 #102]: #111
+#116 := [trans #112 #114]: #115
+#86 := [not-or-elim #85]: #66
+[mp #86 #116]: false
+unsat
+7a1f8b0dc0880c922314ec30bd73e7304dc52ec4 65 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#42 := (not #10)
+#81 := [hypothesis]: #42
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#38 := (not #8)
+#39 := (or #38 #10)
+#43 := (or #42 #8)
+#46 := (and #39 #43)
+#14 := (iff #8 #10)
+#52 := (not #46)
+#53 := (or #52 #14)
+#58 := (not #53)
+#12 := (implies #10 #8)
+#11 := (implies #8 #10)
+#13 := (and #11 #12)
+#15 := (implies #13 #14)
+#16 := (not #15)
+#59 := (iff #16 #58)
+#56 := (iff #15 #53)
+#49 := (implies #46 #14)
+#54 := (iff #49 #53)
+#55 := [rewrite]: #54
+#50 := (iff #15 #49)
+#47 := (iff #13 #46)
 #44 := (iff #12 #43)
 #45 := [rewrite]: #44
-#57 := [quant-intro #45]: #56
-#53 := (iff #15 #52)
-#41 := (iff #10 #40)
-#42 := [rewrite]: #41
-#54 := [quant-intro #42]: #53
-#60 := [monotonicity #54 #57]: #59
-#50 := (iff #14 #49)
-#47 := (iff #13 #46)
-#48 := [monotonicity #42 #45]: #47
-#51 := [quant-intro #48]: #50
-#63 := [monotonicity #51 #60]: #62
-#66 := [monotonicity #63]: #65
-#72 := [trans #66 #70]: #71
-#39 := [asserted]: #19
-#75 := [mp #39 #72]: #68
-#136 := [mp~ #75 #135]: #133
-#137 := [mp #136 #147]: #145
-#138 := [and-elim #137]: #139
-#157 := [mp #138 #156]: #152
-#665 := [mp #157 #664]: #662
-#622 := [unit-resolution #665 #632]: #657
-#288 := (not #76)
-#414 := (or #282 #288)
-#621 := [quant-inst #79]: #414
-#280 := [unit-resolution #621 #622 #625]: false
-#285 := [lemma #280]: #295
-#609 := (f3 ?v0!2)
-#615 := (= f1 #609)
-#618 := (or #123 #615)
-#619 := (not #618)
-#316 := (or #619 #282)
-#314 := [hypothesis]: #618
-#606 := (or #282 #619)
-#251 := (or #615 #123)
-#616 := (not #251)
-#607 := (or #282 #616)
-#329 := (iff #607 #606)
-#331 := (iff #606 #606)
-#317 := [rewrite]: #331
-#617 := (iff #616 #619)
-#256 := (iff #251 #618)
-#257 := [rewrite]: #256
-#620 := [monotonicity #257]: #617
-#330 := [monotonicity #620]: #329
-#332 := [trans #330 #317]: #329
-#313 := [quant-inst #121]: #607
-#223 := [mp #313 #332]: #606
-#315 := [unit-resolution #223 #623 #314]: false
-#318 := [lemma #315]: #316
-#588 := [unit-resolution #318 #623]: #619
-#603 := (or #618 #602)
-#325 := [def-axiom]: #603
-#589 := [unit-resolution #325 #588]: #602
-#148 := [and-elim #137]: #142
-#590 := [unit-resolution #148 #589 #285 #597]: #81
-#310 := (not #81)
-#594 := (or #76 #310)
-#598 := [def-axiom]: #594
-#585 := [unit-resolution #598 #590]: #76
-#586 := [unit-resolution #621 #623 #585]: false
-#591 := [lemma #586]: #282
-#599 := [unit-resolution #665 #591]: #654
-#216 := (or #651 #643)
-#303 := [def-axiom]: #216
-#593 := [unit-resolution #303 #599]: #643
-#592 := (or #648 #602)
-#587 := [quant-inst #121]: #592
-#434 := [unit-resolution #587 #593 #595]: false
-#435 := [lemma #434]: #602
-#436 := [hypothesis]: #81
-#579 := (or #648 #310)
-#580 := [quant-inst #79]: #579
-#578 := [unit-resolution #580 #593 #436]: false
-#581 := [lemma #578]: #310
-#575 := (or #81 #116 #123)
-#576 := [unit-resolution #148 #285]: #575
-#577 := [unit-resolution #576 #581 #435]: #116
-#584 := [unit-resolution #302 #599]: #634
-#582 := (or #639 #265)
-#583 := [quant-inst #114]: #582
-[unit-resolution #583 #584 #577]: false
-unsat
-49837552f1674d9522be923aa91cdae0b305a0be 222 0
-#2 := false
-decl f3 :: (-> S2 S1)
-decl ?v0!1 :: S2
-#108 := ?v0!1
-#109 := (f3 ?v0!1)
-decl f1 :: S1
-#4 := f1
-#110 := (= f1 #109)
-#154 := (not #110)
-decl f4 :: S1
-#12 := f4
-#45 := (= f1 f4)
-#95 := (not #45)
-#155 := (or #95 #154)
-#156 := (not #155)
-decl ?v0!0 :: S2
-#75 := ?v0!0
-#76 := (f3 ?v0!0)
-#77 := (= f1 #76)
-#159 := (not #77)
-#160 := (or #95 #159)
-#161 := (not #160)
-#618 := [hypothesis]: #161
-#317 := (or #160 #77)
-#245 := [def-axiom]: #317
-#279 := [unit-resolution #245 #618]: #77
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#643 := (pattern #9)
-#39 := (= f1 #9)
-#88 := (not #39)
-#114 := (or #88 #95)
-#649 := (forall (vars (?v0 S2)) (:pat #643) #114)
-#305 := (or #160 #45)
-#316 := [def-axiom]: #305
-#280 := [unit-resolution #316 #618]: #45
-#644 := (forall (vars (?v0 S2)) (:pat #643) #88)
-#635 := (not #644)
-#637 := (or #635 #159)
-#319 := [hypothesis]: #77
-#298 := [hypothesis]: #644
-#292 := [quant-inst #75]: #637
-#424 := [unit-resolution #292 #298 #319]: false
-#631 := [lemma #424]: #637
-#281 := [unit-resolution #631 #279]: #635
-#654 := (or #95 #644 #649)
-#147 := (forall (vars (?v0 S2)) #114)
-#91 := (forall (vars (?v0 S2)) #88)
-#150 := (or #95 #91 #147)
-#655 := (iff #150 #654)
-#652 := (iff #147 #649)
-#650 := (iff #114 #114)
-#651 := [refl]: #650
-#653 := [quant-intro #651]: #652
-#647 := (iff #91 #644)
-#645 := (iff #88 #88)
-#646 := [refl]: #645
-#648 := [quant-intro #646]: #647
-#656 := [monotonicity #648 #653]: #655
-#51 := (and #39 #45)
-#101 := (not #51)
-#104 := (forall (vars (?v0 S2)) #101)
-#124 := (or #95 #91 #104)
-#151 := (iff #124 #150)
-#148 := (iff #104 #147)
-#145 := (iff #101 #114)
-#115 := (not #114)
-#140 := (not #115)
-#143 := (iff #140 #114)
-#144 := [rewrite]: #143
-#141 := (iff #101 #140)
-#72 := (iff #51 #115)
-#79 := [rewrite]: #72
-#142 := [monotonicity #79]: #141
-#146 := [trans #142 #144]: #145
-#149 := [quant-intro #146]: #148
-#152 := [monotonicity #149]: #151
-#130 := (and #45 #77)
-#127 := (and #45 #110)
-#133 := (or #127 #130)
-#136 := (and #124 #133)
-#82 := (and #77 #45)
-#111 := (and #110 #45)
-#116 := (or #111 #82)
-#98 := (or #91 #95)
-#117 := (or #104 #98)
-#118 := (and #117 #116)
-#137 := (iff #118 #136)
-#134 := (iff #116 #133)
-#131 := (iff #82 #130)
-#132 := [rewrite]: #131
-#128 := (iff #111 #127)
-#129 := [rewrite]: #128
-#135 := [monotonicity #129 #132]: #134
-#125 := (iff #117 #124)
-#126 := [rewrite]: #125
-#138 := [monotonicity #126 #135]: #137
-#42 := (exists (vars (?v0 S2)) #39)
-#48 := (and #42 #45)
-#63 := (not #48)
-#54 := (exists (vars (?v0 S2)) #51)
-#64 := (iff #54 #63)
-#119 := (~ #64 #118)
-#99 := (~ #63 #98)
-#96 := (~ #95 #95)
-#97 := [refl]: #96
-#92 := (not #42)
-#93 := (~ #92 #91)
-#89 := (~ #88 #88)
-#90 := [refl]: #89
-#94 := [nnf-neg #90]: #93
-#100 := [nnf-neg #94 #97]: #99
-#85 := (not #63)
-#86 := (~ #85 #82)
-#83 := (~ #48 #82)
-#80 := (~ #45 #45)
-#81 := [refl]: #80
-#78 := (~ #42 #77)
-#70 := [sk]: #78
-#84 := [monotonicity #70 #81]: #83
-#87 := [nnf-neg #84]: #86
-#112 := (~ #54 #111)
-#113 := [sk]: #112
-#105 := (not #54)
-#106 := (~ #105 #104)
-#102 := (~ #101 #101)
-#103 := [refl]: #102
-#107 := [nnf-neg #103]: #106
-#120 := [nnf-pos #107 #113 #87 #100]: #119
-#13 := (= f4 f1)
-#10 := (= #9 f1)
-#15 := (and #10 #13)
-#16 := (exists (vars (?v0 S2)) #15)
-#11 := (exists (vars (?v0 S2)) #10)
-#14 := (and #11 #13)
-#17 := (iff #14 #16)
-#18 := (not #17)
-#67 := (iff #18 #64)
-#57 := (iff #48 #54)
-#60 := (not #57)
-#65 := (iff #60 #64)
-#66 := [rewrite]: #65
-#61 := (iff #18 #60)
-#58 := (iff #17 #57)
-#55 := (iff #16 #54)
-#52 := (iff #15 #51)
-#46 := (iff #13 #45)
-#47 := [rewrite]: #46
-#40 := (iff #10 #39)
-#41 := [rewrite]: #40
-#53 := [monotonicity #41 #47]: #52
-#56 := [quant-intro #53]: #55
-#49 := (iff #14 #48)
-#43 := (iff #11 #42)
-#44 := [quant-intro #41]: #43
-#50 := [monotonicity #44 #47]: #49
-#59 := [monotonicity #50 #56]: #58
-#62 := [monotonicity #59]: #61
-#68 := [trans #62 #66]: #67
-#38 := [asserted]: #18
-#71 := [mp #38 #68]: #64
-#121 := [mp~ #71 #120]: #118
-#122 := [mp #121 #138]: #136
-#123 := [and-elim #122]: #124
-#153 := [mp #123 #152]: #150
-#657 := [mp #153 #656]: #654
-#282 := [unit-resolution #657 #281 #280]: #649
-#639 := (not #649)
-#640 := (or #639 #95 #159)
-#303 := (or #159 #95)
-#641 := (or #639 #303)
-#291 := (iff #641 #640)
-#642 := (or #639 #160)
-#295 := (iff #642 #640)
-#633 := [rewrite]: #295
-#632 := (iff #641 #642)
-#304 := (iff #303 #160)
-#638 := [rewrite]: #304
-#290 := [monotonicity #638]: #632
-#634 := [trans #290 #633]: #291
-#636 := [quant-inst #75]: #641
-#275 := [mp #636 #634]: #640
-#620 := [unit-resolution #275 #280 #282 #279]: false
-#621 := [lemma #620]: #160
-#164 := (or #156 #161)
-#165 := (iff #133 #164)
-#162 := (iff #130 #161)
-#163 := [rewrite]: #162
-#157 := (iff #127 #156)
-#158 := [rewrite]: #157
-#166 := [monotonicity #158 #163]: #165
-#139 := [and-elim #122]: #133
-#167 := [mp #139 #166]: #164
-#617 := [unit-resolution #167 #621]: #156
-#226 := (or #155 #110)
-#313 := [def-axiom]: #226
-#323 := [unit-resolution #313 #617]: #110
-#225 := (or #155 #45)
-#312 := [def-axiom]: #225
-#340 := [unit-resolution #312 #617]: #45
-#339 := [hypothesis]: #649
-#619 := (or #639 #95 #154)
-#622 := (or #154 #95)
-#625 := (or #639 #622)
-#627 := (iff #625 #619)
-#626 := (or #639 #155)
-#267 := (iff #626 #619)
-#629 := [rewrite]: #267
-#628 := (iff #625 #626)
-#623 := (iff #622 #155)
-#624 := [rewrite]: #623
-#266 := [monotonicity #624]: #628
-#630 := [trans #266 #629]: #627
-#261 := [quant-inst #108]: #625
-#616 := [mp #261 #630]: #619
-#341 := [unit-resolution #616 #340 #339 #323]: false
-#327 := [lemma #341]: #639
-#342 := [unit-resolution #657 #327 #340]: #644
-#612 := (or #635 #154)
-#613 := [quant-inst #108]: #612
-[unit-resolution #613 #342 #323]: false
-unsat
-ae4569403e4041d6e7e74864d4d8162485073321 49 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: (-> S2 S4 S1)
-#9 := (:var 0 S4)
-#13 := (:var 1 S2)
-#14 := (f3 #13 #9)
-#15 := (= #14 f1)
-#16 := (exists (vars (?v0 S2) (?v1 S4)) #15)
-#8 := (:var 2 S2)
-#10 := (f3 #8 #9)
-#11 := (= #10 f1)
-#12 := (exists (vars (?v0 S2) (?v1 S3) (?v2 S4)) #11)
-#17 := (iff #12 #16)
-#18 := (not #17)
-#67 := (iff #18 false)
-#1 := true
-#62 := (not true)
-#65 := (iff #62 false)
-#66 := [rewrite]: #65
-#63 := (iff #18 #62)
-#60 := (iff #17 true)
-#45 := (= f1 #14)
-#46 := (exists (vars (?v0 S2) (?v2 S4)) #45)
-#55 := (iff #46 #46)
-#58 := (iff #55 true)
-#59 := [rewrite]: #58
-#56 := (iff #17 #55)
-#53 := (iff #16 #46)
-#51 := (iff #15 #45)
-#52 := [rewrite]: #51
-#54 := [quant-intro #52]: #53
-#49 := (iff #12 #46)
-#39 := (= f1 #10)
-#42 := (exists (vars (?v0 S2) (?v1 S3) (?v2 S4)) #39)
-#47 := (iff #42 #46)
-#48 := [elim-unused]: #47
-#43 := (iff #12 #42)
 #40 := (iff #11 #39)
 #41 := [rewrite]: #40
-#44 := [quant-intro #41]: #43
-#50 := [trans #44 #48]: #49
-#57 := [monotonicity #50 #54]: #56
-#61 := [trans #57 #59]: #60
-#64 := [monotonicity #61]: #63
-#68 := [trans #64 #66]: #67
-#38 := [asserted]: #18
-[mp #38 #68]: false
-unsat
-d1b3651883bd583f235d214bf142f4826c696167 122 0
-#2 := false
-decl f3 :: (-> S2 S1)
-decl ?v0!1 :: S2
-#125 := ?v0!1
-#128 := (f3 ?v0!1)
-decl f1 :: S1
-#4 := f1
-#129 := (= f1 #128)
-decl f4 :: (-> S2 S1)
-#126 := (f4 ?v0!1)
-#127 := (= f1 #126)
-#138 := (and #127 #129)
-#130 := (and #129 #127)
-#139 := (iff #130 #138)
-#140 := [rewrite]: #139
-#8 := (:var 0 S2)
-#14 := (f4 #8)
-#56 := (= f1 #14)
-#9 := (f3 #8)
-#44 := (= f1 #9)
-#59 := (and #44 #56)
-#62 := (exists (vars (?v0 S2)) #59)
-#131 := (~ #62 #130)
-#132 := [sk]: #131
-#53 := (exists (vars (?v0 S2)) #44)
-#65 := (or #53 #62)
-#113 := (iff #65 #62)
-#108 := (or false #62)
-#111 := (iff #108 #62)
-#112 := [rewrite]: #111
-#109 := (iff #65 #108)
-#106 := (iff #53 false)
-#68 := (not #53)
-#47 := (not #44)
-#50 := (exists (vars (?v0 S2)) #47)
-#92 := (and #50 #68 #65)
-#10 := (= #9 f1)
-#13 := (exists (vars (?v0 S2)) #10)
-#19 := (not #13)
-#15 := (= #14 f1)
-#16 := (and #10 #15)
-#17 := (exists (vars (?v0 S2)) #16)
-#18 := (or #13 #17)
-#20 := (and #18 #19)
-#11 := (not #10)
-#12 := (exists (vars (?v0 S2)) #11)
-#21 := (and #12 #20)
-#22 := (not #21)
-#23 := (not #22)
-#95 := (iff #23 #92)
-#74 := (and #68 #65)
-#79 := (and #50 #74)
-#93 := (iff #79 #92)
-#94 := [rewrite]: #93
-#90 := (iff #23 #79)
-#82 := (not #79)
-#85 := (not #82)
-#88 := (iff #85 #79)
-#89 := [rewrite]: #88
-#86 := (iff #23 #85)
-#83 := (iff #22 #82)
-#80 := (iff #21 #79)
-#77 := (iff #20 #74)
-#71 := (and #65 #68)
-#75 := (iff #71 #74)
-#76 := [rewrite]: #75
-#72 := (iff #20 #71)
-#69 := (iff #19 #68)
-#54 := (iff #13 #53)
-#45 := (iff #10 #44)
-#46 := [rewrite]: #45
-#55 := [quant-intro #46]: #54
-#70 := [monotonicity #55]: #69
-#66 := (iff #18 #65)
-#63 := (iff #17 #62)
-#60 := (iff #16 #59)
-#57 := (iff #15 #56)
-#58 := [rewrite]: #57
-#61 := [monotonicity #46 #58]: #60
-#64 := [quant-intro #61]: #63
-#67 := [monotonicity #55 #64]: #66
-#73 := [monotonicity #67 #70]: #72
-#78 := [trans #73 #76]: #77
-#51 := (iff #12 #50)
-#48 := (iff #11 #47)
-#49 := [monotonicity #46]: #48
-#52 := [quant-intro #49]: #51
-#81 := [monotonicity #52 #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [monotonicity #84]: #86
-#91 := [trans #87 #89]: #90
-#96 := [trans #91 #94]: #95
-#43 := [asserted]: #23
-#97 := [mp #43 #96]: #92
-#99 := [and-elim #97]: #68
-#107 := [iff-false #99]: #106
-#110 := [monotonicity #107]: #109
-#114 := [trans #110 #112]: #113
-#100 := [and-elim #97]: #65
-#115 := [mp #100 #114]: #62
-#135 := [mp~ #115 #132]: #130
-#136 := [mp #135 #140]: #138
-#141 := [and-elim #136]: #129
-#615 := (pattern #9)
-#616 := (forall (vars (?v0 S2)) (:pat #615) #47)
-#121 := (forall (vars (?v0 S2)) #47)
-#619 := (iff #121 #616)
-#617 := (iff #47 #47)
-#618 := [refl]: #617
-#620 := [quant-intro #618]: #619
-#122 := (~ #68 #121)
-#118 := (~ #47 #47)
-#119 := [refl]: #118
-#123 := [nnf-neg #119]: #122
-#124 := [mp~ #99 #123]: #121
-#621 := [mp #124 #620]: #616
-#197 := (not #129)
-#285 := (not #616)
-#199 := (or #285 #197)
-#286 := [quant-inst #125]: #199
-[unit-resolution #286 #621 #141]: false
-unsat
-5dbb54e3f79f77198d3a0109880c6612eee2c993 1 2
-unsat
-WARNING: failed to find a pattern for quantifier (quantifier id: k!10)
-
-317998ded3ba09b3ca0b4841fddbf22609971173 1 0
-unsat
-5d41ec3d43526a42a83f6a2101e1fdacb01a1e18 1 0
-unsat
-4353868152099814cbf92f87fbe5cfd7c0e847d9 1 0
-unsat
-d1960c3de8c282f29b8966d1941c342d346c0824 1 0
-unsat
-0bb08ec8e7f02569dc9b5667cb6facd8b7ac2d68 1 0
-unsat
-1ac5f2b326a5a2213b4bbc21839ed6c4581cf4ef 107 0
-#2 := false
-decl f3 :: (-> S2 S1 S1)
-decl ?v0!1 :: S1
-#84 := ?v0!1
-decl f4 :: S2
-#8 := f4
-#85 := (f3 f4 ?v0!1)
-decl f1 :: S1
-#4 := f1
-#86 := (= f1 #85)
-decl ?v0!0 :: S1
-#70 := ?v0!0
-#71 := (f3 f4 ?v0!0)
-#72 := (= f1 #71)
-#73 := (not #72)
-#168 := [hypothesis]: #72
-#9 := (:var 0 S1)
-#10 := (f3 f4 #9)
-#586 := (pattern #10)
-#38 := (= f1 #10)
-#47 := (not #38)
-#587 := (forall (vars (?v0 S1)) (:pat #586) #47)
-#50 := (forall (vars (?v0 S1)) #47)
-#590 := (iff #50 #587)
-#588 := (iff #47 #47)
-#589 := [refl]: #588
-#591 := [quant-intro #589]: #590
-#106 := (or #72 #86)
-#111 := (and #50 #106)
-#65 := (not #73)
-#91 := (or #86 #65)
-#92 := (or #50 #50)
-#93 := (and #92 #91)
-#112 := (iff #93 #111)
-#109 := (iff #91 #106)
-#103 := (or #86 #72)
-#107 := (iff #103 #106)
-#108 := [rewrite]: #107
-#104 := (iff #91 #103)
-#101 := (iff #65 #72)
-#102 := [rewrite]: #101
-#105 := [monotonicity #102]: #104
-#110 := [trans #105 #108]: #109
-#99 := (iff #92 #50)
-#100 := [rewrite]: #99
-#113 := [monotonicity #100 #110]: #112
-#41 := (exists (vars (?v0 S1)) #38)
-#59 := (iff #41 #50)
-#94 := (~ #59 #93)
-#80 := (~ #50 #50)
-#78 := (~ #47 #47)
-#79 := [refl]: #78
-#81 := [nnf-pos #79]: #80
-#67 := (not #50)
-#74 := (~ #67 #65)
-#75 := [sk]: #74
-#87 := (~ #41 #86)
-#88 := [sk]: #87
-#44 := (not #41)
-#82 := (~ #44 #50)
-#83 := [nnf-neg #79]: #82
-#95 := [nnf-pos #83 #88 #75 #81]: #94
-#11 := (= #10 f1)
-#14 := (not #11)
-#15 := (forall (vars (?v0 S1)) #14)
-#12 := (exists (vars (?v0 S1)) #11)
-#13 := (not #12)
-#16 := (iff #13 #15)
-#17 := (not #16)
-#62 := (iff #17 #59)
-#53 := (iff #44 #50)
-#56 := (not #53)
-#60 := (iff #56 #59)
-#61 := [rewrite]: #60
-#57 := (iff #17 #56)
-#54 := (iff #16 #53)
-#51 := (iff #15 #50)
-#48 := (iff #14 #47)
-#39 := (iff #11 #38)
-#40 := [rewrite]: #39
-#49 := [monotonicity #40]: #48
-#52 := [quant-intro #49]: #51
-#45 := (iff #13 #44)
-#42 := (iff #12 #41)
-#43 := [quant-intro #40]: #42
-#46 := [monotonicity #43]: #45
-#55 := [monotonicity #46 #52]: #54
-#58 := [monotonicity #55]: #57
-#63 := [trans #58 #61]: #62
-#37 := [asserted]: #17
-#66 := [mp #37 #63]: #59
-#96 := [mp~ #66 #95]: #93
-#97 := [mp #96 #113]: #111
-#98 := [and-elim #97]: #50
-#592 := [mp #98 #591]: #587
-#169 := (not #587)
-#256 := (or #169 #73)
-#170 := [quant-inst #70]: #256
-#255 := [unit-resolution #170 #592 #168]: false
-#257 := [lemma #255]: #73
-#114 := [and-elim #97]: #106
-#259 := [unit-resolution #114 #257]: #86
-#248 := (not #86)
-#188 := (or #169 #248)
-#261 := [quant-inst #84]: #188
-[unit-resolution #261 #592 #259]: false
-unsat
-1af05fd396617468d45aac672c15e8ac2f621100 228 0
-#2 := false
-decl f3 :: (-> S2 S1 S1)
-decl ?v0!0 :: S1
-#88 := ?v0!0
-decl f4 :: S2
-#8 := f4
-#89 := (f3 f4 ?v0!0)
-decl f1 :: S1
-#4 := f1
-#90 := (= f1 #89)
-#91 := (not #90)
-decl ?v0!1 :: S1
-#120 := ?v0!1
-#121 := (f3 f4 ?v0!1)
-#122 := (= f1 #121)
-#123 := (not #122)
-#255 := [hypothesis]: #123
-#9 := (:var 0 S1)
-#10 := (f3 f4 #9)
-#631 := (pattern #10)
-#40 := (= f1 #10)
-#632 := (forall (vars (?v0 S1)) (:pat #631) #40)
-#637 := (not #632)
-decl f5 :: S1
-#12 := f5
-#43 := (= f1 f5)
-#640 := (or #43 #637)
-#643 := (not #640)
-#49 := (not #40)
-#50 := (or #49 #43)
-#98 := (not #50)
-#646 := (forall (vars (?v0 S1)) (:pat #631) #98)
-#286 := (not #646)
-#267 := (or #43 #91)
-#128 := (or #43 #123)
-#306 := (not #128)
-#621 := [hypothesis]: #646
-#622 := (or #306 #286)
-#283 := [hypothesis]: #128
-#623 := (or #286 #306)
-#293 := (or #123 #43)
-#304 := (not #293)
-#625 := (or #286 #304)
-#412 := (iff #625 #623)
-#291 := (iff #623 #623)
-#292 := [rewrite]: #291
-#303 := (iff #304 #306)
-#305 := (iff #293 #128)
-#233 := [rewrite]: #305
-#307 := [monotonicity #233]: #303
-#619 := [monotonicity #307]: #412
-#626 := [trans #619 #292]: #412
-#280 := [quant-inst #120]: #625
-#627 := [mp #280 #626]: #623
-#279 := [unit-resolution #627 #621 #283]: false
-#263 := [lemma #279]: #622
-#311 := [unit-resolution #263 #621]: #306
-#624 := (or #128 #122)
-#630 := [def-axiom]: #624
-#327 := [unit-resolution #630 #311]: #122
-#104 := (not #43)
-#628 := (or #128 #104)
-#629 := [def-axiom]: #628
-#328 := [unit-resolution #629 #311]: #104
-#142 := (or #43 #91 #123)
-#58 := (forall (vars (?v0 S1)) #40)
-#114 := (and #104 #58)
-#101 := (forall (vars (?v0 S1)) #98)
-#139 := (or #101 #114)
-#145 := (and #139 #142)
-#83 := (or #91 #43)
-#131 := (or #128 #83)
-#132 := (or #114 #101)
-#133 := (and #132 #131)
-#146 := (iff #133 #145)
-#143 := (iff #131 #142)
-#144 := [rewrite]: #143
-#140 := (iff #132 #139)
-#141 := [rewrite]: #140
-#147 := [monotonicity #141 #144]: #146
-#55 := (exists (vars (?v0 S1)) #50)
-#76 := (not #55)
-#64 := (not #58)
-#65 := (or #43 #64)
-#77 := (iff #65 #76)
-#134 := (~ #77 #133)
-#102 := (~ #76 #101)
-#99 := (~ #98 #98)
-#100 := [refl]: #99
-#103 := [nnf-neg #100]: #102
-#95 := (not #76)
-#96 := (~ #95 #83)
-#85 := (~ #55 #83)
-#92 := [sk]: #85
-#97 := [nnf-neg #92]: #96
-#129 := (~ #65 #128)
-#124 := (~ #64 #123)
-#125 := [sk]: #124
-#118 := (~ #43 #43)
-#119 := [refl]: #118
-#130 := [monotonicity #119 #125]: #129
-#115 := (not #65)
-#116 := (~ #115 #114)
-#111 := (not #64)
-#112 := (~ #111 #58)
-#109 := (~ #58 #58)
-#107 := (~ #40 #40)
-#108 := [refl]: #107
-#110 := [nnf-pos #108]: #109
-#113 := [nnf-neg #110]: #112
-#105 := (~ #104 #104)
-#106 := [refl]: #105
-#117 := [nnf-neg #106 #113]: #116
-#135 := [nnf-pos #117 #130 #97 #103]: #134
-#13 := (= f5 f1)
-#11 := (= #10 f1)
-#16 := (forall (vars (?v0 S1)) #11)
-#17 := (implies #16 #13)
-#14 := (implies #11 #13)
-#15 := (exists (vars (?v0 S1)) #14)
-#18 := (iff #15 #17)
-#19 := (not #18)
-#80 := (iff #19 #77)
-#70 := (iff #55 #65)
-#73 := (not #70)
-#78 := (iff #73 #77)
-#79 := [rewrite]: #78
-#74 := (iff #19 #73)
-#71 := (iff #18 #70)
-#68 := (iff #17 #65)
-#61 := (implies #58 #43)
-#66 := (iff #61 #65)
-#67 := [rewrite]: #66
-#62 := (iff #17 #61)
-#44 := (iff #13 #43)
-#45 := [rewrite]: #44
-#59 := (iff #16 #58)
-#41 := (iff #11 #40)
-#42 := [rewrite]: #41
-#60 := [quant-intro #42]: #59
-#63 := [monotonicity #60 #45]: #62
-#69 := [trans #63 #67]: #68
-#56 := (iff #15 #55)
-#53 := (iff #14 #50)
-#46 := (implies #40 #43)
-#51 := (iff #46 #50)
-#52 := [rewrite]: #51
-#47 := (iff #14 #46)
-#48 := [monotonicity #42 #45]: #47
-#54 := [trans #48 #52]: #53
-#57 := [quant-intro #54]: #56
-#72 := [monotonicity #57 #69]: #71
-#75 := [monotonicity #72]: #74
-#81 := [trans #75 #79]: #80
-#39 := [asserted]: #19
-#84 := [mp #39 #81]: #77
-#136 := [mp~ #84 #135]: #133
-#137 := [mp #136 #147]: #145
-#148 := [and-elim #137]: #142
-#329 := [unit-resolution #148 #328 #327]: #91
-#615 := (or #267 #90)
-#618 := [def-axiom]: #615
-#315 := [unit-resolution #618 #329]: #267
-#270 := (not #267)
-#610 := (or #286 #270)
-#606 := (not #83)
-#611 := (or #286 #606)
-#607 := (iff #611 #610)
-#249 := (iff #610 #610)
-#614 := [rewrite]: #249
-#608 := (iff #606 #270)
-#268 := (iff #83 #267)
-#269 := [rewrite]: #268
-#609 := [monotonicity #269]: #608
-#613 := [monotonicity #609]: #607
-#616 := [trans #613 #614]: #607
-#612 := [quant-inst #88]: #611
-#254 := [mp #612 #616]: #610
-#330 := [unit-resolution #254 #621 #315]: false
-#221 := [lemma #330]: #286
-#651 := (or #643 #646)
-#150 := (or #115 #101)
-#652 := (iff #150 #651)
-#649 := (iff #101 #646)
-#647 := (iff #98 #98)
-#648 := [refl]: #647
-#650 := [quant-intro #648]: #649
-#644 := (iff #115 #643)
-#641 := (iff #65 #640)
-#638 := (iff #64 #637)
-#635 := (iff #58 #632)
-#633 := (iff #40 #40)
-#634 := [refl]: #633
-#636 := [quant-intro #634]: #635
-#639 := [monotonicity #636]: #638
-#642 := [monotonicity #639]: #641
-#645 := [monotonicity #642]: #644
-#653 := [monotonicity #645 #650]: #652
-#153 := (iff #139 #150)
-#93 := (or #101 #115)
-#151 := (iff #93 #150)
-#152 := [rewrite]: #151
-#94 := (iff #139 #93)
-#126 := (iff #114 #115)
-#127 := [rewrite]: #126
-#149 := [monotonicity #127]: #94
-#154 := [trans #149 #152]: #153
-#138 := [and-elim #137]: #139
-#155 := [mp #138 #154]: #150
-#654 := [mp #155 #653]: #651
-#617 := [unit-resolution #654 #221]: #643
-#214 := (or #640 #632)
-#301 := [def-axiom]: #214
-#600 := [unit-resolution #301 #617]: #632
-#604 := (or #637 #122)
-#605 := [quant-inst #120]: #604
-#601 := [unit-resolution #605 #600 #255]: false
-#323 := [lemma #601]: #122
-#598 := (or #91 #123)
-#213 := (or #640 #104)
-#300 := [def-axiom]: #213
-#324 := [unit-resolution #300 #617]: #104
-#603 := [unit-resolution #148 #324]: #598
-#312 := [unit-resolution #603 #323]: #91
-#602 := (or #637 #90)
-#599 := [quant-inst #88]: #602
-[unit-resolution #599 #600 #312]: false
-unsat
-46ded07bd280adcfd682a42ca03ae99c0bb1cbfc 161 0
-#2 := false
-decl f3 :: (-> S3 S2 S1)
-#11 := (:var 0 S2)
-decl f4 :: (-> S4 S1 S3)
-decl f6 :: S1
-#17 := f6
-decl f5 :: S4
-#8 := f5
-#18 := (f4 f5 f6)
-#19 := (f3 #18 #11)
-#612 := (pattern #19)
-decl f1 :: S1
-#4 := f1
-#60 := (= f1 #19)
-#109 := (not #60)
-#613 := (forall (vars (?v0 S2)) (:pat #612) #109)
-decl f7 :: S2
-#22 := f7
-#23 := (f3 #18 f7)
-#66 := (= f1 #23)
-#187 := (= f1 f6)
-#188 := (iff #66 #187)
-#9 := (:var 1 S1)
-#10 := (f4 f5 #9)
-#12 := (f3 #10 #11)
-#605 := (pattern #12)
-#51 := (= f1 #9)
-#48 := (= f1 #12)
-#54 := (iff #48 #51)
-#606 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #605) #54)
-#57 := (forall (vars (?v0 S1) (?v1 S2)) #54)
-#609 := (iff #57 #606)
-#607 := (iff #54 #54)
-#608 := [refl]: #607
-#610 := [quant-intro #608]: #609
-#91 := (~ #57 #57)
-#98 := (~ #54 #54)
-#99 := [refl]: #98
-#92 := [nnf-pos #99]: #91
-#63 := (exists (vars (?v0 S2)) #60)
-#69 := (iff #63 #66)
-#75 := (not #57)
-#76 := (or #75 #69)
-#81 := (not #76)
-#24 := (= #23 f1)
-#20 := (= #19 f1)
-#21 := (exists (vars (?v0 S2)) #20)
-#25 := (iff #21 #24)
-#14 := (= #9 f1)
-#13 := (= #12 f1)
-#15 := (iff #13 #14)
-#16 := (forall (vars (?v0 S1) (?v1 S2)) #15)
-#26 := (implies #16 #25)
-#27 := (not #26)
-#82 := (iff #27 #81)
-#79 := (iff #26 #76)
-#72 := (implies #57 #69)
-#77 := (iff #72 #76)
-#78 := [rewrite]: #77
-#73 := (iff #26 #72)
-#70 := (iff #25 #69)
-#67 := (iff #24 #66)
-#68 := [rewrite]: #67
-#64 := (iff #21 #63)
-#61 := (iff #20 #60)
-#62 := [rewrite]: #61
-#65 := [quant-intro #62]: #64
-#71 := [monotonicity #65 #68]: #70
-#58 := (iff #16 #57)
-#55 := (iff #15 #54)
-#52 := (iff #14 #51)
-#53 := [rewrite]: #52
-#49 := (iff #13 #48)
-#50 := [rewrite]: #49
-#56 := [monotonicity #50 #53]: #55
-#59 := [quant-intro #56]: #58
-#74 := [monotonicity #59 #71]: #73
-#80 := [trans #74 #78]: #79
-#83 := [monotonicity #80]: #82
-#47 := [asserted]: #27
-#86 := [mp #47 #83]: #81
-#84 := [not-or-elim #86]: #57
-#89 := [mp~ #84 #92]: #57
-#611 := [mp #89 #610]: #606
-#189 := (not #606)
-#265 := (or #189 #188)
-#266 := [quant-inst #17 #22]: #265
-#275 := [unit-resolution #266 #611]: #188
-decl ?v0!0 :: S2
-#90 := ?v0!0
-#100 := (f3 #18 ?v0!0)
-#101 := (= f1 #100)
-#274 := (iff #101 #187)
-#276 := (or #189 #274)
-#267 := [quant-inst #17 #90]: #276
-#593 := [unit-resolution #267 #611]: #274
-#278 := (not #274)
-#596 := (or #278 #187)
-#115 := (not #66)
-#595 := [hypothesis]: #115
-#120 := (or #66 #101)
-#112 := (forall (vars (?v0 S2)) #109)
-#121 := (or #115 #112)
-#128 := (and #120 #121)
-#122 := (and #121 #120)
-#129 := (iff #122 #128)
-#130 := [rewrite]: #129
-#93 := (not #63)
-#94 := (iff #66 #93)
-#123 := (~ #94 #122)
-#113 := (~ #93 #112)
-#110 := (~ #109 #109)
-#111 := [refl]: #110
-#114 := [nnf-neg #111]: #113
-#106 := (not #93)
-#107 := (~ #106 #101)
-#102 := (~ #63 #101)
-#103 := [sk]: #102
-#108 := [nnf-neg #103]: #107
-#118 := (~ #66 #66)
-#119 := [refl]: #118
-#116 := (~ #115 #115)
-#117 := [refl]: #116
-#124 := [nnf-pos #117 #119 #108 #114]: #123
-#85 := (not #69)
-#95 := (iff #85 #94)
-#96 := [rewrite]: #95
-#87 := [not-or-elim #86]: #85
-#97 := [mp #87 #96]: #94
-#125 := [mp~ #97 #124]: #122
-#126 := [mp #125 #130]: #128
-#127 := [and-elim #126]: #120
-#253 := [unit-resolution #127 #595]: #101
-#277 := (not #101)
-#281 := (or #278 #277 #187)
-#260 := [def-axiom]: #281
-#237 := [unit-resolution #260 #253]: #596
-#580 := [unit-resolution #237 #593]: #187
-#279 := (not #187)
-#600 := (not #188)
-#241 := (or #600 #279)
-#601 := (or #600 #66 #279)
-#602 := [def-axiom]: #601
-#242 := [unit-resolution #602 #595]: #241
-#243 := [unit-resolution #242 #580 #275]: false
-#244 := [lemma #243]: #66
-#618 := (or #115 #613)
-#619 := (iff #121 #618)
-#616 := (iff #112 #613)
-#614 := (iff #109 #109)
-#615 := [refl]: #614
-#617 := [quant-intro #615]: #616
-#620 := [monotonicity #617]: #619
-#131 := [and-elim #126]: #121
-#621 := [mp #131 #620]: #618
-#207 := [unit-resolution #621 #244]: #613
-#604 := (not #613)
-#594 := (or #604 #115)
-#252 := [quant-inst #22]: #594
-[unit-resolution #252 #244 #207]: false
-unsat
-61574c1108ca575449f952349f2919221122b716 110 0
-#2 := false
-decl f3 :: (-> S2 S1 S1)
-#12 := (:var 0 S1)
-decl f4 :: S2
-#8 := f4
-#13 := (f3 f4 #12)
-#595 := (pattern #13)
-decl f1 :: S1
-#4 := f1
-#49 := (= f1 #13)
-#58 := (not #49)
-#596 := (forall (vars (?v0 S1)) (:pat #595) #58)
-#61 := (forall (vars (?v0 S1)) #58)
-#599 := (iff #61 #596)
-#597 := (iff #58 #58)
-#598 := [refl]: #597
-#600 := [quant-intro #598]: #599
-#52 := (exists (vars (?v0 S1)) #49)
-#55 := (not #52)
-#117 := (~ #55 #61)
-#119 := (~ #58 #58)
-#120 := [refl]: #119
-#118 := [nnf-neg #120]: #117
-decl f5 :: S1
-#9 := f5
-#10 := (f3 f4 f5)
-#46 := (= f1 #10)
-#64 := (ite #46 #55 #61)
-#114 := (iff #64 #55)
-#1 := true
-#109 := (ite true #55 #61)
-#112 := (iff #109 #55)
-#113 := [rewrite]: #112
-#110 := (iff #64 #109)
-#107 := (iff #46 true)
-decl f6 :: S1
-#20 := f6
-#21 := (f3 f4 f6)
-#67 := (= f1 #21)
-#82 := (not #64)
-#73 := (not #46)
-#91 := (or #73 #82 #67)
-#94 := (not #91)
-#22 := (= #21 f1)
-#11 := (= #10 f1)
-#23 := (implies #11 #22)
-#14 := (= #13 f1)
-#17 := (not #14)
-#18 := (forall (vars (?v0 S1)) #17)
-#15 := (exists (vars (?v0 S1)) #14)
-#16 := (not #15)
-#19 := (ite #11 #16 #18)
-#24 := (implies #19 #23)
-#25 := (not #24)
-#97 := (iff #25 #94)
-#74 := (or #73 #67)
-#83 := (or #82 #74)
-#88 := (not #83)
-#95 := (iff #88 #94)
-#92 := (iff #83 #91)
-#93 := [rewrite]: #92
-#96 := [monotonicity #93]: #95
-#89 := (iff #25 #88)
-#86 := (iff #24 #83)
-#79 := (implies #64 #74)
-#84 := (iff #79 #83)
-#85 := [rewrite]: #84
-#80 := (iff #24 #79)
-#77 := (iff #23 #74)
-#70 := (implies #46 #67)
-#75 := (iff #70 #74)
+#48 := [monotonicity #41 #45]: #47
+#51 := [monotonicity #48]: #50
+#57 := [trans #51 #55]: #56
+#60 := [monotonicity #57]: #59
+#37 := [asserted]: #16
+#63 := [mp #37 #60]: #58
+#61 := [not-or-elim #63]: #46
+#62 := [and-elim #61]: #39
+#82 := [unit-resolution #62 #81]: #38
+#69 := (or #8 #10)
+#74 := (iff #38 #10)
+#65 := (not #14)
+#75 := (iff #65 #74)
 #76 := [rewrite]: #75
-#71 := (iff #23 #70)
-#68 := (iff #22 #67)
-#69 := [rewrite]: #68
-#47 := (iff #11 #46)
-#48 := [rewrite]: #47
-#72 := [monotonicity #48 #69]: #71
-#78 := [trans #72 #76]: #77
-#65 := (iff #19 #64)
-#62 := (iff #18 #61)
-#59 := (iff #17 #58)
-#50 := (iff #14 #49)
-#51 := [rewrite]: #50
-#60 := [monotonicity #51]: #59
-#63 := [quant-intro #60]: #62
-#56 := (iff #16 #55)
-#53 := (iff #15 #52)
-#54 := [quant-intro #51]: #53
-#57 := [monotonicity #54]: #56
-#66 := [monotonicity #48 #57 #63]: #65
-#81 := [monotonicity #66 #78]: #80
-#87 := [trans #81 #85]: #86
-#90 := [monotonicity #87]: #89
-#98 := [trans #90 #96]: #97
-#45 := [asserted]: #25
-#99 := [mp #45 #98]: #94
-#100 := [not-or-elim #99]: #46
-#108 := [iff-true #100]: #107
-#111 := [monotonicity #108]: #110
-#115 := [trans #111 #113]: #114
-#101 := [not-or-elim #99]: #64
-#116 := [mp #101 #115]: #55
-#105 := [mp~ #116 #118]: #61
-#601 := [mp #105 #600]: #596
-#178 := (not #596)
-#265 := (or #178 #73)
-#179 := [quant-inst #9]: #265
-[unit-resolution #179 #100 #601]: false
-unsat
-378ceaf70d81cc1e628d67f3e8faa04e3659aa70 189 0
-#2 := false
-decl f3 :: (-> S3 S2 S1)
-#11 := (:var 0 S2)
-decl f4 :: (-> S4 S1 S3)
-decl f7 :: S1
-#27 := f7
-decl f5 :: S4
-#8 := f5
-#28 := (f4 f5 f7)
-#29 := (f3 #28 #11)
-#721 := (pattern #29)
-decl f1 :: S1
-#4 := f1
-#87 := (= f1 #29)
-#193 := (not #87)
-#722 := (forall (vars (?v0 S2)) (:pat #721) #193)
-decl f6 :: S2
-#21 := f6
-#32 := (f3 #28 f6)
-#93 := (= f1 #32)
-#271 := (= f1 f7)
-#272 := (iff #93 #271)
-#9 := (:var 1 S1)
-#10 := (f4 f5 #9)
-#12 := (f3 #10 #11)
-#689 := (pattern #12)
-#60 := (= f1 #9)
-#57 := (= f1 #12)
-#63 := (iff #57 #60)
-#690 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #689) #63)
-#66 := (forall (vars (?v0 S1) (?v1 S2)) #63)
-#693 := (iff #66 #690)
-#691 := (iff #63 #63)
-#692 := [refl]: #691
-#694 := [quant-intro #692]: #693
-#122 := (~ #66 #66)
-#129 := (~ #63 #63)
-#130 := [refl]: #129
-#123 := [nnf-pos #130]: #122
-#19 := (:var 0 S1)
-#20 := (f4 f5 #19)
-#22 := (f3 #20 f6)
-#75 := (= f1 #22)
-#78 := (forall (vars (?v0 S1)) #75)
-#69 := (exists (vars (?v1 S2)) #57)
-#72 := (forall (vars (?v0 S1)) #69)
-#81 := (iff #72 #78)
-#84 := (and #66 #81)
-#90 := (exists (vars (?v0 S2)) #87)
-#96 := (iff #90 #93)
-#102 := (not #84)
-#103 := (or #102 #96)
-#108 := (not #103)
-#33 := (= #32 f1)
-#30 := (= #29 f1)
-#31 := (exists (vars (?v0 S2)) #30)
-#34 := (iff #31 #33)
-#23 := (= #22 f1)
-#24 := (forall (vars (?v0 S1)) #23)
-#13 := (= #12 f1)
-#17 := (exists (vars (?v1 S2)) #13)
-#18 := (forall (vars (?v0 S1)) #17)
-#25 := (iff #18 #24)
-#14 := (= #9 f1)
-#15 := (iff #13 #14)
-#16 := (forall (vars (?v0 S1) (?v1 S2)) #15)
-#26 := (and #16 #25)
-#35 := (implies #26 #34)
-#36 := (not #35)
-#109 := (iff #36 #108)
-#106 := (iff #35 #103)
-#99 := (implies #84 #96)
-#104 := (iff #99 #103)
-#105 := [rewrite]: #104
-#100 := (iff #35 #99)
-#97 := (iff #34 #96)
-#94 := (iff #33 #93)
-#95 := [rewrite]: #94
-#91 := (iff #31 #90)
-#88 := (iff #30 #87)
-#89 := [rewrite]: #88
-#92 := [quant-intro #89]: #91
-#98 := [monotonicity #92 #95]: #97
-#85 := (iff #26 #84)
-#82 := (iff #25 #81)
-#79 := (iff #24 #78)
-#76 := (iff #23 #75)
-#77 := [rewrite]: #76
-#80 := [quant-intro #77]: #79
-#73 := (iff #18 #72)
-#70 := (iff #17 #69)
-#58 := (iff #13 #57)
-#59 := [rewrite]: #58
-#71 := [quant-intro #59]: #70
-#74 := [quant-intro #71]: #73
-#83 := [monotonicity #74 #80]: #82
-#67 := (iff #16 #66)
-#64 := (iff #15 #63)
-#61 := (iff #14 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #59 #62]: #64
-#68 := [quant-intro #65]: #67
-#86 := [monotonicity #68 #83]: #85
-#101 := [monotonicity #86 #98]: #100
-#107 := [trans #101 #105]: #106
-#110 := [monotonicity #107]: #109
-#56 := [asserted]: #36
-#113 := [mp #56 #110]: #108
-#111 := [not-or-elim #113]: #84
-#112 := [and-elim #111]: #66
-#120 := [mp~ #112 #123]: #66
-#695 := [mp #120 #694]: #690
-#273 := (not #690)
-#349 := (or #273 #272)
-#350 := [quant-inst #27 #21]: #349
-#359 := [unit-resolution #350 #695]: #272
-decl ?v0!3 :: S2
-#136 := ?v0!3
-#137 := (f3 #28 ?v0!3)
-#164 := (= f1 #137)
-#358 := (iff #164 #271)
-#360 := (or #273 #358)
-#351 := [quant-inst #27 #136]: #360
-#677 := [unit-resolution #351 #695]: #358
-#362 := (not #358)
-#680 := (or #362 #271)
-#199 := (not #93)
-#679 := [hypothesis]: #199
-#204 := (or #93 #164)
-#196 := (forall (vars (?v0 S2)) #193)
-#205 := (or #199 #196)
-#212 := (and #204 #205)
-#206 := (and #205 #204)
-#213 := (iff #206 #212)
-#214 := [rewrite]: #213
-#124 := (not #90)
-#125 := (iff #93 #124)
-#207 := (~ #125 #206)
-#197 := (~ #124 #196)
-#194 := (~ #193 #193)
-#195 := [refl]: #194
-#198 := [nnf-neg #195]: #197
-#190 := (not #124)
-#191 := (~ #190 #164)
-#165 := (~ #90 #164)
-#187 := [sk]: #165
-#192 := [nnf-neg #187]: #191
-#202 := (~ #93 #93)
-#203 := [refl]: #202
-#200 := (~ #199 #199)
-#201 := [refl]: #200
-#208 := [nnf-pos #201 #203 #192 #198]: #207
-#115 := (not #96)
-#126 := (iff #115 #125)
-#127 := [rewrite]: #126
-#116 := [not-or-elim #113]: #115
-#128 := [mp #116 #127]: #125
-#209 := [mp~ #128 #208]: #206
-#210 := [mp #209 #214]: #212
-#211 := [and-elim #210]: #204
-#337 := [unit-resolution #211 #679]: #164
-#361 := (not #164)
-#365 := (or #362 #361 #271)
-#344 := [def-axiom]: #365
-#321 := [unit-resolution #344 #337]: #680
-#664 := [unit-resolution #321 #677]: #271
-#363 := (not #271)
-#684 := (not #272)
-#325 := (or #684 #363)
-#685 := (or #684 #93 #363)
-#686 := [def-axiom]: #685
-#326 := [unit-resolution #686 #679]: #325
-#327 := [unit-resolution #326 #664 #359]: false
-#328 := [lemma #327]: #93
-#727 := (or #199 #722)
-#728 := (iff #205 #727)
-#725 := (iff #196 #722)
-#723 := (iff #193 #193)
-#724 := [refl]: #723
-#726 := [quant-intro #724]: #725
-#729 := [monotonicity #726]: #728
-#215 := [and-elim #210]: #205
-#730 := [mp #215 #729]: #727
-#291 := [unit-resolution #730 #328]: #722
-#688 := (not #722)
-#678 := (or #688 #199)
-#336 := [quant-inst #21]: #678
-[unit-resolution #336 #328 #291]: false
-unsat
-805c18c78cece7578f6235471e947733267a5411 1 0
-unsat
-626a766d3e6816fc4d39780448f9c6b7965da15c 1 0
-unsat
-50072264e2ef93269d01148a43be95c93e8e95a2 1 2
-unsat
-WARNING: failed to find a pattern for quantifier (quantifier id: k!16)
-
-7ff73f8c9727b866009974cd8b3025b90d61fd57 1 0
-unsat
-1d553b580169e91a5cf9cde1ec11372e8b99f6a5 1 0
-unsat
-f010ef4b805535e5ca8fec6afaee63fc30f4e69e 1 0
-unsat
-9cb750c0f8a06bad91d2052f6046dd5974818efe 1 0
-unsat
-08358038248416355849cc7ae66f2673721af28b 1 0
-unsat
-ac618ea2f315b87a071d15251b68179d70f7a036 107 0
-#2 := false
-decl f3 :: (-> S2 S1)
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#597 := (pattern #9)
-decl f1 :: S1
-#4 := f1
-#40 := (= f1 #9)
-#46 := (not #40)
-#604 := (forall (vars (?v0 S2)) (:pat #597) #46)
-#118 := (forall (vars (?v0 S2)) #46)
-#607 := (iff #118 #604)
-#605 := (iff #46 #46)
-#606 := [refl]: #605
-#608 := [quant-intro #606]: #607
-#61 := (exists (vars (?v0 S2)) #40)
-#77 := (not #61)
-#119 := (~ #77 #118)
-#116 := (~ #46 #46)
-#117 := [refl]: #116
-#120 := [nnf-neg #117]: #119
-#11 := (:var 1 S2)
-#12 := (= #8 #11)
-#47 := (or #12 #46)
-#52 := (forall (vars (?v1 S2)) #47)
-#55 := (and #40 #52)
-#58 := (exists (vars (?v0 S2)) #55)
-#67 := (not #58)
-#68 := (or #67 #61)
-#73 := (not #68)
-#10 := (= #9 f1)
-#17 := (exists (vars (?v0 S2)) #10)
-#13 := (implies #10 #12)
-#14 := (forall (vars (?v1 S2)) #13)
-#15 := (and #10 #14)
-#16 := (exists (vars (?v0 S2)) #15)
-#18 := (implies #16 #17)
-#19 := (not #18)
-#74 := (iff #19 #73)
-#71 := (iff #18 #68)
-#64 := (implies #58 #61)
-#69 := (iff #64 #68)
-#70 := [rewrite]: #69
-#65 := (iff #18 #64)
-#62 := (iff #17 #61)
-#41 := (iff #10 #40)
-#42 := [rewrite]: #41
-#63 := [quant-intro #42]: #62
-#59 := (iff #16 #58)
-#56 := (iff #15 #55)
-#53 := (iff #14 #52)
-#50 := (iff #13 #47)
-#43 := (implies #40 #12)
-#48 := (iff #43 #47)
-#49 := [rewrite]: #48
-#44 := (iff #13 #43)
-#45 := [monotonicity #42]: #44
-#51 := [trans #45 #49]: #50
-#54 := [quant-intro #51]: #53
-#57 := [monotonicity #42 #54]: #56
-#60 := [quant-intro #57]: #59
-#66 := [monotonicity #60 #63]: #65
-#72 := [trans #66 #70]: #71
-#75 := [monotonicity #72]: #74
-#39 := [asserted]: #19
-#78 := [mp #39 #75]: #73
-#79 := [not-or-elim #78]: #77
-#121 := [mp~ #79 #120]: #118
-#609 := [mp #121 #608]: #604
-decl ?v0!0 :: S2
-#87 := ?v0!0
-#81 := (f3 ?v0!0)
-#82 := (= f1 #81)
-#88 := (= #8 ?v0!0)
-#106 := (or #46 #88)
-#109 := (forall (vars (?v1 S2)) #106)
-#112 := (and #82 #109)
-#89 := (or #88 #46)
-#90 := (forall (vars (?v1 S2)) #89)
-#91 := (and #82 #90)
-#113 := (iff #91 #112)
-#110 := (iff #90 #109)
-#107 := (iff #89 #106)
-#108 := [rewrite]: #107
-#111 := [quant-intro #108]: #110
-#114 := [monotonicity #111]: #113
-#92 := (~ #58 #91)
-#100 := (~ #91 #91)
-#98 := (~ #90 #90)
-#96 := (~ #89 #89)
-#97 := [refl]: #96
-#99 := [nnf-pos #97]: #98
-#94 := (~ #82 #82)
-#95 := [refl]: #94
-#101 := [monotonicity #95 #99]: #100
-#93 := [sk]: #92
-#102 := [trans #93 #101]: #92
-#76 := [not-or-elim #78]: #58
-#103 := [mp~ #76 #102]: #91
-#104 := [mp #103 #114]: #112
-#105 := [and-elim #104]: #82
-#179 := (not #82)
-#267 := (not #604)
-#181 := (or #267 #179)
-#268 := [quant-inst #87]: #181
-[unit-resolution #268 #105 #609]: false
-unsat
-c1764d5fdaaf5fcd099b25c4b805ce423c186fa4 75 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: (-> S2 S1)
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#10 := (= #9 f1)
-#18 := (not #10)
-#11 := (:var 1 S2)
-#12 := (= #8 #11)
-#17 := (not #12)
-#19 := (implies #17 #18)
-#20 := (forall (vars (?v1 S2)) #19)
-#21 := (and #10 #20)
-#22 := (exists (vars (?v0 S2)) #21)
-#13 := (implies #10 #12)
-#14 := (forall (vars (?v1 S2)) #13)
-#15 := (and #10 #14)
-#16 := (exists (vars (?v0 S2)) #15)
-#23 := (iff #16 #22)
-#24 := (not #23)
-#93 := (iff #24 false)
-#1 := true
-#88 := (not true)
-#91 := (iff #88 false)
-#92 := [rewrite]: #91
-#89 := (iff #24 #88)
-#86 := (iff #23 true)
-#45 := (= f1 #9)
-#51 := (not #45)
-#52 := (or #12 #51)
-#57 := (forall (vars (?v1 S2)) #52)
-#60 := (and #45 #57)
-#63 := (exists (vars (?v0 S2)) #60)
-#81 := (iff #63 #63)
-#84 := (iff #81 true)
-#85 := [rewrite]: #84
-#82 := (iff #23 #81)
-#79 := (iff #22 #63)
-#77 := (iff #21 #60)
-#75 := (iff #20 #57)
-#73 := (iff #19 #52)
-#68 := (implies #17 #51)
-#71 := (iff #68 #52)
-#72 := [rewrite]: #71
-#69 := (iff #19 #68)
-#66 := (iff #18 #51)
-#46 := (iff #10 #45)
-#47 := [rewrite]: #46
-#67 := [monotonicity #47]: #66
-#70 := [monotonicity #67]: #69
-#74 := [trans #70 #72]: #73
-#76 := [quant-intro #74]: #75
-#78 := [monotonicity #47 #76]: #77
-#80 := [quant-intro #78]: #79
-#64 := (iff #16 #63)
-#61 := (iff #15 #60)
-#58 := (iff #14 #57)
-#55 := (iff #13 #52)
-#48 := (implies #45 #12)
-#53 := (iff #48 #52)
-#54 := [rewrite]: #53
-#49 := (iff #13 #48)
-#50 := [monotonicity #47]: #49
-#56 := [trans #50 #54]: #55
-#59 := [quant-intro #56]: #58
-#62 := [monotonicity #47 #59]: #61
-#65 := [quant-intro #62]: #64
-#83 := [monotonicity #65 #80]: #82
-#87 := [trans #83 #85]: #86
-#90 := [monotonicity #87]: #89
-#94 := [trans #90 #92]: #93
-#44 := [asserted]: #24
-[mp #44 #94]: false
-unsat
-39e6e981f54bfbbd33de190a32e637bca3addace 207 0
-#2 := false
-decl f3 :: (-> S2 S1)
-decl ?v1!0 :: (-> S2 S2)
-decl f4 :: S2
-#8 := f4
-#224 := (?v1!0 f4)
-#225 := (f3 #224)
-decl f1 :: S1
-#4 := f1
-#312 := (= f1 #225)
-#226 := (not #312)
-#311 := (= f4 #224)
-#316 := (or #311 #226)
-#314 := (not #316)
-#11 := (:var 0 S2)
-#12 := (f3 #11)
-#642 := (pattern #12)
-#123 := (?v1!0 #11)
-#150 := (= #11 #123)
-#124 := (f3 #123)
-#120 := (= f1 #124)
-#131 := (not #120)
-#156 := (or #131 #150)
-#161 := (not #156)
-#49 := (= f1 #12)
-#58 := (not #49)
-#164 := (or #58 #161)
-#649 := (forall (vars (?v0 S2)) (:pat #642) #164)
-#167 := (forall (vars (?v0 S2)) #164)
-#652 := (iff #167 #649)
-#650 := (iff #164 #164)
-#651 := [refl]: #650
-#653 := [quant-intro #651]: #652
-#132 := (= #123 #11)
-#133 := (or #132 #131)
-#134 := (not #133)
-#140 := (or #58 #134)
-#144 := (forall (vars (?v0 S2)) #140)
-#168 := (iff #144 #167)
-#165 := (iff #140 #164)
-#162 := (iff #134 #161)
-#159 := (iff #133 #156)
-#153 := (or #150 #131)
-#157 := (iff #153 #156)
-#158 := [rewrite]: #157
-#154 := (iff #133 #153)
-#151 := (iff #132 #150)
-#152 := [rewrite]: #151
-#155 := [monotonicity #152]: #154
-#160 := [trans #155 #158]: #159
-#163 := [monotonicity #160]: #162
-#166 := [monotonicity #163]: #165
-#169 := [quant-intro #166]: #168
-#17 := (:var 1 S2)
-#18 := (= #11 #17)
-#70 := (or #18 #58)
-#75 := (forall (vars (?v1 S2)) #70)
-#78 := (and #49 #75)
-#81 := (exists (vars (?v0 S2)) #78)
-#116 := (not #81)
-#145 := (~ #116 #144)
-#141 := (not #78)
-#142 := (~ #141 #140)
-#135 := (not #75)
-#136 := (~ #135 #134)
-#137 := [sk]: #136
-#122 := (~ #58 #58)
-#119 := [refl]: #122
-#143 := [nnf-neg #119 #137]: #142
-#146 := [nnf-neg #143]: #145
-#52 := (= f4 #11)
-#59 := (or #58 #52)
-#64 := (forall (vars (?v0 S2)) #59)
-#87 := (not #64)
-#9 := (f3 f4)
-#46 := (= f1 #9)
-#96 := (not #46)
-#105 := (or #96 #87 #81)
-#108 := (not #105)
-#13 := (= #12 f1)
-#19 := (implies #13 #18)
-#20 := (forall (vars (?v1 S2)) #19)
-#21 := (and #13 #20)
-#22 := (exists (vars (?v0 S2)) #21)
-#14 := (= #11 f4)
-#15 := (implies #13 #14)
-#16 := (forall (vars (?v0 S2)) #15)
-#23 := (implies #16 #22)
-#10 := (= #9 f1)
-#24 := (implies #10 #23)
-#25 := (not #24)
-#111 := (iff #25 #108)
-#88 := (or #87 #81)
-#97 := (or #96 #88)
-#102 := (not #97)
-#109 := (iff #102 #108)
-#106 := (iff #97 #105)
-#107 := [rewrite]: #106
-#110 := [monotonicity #107]: #109
-#103 := (iff #25 #102)
-#100 := (iff #24 #97)
-#93 := (implies #46 #88)
-#98 := (iff #93 #97)
-#99 := [rewrite]: #98
-#94 := (iff #24 #93)
-#91 := (iff #23 #88)
-#84 := (implies #64 #81)
-#89 := (iff #84 #88)
-#90 := [rewrite]: #89
-#85 := (iff #23 #84)
-#82 := (iff #22 #81)
-#79 := (iff #21 #78)
-#76 := (iff #20 #75)
-#73 := (iff #19 #70)
-#67 := (implies #49 #18)
-#71 := (iff #67 #70)
-#72 := [rewrite]: #71
-#68 := (iff #19 #67)
-#50 := (iff #13 #49)
-#51 := [rewrite]: #50
-#69 := [monotonicity #51]: #68
-#74 := [trans #69 #72]: #73
-#77 := [quant-intro #74]: #76
-#80 := [monotonicity #51 #77]: #79
-#83 := [quant-intro #80]: #82
-#65 := (iff #16 #64)
-#62 := (iff #15 #59)
-#55 := (implies #49 #52)
-#60 := (iff #55 #59)
-#61 := [rewrite]: #60
-#56 := (iff #15 #55)
-#53 := (iff #14 #52)
-#54 := [rewrite]: #53
-#57 := [monotonicity #51 #54]: #56
-#63 := [trans #57 #61]: #62
-#66 := [quant-intro #63]: #65
-#86 := [monotonicity #66 #83]: #85
-#92 := [trans #86 #90]: #91
-#47 := (iff #10 #46)
-#48 := [rewrite]: #47
-#95 := [monotonicity #48 #92]: #94
-#101 := [trans #95 #99]: #100
-#104 := [monotonicity #101]: #103
-#112 := [trans #104 #110]: #111
-#45 := [asserted]: #25
-#113 := [mp #45 #112]: #108
-#117 := [not-or-elim #113]: #116
-#147 := [mp~ #117 #146]: #144
-#148 := [mp #147 #169]: #167
-#654 := [mp #148 #653]: #649
-#114 := [not-or-elim #113]: #46
-#423 := (not #649)
-#630 := (or #423 #96 #314)
-#313 := (or #226 #311)
-#304 := (not #313)
-#315 := (or #96 #304)
-#302 := (or #423 #315)
-#641 := (iff #302 #630)
-#634 := (or #96 #314)
-#637 := (or #423 #634)
-#640 := (iff #637 #630)
-#635 := [rewrite]: #640
-#638 := (iff #302 #637)
-#636 := (iff #315 #634)
-#318 := (iff #304 #314)
-#244 := (iff #313 #316)
-#317 := [rewrite]: #244
-#297 := [monotonicity #317]: #318
-#291 := [monotonicity #297]: #636
-#639 := [monotonicity #291]: #638
-#631 := [trans #639 #635]: #641
-#303 := [quant-inst #8]: #302
-#289 := [mp #303 #631]: #630
-#598 := [unit-resolution #289 #114 #654]: #314
-#633 := (or #316 #312)
-#274 := [def-axiom]: #633
-#599 := [unit-resolution #274 #598]: #312
-#294 := (not #311)
-#632 := (or #316 #294)
-#290 := [def-axiom]: #632
-#594 := [unit-resolution #290 #598]: #294
-#643 := (forall (vars (?v0 S2)) (:pat #642) #59)
-#646 := (iff #64 #643)
-#644 := (iff #59 #59)
-#645 := [refl]: #644
-#647 := [quant-intro #645]: #646
-#129 := (~ #64 #64)
-#127 := (~ #59 #59)
-#128 := [refl]: #127
-#130 := [nnf-pos #128]: #129
-#115 := [not-or-elim #113]: #64
-#121 := [mp~ #115 #130]: #64
-#648 := [mp #121 #647]: #643
-#279 := (not #643)
-#280 := (or #279 #311 #226)
-#281 := (or #279 #313)
-#624 := (iff #281 #280)
-#620 := (or #279 #316)
-#623 := (iff #620 #280)
-#618 := [rewrite]: #623
-#621 := (iff #281 #620)
-#622 := [monotonicity #317]: #621
-#260 := [trans #622 #618]: #624
-#619 := [quant-inst #224]: #281
-#625 := [mp #619 #260]: #280
-[unit-resolution #625 #648 #594 #599]: false
-unsat
-4b1b63f9918482e3acffbd2b8d473f76fd800caf 250 0
-#2 := false
-decl f3 :: (-> S2 S1)
-decl ?v1!1 :: (-> S2 S2)
-decl ?v0!0 :: S2
-#126 := ?v0!0
-#255 := (?v1!1 ?v0!0)
-#256 := (f3 #255)
-decl f1 :: S1
-#4 := f1
-#343 := (= f1 #256)
-#257 := (not #343)
-#342 := (= ?v0!0 #255)
-#275 := (or #342 #257)
-#349 := (not #275)
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#680 := (pattern #9)
-#122 := (?v1!1 #8)
-#157 := (= #8 #122)
-#123 := (f3 #122)
-#137 := (= f1 #123)
-#138 := (not #137)
-#163 := (or #138 #157)
-#168 := (not #163)
-#47 := (= f1 #9)
-#84 := (not #47)
-#171 := (or #84 #168)
-#681 := (forall (vars (?v0 S2)) (:pat #680) #171)
-#174 := (forall (vars (?v0 S2)) #171)
-#684 := (iff #174 #681)
-#682 := (iff #171 #171)
-#683 := [refl]: #682
-#685 := [quant-intro #683]: #684
-#139 := (= #122 #8)
-#140 := (or #139 #138)
-#141 := (not #140)
-#147 := (or #84 #141)
-#151 := (forall (vars (?v0 S2)) #147)
-#175 := (iff #151 #174)
-#172 := (iff #147 #171)
-#169 := (iff #141 #168)
-#166 := (iff #140 #163)
-#160 := (or #157 #138)
-#164 := (iff #160 #163)
-#165 := [rewrite]: #164
-#161 := (iff #140 #160)
-#158 := (iff #139 #157)
-#159 := [rewrite]: #158
-#162 := [monotonicity #159]: #161
-#167 := [trans #162 #165]: #166
-#170 := [monotonicity #167]: #169
-#173 := [monotonicity #170]: #172
-#176 := [quant-intro #173]: #175
-#12 := (:var 1 S2)
-#20 := (= #8 #12)
-#85 := (or #20 #84)
-#90 := (forall (vars (?v1 S2)) #85)
-#93 := (and #47 #90)
-#96 := (exists (vars (?v0 S2)) #93)
-#115 := (not #96)
-#152 := (~ #115 #151)
-#148 := (not #93)
-#149 := (~ #148 #147)
-#142 := (not #90)
-#143 := (~ #142 #141)
-#144 := [sk]: #143
-#135 := (~ #84 #84)
-#136 := [refl]: #135
-#150 := [nnf-neg #136 #144]: #149
-#153 := [nnf-neg #150]: #152
-#13 := (f3 #12)
-#53 := (= f1 #13)
-#59 := (and #47 #53)
-#69 := (not #59)
-#70 := (or #20 #69)
-#75 := (forall (vars (?v0 S2) (?v1 S2)) #70)
-#50 := (exists (vars (?v0 S2)) #47)
-#78 := (and #50 #75)
-#102 := (not #78)
-#103 := (or #102 #96)
-#108 := (not #103)
-#10 := (= #9 f1)
-#21 := (implies #10 #20)
-#22 := (forall (vars (?v1 S2)) #21)
-#23 := (and #10 #22)
-#24 := (exists (vars (?v0 S2)) #23)
-#16 := (= #12 #8)
-#14 := (= #13 f1)
-#15 := (and #14 #10)
-#17 := (implies #15 #16)
-#18 := (forall (vars (?v0 S2) (?v1 S2)) #17)
-#11 := (exists (vars (?v0 S2)) #10)
-#19 := (and #11 #18)
-#25 := (implies #19 #24)
-#26 := (not #25)
-#109 := (iff #26 #108)
-#106 := (iff #25 #103)
-#99 := (implies #78 #96)
-#104 := (iff #99 #103)
-#105 := [rewrite]: #104
-#100 := (iff #25 #99)
-#97 := (iff #24 #96)
-#94 := (iff #23 #93)
-#91 := (iff #22 #90)
-#88 := (iff #21 #85)
-#81 := (implies #47 #20)
-#86 := (iff #81 #85)
-#87 := [rewrite]: #86
-#82 := (iff #21 #81)
-#48 := (iff #10 #47)
-#49 := [rewrite]: #48
-#83 := [monotonicity #49]: #82
-#89 := [trans #83 #87]: #88
-#92 := [quant-intro #89]: #91
-#95 := [monotonicity #49 #92]: #94
-#98 := [quant-intro #95]: #97
-#79 := (iff #19 #78)
-#76 := (iff #18 #75)
-#73 := (iff #17 #70)
-#66 := (implies #59 #20)
-#71 := (iff #66 #70)
-#72 := [rewrite]: #71
-#67 := (iff #17 #66)
-#64 := (iff #16 #20)
-#65 := [rewrite]: #64
-#62 := (iff #15 #59)
-#56 := (and #53 #47)
-#60 := (iff #56 #59)
-#61 := [rewrite]: #60
-#57 := (iff #15 #56)
-#54 := (iff #14 #53)
-#55 := [rewrite]: #54
-#58 := [monotonicity #55 #49]: #57
-#63 := [trans #58 #61]: #62
-#68 := [monotonicity #63 #65]: #67
-#74 := [trans #68 #72]: #73
-#77 := [quant-intro #74]: #76
-#51 := (iff #11 #50)
-#52 := [quant-intro #49]: #51
-#80 := [monotonicity #52 #77]: #79
-#101 := [monotonicity #80 #98]: #100
-#107 := [trans #101 #105]: #106
-#110 := [monotonicity #107]: #109
-#46 := [asserted]: #26
-#113 := [mp #46 #110]: #108
-#116 := [not-or-elim #113]: #115
-#154 := [mp~ #116 #153]: #151
-#155 := [mp #154 #176]: #174
-#686 := [mp #155 #685]: #681
-#127 := (f3 ?v0!0)
-#128 := (= f1 #127)
-#129 := (~ #50 #128)
-#118 := [sk]: #129
-#111 := [not-or-elim #113]: #78
-#112 := [and-elim #111]: #50
-#131 := [mp~ #112 #118]: #128
-#346 := (not #128)
-#661 := (not #681)
-#333 := (or #661 #346 #349)
-#344 := (or #257 #342)
-#335 := (not #344)
-#347 := (or #346 #335)
-#334 := (or #661 #347)
-#662 := (iff #334 #333)
-#667 := (or #346 #349)
-#669 := (or #661 #667)
-#666 := (iff #669 #333)
-#672 := [rewrite]: #666
-#670 := (iff #334 #669)
-#322 := (iff #347 #667)
-#328 := (iff #335 #349)
-#348 := (iff #344 #275)
-#345 := [rewrite]: #348
-#665 := [monotonicity #345]: #328
-#454 := [monotonicity #665]: #322
-#671 := [monotonicity #454]: #670
-#320 := [trans #671 #672]: #662
-#668 := [quant-inst #126]: #334
-#325 := [mp #668 #320]: #333
-#456 := [unit-resolution #325 #131 #686]: #349
-#305 := (or #275 #343)
-#648 := [def-axiom]: #305
-#609 := [unit-resolution #648 #456]: #343
-#663 := (not #342)
-#321 := (or #275 #663)
-#664 := [def-axiom]: #321
-#610 := [unit-resolution #664 #456]: #663
-#673 := (pattern #9 #13)
-#145 := (not #53)
-#189 := (or #20 #84 #145)
-#674 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #673) #189)
-#194 := (forall (vars (?v0 S2) (?v1 S2)) #189)
-#677 := (iff #194 #674)
-#675 := (iff #189 #189)
-#676 := [refl]: #675
-#678 := [quant-intro #676]: #677
-#195 := (iff #75 #194)
-#192 := (iff #70 #189)
-#146 := (or #84 #145)
-#186 := (or #20 #146)
-#190 := (iff #186 #189)
-#191 := [rewrite]: #190
-#187 := (iff #70 #186)
-#184 := (iff #69 #146)
-#156 := (not #146)
-#179 := (not #156)
-#182 := (iff #179 #146)
-#183 := [rewrite]: #182
-#180 := (iff #69 #179)
-#177 := (iff #59 #156)
-#178 := [rewrite]: #177
-#181 := [monotonicity #178]: #180
-#185 := [trans #181 #183]: #184
-#188 := [monotonicity #185]: #187
-#193 := [trans #188 #191]: #192
-#196 := [quant-intro #193]: #195
-#132 := (~ #75 #75)
-#119 := (~ #70 #70)
-#130 := [refl]: #119
-#133 := [nnf-pos #130]: #132
-#114 := [and-elim #111]: #75
-#134 := [mp~ #114 #133]: #75
-#197 := [mp #134 #196]: #194
-#679 := [mp #197 #678]: #674
-#630 := (not #674)
-#625 := (or #630 #346 #342 #257)
-#355 := (= #255 ?v0!0)
-#356 := (or #355 #257 #346)
-#626 := (or #630 #356)
-#476 := (iff #626 #625)
-#638 := (or #346 #342 #257)
-#632 := (or #630 #638)
-#474 := (iff #632 #625)
-#475 := [rewrite]: #474
-#627 := (iff #626 #632)
-#628 := (iff #356 #638)
-#637 := (or #342 #257 #346)
-#635 := (iff #637 #638)
-#639 := [rewrite]: #635
-#350 := (iff #356 #637)
-#358 := (iff #355 #342)
-#636 := [rewrite]: #358
-#634 := [monotonicity #636]: #350
-#629 := [trans #634 #639]: #628
-#633 := [monotonicity #629]: #627
-#618 := [trans #633 #475]: #476
-#631 := [quant-inst #126 #255]: #626
-#619 := [mp #631 #618]: #625
-[unit-resolution #619 #131 #679 #610 #609]: false
-unsat
-414b387cf896c5f2a72e6de8d5c3cc3d003f29bc 238 0
-#2 := false
-decl f3 :: (-> S2 S1)
-decl ?v1!1 :: (-> S2 S2)
-decl ?v0!0 :: S2
-#119 := ?v0!0
-#243 := (?v1!1 ?v0!0)
-#244 := (f3 #243)
-decl f1 :: S1
-#4 := f1
-#331 := (= f1 #244)
-#245 := (not #331)
-#330 := (= ?v0!0 #243)
-#263 := (or #330 #245)
-#337 := (not #263)
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#661 := (pattern #9)
-#148 := (?v1!1 #8)
-#169 := (= #8 #148)
-#149 := (f3 #148)
-#150 := (= f1 #149)
-#151 := (not #150)
-#175 := (or #151 #169)
-#180 := (not #175)
-#44 := (= f1 #9)
-#50 := (not #44)
-#183 := (or #50 #180)
-#668 := (forall (vars (?v0 S2)) (:pat #661) #183)
-#186 := (forall (vars (?v0 S2)) #183)
-#671 := (iff #186 #668)
-#669 := (iff #183 #183)
-#670 := [refl]: #669
-#672 := [quant-intro #670]: #671
-#152 := (= #148 #8)
-#153 := (or #152 #151)
-#154 := (not #153)
-#160 := (or #50 #154)
-#163 := (forall (vars (?v0 S2)) #160)
-#187 := (iff #163 #186)
-#184 := (iff #160 #183)
-#181 := (iff #154 #180)
-#178 := (iff #153 #175)
-#172 := (or #169 #151)
-#176 := (iff #172 #175)
-#177 := [rewrite]: #176
-#173 := (iff #153 #172)
-#170 := (iff #152 #169)
-#171 := [rewrite]: #170
-#174 := [monotonicity #171]: #173
-#179 := [trans #174 #177]: #178
-#182 := [monotonicity #179]: #181
-#185 := [monotonicity #182]: #184
-#188 := [quant-intro #185]: #187
-#11 := (:var 1 S2)
-#12 := (= #8 #11)
-#51 := (or #12 #50)
-#56 := (forall (vars (?v1 S2)) #51)
-#59 := (and #44 #56)
-#71 := (not #59)
-#115 := (forall (vars (?v0 S2)) #71)
-#164 := (~ #115 #163)
-#161 := (~ #71 #160)
-#155 := (not #56)
-#156 := (~ #155 #154)
-#157 := [sk]: #156
-#146 := (~ #50 #50)
-#147 := [refl]: #146
-#162 := [nnf-neg #147 #157]: #161
-#165 := [nnf-pos #162]: #164
+#66 := [not-or-elim #63]: #65
+#77 := [mp #66 #76]: #74
+#78 := (not #74)
+#71 := (or #8 #10 #78)
+#68 := [def-axiom]: #71
+#80 := [unit-resolution #68 #77]: #69
+#83 := [unit-resolution #80 #82 #81]: false
+#84 := [lemma #83]: #10
+#64 := [and-elim #61]: #43
+#85 := [unit-resolution #64 #84]: #8
+#73 := (or #38 #42)
+#79 := (or #38 #42 #78)
+#72 := [def-axiom]: #79
+#70 := [unit-resolution #72 #77]: #73
+[unit-resolution #70 #85 #84]: false
+unsat
+d8026f1269406972caa34c57a14a407df7dff9ee 67 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
 decl f4 :: S1
-#17 := f4
-#65 := (= f1 f4)
-#72 := (or #71 #65)
-#77 := (forall (vars (?v0 S2)) #72)
-#116 := (iff #77 #115)
-#113 := (iff #72 #71)
-#108 := (or #71 false)
-#111 := (iff #108 #71)
-#112 := [rewrite]: #111
-#109 := (iff #72 #108)
-#104 := (iff #65 false)
-#95 := (not #65)
-#62 := (exists (vars (?v0 S2)) #59)
-#80 := (and #62 #77)
-#86 := (not #80)
-#87 := (or #65 #86)
-#92 := (not #87)
-#18 := (= f4 f1)
-#10 := (= #9 f1)
-#13 := (implies #10 #12)
-#14 := (forall (vars (?v1 S2)) #13)
-#15 := (and #10 #14)
-#19 := (implies #15 #18)
-#20 := (forall (vars (?v0 S2)) #19)
-#16 := (exists (vars (?v0 S2)) #15)
-#21 := (and #16 #20)
-#22 := (implies #21 #18)
-#23 := (not #22)
-#93 := (iff #23 #92)
-#90 := (iff #22 #87)
-#83 := (implies #80 #65)
-#88 := (iff #83 #87)
-#89 := [rewrite]: #88
-#84 := (iff #22 #83)
-#66 := (iff #18 #65)
-#67 := [rewrite]: #66
-#81 := (iff #21 #80)
-#78 := (iff #20 #77)
-#75 := (iff #19 #72)
-#68 := (implies #59 #65)
-#73 := (iff #68 #72)
-#74 := [rewrite]: #73
-#69 := (iff #19 #68)
-#60 := (iff #15 #59)
-#57 := (iff #14 #56)
-#54 := (iff #13 #51)
-#47 := (implies #44 #12)
-#52 := (iff #47 #51)
-#53 := [rewrite]: #52
-#48 := (iff #13 #47)
-#45 := (iff #10 #44)
-#46 := [rewrite]: #45
-#49 := [monotonicity #46]: #48
-#55 := [trans #49 #53]: #54
-#58 := [quant-intro #55]: #57
-#61 := [monotonicity #46 #58]: #60
-#70 := [monotonicity #61 #67]: #69
-#76 := [trans #70 #74]: #75
-#79 := [quant-intro #76]: #78
-#63 := (iff #16 #62)
-#64 := [quant-intro #61]: #63
-#82 := [monotonicity #64 #79]: #81
-#85 := [monotonicity #82 #67]: #84
-#91 := [trans #85 #89]: #90
-#94 := [monotonicity #91]: #93
-#43 := [asserted]: #23
-#97 := [mp #43 #94]: #92
-#96 := [not-or-elim #97]: #95
-#105 := [iff-false #96]: #104
-#110 := [monotonicity #105]: #109
-#114 := [trans #110 #112]: #113
-#117 := [quant-intro #114]: #116
-#98 := [not-or-elim #97]: #80
-#100 := [and-elim #98]: #77
-#118 := [mp #100 #117]: #115
-#166 := [mp~ #118 #165]: #163
-#167 := [mp #166 #188]: #186
-#673 := [mp #167 #672]: #668
-#102 := (f3 ?v0!0)
-#103 := (= f1 #102)
-#120 := (= #8 ?v0!0)
-#136 := (or #50 #120)
-#139 := (forall (vars (?v1 S2)) #136)
-#142 := (and #103 #139)
-#106 := (or #120 #50)
-#107 := (forall (vars (?v1 S2)) #106)
-#121 := (and #103 #107)
-#143 := (iff #121 #142)
-#140 := (iff #107 #139)
-#137 := (iff #106 #136)
-#138 := [rewrite]: #137
-#141 := [quant-intro #138]: #140
-#144 := [monotonicity #141]: #143
-#122 := (~ #62 #121)
-#130 := (~ #121 #121)
-#128 := (~ #107 #107)
-#126 := (~ #106 #106)
-#127 := [refl]: #126
-#129 := [nnf-pos #127]: #128
-#124 := (~ #103 #103)
-#125 := [refl]: #124
-#131 := [monotonicity #125 #129]: #130
-#123 := [sk]: #122
-#132 := [trans #123 #131]: #122
-#99 := [and-elim #98]: #62
-#133 := [mp~ #99 #132]: #121
-#134 := [mp #133 #144]: #142
-#135 := [and-elim #134]: #103
-#334 := (not #103)
-#649 := (not #668)
-#321 := (or #649 #334 #337)
-#332 := (or #245 #330)
-#323 := (not #332)
-#335 := (or #334 #323)
-#322 := (or #649 #335)
-#650 := (iff #322 #321)
-#655 := (or #334 #337)
-#657 := (or #649 #655)
-#654 := (iff #657 #321)
-#660 := [rewrite]: #654
-#658 := (iff #322 #657)
-#310 := (iff #335 #655)
-#316 := (iff #323 #337)
-#336 := (iff #332 #263)
-#333 := [rewrite]: #336
-#653 := [monotonicity #333]: #316
-#442 := [monotonicity #653]: #310
-#659 := [monotonicity #442]: #658
-#308 := [trans #659 #660]: #650
-#656 := [quant-inst #119]: #322
-#313 := [mp #656 #308]: #321
-#614 := [unit-resolution #313 #135 #673]: #337
-#293 := (or #263 #331)
-#636 := [def-axiom]: #293
-#619 := [unit-resolution #636 #614]: #331
-#651 := (not #330)
-#309 := (or #263 #651)
-#652 := [def-axiom]: #309
-#620 := [unit-resolution #652 #614]: #651
-#662 := (forall (vars (?v1 S2)) (:pat #661) #136)
-#665 := (iff #139 #662)
-#663 := (iff #136 #136)
-#664 := [refl]: #663
-#666 := [quant-intro #664]: #665
-#145 := [and-elim #134]: #139
-#667 := [mp #145 #666]: #662
-#643 := (not #662)
-#279 := (or #643 #330 #245)
-#299 := (= #243 ?v0!0)
-#300 := (or #245 #299)
-#644 := (or #643 #300)
-#634 := (iff #644 #279)
-#284 := (or #643 #263)
-#645 := (iff #284 #279)
-#648 := [rewrite]: #645
-#285 := (iff #644 #284)
-#642 := (iff #300 #263)
-#640 := (iff #300 #332)
-#638 := (iff #299 #330)
-#639 := [rewrite]: #638
-#641 := [monotonicity #639]: #640
-#637 := [trans #641 #333]: #642
-#647 := [monotonicity #637]: #285
-#635 := [trans #647 #648]: #634
-#646 := [quant-inst #243]: #644
-#341 := [mp #646 #635]: #279
-[unit-resolution #341 #667 #620 #619]: false
-unsat
-43a06f7db71bb40e30122f32a94b922612b5b5ed 93 0
-#2 := false
-decl f5 :: (-> S2 S1)
-decl f6 :: S2
-#16 := f6
-#20 := (f5 f6)
-decl f1 :: S1
-#4 := f1
-#68 := (= f1 #20)
-#87 := (not #68)
-decl f3 :: (-> S2 S3 S1)
-decl f4 :: S3
 #9 := f4
-#17 := (f3 f6 f4)
-#62 := (= f1 #17)
-#8 := (:var 0 S2)
-#12 := (f5 #8)
-#47 := (= f1 #12)
-#10 := (f3 #8 f4)
-#44 := (= f1 #10)
-#53 := (not #44)
-#54 := (or #53 #47)
-#59 := (forall (vars (?v0 S2)) #54)
-#65 := (and #59 #62)
-#74 := (not #65)
-#75 := (or #74 #68)
-#80 := (not #75)
-#21 := (= #20 f1)
-#18 := (= #17 f1)
-#13 := (= #12 f1)
-#11 := (= #10 f1)
-#14 := (implies #11 #13)
-#15 := (forall (vars (?v0 S2)) #14)
-#19 := (and #15 #18)
-#22 := (implies #19 #21)
-#23 := (not #22)
-#81 := (iff #23 #80)
-#78 := (iff #22 #75)
-#71 := (implies #65 #68)
-#76 := (iff #71 #75)
-#77 := [rewrite]: #76
-#72 := (iff #22 #71)
-#69 := (iff #21 #68)
-#70 := [rewrite]: #69
-#66 := (iff #19 #65)
-#63 := (iff #18 #62)
-#64 := [rewrite]: #63
-#60 := (iff #15 #59)
-#57 := (iff #14 #54)
-#50 := (implies #44 #47)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #14 #50)
-#48 := (iff #13 #47)
-#49 := [rewrite]: #48
-#45 := (iff #11 #44)
-#46 := [rewrite]: #45
-#52 := [monotonicity #46 #49]: #51
-#58 := [trans #52 #56]: #57
-#61 := [quant-intro #58]: #60
-#67 := [monotonicity #61 #64]: #66
-#73 := [monotonicity #67 #70]: #72
-#79 := [trans #73 #77]: #78
-#82 := [monotonicity #79]: #81
-#43 := [asserted]: #23
-#85 := [mp #43 #82]: #80
-#88 := [not-or-elim #85]: #87
-#83 := [not-or-elim #85]: #65
-#86 := [and-elim #83]: #62
-#571 := (pattern #12)
-#570 := (pattern #10)
-#572 := (forall (vars (?v0 S2)) (:pat #570 #571) #54)
-#575 := (iff #59 #572)
-#573 := (iff #54 #54)
-#574 := [refl]: #573
-#576 := [quant-intro #574]: #575
-#100 := (~ #59 #59)
-#98 := (~ #54 #54)
-#99 := [refl]: #98
-#101 := [nnf-pos #99]: #100
-#84 := [and-elim #83]: #59
-#90 := [mp~ #84 #101]: #59
-#577 := [mp #90 #576]: #572
-#152 := (not #62)
-#154 := (not #572)
-#241 := (or #154 #152 #68)
-#239 := (or #152 #68)
-#232 := (or #154 #239)
-#244 := (iff #232 #241)
-#172 := [rewrite]: #244
-#243 := [quant-inst #16]: #232
-#245 := [mp #243 #172]: #241
-[unit-resolution #245 #577 #86 #88]: false
-unsat
-10b0ad71f1792bc4343d482448bd439666bec7e5 113 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f4 :: S3
-#9 := f4
-decl f6 :: S2
-#16 := f6
-#19 := (f3 f6 f4)
-decl f1 :: S1
-#4 := f1
-#60 := (= f1 #19)
-decl f5 :: (-> S2 S1)
-#17 := (f5 f6)
-#57 := (= f1 #17)
-#63 := (and #57 #60)
-#66 := (not #63)
-#8 := (:var 0 S2)
-#12 := (f5 #8)
-#48 := (= f1 #12)
-#10 := (f3 #8 f4)
-#45 := (= f1 #10)
-#51 := (and #45 #48)
-#54 := (exists (vars (?v0 S2)) #51)
-#69 := (or #54 #66)
-#72 := (not #69)
-#20 := (= #19 f1)
-#18 := (= #17 f1)
-#21 := (and #18 #20)
-#22 := (not #21)
-#13 := (= #12 f1)
-#11 := (= #10 f1)
-#14 := (and #11 #13)
-#15 := (exists (vars (?v0 S2)) #14)
-#23 := (or #15 #22)
-#24 := (not #23)
-#73 := (iff #24 #72)
-#70 := (iff #23 #69)
-#67 := (iff #22 #66)
-#64 := (iff #21 #63)
-#61 := (iff #20 #60)
-#62 := [rewrite]: #61
-#58 := (iff #18 #57)
-#59 := [rewrite]: #58
-#65 := [monotonicity #59 #62]: #64
-#68 := [monotonicity #65]: #67
-#55 := (iff #15 #54)
-#52 := (iff #14 #51)
-#49 := (iff #13 #48)
-#50 := [rewrite]: #49
-#46 := (iff #11 #45)
-#47 := [rewrite]: #46
-#53 := [monotonicity #47 #50]: #52
-#56 := [quant-intro #53]: #55
-#71 := [monotonicity #56 #68]: #70
-#74 := [monotonicity #71]: #73
-#44 := [asserted]: #24
-#77 := [mp #44 #74]: #72
-#78 := [not-or-elim #77]: #63
-#80 := [and-elim #78]: #60
-#79 := [and-elim #78]: #57
-#584 := (pattern #12)
-#583 := (pattern #10)
-#96 := (not #48)
-#95 := (not #45)
-#97 := (or #95 #96)
-#585 := (forall (vars (?v0 S2)) (:pat #583 #584) #97)
-#104 := (forall (vars (?v0 S2)) #97)
-#588 := (iff #104 #585)
-#586 := (iff #97 #97)
-#587 := [refl]: #586
-#589 := [quant-intro #587]: #588
-#90 := (not #51)
-#93 := (forall (vars (?v0 S2)) #90)
-#105 := (iff #93 #104)
-#102 := (iff #90 #97)
-#98 := (not #97)
-#86 := (not #98)
-#100 := (iff #86 #97)
-#101 := [rewrite]: #100
-#87 := (iff #90 #86)
-#88 := (iff #51 #98)
-#89 := [rewrite]: #88
-#99 := [monotonicity #89]: #87
-#103 := [trans #99 #101]: #102
-#106 := [quant-intro #103]: #105
-#75 := (not #54)
-#82 := (~ #75 #93)
-#91 := (~ #90 #90)
-#92 := [refl]: #91
-#83 := [nnf-neg #92]: #82
-#76 := [not-or-elim #77]: #75
-#94 := [mp~ #76 #83]: #93
-#107 := [mp #94 #106]: #104
-#590 := [mp #107 #589]: #585
-#252 := (not #60)
-#165 := (not #57)
-#245 := (not #585)
-#256 := (or #245 #165 #252)
-#166 := (or #252 #165)
-#257 := (or #245 #166)
-#577 := (iff #257 #256)
-#253 := (or #165 #252)
-#258 := (or #245 #253)
-#238 := (iff #258 #256)
-#575 := [rewrite]: #238
-#255 := (iff #257 #258)
-#167 := (iff #166 #253)
-#254 := [rewrite]: #167
-#259 := [monotonicity #254]: #255
-#232 := [trans #259 #575]: #577
-#185 := [quant-inst #16]: #257
-#364 := [mp #185 #232]: #256
-[unit-resolution #364 #590 #79 #80]: false
-unsat
-1ea0edf79c861d93e0b6cff855e43197b6927af2 43 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
+#10 := (= f4 f1)
+#12 := (iff #10 #8)
+#53 := (not #12)
+#71 := [hypothesis]: #53
+#76 := (or #10 #12)
+#48 := (not #10)
+#72 := [hypothesis]: #48
+#36 := (not #8)
+#37 := (iff #36 #10)
+#47 := (not #37)
+#69 := (or #47 #12)
+#38 := (iff #37 #12)
+#11 := (iff #8 #10)
+#13 := (iff #11 #12)
+#14 := (not #13)
+#39 := (iff #14 #38)
+#40 := [rewrite]: #39
+#35 := [asserted]: #14
+#43 := [mp #35 #40]: #38
+#62 := (not #38)
+#67 := (or #47 #12 #62)
+#68 := [def-axiom]: #67
+#70 := [unit-resolution #68 #43]: #69
+#73 := [unit-resolution #70 #71]: #47
+#42 := (or #37 #36 #10)
+#44 := [def-axiom]: #42
+#74 := [unit-resolution #44 #72 #73]: #36
+#58 := (or #12 #10 #8)
+#59 := [def-axiom]: #58
+#75 := [unit-resolution #59 #74 #72 #71]: false
+#77 := [lemma #75]: #76
+#78 := [unit-resolution #77 #71]: #10
+#51 := (or #37 #8 #48)
+#52 := [def-axiom]: #51
+#79 := [unit-resolution #52 #78 #73]: #8
+#60 := (or #12 #48 #36)
+#61 := [def-axiom]: #60
+#80 := [unit-resolution #61 #79 #78 #71]: false
+#81 := [lemma #80]: #12
+#82 := [hypothesis]: #36
+#65 := (or #37 #53)
+#63 := (or #37 #53 #62)
+#64 := [def-axiom]: #63
+#66 := [unit-resolution #64 #43]: #65
+#83 := [unit-resolution #66 #81]: #37
+#45 := (or #47 #8 #10)
+#46 := [def-axiom]: #45
+#84 := [unit-resolution #46 #82 #83]: #10
+#56 := (or #53 #48 #8)
+#57 := [def-axiom]: #56
+#85 := [unit-resolution #57 #84 #82 #81]: false
+#86 := [lemma #85]: #8
+#49 := (or #47 #36 #48)
+#50 := [def-axiom]: #49
+#87 := [unit-resolution #50 #86 #83]: #48
+#54 := (or #53 #10 #36)
+#55 := [def-axiom]: #54
+[unit-resolution #55 #87 #86 #81]: false
+unsat
+3363d204e860e90fc7410c9b98599a08737e98bf 30 0
+#2 := false
+decl f1 :: S1
+#3 := f1
 decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#12 := (or #9 #11)
-#13 := (not #12)
-#14 := (or #12 #13)
-#15 := (not #14)
-#60 := (iff #15 false)
-#1 := true
-#55 := (not true)
-#58 := (iff #55 false)
-#59 := [rewrite]: #58
-#56 := (iff #15 #55)
-#53 := (iff #14 true)
-#39 := (= f1 f4)
-#36 := (= f1 f3)
-#42 := (or #36 #39)
-#45 := (not #42)
-#48 := (or #42 #45)
-#51 := (iff #48 true)
-#52 := [rewrite]: #51
-#49 := (iff #14 #48)
-#46 := (iff #13 #45)
-#43 := (iff #12 #42)
-#40 := (iff #11 #39)
-#41 := [rewrite]: #40
-#37 := (iff #9 #36)
-#38 := [rewrite]: #37
-#44 := [monotonicity #38 #41]: #43
-#47 := [monotonicity #44]: #46
-#50 := [monotonicity #44 #47]: #49
-#54 := [trans #50 #52]: #53
-#57 := [monotonicity #54]: #56
-#61 := [trans #57 #59]: #60
-#35 := [asserted]: #15
-[mp #35 #61]: false
-unsat
-2efe31821fea4e444f1f58e423b1a3e1ab9b4cac 27 0
-#2 := false
-#1 := true
-#9 := (or false true)
-#8 := (and true false)
-#10 := (implies #8 #9)
+#7 := f3
+#8 := (= f3 f1)
+#9 := (not #8)
+#10 := (iff #8 #9)
 #11 := (not #10)
-#48 := (iff #11 false)
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #11 #43)
-#41 := (iff #10 true)
-#36 := (implies false true)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #10 #36)
-#34 := (iff #9 true)
-#35 := [rewrite]: #34
-#32 := (iff #8 false)
-#33 := [rewrite]: #32
-#38 := [monotonicity #33 #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#31 := [asserted]: #11
-[mp #31 #49]: false
-unsat
-eee4a504043afccce3195787f9f287f21c12ec9e 31 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: (-> S2 S1)
-decl f4 :: S2
-#8 := f4
-#9 := (f3 f4)
-#10 := (= #9 f1)
-#11 := (iff #10 #10)
 #12 := (not #11)
 #48 := (iff #12 false)
 #1 := true
@@ -8804,4542 +2421,10912 @@
 #47 := [rewrite]: #46
 #44 := (iff #12 #43)
 #41 := (iff #11 true)
-#33 := (= f1 #9)
-#36 := (iff #33 #33)
+#36 := (not false)
 #39 := (iff #36 true)
 #40 := [rewrite]: #39
 #37 := (iff #11 #36)
-#34 := (iff #10 #33)
+#34 := (iff #10 false)
 #35 := [rewrite]: #34
-#38 := [monotonicity #35 #35]: #37
+#38 := [monotonicity #35]: #37
 #42 := [trans #38 #40]: #41
 #45 := [monotonicity #42]: #44
 #49 := [trans #45 #47]: #48
-#32 := [asserted]: #12
-[mp #32 #49]: false
-unsat
-278fae448e44a4b7b524e9ac29b485b32979de5b 33 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: (-> S2 S3 S1)
-decl f5 :: S3
-#9 := f5
-decl f4 :: S2
-#8 := f4
-#10 := (f3 f4 f5)
-#11 := (= #10 f1)
-#12 := (iff #11 #11)
-#13 := (not #12)
-#49 := (iff #13 false)
-#1 := true
-#44 := (not true)
-#47 := (iff #44 false)
-#48 := [rewrite]: #47
-#45 := (iff #13 #44)
-#42 := (iff #12 true)
-#34 := (= f1 #10)
-#37 := (iff #34 #34)
-#40 := (iff #37 true)
+#33 := [asserted]: #12
+[mp #33 #49]: false
+unsat
+307fe479d3024f1d782f30fc995cff7558bffef8 68 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#13 := (not #8)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#41 := (or #10 #13)
+#38 := (or #13 #10)
+#68 := (not #41)
+#80 := [hypothesis]: #68
+#78 := (or #38 #41)
+#50 := (not #38)
+#51 := (iff #50 #41)
+#12 := (not #10)
+#14 := (implies #12 #13)
+#11 := (implies #8 #10)
+#15 := (iff #11 #14)
+#16 := (not #15)
+#54 := (iff #16 #51)
+#44 := (iff #38 #41)
+#47 := (not #44)
+#52 := (iff #47 #51)
+#53 := [rewrite]: #52
+#48 := (iff #16 #47)
+#45 := (iff #15 #44)
+#42 := (iff #14 #41)
+#43 := [rewrite]: #42
+#39 := (iff #11 #38)
+#40 := [rewrite]: #39
+#46 := [monotonicity #40 #43]: #45
+#49 := [monotonicity #46]: #48
+#55 := [trans #49 #53]: #54
+#37 := [asserted]: #16
+#58 := [mp #37 #55]: #51
+#71 := (not #51)
+#76 := (or #38 #41 #71)
+#77 := [def-axiom]: #76
+#79 := [unit-resolution #77 #58]: #78
+#81 := [unit-resolution #79 #80]: #38
+#57 := (or #41 #12)
+#59 := [def-axiom]: #57
+#82 := [unit-resolution #59 #80]: #12
+#66 := (or #41 #8)
+#67 := [def-axiom]: #66
+#83 := [unit-resolution #67 #80]: #8
+#60 := (or #50 #13 #10)
+#61 := [def-axiom]: #60
+#84 := [unit-resolution #61 #83 #82 #81]: false
+#85 := [lemma #84]: #41
+#74 := (or #50 #68)
+#72 := (or #50 #68 #71)
+#73 := [def-axiom]: #72
+#75 := [unit-resolution #73 #58]: #74
+#86 := [unit-resolution #75 #85]: #50
+#62 := (or #38 #8)
+#63 := [def-axiom]: #62
+#87 := [unit-resolution #63 #86]: #8
+#64 := (or #38 #12)
+#65 := [def-axiom]: #64
+#88 := [unit-resolution #65 #86]: #12
+#69 := (or #68 #10 #13)
+#70 := [def-axiom]: #69
+[unit-resolution #70 #88 #87 #85]: false
+unsat
+8cebbbdf59241f53ca8f7ba4ba97c397eebb23a4 64 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#9 := (iff #8 #8)
+#10 := (iff #8 #9)
+#11 := (iff #8 #10)
+#12 := (iff #8 #11)
+#13 := (iff #8 #12)
+#14 := (iff #8 #13)
+#15 := (iff #8 #14)
+#16 := (iff #8 #15)
+#17 := (iff #8 #16)
+#18 := (not #17)
+#82 := (iff #18 false)
+#1 := true
+#77 := (not true)
+#80 := (iff #77 false)
+#81 := [rewrite]: #80
+#78 := (iff #18 #77)
+#75 := (iff #17 true)
+#40 := (iff #9 true)
 #41 := [rewrite]: #40
-#38 := (iff #12 #37)
-#35 := (iff #11 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36 #36]: #38
-#43 := [trans #39 #41]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#33 := [asserted]: #13
-[mp #33 #50]: false
-unsat
-543fe903b7fa43c36b6d0fa84d517158fd95fbda 38 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: (-> S2 S1)
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#10 := (= #9 f1)
-#11 := (forall (vars (?v0 S2)) #10)
-#12 := (not #11)
-#13 := (ite #11 #11 #12)
+#73 := (iff #17 #9)
+#71 := (iff #16 #8)
+#42 := (iff #8 true)
+#45 := (iff #42 #8)
+#46 := [rewrite]: #45
+#69 := (iff #16 #42)
+#67 := (iff #15 true)
+#65 := (iff #15 #9)
+#63 := (iff #14 #8)
+#61 := (iff #14 #42)
+#59 := (iff #13 true)
+#57 := (iff #13 #9)
+#55 := (iff #12 #8)
+#53 := (iff #12 #42)
+#51 := (iff #11 true)
+#49 := (iff #11 #9)
+#47 := (iff #10 #8)
+#43 := (iff #10 #42)
+#44 := [monotonicity #41]: #43
+#48 := [trans #44 #46]: #47
+#50 := [monotonicity #48]: #49
+#52 := [trans #50 #41]: #51
+#54 := [monotonicity #52]: #53
+#56 := [trans #54 #46]: #55
+#58 := [monotonicity #56]: #57
+#60 := [trans #58 #41]: #59
+#62 := [monotonicity #60]: #61
+#64 := [trans #62 #46]: #63
+#66 := [monotonicity #64]: #65
+#68 := [trans #66 #41]: #67
+#70 := [monotonicity #68]: #69
+#72 := [trans #70 #46]: #71
+#74 := [monotonicity #72]: #73
+#76 := [trans #74 #41]: #75
+#79 := [monotonicity #76]: #78
+#83 := [trans #79 #81]: #82
+#39 := [asserted]: #18
+[mp #39 #83]: false
+unsat
+7065d1b00bad74db5477c46f555fb695c1bbcb2b 121 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+decl f5 :: S1
+#11 := f5
+#12 := (= f5 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#13 := (if #8 #10 #12)
+#44 := (or #8 #12)
+#69 := (not #44)
+#15 := (not #8)
+#41 := (or #15 #10)
+#68 := (not #41)
+#70 := (or #68 #69)
+#71 := (not #70)
+#123 := [hypothesis]: #71
+#103 := (or #70 #44)
+#104 := [def-axiom]: #103
+#124 := [unit-resolution #104 #123]: #44
+#56 := (not #13)
+#114 := (or #56 #70)
+#73 := (iff #13 #70)
+#47 := (and #41 #44)
+#57 := (iff #56 #47)
+#76 := (iff #57 #73)
+#63 := (iff #56 #71)
+#74 := (iff #63 #73)
+#75 := [rewrite]: #74
+#65 := (iff #57 #63)
+#66 := (iff #47 #71)
+#67 := [rewrite]: #66
+#72 := [monotonicity #67]: #65
+#77 := [trans #72 #75]: #76
+#16 := (implies #15 #12)
+#14 := (implies #8 #10)
+#17 := (and #14 #16)
+#18 := (iff #13 #17)
+#19 := (not #18)
+#60 := (iff #19 #57)
+#50 := (iff #13 #47)
+#53 := (not #50)
+#58 := (iff #53 #57)
+#59 := [rewrite]: #58
+#54 := (iff #19 #53)
+#51 := (iff #18 #50)
+#48 := (iff #17 #47)
+#45 := (iff #16 #44)
+#46 := [rewrite]: #45
+#42 := (iff #14 #41)
+#43 := [rewrite]: #42
+#49 := [monotonicity #43 #46]: #48
+#52 := [monotonicity #49]: #51
+#55 := [monotonicity #52]: #54
+#61 := [trans #55 #59]: #60
+#40 := [asserted]: #19
+#64 := [mp #40 #61]: #57
+#78 := [mp #64 #77]: #73
+#107 := (not #73)
+#112 := (or #56 #70 #107)
+#113 := [def-axiom]: #112
+#115 := [unit-resolution #113 #78]: #114
+#125 := [unit-resolution #115 #123]: #56
+#101 := (or #70 #41)
+#102 := [def-axiom]: #101
+#126 := [unit-resolution #102 #123]: #41
+#121 := (or #15 #68 #13)
+#116 := [hypothesis]: #41
+#117 := [hypothesis]: #8
+#83 := (not #10)
+#118 := [hypothesis]: #56
+#84 := (or #13 #15 #83)
+#85 := [def-axiom]: #84
+#119 := [unit-resolution #85 #117 #118]: #83
+#93 := (or #68 #15 #10)
+#94 := [def-axiom]: #93
+#120 := [unit-resolution #94 #119 #117 #116]: false
+#122 := [lemma #120]: #121
+#127 := [unit-resolution #122 #126 #125]: #15
+#86 := (not #12)
+#87 := (or #13 #8 #86)
+#88 := [def-axiom]: #87
+#128 := [unit-resolution #88 #127 #125]: #86
+#99 := (or #69 #8 #12)
+#100 := [def-axiom]: #99
+#129 := [unit-resolution #100 #128 #127 #124]: false
+#130 := [lemma #129]: #70
+#110 := (or #13 #71)
+#108 := (or #13 #71 #107)
+#109 := [def-axiom]: #108
+#111 := [unit-resolution #109 #78]: #110
+#133 := [unit-resolution #111 #130]: #13
+#131 := [hypothesis]: #15
+#89 := (or #41 #8)
+#90 := [def-axiom]: #89
+#132 := [unit-resolution #90 #131]: #41
+#81 := (or #56 #8 #12)
+#82 := [def-axiom]: #81
+#134 := [unit-resolution #82 #131 #133]: #12
+#97 := (or #44 #86)
+#98 := [def-axiom]: #97
+#135 := [unit-resolution #98 #134]: #44
+#105 := (or #71 #68 #69)
+#106 := [def-axiom]: #105
+#136 := [unit-resolution #106 #135 #132 #130]: false
+#137 := [lemma #136]: #8
+#79 := (or #56 #15 #10)
+#80 := [def-axiom]: #79
+#138 := [unit-resolution #80 #137 #133]: #10
+#95 := (or #44 #15)
+#96 := [def-axiom]: #95
+#139 := [unit-resolution #96 #137]: #44
+#140 := [unit-resolution #106 #139 #130]: #68
+#91 := (or #41 #83)
+#92 := [def-axiom]: #91
+[unit-resolution #92 #140 #138]: false
+unsat
+aac8bd622b8d3f29643acf747f849dbeac65edf3 50 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#40 := (not #8)
+#74 := [hypothesis]: #8
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#36 := (not #10)
+#37 := (or #36 #8)
+#58 := (or #37 #40)
+#59 := [def-axiom]: #58
+#75 := [unit-resolution #59 #74]: #37
+#54 := (not #37)
+#76 := (or #40 #54)
+#41 := (or #40 #10)
+#44 := (if #8 #37 #41)
+#47 := (not #44)
+#12 := (implies #8 #10)
+#11 := (implies #10 #8)
+#13 := (if #8 #11 #12)
 #14 := (not #13)
-#56 := (iff #14 false)
-#1 := true
-#51 := (not true)
-#54 := (iff #51 false)
-#55 := [rewrite]: #54
-#52 := (iff #14 #51)
-#49 := (iff #13 true)
-#35 := (= f1 #9)
-#38 := (forall (vars (?v0 S2)) #35)
-#41 := (not #38)
-#44 := (ite #38 #38 #41)
-#47 := (iff #44 true)
-#48 := [rewrite]: #47
+#48 := (iff #14 #47)
 #45 := (iff #13 #44)
 #42 := (iff #12 #41)
-#39 := (iff #11 #38)
-#36 := (iff #10 #35)
+#43 := [rewrite]: #42
+#38 := (iff #11 #37)
+#39 := [rewrite]: #38
+#46 := [monotonicity #39 #43]: #45
+#49 := [monotonicity #46]: #48
+#35 := [asserted]: #14
+#52 := [mp #35 #49]: #47
+#70 := (or #44 #40 #54)
+#71 := [def-axiom]: #70
+#77 := [unit-resolution #71 #52]: #76
+#78 := [unit-resolution #77 #75 #74]: false
+#79 := [lemma #78]: #40
+#53 := (or #41 #8)
+#60 := [def-axiom]: #53
+#80 := [unit-resolution #60 #79]: #41
+#63 := (not #41)
+#81 := (or #8 #63)
+#72 := (or #44 #8 #63)
+#73 := [def-axiom]: #72
+#82 := [unit-resolution #73 #52]: #81
+[unit-resolution #82 #80 #79]: false
+unsat
+627c25c71422f379340a41c5a2991827f13b6eeb 108 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f5 :: S1
+#12 := f5
+#13 := (= f5 f1)
+decl f6 :: S1
+#14 := f6
+#15 := (= f6 f1)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#11 := (or #8 #10)
+#16 := (if #11 #13 #15)
+#42 := (not #16)
+#94 := [hypothesis]: #42
+#108 := (or #10 #16)
+#47 := (not #11)
+#52 := (not #8)
+#100 := (or #52 #16)
+#95 := [hypothesis]: #8
+#53 := (or #11 #52)
+#54 := [def-axiom]: #53
+#96 := [unit-resolution #54 #95]: #11
+#17 := (if #10 #13 #15)
+#18 := (if #8 #13 #17)
+#92 := (or #16 #18)
+#43 := (iff #42 #18)
+#19 := (iff #16 #18)
+#20 := (not #19)
+#44 := (iff #20 #43)
+#45 := [rewrite]: #44
+#41 := [asserted]: #20
+#48 := [mp #41 #45]: #43
+#85 := (not #43)
+#90 := (or #16 #18 #85)
+#91 := [def-axiom]: #90
+#93 := [unit-resolution #91 #48]: #92
+#97 := [unit-resolution #93 #94]: #18
+#76 := (not #18)
+#77 := (or #76 #52 #13)
+#78 := [def-axiom]: #77
+#98 := [unit-resolution #78 #95 #97]: #13
+#61 := (not #13)
+#62 := (or #16 #47 #61)
+#63 := [def-axiom]: #62
+#99 := [unit-resolution #63 #98 #96 #94]: false
+#101 := [lemma #99]: #100
+#102 := [unit-resolution #101 #94]: #52
+#55 := (not #10)
+#103 := [hypothesis]: #55
+#49 := (or #47 #8 #10)
+#56 := [def-axiom]: #49
+#104 := [unit-resolution #56 #103 #102]: #47
+#79 := (or #76 #8 #17)
+#80 := [def-axiom]: #79
+#105 := [unit-resolution #80 #102 #97]: #17
+#67 := (not #17)
+#70 := (or #67 #10 #15)
+#71 := [def-axiom]: #70
+#106 := [unit-resolution #71 #103 #105]: #15
+#64 := (not #15)
+#65 := (or #16 #11 #64)
+#66 := [def-axiom]: #65
+#107 := [unit-resolution #66 #106 #104 #94]: false
+#109 := [lemma #107]: #108
+#110 := [unit-resolution #109 #94]: #10
+#50 := (or #11 #55)
+#51 := [def-axiom]: #50
+#111 := [unit-resolution #51 #110]: #11
+#68 := (or #67 #55 #13)
+#69 := [def-axiom]: #68
+#112 := [unit-resolution #69 #110 #105]: #13
+#113 := [unit-resolution #63 #112 #111 #94]: false
+#114 := [lemma #113]: #16
+#115 := [hypothesis]: #47
+#116 := [unit-resolution #51 #115]: #55
+#59 := (or #42 #11 #15)
+#60 := [def-axiom]: #59
+#117 := [unit-resolution #60 #115 #114]: #15
+#88 := (or #42 #76)
+#86 := (or #42 #76 #85)
+#87 := [def-axiom]: #86
+#89 := [unit-resolution #87 #48]: #88
+#118 := [unit-resolution #89 #114]: #76
+#119 := [unit-resolution #54 #115]: #52
+#83 := (or #18 #8 #67)
+#84 := [def-axiom]: #83
+#120 := [unit-resolution #84 #119 #118]: #67
+#74 := (or #17 #10 #64)
+#75 := [def-axiom]: #74
+#121 := [unit-resolution #75 #120 #117 #116]: false
+#122 := [lemma #121]: #11
+#57 := (or #42 #47 #13)
+#58 := [def-axiom]: #57
+#123 := [unit-resolution #58 #122 #114]: #13
+#81 := (or #18 #52 #61)
+#82 := [def-axiom]: #81
+#124 := [unit-resolution #82 #123 #118]: #52
+#125 := [unit-resolution #84 #124 #118]: #67
+#126 := [unit-resolution #56 #124 #122]: #10
+#72 := (or #17 #55 #61)
+#73 := [def-axiom]: #72
+[unit-resolution #73 #126 #125 #123]: false
+unsat
+a8caac95ba6f91aa44f76da5a19b4261970d10e2 126 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f6 :: S1
+#14 := f6
+#15 := (= f6 f1)
+decl f5 :: S1
+#12 := f5
+#13 := (= f5 f1)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#53 := (not #10)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#52 := (not #8)
+#54 := (or #52 #53)
+#57 := (if #54 #15 #13)
+#62 := (not #57)
+#112 := [hypothesis]: #62
+#126 := (or #53 #57)
+#55 := (not #54)
+#118 := (or #8 #57)
+#113 := [hypothesis]: #52
+#69 := (or #54 #8)
+#70 := [def-axiom]: #69
+#114 := [unit-resolution #70 #113]: #54
+#17 := (if #10 #13 #15)
+#18 := (if #8 #17 #15)
+#110 := (or #57 #18)
+#65 := (iff #62 #18)
+#11 := (and #8 #10)
+#16 := (if #11 #13 #15)
+#42 := (not #16)
+#43 := (iff #42 #18)
+#66 := (iff #43 #65)
+#63 := (iff #42 #62)
+#60 := (iff #16 #57)
+#47 := (if #55 #13 #15)
+#58 := (iff #47 #57)
+#59 := [rewrite]: #58
+#49 := (iff #16 #47)
+#50 := (iff #11 #55)
+#51 := [rewrite]: #50
+#56 := [monotonicity #51]: #49
+#61 := [trans #56 #59]: #60
+#64 := [monotonicity #61]: #63
+#67 := [monotonicity #64]: #66
+#19 := (iff #16 #18)
+#20 := (not #19)
+#44 := (iff #20 #43)
+#45 := [rewrite]: #44
+#41 := [asserted]: #20
+#48 := [mp #41 #45]: #43
+#68 := [mp #48 #67]: #65
+#103 := (not #65)
+#108 := (or #57 #18 #103)
+#109 := [def-axiom]: #108
+#111 := [unit-resolution #109 #68]: #110
+#115 := [unit-resolution #111 #112]: #18
+#94 := (not #18)
+#97 := (or #94 #8 #15)
+#98 := [def-axiom]: #97
+#116 := [unit-resolution #98 #113 #115]: #15
+#79 := (not #15)
+#80 := (or #57 #55 #79)
+#81 := [def-axiom]: #80
+#117 := [unit-resolution #81 #116 #114 #112]: false
+#119 := [lemma #117]: #118
+#120 := [unit-resolution #119 #112]: #8
+#121 := [hypothesis]: #10
+#73 := (or #55 #52 #53)
+#74 := [def-axiom]: #73
+#122 := [unit-resolution #74 #121 #120]: #55
+#95 := (or #94 #52 #17)
+#96 := [def-axiom]: #95
+#123 := [unit-resolution #96 #120 #115]: #17
+#85 := (not #17)
+#86 := (or #85 #53 #13)
+#87 := [def-axiom]: #86
+#124 := [unit-resolution #87 #121 #123]: #13
+#82 := (not #13)
+#83 := (or #57 #54 #82)
+#84 := [def-axiom]: #83
+#125 := [unit-resolution #84 #124 #122 #112]: false
+#127 := [lemma #125]: #126
+#128 := [unit-resolution #127 #112]: #53
+#71 := (or #54 #10)
+#72 := [def-axiom]: #71
+#129 := [unit-resolution #72 #128]: #54
+#88 := (or #85 #10 #15)
+#89 := [def-axiom]: #88
+#130 := [unit-resolution #89 #128 #123]: #15
+#131 := [unit-resolution #81 #130 #129 #112]: false
+#132 := [lemma #131]: #57
+#133 := [hypothesis]: #55
+#134 := [unit-resolution #72 #133]: #10
+#77 := (or #62 #54 #13)
+#78 := [def-axiom]: #77
+#135 := [unit-resolution #78 #133 #132]: #13
+#106 := (or #62 #94)
+#104 := (or #62 #94 #103)
+#105 := [def-axiom]: #104
+#107 := [unit-resolution #105 #68]: #106
+#136 := [unit-resolution #107 #132]: #94
+#137 := [unit-resolution #70 #133]: #8
+#99 := (or #18 #52 #85)
+#100 := [def-axiom]: #99
+#138 := [unit-resolution #100 #137 #136]: #85
+#90 := (or #17 #53 #82)
+#91 := [def-axiom]: #90
+#139 := [unit-resolution #91 #138 #135 #134]: false
+#140 := [lemma #139]: #54
+#75 := (or #62 #55 #15)
+#76 := [def-axiom]: #75
+#141 := [unit-resolution #76 #140 #132]: #15
+#101 := (or #18 #8 #79)
+#102 := [def-axiom]: #101
+#142 := [unit-resolution #102 #141 #136]: #8
+#143 := [unit-resolution #100 #142 #136]: #85
+#144 := [unit-resolution #74 #142 #140]: #53
+#92 := (or #17 #10 #79)
+#93 := [def-axiom]: #92
+[unit-resolution #93 #144 #143 #141]: false
+unsat
+addce7e2dc4a26b8ce7ed621258f4ce1254da3f8 144 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+decl f6 :: S1
+#13 := f6
+#14 := (= f6 f1)
+decl f5 :: S1
+#11 := f5
+#12 := (= f5 f1)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#15 := (if #10 #12 #14)
+#44 := (not #8)
+#45 := (or #44 #15)
+#66 := (not #45)
+#54 := (or #44 #14)
+#51 := (or #44 #12)
+#48 := (or #44 #10)
+#57 := (if #48 #51 #54)
+#113 := (not #57)
+#131 := [hypothesis]: #113
+#129 := (or #45 #57)
+#67 := (iff #66 #57)
+#19 := (implies #8 #14)
+#18 := (implies #8 #12)
+#17 := (implies #8 #10)
+#20 := (if #17 #18 #19)
+#16 := (implies #8 #15)
+#21 := (iff #16 #20)
+#22 := (not #21)
+#70 := (iff #22 #67)
+#60 := (iff #45 #57)
+#63 := (not #60)
+#68 := (iff #63 #67)
+#69 := [rewrite]: #68
+#64 := (iff #22 #63)
+#61 := (iff #21 #60)
+#58 := (iff #20 #57)
+#55 := (iff #19 #54)
+#56 := [rewrite]: #55
+#52 := (iff #18 #51)
+#53 := [rewrite]: #52
+#49 := (iff #17 #48)
+#50 := [rewrite]: #49
+#59 := [monotonicity #50 #53 #56]: #58
+#46 := (iff #16 #45)
+#47 := [rewrite]: #46
+#62 := [monotonicity #47 #59]: #61
+#65 := [monotonicity #62]: #64
+#71 := [trans #65 #69]: #70
+#43 := [asserted]: #22
+#74 := [mp #43 #71]: #67
+#122 := (not #67)
+#127 := (or #45 #57 #122)
+#128 := [def-axiom]: #127
+#130 := [unit-resolution #128 #74]: #129
+#132 := [unit-resolution #130 #131]: #45
+#103 := (not #51)
+#142 := (or #54 #57)
+#110 := (not #54)
+#133 := [hypothesis]: #110
+#106 := (or #54 #8)
+#107 := [def-axiom]: #106
+#134 := [unit-resolution #107 #133]: #8
+#90 := (or #66 #44 #15)
+#91 := [def-axiom]: #90
+#135 := [unit-resolution #91 #134 #132]: #15
+#83 := (not #14)
+#108 := (or #54 #83)
+#109 := [def-axiom]: #108
+#136 := [unit-resolution #109 #133]: #83
+#78 := (not #15)
+#76 := (or #78 #10 #14)
+#77 := [def-axiom]: #76
+#137 := [unit-resolution #77 #136 #135]: #10
+#79 := (not #10)
+#94 := (or #48 #79)
+#95 := [def-axiom]: #94
+#138 := [unit-resolution #95 #137]: #48
+#80 := (or #78 #79 #12)
+#81 := [def-axiom]: #80
+#139 := [unit-resolution #81 #137 #135]: #12
+#73 := (not #12)
+#101 := (or #51 #73)
+#102 := [def-axiom]: #101
+#140 := [unit-resolution #102 #139]: #51
+#96 := (not #48)
+#118 := (or #57 #96 #103)
+#119 := [def-axiom]: #118
+#141 := [unit-resolution #119 #140 #138 #131]: false
+#143 := [lemma #141]: #142
+#144 := [unit-resolution #143 #131]: #54
+#120 := (or #57 #48 #110)
+#121 := [def-axiom]: #120
+#145 := [unit-resolution #121 #144 #131]: #48
+#146 := [unit-resolution #119 #145 #131]: #103
+#99 := (or #51 #8)
+#100 := [def-axiom]: #99
+#147 := [unit-resolution #100 #146]: #8
+#148 := [unit-resolution #91 #147 #132]: #15
+#149 := [unit-resolution #102 #146]: #73
+#97 := (or #96 #44 #10)
+#98 := [def-axiom]: #97
+#150 := [unit-resolution #98 #147 #145]: #10
+#151 := [unit-resolution #81 #150 #149 #148]: false
+#152 := [lemma #151]: #57
+#125 := (or #66 #113)
+#123 := (or #66 #113 #122)
+#124 := [def-axiom]: #123
+#126 := [unit-resolution #124 #74]: #125
+#153 := [unit-resolution #126 #152]: #66
+#86 := (or #45 #8)
+#87 := [def-axiom]: #86
+#154 := [unit-resolution #87 #153]: #8
+#88 := (or #45 #78)
+#89 := [def-axiom]: #88
+#157 := [unit-resolution #89 #153]: #78
+#155 := [hypothesis]: #79
+#156 := [unit-resolution #98 #155 #154]: #96
+#84 := (or #15 #10 #83)
+#85 := [def-axiom]: #84
+#158 := [unit-resolution #85 #155 #157]: #83
+#111 := (or #110 #44 #14)
+#112 := [def-axiom]: #111
+#159 := [unit-resolution #112 #158 #154]: #110
+#116 := (or #113 #48 #54)
+#117 := [def-axiom]: #116
+#160 := [unit-resolution #117 #159 #156 #152]: false
+#161 := [lemma #160]: #10
+#75 := (or #15 #79 #73)
+#82 := [def-axiom]: #75
+#162 := [unit-resolution #82 #161 #157]: #73
+#163 := [unit-resolution #95 #161]: #48
+#114 := (or #113 #96 #51)
+#115 := [def-axiom]: #114
+#164 := [unit-resolution #115 #163 #152]: #51
+#104 := (or #103 #44 #12)
+#105 := [def-axiom]: #104
+[unit-resolution #105 #164 #162 #154]: false
+unsat
+3805a38de71c30eca319b0409c21700a7cb06990 22 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#9 := (not #8)
+#10 := (if #8 #8 #9)
+#11 := (not #10)
+#40 := (iff #11 false)
+#1 := true
+#35 := (not true)
+#38 := (iff #35 false)
+#39 := [rewrite]: #38
+#36 := (iff #11 #35)
+#33 := (iff #10 true)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#41 := [trans #37 #39]: #40
+#32 := [asserted]: #11
+[mp #32 #41]: false
+unsat
+10863ac83131ef76f72a772c8cf85cc3dc6dde68 22 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#9 := (not #8)
+#10 := (if #9 #9 #8)
+#11 := (not #10)
+#40 := (iff #11 false)
+#1 := true
+#35 := (not true)
+#38 := (iff #35 false)
+#39 := [rewrite]: #38
+#36 := (iff #11 #35)
+#33 := (iff #10 true)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#41 := [trans #37 #39]: #40
+#32 := [asserted]: #11
+[mp #32 #41]: false
+unsat
+07351d51d95fc2b79e016724eb51f565136165bb 18 0
+#2 := false
+decl f3 :: S2
+#7 := f3
+#8 := (= f3 f3)
+#9 := (not #8)
+#38 := (iff #9 false)
+#1 := true
+#33 := (not true)
+#36 := (iff #33 false)
 #37 := [rewrite]: #36
-#40 := [quant-intro #37]: #39
+#34 := (iff #9 #33)
+#31 := (iff #8 true)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#30 := [asserted]: #9
+[mp #30 #39]: false
+unsat
+560c329fd96a3052b170500832713e5713a0d957 28 0
+#2 := false
+decl f3 :: S2
+#7 := f3
+decl f4 :: S2
+#8 := f4
+#10 := (= f4 f3)
+#9 := (= f3 f4)
+#54 := (iff #9 #10)
+#52 := (iff #10 #9)
+#53 := [commutativity]: #52
+#55 := [symm #53]: #54
+#34 := (not #9)
+#35 := (or #34 #10)
+#38 := (not #35)
+#11 := (implies #9 #10)
+#12 := (not #11)
+#39 := (iff #12 #38)
+#36 := (iff #11 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#33 := [asserted]: #12
+#43 := [mp #33 #40]: #38
+#41 := [not-or-elim #43]: #9
+#50 := [mp #41 #55]: #10
+#42 := (not #10)
+#44 := [not-or-elim #43]: #42
+[unit-resolution #44 #50]: false
+unsat
+0ea41c66095cc88193b1f1c4879ce9546452087f 34 0
+#2 := false
+decl f5 :: S2
+#10 := f5
+decl f3 :: S2
+#7 := f3
+#13 := (= f3 f5)
+decl f4 :: S2
+#8 := f4
+#11 := (= f4 f5)
+#61 := (iff #11 #13)
+#59 := (iff #13 #11)
+#9 := (= f3 f4)
+#12 := (and #9 #11)
+#37 := (not #12)
+#38 := (or #37 #13)
+#41 := (not #38)
+#14 := (implies #12 #13)
+#15 := (not #14)
+#42 := (iff #15 #41)
+#39 := (iff #14 #38)
+#40 := [rewrite]: #39
 #43 := [monotonicity #40]: #42
-#46 := [monotonicity #40 #40 #43]: #45
-#50 := [trans #46 #48]: #49
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#34 := [asserted]: #14
-[mp #34 #57]: false
-unsat
-e82a6cc10c3ef4d2130dbd751caaaa2ceb41a37f 138 0
-#2 := false
+#36 := [asserted]: #15
+#46 := [mp #36 #43]: #41
+#44 := [not-or-elim #46]: #12
+#45 := [and-elim #44]: #9
+#60 := [monotonicity #45]: #59
+#62 := [symm #60]: #61
+#47 := [and-elim #44]: #11
+#57 := [mp #47 #62]: #13
+#48 := (not #13)
+#49 := [not-or-elim #46]: #48
+[unit-resolution #49 #57]: false
+unsat
+aa496f11d9d656ea523f5c18607a0927eb3d7a4a 27 0
+#2 := false
+decl f5 :: (-> S2 S2)
+decl f4 :: S2
+#8 := f4
+#11 := (f5 f4)
+decl f3 :: S2
+#7 := f3
+#10 := (f5 f3)
+#12 := (= #10 #11)
+#9 := (= f3 f4)
+#36 := (not #9)
+#37 := (or #36 #12)
+#40 := (not #37)
+#13 := (implies #9 #12)
+#14 := (not #13)
+#41 := (iff #14 #40)
+#38 := (iff #13 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#35 := [asserted]: #14
+#45 := [mp #35 #42]: #40
+#43 := [not-or-elim #45]: #9
+#54 := [monotonicity #43]: #12
+#44 := (not #12)
+#46 := [not-or-elim #45]: #44
+[unit-resolution #46 #54]: false
+unsat
+8b4dbc6c33c1705fe009e2d7608ca932d6b53399 31 0
+#2 := false
+decl f5 :: (-> S2 S2 S3)
+decl f3 :: S2
+#7 := f3
+decl f4 :: S2
+#8 := f4
+#11 := (f5 f4 f3)
+#10 := (f5 f3 f4)
+#12 := (= #10 #11)
+#56 := (= #11 #10)
+#9 := (= f3 f4)
+#36 := (not #9)
+#37 := (or #36 #12)
+#40 := (not #37)
+#13 := (implies #9 #12)
+#14 := (not #13)
+#41 := (iff #14 #40)
+#38 := (iff #13 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#35 := [asserted]: #14
+#45 := [mp #35 #42]: #40
+#43 := [not-or-elim #45]: #9
+#54 := (= f4 f3)
+#55 := [symm #43]: #54
+#57 := [monotonicity #55 #43]: #56
+#52 := [symm #57]: #12
+#44 := (not #12)
+#46 := [not-or-elim #45]: #44
+[unit-resolution #46 #52]: false
+unsat
+45c0bd6cde55221dd5a9503ffdc9267b7373c6c9 44 0
+#2 := false
+decl f4 :: S2
+#7 := f4
+decl f3 :: (-> S2 S2)
+#8 := (f3 f4)
+#16 := (= #8 f4)
+#9 := (f3 #8)
+#11 := (f3 #9)
+#12 := (f3 #11)
+#13 := (f3 #12)
+#14 := (= #13 f4)
+#10 := (= #9 f4)
+#15 := (and #10 #14)
+#40 := (not #15)
+#41 := (or #40 #16)
+#44 := (not #41)
+#17 := (implies #15 #16)
+#18 := (not #17)
+#45 := (iff #18 #44)
+#42 := (iff #17 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#39 := [asserted]: #18
+#49 := [mp #39 #46]: #44
+#47 := [not-or-elim #49]: #15
+#50 := [and-elim #47]: #14
+#54 := (= #8 #13)
+#56 := (= f4 #12)
+#58 := (= #9 #12)
+#64 := (= #12 #9)
+#62 := (= #11 #8)
+#48 := [and-elim #47]: #10
+#63 := [monotonicity #48]: #62
+#65 := [monotonicity #63]: #64
+#59 := [symm #65]: #58
+#60 := (= f4 #9)
+#61 := [symm #48]: #60
+#57 := [trans #61 #59]: #56
+#55 := [monotonicity #57]: #54
+#66 := [trans #55 #50]: #16
+#51 := (not #16)
+#52 := [not-or-elim #49]: #51
+[unit-resolution #52 #66]: false
+unsat
+25a1abffb915b82d17c18374398b74c5d385ed65 137 0
+#2 := false
+decl f6 :: S2
+#12 := f6
+decl f5 :: S2
+#10 := f5
 decl f4 :: S2
 #9 := f4
-decl f3 :: S2
-#8 := f3
-#152 := (= f3 f4)
-decl inj!0 :: (-> S3 S2)
-decl f6 :: (-> S2 S3)
-#22 := (f6 f4)
-#207 := (inj!0 #22)
-#208 := (= #207 f4)
-#209 := (= f4 #207)
-#14 := (:var 0 S2)
-#15 := (f6 #14)
-#89 := (pattern #15)
-#88 := (inj!0 #15)
-#85 := (= #88 #14)
-#570 := (forall (vars (k!0 S2)) (:pat #89) #85)
-#90 := (forall (vars (k!0 S2)) (:pat #89) #85)
-#571 := (iff #90 #570)
-#573 := (iff #570 #570)
-#574 := [rewrite]: #573
-#572 := [rewrite]: #571
-#575 := [trans #572 #574]: #571
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#11 := (if #8 f4 f5)
+#13 := (= #11 f6)
+#17 := (= f5 f6)
+#46 := (or #8 #17)
+#71 := (not #46)
+#14 := (= f4 f6)
+#16 := (not #8)
+#43 := (or #16 #14)
+#70 := (not #43)
+#72 := (or #70 #71)
+#116 := [hypothesis]: #71
+#103 := (or #72 #46)
+#104 := [def-axiom]: #103
+#118 := [unit-resolution #104 #116]: #72
+#73 := (not #72)
+#110 := (or #13 #73)
+#75 := (iff #13 #72)
+#49 := (and #43 #46)
+#58 := (not #13)
+#59 := (iff #58 #49)
+#78 := (iff #59 #75)
+#65 := (iff #58 #73)
+#76 := (iff #65 #75)
+#77 := [rewrite]: #76
+#67 := (iff #59 #65)
+#68 := (iff #49 #73)
+#69 := [rewrite]: #68
+#74 := [monotonicity #69]: #67
+#79 := [trans #74 #77]: #78
+#18 := (implies #16 #17)
+#15 := (implies #8 #14)
+#19 := (and #15 #18)
+#20 := (iff #13 #19)
+#21 := (not #20)
+#62 := (iff #21 #59)
+#52 := (iff #13 #49)
+#55 := (not #52)
+#60 := (iff #55 #59)
+#61 := [rewrite]: #60
+#56 := (iff #21 #55)
+#53 := (iff #20 #52)
+#50 := (iff #19 #49)
+#47 := (iff #18 #46)
+#48 := [rewrite]: #47
+#44 := (iff #15 #43)
+#45 := [rewrite]: #44
+#51 := [monotonicity #45 #48]: #50
+#54 := [monotonicity #51]: #53
+#57 := [monotonicity #54]: #56
+#63 := [trans #57 #61]: #62
+#42 := [asserted]: #21
+#66 := [mp #42 #63]: #59
+#80 := [mp #66 #79]: #75
+#107 := (not #75)
+#108 := (or #13 #73 #107)
+#109 := [def-axiom]: #108
+#111 := [unit-resolution #109 #80]: #110
+#119 := [unit-resolution #111 #118]: #13
+#82 := (= f5 #11)
+#94 := (or #46 #16)
+#95 := [def-axiom]: #94
+#120 := [unit-resolution #95 #116]: #16
+#85 := (or #8 #82)
+#86 := [def-axiom]: #85
+#121 := [unit-resolution #86 #120]: #82
+#122 := [trans #121 #119]: #17
+#96 := (not #17)
+#97 := (or #46 #96)
+#98 := [def-axiom]: #97
+#117 := [unit-resolution #98 #116]: #96
+#123 := [unit-resolution #117 #122]: false
+#124 := [lemma #123]: #46
+#133 := (iff #13 #14)
+#131 := (iff #14 #13)
+#81 := (= f4 #11)
+#125 := [hypothesis]: #8
+#83 := (or #16 #81)
+#84 := [def-axiom]: #83
+#130 := [unit-resolution #84 #125]: #81
+#132 := [monotonicity #130]: #131
+#134 := [symm #132]: #133
+#139 := (or #72 #16)
+#89 := (not #14)
+#135 := (iff #58 #89)
+#136 := [monotonicity #134]: #135
+#126 := [hypothesis]: #73
+#114 := (or #58 #72)
+#112 := (or #58 #72 #107)
+#113 := [def-axiom]: #112
+#115 := [unit-resolution #113 #80]: #114
+#129 := [unit-resolution #115 #126]: #58
+#137 := [mp #129 #136]: #89
+#101 := (or #72 #43)
+#102 := [def-axiom]: #101
+#127 := [unit-resolution #102 #126]: #43
+#92 := (or #70 #16 #14)
+#93 := [def-axiom]: #92
+#128 := [unit-resolution #93 #127 #125]: #14
+#138 := [unit-resolution #128 #137]: false
+#140 := [lemma #138]: #139
+#141 := [unit-resolution #140 #125]: #72
+#144 := [unit-resolution #111 #141]: #13
+#145 := [mp #144 #134]: #14
+#105 := (or #73 #70 #71)
+#106 := [def-axiom]: #105
+#142 := [unit-resolution #106 #141 #124]: #70
+#90 := (or #43 #89)
+#91 := [def-axiom]: #90
+#143 := [unit-resolution #91 #142]: #89
+#146 := [unit-resolution #143 #145]: false
+#147 := [lemma #146]: #16
+#99 := (or #71 #8 #17)
+#100 := [def-axiom]: #99
+#152 := [unit-resolution #100 #147 #124]: #17
+#155 := (= #11 f5)
+#151 := [unit-resolution #86 #147]: #82
+#156 := [symm #151]: #155
+#157 := [trans #156 #152]: #13
+#87 := (or #43 #8)
+#88 := [def-axiom]: #87
+#148 := [unit-resolution #88 #147]: #43
+#149 := [unit-resolution #106 #148 #124]: #73
+#150 := [unit-resolution #115 #149]: #58
+[unit-resolution #150 #157]: false
+unsat
+67737c4b09a83cd04939395b326a7d8f955a194d 25 0
+#2 := false
+#7 := (:var 0 S2)
+#8 := (= #7 #7)
+#9 := (forall (vars (?v0 S2)) #8)
+#10 := (not #9)
+#46 := (iff #10 false)
+#1 := true
+#41 := (not true)
+#44 := (iff #41 false)
+#45 := [rewrite]: #44
+#42 := (iff #10 #41)
+#39 := (iff #9 true)
+#34 := (forall (vars (?v0 S2)) true)
+#37 := (iff #34 true)
+#38 := [elim-unused]: #37
+#35 := (iff #9 #34)
+#32 := (iff #8 true)
+#33 := [rewrite]: #32
+#36 := [quant-intro #33]: #35
+#40 := [trans #36 #38]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#31 := [asserted]: #10
+[mp #31 #47]: false
+unsat
+46c9d6a29d282ccf0878986fd29578adc8a38dd4 23 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#9 := (= #8 f1)
+#10 := (forall (vars (?v0 S2)) #9)
+#11 := (iff #10 #10)
+#12 := (not #11)
+#41 := (iff #12 false)
+#1 := true
+#36 := (not true)
+#39 := (iff #36 false)
+#40 := [rewrite]: #39
+#37 := (iff #12 #36)
+#34 := (iff #11 true)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#42 := [trans #38 #40]: #41
+#33 := [asserted]: #12
+[mp #33 #42]: false
+unsat
+5ba00f30800797eb07b09f84e102de0c826f49ed 67 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+decl ?v0!0 :: S2
+#55 := ?v0!0
+#56 := (f3 ?v0!0)
+#57 := (= #56 f1)
+#58 := (not #57)
+decl ?v1!1 :: S2
+#66 := ?v1!1
+#67 := (f3 ?v1!1)
+#68 := (= #67 f1)
+#69 := (or #57 #68)
+#70 := (not #69)
+#86 := (and #57 #70)
+#63 := (not #58)
+#76 := (and #63 #70)
+#87 := (iff #76 #86)
+#84 := (iff #63 #57)
+#85 := [rewrite]: #84
+#88 := [monotonicity #85]: #87
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#9 := (= #8 f1)
+#10 := (:var 1 S2)
+#11 := (f3 #10)
+#12 := (= #11 f1)
+#13 := (or #12 #9)
+#14 := (forall (vars (?v1 S2)) #13)
+#39 := (not #9)
+#40 := (or #39 #14)
+#43 := (forall (vars (?v0 S2)) #40)
+#46 := (not #43)
+#79 := (~ #46 #76)
+#50 := (or #57 #9)
+#52 := (forall (vars (?v1 S2)) #50)
+#59 := (or #58 #52)
+#60 := (not #59)
+#77 := (~ #60 #76)
+#71 := (not #52)
+#72 := (~ #71 #70)
+#73 := [sk]: #72
+#64 := (~ #63 #63)
+#65 := [refl]: #64
+#78 := [nnf-neg #65 #73]: #77
+#61 := (~ #46 #60)
+#62 := [sk]: #61
+#80 := [trans #62 #78]: #79
+#15 := (implies #9 #14)
+#16 := (forall (vars (?v0 S2)) #15)
+#17 := (not #16)
+#47 := (iff #17 #46)
+#44 := (iff #16 #43)
+#41 := (iff #15 #40)
+#42 := [rewrite]: #41
+#45 := [quant-intro #42]: #44
+#48 := [monotonicity #45]: #47
+#38 := [asserted]: #17
+#51 := [mp #38 #48]: #46
+#81 := [mp~ #51 #80]: #76
+#82 := [mp #81 #88]: #86
+#89 := [and-elim #82]: #70
+#90 := [not-or-elim #89]: #58
+#83 := [and-elim #82]: #57
+[unit-resolution #83 #90]: false
+unsat
+c2ff93c1c8c2d33d86971297c56d2ab2a9dc9fb6 235 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+decl ?v0!2 :: S2
+#87 := ?v0!2
+#88 := (f3 ?v0!2)
+#89 := (= #88 f1)
+#124 := (not #89)
+decl ?v0!0 :: S2
+#50 := ?v0!0
+#51 := (f3 ?v0!0)
+#52 := (= #51 f1)
+#53 := (not #52)
+#216 := [hypothesis]: #53
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#624 := (pattern #8)
+#9 := (= #8 f1)
+#631 := (forall (vars (?v0 S2)) (:pat #624) #9)
+decl f4 :: (-> S2 S1)
+#10 := (f4 #7)
+#625 := (pattern #10)
+#11 := (= #10 f1)
+#639 := (forall (vars (?v0 S2)) (:pat #625) #11)
+#644 := (not #639)
+#636 := (not #631)
+#647 := (or #636 #644)
+#650 := (not #647)
+#56 := (not #11)
+#55 := (not #9)
+#64 := (or #55 #56)
+#65 := (not #64)
+#626 := (forall (vars (?v0 S2)) (:pat #624 #625) #65)
+#618 := (not #626)
+#249 := (f4 ?v0!0)
+#610 := (= #249 f1)
+#608 := (not #610)
+#611 := (or #53 #608)
+#90 := (f4 ?v0!2)
+#91 := (= #90 f1)
+#125 := (not #91)
+#126 := (or #124 #125)
+#127 := (not #126)
+#285 := [hypothesis]: #626
+#273 := (or #127 #618)
+#612 := [hypothesis]: #126
+#274 := (or #618 #127)
+#405 := [quant-inst #87]: #274
+#614 := [unit-resolution #405 #285 #612]: false
+#615 := [lemma #614]: #273
+#598 := [unit-resolution #615 #285]: #127
+#620 := (or #126 #89)
+#621 := [def-axiom]: #620
+#305 := [unit-resolution #621 #598]: #89
+#287 := [hypothesis]: #125
+#286 := (or #126 #91)
+#619 := [def-axiom]: #286
+#280 := [unit-resolution #619 #287]: #126
+#299 := (or #644 #91)
+#298 := [hypothesis]: #639
+#300 := [quant-inst #87]: #299
+#297 := [unit-resolution #300 #298 #287]: false
+#301 := [lemma #297]: #299
+#616 := [unit-resolution #301 #287]: #644
+#209 := (or #647 #639)
+#295 := [def-axiom]: #209
+#622 := [unit-resolution #295 #616]: #647
+#653 := (or #626 #650)
+#15 := (forall (vars (?v0 S2)) #11)
+#61 := (not #15)
+#14 := (forall (vars (?v0 S2)) #9)
+#45 := (not #14)
+#116 := (or #45 #61)
+#117 := (not #116)
+#113 := (forall (vars (?v0 S2)) #65)
+#120 := (or #113 #117)
+#654 := (iff #120 #653)
+#651 := (iff #117 #650)
+#648 := (iff #116 #647)
+#645 := (iff #61 #644)
+#642 := (iff #15 #639)
+#640 := (iff #11 #11)
+#641 := [refl]: #640
+#643 := [quant-intro #641]: #642
+#646 := [monotonicity #643]: #645
+#637 := (iff #45 #636)
+#634 := (iff #14 #631)
+#632 := (iff #9 #9)
+#633 := [refl]: #632
+#635 := [quant-intro #633]: #634
+#638 := [monotonicity #635]: #637
+#649 := [monotonicity #638 #646]: #648
+#652 := [monotonicity #649]: #651
+#629 := (iff #113 #626)
+#627 := (iff #65 #65)
+#628 := [refl]: #627
+#630 := [quant-intro #628]: #629
+#655 := [monotonicity #630 #652]: #654
+#16 := (and #14 #15)
+#12 := (and #9 #11)
+#13 := (forall (vars (?v0 S2)) #12)
+#99 := (or #13 #16)
+#121 := (iff #99 #120)
+#118 := (iff #16 #117)
+#119 := [rewrite]: #118
+#114 := (iff #13 #113)
+#96 := (iff #12 #65)
+#97 := [rewrite]: #96
+#115 := [quant-intro #97]: #114
+#122 := [monotonicity #115 #119]: #121
+decl ?v0!1 :: S2
+#57 := ?v0!1
+#58 := (f4 ?v0!1)
+#59 := (= #58 f1)
+#60 := (not #59)
+#92 := (and #89 #91)
+#93 := (not #92)
+#106 := (or #93 #53 #60)
+#109 := (and #99 #106)
+#66 := (or #53 #60)
+#98 := (or #93 #66)
+#100 := (and #99 #98)
+#110 := (iff #100 #109)
+#107 := (iff #98 #106)
+#108 := [rewrite]: #107
+#111 := [monotonicity #108]: #110
+#40 := (not #13)
+#41 := (iff #40 #16)
+#101 := (~ #41 #100)
+#78 := (~ #16 #16)
+#76 := (~ #15 #15)
+#74 := (~ #11 #11)
+#75 := [refl]: #74
+#77 := [nnf-pos #75]: #76
+#72 := (~ #14 #14)
+#70 := (~ #9 #9)
+#71 := [refl]: #70
+#73 := [nnf-pos #71]: #72
+#79 := [monotonicity #73 #77]: #78
+#67 := (not #16)
+#68 := (~ #67 #66)
+#62 := (~ #61 #60)
+#63 := [sk]: #62
+#47 := (~ #45 #53)
+#54 := [sk]: #47
+#69 := [nnf-neg #54 #63]: #68
+#94 := (~ #40 #93)
+#95 := [sk]: #94
+#84 := (not #40)
+#85 := (~ #84 #13)
+#82 := (~ #13 #13)
+#80 := (~ #12 #12)
+#81 := [refl]: #80
+#83 := [nnf-pos #81]: #82
+#86 := [nnf-neg #83]: #85
+#102 := [nnf-pos #86 #95 #69 #79]: #101
+#17 := (iff #13 #16)
+#18 := (not #17)
+#42 := (iff #18 #41)
+#43 := [rewrite]: #42
+#39 := [asserted]: #18
+#46 := [mp #39 #43]: #41
+#103 := [mp~ #46 #102]: #100
+#104 := [mp #103 #111]: #109
+#105 := [and-elim #104]: #99
+#123 := [mp #105 #122]: #120
+#656 := [mp #123 #655]: #653
+#617 := [unit-resolution #656 #622]: #626
+#623 := [unit-resolution #405 #617 #280]: false
+#613 := [lemma #623]: #91
+#257 := (f3 ?v0!1)
+#599 := (= #257 f1)
+#261 := (not #599)
+#262 := (or #261 #60)
+#263 := (not #262)
+#609 := (or #263 #618)
+#264 := [hypothesis]: #262
+#602 := (or #618 #263)
+#603 := [quant-inst #57]: #602
+#601 := [unit-resolution #603 #285 #264]: false
+#248 := [lemma #601]: #609
+#317 := [unit-resolution #248 #285]: #263
+#600 := (or #262 #59)
+#606 := [def-axiom]: #600
+#591 := [unit-resolution #606 #317]: #59
+#140 := (or #124 #125 #53 #60)
+#143 := (iff #106 #140)
+#137 := (or #126 #53 #60)
+#141 := (iff #137 #140)
+#142 := [rewrite]: #141
+#138 := (iff #106 #137)
+#135 := (iff #93 #126)
+#130 := (not #127)
+#133 := (iff #130 #126)
+#134 := [rewrite]: #133
+#131 := (iff #93 #130)
+#128 := (iff #92 #127)
+#129 := [rewrite]: #128
+#132 := [monotonicity #129]: #131
+#136 := [trans #132 #134]: #135
+#139 := [monotonicity #136]: #138
+#144 := [trans #139 #142]: #143
+#112 := [and-elim #104]: #106
+#145 := [mp #112 #144]: #140
+#595 := [unit-resolution #145 #591 #613 #305]: #53
+#322 := (or #611 #52)
+#323 := [def-axiom]: #322
+#592 := [unit-resolution #323 #595]: #611
+#597 := (not #611)
+#320 := (or #618 #597)
+#321 := [quant-inst #50]: #320
+#596 := [unit-resolution #321 #285 #592]: false
+#306 := [lemma #596]: #618
+#593 := [unit-resolution #656 #306]: #650
+#208 := (or #647 #631)
+#294 := [def-axiom]: #208
+#307 := [unit-resolution #294 #593]: #631
+#594 := (or #636 #52)
+#316 := [quant-inst #50]: #594
+#308 := [unit-resolution #316 #307 #216]: false
+#309 := [lemma #308]: #52
+#587 := [hypothesis]: #60
+#588 := [unit-resolution #295 #593]: #639
+#302 := (or #644 #59)
+#585 := [quant-inst #57]: #302
+#589 := [unit-resolution #585 #588 #587]: false
+#586 := [lemma #589]: #59
+#590 := (or #124 #53 #60)
+#579 := [unit-resolution #145 #613]: #590
+#576 := [unit-resolution #579 #586 #309]: #124
+#580 := (or #636 #89)
+#581 := [quant-inst #87]: #580
+[unit-resolution #581 #307 #576]: false
+unsat
+5190783c8781fcea24c1c610b455b71cf0eb75c2 145 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+decl ?v0!1 :: S2
+#72 := ?v0!1
+#73 := (f3 ?v0!1)
+#74 := (= #73 f1)
+#75 := (not #74)
+decl f4 :: S1
+#11 := f4
+#12 := (= f4 f1)
+#55 := (or #74 #12)
+#56 := (not #55)
+decl ?v0!0 :: S2
+#49 := ?v0!0
+#50 := (f3 ?v0!0)
+#51 := (= #50 f1)
+#52 := (or #51 #12)
+#247 := (not #51)
+#44 := (not #52)
+#579 := [hypothesis]: #44
+#258 := (or #52 #247)
+#259 := [def-axiom]: #258
+#580 := [unit-resolution #259 #579]: #247
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#584 := (pattern #8)
+#9 := (= #8 f1)
+#14 := (or #9 #12)
+#590 := (forall (vars (?v0 S2)) (:pat #584) #14)
+#81 := (not #12)
+#260 := (or #52 #81)
+#257 := [def-axiom]: #260
+#574 := [unit-resolution #257 #579]: #81
+#585 := (forall (vars (?v0 S2)) (:pat #584) #9)
+#234 := (not #585)
+#365 := (or #234 #51)
+#576 := [hypothesis]: #247
+#578 := [hypothesis]: #585
+#572 := [quant-inst #49]: #365
+#245 := [unit-resolution #572 #578 #576]: false
+#246 := [lemma #245]: #365
+#233 := [unit-resolution #246 #580]: #234
+#595 := (or #585 #12 #590)
+#15 := (forall (vars (?v0 S2)) #14)
+#10 := (forall (vars (?v0 S2)) #9)
+#95 := (or #10 #12 #15)
+#596 := (iff #95 #595)
+#593 := (iff #15 #590)
+#591 := (iff #14 #14)
+#592 := [refl]: #591
+#594 := [quant-intro #592]: #593
+#588 := (iff #10 #585)
+#586 := (iff #9 #9)
+#587 := [refl]: #586
+#589 := [quant-intro #587]: #588
+#597 := [monotonicity #589 #594]: #596
+#84 := (and #75 #81)
+#87 := (or #84 #44)
+#98 := (and #95 #87)
+#13 := (or #10 #12)
+#88 := (or #13 #15)
+#89 := (and #88 #87)
+#99 := (iff #89 #98)
+#96 := (iff #88 #95)
+#97 := [rewrite]: #96
+#100 := [monotonicity #97]: #99
+#39 := (not #13)
+#40 := (iff #39 #15)
+#90 := (~ #40 #89)
+#59 := (~ #15 #15)
+#57 := (~ #14 #14)
+#58 := [refl]: #57
+#60 := [nnf-pos #58]: #59
+#46 := (not #15)
+#53 := (~ #46 #44)
+#54 := [sk]: #53
+#85 := (~ #39 #84)
+#82 := (~ #81 #81)
+#83 := [refl]: #82
+#76 := (not #10)
+#77 := (~ #76 #75)
+#78 := [sk]: #77
+#86 := [nnf-neg #78 #83]: #85
+#69 := (not #39)
+#70 := (~ #69 #13)
+#67 := (~ #13 #13)
+#65 := (~ #12 #12)
+#66 := [refl]: #65
+#63 := (~ #10 #10)
+#61 := (~ #9 #9)
+#62 := [refl]: #61
+#64 := [nnf-pos #62]: #63
+#68 := [monotonicity #64 #66]: #67
+#71 := [nnf-neg #68]: #70
+#91 := [nnf-pos #71 #86 #54 #60]: #90
+#16 := (iff #13 #15)
+#17 := (not #16)
+#41 := (iff #17 #40)
+#42 := [rewrite]: #41
+#38 := [asserted]: #17
+#45 := [mp #38 #42]: #40
+#92 := [mp~ #45 #91]: #89
+#93 := [mp #92 #100]: #98
+#94 := [and-elim #93]: #95
+#598 := [mp #94 #597]: #595
+#575 := [unit-resolution #598 #233 #574]: #590
+#581 := (not #590)
+#582 := (or #581 #51 #12)
+#577 := (or #581 #52)
+#573 := (iff #577 #582)
+#232 := [rewrite]: #573
+#583 := [quant-inst #49]: #577
+#237 := [mp #583 #232]: #582
+#217 := [unit-resolution #237 #574 #575 #580]: false
+#559 := [lemma #217]: #52
+#102 := (or #56 #44)
+#103 := (iff #87 #102)
+#79 := (iff #84 #56)
+#80 := [rewrite]: #79
+#104 := [monotonicity #80]: #103
+#101 := [and-elim #93]: #87
+#105 := [mp #101 #104]: #102
+#221 := [unit-resolution #105 #559]: #56
+#168 := (or #55 #75)
+#254 := [def-axiom]: #168
+#222 := [unit-resolution #254 #221]: #75
+#169 := (or #55 #81)
+#255 := [def-axiom]: #169
+#560 := [unit-resolution #255 #221]: #81
+#565 := [hypothesis]: #590
+#223 := (or #581 #74 #12)
+#224 := (or #581 #55)
+#562 := (iff #224 #223)
+#563 := [rewrite]: #562
+#561 := [quant-inst #72]: #224
+#564 := [mp #561 #563]: #223
+#566 := [unit-resolution #564 #560 #565 #222]: false
+#203 := [lemma #566]: #581
+#567 := [unit-resolution #598 #203 #560]: #585
+#208 := (or #234 #74)
+#209 := [quant-inst #72]: #208
+[unit-resolution #209 #567 #222]: false
+unsat
+53f53012b8ceb61c467342994ec79dc318df7837 189 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+decl ?v0!1 :: S2
+#75 := ?v0!1
+#76 := (f3 ?v0!1)
+#77 := (= #76 f1)
+#114 := (not #77)
+decl ?v0!0 :: S2
+#47 := ?v0!0
+#48 := (f3 ?v0!0)
+#49 := (= #48 f1)
+#50 := (not #49)
+#538 := [hypothesis]: #50
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#552 := (pattern #8)
+#9 := (= #8 f1)
+#553 := (forall (vars (?v0 S2)) (:pat #552) #9)
+decl f4 :: S1
+#11 := f4
+#12 := (= f4 f1)
+#54 := (not #12)
+#558 := (not #553)
+#561 := (or #558 #54)
+#564 := (not #561)
+#102 := (not #9)
+#103 := (or #102 #54)
+#104 := (not #103)
+#567 := (forall (vars (?v0 S2)) (:pat #552) #104)
+#213 := (not #567)
+#57 := (or #50 #54)
+decl elem!2 :: S2
+#228 := elem!2
+#546 := (f3 elem!2)
+#214 := (= #546 f1)
+#548 := (not #214)
+#549 := (or #548 #54)
+#540 := (not #549)
+#550 := [hypothesis]: #567
+#545 := (or #213 #540)
+#551 := [quant-inst #228]: #545
+#534 := [unit-resolution #551 #550]: #540
+#205 := (or #549 #12)
+#542 := [def-axiom]: #205
+#171 := [unit-resolution #542 #534]: #12
+#115 := (or #114 #54)
+#116 := (not #115)
+#532 := (or #116 #213)
+#547 := [hypothesis]: #115
+#185 := (or #213 #116)
+#527 := [quant-inst #75]: #185
+#531 := [unit-resolution #527 #550 #547]: false
+#533 := [lemma #531]: #532
+#526 := [unit-resolution #533 #550]: #116
+#189 := (or #115 #77)
+#190 := [def-axiom]: #189
+#233 := [unit-resolution #190 #526]: #77
+#129 := (or #50 #114 #54)
+#78 := (and #77 #12)
+#79 := (not #78)
+#91 := (or #50 #54 #79)
+#132 := (iff #91 #129)
+#126 := (or #50 #54 #115)
+#130 := (iff #126 #129)
+#131 := [rewrite]: #130
+#127 := (iff #91 #126)
+#124 := (iff #79 #115)
+#119 := (not #116)
+#122 := (iff #119 #115)
+#123 := [rewrite]: #122
+#120 := (iff #79 #119)
+#117 := (iff #78 #116)
+#118 := [rewrite]: #117
+#121 := [monotonicity #118]: #120
+#125 := [trans #121 #123]: #124
+#128 := [monotonicity #125]: #127
+#133 := [trans #128 #131]: #132
+#14 := (and #9 #12)
+#15 := (forall (vars (?v0 S2)) #14)
+#10 := (forall (vars (?v0 S2)) #9)
+#13 := (and #10 #12)
+#84 := (or #13 #15)
+#94 := (and #84 #91)
+#83 := (or #57 #79)
+#85 := (and #84 #83)
+#95 := (iff #85 #94)
+#92 := (iff #83 #91)
+#93 := [rewrite]: #92
+#96 := [monotonicity #93]: #95
+#23 := (not #13)
+#24 := (iff #23 #15)
+#86 := (~ #24 #85)
+#80 := (not #15)
+#81 := (~ #80 #79)
+#82 := [sk]: #81
+#73 := (~ #15 #15)
+#71 := (~ #14 #14)
+#72 := [refl]: #71
+#74 := [nnf-pos #72]: #73
+#68 := (not #23)
+#69 := (~ #68 #13)
+#66 := (~ #13 #13)
+#64 := (~ #12 #12)
+#65 := [refl]: #64
+#62 := (~ #10 #10)
+#60 := (~ #9 #9)
+#61 := [refl]: #60
+#63 := [nnf-pos #61]: #62
+#67 := [monotonicity #63 #65]: #66
+#70 := [nnf-neg #67]: #69
+#58 := (~ #23 #57)
+#55 := (~ #54 #54)
+#56 := [refl]: #55
+#51 := (not #10)
+#52 := (~ #51 #50)
+#53 := [sk]: #52
+#59 := [nnf-neg #53 #56]: #58
+#87 := [nnf-pos #59 #70 #74 #82]: #86
+#16 := (iff #13 #15)
+#17 := (not #16)
+#25 := (iff #17 #24)
+#26 := [rewrite]: #25
+#19 := [asserted]: #17
+#27 := [mp #19 #26]: #24
+#88 := [mp~ #27 #87]: #85
+#89 := [mp #88 #96]: #94
+#97 := [and-elim #89]: #91
+#134 := [mp #97 #133]: #129
+#248 := [unit-resolution #134 #233 #171]: #50
+#176 := (or #57 #49)
+#177 := [def-axiom]: #176
+#249 := [unit-resolution #177 #248]: #57
+#528 := (not #57)
+#535 := (or #213 #528)
+#537 := [quant-inst #47]: #535
+#250 := [unit-resolution #537 #550 #249]: false
+#251 := [lemma #250]: #213
+#572 := (or #564 #567)
+#107 := (forall (vars (?v0 S2)) #104)
+#98 := (or #51 #54)
+#99 := (not #98)
+#110 := (or #99 #107)
+#573 := (iff #110 #572)
+#570 := (iff #107 #567)
+#568 := (iff #104 #104)
+#569 := [refl]: #568
+#571 := [quant-intro #569]: #570
+#565 := (iff #99 #564)
+#562 := (iff #98 #561)
+#559 := (iff #51 #558)
+#556 := (iff #10 #553)
+#554 := (iff #9 #9)
+#555 := [refl]: #554
+#557 := [quant-intro #555]: #556
+#560 := [monotonicity #557]: #559
+#563 := [monotonicity #560]: #562
+#566 := [monotonicity #563]: #565
+#574 := [monotonicity #566 #571]: #573
+#111 := (iff #84 #110)
+#108 := (iff #15 #107)
+#105 := (iff #14 #104)
+#106 := [rewrite]: #105
+#109 := [quant-intro #106]: #108
+#100 := (iff #13 #99)
+#101 := [rewrite]: #100
+#112 := [monotonicity #101 #109]: #111
+#90 := [and-elim #89]: #84
+#113 := [mp #90 #112]: #110
+#575 := [mp #113 #574]: #572
+#536 := [unit-resolution #575 #251]: #564
+#135 := (or #561 #553)
+#222 := [def-axiom]: #135
+#143 := [unit-resolution #222 #536]: #553
+#539 := (or #558 #49)
+#525 := [quant-inst #47]: #539
+#521 := [unit-resolution #525 #143 #538]: false
+#522 := [lemma #521]: #49
+#245 := (or #50 #114)
+#136 := (or #561 #12)
+#223 := [def-axiom]: #136
+#244 := [unit-resolution #223 #536]: #12
+#520 := [unit-resolution #134 #244]: #245
+#524 := [unit-resolution #520 #522]: #114
+#519 := (or #558 #77)
+#523 := [quant-inst #75]: #519
+[unit-resolution #523 #143 #524]: false
+40817fbcafdc8d21718702405c773ccd33ea7f23 34 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S2 S1)
+#8 := (:var 0 S2)
 #12 := (:var 1 S2)
-#47 := (= #12 #14)
-#13 := (f6 #12)
-#16 := (= #13 #15)
-#53 := (not #16)
-#54 := (or #53 #47)
-#59 := (forall (vars (?v0 S2) (?v1 S2)) #54)
-#86 := (iff #59 #90)
-#83 := [rewrite]: #86
-#93 := (~ #59 #59)
-#91 := (~ #54 #54)
-#92 := [refl]: #91
-#94 := [nnf-pos #92]: #93
+#13 := (f3 #12 #8)
+#14 := (= #13 f1)
+#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
+#7 := (:var 2 S2)
+#9 := (f3 #7 #8)
+#10 := (= #9 f1)
+#11 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #10)
+#16 := (iff #11 #15)
+#17 := (not #16)
+#36 := (iff #17 false)
+#1 := true
+#31 := (not true)
+#34 := (iff #31 false)
+#35 := [rewrite]: #34
+#32 := (iff #17 #31)
+#29 := (iff #16 true)
+#24 := (iff #15 #15)
+#27 := (iff #24 true)
+#28 := [rewrite]: #27
+#25 := (iff #16 #24)
+#23 := [elim-unused]: #16
+#26 := [monotonicity #23]: #25
+#30 := [trans #26 #28]: #29
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#19 := [asserted]: #17
+[mp #19 #37]: false
+259e8b1baa5df2fdd772840446c5eb3162d97d06 95 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S2 S1)
+decl f4 :: S2
+#15 := f4
 decl f5 :: S2
+#19 := f5
+#174 := (f3 f5 f4)
+#90 := (= #174 f1)
+#175 := (not #90)
+#20 := (f3 f4 f5)
+#21 := (= #20 f1)
+#56 := (not #21)
+#8 := (:var 0 S2)
+#16 := (f3 #8 f4)
+#17 := (= #16 f1)
+#18 := (forall (vars (?v0 S2)) #17)
+#37 := (not #18)
+#7 := (:var 1 S2)
+#11 := (f3 #8 #7)
+#12 := (= #11 f1)
+#9 := (f3 #7 #8)
+#10 := (= #9 f1)
+#30 := (not #10)
+#31 := (or #30 #12)
+#34 := (forall (vars (?v0 S2) (?v1 S2)) #31)
+#44 := (not #34)
+#45 := (or #44 #37 #21)
+#50 := (not #45)
+#22 := (implies #18 #21)
+#13 := (implies #10 #12)
+#14 := (forall (vars (?v0 S2) (?v1 S2)) #13)
+#23 := (implies #14 #22)
+#24 := (not #23)
+#51 := (iff #24 #50)
+#48 := (iff #23 #45)
+#38 := (or #37 #21)
+#41 := (implies #34 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #23 #41)
+#39 := (iff #22 #38)
+#40 := [rewrite]: #39
+#35 := (iff #14 #34)
+#32 := (iff #13 #31)
+#33 := [rewrite]: #32
+#36 := [quant-intro #33]: #35
+#43 := [monotonicity #36 #40]: #42
+#49 := [trans #43 #47]: #48
+#52 := [monotonicity #49]: #51
+#26 := [asserted]: #24
+#53 := [mp #26 #52]: #50
+#57 := [not-or-elim #53]: #56
+#505 := (pattern #11)
+#504 := (pattern #9)
+#506 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #504 #505) #31)
+#509 := (iff #34 #506)
+#507 := (iff #31 #31)
+#508 := [refl]: #507
+#510 := [quant-intro #508]: #509
+#81 := (~ #34 #34)
+#83 := (~ #31 #31)
+#84 := [refl]: #83
+#82 := [nnf-pos #84]: #81
+#54 := [not-or-elim #53]: #34
+#79 := [mp~ #54 #82]: #34
+#511 := [mp #79 #510]: #506
+#178 := (not #506)
+#179 := (or #178 #175 #21)
+#87 := (or #175 #21)
+#180 := (or #178 #87)
+#181 := (iff #180 #179)
+#160 := [rewrite]: #181
+#177 := [quant-inst #19 #15]: #180
+#496 := [mp #177 #160]: #179
+#176 := [unit-resolution #496 #511 #57]: #175
+#512 := (pattern #16)
+#513 := (forall (vars (?v0 S2)) (:pat #512) #17)
+#516 := (iff #18 #513)
+#514 := (iff #17 #17)
+#515 := [refl]: #514
+#517 := [quant-intro #515]: #516
+#78 := (~ #18 #18)
+#80 := (~ #17 #17)
+#77 := [refl]: #80
+#85 := [nnf-pos #77]: #78
+#55 := [not-or-elim #53]: #18
+#86 := [mp~ #55 #85]: #18
+#518 := [mp #86 #517]: #513
+#498 := (not #513)
+#154 := (or #498 #90)
+#285 := [quant-inst #19]: #154
+[unit-resolution #285 #518 #176]: false
+44a8a010d20c75dbd110b4ba979d4cfad7872b87 101 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+decl f4 :: (-> S3 S2 S2)
+decl f6 :: S2
+#16 := f6
+decl f5 :: S3
 #10 := f5
-#11 := (distinct f3 f4 f5)
-#62 := (and #11 #59)
-#68 := (not #62)
-#21 := (f6 f3)
-#23 := (= #21 #22)
-#24 := (not #23)
-#69 := (or #24 #68)
+#20 := (f4 f5 f6)
+#21 := (f4 f5 #20)
+#173 := (f3 #21)
+#493 := (= #173 f1)
+#171 := (f3 #20)
+#79 := (= #171 f1)
+#17 := (f3 f6)
+#18 := (= #17 f1)
+#7 := (:var 0 S2)
+#11 := (f4 f5 #7)
+#12 := (f3 #11)
+#13 := (= #12 f1)
+#8 := (f3 #7)
+#9 := (= #8 f1)
+#32 := (not #9)
+#33 := (or #32 #13)
+#36 := (forall (vars (?v0 S2)) #33)
+#39 := (and #36 #18)
+#22 := (f4 f5 #21)
+#23 := (f3 #22)
+#24 := (= #23 f1)
+#45 := (not #39)
+#46 := (or #45 #24)
+#51 := (not #46)
+#14 := (implies #9 #13)
+#15 := (forall (vars (?v0 S2)) #14)
+#19 := (and #15 #18)
+#25 := (implies #19 #24)
+#26 := (not #25)
+#52 := (iff #26 #51)
+#49 := (iff #25 #46)
+#42 := (implies #39 #24)
+#47 := (iff #42 #46)
+#48 := [rewrite]: #47
+#43 := (iff #25 #42)
+#40 := (iff #19 #39)
+#37 := (iff #15 #36)
+#34 := (iff #14 #33)
+#35 := [rewrite]: #34
+#38 := [quant-intro #35]: #37
+#41 := [monotonicity #38]: #40
+#44 := [monotonicity #41]: #43
+#50 := [trans #44 #48]: #49
+#53 := [monotonicity #50]: #52
+#28 := [asserted]: #26
+#54 := [mp #28 #53]: #51
+#55 := [not-or-elim #54]: #39
+#57 := [and-elim #55]: #18
+#501 := (pattern #11)
+#502 := (forall (vars (?v0 S2)) (:pat #501) #33)
+#505 := (iff #36 #502)
+#503 := (iff #33 #33)
+#504 := [refl]: #503
+#506 := [quant-intro #504]: #505
+#81 := (~ #36 #36)
+#83 := (~ #33 #33)
+#84 := [refl]: #83
+#82 := [nnf-pos #84]: #81
+#56 := [and-elim #55]: #36
+#85 := [mp~ #56 #82]: #36
+#507 := [mp #85 #506]: #502
+#86 := (not #18)
+#164 := (not #502)
+#175 := (or #164 #86 #79)
+#172 := (or #86 #79)
+#176 := (or #164 #172)
+#174 := (iff #176 #175)
+#178 := [rewrite]: #174
+#177 := [quant-inst #16]: #176
+#157 := [mp #177 #178]: #175
+#499 := [unit-resolution #157 #507 #57]: #79
+#80 := (not #79)
+#489 := (or #164 #80 #493)
+#495 := (or #80 #493)
+#162 := (or #164 #495)
+#496 := (iff #162 #489)
+#497 := [rewrite]: #496
+#163 := [quant-inst #20]: #162
+#498 := [mp #163 #497]: #489
+#494 := [unit-resolution #498 #507 #499]: #493
+#58 := (not #24)
+#59 := [not-or-elim #54]: #58
+#151 := (not #493)
+#500 := (or #164 #151 #24)
+#282 := (or #151 #24)
+#490 := (or #164 #282)
+#154 := (iff #490 #500)
+#491 := [rewrite]: #154
+#149 := [quant-inst #21]: #490
+#150 := [mp #149 #491]: #500
+[unit-resolution #150 #507 #59 #494]: false
+60e1704ec347155327350daf08c9fa7301bbf00c 64 0
+unsat
+#2 := false
+decl f3 :: (-> S2 S2 S3)
+decl f4 :: S2
+#13 := f4
+decl f5 :: S2
+#15 := f5
+#17 := (f3 f5 f4)
+#16 := (f3 f4 f5)
+#18 := (= #16 #17)
+#50 := (not #18)
+#7 := (:var 1 S2)
+#8 := (:var 0 S2)
+#10 := (f3 #8 #7)
+#9 := (f3 #7 #8)
+#11 := (= #9 #10)
+#12 := (forall (vars (?v0 S2) (?v1 S2)) #11)
+#39 := (not #12)
+#40 := (or #39 #18)
+#45 := (not #40)
+#14 := (= f4 f4)
+#19 := (and #14 #18)
+#20 := (implies #12 #19)
+#21 := (not #20)
+#46 := (iff #21 #45)
+#43 := (iff #20 #40)
+#36 := (implies #12 #18)
+#41 := (iff #36 #40)
+#42 := [rewrite]: #41
+#37 := (iff #20 #36)
+#34 := (iff #19 #18)
+#1 := true
+#29 := (and true #18)
+#32 := (iff #29 #18)
+#33 := [rewrite]: #32
+#30 := (iff #19 #29)
+#27 := (iff #14 true)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#35 := [trans #31 #33]: #34
+#38 := [monotonicity #35]: #37
+#44 := [trans #38 #42]: #43
+#47 := [monotonicity #44]: #46
+#23 := [asserted]: #21
+#48 := [mp #23 #47]: #45
+#51 := [not-or-elim #48]: #50
+#494 := (pattern #10)
+#493 := (pattern #9)
+#495 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #493 #494) #11)
+#498 := (iff #12 #495)
+#496 := (iff #11 #11)
+#497 := [refl]: #496
+#499 := [quant-intro #497]: #498
+#73 := (~ #12 #12)
+#71 := (~ #11 #11)
+#72 := [refl]: #71
+#74 := [nnf-pos #72]: #73
+#49 := [not-or-elim #48]: #12
+#75 := [mp~ #49 #74]: #12
+#500 := [mp #75 #499]: #495
+#79 := (not #495)
+#164 := (or #79 #18)
+#76 := [quant-inst #13 #15]: #164
+[unit-resolution #76 #500 #51]: false
+03e5c09109dcecda750af8f377268d580b063674 175 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+decl f7 :: S2
+#21 := f7
+#24 := (f3 f7)
+#25 := (= #24 f1)
+decl f5 :: S2
+#14 := f5
+#152 := (f3 f5)
+#240 := (= #152 f1)
+#154 := (not #240)
+decl f4 :: (-> S2 S1)
+#15 := (f4 f5)
+#16 := (= #15 f1)
+#17 := (not #16)
+decl f6 :: (-> S2 S1)
+#22 := (f6 f7)
+#23 := (= #22 f1)
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#9 := (= #8 f1)
+#19 := (not #9)
+#10 := (f4 #7)
+#11 := (= #10 f1)
+#18 := (not #11)
+#20 := (and #18 #19)
+#47 := (not #20)
+#48 := (or #47 #23 #25)
+#51 := (forall (vars (?v0 S2)) #48)
+#41 := (or #19 #11)
+#44 := (forall (vars (?v0 S2)) #41)
+#60 := (and #44 #17 #51)
+#31 := (f4 f7)
+#32 := (= #31 f1)
+#68 := (not #60)
+#69 := (or #68 #23 #32)
 #74 := (not #69)
-#17 := (= #14 #12)
-#18 := (implies #16 #17)
-#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
-#20 := (and #11 #19)
-#25 := (implies #20 #24)
-#26 := (not #25)
-#75 := (iff #26 #74)
-#72 := (iff #25 #69)
-#65 := (implies #62 #24)
+#33 := (or #23 #32)
+#26 := (or #23 #25)
+#27 := (implies #20 #26)
+#28 := (forall (vars (?v0 S2)) #27)
+#29 := (and #17 #28)
+#12 := (implies #9 #11)
+#13 := (forall (vars (?v0 S2)) #12)
+#30 := (and #13 #29)
+#34 := (implies #30 #33)
+#35 := (not #34)
+#75 := (iff #35 #74)
+#72 := (iff #34 #69)
+#65 := (implies #60 #33)
 #70 := (iff #65 #69)
 #71 := [rewrite]: #70
-#66 := (iff #25 #65)
-#63 := (iff #20 #62)
-#60 := (iff #19 #59)
-#57 := (iff #18 #54)
-#50 := (implies #16 #47)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #18 #50)
-#48 := (iff #17 #47)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#58 := [trans #52 #56]: #57
-#61 := [quant-intro #58]: #60
-#64 := [monotonicity #61]: #63
+#66 := (iff #34 #65)
+#63 := (iff #30 #60)
+#54 := (and #17 #51)
+#57 := (and #44 #54)
+#61 := (iff #57 #60)
+#62 := [rewrite]: #61
+#58 := (iff #30 #57)
+#55 := (iff #29 #54)
+#52 := (iff #28 #51)
+#49 := (iff #27 #48)
+#50 := [rewrite]: #49
+#53 := [quant-intro #50]: #52
+#56 := [monotonicity #53]: #55
+#45 := (iff #13 #44)
+#42 := (iff #12 #41)
+#43 := [rewrite]: #42
+#46 := [quant-intro #43]: #45
+#59 := [monotonicity #46 #56]: #58
+#64 := [trans #59 #62]: #63
 #67 := [monotonicity #64]: #66
 #73 := [trans #67 #71]: #72
 #76 := [monotonicity #73]: #75
-#46 := [asserted]: #26
-#79 := [mp #46 #76]: #74
-#78 := [not-or-elim #79]: #62
-#81 := [and-elim #78]: #59
-#87 := [mp~ #81 #94]: #59
-#84 := [mp #87 #83]: #90
-#576 := [mp #84 #575]: #570
-#569 := (not #570)
-#549 := (or #569 #209)
-#550 := (or #569 #208)
-#546 := (iff #550 #549)
-#188 := (iff #549 #549)
-#553 := [rewrite]: #188
-#547 := (iff #208 #209)
-#548 := [rewrite]: #547
-#552 := [monotonicity #548]: #546
-#555 := [trans #552 #553]: #546
-#551 := [quant-inst #9]: #550
-#193 := [mp #551 #555]: #549
-#543 := [unit-resolution #193 #576]: #209
-#254 := [symm #543]: #208
-#269 := (= f3 #207)
-#565 := (inj!0 #21)
-#267 := (= #565 #207)
-#250 := (= #207 #565)
-#554 := (= #22 #21)
-#77 := [not-or-elim #79]: #23
-#557 := [symm #77]: #554
-#266 := [monotonicity #557]: #250
-#268 := [symm #266]: #267
-#567 := (= f3 #565)
-#559 := (or #569 #567)
-#566 := (= #565 f3)
-#217 := (or #569 #566)
-#560 := (iff #217 #559)
-#561 := (iff #559 #559)
-#202 := [rewrite]: #561
-#568 := (iff #566 #567)
-#563 := [rewrite]: #568
-#218 := [monotonicity #563]: #560
-#545 := [trans #218 #202]: #560
-#222 := [quant-inst #8]: #217
-#206 := [mp #222 #545]: #559
-#544 := [unit-resolution #206 #576]: #567
-#160 := [trans #544 #268]: #269
-#539 := [trans #160 #254]: #152
-#239 := (not #152)
-#154 := (= f4 f5)
-#241 := (not #154)
-#153 := (= f3 f5)
-#240 := (not #153)
-#232 := (and #239 #240 #241)
-#80 := [and-elim #78]: #11
-#219 := (not #11)
-#351 := (or #219 #232)
-#558 := [def-axiom]: #351
-#194 := [unit-resolution #558 #80]: #232
-#243 := (not #232)
-#244 := (or #243 #239)
-#172 := [def-axiom]: #244
-#556 := [unit-resolution #172 #194]: #239
-[unit-resolution #556 #539]: false
-unsat
-03a4fcd182047beb0b3be329b34440294749812c 117 0
-#2 := false
-decl f5 :: S3
-#18 := f5
+#37 := [asserted]: #35
+#77 := [mp #37 #76]: #74
+#78 := [not-or-elim #77]: #60
+#80 := [and-elim #78]: #17
+#570 := (pattern #10)
+#569 := (pattern #8)
+#571 := (forall (vars (?v0 S2)) (:pat #569 #570) #41)
+#574 := (iff #44 #571)
+#572 := (iff #41 #41)
+#573 := [refl]: #572
+#575 := [quant-intro #573]: #574
+#121 := (~ #44 #44)
+#107 := (~ #41 #41)
+#108 := [refl]: #107
+#122 := [nnf-pos #108]: #121
+#79 := [and-elim #78]: #44
+#125 := [mp~ #79 #122]: #44
+#576 := [mp #125 #575]: #571
+#244 := (not #571)
+#245 := (or #244 #154 #16)
+#241 := (or #154 #16)
+#242 := (or #244 #241)
+#225 := (iff #242 #245)
+#561 := [rewrite]: #225
+#246 := [quant-inst #14]: #242
+#563 := [mp #246 #561]: #245
+#567 := [unit-resolution #563 #576 #80]: #154
+#143 := (or #11 #9 #25)
+#577 := (forall (vars (?v0 S2)) (:pat #570 #569) #143)
+#148 := (forall (vars (?v0 S2)) #143)
+#580 := (iff #148 #577)
+#578 := (iff #143 #143)
+#579 := [refl]: #578
+#581 := [quant-intro #579]: #580
+#112 := (or #47 #25)
+#117 := (forall (vars (?v0 S2)) #112)
+#149 := (iff #117 #148)
+#146 := (iff #112 #143)
+#129 := (or #11 #9)
+#140 := (or #129 #25)
+#144 := (iff #140 #143)
+#145 := [rewrite]: #144
+#141 := (iff #112 #140)
+#138 := (iff #47 #129)
+#130 := (not #129)
+#133 := (not #130)
+#136 := (iff #133 #129)
+#137 := [rewrite]: #136
+#134 := (iff #47 #133)
+#131 := (iff #20 #130)
+#132 := [rewrite]: #131
+#135 := [monotonicity #132]: #134
+#139 := [trans #135 #137]: #138
+#142 := [monotonicity #139]: #141
+#147 := [trans #142 #145]: #146
+#150 := [quant-intro #147]: #149
+#126 := (~ #117 #117)
+#124 := (~ #112 #112)
+#127 := [refl]: #124
+#123 := [nnf-pos #127]: #126
+#118 := (iff #51 #117)
+#115 := (iff #48 #112)
+#113 := (or #47 false #25)
+#109 := (iff #113 #112)
+#110 := [rewrite]: #109
+#114 := (iff #48 #113)
+#105 := (iff #23 false)
+#82 := (not #23)
+#83 := [not-or-elim #77]: #82
+#106 := [iff-false #83]: #105
+#111 := [monotonicity #106]: #114
+#116 := [trans #111 #110]: #115
+#119 := [quant-intro #116]: #118
+#81 := [and-elim #78]: #51
+#120 := [mp #81 #119]: #117
+#128 := [mp~ #120 #123]: #117
+#151 := [mp #128 #150]: #148
+#582 := [mp #151 #581]: #577
+#350 := (not #577)
+#557 := (or #350 #16 #240 #25)
+#232 := (or #16 #240 #25)
+#230 := (or #350 #232)
+#564 := (iff #230 #557)
+#565 := [rewrite]: #564
+#231 := [quant-inst #14]: #230
+#566 := [mp #231 #565]: #557
+#562 := [unit-resolution #566 #80 #582 #567]: #25
+#84 := (not #32)
+#85 := [not-or-elim #77]: #84
+#243 := (not #25)
+#568 := (or #244 #243 #32)
+#219 := (or #243 #32)
+#558 := (or #244 #219)
+#222 := (iff #558 #568)
+#559 := [rewrite]: #222
+#217 := [quant-inst #21]: #558
+#218 := [mp #217 #559]: #568
+[unit-resolution #218 #576 #85 #562]: false
+dad47c0dccdde5aaf69b20f49e2beb333b7d1c8d 25 0
+unsat
+#2 := false
+#7 := (:var 0 S2)
+#8 := (= #7 #7)
+#9 := (exists (vars (?v0 S2)) #8)
+#10 := (not #9)
+#30 := (iff #10 false)
+#1 := true
+#25 := (not true)
+#28 := (iff #25 false)
+#29 := [rewrite]: #28
+#26 := (iff #10 #25)
+#23 := (iff #9 true)
+#18 := (exists (vars (?v0 S2)) true)
+#21 := (iff #18 true)
+#22 := [elim-unused]: #21
+#19 := (iff #9 #18)
+#16 := (iff #8 true)
+#17 := [rewrite]: #16
+#20 := [quant-intro #17]: #19
+#24 := [trans #20 #22]: #23
+#27 := [monotonicity #24]: #26
+#31 := [trans #27 #29]: #30
+#12 := [asserted]: #10
+[mp #12 #31]: false
+fc36fcb821679c8080c506c122956d27caba0078 23 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#9 := (= #8 f1)
+#10 := (exists (vars (?v0 S2)) #9)
+#11 := (iff #10 #10)
+#12 := (not #11)
+#25 := (iff #12 false)
+#1 := true
+#20 := (not true)
+#23 := (iff #20 false)
+#24 := [rewrite]: #23
+#21 := (iff #12 #20)
+#18 := (iff #11 true)
+#19 := [rewrite]: #18
+#22 := [monotonicity #19]: #21
+#26 := [trans #22 #24]: #25
+#14 := [asserted]: #12
+[mp #14 #26]: false
+7ef14cc2eb8981200f35e7bb0dd9d8dc37927aaa 205 0
+unsat
+#2 := false
+decl f4 :: (-> S2 S1)
+#7 := (:var 0 S2)
+#10 := (f4 #7)
+#539 := (pattern #10)
+decl f1 :: S1
+#3 := f1
+#11 := (= #10 f1)
+#85 := (not #11)
+#553 := (forall (vars (?v0 S2)) (:pat #539) #85)
+#558 := (not #553)
+decl f3 :: (-> S2 S1)
+#8 := (f3 #7)
+#538 := (pattern #8)
+#9 := (= #8 f1)
+#78 := (not #9)
+#545 := (forall (vars (?v0 S2)) (:pat #538) #78)
+#550 := (not #545)
+#561 := (or #550 #558)
+#564 := (not #561)
+#12 := (or #9 #11)
+#48 := (not #12)
+#540 := (forall (vars (?v0 S2)) (:pat #538 #539) #48)
+#214 := (not #540)
+decl ?v0!2 :: S2
+#70 := ?v0!2
+#71 := (f4 ?v0!2)
+#72 := (= #71 f1)
+#518 := (f3 ?v0!2)
+#519 := (= #518 f1)
+#514 := (or #519 #72)
+decl ?v0!0 :: S2
+#54 := ?v0!0
+#57 := (f4 ?v0!0)
+#58 := (= #57 f1)
+#188 := (not #58)
+#55 := (f3 ?v0!0)
+#56 := (= #55 f1)
+#59 := (or #56 #58)
+#201 := (not #59)
+#213 := [hypothesis]: #540
+#534 := (or #201 #214)
+#212 := [hypothesis]: #59
+#211 := (or #214 #201)
+#215 := [quant-inst #54]: #211
+#533 := [unit-resolution #215 #213 #212]: false
+#535 := [lemma #533]: #534
+#157 := [unit-resolution #535 #213]: #201
+#319 := (or #59 #188)
+#526 := [def-axiom]: #319
+#521 := [unit-resolution #526 #157]: #188
+#194 := (not #56)
+#530 := (or #59 #194)
+#532 := [def-axiom]: #530
+#235 := [unit-resolution #532 #157]: #194
+decl ?v0!1 :: S2
+#65 := ?v0!1
+#66 := (f3 ?v0!1)
+#67 := (= #66 f1)
+#529 := (not #67)
+#536 := (f4 ?v0!1)
+#531 := (= #536 f1)
+#537 := (or #67 #531)
+#527 := (not #537)
+#516 := (or #527 #214)
+#186 := [hypothesis]: #537
+#528 := (or #214 #527)
+#187 := [quant-inst #65]: #528
+#191 := [unit-resolution #187 #213 #186]: false
+#517 := [lemma #191]: #516
+#236 := [unit-resolution #517 #213]: #527
+#171 := (or #537 #529)
+#513 := [def-axiom]: #171
+#237 := [unit-resolution #513 #236]: #529
+#104 := (or #56 #58 #67 #72)
+#88 := (forall (vars (?v0 S2)) #85)
+#81 := (forall (vars (?v0 S2)) #78)
+#92 := (and #81 #88)
+#51 := (forall (vars (?v0 S2)) #48)
+#96 := (or #51 #92)
+#107 := (and #104 #96)
+#75 := (or #67 #72)
+#97 := (or #59 #75)
+#98 := (and #97 #96)
+#108 := (iff #98 #107)
+#105 := (iff #97 #104)
+#106 := [rewrite]: #105
+#109 := [monotonicity #106]: #108
+#15 := (exists (vars (?v0 S2)) #11)
+#14 := (exists (vars (?v0 S2)) #9)
+#16 := (or #14 #15)
+#13 := (exists (vars (?v0 S2)) #12)
+#24 := (not #13)
+#25 := (iff #24 #16)
+#99 := (~ #25 #98)
+#93 := (not #16)
+#94 := (~ #93 #92)
+#89 := (not #15)
+#90 := (~ #89 #88)
+#86 := (~ #85 #85)
+#87 := [refl]: #86
+#91 := [nnf-neg #87]: #90
+#82 := (not #14)
+#83 := (~ #82 #81)
+#79 := (~ #78 #78)
+#80 := [refl]: #79
+#84 := [nnf-neg #80]: #83
+#95 := [nnf-neg #84 #91]: #94
+#76 := (~ #16 #75)
+#73 := (~ #15 #72)
+#74 := [sk]: #73
+#68 := (~ #14 #67)
+#69 := [sk]: #68
+#77 := [monotonicity #69 #74]: #76
+#62 := (not #24)
+#63 := (~ #62 #59)
+#60 := (~ #13 #59)
+#61 := [sk]: #60
+#64 := [nnf-neg #61]: #63
+#52 := (~ #24 #51)
+#49 := (~ #48 #48)
+#50 := [refl]: #49
+#53 := [nnf-neg #50]: #52
+#100 := [nnf-pos #53 #64 #77 #95]: #99
+#17 := (iff #13 #16)
+#18 := (not #17)
+#26 := (iff #18 #25)
+#27 := [rewrite]: #26
+#20 := [asserted]: #18
+#28 := [mp #20 #27]: #25
+#101 := [mp~ #28 #100]: #98
+#102 := [mp #101 #109]: #107
+#103 := [and-elim #102]: #104
+#129 := [unit-resolution #103 #237 #235 #521]: #72
+#525 := (not #72)
+#511 := (or #514 #525)
+#512 := [def-axiom]: #511
+#507 := [unit-resolution #512 #129]: #514
+#520 := (not #514)
+#523 := (or #214 #520)
+#162 := [quant-inst #70]: #523
+#508 := [unit-resolution #162 #213 #507]: false
+#230 := [lemma #508]: #214
+#567 := (or #540 #564)
+#112 := (not #88)
+#111 := (not #81)
+#113 := (or #111 #112)
+#114 := (not #113)
+#117 := (or #51 #114)
+#568 := (iff #117 #567)
+#565 := (iff #114 #564)
+#562 := (iff #113 #561)
+#559 := (iff #112 #558)
+#556 := (iff #88 #553)
+#554 := (iff #85 #85)
+#555 := [refl]: #554
+#557 := [quant-intro #555]: #556
+#560 := [monotonicity #557]: #559
+#551 := (iff #111 #550)
+#548 := (iff #81 #545)
+#546 := (iff #78 #78)
+#547 := [refl]: #546
+#549 := [quant-intro #547]: #548
+#552 := [monotonicity #549]: #551
+#563 := [monotonicity #552 #560]: #562
+#566 := [monotonicity #563]: #565
+#543 := (iff #51 #540)
+#541 := (iff #48 #48)
+#542 := [refl]: #541
+#544 := [quant-intro #542]: #543
+#569 := [monotonicity #544 #566]: #568
+#118 := (iff #96 #117)
+#115 := (iff #92 #114)
+#116 := [rewrite]: #115
+#119 := [monotonicity #116]: #118
+#110 := [and-elim #102]: #96
+#120 := [mp #110 #119]: #117
+#570 := [mp #120 #569]: #567
+#163 := [unit-resolution #570 #230]: #564
+#122 := (or #561 #553)
+#209 := [def-axiom]: #122
+#222 := [unit-resolution #209 #163]: #553
+#121 := (or #561 #545)
+#208 := [def-axiom]: #121
+#524 := [unit-resolution #208 #163]: #545
+#509 := [hypothesis]: #67
+#510 := (or #550 #529)
+#220 := [quant-inst #65]: #510
+#506 := [unit-resolution #220 #509 #524]: false
+#221 := [lemma #506]: #529
+#234 := [hypothesis]: #56
+#522 := (or #550 #194)
+#219 := [quant-inst #54]: #522
+#231 := [unit-resolution #219 #234 #524]: false
+#505 := [lemma #231]: #194
+#223 := [hypothesis]: #58
+#501 := (or #558 #188)
+#502 := [quant-inst #54]: #501
+#216 := [unit-resolution #502 #223 #222]: false
+#499 := [lemma #216]: #188
+#503 := [unit-resolution #103 #499 #505 #221]: #72
+#504 := (or #558 #525)
+#493 := [quant-inst #70]: #504
+[unit-resolution #493 #503 #222]: false
+971101afe4e49303a8bf2ce8173c0b2d6a20580f 173 0
+unsat
+#2 := false
+decl f3 :: (-> S2 S1)
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#550 := (pattern #8)
+decl f1 :: S1
+#3 := f1
+#9 := (= #8 f1)
+#47 := (not #9)
+#551 := (forall (vars (?v0 S2)) (:pat #550) #47)
+decl f4 :: S1
+#11 := f4
+#12 := (= f4 f1)
+#54 := (not #12)
+decl ?v0!0 :: S2
+#60 := ?v0!0
+#61 := (f3 ?v0!0)
+#62 := (= #61 f1)
+#101 := (not #62)
+#102 := (or #101 #54)
+#206 := [hypothesis]: #54
+#134 := (or #102 #12)
+#221 := [def-axiom]: #134
+#542 := [unit-resolution #221 #206]: #102
+decl ?v0!1 :: S2
+#73 := ?v0!1
+#74 := (f3 ?v0!1)
+#75 := (= #74 f1)
+#106 := (not #75)
+#107 := (or #106 #54)
+#225 := (or #107 #12)
+#226 := [def-axiom]: #225
+#544 := [unit-resolution #226 #206]: #107
+#108 := (not #107)
+#103 := (not #102)
+#111 := (or #103 #108)
+#76 := (and #75 #12)
+#67 := (and #62 #12)
+#87 := (or #67 #76)
+#112 := (iff #87 #111)
+#109 := (iff #76 #108)
+#110 := [rewrite]: #109
+#104 := (iff #67 #103)
+#105 := [rewrite]: #104
+#113 := [monotonicity #105 #110]: #112
+#14 := (and #9 #12)
+#79 := (not #14)
+#82 := (forall (vars (?v0 S2)) #79)
+#50 := (forall (vars (?v0 S2)) #47)
+#94 := (or #50 #54 #82)
+#97 := (and #87 #94)
+#57 := (or #50 #54)
+#86 := (or #57 #82)
+#88 := (and #87 #86)
+#98 := (iff #88 #97)
+#95 := (iff #86 #94)
+#96 := [rewrite]: #95
+#99 := [monotonicity #96]: #98
+#15 := (exists (vars (?v0 S2)) #14)
+#10 := (exists (vars (?v0 S2)) #9)
+#13 := (and #10 #12)
+#23 := (not #13)
+#24 := (iff #23 #15)
+#89 := (~ #24 #88)
+#83 := (not #15)
+#84 := (~ #83 #82)
+#80 := (~ #79 #79)
+#81 := [refl]: #80
+#85 := [nnf-neg #81]: #84
+#77 := (~ #15 #76)
+#78 := [sk]: #77
+#70 := (not #23)
+#71 := (~ #70 #67)
+#68 := (~ #13 #67)
+#65 := (~ #12 #12)
+#66 := [refl]: #65
+#63 := (~ #10 #62)
+#64 := [sk]: #63
+#69 := [monotonicity #64 #66]: #68
+#72 := [nnf-neg #69]: #71
+#58 := (~ #23 #57)
+#55 := (~ #54 #54)
+#56 := [refl]: #55
+#51 := (not #10)
+#52 := (~ #51 #50)
+#48 := (~ #47 #47)
+#49 := [refl]: #48
+#53 := [nnf-neg #49]: #52
+#59 := [nnf-neg #53 #56]: #58
+#90 := [nnf-pos #59 #72 #78 #85]: #89
+#16 := (iff #13 #15)
+#17 := (not #16)
+#25 := (iff #17 #24)
+#26 := [rewrite]: #25
+#19 := [asserted]: #17
+#27 := [mp #19 #26]: #24
+#91 := [mp~ #27 #90]: #88
+#92 := [mp #91 #99]: #97
+#93 := [and-elim #92]: #87
+#114 := [mp #93 #113]: #111
+#200 := [unit-resolution #114 #544 #542]: false
+#331 := [lemma #200]: #12
+#115 := (or #47 #54)
+#556 := (forall (vars (?v0 S2)) (:pat #550) #115)
+#539 := (not #556)
+#188 := [hypothesis]: #556
+#212 := (not #551)
+#211 := [hypothesis]: #75
+#545 := (or #212 #106)
+#538 := [hypothesis]: #551
+#546 := [quant-inst #73]: #545
+#547 := [unit-resolution #546 #211 #538]: false
+#548 := [lemma #547]: #545
+#543 := [unit-resolution #548 #211]: #212
+#561 := (or #551 #54 #556)
+#126 := (forall (vars (?v0 S2)) #115)
+#129 := (or #50 #54 #126)
+#562 := (iff #129 #561)
+#559 := (iff #126 #556)
+#557 := (iff #115 #115)
+#558 := [refl]: #557
+#560 := [quant-intro #558]: #559
+#554 := (iff #50 #551)
+#552 := (iff #47 #47)
+#553 := [refl]: #552
+#555 := [quant-intro #553]: #554
+#563 := [monotonicity #555 #560]: #562
+#130 := (iff #94 #129)
+#127 := (iff #82 #126)
+#124 := (iff #79 #115)
+#116 := (not #115)
+#119 := (not #116)
+#122 := (iff #119 #115)
+#123 := [rewrite]: #122
+#120 := (iff #79 #119)
+#117 := (iff #14 #116)
+#118 := [rewrite]: #117
+#121 := [monotonicity #118]: #120
+#125 := [trans #121 #123]: #124
+#128 := [quant-intro #125]: #127
+#131 := [monotonicity #128]: #130
+#100 := [and-elim #92]: #94
+#132 := [mp #100 #131]: #129
+#564 := [mp #132 #563]: #561
+#549 := [unit-resolution #564 #543 #331]: #556
+#198 := (or #539 #106 #54)
+#203 := (or #539 #107)
+#199 := (iff #203 #198)
+#541 := [rewrite]: #199
+#540 := [quant-inst #73]: #203
+#183 := [mp #540 #541]: #198
+#525 := [unit-resolution #183 #331 #211 #549]: false
+#187 := [lemma #525]: #106
+#213 := (or #107 #75)
+#224 := [def-axiom]: #213
+#189 := [unit-resolution #224 #187]: #107
+#526 := [unit-resolution #114 #189]: #103
+#133 := (or #102 #62)
+#220 := [def-axiom]: #133
+#532 := [unit-resolution #220 #526]: #62
+#190 := (or #539 #101 #54)
+#527 := (or #539 #102)
+#529 := (iff #527 #190)
+#530 := [rewrite]: #529
+#528 := [quant-inst #60]: #527
+#531 := [mp #528 #530]: #190
+#169 := [unit-resolution #531 #532 #331 #188]: false
+#533 := [lemma #169]: #539
+#535 := [unit-resolution #564 #533 #331]: #551
+#175 := (or #212 #101)
+#536 := [quant-inst #60]: #175
+[unit-resolution #536 #532 #535]: false
+1ef8ef2e60d46143c5456e75da2d8083df054812 34 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S4 S1)
+#8 := (:var 0 S4)
+#12 := (:var 1 S2)
+#13 := (f3 #12 #8)
+#14 := (= #13 f1)
+#15 := (exists (vars (?v0 S2) (?v1 S4)) #14)
+#7 := (:var 2 S2)
+#9 := (f3 #7 #8)
+#10 := (= #9 f1)
+#11 := (exists (vars (?v0 S2) (?v1 S3) (?v2 S4)) #10)
+#16 := (iff #11 #15)
+#17 := (not #16)
+#36 := (iff #17 false)
+#1 := true
+#31 := (not true)
+#34 := (iff #31 false)
+#35 := [rewrite]: #34
+#32 := (iff #17 #31)
+#29 := (iff #16 true)
+#24 := (iff #15 #15)
+#27 := (iff #24 true)
+#28 := [rewrite]: #27
+#25 := (iff #16 #24)
+#23 := [elim-unused]: #16
+#26 := [monotonicity #23]: #25
+#30 := [trans #26 #28]: #29
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#19 := [asserted]: #17
+[mp #19 #37]: false
+1d545e5a8707fb488f0ac2e96346b291c3993c78 78 0
+unsat
+#2 := false
+decl f3 :: (-> S2 S1)
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#515 := (pattern #8)
+decl f1 :: S1
+#3 := f1
+#9 := (= #8 f1)
+#10 := (not #9)
+#516 := (forall (vars (?v0 S2)) (:pat #515) #10)
+#94 := (forall (vars (?v0 S2)) #10)
+#519 := (iff #94 #516)
+#517 := (iff #10 #10)
+#518 := [refl]: #517
+#520 := [quant-intro #518]: #519
+#12 := (exists (vars (?v0 S2)) #9)
+#18 := (not #12)
+#95 := (~ #18 #94)
+#90 := (~ #10 #10)
+#91 := [refl]: #90
+#96 := [nnf-neg #91]: #95
+decl f4 :: (-> S2 S1)
+#13 := (f4 #7)
+#14 := (= #13 f1)
+#15 := (and #9 #14)
+#16 := (exists (vars (?v0 S2)) #15)
+#17 := (or #12 #16)
+#11 := (exists (vars (?v0 S2)) #10)
+#28 := (and #11 #17 #18)
+#19 := (and #17 #18)
+#20 := (and #11 #19)
+#21 := (not #20)
+#22 := (not #21)
+#39 := (iff #22 #28)
+#31 := (not #28)
+#34 := (not #31)
+#37 := (iff #34 #28)
+#38 := [rewrite]: #37
+#35 := (iff #22 #34)
+#32 := (iff #21 #31)
+#29 := (iff #20 #28)
+#30 := [rewrite]: #29
+#33 := [monotonicity #30]: #32
+#36 := [monotonicity #33]: #35
+#40 := [trans #36 #38]: #39
+#24 := [asserted]: #22
+#41 := [mp #24 #40]: #28
+#44 := [and-elim #41]: #18
+#97 := [mp~ #44 #96]: #94
+#521 := [mp #97 #520]: #516
+decl ?v0!1 :: S2
+#81 := ?v0!1
+#82 := (f3 ?v0!1)
+#83 := (= #82 f1)
+#84 := (f4 ?v0!1)
+#85 := (= #84 f1)
+#86 := (and #83 #85)
+#87 := (~ #16 #86)
+#88 := [sk]: #87
+#69 := (iff #17 #16)
+#64 := (or false #16)
+#71 := (iff #64 #16)
+#68 := [rewrite]: #71
+#65 := (iff #17 #64)
+#66 := (iff #12 false)
+#67 := [iff-false #44]: #66
+#70 := [monotonicity #67]: #65
+#72 := [trans #70 #68]: #69
+#43 := [and-elim #41]: #17
+#73 := [mp #43 #72]: #16
+#89 := [mp~ #73 #88]: #86
+#92 := [and-elim #89]: #83
+#98 := (not #83)
+#186 := (not #516)
+#100 := (or #186 #98)
+#187 := [quant-inst #81]: #100
+[unit-resolution #187 #92 #521]: false
+64ac5cdd2e2bbc8090d1b1182bdc796d3bfd82c3 42 0
+WARNING: failed to find a pattern for quantifier (quantifier id: k!10)
+unsat
+#2 := false
+#8 := (:var 0 S2)
+#7 := (:var 1 S2)
+#9 := (= #7 #8)
+#36 := (not #9)
+#39 := (forall (vars (?v0 S2) (?v1 S2)) #36)
+#448 := (not #39)
+decl elem!0 :: S2
+#44 := elem!0
+#45 := (= elem!0 elem!0)
+#454 := (not #45)
+#121 := (or #448 #454)
+#459 := (iff #121 #448)
+#108 := (or #448 false)
+#435 := (iff #108 #448)
+#453 := [rewrite]: #435
+#113 := (iff #121 #108)
+#455 := (iff #454 false)
+#1 := true
+#123 := (not true)
+#136 := (iff #123 false)
+#116 := [rewrite]: #136
+#134 := (iff #454 #123)
+#122 := (iff #45 true)
+#132 := [rewrite]: #122
+#135 := [monotonicity #132]: #134
+#457 := [trans #135 #116]: #455
+#93 := [monotonicity #457]: #113
+#450 := [trans #93 #453]: #459
+#458 := [quant-inst #44 #44]: #121
+#109 := [mp #458 #450]: #448
+#10 := (exists (vars (?v0 S2) (?v1 S2)) #9)
+#11 := (not #10)
+#40 := (~ #11 #39)
+#37 := (~ #36 #36)
+#38 := [refl]: #37
+#41 := [nnf-neg #38]: #40
+#13 := [asserted]: #11
+#42 := [mp~ #13 #41]: #39
+[unit-resolution #42 #109]: false
+9067d5c00609a8193d1707b7db4e437e84211a7e 137 0
+WARNING: For problems containing quantifiers, the model finding capabilities of Z3 work better when the formula does not contain nested quantifiers. You can use PULL_NESTED_QUANTIFIERS=true to eliminate nested quantifiers.
+unsat
+#2 := false
+decl f3 :: (-> S2 S1)
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#526 := (pattern #8)
+decl f1 :: S1
+#3 := f1
+#9 := (= #8 f1)
+#23 := (not #9)
+decl elem!0 :: S2
+#110 := elem!0
+#189 := (f3 elem!0)
+#518 := (= #189 f1)
+#523 := (not #518)
+#200 := (or #523 #23)
+#111 := (forall (vars (?v1 S2)) (:pat #526) #200)
+#201 := (not #111)
+#202 := (or #523 #201)
+#199 := (not #202)
+#10 := (:var 1 S2)
+#11 := (f3 #10)
+#12 := (= #11 f1)
+#72 := (not #12)
+#81 := (or #72 #23)
+#527 := (forall (vars (?v1 S2)) (:pat #526) #81)
+#532 := (not #527)
+#535 := (or #23 #532)
+#538 := (not #535)
+#541 := (forall (vars (?v0 S2)) (:pat #526) #538)
+#92 := (forall (vars (?v1 S2)) #81)
+#98 := (not #92)
+#99 := (or #23 #98)
+#100 := (not #99)
+#105 := (forall (vars (?v0 S2)) #100)
+#542 := (iff #105 #541)
+#539 := (iff #100 #538)
+#536 := (iff #99 #535)
+#533 := (iff #98 #532)
+#530 := (iff #92 #527)
+#528 := (iff #81 #81)
+#529 := [refl]: #528
+#531 := [quant-intro #529]: #530
+#534 := [monotonicity #531]: #533
+#537 := [monotonicity #534]: #536
+#540 := [monotonicity #537]: #539
+#543 := [quant-intro #540]: #542
+#13 := (and #12 #9)
+#56 := (not #13)
+#59 := (forall (vars (?v1 S2)) #56)
+#75 := (and #9 #59)
+#78 := (forall (vars (?v0 S2)) #75)
+#106 := (iff #78 #105)
+#103 := (iff #75 #100)
+#95 := (and #9 #92)
+#101 := (iff #95 #100)
+#102 := [rewrite]: #101
+#96 := (iff #75 #95)
+#93 := (iff #59 #92)
+#90 := (iff #56 #81)
+#82 := (not #81)
+#85 := (not #82)
+#88 := (iff #85 #81)
+#89 := [rewrite]: #88
+#86 := (iff #56 #85)
+#83 := (iff #13 #82)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84]: #86
+#91 := [trans #87 #89]: #90
+#94 := [quant-intro #91]: #93
+#97 := [monotonicity #94]: #96
+#104 := [trans #97 #102]: #103
+#107 := [quant-intro #104]: #106
+#53 := (not #23)
+#63 := (and #53 #59)
+#67 := (forall (vars (?v0 S2)) #63)
+#79 := (iff #67 #78)
+#76 := (iff #63 #75)
+#73 := (iff #53 #9)
+#74 := [rewrite]: #73
+#77 := [monotonicity #74]: #76
+#80 := [quant-intro #77]: #79
+#14 := (exists (vars (?v1 S2)) #13)
+#24 := (or #23 #14)
+#27 := (exists (vars (?v0 S2)) #24)
+#30 := (not #27)
+#68 := (~ #30 #67)
+#64 := (not #24)
+#65 := (~ #64 #63)
+#60 := (not #14)
+#61 := (~ #60 #59)
+#57 := (~ #56 #56)
+#58 := [refl]: #57
+#62 := [nnf-neg #58]: #61
+#54 := (~ #53 #53)
+#55 := [refl]: #54
+#66 := [nnf-neg #55 #62]: #65
+#69 := [nnf-neg #66]: #68
+#15 := (implies #9 #14)
+#16 := (exists (vars (?v0 S2)) #15)
+#17 := (not #16)
+#31 := (iff #17 #30)
+#28 := (iff #16 #27)
+#25 := (iff #15 #24)
+#26 := [rewrite]: #25
+#29 := [quant-intro #26]: #28
+#32 := [monotonicity #29]: #31
+#19 := [asserted]: #17
+#33 := [mp #19 #32]: #30
+#70 := [mp~ #33 #69]: #67
+#71 := [mp #70 #80]: #78
+#108 := [mp #71 #107]: #105
+#544 := [mp #108 #543]: #541
+#525 := (not #541)
+#188 := (or #525 #199)
+#524 := [quant-inst #110]: #188
+#506 := [unit-resolution #524 #544]: #199
+#174 := (or #202 #111)
+#179 := [def-axiom]: #174
+#507 := [unit-resolution #179 #506]: #111
+#515 := (or #202 #518)
+#521 := [def-axiom]: #515
+#502 := [unit-resolution #521 #506]: #518
+#159 := (or #201 #523)
+#176 := (or #523 #523)
+#501 := (or #201 #176)
+#164 := (iff #501 #159)
+#166 := (iff #159 #159)
+#503 := [rewrite]: #166
+#519 := (iff #176 #523)
+#517 := [rewrite]: #519
+#165 := [monotonicity #517]: #164
+#504 := [trans #165 #503]: #164
+#163 := [quant-inst #110]: #501
+#505 := [mp #163 #504]: #159
+[unit-resolution #505 #502 #507]: false
+cfadbe698d1c93f37fd55e77c41527ea8fc85b34 168 0
+unsat
+#2 := false
+decl f3 :: (-> S2 S1)
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#527 := (pattern #8)
+decl f1 :: S1
+#3 := f1
+#9 := (= #8 f1)
+#47 := (not #9)
+#528 := (forall (vars (?v0 S2)) (:pat #527) #47)
+decl f4 :: S1
+#11 := f4
+#12 := (= f4 f1)
+#533 := (not #528)
+#536 := (or #533 #12)
+#539 := (not #536)
+#14 := (or #9 #12)
+#79 := (not #14)
+#542 := (forall (vars (?v0 S2)) (:pat #527) #79)
+#164 := (not #542)
+decl ?v0!1 :: S2
+#73 := ?v0!1
+#74 := (f3 ?v0!1)
+#75 := (= #74 f1)
+#76 := (or #75 #12)
+#54 := (not #12)
+decl elem!2 :: S2
+#522 := elem!2
+#526 := (f3 elem!2)
+#176 := (= #526 f1)
+#160 := (or #176 #12)
+#502 := (not #160)
+#503 := [hypothesis]: #542
+#517 := (or #164 #502)
+#165 := [quant-inst #522]: #517
+#223 := [unit-resolution #165 #503]: #502
+#505 := (or #160 #54)
+#506 := [def-axiom]: #505
+#224 := [unit-resolution #506 #223]: #54
+decl ?v0!0 :: S2
+#60 := ?v0!0
+#61 := (f3 ?v0!0)
+#62 := (= #61 f1)
+#190 := (not #62)
+#67 := (or #62 #12)
+#180 := (not #67)
+#500 := (or #180 #164)
+#518 := [hypothesis]: #67
+#509 := (or #164 #180)
+#146 := [quant-inst #60]: #509
+#514 := [unit-resolution #146 #503 #518]: false
+#501 := [lemma #514]: #500
+#498 := [unit-resolution #501 #503]: #180
+#510 := (or #67 #190)
+#512 := [def-axiom]: #510
+#495 := [unit-resolution #512 #498]: #190
+#94 := (or #62 #75 #12)
+#82 := (forall (vars (?v0 S2)) #79)
+#50 := (forall (vars (?v0 S2)) #47)
+#57 := (and #50 #54)
+#86 := (or #57 #82)
+#97 := (and #94 #86)
+#87 := (or #67 #76)
+#88 := (and #87 #86)
+#98 := (iff #88 #97)
+#95 := (iff #87 #94)
+#96 := [rewrite]: #95
+#99 := [monotonicity #96]: #98
+#15 := (exists (vars (?v0 S2)) #14)
+#10 := (exists (vars (?v0 S2)) #9)
+#13 := (or #10 #12)
+#23 := (not #13)
+#24 := (iff #23 #15)
+#89 := (~ #24 #88)
+#83 := (not #15)
+#84 := (~ #83 #82)
+#80 := (~ #79 #79)
+#81 := [refl]: #80
+#85 := [nnf-neg #81]: #84
+#77 := (~ #15 #76)
+#78 := [sk]: #77
+#70 := (not #23)
+#71 := (~ #70 #67)
+#68 := (~ #13 #67)
+#65 := (~ #12 #12)
+#66 := [refl]: #65
+#63 := (~ #10 #62)
+#64 := [sk]: #63
+#69 := [monotonicity #64 #66]: #68
+#72 := [nnf-neg #69]: #71
+#58 := (~ #23 #57)
+#55 := (~ #54 #54)
+#56 := [refl]: #55
+#51 := (not #10)
+#52 := (~ #51 #50)
+#48 := (~ #47 #47)
+#49 := [refl]: #48
+#53 := [nnf-neg #49]: #52
+#59 := [nnf-neg #53 #56]: #58
+#90 := [nnf-pos #59 #72 #78 #85]: #89
+#16 := (iff #13 #15)
+#17 := (not #16)
+#25 := (iff #17 #24)
+#26 := [rewrite]: #25
+#19 := [asserted]: #17
+#27 := [mp #19 #26]: #24
+#91 := [mp~ #27 #90]: #88
+#92 := [mp #91 #99]: #97
+#93 := [and-elim #92]: #94
+#499 := [unit-resolution #93 #495 #224]: #75
+#204 := (not #75)
+#118 := (or #76 #204)
+#496 := [def-axiom]: #118
+#209 := [unit-resolution #496 #499]: #76
+#208 := (not #76)
+#225 := (or #164 #208)
+#226 := [quant-inst #73]: #225
+#210 := [unit-resolution #226 #503 #209]: false
+#211 := [lemma #210]: #164
+#547 := (or #539 #542)
+#101 := (not #50)
+#102 := (or #101 #12)
+#103 := (not #102)
+#106 := (or #103 #82)
+#548 := (iff #106 #547)
+#545 := (iff #82 #542)
+#543 := (iff #79 #79)
+#544 := [refl]: #543
+#546 := [quant-intro #544]: #545
+#540 := (iff #103 #539)
+#537 := (iff #102 #536)
+#534 := (iff #101 #533)
+#531 := (iff #50 #528)
+#529 := (iff #47 #47)
+#530 := [refl]: #529
+#532 := [quant-intro #530]: #531
+#535 := [monotonicity #532]: #534
+#538 := [monotonicity #535]: #537
+#541 := [monotonicity #538]: #540
+#549 := [monotonicity #541 #546]: #548
+#107 := (iff #86 #106)
+#104 := (iff #57 #103)
+#105 := [rewrite]: #104
+#108 := [monotonicity #105]: #107
+#100 := [and-elim #92]: #86
+#109 := [mp #100 #108]: #106
+#550 := [mp #109 #549]: #547
+#497 := [unit-resolution #550 #211]: #539
+#110 := (or #536 #528)
+#197 := [def-axiom]: #110
+#219 := [unit-resolution #197 #497]: #528
+#308 := (or #536 #75)
+#201 := [hypothesis]: #539
+#202 := [unit-resolution #197 #201]: #528
+#183 := [hypothesis]: #204
+#111 := (or #536 #54)
+#198 := [def-axiom]: #111
+#519 := [unit-resolution #198 #201]: #54
+#521 := [unit-resolution #93 #519 #183]: #62
+#203 := (or #533 #190)
+#200 := [quant-inst #60]: #203
+#177 := [unit-resolution #200 #521 #202]: false
+#515 := [lemma #177]: #308
+#212 := [unit-resolution #515 #497]: #75
+#220 := (or #533 #204)
+#494 := [quant-inst #73]: #220
+[unit-resolution #494 #212 #219]: false
+faa0d29344cac3f1cd8aa3672c93e609546ff0cf 98 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+decl f5 :: S2
+#13 := f5
+#14 := (f3 f5)
+#15 := (= #14 f1)
+#63 := (not #15)
+decl f4 :: S2
+#10 := f4
+#11 := (f3 f4)
+#12 := (= #11 f1)
+#62 := (not #12)
+#64 := (or #62 #63)
+#65 := (not #64)
+#476 := (or #62 #65)
+#487 := (or #63 #65)
+#276 := (not #487)
+#486 := [hypothesis]: #487
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#495 := (pattern #8)
+#9 := (= #8 f1)
+#25 := (not #9)
+#68 := (or #25 #65)
+#71 := (not #68)
+#496 := (forall (vars (?v0 S2)) (:pat #495) #71)
+#74 := (forall (vars (?v0 S2)) #71)
+#499 := (iff #74 #496)
+#497 := (iff #71 #71)
+#498 := [refl]: #497
+#500 := [quant-intro #498]: #499
+#16 := (and #12 #15)
+#26 := (or #25 #16)
+#55 := (not #26)
+#58 := (forall (vars (?v0 S2)) #55)
+#75 := (iff #58 #74)
+#72 := (iff #55 #71)
+#69 := (iff #26 #68)
+#66 := (iff #16 #65)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#73 := [monotonicity #70]: #72
+#76 := [quant-intro #73]: #75
+#29 := (exists (vars (?v0 S2)) #26)
+#32 := (not #29)
+#59 := (~ #32 #58)
+#56 := (~ #55 #55)
+#57 := [refl]: #56
+#60 := [nnf-neg #57]: #59
+#17 := (implies #9 #16)
+#18 := (exists (vars (?v0 S2)) #17)
+#19 := (not #18)
+#33 := (iff #19 #32)
+#30 := (iff #18 #29)
+#27 := (iff #17 #26)
+#28 := [rewrite]: #27
+#31 := [quant-intro #28]: #30
+#34 := [monotonicity #31]: #33
+#21 := [asserted]: #19
+#35 := [mp #21 #34]: #32
+#61 := [mp~ #35 #60]: #58
+#77 := [mp #61 #76]: #74
+#501 := [mp #77 #500]: #496
+#172 := (not #496)
+#470 := (or #172 #276)
+#132 := [quant-inst #13]: #470
+#128 := [unit-resolution #132 #501 #486]: false
+#475 := [lemma #128]: #276
+#133 := (or #487 #15)
+#134 := [def-axiom]: #133
+#477 := [unit-resolution #134 #475]: #15
+decl elem!0 :: S2
+#79 := elem!0
+#169 := (f3 elem!0)
+#151 := (= #169 f1)
+#489 := (not #151)
+#145 := (or #489 #65)
+#168 := (not #145)
+#483 := (or #172 #168)
+#156 := [quant-inst #79]: #483
+#114 := [unit-resolution #156 #501]: #168
+#143 := (or #145 #64)
+#148 := [def-axiom]: #143
+#469 := [unit-resolution #148 #114]: #64
+#493 := (or #65 #62 #63)
+#488 := [def-axiom]: #493
+#176 := [unit-resolution #488 #469]: #64
+#191 := [unit-resolution #176 #477]: #62
+#119 := (or #476 #12)
+#120 := [def-axiom]: #119
+#192 := [unit-resolution #120 #191]: #476
+#471 := (not #476)
+#478 := (or #172 #471)
+#480 := [quant-inst #10]: #478
+[unit-resolution #480 #501 #192]: false
+68f7af3545a2e0a392ee944cd5535bbc7c76b3dc 84 0
+unsat
+#2 := false
+decl f3 :: (-> S2 S1)
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#494 := (pattern #8)
+decl f1 :: S1
+#3 := f1
+#9 := (= #8 f1)
+decl ?v1!0 :: S2
+#49 := ?v1!0
+#50 := (f3 ?v1!0)
+#51 := (= #50 f1)
+#68 := (not #51)
+#69 := (or #68 #9)
+#70 := (not #69)
+#495 := (forall (vars (?v0 S2)) (:pat #494) #70)
+#275 := (not #495)
+#167 := (or #68 #51)
+#486 := (not #167)
+#131 := (or #275 #486)
+#474 := (iff #131 #275)
+#133 := (or #275 false)
+#472 := (iff #133 #275)
+#473 := [rewrite]: #472
+#134 := (iff #131 #133)
+#127 := (iff #486 false)
+#1 := true
+#142 := (not true)
+#143 := (iff #142 false)
+#485 := [rewrite]: #143
+#147 := (iff #486 #142)
+#493 := (iff #167 true)
+#483 := [rewrite]: #493
+#484 := [monotonicity #483]: #147
+#469 := [trans #484 #485]: #127
+#471 := [monotonicity #469]: #134
+#475 := [trans #471 #473]: #474
+#132 := [quant-inst #49]: #131
+#470 := [mp #132 #475]: #275
+#73 := (forall (vars (?v0 S2)) #70)
+#498 := (iff #73 #495)
+#496 := (iff #70 #70)
+#497 := [refl]: #496
+#499 := [quant-intro #497]: #498
+#57 := (not #9)
+#60 := (and #51 #57)
+#64 := (forall (vars (?v0 S2)) #60)
+#74 := (iff #64 #73)
+#71 := (iff #60 #70)
+#72 := [rewrite]: #71
+#75 := [quant-intro #72]: #74
+#10 := (exists (vars (?v1 S2)) #9)
+#19 := (not #10)
+#20 := (or #19 #9)
+#23 := (exists (vars (?v0 S2)) #20)
+#26 := (not #23)
+#65 := (~ #26 #64)
+#61 := (not #20)
+#62 := (~ #61 #60)
+#58 := (~ #57 #57)
+#59 := [refl]: #58
+#54 := (not #19)
+#55 := (~ #54 #51)
+#52 := (~ #10 #51)
+#53 := [sk]: #52
+#56 := [nnf-neg #53]: #55
+#63 := [nnf-neg #56 #59]: #62
+#66 := [nnf-neg #63]: #65
+#11 := (implies #10 #9)
+#12 := (exists (vars (?v0 S2)) #11)
+#13 := (not #12)
+#27 := (iff #13 #26)
+#24 := (iff #12 #23)
+#21 := (iff #11 #20)
+#22 := [rewrite]: #21
+#25 := [quant-intro #22]: #24
+#28 := [monotonicity #25]: #27
+#15 := [asserted]: #13
+#29 := [mp #15 #28]: #26
+#67 := [mp~ #29 #66]: #64
+#76 := [mp #67 #75]: #73
+#500 := [mp #76 #499]: #495
+[unit-resolution #500 #470]: false
+c7dcc81d0a2f31db2403b790a9ba1ebc57f8c894 195 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: (-> S2 S1)
+decl ?v0!0 :: S2
+#71 := ?v0!0
+#72 := (f4 ?v0!0)
+#73 := (= #72 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#23 := (not #8)
+#74 := (or #23 #73)
+decl ?v0!1 :: S2
+#82 := ?v0!1
+#83 := (f4 ?v0!1)
+#84 := (= #83 f1)
+#535 := (not #84)
+#87 := (or #23 #84)
+#537 := (not #87)
+#540 := [hypothesis]: #87
+#9 := (:var 0 S2)
+#10 := (f4 #9)
+#553 := (pattern #10)
+#11 := (= #10 f1)
+#24 := (or #23 #11)
+#65 := (not #24)
+#554 := (forall (vars (?v0 S2)) (:pat #553) #65)
+#93 := (not #11)
+#559 := (forall (vars (?v0 S2)) (:pat #553) #93)
+#564 := (not #559)
+#567 := (or #23 #564)
+#193 := [hypothesis]: #559
+decl elem!2 :: S2
+#229 := elem!2
+#547 := (f4 elem!2)
+#215 := (= #547 f1)
+#549 := (or #23 #215)
+#541 := [hypothesis]: #23
+#552 := (or #549 #8)
+#542 := [def-axiom]: #552
+#548 := [unit-resolution #542 #541]: #549
+#136 := (or #567 #8)
+#223 := [def-axiom]: #136
+#186 := [unit-resolution #223 #541]: #567
+#570 := (not #567)
+#573 := (or #554 #570)
+#96 := (forall (vars (?v0 S2)) #93)
+#127 := (not #96)
+#128 := (or #23 #127)
+#129 := (not #128)
+#68 := (forall (vars (?v0 S2)) #65)
+#132 := (or #68 #129)
+#574 := (iff #132 #573)
+#571 := (iff #129 #570)
+#568 := (iff #128 #567)
+#565 := (iff #127 #564)
+#562 := (iff #96 #559)
+#560 := (iff #93 #93)
+#561 := [refl]: #560
+#563 := [quant-intro #561]: #562
+#566 := [monotonicity #563]: #565
+#569 := [monotonicity #566]: #568
+#572 := [monotonicity #569]: #571
+#557 := (iff #68 #554)
+#555 := (iff #65 #65)
+#556 := [refl]: #555
+#558 := [quant-intro #556]: #557
+#575 := [monotonicity #558 #572]: #574
+#117 := (and #8 #96)
+#120 := (or #68 #117)
+#133 := (iff #120 #132)
+#130 := (iff #117 #129)
+#131 := [rewrite]: #130
+#134 := [monotonicity #131]: #133
+#112 := (or #73 #23 #84)
+#123 := (and #112 #120)
+#90 := (not #23)
+#100 := (and #90 #96)
+#104 := (or #68 #100)
+#105 := (or #74 #87)
+#106 := (and #105 #104)
+#124 := (iff #106 #123)
+#121 := (iff #104 #120)
+#118 := (iff #100 #117)
+#115 := (iff #90 #8)
+#116 := [rewrite]: #115
+#119 := [monotonicity #116]: #118
+#122 := [monotonicity #119]: #121
+#113 := (iff #105 #112)
+#114 := [rewrite]: #113
+#125 := [monotonicity #114 #122]: #124
+#14 := (exists (vars (?v0 S2)) #11)
+#30 := (or #23 #14)
+#27 := (exists (vars (?v0 S2)) #24)
+#39 := (not #27)
+#40 := (iff #39 #30)
+#107 := (~ #40 #106)
+#101 := (not #30)
+#102 := (~ #101 #100)
+#97 := (not #14)
+#98 := (~ #97 #96)
+#94 := (~ #93 #93)
+#95 := [refl]: #94
+#99 := [nnf-neg #95]: #98
+#91 := (~ #90 #90)
+#92 := [refl]: #91
+#103 := [nnf-neg #92 #99]: #102
+#88 := (~ #30 #87)
+#85 := (~ #14 #84)
+#86 := [sk]: #85
+#80 := (~ #23 #23)
+#81 := [refl]: #80
+#89 := [monotonicity #81 #86]: #88
+#77 := (not #39)
+#78 := (~ #77 #74)
+#75 := (~ #27 #74)
+#76 := [sk]: #75
+#79 := [nnf-neg #76]: #78
+#69 := (~ #39 #68)
+#66 := (~ #65 #65)
+#67 := [refl]: #66
+#70 := [nnf-neg #67]: #69
+#108 := [nnf-pos #70 #79 #89 #103]: #107
+#15 := (implies #8 #14)
+#12 := (implies #8 #11)
+#13 := (exists (vars (?v0 S2)) #12)
+#16 := (iff #13 #15)
+#17 := (not #16)
+#43 := (iff #17 #40)
+#33 := (iff #27 #30)
+#36 := (not #33)
+#41 := (iff #36 #40)
+#42 := [rewrite]: #41
+#37 := (iff #17 #36)
+#34 := (iff #16 #33)
+#31 := (iff #15 #30)
+#32 := [rewrite]: #31
+#28 := (iff #13 #27)
+#25 := (iff #12 #24)
+#26 := [rewrite]: #25
+#29 := [quant-intro #26]: #28
+#35 := [monotonicity #29 #32]: #34
+#38 := [monotonicity #35]: #37
+#44 := [trans #38 #42]: #43
+#19 := [asserted]: #17
+#45 := [mp #19 #44]: #40
+#109 := [mp~ #45 #108]: #106
+#110 := [mp #109 #125]: #123
+#126 := [and-elim #110]: #120
+#135 := [mp #126 #134]: #132
+#576 := [mp #135 #575]: #573
+#528 := [unit-resolution #576 #186]: #554
+#550 := (not #549)
+#551 := (not #554)
+#214 := (or #551 #550)
+#546 := [quant-inst #229]: #214
+#190 := [unit-resolution #546 #528 #548]: false
+#191 := [lemma #190]: #8
+#192 := (not #73)
+#534 := (or #192 #564)
+#530 := [hypothesis]: #73
+#531 := (or #564 #192)
+#532 := [quant-inst #71]: #531
+#533 := [unit-resolution #532 #530 #193]: false
+#529 := [lemma #533]: #534
+#172 := [unit-resolution #529 #193]: #192
+#111 := [and-elim #110]: #112
+#536 := [unit-resolution #111 #172 #191]: #84
+#538 := (or #564 #535)
+#177 := [quant-inst #82]: #538
+#178 := [unit-resolution #177 #536 #193]: false
+#539 := [lemma #178]: #564
+#137 := (or #567 #559)
+#224 := [def-axiom]: #137
+#526 := [unit-resolution #224 #539]: #567
+#523 := [unit-resolution #576 #526]: #554
+#527 := (or #551 #537)
+#234 := [quant-inst #82]: #527
+#245 := [unit-resolution #234 #523 #540]: false
+#246 := [lemma #245]: #537
+#251 := (or #87 #535)
+#252 := [def-axiom]: #251
+#524 := [unit-resolution #252 #246]: #535
+#521 := (or #73 #84)
+#514 := [unit-resolution #111 #191]: #521
+#518 := [unit-resolution #514 #524]: #73
+#238 := (or #74 #192)
+#516 := [def-axiom]: #238
+#515 := [unit-resolution #516 #518]: #74
+#520 := (not #74)
+#525 := (or #551 #520)
+#235 := [quant-inst #71]: #525
+[unit-resolution #235 #523 #515]: false
+b3778beae28d076e6c36fc9b45a5fba8752cdac2 79 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1 S1)
+decl ?v0!1 :: S1
+#56 := ?v0!1
+decl f4 :: S2
+#7 := f4
+#57 := (f3 f4 ?v0!1)
+#58 := (= #57 f1)
+decl ?v0!0 :: S1
+#45 := ?v0!0
+#46 := (f3 f4 ?v0!0)
+#47 := (= #46 f1)
+#83 := (not #47)
+#170 := [hypothesis]: #47
+#8 := (:var 0 S1)
+#9 := (f3 f4 #8)
+#500 := (pattern #9)
+#10 := (= #9 f1)
+#13 := (not #10)
+#501 := (forall (vars (?v0 S1)) (:pat #500) #13)
+#14 := (forall (vars (?v0 S1)) #13)
+#504 := (iff #14 #501)
+#502 := (iff #13 #13)
+#503 := [refl]: #502
+#505 := [quant-intro #503]: #504
+#76 := (or #47 #58)
+#79 := (and #14 #76)
+#59 := (not #58)
+#60 := (not #59)
+#64 := (or #47 #60)
+#65 := (or #14 #14)
+#66 := (and #65 #64)
+#80 := (iff #66 #79)
+#77 := (iff #64 #76)
+#74 := (iff #60 #58)
+#75 := [rewrite]: #74
+#78 := [monotonicity #75]: #77
+#72 := (iff #65 #14)
+#73 := [rewrite]: #72
+#81 := [monotonicity #73 #78]: #80
+#11 := (exists (vars (?v0 S1)) #10)
+#22 := (iff #11 #14)
+#67 := (~ #22 #66)
+#61 := (not #14)
+#62 := (~ #61 #60)
+#63 := [sk]: #62
+#54 := (~ #14 #14)
+#50 := (~ #13 #13)
+#51 := [refl]: #50
+#55 := [nnf-pos #51]: #54
+#12 := (not #11)
+#52 := (~ #12 #14)
+#53 := [nnf-neg #51]: #52
+#48 := (~ #11 #47)
+#49 := [sk]: #48
+#68 := [nnf-pos #49 #53 #55 #63]: #67
+#15 := (iff #12 #14)
+#16 := (not #15)
+#23 := (iff #16 #22)
+#24 := [rewrite]: #23
+#18 := [asserted]: #16
+#25 := [mp #18 #24]: #22
+#69 := [mp~ #25 #68]: #66
+#70 := [mp #69 #81]: #79
+#71 := [and-elim #70]: #14
+#506 := [mp #71 #505]: #501
+#171 := (not #501)
+#85 := (or #171 #83)
+#172 := [quant-inst #45]: #85
+#84 := [unit-resolution #172 #506 #170]: false
+#163 := [lemma #84]: #83
+#82 := [and-elim #70]: #76
+#174 := [unit-resolution #82 #163]: #58
+#176 := (or #171 #59)
+#173 := [quant-inst #56]: #176
+[unit-resolution #173 #506 #174]: false
+2d8fd1a0ef67720701cd879eda1b0854a5ebf849 179 0
+unsat
+#2 := false
+decl f3 :: (-> S2 S1 S1)
+#8 := (:var 0 S1)
+decl f4 :: S2
+#7 := f4
+#9 := (f3 f4 #8)
+#546 := (pattern #9)
+decl f1 :: S1
+#3 := f1
+#10 := (= #9 f1)
+#552 := (forall (vars (?v0 S1)) (:pat #546) #10)
+decl f5 :: S1
+#11 := f5
+#12 := (= f5 f1)
+#557 := (not #552)
+#560 := (or #557 #12)
+#563 := (not #560)
+#24 := (not #10)
+#25 := (or #24 #12)
+#67 := (not #25)
+#547 := (forall (vars (?v0 S1)) (:pat #546) #67)
+#534 := (not #547)
+decl ?v0!0 :: S1
+#73 := ?v0!0
+#74 := (f3 f4 ?v0!0)
+#75 := (= #74 f1)
+#76 := (not #75)
+#77 := (or #76 #12)
+decl ?v0!1 :: S1
+#83 := ?v0!1
+#84 := (f3 f4 ?v0!1)
+#85 := (= #84 f1)
+#86 := (not #85)
+#91 := (or #86 #12)
+#222 := [hypothesis]: #86
+#541 := (or #91 #85)
+#542 := [def-axiom]: #541
+#196 := [unit-resolution #542 #222]: #91
+#219 := (or #557 #85)
+#221 := [hypothesis]: #552
+#223 := [quant-inst #83]: #219
+#202 := [unit-resolution #223 #222 #221]: false
+#538 := [lemma #202]: #219
+#327 := [unit-resolution #538 #222]: #557
+#129 := (or #560 #552)
+#130 := [def-axiom]: #129
+#535 := [unit-resolution #130 #327]: #560
+#566 := (or #547 #563)
+#15 := (forall (vars (?v0 S1)) #10)
+#31 := (not #15)
+#32 := (or #31 #12)
+#105 := (not #32)
+#70 := (forall (vars (?v0 S1)) #67)
+#125 := (or #70 #105)
+#567 := (iff #125 #566)
+#564 := (iff #105 #563)
+#561 := (iff #32 #560)
+#558 := (iff #31 #557)
+#555 := (iff #15 #552)
+#553 := (iff #10 #10)
+#554 := [refl]: #553
+#556 := [quant-intro #554]: #555
+#559 := [monotonicity #556]: #558
+#562 := [monotonicity #559]: #561
+#565 := [monotonicity #562]: #564
+#550 := (iff #70 #547)
+#548 := (iff #67 #67)
+#549 := [refl]: #548
+#551 := [quant-intro #549]: #550
+#568 := [monotonicity #551 #565]: #567
+#101 := (not #12)
+#104 := (and #15 #101)
+#108 := (or #70 #104)
+#126 := (iff #108 #125)
+#123 := (iff #104 #105)
+#124 := [rewrite]: #123
+#127 := [monotonicity #124]: #126
+#116 := (or #76 #86 #12)
+#119 := (and #116 #108)
+#109 := (or #77 #91)
+#110 := (and #109 #108)
+#120 := (iff #110 #119)
+#117 := (iff #109 #116)
+#118 := [rewrite]: #117
+#121 := [monotonicity #118]: #120
+#28 := (exists (vars (?v0 S1)) #25)
+#41 := (not #28)
+#42 := (iff #41 #32)
+#111 := (~ #42 #110)
+#106 := (~ #105 #104)
+#102 := (~ #101 #101)
+#103 := [refl]: #102
+#98 := (not #31)
+#99 := (~ #98 #15)
+#96 := (~ #15 #15)
+#94 := (~ #10 #10)
+#95 := [refl]: #94
+#97 := [nnf-pos #95]: #96
+#100 := [nnf-neg #97]: #99
+#107 := [nnf-neg #100 #103]: #106
+#92 := (~ #32 #91)
+#89 := (~ #12 #12)
+#90 := [refl]: #89
+#87 := (~ #31 #86)
+#88 := [sk]: #87
+#93 := [monotonicity #88 #90]: #92
+#80 := (not #41)
+#81 := (~ #80 #77)
+#78 := (~ #28 #77)
+#79 := [sk]: #78
+#82 := [nnf-neg #79]: #81
+#71 := (~ #41 #70)
+#68 := (~ #67 #67)
+#69 := [refl]: #68
+#72 := [nnf-neg #69]: #71
+#112 := [nnf-pos #72 #82 #93 #107]: #111
+#16 := (implies #15 #12)
+#13 := (implies #10 #12)
+#14 := (exists (vars (?v0 S1)) #13)
+#17 := (iff #14 #16)
+#18 := (not #17)
+#45 := (iff #18 #42)
+#35 := (iff #28 #32)
+#38 := (not #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #18 #38)
+#36 := (iff #17 #35)
+#33 := (iff #16 #32)
+#34 := [rewrite]: #33
+#29 := (iff #14 #28)
+#26 := (iff #13 #25)
+#27 := [rewrite]: #26
+#30 := [quant-intro #27]: #29
+#37 := [monotonicity #30 #34]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#20 := [asserted]: #18
+#47 := [mp #20 #46]: #42
+#113 := [mp~ #47 #112]: #110
+#114 := [mp #113 #121]: #119
+#122 := [and-elim #114]: #108
+#128 := [mp #122 #127]: #125
+#569 := [mp #128 #568]: #566
+#194 := [unit-resolution #569 #535]: #547
+#540 := (not #91)
+#207 := (or #534 #540)
+#208 := [quant-inst #83]: #207
+#199 := [unit-resolution #208 #194 #196]: false
+#536 := [lemma #199]: #85
+#543 := (not #77)
+#525 := [hypothesis]: #543
+#537 := (or #77 #75)
+#179 := [def-axiom]: #537
+#526 := [unit-resolution #179 #525]: #75
+#521 := (or #77 #101)
+#183 := [def-axiom]: #521
+#527 := [unit-resolution #183 #525]: #101
+#115 := [and-elim #114]: #116
+#522 := [unit-resolution #115 #527 #526 #536]: false
+#528 := [lemma #522]: #77
+#523 := (or #543 #534)
+#544 := [hypothesis]: #77
+#539 := [hypothesis]: #547
+#545 := (or #534 #543)
+#195 := [quant-inst #73]: #545
+#186 := [unit-resolution #195 #539 #544]: false
+#524 := [lemma #186]: #523
+#165 := [unit-resolution #524 #528]: #534
+#529 := [unit-resolution #569 #165]: #563
+#171 := [unit-resolution #130 #529]: #552
+#216 := (or #560 #101)
+#217 := [def-axiom]: #216
+#532 := [unit-resolution #217 #529]: #101
+#530 := [unit-resolution #115 #532 #536]: #76
+#531 := (or #557 #75)
+#170 := [quant-inst #73]: #531
+[unit-resolution #170 #530 #171]: false
+5068ada6674873a5a5e5c36bb6eb28fe2d67f362 128 0
+unsat
+#2 := false
+decl f3 :: (-> S3 S2 S1)
+#10 := (:var 0 S2)
+decl f4 :: (-> S4 S1 S3)
+decl f6 :: S1
+#16 := f6
+decl f5 :: S4
+#7 := f5
+#17 := (f4 f5 f6)
+#18 := (f3 #17 #10)
+#523 := (pattern #18)
+decl f1 :: S1
+#3 := f1
+#19 := (= #18 f1)
+#67 := (not #19)
+#524 := (forall (vars (?v0 S2)) (:pat #523) #67)
+decl f7 :: S2
+#21 := f7
+#22 := (f3 #17 f7)
+#23 := (= #22 f1)
+#97 := (= f6 f1)
+#98 := (iff #23 #97)
+#8 := (:var 1 S1)
+#9 := (f4 f5 #8)
+#11 := (f3 #9 #10)
+#516 := (pattern #11)
+#13 := (= #8 f1)
+#12 := (= #11 f1)
+#14 := (iff #12 #13)
+#517 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #516) #14)
+#15 := (forall (vars (?v0 S1) (?v1 S2)) #14)
+#520 := (iff #15 #517)
+#518 := (iff #14 #14)
+#519 := [refl]: #518
+#521 := [quant-intro #519]: #520
+#69 := (~ #15 #15)
+#71 := (~ #14 #14)
+#72 := [refl]: #71
+#70 := [nnf-pos #72]: #69
+#20 := (exists (vars (?v0 S2)) #19)
+#24 := (iff #20 #23)
+#32 := (not #15)
+#33 := (or #32 #24)
+#36 := (not #33)
+#25 := (implies #15 #24)
+#26 := (not #25)
+#37 := (iff #26 #36)
+#34 := (iff #25 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#28 := [asserted]: #26
+#39 := [mp #28 #38]: #36
+#40 := [not-or-elim #39]: #15
+#66 := [mp~ #40 #70]: #15
+#522 := [mp #66 #521]: #517
+#101 := (not #517)
+#178 := (or #101 #98)
+#511 := [quant-inst #16 #21]: #178
+#187 := [unit-resolution #511 #522]: #98
+decl ?v0!0 :: S2
+#78 := ?v0!0
+#79 := (f3 #17 ?v0!0)
+#80 := (= #79 f1)
+#186 := (iff #80 #97)
+#188 := (or #101 #186)
+#179 := [quant-inst #16 #78]: #188
+#177 := [unit-resolution #179 #522]: #186
+#190 := (not #186)
+#149 := (or #190 #97)
+#88 := (not #23)
+#165 := [hypothesis]: #88
+#92 := (or #80 #23)
+#75 := (forall (vars (?v0 S2)) #67)
+#91 := (or #75 #88)
+#93 := (and #92 #91)
+#62 := (not #20)
+#63 := (iff #62 #23)
+#94 := (~ #63 #93)
+#89 := (~ #88 #88)
+#90 := [refl]: #89
+#86 := (~ #23 #23)
+#87 := [refl]: #86
+#83 := (not #62)
+#84 := (~ #83 #80)
+#81 := (~ #20 #80)
+#82 := [sk]: #81
+#85 := [nnf-neg #82]: #84
+#76 := (~ #62 #75)
+#73 := (~ #67 #67)
+#74 := [refl]: #73
+#77 := [nnf-neg #74]: #76
+#95 := [nnf-pos #77 #85 #87 #90]: #94
+#41 := (not #24)
+#64 := (iff #41 #63)
+#65 := [rewrite]: #64
+#42 := [not-or-elim #39]: #41
+#68 := [mp #42 #65]: #63
+#96 := [mp~ #68 #95]: #93
+#99 := [and-elim #96]: #92
+#507 := [unit-resolution #99 #165]: #80
+#193 := (not #80)
+#172 := (or #190 #193 #97)
+#508 := [def-axiom]: #172
+#491 := [unit-resolution #508 #507]: #149
+#153 := [unit-resolution #491 #177]: #97
+#191 := (not #97)
+#512 := (not #98)
+#154 := (or #512 #191)
+#513 := (or #512 #23 #191)
+#514 := [def-axiom]: #513
+#155 := [unit-resolution #514 #165]: #154
+#156 := [unit-resolution #155 #153 #187]: false
+#493 := [lemma #156]: #23
+#529 := (or #524 #88)
+#530 := (iff #91 #529)
+#527 := (iff #75 #524)
+#525 := (iff #67 #67)
+#526 := [refl]: #525
+#528 := [quant-intro #526]: #527
+#531 := [monotonicity #528]: #530
+#100 := [and-elim #96]: #91
+#532 := [mp #100 #531]: #529
+#192 := [unit-resolution #532 #493]: #524
+#505 := (not #524)
+#164 := (or #505 #88)
+#169 := [quant-inst #21]: #164
+[unit-resolution #169 #493 #192]: false
+e77b347bc6ad4af31e73ee2068809dd306b3d8ad 73 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1 S1)
+decl f5 :: S1
+#8 := f5
+decl f4 :: S2
+#7 := f4
+#9 := (f3 f4 f5)
+#10 := (= #9 f1)
+decl f6 :: S1
+#19 := f6
+#20 := (f3 f4 f6)
+#21 := (= #20 f1)
+#30 := (not #10)
+#11 := (:var 0 S1)
+#12 := (f3 f4 #11)
+#13 := (= #12 f1)
+#16 := (not #13)
+#17 := (forall (vars (?v0 S1)) #16)
+#14 := (exists (vars (?v0 S1)) #13)
+#15 := (not #14)
+#18 := (if #10 #15 #17)
+#37 := (not #18)
+#38 := (or #37 #30 #21)
+#43 := (not #38)
+#22 := (implies #10 #21)
+#23 := (implies #18 #22)
+#24 := (not #23)
+#44 := (iff #24 #43)
+#41 := (iff #23 #38)
+#31 := (or #30 #21)
+#34 := (implies #18 #31)
+#39 := (iff #34 #38)
+#40 := [rewrite]: #39
+#35 := (iff #23 #34)
+#32 := (iff #22 #31)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#42 := [trans #36 #40]: #41
+#45 := [monotonicity #42]: #44
+#26 := [asserted]: #24
+#46 := [mp #26 #45]: #43
+#48 := [not-or-elim #46]: #10
+#502 := (pattern #12)
+#503 := (forall (vars (?v0 S1)) (:pat #502) #16)
+#506 := (iff #17 #503)
+#504 := (iff #16 #16)
+#505 := [refl]: #504
+#507 := [quant-intro #505]: #506
+#74 := (~ #15 #17)
+#82 := (~ #16 #16)
+#83 := [refl]: #82
+#75 := [nnf-neg #83]: #74
+#79 := (iff #18 #15)
+#1 := true
+#72 := (if true #15 #17)
+#77 := (iff #72 #15)
+#78 := [rewrite]: #77
+#73 := (iff #18 #72)
+#70 := (iff #10 true)
+#71 := [iff-true #48]: #70
+#76 := [monotonicity #71]: #73
+#80 := [trans #76 #78]: #79
+#47 := [not-or-elim #46]: #18
+#81 := [mp #47 #80]: #15
+#84 := [mp~ #81 #75]: #17
+#508 := [mp #84 #507]: #503
+#86 := (not #503)
+#173 := (or #86 #30)
+#87 := [quant-inst #8]: #173
+[unit-resolution #87 #508 #48]: false
+5b310cc250a1d70ecf53090e27cc613cfbdee1d0 138 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f7 :: S1
+#26 := f7
+#153 := (= f7 f1)
+decl f3 :: (-> S3 S2 S1)
+decl f6 :: S2
+#20 := f6
+decl f4 :: (-> S4 S1 S3)
+decl f5 :: S4
+#7 := f5
+#27 := (f4 f5 f7)
+#31 := (f3 #27 f6)
+#32 := (= #31 f1)
+#242 := (iff #32 #153)
+#10 := (:var 0 S2)
+#8 := (:var 1 S1)
+#9 := (f4 f5 #8)
+#11 := (f3 #9 #10)
+#572 := (pattern #11)
+#13 := (= #8 f1)
+#12 := (= #11 f1)
+#14 := (iff #12 #13)
+#573 := (forall (vars (?v0 S1) (?v1 S2)) (:pat #572) #14)
+#15 := (forall (vars (?v0 S1) (?v1 S2)) #14)
+#576 := (iff #15 #573)
+#574 := (iff #14 #14)
+#575 := [refl]: #574
+#577 := [quant-intro #575]: #576
+#84 := (~ #15 #15)
+#80 := (~ #14 #14)
+#81 := [refl]: #80
+#85 := [nnf-pos #81]: #84
+#18 := (:var 0 S1)
+#19 := (f4 f5 #18)
+#21 := (f3 #19 f6)
+#22 := (= #21 f1)
+#23 := (forall (vars (?v0 S1)) #22)
+#16 := (exists (vars (?v1 S2)) #12)
+#17 := (forall (vars (?v0 S1)) #16)
+#24 := (iff #17 #23)
+#25 := (and #15 #24)
+#28 := (f3 #27 #10)
+#29 := (= #28 f1)
+#30 := (exists (vars (?v0 S2)) #29)
+#33 := (iff #30 #32)
+#41 := (not #25)
+#42 := (or #41 #33)
+#45 := (not #42)
+#34 := (implies #25 #33)
+#35 := (not #34)
+#46 := (iff #35 #45)
+#43 := (iff #34 #42)
+#44 := [rewrite]: #43
+#47 := [monotonicity #44]: #46
+#37 := [asserted]: #35
+#48 := [mp #37 #47]: #45
+#49 := [not-or-elim #48]: #25
+#50 := [and-elim #49]: #15
+#77 := [mp~ #50 #85]: #15
+#578 := [mp #77 #577]: #573
+#245 := (not #573)
+#561 := (or #245 #242)
+#220 := [quant-inst #26 #20]: #561
+#247 := [unit-resolution #220 #578]: #242
+decl ?v0!3 :: S2
+#134 := ?v0!3
+#135 := (f3 #27 ?v0!3)
+#136 := (= #135 f1)
+#246 := (iff #136 #153)
+#249 := (or #245 #246)
+#228 := [quant-inst #26 #134]: #249
+#248 := [unit-resolution #228 #578]: #246
+#564 := (not #246)
+#549 := (or #564 #153)
+#144 := (not #32)
+#604 := (pattern #28)
+#126 := (not #29)
+#605 := (forall (vars (?v0 S2)) (:pat #604) #126)
+#154 := [hypothesis]: #32
+#610 := (or #605 #144)
+#131 := (forall (vars (?v0 S2)) #126)
+#147 := (or #131 #144)
+#611 := (iff #147 #610)
+#608 := (iff #131 #605)
+#606 := (iff #126 #126)
+#607 := [refl]: #606
+#609 := [quant-intro #607]: #608
+#612 := [monotonicity #609]: #611
+#148 := (or #136 #32)
+#149 := (and #148 #147)
+#73 := (not #30)
+#74 := (iff #73 #32)
+#150 := (~ #74 #149)
+#145 := (~ #144 #144)
+#146 := [refl]: #145
+#142 := (~ #32 #32)
+#143 := [refl]: #142
+#139 := (not #73)
+#140 := (~ #139 #136)
+#137 := (~ #30 #136)
+#138 := [sk]: #137
+#141 := [nnf-neg #138]: #140
+#132 := (~ #73 #131)
+#127 := (~ #126 #126)
+#130 := [refl]: #127
+#133 := [nnf-neg #130]: #132
+#151 := [nnf-pos #133 #141 #143 #146]: #150
+#52 := (not #33)
+#75 := (iff #52 #74)
+#76 := [rewrite]: #75
+#53 := [not-or-elim #48]: #52
+#79 := [mp #53 #76]: #74
+#152 := [mp~ #79 #151]: #149
+#156 := [and-elim #152]: #147
+#613 := [mp #156 #612]: #610
+#243 := [unit-resolution #613 #154]: #605
+#560 := (not #605)
+#233 := (or #560 #144)
+#234 := [quant-inst #20]: #233
+#567 := [unit-resolution #234 #154 #243]: false
+#568 := [lemma #567]: #144
+#155 := [and-elim #152]: #148
+#212 := [unit-resolution #155 #568]: #136
+#157 := (not #136)
+#244 := (or #564 #157 #153)
+#235 := [def-axiom]: #244
+#550 := [unit-resolution #235 #212]: #549
+#551 := [unit-resolution #550 #248]: #153
+#566 := (not #153)
+#225 := (not #242)
+#552 := (or #225 #566)
+#562 := (or #225 #32 #566)
+#221 := [def-axiom]: #562
+#553 := [unit-resolution #221 #568]: #552
+[unit-resolution #553 #551 #247]: false
+0b72ca47b596bf4617b3c43ccb84578bda9d4bf9 66 0
+unsat
+#2 := false
+decl f3 :: (-> S2 S3 S4)
+#8 := (:var 0 S3)
+decl ?v0!0 :: S2
+#41 := ?v0!0
+#42 := (f3 ?v0!0 #8)
+#476 := (pattern #42)
+decl f4 :: (-> S5 S2 S3)
+decl f5 :: S5
+#10 := f5
+#43 := (f4 f5 ?v0!0)
+#44 := (f3 ?v0!0 #43)
+#45 := (= #42 #44)
+#50 := (not #45)
+#477 := (forall (vars (?v1 S3)) (:pat #476) #50)
+#257 := (not #477)
+#137 := (= #44 #44)
+#468 := (not #137)
+#466 := (or #257 #468)
+#115 := (iff #466 #257)
+#467 := (or #257 false)
+#113 := (iff #467 #257)
+#114 := [rewrite]: #113
+#109 := (iff #466 #467)
+#124 := (iff #468 false)
+#1 := true
+#473 := (not true)
+#475 := (iff #473 false)
+#465 := [rewrite]: #475
+#474 := (iff #468 #473)
+#471 := (iff #137 true)
+#472 := [rewrite]: #471
+#469 := [monotonicity #472]: #474
+#129 := [trans #469 #465]: #124
+#451 := [monotonicity #129]: #109
+#116 := [trans #451 #114]: #115
+#125 := [quant-inst #43]: #466
+#453 := [mp #125 #116]: #257
+#53 := (forall (vars (?v1 S3)) #50)
+#480 := (iff #53 #477)
+#478 := (iff #50 #50)
+#479 := [refl]: #478
+#481 := [quant-intro #479]: #480
+#7 := (:var 1 S2)
+#11 := (f4 f5 #7)
+#12 := (f3 #7 #11)
+#9 := (f3 #7 #8)
+#13 := (= #9 #12)
+#14 := (exists (vars (?v1 S3)) #13)
+#15 := (forall (vars (?v0 S2)) #14)
+#16 := (not #15)
+#56 := (~ #16 #53)
+#46 := (exists (vars (?v1 S3)) #45)
+#47 := (not #46)
+#54 := (~ #47 #53)
+#51 := (~ #50 #50)
+#52 := [refl]: #51
+#55 := [nnf-neg #52]: #54
+#48 := (~ #16 #47)
+#49 := [sk]: #48
+#57 := [trans #49 #55]: #56
+#18 := [asserted]: #16
+#58 := [mp~ #18 #57]: #53
+#482 := [mp #58 #481]: #477
+[unit-resolution #482 #453]: false
+d60a61e097c059599bc1ac624893b062d56af4fe 88 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+decl ?v0!1 :: S2
+#67 := ?v0!1
+#68 := (f3 ?v0!1)
+#69 := (= #68 f1)
+decl ?v0!0 :: S2
+#56 := ?v0!0
+#57 := (f3 ?v0!0)
+#58 := (= #57 f1)
+#93 := (not #58)
+#180 := [hypothesis]: #58
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#510 := (pattern #8)
+#9 := (= #8 f1)
+#13 := (not #9)
+#511 := (forall (vars (?v0 S2)) (:pat #510) #13)
+#14 := (forall (vars (?v0 S2)) #13)
+#514 := (iff #14 #511)
+#512 := (iff #13 #13)
+#513 := [refl]: #512
+#515 := [quant-intro #513]: #514
+#86 := (or #58 #69)
+#89 := (and #14 #86)
+#70 := (not #69)
+#71 := (not #70)
+#74 := (or #58 #71)
+#75 := (or #14 #14)
+#76 := (and #75 #74)
+#90 := (iff #76 #89)
+#87 := (iff #74 #86)
+#84 := (iff #71 #69)
+#85 := [rewrite]: #84
+#88 := [monotonicity #85]: #87
+#82 := (iff #75 #14)
+#83 := [rewrite]: #82
+#91 := [monotonicity #83 #88]: #90
+#10 := (exists (vars (?v0 S2)) #9)
+#31 := (iff #10 #14)
+#77 := (~ #31 #76)
+#15 := (not #14)
+#72 := (~ #15 #71)
+#73 := [sk]: #72
+#65 := (~ #14 #14)
+#61 := (~ #13 #13)
+#62 := [refl]: #61
+#66 := [nnf-pos #62]: #65
+#11 := (not #10)
+#63 := (~ #11 #14)
+#64 := [nnf-neg #62]: #63
+#59 := (~ #10 #58)
+#60 := [sk]: #59
+#78 := [nnf-pos #60 #64 #66 #73]: #77
+#12 := (not #11)
+#16 := (iff #12 #15)
+#17 := (not #16)
+#34 := (iff #17 #31)
+#25 := (iff #10 #15)
+#28 := (not #25)
+#32 := (iff #28 #31)
+#33 := [rewrite]: #32
+#29 := (iff #17 #28)
+#26 := (iff #16 #25)
+#23 := (iff #12 #10)
+#24 := [rewrite]: #23
+#27 := [monotonicity #24]: #26
+#30 := [monotonicity #27]: #29
+#35 := [trans #30 #33]: #34
+#19 := [asserted]: #17
+#36 := [mp #19 #35]: #31
+#79 := [mp~ #36 #78]: #76
+#80 := [mp #79 #91]: #89
+#81 := [and-elim #80]: #14
+#516 := [mp #81 #515]: #511
+#181 := (not #511)
+#95 := (or #181 #93)
+#182 := [quant-inst #56]: #95
+#94 := [unit-resolution #182 #516 #180]: false
+#173 := [lemma #94]: #93
+#92 := [and-elim #80]: #86
+#184 := [unit-resolution #92 #173]: #69
+#186 := (or #181 #70)
+#183 := [quant-inst #67]: #186
+[unit-resolution #183 #516 #184]: false
+6922ad0f6e3b3d7df4f6fe17773064fca3f13ce2 98 0
+WARNING: failed to find a pattern for quantifier (quantifier id: k!16)
+unsat
+#2 := false
+decl f3 :: (-> S2 S3 S4 S5 S6)
+decl f6 :: (-> S8 S4 S5)
+decl ?v2!1 :: (-> S3 S4)
+#63 := (:var 1 S3)
+#64 := (?v2!1 #63)
+decl f7 :: (-> S9 S2 S8)
+decl ?v0!0 :: S2
+#48 := ?v0!0
+decl f8 :: S9
+#14 := f8
+#51 := (f7 f8 ?v0!0)
+#66 := (f6 #51 #64)
+decl f4 :: (-> S7 S2 S3)
+decl f5 :: S7
+#12 := f5
+#50 := (f4 f5 ?v0!0)
+#67 := (f3 ?v0!0 #50 #64 #66)
+#10 := (:var 0 S5)
+#65 := (f3 ?v0!0 #63 #64 #10)
+#68 := (= #65 #67)
+#61 := (not #68)
+#88 := (forall (vars (?v1 S3) (?v3 S5)) #61)
+#502 := (not #88)
+#192 := (?v2!1 #50)
+#471 := (f6 #51 #192)
+#169 := (f3 ?v0!0 #50 #192 #471)
+#131 := (= #169 #169)
+#310 := (not #131)
+#323 := (or #502 #310)
+#304 := (iff #323 #502)
+#300 := (or #502 false)
+#303 := (iff #300 #502)
+#286 := [rewrite]: #303
+#301 := (iff #323 #300)
+#422 := (iff #310 false)
+#1 := true
+#490 := (not true)
+#325 := (iff #490 false)
+#420 := [rewrite]: #325
+#203 := (iff #310 #490)
+#452 := (iff #131 true)
+#477 := [rewrite]: #452
+#440 := [monotonicity #477]: #203
+#307 := [trans #440 #420]: #422
+#302 := [monotonicity #307]: #301
+#274 := [trans #302 #286]: #304
+#299 := [quant-inst #50 #471]: #323
+#275 := [mp #299 #274]: #502
+#75 := (forall (vars (?v3 S5)) #61)
+#80 := (forall (vars (?v1 S3)) #75)
+#89 := (iff #80 #88)
+#90 := [pull-quant]: #89
+#9 := (:var 1 S4)
+#7 := (:var 3 S2)
+#15 := (f7 f8 #7)
+#16 := (f6 #15 #9)
+#13 := (f4 f5 #7)
+#17 := (f3 #7 #13 #9 #16)
+#8 := (:var 2 S3)
+#11 := (f3 #7 #8 #9 #10)
+#18 := (= #11 #17)
+#19 := (exists (vars (?v3 S5)) #18)
+#20 := (forall (vars (?v2 S4)) #19)
+#21 := (exists (vars (?v1 S3)) #20)
+#22 := (forall (vars (?v0 S2)) #21)
+#23 := (not #22)
+#83 := (~ #23 #80)
+#52 := (f6 #51 #9)
+#53 := (f3 ?v0!0 #50 #9 #52)
+#49 := (f3 ?v0!0 #8 #9 #10)
+#54 := (= #49 #53)
+#55 := (exists (vars (?v3 S5)) #54)
+#56 := (forall (vars (?v2 S4)) #55)
+#57 := (exists (vars (?v1 S3)) #56)
+#58 := (not #57)
+#81 := (~ #58 #80)
+#71 := (not #56)
+#78 := (~ #71 #75)
+#69 := (exists (vars (?v3 S5)) #68)
+#70 := (not #69)
+#76 := (~ #70 #75)
+#62 := (~ #61 #61)
+#74 := [refl]: #62
+#77 := [nnf-neg #74]: #76
+#72 := (~ #71 #70)
+#73 := [sk]: #72
+#79 := [trans #73 #77]: #78
+#82 := [nnf-neg #79]: #81
+#59 := (~ #23 #58)
+#60 := [sk]: #59
+#84 := [trans #60 #82]: #83
+#25 := [asserted]: #23
+#85 := [mp~ #25 #84]: #80
+#86 := [mp #85 #90]: #88
+[unit-resolution #86 #275]: false
+5766ec783f34908a29512d5f77d60ab824e52afb 67 0
+unsat
+#2 := false
+decl f4 :: (-> S4 S2 S3)
+#10 := (:var 1 S2)
+decl f5 :: (-> S5 S2 S4)
+decl f6 :: S5
+#16 := f6
+#17 := (f5 f6 #10)
+#18 := (f4 #17 #10)
+#15 := (:var 0 S3)
+#19 := (= #15 #18)
+#20 := (not #19)
+#21 := (or #19 #20)
+#22 := (forall (vars (?v1 S3)) #21)
+#7 := (:var 0 S2)
+#11 := (= #7 #10)
+#12 := (not #11)
+#13 := (or #11 #12)
+#14 := (forall (vars (?v1 S2)) #13)
+decl f3 :: S2
+#8 := f3
+#9 := (= #7 f3)
+#23 := (if #9 #14 #22)
+#24 := (exists (vars (?v0 S2)) #23)
+#25 := (not #24)
+#68 := (iff #25 false)
+#1 := true
+#63 := (not true)
+#66 := (iff #63 false)
+#67 := [rewrite]: #66
+#64 := (iff #25 #63)
+#61 := (iff #24 true)
+#56 := (exists (vars (?v0 S2)) true)
+#59 := (iff #56 true)
+#60 := [elim-unused]: #59
+#57 := (iff #24 #56)
+#54 := (iff #23 true)
+#49 := (if #9 true true)
+#52 := (iff #49 true)
+#53 := [rewrite]: #52
+#50 := (iff #23 #49)
+#47 := (iff #22 true)
+#42 := (forall (vars (?v1 S3)) true)
+#45 := (iff #42 true)
+#46 := [elim-unused]: #45
+#43 := (iff #22 #42)
+#40 := (iff #21 true)
+#41 := [rewrite]: #40
+#44 := [quant-intro #41]: #43
+#48 := [trans #44 #46]: #47
+#38 := (iff #14 true)
+#33 := (forall (vars (?v1 S2)) true)
+#36 := (iff #33 true)
+#37 := [elim-unused]: #36
+#34 := (iff #14 #33)
+#31 := (iff #13 true)
+#32 := [rewrite]: #31
+#35 := [quant-intro #32]: #34
+#39 := [trans #35 #37]: #38
+#51 := [monotonicity #39 #48]: #50
+#55 := [trans #51 #53]: #54
+#58 := [quant-intro #55]: #57
+#62 := [trans #58 #60]: #61
+#65 := [monotonicity #62]: #64
+#69 := [trans #65 #67]: #68
+#27 := [asserted]: #25
+[mp #27 #69]: false
+d50ade7a66202a86d82309f756df6dcdc43ac7f2 64 0
+unsat
+#2 := false
+decl f4 :: (-> S4 S2 S3)
+#10 := (:var 1 S2)
+decl f5 :: (-> S5 S2 S4)
+decl f6 :: S5
+#16 := f6
+#17 := (f5 f6 #10)
+#18 := (f4 #17 #10)
+#15 := (:var 0 S3)
+#19 := (= #15 #18)
+#20 := (not #19)
+#21 := (or #19 #20)
+#22 := (exists (vars (?v1 S3)) #21)
+#7 := (:var 0 S2)
+#11 := (= #7 #10)
+#12 := (not #11)
+#13 := (or #11 #12)
+#14 := (exists (vars (?v1 S2)) #13)
+decl f3 :: S2
+#8 := f3
+#9 := (= #7 f3)
+#23 := (if #9 #14 #22)
+#24 := (exists (vars (?v0 S2)) #23)
+#25 := (not #24)
+#65 := (iff #25 false)
+#1 := true
+#60 := (not true)
+#63 := (iff #60 false)
+#64 := [rewrite]: #63
+#61 := (iff #25 #60)
+#58 := (iff #24 true)
+#33 := (exists (vars (?v1 S2)) true)
+#36 := (iff #33 true)
+#37 := [elim-unused]: #36
+#56 := (iff #24 #33)
+#54 := (iff #23 true)
+#49 := (if #9 true true)
+#52 := (iff #49 true)
+#53 := [rewrite]: #52
+#50 := (iff #23 #49)
+#47 := (iff #22 true)
+#42 := (exists (vars (?v1 S3)) true)
+#45 := (iff #42 true)
+#46 := [elim-unused]: #45
+#43 := (iff #22 #42)
+#40 := (iff #21 true)
+#41 := [rewrite]: #40
+#44 := [quant-intro #41]: #43
+#48 := [trans #44 #46]: #47
+#38 := (iff #14 true)
+#34 := (iff #14 #33)
+#31 := (iff #13 true)
+#32 := [rewrite]: #31
+#35 := [quant-intro #32]: #34
+#39 := [trans #35 #37]: #38
+#51 := [monotonicity #39 #48]: #50
+#55 := [trans #51 #53]: #54
+#57 := [quant-intro #55]: #56
+#59 := [trans #57 #37]: #58
+#62 := [monotonicity #59]: #61
+#66 := [trans #62 #64]: #65
+#27 := [asserted]: #25
+[mp #27 #66]: false
+d9ff4d0f7d0f6b7f97a94ecc044fa5ef73c485d9 154 0
+unsat
+#2 := false
+decl f3 :: (-> S2 S1)
+#10 := (:var 0 S2)
+#11 := (f3 #10)
+#524 := (pattern #11)
+decl f1 :: S1
+#3 := f1
+#12 := (= #11 f1)
+#74 := (not #12)
+#540 := (forall (vars (?v0 S2)) (:pat #524) #74)
+decl ?v0!2 :: S2
+#92 := ?v0!2
+#93 := (f3 ?v0!2)
+#94 := (= #93 f1)
+decl ?v0!0 :: S2
+#63 := ?v0!0
+#64 := (f3 ?v0!0)
+#65 := (= #64 f1)
+#105 := (iff #65 #94)
+#513 := (not #105)
+#521 := [hypothesis]: #513
+#66 := (iff #65 #12)
+#525 := (forall (vars (?v1 S2)) (:pat #524) #66)
+#60 := (forall (vars (?v1 S2)) #66)
+#528 := (iff #60 #525)
+#526 := (iff #66 #66)
+#527 := [refl]: #526
+#529 := [quant-intro #527]: #528
+#7 := (:var 1 S2)
+#8 := (f3 #7)
+#9 := (= #8 f1)
+#13 := (iff #9 #12)
+#14 := (forall (vars (?v1 S2)) #13)
+#15 := (exists (vars (?v0 S2)) #14)
+#61 := (~ #15 #60)
+#70 := (~ #60 #60)
+#68 := (~ #66 #66)
+#69 := [refl]: #68
+#71 := [nnf-pos #69]: #70
+#67 := [sk]: #61
+#72 := [trans #67 #71]: #61
+#17 := (forall (vars (?v0 S2)) #12)
+#16 := (exists (vars (?v0 S2)) #12)
+#18 := (iff #16 #17)
+#26 := (not #15)
+#27 := (or #26 #18)
+#30 := (not #27)
+#19 := (implies #15 #18)
+#20 := (not #19)
+#31 := (iff #20 #30)
+#28 := (iff #19 #27)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#22 := [asserted]: #20
+#33 := [mp #22 #32]: #30
+#34 := [not-or-elim #33]: #15
+#73 := [mp~ #34 #72]: #60
+#530 := [mp #73 #529]: #525
+#195 := (not #525)
+#517 := (or #195 #105)
+#523 := [quant-inst #92]: #517
+#522 := [unit-resolution #523 #530 #521]: false
+#505 := [lemma #522]: #105
+#500 := (or #513 #94)
+#200 := (not #65)
+#109 := [hypothesis]: #200
+#531 := (forall (vars (?v0 S2)) (:pat #524) #12)
+decl ?v0!1 :: S2
+#80 := ?v0!1
+#81 := (f3 ?v0!1)
+#82 := (= #81 f1)
+#187 := (not #82)
+#196 := (or #65 #187)
+#194 := (iff #65 #82)
+#186 := (not #194)
+#106 := [hypothesis]: #186
+#512 := (or #195 #194)
+#185 := [quant-inst #80]: #512
+#305 := [unit-resolution #185 #530 #106]: false
+#514 := [lemma #305]: #194
+#198 := (or #186 #65 #187)
+#199 := [def-axiom]: #198
+#164 := [unit-resolution #199 #514]: #196
+#501 := [unit-resolution #164 #109]: #187
+#536 := (or #82 #531)
+#100 := (or #82 #17)
+#537 := (iff #100 #536)
+#534 := (iff #17 #531)
+#532 := (iff #12 #12)
+#533 := [refl]: #532
+#535 := [quant-intro #533]: #534
+#538 := [monotonicity #535]: #537
+#95 := (not #94)
+#77 := (forall (vars (?v0 S2)) #74)
+#99 := (or #77 #95)
+#101 := (and #100 #99)
+#56 := (not #16)
+#57 := (iff #56 #17)
+#102 := (~ #57 #101)
+#96 := (not #17)
+#97 := (~ #96 #95)
+#98 := [sk]: #97
+#90 := (~ #17 #17)
+#88 := (~ #12 #12)
+#89 := [refl]: #88
+#91 := [nnf-pos #89]: #90
+#85 := (not #56)
+#86 := (~ #85 #82)
+#83 := (~ #16 #82)
+#84 := [sk]: #83
+#87 := [nnf-neg #84]: #86
+#78 := (~ #56 #77)
+#75 := (~ #74 #74)
+#76 := [refl]: #75
+#79 := [nnf-neg #76]: #78
+#103 := [nnf-pos #79 #87 #91 #98]: #102
+#35 := (not #18)
+#58 := (iff #35 #57)
+#59 := [rewrite]: #58
+#36 := [not-or-elim #33]: #35
+#62 := [mp #36 #59]: #57
+#104 := [mp~ #62 #103]: #101
+#107 := [and-elim #104]: #100
+#539 := [mp #107 #538]: #536
+#502 := [unit-resolution #539 #501]: #531
+#157 := (not #531)
+#499 := (or #157 #65)
+#161 := [quant-inst #63]: #499
+#503 := [unit-resolution #161 #502 #109]: false
+#504 := [lemma #503]: #65
+#173 := (or #513 #200 #94)
+#515 := [def-axiom]: #173
+#506 := [unit-resolution #515 #504]: #500
+#510 := [unit-resolution #506 #505]: #94
+#545 := (or #540 #95)
+#546 := (iff #99 #545)
+#543 := (iff #77 #540)
+#541 := (iff #74 #74)
+#542 := [refl]: #541
+#544 := [quant-intro #542]: #543
+#547 := [monotonicity #544]: #546
+#108 := [and-elim #104]: #99
+#548 := [mp #108 #547]: #545
+#508 := [unit-resolution #548 #510]: #540
+#511 := (or #200 #82)
+#197 := (or #186 #200 #82)
+#201 := [def-axiom]: #197
+#497 := [unit-resolution #201 #514]: #511
+#498 := [unit-resolution #497 #504]: #82
+#143 := (not #540)
+#507 := (or #143 #187)
+#509 := [quant-inst #80]: #507
+[unit-resolution #509 #498 #508]: false
+d534bf4d94631425253e66e919c95e7c6095820e 91 0
+unsat
+#2 := false
+decl f3 :: (-> S2 S1)
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#501 := (pattern #8)
+decl f1 :: S1
+#3 := f1
+decl ?v1!0 :: S2
+#52 := ?v1!0
+#53 := (f3 ?v1!0)
+#54 := (= #53 f1)
+#9 := (= #8 f1)
+#19 := (not #9)
+#68 := (or #19 #54)
+#77 := (not #68)
+#502 := (forall (vars (?v0 S2)) (:pat #501) #77)
+#178 := (not #502)
+#55 := (not #54)
+#493 := (or #55 #54)
+#282 := (not #493)
+#138 := (or #178 #282)
+#481 := (iff #138 #178)
+#140 := (or #178 false)
+#479 := (iff #140 #178)
+#480 := [rewrite]: #479
+#141 := (iff #138 #140)
+#134 := (iff #282 false)
+#1 := true
+#149 := (not true)
+#150 := (iff #149 false)
+#492 := [rewrite]: #150
+#154 := (iff #282 #149)
+#500 := (iff #493 true)
+#490 := [rewrite]: #500
+#491 := [monotonicity #490]: #154
+#476 := [trans #491 #492]: #134
+#478 := [monotonicity #476]: #141
+#482 := [trans #478 #480]: #481
+#139 := [quant-inst #52]: #138
+#477 := [mp #139 #482]: #178
+#80 := (forall (vars (?v0 S2)) #77)
+#505 := (iff #80 #502)
+#503 := (iff #77 #77)
+#504 := [refl]: #503
+#506 := [quant-intro #504]: #505
+#71 := (and #9 #55)
+#74 := (forall (vars (?v0 S2)) #71)
+#81 := (iff #74 #80)
+#78 := (iff #71 #77)
+#79 := [rewrite]: #78
+#82 := [quant-intro #79]: #81
+#49 := (not #19)
+#59 := (and #49 #55)
+#63 := (forall (vars (?v0 S2)) #59)
+#75 := (iff #63 #74)
+#72 := (iff #59 #71)
+#69 := (iff #49 #9)
+#70 := [rewrite]: #69
+#73 := [monotonicity #70]: #72
+#76 := [quant-intro #73]: #75
+#10 := (forall (vars (?v1 S2)) #9)
+#20 := (or #19 #10)
+#23 := (exists (vars (?v0 S2)) #20)
+#26 := (not #23)
+#64 := (~ #26 #63)
+#60 := (not #20)
+#61 := (~ #60 #59)
+#56 := (not #10)
+#57 := (~ #56 #55)
+#58 := [sk]: #57
+#50 := (~ #49 #49)
+#51 := [refl]: #50
+#62 := [nnf-neg #51 #58]: #61
+#65 := [nnf-neg #62]: #64
+#11 := (implies #9 #10)
+#12 := (exists (vars (?v0 S2)) #11)
+#13 := (not #12)
+#27 := (iff #13 #26)
+#24 := (iff #12 #23)
+#21 := (iff #11 #20)
+#22 := [rewrite]: #21
+#25 := [quant-intro #22]: #24
+#28 := [monotonicity #25]: #27
+#15 := [asserted]: #13
+#29 := [mp #15 #28]: #26
+#66 := [mp~ #29 #65]: #63
+#67 := [mp #66 #76]: #74
+#83 := [mp #67 #82]: #80
+#507 := [mp #83 #506]: #502
+[unit-resolution #507 #477]: false
+d77b8725117f9972715128acd88585ba586b4971 86 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S3 S2 S1)
+decl ?v0!0 :: S2
+#60 := ?v0!0
+decl ?v0!1 :: S3
+#68 := ?v0!1
+#149 := (f3 ?v0!1 ?v0!0)
+#493 := (= #149 f1)
+#499 := (not #493)
+#14 := (:var 0 S2)
+#69 := (f3 ?v0!1 #14)
+#508 := (pattern #69)
+#70 := (= #69 f1)
+#75 := (not #70)
+#509 := (forall (vars (?v1 S2)) (:pat #508) #75)
+#78 := (forall (vars (?v1 S2)) #75)
+#512 := (iff #78 #509)
+#510 := (iff #75 #75)
+#511 := [refl]: #510
+#513 := [quant-intro #511]: #512
+#13 := (:var 1 S3)
+#15 := (f3 #13 #14)
+#16 := (= #15 f1)
+#17 := (exists (vars (?v1 S2)) #16)
+#18 := (forall (vars (?v0 S3)) #17)
+#35 := (not #18)
+#81 := (~ #35 #78)
+#71 := (exists (vars (?v1 S2)) #70)
+#72 := (not #71)
+#79 := (~ #72 #78)
+#76 := (~ #75 #75)
+#77 := [refl]: #76
+#80 := [nnf-neg #77]: #79
+#73 := (~ #35 #72)
+#74 := [sk]: #73
+#82 := [trans #74 #80]: #81
+#8 := (:var 1 S2)
+#7 := (:var 0 S3)
+#9 := (f3 #7 #8)
+#10 := (= #9 f1)
+#11 := (forall (vars (?v1 S3)) #10)
+#12 := (exists (vars (?v0 S2)) #11)
+#26 := (not #12)
+#27 := (or #26 #18)
+#30 := (not #27)
+#19 := (implies #12 #18)
+#20 := (not #19)
+#31 := (iff #20 #30)
+#28 := (iff #19 #27)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#22 := [asserted]: #20
+#33 := [mp #22 #32]: #30
+#36 := [not-or-elim #33]: #35
+#83 := [mp~ #36 #82]: #78
+#514 := [mp #83 #513]: #509
+#150 := (not #509)
+#492 := (or #150 #499)
+#134 := [quant-inst #60]: #492
+#154 := [unit-resolution #134 #514]: #499
+#61 := (f3 #7 ?v0!0)
+#501 := (pattern #61)
+#56 := (= #61 f1)
+#502 := (forall (vars (?v1 S3)) (:pat #501) #56)
+#57 := (forall (vars (?v1 S3)) #56)
+#505 := (iff #57 #502)
+#503 := (iff #56 #56)
+#504 := [refl]: #503
+#506 := [quant-intro #504]: #505
+#58 := (~ #12 #57)
+#64 := (~ #57 #57)
+#62 := (~ #56 #56)
+#63 := [refl]: #62
+#65 := [nnf-pos #63]: #64
+#59 := [sk]: #58
+#66 := [trans #59 #65]: #58
+#34 := [not-or-elim #33]: #12
+#67 := [mp~ #34 #66]: #57
+#507 := [mp #67 #506]: #502
+#489 := (not #502)
+#476 := (or #489 #493)
+#138 := [quant-inst #68]: #476
+[unit-resolution #138 #507 #154]: false
+9638ce96f32e5b3c45238a3f152e07fc20508886 86 0
+unsat
+#2 := false
+decl f3 :: (-> S2 S1)
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#516 := (pattern #8)
+decl f1 :: S1
+#3 := f1
+#9 := (= #8 f1)
+#24 := (not #9)
+#523 := (forall (vars (?v0 S2)) (:pat #516) #24)
+#95 := (forall (vars (?v0 S2)) #24)
+#526 := (iff #95 #523)
+#524 := (iff #24 #24)
+#525 := [refl]: #524
+#527 := [quant-intro #525]: #526
+#16 := (exists (vars (?v0 S2)) #9)
+#51 := (not #16)
+#96 := (~ #51 #95)
+#91 := (~ #24 #24)
+#92 := [refl]: #91
+#97 := [nnf-neg #92]: #96
+#10 := (:var 1 S2)
+#11 := (= #7 #10)
+#25 := (or #24 #11)
+#28 := (forall (vars (?v1 S2)) #25)
+#31 := (and #9 #28)
+#34 := (exists (vars (?v0 S2)) #31)
+#40 := (not #34)
+#41 := (or #40 #16)
+#46 := (not #41)
+#12 := (implies #9 #11)
+#13 := (forall (vars (?v1 S2)) #12)
+#14 := (and #9 #13)
+#15 := (exists (vars (?v0 S2)) #14)
+#17 := (implies #15 #16)
+#18 := (not #17)
+#47 := (iff #18 #46)
+#44 := (iff #17 #41)
+#37 := (implies #34 #16)
+#42 := (iff #37 #41)
+#43 := [rewrite]: #42
+#38 := (iff #17 #37)
+#35 := (iff #15 #34)
+#32 := (iff #14 #31)
+#29 := (iff #13 #28)
+#26 := (iff #12 #25)
+#27 := [rewrite]: #26
+#30 := [quant-intro #27]: #29
+#33 := [monotonicity #30]: #32
+#36 := [quant-intro #33]: #35
+#39 := [monotonicity #36]: #38
+#45 := [trans #39 #43]: #44
+#48 := [monotonicity #45]: #47
+#20 := [asserted]: #18
+#49 := [mp #20 #48]: #46
+#52 := [not-or-elim #49]: #51
+#98 := [mp~ #52 #97]: #95
+#528 := [mp #98 #527]: #523
+decl ?v0!0 :: S2
+#76 := ?v0!0
+#77 := (f3 ?v0!0)
+#72 := (= #77 f1)
+#73 := (= #7 ?v0!0)
+#74 := (or #24 #73)
+#75 := (forall (vars (?v1 S2)) #74)
+#78 := (and #72 #75)
+#79 := (~ #34 #78)
+#87 := (~ #78 #78)
+#85 := (~ #75 #75)
+#83 := (~ #74 #74)
+#84 := [refl]: #83
+#86 := [nnf-pos #84]: #85
+#81 := (~ #72 #72)
+#82 := [refl]: #81
+#88 := [monotonicity #82 #86]: #87
+#80 := [sk]: #79
+#89 := [trans #80 #88]: #79
+#50 := [not-or-elim #49]: #34
+#90 := [mp~ #50 #89]: #78
+#93 := [and-elim #90]: #72
+#99 := (not #72)
+#187 := (not #523)
+#101 := (or #187 #99)
+#188 := [quant-inst #76]: #101
+[unit-resolution #188 #93 #528]: false
+b5293938cecaf4bb094f82623a01427d239246df 362 0
+unsat
+#2 := false
+decl ?v0!1 :: S2
+#104 := ?v0!1
+decl ?v1!0 :: (-> S2 S2)
+#513 := (?v1!0 ?v0!1)
+#522 := (= #513 ?v0!1)
+#494 := (not #522)
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+#509 := (f3 #513)
+#514 := (= #509 f1)
+#521 := (not #514)
+#520 := (or #521 #522)
+#516 := (not #520)
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#602 := (pattern #8)
+#87 := (?v1!0 #7)
+#91 := (= #87 #7)
+#88 := (f3 #87)
+#89 := (= #88 f1)
+#90 := (not #89)
+#92 := (or #90 #91)
+#93 := (not #92)
+#9 := (= #8 f1)
+#17 := (not #9)
+#97 := (or #17 #93)
+#635 := (forall (vars (?v0 S2)) (:pat #602) #97)
+decl ?v1!3 :: (-> S2 S2)
+#143 := (?v1!3 #7)
+#145 := (f3 #143)
+#146 := (= #145 f1)
+#147 := (not #146)
+#144 := (= #143 #7)
+#148 := (or #144 #147)
+#149 := (not #148)
+#153 := (or #17 #149)
+#640 := (forall (vars (?v0 S2)) (:pat #602) #153)
+#286 := (not #640)
+#554 := (?v1!3 ?v0!1)
+#538 := (f3 #554)
+#539 := (= #538 f1)
+#541 := (not #539)
+#555 := (= #554 ?v0!1)
+#542 := (or #555 #541)
+#540 := (not #542)
+#530 := [hypothesis]: #540
+#439 := (or #542 #539)
+#440 := [def-axiom]: #439
+#519 := [unit-resolution #440 #530]: #539
+#437 := (not #555)
+#438 := (or #542 #437)
+#431 := [def-axiom]: #438
+#500 := [unit-resolution #431 #530]: #437
+#107 := (= #7 ?v0!1)
+#108 := (or #17 #107)
+#603 := (forall (vars (?v1 S2)) (:pat #602) #108)
+#608 := (not #603)
+#105 := (f3 ?v0!1)
+#106 := (= #105 f1)
+#167 := (not #106)
+#611 := (or #167 #608)
+#614 := (not #611)
+decl ?v0!2 :: S2
+#125 := ?v0!2
+#128 := (= #7 ?v0!2)
+#129 := (or #128 #17)
+#617 := (forall (vars (?v1 S2)) (:pat #602) #129)
+#622 := (not #617)
+#126 := (f3 ?v0!2)
+#127 := (= #126 f1)
+#175 := (not #127)
+#625 := (or #175 #622)
+#572 := (?v1!3 ?v0!2)
+#589 := (f3 #572)
+#575 := (= #589 f1)
+#586 := (not #575)
+#294 := (= #572 ?v0!2)
+#576 := (or #294 #586)
+#283 := (not #576)
+#601 := (not #635)
+#258 := (?v1!0 ?v0!2)
+#383 := (= #258 ?v0!2)
+#594 := (f3 #258)
+#596 := (= #594 f1)
+#252 := (not #596)
+#590 := (or #252 #383)
+#628 := (not #625)
+#545 := [hypothesis]: #628
+#277 := (or #625 #617)
+#278 := [def-axiom]: #277
+#551 := [unit-resolution #278 #545]: #617
+#570 := (or #590 #622)
+#593 := (not #383)
+#263 := (not #590)
+#227 := [hypothesis]: #263
+#235 := (or #590 #593)
+#577 := [def-axiom]: #235
+#588 := [unit-resolution #577 #227]: #593
+#592 := (or #590 #596)
+#251 := [def-axiom]: #592
+#295 := [unit-resolution #251 #227]: #596
+#569 := [hypothesis]: #617
+#242 := (or #622 #383 #252)
+#597 := (or #383 #252)
+#579 := (or #622 #597)
+#581 := (iff #579 #242)
+#582 := [rewrite]: #581
+#580 := [quant-inst #258]: #579
+#583 := [mp #580 #582]: #242
+#573 := [unit-resolution #583 #569 #295 #588]: false
+#574 := [lemma #573]: #570
+#426 := [unit-resolution #574 #551]: #590
+#265 := (or #625 #127)
+#276 := [def-axiom]: #265
+#427 := [unit-resolution #276 #545]: #127
+#600 := (or #601 #175 #263)
+#599 := [hypothesis]: #590
+#595 := [hypothesis]: #635
+#301 := [hypothesis]: #127
+#264 := (or #175 #263)
+#591 := (or #601 #264)
+#255 := (iff #591 #600)
+#299 := [rewrite]: #255
+#250 := [quant-inst #125]: #591
+#300 := [mp #250 #299]: #600
+#193 := [unit-resolution #300 #301 #595 #599]: false
+#571 := [lemma #193]: #600
+#386 := [unit-resolution #571 #427 #426]: #601
+#645 := (or #635 #640)
+#157 := (forall (vars (?v0 S2)) #153)
+#101 := (forall (vars (?v0 S2)) #97)
+#161 := (or #101 #157)
+#646 := (iff #161 #645)
+#643 := (iff #157 #640)
+#641 := (iff #153 #153)
+#642 := [refl]: #641
+#644 := [quant-intro #642]: #643
+#638 := (iff #101 #635)
+#636 := (iff #97 #97)
+#637 := [refl]: #636
+#639 := [quant-intro #637]: #638
+#647 := [monotonicity #639 #644]: #646
+#130 := (forall (vars (?v1 S2)) #129)
+#131 := (and #127 #130)
+#109 := (forall (vars (?v1 S2)) #108)
+#110 := (and #106 #109)
+#162 := (or #110 #131)
+#163 := (and #162 #161)
+#10 := (:var 1 S2)
+#11 := (= #7 #10)
+#41 := (or #11 #17)
+#44 := (forall (vars (?v1 S2)) #41)
+#47 := (and #9 #44)
+#50 := (exists (vars (?v0 S2)) #47)
+#29 := (or #17 #11)
+#32 := (forall (vars (?v1 S2)) #29)
+#35 := (and #9 #32)
+#38 := (exists (vars (?v0 S2)) #35)
+#59 := (not #38)
+#60 := (iff #59 #50)
+#164 := (~ #60 #163)
+#158 := (not #50)
+#159 := (~ #158 #157)
+#154 := (not #47)
+#155 := (~ #154 #153)
+#150 := (not #44)
+#151 := (~ #150 #149)
+#152 := [sk]: #151
+#85 := (~ #17 #17)
+#86 := [refl]: #85
+#156 := [nnf-neg #86 #152]: #155
+#160 := [nnf-neg #156]: #159
+#132 := (~ #50 #131)
+#140 := (~ #131 #131)
+#138 := (~ #130 #130)
+#136 := (~ #129 #129)
+#137 := [refl]: #136
+#139 := [nnf-pos #137]: #138
+#134 := (~ #127 #127)
+#135 := [refl]: #134
+#141 := [monotonicity #135 #139]: #140
+#133 := [sk]: #132
+#142 := [trans #133 #141]: #132
+#122 := (not #59)
+#123 := (~ #122 #110)
+#111 := (~ #38 #110)
+#119 := (~ #110 #110)
+#117 := (~ #109 #109)
+#115 := (~ #108 #108)
+#116 := [refl]: #115
+#118 := [nnf-pos #116]: #117
+#113 := (~ #106 #106)
+#114 := [refl]: #113
+#120 := [monotonicity #114 #118]: #119
+#112 := [sk]: #111
+#121 := [trans #112 #120]: #111
+#124 := [nnf-neg #121]: #123
+#102 := (~ #59 #101)
+#98 := (not #35)
+#99 := (~ #98 #97)
+#94 := (not #32)
+#95 := (~ #94 #93)
+#96 := [sk]: #95
+#100 := [nnf-neg #86 #96]: #99
+#103 := [nnf-neg #100]: #102
+#165 := [nnf-pos #103 #124 #142 #160]: #164
+#16 := (not #11)
+#18 := (implies #16 #17)
+#19 := (forall (vars (?v1 S2)) #18)
+#20 := (and #9 #19)
+#21 := (exists (vars (?v0 S2)) #20)
+#12 := (implies #9 #11)
+#13 := (forall (vars (?v1 S2)) #12)
+#14 := (and #9 #13)
+#15 := (exists (vars (?v0 S2)) #14)
+#22 := (iff #15 #21)
+#23 := (not #22)
+#63 := (iff #23 #60)
+#53 := (iff #38 #50)
+#56 := (not #53)
+#61 := (iff #56 #60)
+#62 := [rewrite]: #61
+#57 := (iff #23 #56)
+#54 := (iff #22 #53)
+#51 := (iff #21 #50)
+#48 := (iff #20 #47)
+#45 := (iff #19 #44)
+#42 := (iff #18 #41)
+#43 := [rewrite]: #42
+#46 := [quant-intro #43]: #45
+#49 := [monotonicity #46]: #48
+#52 := [quant-intro #49]: #51
+#39 := (iff #15 #38)
+#36 := (iff #14 #35)
+#33 := (iff #13 #32)
+#30 := (iff #12 #29)
+#31 := [rewrite]: #30
+#34 := [quant-intro #31]: #33
+#37 := [monotonicity #34]: #36
+#40 := [quant-intro #37]: #39
+#55 := [monotonicity #40 #52]: #54
+#58 := [monotonicity #55]: #57
+#64 := [trans #58 #62]: #63
+#25 := [asserted]: #23
+#65 := [mp #25 #64]: #60
+#166 := [mp~ #65 #165]: #163
+#170 := [and-elim #166]: #161
+#648 := [mp #170 #647]: #645
+#534 := [unit-resolution #648 #386]: #640
+#287 := (or #286 #175 #283)
+#298 := (or #175 #283)
+#565 := (or #286 #298)
+#280 := (iff #565 #287)
+#563 := [rewrite]: #280
+#566 := [quant-inst #125]: #565
+#567 := [mp #566 #563]: #287
+#436 := [unit-resolution #567 #427 #534]: #283
+#558 := (or #576 #575)
+#559 := [def-axiom]: #558
+#531 := [unit-resolution #559 #436]: #575
+#564 := (not #294)
+#568 := (or #576 #564)
+#557 := [def-axiom]: #568
+#532 := [unit-resolution #557 #436]: #564
+#560 := (or #622 #294 #586)
+#561 := (or #622 #576)
+#562 := (iff #561 #560)
+#403 := [rewrite]: #562
+#556 := [quant-inst #572]: #561
+#404 := [mp #556 #403]: #560
+#535 := [unit-resolution #404 #551 #532 #531]: false
+#420 := [lemma #535]: #625
+#631 := (or #614 #628)
+#176 := (not #130)
+#177 := (or #175 #176)
+#178 := (not #177)
+#168 := (not #109)
+#171 := (or #167 #168)
+#172 := (not #171)
+#181 := (or #172 #178)
+#632 := (iff #181 #631)
+#629 := (iff #178 #628)
+#626 := (iff #177 #625)
+#623 := (iff #176 #622)
+#620 := (iff #130 #617)
+#618 := (iff #129 #129)
+#619 := [refl]: #618
+#621 := [quant-intro #619]: #620
+#624 := [monotonicity #621]: #623
+#627 := [monotonicity #624]: #626
+#630 := [monotonicity #627]: #629
+#615 := (iff #172 #614)
+#612 := (iff #171 #611)
+#609 := (iff #168 #608)
+#606 := (iff #109 #603)
+#604 := (iff #108 #108)
+#605 := [refl]: #604
+#607 := [quant-intro #605]: #606
+#610 := [monotonicity #607]: #609
+#613 := [monotonicity #610]: #612
+#616 := [monotonicity #613]: #615
+#633 := [monotonicity #616 #630]: #632
+#182 := (iff #162 #181)
+#179 := (iff #131 #178)
+#180 := [rewrite]: #179
+#173 := (iff #110 #172)
+#174 := [rewrite]: #173
+#183 := [monotonicity #174 #180]: #182
+#169 := [and-elim #166]: #162
+#184 := [mp #169 #183]: #181
+#634 := [mp #184 #633]: #631
+#501 := [unit-resolution #634 #420]: #614
+#186 := (or #611 #603)
+#273 := [def-axiom]: #186
+#503 := [unit-resolution #273 #501]: #603
+#536 := (or #608 #541 #555)
+#425 := (or #541 #555)
+#533 := (or #608 #425)
+#524 := (iff #533 #536)
+#526 := [rewrite]: #524
+#537 := [quant-inst #554]: #533
+#518 := [mp #537 #526]: #536
+#504 := [unit-resolution #518 #503 #500 #519]: false
+#505 := [lemma #504]: #542
+#552 := [hypothesis]: #640
+#185 := (or #611 #106)
+#272 := [def-axiom]: #185
+#382 := [unit-resolution #272 #501]: #106
+#553 := (or #286 #167 #540)
+#543 := (or #167 #540)
+#384 := (or #286 #543)
+#435 := (iff #384 #553)
+#508 := [rewrite]: #435
+#385 := [quant-inst #104]: #384
+#510 := [mp #385 #508]: #553
+#511 := [unit-resolution #510 #382 #552 #505]: false
+#512 := [lemma #511]: #286
+#467 := [unit-resolution #648 #512]: #635
+#506 := (or #601 #167 #516)
+#523 := (or #167 #516)
+#486 := (or #601 #523)
+#489 := (iff #486 #506)
+#490 := [rewrite]: #489
+#487 := [quant-inst #104]: #486
+#491 := [mp #487 #490]: #506
+#468 := [unit-resolution #491 #382 #467]: #516
+#495 := (or #520 #494)
+#496 := [def-axiom]: #495
+#457 := [unit-resolution #496 #468]: #494
+#492 := (or #520 #514)
+#493 := [def-axiom]: #492
+#462 := [unit-resolution #493 #468]: #514
+#488 := (or #608 #521 #522)
+#499 := (or #608 #520)
+#478 := (iff #499 #488)
+#480 := [rewrite]: #478
+#477 := [quant-inst #513]: #499
+#481 := [mp #477 #480]: #488
+[unit-resolution #481 #503 #462 #457]: false
+96dbad9d0f21930a89355df3d0c25d735ace8a1e 140 0
+unsat
+#2 := false
+decl f4 :: S2
+#7 := f4
+decl ?v1!0 :: (-> S2 S2)
+#119 := (?v1!0 f4)
+#121 := (= #119 f4)
+#198 := (not #121)
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+#206 := (f3 #119)
+#120 := (= #206 f1)
+#207 := (not #120)
+#208 := (or #207 #121)
+#199 := (not #208)
+#10 := (:var 0 S2)
+#11 := (f3 #10)
+#536 := (pattern #11)
+#95 := (?v1!0 #10)
+#105 := (= #95 #10)
+#102 := (f3 #95)
+#103 := (= #102 f1)
+#104 := (not #103)
+#106 := (or #104 #105)
+#107 := (not #106)
+#12 := (= #11 f1)
+#30 := (not #12)
+#111 := (or #30 #107)
+#543 := (forall (vars (?v0 S2)) (:pat #536) #111)
+#115 := (forall (vars (?v0 S2)) #111)
+#546 := (iff #115 #543)
+#544 := (iff #111 #111)
+#545 := [refl]: #544
+#547 := [quant-intro #545]: #546
+#16 := (:var 1 S2)
+#17 := (= #10 #16)
+#37 := (or #30 #17)
+#40 := (forall (vars (?v1 S2)) #37)
+#43 := (and #12 #40)
+#46 := (exists (vars (?v0 S2)) #43)
+#73 := (not #46)
+#116 := (~ #73 #115)
+#112 := (not #43)
+#113 := (~ #112 #111)
+#108 := (not #40)
+#109 := (~ #108 #107)
+#110 := [sk]: #109
+#97 := (~ #30 #30)
+#94 := [refl]: #97
+#114 := [nnf-neg #94 #110]: #113
+#117 := [nnf-neg #114]: #116
+#13 := (= #10 f4)
+#31 := (or #30 #13)
+#34 := (forall (vars (?v0 S2)) #31)
+#52 := (not #34)
+#8 := (f3 f4)
+#9 := (= #8 f1)
+#61 := (not #9)
+#62 := (or #61 #52 #46)
+#67 := (not #62)
+#18 := (implies #12 #17)
+#19 := (forall (vars (?v1 S2)) #18)
+#20 := (and #12 #19)
+#21 := (exists (vars (?v0 S2)) #20)
+#14 := (implies #12 #13)
+#15 := (forall (vars (?v0 S2)) #14)
+#22 := (implies #15 #21)
+#23 := (implies #9 #22)
+#24 := (not #23)
+#68 := (iff #24 #67)
+#65 := (iff #23 #62)
+#53 := (or #52 #46)
+#58 := (implies #9 #53)
+#63 := (iff #58 #62)
+#64 := [rewrite]: #63
+#59 := (iff #23 #58)
+#56 := (iff #22 #53)
+#49 := (implies #34 #46)
+#54 := (iff #49 #53)
+#55 := [rewrite]: #54
+#50 := (iff #22 #49)
+#47 := (iff #21 #46)
+#44 := (iff #20 #43)
+#41 := (iff #19 #40)
+#38 := (iff #18 #37)
+#39 := [rewrite]: #38
+#42 := [quant-intro #39]: #41
+#45 := [monotonicity #42]: #44
+#48 := [quant-intro #45]: #47
+#35 := (iff #15 #34)
+#32 := (iff #14 #31)
+#33 := [rewrite]: #32
+#36 := [quant-intro #33]: #35
+#51 := [monotonicity #36 #48]: #50
+#57 := [trans #51 #55]: #56
+#60 := [monotonicity #57]: #59
+#66 := [trans #60 #64]: #65
+#69 := [monotonicity #66]: #68
+#26 := [asserted]: #24
+#70 := [mp #26 #69]: #67
+#74 := [not-or-elim #70]: #73
+#118 := [mp~ #74 #117]: #115
+#548 := [mp #118 #547]: #543
+#71 := [not-or-elim #70]: #9
+#209 := (not #543)
+#213 := (or #209 #61 #199)
+#210 := (or #61 #199)
+#192 := (or #209 #210)
+#530 := (iff #192 #213)
+#186 := [rewrite]: #530
+#528 := [quant-inst #7]: #192
+#317 := [mp #528 #186]: #213
+#176 := [unit-resolution #317 #71 #548]: #199
+#531 := (or #208 #198)
+#532 := [def-axiom]: #531
+#513 := [unit-resolution #532 #176]: #198
+#524 := (or #208 #120)
+#197 := [def-axiom]: #524
+#523 := [unit-resolution #197 #176]: #120
+#537 := (forall (vars (?v0 S2)) (:pat #536) #31)
+#540 := (iff #34 #537)
+#538 := (iff #31 #31)
+#539 := [refl]: #538
+#541 := [quant-intro #539]: #540
+#98 := (~ #34 #34)
+#100 := (~ #31 #31)
+#101 := [refl]: #100
+#99 := [nnf-pos #101]: #98
+#72 := [not-or-elim #70]: #34
+#96 := [mp~ #72 #99]: #34
+#542 := [mp #96 #541]: #537
+#529 := (not #537)
+#535 := (or #529 #207 #121)
+#525 := (or #529 #208)
+#189 := (iff #525 #535)
+#526 := [rewrite]: #189
+#184 := [quant-inst #119]: #525
+#185 := [mp #184 #526]: #535
+[unit-resolution #185 #542 #523 #513]: false
+3973423ac9fa582b2790c4d37bd8bded688f8e45 170 0
+unsat
+#2 := false
+decl ?v0!0 :: S2
+#93 := ?v0!0
+decl ?v1!1 :: (-> S2 S2)
+#233 := (?v1!1 ?v0!0)
+#235 := (= #233 ?v0!0)
+#558 := (not #235)
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+#147 := (f3 #233)
+#234 := (= #147 f1)
+#148 := (not #234)
+#226 := (or #148 #235)
+#237 := (not #226)
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#570 := (pattern #8)
+#104 := (?v1!1 #7)
+#108 := (= #104 #7)
+#105 := (f3 #104)
+#106 := (= #105 f1)
+#107 := (not #106)
+#109 := (or #107 #108)
+#110 := (not #109)
+#9 := (= #8 f1)
+#41 := (not #9)
+#114 := (or #41 #110)
+#571 := (forall (vars (?v0 S2)) (:pat #570) #114)
+#118 := (forall (vars (?v0 S2)) #114)
+#574 := (iff #118 #571)
+#572 := (iff #114 #114)
+#573 := [refl]: #572
+#575 := [quant-intro #573]: #574
+#11 := (:var 1 S2)
+#19 := (= #7 #11)
+#42 := (or #41 #19)
+#45 := (forall (vars (?v1 S2)) #42)
+#48 := (and #9 #45)
+#51 := (exists (vars (?v0 S2)) #48)
+#70 := (not #51)
+#119 := (~ #70 #118)
+#115 := (not #48)
+#116 := (~ #115 #114)
+#111 := (not #45)
+#112 := (~ #111 #110)
+#113 := [sk]: #112
+#102 := (~ #41 #41)
+#103 := [refl]: #102
+#117 := [nnf-neg #103 #113]: #116
+#120 := [nnf-neg #117]: #119
+#15 := (= #11 #7)
+#12 := (f3 #11)
+#13 := (= #12 f1)
+#14 := (and #13 #9)
+#31 := (not #14)
+#32 := (or #31 #15)
+#35 := (forall (vars (?v0 S2) (?v1 S2)) #32)
+#10 := (exists (vars (?v0 S2)) #9)
+#38 := (and #10 #35)
+#57 := (not #38)
+#58 := (or #57 #51)
+#63 := (not #58)
+#20 := (implies #9 #19)
+#21 := (forall (vars (?v1 S2)) #20)
+#22 := (and #9 #21)
+#23 := (exists (vars (?v0 S2)) #22)
+#16 := (implies #14 #15)
+#17 := (forall (vars (?v0 S2) (?v1 S2)) #16)
+#18 := (and #10 #17)
+#24 := (implies #18 #23)
+#25 := (not #24)
+#64 := (iff #25 #63)
+#61 := (iff #24 #58)
+#54 := (implies #38 #51)
+#59 := (iff #54 #58)
+#60 := [rewrite]: #59
+#55 := (iff #24 #54)
+#52 := (iff #23 #51)
+#49 := (iff #22 #48)
+#46 := (iff #21 #45)
+#43 := (iff #20 #42)
+#44 := [rewrite]: #43
+#47 := [quant-intro #44]: #46
+#50 := [monotonicity #47]: #49
+#53 := [quant-intro #50]: #52
+#39 := (iff #18 #38)
+#36 := (iff #17 #35)
+#33 := (iff #16 #32)
+#34 := [rewrite]: #33
+#37 := [quant-intro #34]: #36
+#40 := [monotonicity #37]: #39
+#56 := [monotonicity #40 #53]: #55
+#62 := [trans #56 #60]: #61
+#65 := [monotonicity #62]: #64
+#27 := [asserted]: #25
+#66 := [mp #27 #65]: #63
+#71 := [not-or-elim #66]: #70
+#121 := [mp~ #71 #120]: #118
+#576 := [mp #121 #575]: #571
+#94 := (f3 ?v0!0)
+#97 := (= #94 f1)
+#98 := (~ #10 #97)
+#95 := [sk]: #98
+#67 := [not-or-elim #66]: #38
+#68 := [and-elim #67]: #10
+#96 := [mp~ #68 #95]: #97
+#146 := (not #97)
+#240 := (not #571)
+#219 := (or #240 #146 #237)
+#238 := (or #146 #237)
+#555 := (or #240 #238)
+#213 := (iff #555 #219)
+#344 := [rewrite]: #213
+#557 := [quant-inst #93]: #555
+#551 := [mp #557 #344]: #219
+#537 := [unit-resolution #551 #96 #576]: #237
+#559 := (or #226 #558)
+#560 := [def-axiom]: #559
+#244 := [unit-resolution #560 #537]: #558
+#224 := (or #226 #234)
+#225 := [def-axiom]: #224
+#533 := [unit-resolution #225 #537]: #234
+#563 := (pattern #12 #8)
+#122 := (not #13)
+#137 := (or #122 #41 #15)
+#564 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #563) #137)
+#142 := (forall (vars (?v0 S2) (?v1 S2)) #137)
+#567 := (iff #142 #564)
+#565 := (iff #137 #137)
+#566 := [refl]: #565
+#568 := [quant-intro #566]: #567
+#143 := (iff #35 #142)
+#140 := (iff #32 #137)
+#123 := (or #122 #41)
+#134 := (or #123 #15)
+#138 := (iff #134 #137)
+#139 := [rewrite]: #138
+#135 := (iff #32 #134)
+#132 := (iff #31 #123)
+#124 := (not #123)
+#127 := (not #124)
+#130 := (iff #127 #123)
+#131 := [rewrite]: #130
+#128 := (iff #31 #127)
+#125 := (iff #14 #124)
+#126 := [rewrite]: #125
+#129 := [monotonicity #126]: #128
+#133 := [trans #129 #131]: #132
+#136 := [monotonicity #133]: #135
+#141 := [trans #136 #139]: #140
+#144 := [quant-intro #141]: #143
+#99 := (~ #35 #35)
+#91 := (~ #32 #32)
+#92 := [refl]: #91
+#100 := [nnf-pos #92]: #99
+#69 := [and-elim #67]: #35
+#101 := [mp~ #69 #100]: #35
+#145 := [mp #101 #144]: #142
+#569 := [mp #145 #568]: #564
+#548 := (not #564)
+#187 := (or #548 #148 #146 #235)
+#554 := (or #148 #146 #235)
+#188 := (or #548 #554)
+#547 := (iff #188 #187)
+#550 := [rewrite]: #547
+#549 := [quant-inst #233 #93]: #188
+#536 := [mp #549 #550]: #187
+[unit-resolution #536 #96 #569 #533 #244]: false
+d849c0627f2c781919ccff42a145d991899a7af1 169 0
+unsat
+#2 := false
+decl ?v0!0 :: S2
+#110 := ?v0!0
+decl ?v1!1 :: (-> S2 S2)
+#233 := (?v1!1 ?v0!0)
+#235 := (= #233 ?v0!0)
+#558 := (not #235)
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+#149 := (f3 #233)
+#234 := (= #149 f1)
+#146 := (not #234)
+#226 := (or #146 #235)
+#237 := (not #226)
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#563 := (pattern #8)
+#129 := (?v1!1 #7)
+#133 := (= #129 #7)
+#130 := (f3 #129)
+#131 := (= #130 f1)
+#132 := (not #131)
+#134 := (or #132 #133)
+#135 := (not #134)
+#9 := (= #8 f1)
+#28 := (not #9)
+#139 := (or #28 #135)
+#570 := (forall (vars (?v0 S2)) (:pat #563) #139)
+#142 := (forall (vars (?v0 S2)) #139)
+#573 := (iff #142 #570)
+#571 := (iff #139 #139)
+#572 := [refl]: #571
+#574 := [quant-intro #572]: #573
+#10 := (:var 1 S2)
+#11 := (= #7 #10)
+#29 := (or #28 #11)
+#32 := (forall (vars (?v1 S2)) #29)
+#35 := (and #9 #32)
+#44 := (not #35)
+#102 := (forall (vars (?v0 S2)) #44)
+#143 := (~ #102 #142)
+#140 := (~ #44 #139)
+#136 := (not #32)
+#137 := (~ #136 #135)
+#138 := [sk]: #137
+#125 := (~ #28 #28)
+#126 := [refl]: #125
+#141 := [nnf-neg #126 #138]: #140
+#144 := [nnf-pos #141]: #143
+decl f4 :: S1
+#16 := f4
+#17 := (= f4 f1)
+#45 := (or #44 #17)
+#50 := (forall (vars (?v0 S2)) #45)
+#103 := (iff #50 #102)
+#100 := (iff #45 #44)
+#93 := (or #44 false)
+#98 := (iff #93 #44)
+#99 := [rewrite]: #98
+#94 := (iff #45 #93)
+#95 := (iff #17 false)
+#72 := (not #17)
+#38 := (exists (vars (?v0 S2)) #35)
+#53 := (and #38 #50)
+#59 := (not #53)
+#60 := (or #59 #17)
+#65 := (not #60)
+#12 := (implies #9 #11)
+#13 := (forall (vars (?v1 S2)) #12)
+#14 := (and #9 #13)
+#18 := (implies #14 #17)
+#19 := (forall (vars (?v0 S2)) #18)
+#15 := (exists (vars (?v0 S2)) #14)
+#20 := (and #15 #19)
+#21 := (implies #20 #17)
+#22 := (not #21)
+#66 := (iff #22 #65)
+#63 := (iff #21 #60)
+#56 := (implies #53 #17)
+#61 := (iff #56 #60)
+#62 := [rewrite]: #61
+#57 := (iff #21 #56)
+#54 := (iff #20 #53)
+#51 := (iff #19 #50)
+#48 := (iff #18 #45)
+#41 := (implies #35 #17)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #18 #41)
+#36 := (iff #14 #35)
+#33 := (iff #13 #32)
+#30 := (iff #12 #29)
+#31 := [rewrite]: #30
+#34 := [quant-intro #31]: #33
+#37 := [monotonicity #34]: #36
+#43 := [monotonicity #37]: #42
+#49 := [trans #43 #47]: #48
+#52 := [quant-intro #49]: #51
+#39 := (iff #15 #38)
+#40 := [quant-intro #37]: #39
+#55 := [monotonicity #40 #52]: #54
+#58 := [monotonicity #55]: #57
+#64 := [trans #58 #62]: #63
+#67 := [monotonicity #64]: #66
+#24 := [asserted]: #22
+#68 := [mp #24 #67]: #65
+#73 := [not-or-elim #68]: #72
+#96 := [iff-false #73]: #95
+#97 := [monotonicity #96]: #94
+#101 := [trans #97 #99]: #100
+#104 := [quant-intro #101]: #103
+#69 := [not-or-elim #68]: #53
+#71 := [and-elim #69]: #50
+#105 := [mp #71 #104]: #102
+#145 := [mp~ #105 #144]: #142
+#575 := [mp #145 #574]: #570
+#111 := (f3 ?v0!0)
+#106 := (= #111 f1)
+#107 := (= #7 ?v0!0)
+#108 := (or #28 #107)
+#109 := (forall (vars (?v1 S2)) #108)
+#112 := (and #106 #109)
+#113 := (~ #38 #112)
+#121 := (~ #112 #112)
+#119 := (~ #109 #109)
+#117 := (~ #108 #108)
+#118 := [refl]: #117
+#120 := [nnf-pos #118]: #119
+#115 := (~ #106 #106)
+#116 := [refl]: #115
+#122 := [monotonicity #116 #120]: #121
+#114 := [sk]: #113
+#123 := [trans #114 #122]: #113
+#70 := [and-elim #69]: #38
+#124 := [mp~ #70 #123]: #112
+#127 := [and-elim #124]: #106
+#148 := (not #106)
+#240 := (not #570)
+#219 := (or #240 #148 #237)
+#238 := (or #148 #237)
+#555 := (or #240 #238)
+#213 := (iff #555 #219)
+#344 := [rewrite]: #213
+#557 := [quant-inst #110]: #555
+#551 := [mp #557 #344]: #219
+#540 := [unit-resolution #551 #127 #575]: #237
+#559 := (or #226 #558)
+#560 := [def-axiom]: #559
+#541 := [unit-resolution #560 #540]: #558
+#224 := (or #226 #234)
+#225 := [def-axiom]: #224
+#536 := [unit-resolution #225 #540]: #234
+#564 := (forall (vars (?v1 S2)) (:pat #563) #108)
+#567 := (iff #109 #564)
+#565 := (iff #108 #108)
+#566 := [refl]: #565
+#568 := [quant-intro #566]: #567
+#128 := [and-elim #124]: #109
+#569 := [mp #128 #568]: #564
+#562 := (not #564)
+#552 := (or #562 #146 #235)
+#211 := (or #562 #226)
+#553 := (iff #211 #552)
+#212 := [rewrite]: #553
+#216 := [quant-inst #233]: #211
+#554 := [mp #216 #212]: #552
+[unit-resolution #554 #569 #536 #541]: false
+5cf9316b3855d8f516ed864997fb3cc182641c7f 76 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f5 :: (-> S2 S1)
+decl f6 :: S2
+#15 := f6
+#19 := (f5 f6)
+#20 := (= #19 f1)
+#54 := (not #20)
+decl f3 :: (-> S2 S3 S1)
 decl f4 :: S3
-#17 := f4
-#19 := (= f4 f5)
-decl inj!0 :: (-> S2 S4 S3)
-decl f3 :: (-> S2 S3 S4)
+#8 := f4
+#16 := (f3 f6 f4)
+#17 := (= #16 f1)
+#7 := (:var 0 S2)
+#11 := (f5 #7)
+#12 := (= #11 f1)
+#9 := (f3 #7 f4)
+#10 := (= #9 f1)
+#28 := (not #10)
+#29 := (or #28 #12)
+#32 := (forall (vars (?v0 S2)) #29)
+#35 := (and #32 #17)
+#41 := (not #35)
+#42 := (or #41 #20)
+#47 := (not #42)
+#13 := (implies #10 #12)
+#14 := (forall (vars (?v0 S2)) #13)
+#18 := (and #14 #17)
+#21 := (implies #18 #20)
+#22 := (not #21)
+#48 := (iff #22 #47)
+#45 := (iff #21 #42)
+#38 := (implies #35 #20)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #21 #38)
+#36 := (iff #18 #35)
+#33 := (iff #14 #32)
+#30 := (iff #13 #29)
+#31 := [rewrite]: #30
+#34 := [quant-intro #31]: #33
+#37 := [monotonicity #34]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #46]: #48
+#24 := [asserted]: #22
+#50 := [mp #24 #49]: #47
+#55 := [not-or-elim #50]: #54
+#51 := [not-or-elim #50]: #35
+#53 := [and-elim #51]: #17
+#498 := (pattern #11)
+#497 := (pattern #9)
+#499 := (forall (vars (?v0 S2)) (:pat #497 #498) #29)
+#502 := (iff #32 #499)
+#500 := (iff #29 #29)
+#501 := [refl]: #500
+#503 := [quant-intro #501]: #502
+#75 := (~ #32 #32)
+#77 := (~ #29 #29)
+#78 := [refl]: #77
+#76 := [nnf-pos #78]: #75
+#52 := [and-elim #51]: #32
+#79 := [mp~ #52 #76]: #32
+#504 := [mp #79 #503]: #499
+#80 := (not #17)
+#82 := (not #499)
+#169 := (or #82 #80 #20)
+#167 := (or #80 #20)
+#160 := (or #82 #167)
+#172 := (iff #160 #169)
+#173 := [rewrite]: #172
+#171 := [quant-inst #15]: #160
+#170 := [mp #171 #173]: #169
+[unit-resolution #170 #504 #53 #55]: false
+36a9521988b6f6920c988fe790beb6e082d3e3e0 74 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S3 S1)
+decl f4 :: S3
+#8 := f4
 decl f6 :: S2
-#22 := f6
-#24 := (f3 f6 f5)
-#565 := (inj!0 f6 #24)
-#220 := (= #565 f5)
-#352 := (= f5 #565)
-#9 := (:var 1 S3)
-#87 := (:var 0 S2)
-#84 := (f3 #87 #9)
-#85 := (pattern #84)
-#88 := (inj!0 #87 #84)
-#89 := (= #88 #9)
-#82 := (forall (vars (k!0 S2) (k!1 S3)) (:pat #85) #89)
-#11 := (:var 0 S3)
-#14 := (= #9 #11)
-#8 := (:var 2 S2)
-#12 := (f3 #8 #11)
-#10 := (f3 #8 #9)
-#13 := (= #10 #12)
-#49 := (not #13)
-#50 := (or #49 #14)
-#53 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #50)
-#83 := (iff #53 #82)
-#94 := [rewrite]: #83
-#92 := (~ #53 #53)
-#90 := (~ #50 #50)
-#91 := [refl]: #90
-#93 := [nnf-pos #91]: #92
-#20 := (not #19)
-#59 := (and #20 #53)
+#15 := f6
+#18 := (f3 f6 f4)
+#19 := (= #18 f1)
+decl f5 :: (-> S2 S1)
+#16 := (f5 f6)
+#17 := (= #16 f1)
+#20 := (and #17 #19)
+#21 := (not #20)
+#7 := (:var 0 S2)
+#11 := (f5 #7)
+#12 := (= #11 f1)
+#9 := (f3 #7 f4)
+#10 := (= #9 f1)
+#13 := (and #10 #12)
+#14 := (exists (vars (?v0 S2)) #13)
+#22 := (or #14 #21)
+#23 := (not #22)
+#25 := [asserted]: #23
+#28 := [not-or-elim #25]: #20
+#30 := [and-elim #28]: #19
+#29 := [and-elim #28]: #17
+#495 := (pattern #11)
+#494 := (pattern #9)
+#61 := (not #12)
+#58 := (not #10)
+#62 := (or #58 #61)
+#496 := (forall (vars (?v0 S2)) (:pat #494 #495) #62)
+#73 := (forall (vars (?v0 S2)) #62)
+#499 := (iff #73 #496)
+#497 := (iff #62 #62)
+#498 := [refl]: #497
+#500 := [quant-intro #498]: #499
+#59 := (not #13)
+#54 := (forall (vars (?v0 S2)) #59)
+#74 := (iff #54 #73)
+#71 := (iff #59 #62)
+#63 := (not #62)
+#66 := (not #63)
+#69 := (iff #66 #62)
+#70 := [rewrite]: #69
+#67 := (iff #59 #66)
+#64 := (iff #13 #63)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#72 := [trans #68 #70]: #71
+#75 := [quant-intro #72]: #74
+#26 := (not #14)
+#55 := (~ #26 #54)
+#60 := (~ #59 #59)
+#53 := [refl]: #60
+#56 := [nnf-neg #53]: #55
+#27 := [not-or-elim #25]: #26
+#57 := [mp~ #27 #56]: #54
+#76 := [mp #57 #75]: #73
+#501 := [mp #76 #500]: #496
+#164 := (not #17)
+#77 := (not #19)
+#166 := (not #496)
+#157 := (or #166 #77 #164)
+#78 := (or #77 #164)
+#168 := (or #166 #78)
+#170 := (iff #168 #157)
+#167 := [rewrite]: #170
+#169 := [quant-inst #15]: #168
+#171 := [mp #169 #167]: #157
+[unit-resolution #171 #501 #29 #30]: false
+3caef628769def96e328f07d5829f3ba60e7a8be 22 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#20 := (not #10)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#11 := (or #8 #10)
+#12 := (not #11)
+#13 := (or #11 #12)
+#14 := (not #13)
+#16 := [asserted]: #14
+#17 := [not-or-elim #16]: #12
+#21 := [not-or-elim #17]: #20
+#18 := (not #8)
+#19 := [not-or-elim #17]: #18
+#22 := [not-or-elim #16]: #11
+[unit-resolution #22 #19 #21]: false
+0e1cdd4a4193b3d95b7ad20189882443e6b18893 27 0
+unsat
+#2 := false
+#1 := true
+#8 := (or false true)
+#7 := (and true false)
+#9 := (implies #7 #8)
+#10 := (not #9)
+#32 := (iff #10 false)
+#27 := (not true)
+#30 := (iff #27 false)
+#31 := [rewrite]: #30
+#28 := (iff #10 #27)
+#25 := (iff #9 true)
+#20 := (implies false true)
+#23 := (iff #20 true)
+#24 := [rewrite]: #23
+#21 := (iff #9 #20)
+#18 := (iff #8 true)
+#19 := [rewrite]: #18
+#16 := (iff #7 false)
+#17 := [rewrite]: #16
+#22 := [monotonicity #17 #19]: #21
+#26 := [trans #22 #24]: #25
+#29 := [monotonicity #26]: #28
+#33 := [trans #29 #31]: #32
+#12 := [asserted]: #10
+[mp #12 #33]: false
+1865879eff2d6a570e2d5d631f9447241f505a6b 23 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+decl f4 :: S2
+#7 := f4
+#8 := (f3 f4)
+#9 := (= #8 f1)
+#10 := (iff #9 #9)
+#11 := (not #10)
+#24 := (iff #11 false)
+#1 := true
+#19 := (not true)
+#22 := (iff #19 false)
+#23 := [rewrite]: #22
+#20 := (iff #11 #19)
+#17 := (iff #10 true)
+#18 := [rewrite]: #17
+#21 := [monotonicity #18]: #20
+#25 := [trans #21 #23]: #24
+#13 := [asserted]: #11
+[mp #13 #25]: false
+22b316633a688953bdb82a6a016351e3b9edef63 25 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S3 S1)
+decl f5 :: S3
+#8 := f5
+decl f4 :: S2
+#7 := f4
+#9 := (f3 f4 f5)
+#10 := (= #9 f1)
+#11 := (iff #10 #10)
+#12 := (not #11)
+#25 := (iff #12 false)
+#1 := true
+#20 := (not true)
+#23 := (iff #20 false)
+#24 := [rewrite]: #23
+#21 := (iff #12 #20)
+#18 := (iff #11 true)
+#19 := [rewrite]: #18
+#22 := [monotonicity #19]: #21
+#26 := [trans #22 #24]: #25
+#14 := [asserted]: #12
+[mp #14 #26]: false
+5d78cef53eb597c269d0bcb51799688adca9f822 24 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#9 := (= #8 f1)
+#10 := (forall (vars (?v0 S2)) #9)
+#11 := (not #10)
+#12 := (if #10 #10 #11)
+#13 := (not #12)
+#26 := (iff #13 false)
+#1 := true
+#21 := (not true)
+#24 := (iff #21 false)
+#25 := [rewrite]: #24
+#22 := (iff #13 #21)
+#19 := (iff #12 true)
+#20 := [rewrite]: #19
+#23 := [monotonicity #20]: #22
+#27 := [trans #23 #25]: #26
+#15 := [asserted]: #13
+[mp #15 #27]: false
+1c9273fda2614079bca73f9f9065cfb199fc506c 119 0
+unsat
+#2 := false
+decl f4 :: S2
+#8 := f4
+decl f3 :: S2
+#7 := f3
+#9 := (= f3 f4)
+decl inj!0 :: (-> S3 S2)
+decl f6 :: (-> S2 S3)
+#28 := (f6 f4)
+#115 := (inj!0 #28)
+#202 := (= #115 f4)
+#18 := (:var 0 S2)
+#19 := (f6 #18)
+#113 := (pattern #19)
+#105 := (inj!0 #19)
+#102 := (= #105 #18)
+#531 := (forall (vars (k!0 S2)) (:pat #113) #102)
+#104 := (forall (vars (k!0 S2)) (:pat #113) #102)
+#532 := (iff #104 #531)
+#534 := (iff #531 #531)
+#535 := [rewrite]: #534
+#533 := [rewrite]: #532
+#536 := [trans #533 #535]: #532
+#16 := (:var 1 S2)
+#21 := (= #18 #16)
+#17 := (f6 #16)
+#20 := (= #17 #19)
+#38 := (not #20)
+#39 := (or #38 #21)
+#42 := (forall (vars (?v0 S2) (?v1 S2)) #39)
+#103 := (iff #42 #104)
+#106 := [rewrite]: #103
+#108 := (~ #42 #42)
+#110 := (~ #39 #39)
+#111 := [refl]: #110
+#109 := [nnf-pos #111]: #108
+decl f5 :: S2
+#11 := f5
+#14 := (= f4 f5)
+#15 := (not #14)
+#12 := (= f3 f5)
+#13 := (not #12)
+#10 := (not #9)
+#59 := (and #10 #13 #15 #42)
+#27 := (f6 f3)
+#29 := (= #27 #28)
+#30 := (not #29)
 #67 := (not #59)
-#23 := (f3 f6 f4)
-#25 := (= #23 #24)
-#26 := (not #25)
-#68 := (or #26 #67)
+#68 := (or #67 #30)
 #73 := (not #68)
-#15 := (implies #13 #14)
-#16 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #15)
-#21 := (and #16 #20)
-#27 := (implies #21 #26)
-#28 := (not #27)
-#74 := (iff #28 #73)
-#71 := (iff #27 #68)
-#64 := (implies #59 #26)
+#22 := (implies #20 #21)
+#23 := (forall (vars (?v0 S2) (?v1 S2)) #22)
+#24 := (and #15 #23)
+#25 := (and #13 #24)
+#26 := (and #10 #25)
+#31 := (implies #26 #30)
+#32 := (not #31)
+#74 := (iff #32 #73)
+#71 := (iff #31 #68)
+#64 := (implies #59 #30)
 #69 := (iff #64 #68)
 #70 := [rewrite]: #69
-#65 := (iff #27 #64)
-#62 := (iff #21 #59)
-#56 := (and #53 #20)
+#65 := (iff #31 #64)
+#62 := (iff #26 #59)
+#51 := (and #13 #15 #42)
+#56 := (and #10 #51)
 #60 := (iff #56 #59)
 #61 := [rewrite]: #60
-#57 := (iff #21 #56)
-#54 := (iff #16 #53)
-#51 := (iff #15 #50)
-#52 := [rewrite]: #51
-#55 := [quant-intro #52]: #54
-#58 := [monotonicity #55]: #57
-#63 := [trans #58 #61]: #62
-#66 := [monotonicity #63]: #65
-#72 := [trans #66 #70]: #71
-#75 := [monotonicity #72]: #74
-#48 := [asserted]: #28
-#78 := [mp #48 #75]: #73
-#77 := [not-or-elim #78]: #59
-#80 := [and-elim #77]: #53
-#86 := [mp~ #80 #93]: #53
-#95 := [mp #86 #94]: #82
-#242 := (not #82)
-#232 := (or #242 #352)
-#566 := (or #242 #220)
-#568 := (iff #566 #232)
-#564 := (iff #232 #232)
-#570 := [rewrite]: #564
-#559 := (iff #220 #352)
-#231 := [rewrite]: #559
-#569 := [monotonicity #231]: #568
-#560 := [trans #569 #570]: #568
-#567 := [quant-inst #18 #22]: #566
-#218 := [mp #567 #560]: #232
-#219 := [unit-resolution #218 #95]: #352
-#209 := [symm #219]: #220
-#210 := (= f4 #565)
-#153 := (inj!0 f6 #23)
-#207 := (= #153 #565)
-#203 := (= #565 #153)
-#223 := (= #24 #23)
-#76 := [not-or-elim #78]: #25
-#561 := [symm #76]: #223
-#546 := [monotonicity #561]: #203
-#208 := [symm #546]: #207
-#154 := (= f4 #153)
-#233 := (or #242 #154)
-#240 := (= #153 f4)
-#244 := (or #242 #240)
-#173 := (iff #244 #233)
-#243 := (iff #233 #233)
-#247 := [rewrite]: #243
-#241 := (iff #240 #154)
-#155 := [rewrite]: #241
-#246 := [monotonicity #155]: #173
-#226 := [trans #246 #247]: #173
-#245 := [quant-inst #17 #22]: #244
-#563 := [mp #245 #226]: #233
-#562 := [unit-resolution #563 #95]: #154
-#548 := [trans #562 #208]: #210
-#549 := [trans #548 #209]: #19
-#79 := [and-elim #77]: #20
-[unit-resolution #79 #549]: false
-unsat
-16237d3c6ed6b1b0d94625f503401c43285f9eec 115 0
-#2 := false
-decl f5 :: S2
-#18 := f5
-decl f4 :: S2
-#17 := f4
-#19 := (= f4 f5)
-decl inj!0 :: (-> S3 S4 S2)
-decl f3 :: (-> S2 S3 S4)
-decl f6 :: S3
-#22 := f6
-#24 := (f3 f5 f6)
-#563 := (inj!0 f6 #24)
-#218 := (= #563 f5)
-#350 := (= f5 #563)
-#9 := (:var 1 S3)
-#11 := (:var 0 S2)
-#12 := (f3 #11 #9)
-#88 := (pattern #12)
-#87 := (inj!0 #9 #12)
-#84 := (= #87 #11)
-#89 := (forall (vars (k!0 S2) (k!1 S3)) (:pat #88) #84)
-#8 := (:var 2 S2)
-#14 := (= #8 #11)
-#10 := (f3 #8 #9)
-#13 := (= #10 #12)
-#49 := (not #13)
-#50 := (or #49 #14)
-#53 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #50)
-#85 := (iff #53 #89)
-#82 := [rewrite]: #85
-#92 := (~ #53 #53)
-#90 := (~ #50 #50)
-#91 := [refl]: #90
-#93 := [nnf-pos #91]: #92
-#20 := (not #19)
-#59 := (and #20 #53)
-#67 := (not #59)
-#23 := (f3 f4 f6)
-#25 := (= #23 #24)
-#26 := (not #25)
-#68 := (or #26 #67)
-#73 := (not #68)
-#15 := (implies #13 #14)
-#16 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #15)
-#21 := (and #16 #20)
-#27 := (implies #21 #26)
-#28 := (not #27)
-#74 := (iff #28 #73)
-#71 := (iff #27 #68)
-#64 := (implies #59 #26)
-#69 := (iff #64 #68)
-#70 := [rewrite]: #69
-#65 := (iff #27 #64)
-#62 := (iff #21 #59)
-#56 := (and #53 #20)
-#60 := (iff #56 #59)
-#61 := [rewrite]: #60
-#57 := (iff #21 #56)
-#54 := (iff #16 #53)
-#51 := (iff #15 #50)
-#52 := [rewrite]: #51
-#55 := [quant-intro #52]: #54
+#57 := (iff #26 #56)
+#54 := (iff #25 #51)
+#45 := (and #15 #42)
+#48 := (and #13 #45)
+#52 := (iff #48 #51)
+#53 := [rewrite]: #52
+#49 := (iff #25 #48)
+#46 := (iff #24 #45)
+#43 := (iff #23 #42)
+#40 := (iff #22 #39)
+#41 := [rewrite]: #40
+#44 := [quant-intro #41]: #43
+#47 := [monotonicity #44]: #46
+#50 := [monotonicity #47]: #49
+#55 := [trans #50 #53]: #54
 #58 := [monotonicity #55]: #57
 #63 := [trans #58 #61]: #62
 #66 := [monotonicity #63]: #65
 #72 := [trans #66 #70]: #71
 #75 := [monotonicity #72]: #74
-#48 := [asserted]: #28
-#78 := [mp #48 #75]: #73
-#77 := [not-or-elim #78]: #59
-#80 := [and-elim #77]: #53
-#86 := [mp~ #80 #93]: #53
-#83 := [mp #86 #82]: #89
-#240 := (not #89)
-#230 := (or #240 #350)
-#564 := (or #240 #218)
-#566 := (iff #564 #230)
-#562 := (iff #230 #230)
-#568 := [rewrite]: #562
-#557 := (iff #218 #350)
-#229 := [rewrite]: #557
-#567 := [monotonicity #229]: #566
-#558 := [trans #567 #568]: #566
-#565 := [quant-inst #22 #18]: #564
-#216 := [mp #565 #558]: #230
-#217 := [unit-resolution #216 #83]: #350
-#207 := [symm #217]: #218
-#208 := (= f4 #563)
-#151 := (inj!0 f6 #23)
-#205 := (= #151 #563)
-#201 := (= #563 #151)
-#221 := (= #24 #23)
-#76 := [not-or-elim #78]: #25
-#559 := [symm #76]: #221
-#544 := [monotonicity #559]: #201
-#206 := [symm #544]: #205
-#152 := (= f4 #151)
-#231 := (or #240 #152)
-#238 := (= #151 f4)
-#242 := (or #240 #238)
-#171 := (iff #242 #231)
-#241 := (iff #231 #231)
-#245 := [rewrite]: #241
-#239 := (iff #238 #152)
-#153 := [rewrite]: #239
-#244 := [monotonicity #153]: #171
-#224 := [trans #244 #245]: #171
-#243 := [quant-inst #22 #17]: #242
-#561 := [mp #243 #224]: #231
-#560 := [unit-resolution #561 #83]: #152
-#546 := [trans #560 #206]: #208
-#547 := [trans #546 #207]: #19
-#79 := [and-elim #77]: #20
-[unit-resolution #79 #547]: false
-unsat
-4c9a79660fa743d8586104c82221b940200355d2 40 0
-#2 := false
+#34 := [asserted]: #32
+#76 := [mp #34 #75]: #73
+#77 := [not-or-elim #76]: #59
+#81 := [and-elim #77]: #42
+#112 := [mp~ #81 #109]: #42
+#107 := [mp #112 #106]: #104
+#537 := [mp #107 #536]: #531
+#116 := (not #531)
+#207 := (or #116 #202)
+#204 := [quant-inst #8]: #207
+#187 := [unit-resolution #204 #537]: #202
+#527 := (= f3 #115)
+#114 := (inj!0 #27)
+#193 := (= #114 #115)
+#181 := (= #115 #114)
+#206 := (= #28 #27)
+#82 := [not-or-elim #76]: #29
+#208 := [symm #82]: #206
+#312 := [monotonicity #208]: #181
+#526 := [symm #312]: #193
+#519 := (= f3 #114)
+#201 := (= #114 f3)
+#203 := (or #116 #201)
+#194 := [quant-inst #7]: #203
+#205 := [unit-resolution #194 #537]: #201
+#192 := [symm #205]: #519
+#528 := [trans #192 #526]: #527
+#529 := [trans #528 #187]: #9
+#78 := [and-elim #77]: #10
+[unit-resolution #78 #529]: false
+6e572f819a5565b824096fa179274d819fc9261b 93 0
+unsat
+#2 := false
+decl f5 :: S3
+#17 := f5
+decl f4 :: S3
+#16 := f4
+#18 := (= f4 f5)
+decl inj!0 :: (-> S2 S4 S3)
+decl f3 :: (-> S2 S3 S4)
+decl f6 :: S2
+#21 := f6
+#23 := (f3 f6 f5)
+#94 := (inj!0 f6 #23)
+#181 := (= #94 f5)
+#8 := (:var 1 S3)
+#82 := (:var 0 S2)
+#79 := (f3 #82 #8)
+#88 := (pattern #79)
+#80 := (inj!0 #82 #79)
+#87 := (= #80 #8)
+#89 := (forall (vars (k!0 S3) (k!1 S2)) (:pat #88) #87)
+#10 := (:var 0 S3)
+#13 := (= #8 #10)
+#7 := (:var 2 S2)
+#11 := (f3 #7 #10)
+#9 := (f3 #7 #8)
+#12 := (= #9 #11)
+#33 := (not #12)
+#34 := (or #33 #13)
+#37 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #34)
+#90 := (iff #37 #89)
+#91 := [rewrite]: #90
+#85 := (~ #37 #37)
+#83 := (~ #34 #34)
+#84 := [refl]: #83
+#86 := [nnf-pos #84]: #85
+#19 := (not #18)
+#40 := (and #37 #19)
+#22 := (f3 f6 f4)
+#24 := (= #22 #23)
+#25 := (not #24)
+#46 := (not #40)
+#47 := (or #46 #25)
+#52 := (not #47)
+#14 := (implies #12 #13)
+#15 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #14)
+#20 := (and #15 #19)
+#26 := (implies #20 #25)
+#27 := (not #26)
+#53 := (iff #27 #52)
+#50 := (iff #26 #47)
+#43 := (implies #40 #25)
+#48 := (iff #43 #47)
+#49 := [rewrite]: #48
+#44 := (iff #26 #43)
+#41 := (iff #20 #40)
+#38 := (iff #15 #37)
+#35 := (iff #14 #34)
+#36 := [rewrite]: #35
+#39 := [quant-intro #36]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#51 := [trans #45 #49]: #50
+#54 := [monotonicity #51]: #53
+#29 := [asserted]: #27
+#55 := [mp #29 #54]: #52
+#56 := [not-or-elim #55]: #40
+#57 := [and-elim #56]: #37
+#81 := [mp~ #57 #86]: #37
+#92 := [mp #81 #91]: #89
+#95 := (not #89)
+#186 := (or #95 #181)
+#183 := [quant-inst #17 #21]: #186
+#166 := [unit-resolution #183 #92]: #181
+#506 := (= f4 #94)
+#93 := (inj!0 f6 #22)
+#172 := (= #93 #94)
+#160 := (= #94 #93)
+#185 := (= #23 #22)
+#59 := [not-or-elim #55]: #24
+#187 := [symm #59]: #185
+#291 := [monotonicity #187]: #160
+#505 := [symm #291]: #172
+#498 := (= f4 #93)
+#180 := (= #93 f4)
+#182 := (or #95 #180)
+#173 := [quant-inst #16 #21]: #182
+#184 := [unit-resolution #173 #92]: #180
+#171 := [symm #184]: #498
+#507 := [trans #171 #505]: #506
+#508 := [trans #507 #166]: #18
+#58 := [and-elim #56]: #19
+[unit-resolution #58 #508]: false
+d7fd68e20eb7b809b8a677cb04f940aa036f5afb 91 0
+unsat
+#2 := false
+decl f5 :: S2
+#17 := f5
+decl f4 :: S2
+#16 := f4
+#18 := (= f4 f5)
+decl inj!0 :: (-> S3 S4 S2)
+decl f3 :: (-> S2 S3 S4)
+decl f6 :: S3
+#21 := f6
+#23 := (f3 f5 f6)
+#92 := (inj!0 f6 #23)
+#179 := (= #92 f5)
+#8 := (:var 1 S3)
+#10 := (:var 0 S2)
+#11 := (f3 #10 #8)
+#82 := (pattern #11)
+#86 := (inj!0 #8 #11)
+#81 := (= #86 #10)
+#87 := (forall (vars (k!0 S3) (k!1 S2)) (:pat #82) #81)
+#7 := (:var 2 S2)
+#13 := (= #7 #10)
+#9 := (f3 #7 #8)
+#12 := (= #9 #11)
+#33 := (not #12)
+#34 := (or #33 #13)
+#37 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #34)
+#88 := (iff #37 #87)
+#89 := [rewrite]: #88
+#79 := (~ #37 #37)
+#83 := (~ #34 #34)
+#84 := [refl]: #83
+#80 := [nnf-pos #84]: #79
+#19 := (not #18)
+#40 := (and #37 #19)
+#22 := (f3 f4 f6)
+#24 := (= #22 #23)
+#25 := (not #24)
+#46 := (not #40)
+#47 := (or #46 #25)
+#52 := (not #47)
+#14 := (implies #12 #13)
+#15 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #14)
+#20 := (and #15 #19)
+#26 := (implies #20 #25)
+#27 := (not #26)
+#53 := (iff #27 #52)
+#50 := (iff #26 #47)
+#43 := (implies #40 #25)
+#48 := (iff #43 #47)
+#49 := [rewrite]: #48
+#44 := (iff #26 #43)
+#41 := (iff #20 #40)
+#38 := (iff #15 #37)
+#35 := (iff #14 #34)
+#36 := [rewrite]: #35
+#39 := [quant-intro #36]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#51 := [trans #45 #49]: #50
+#54 := [monotonicity #51]: #53
+#29 := [asserted]: #27
+#55 := [mp #29 #54]: #52
+#56 := [not-or-elim #55]: #40
+#57 := [and-elim #56]: #37
+#85 := [mp~ #57 #80]: #37
+#90 := [mp #85 #89]: #87
+#93 := (not #87)
+#184 := (or #93 #179)
+#181 := [quant-inst #21 #17]: #184
+#164 := [unit-resolution #181 #90]: #179
+#504 := (= f4 #92)
+#91 := (inj!0 f6 #22)
+#170 := (= #91 #92)
+#158 := (= #92 #91)
+#183 := (= #23 #22)
+#59 := [not-or-elim #55]: #24
+#185 := [symm #59]: #183
+#289 := [monotonicity #185]: #158
+#503 := [symm #289]: #170
+#496 := (= f4 #91)
+#178 := (= #91 f4)
+#180 := (or #93 #178)
+#171 := [quant-inst #21 #16]: #180
+#182 := [unit-resolution #171 #90]: #178
+#169 := [symm #182]: #496
+#505 := [trans #169 #503]: #504
+#506 := [trans #505 #164]: #18
+#58 := [and-elim #56]: #19
+[unit-resolution #58 #506]: false
+06c7eb9f7711ee93da7082f0da081b58762fb7a3 26 0
+unsat
+#2 := false
+decl f5 :: S2
+#13 := f5
 decl f3 :: (-> S3 S2 S2)
-decl f5 :: S2
-#14 := f5
 decl f4 :: S3
-#8 := f4
-#15 := (f3 f4 f5)
-#45 := (= f5 #15)
-#49 := (not #45)
-#16 := (= #15 f5)
-#17 := (not #16)
-#50 := (iff #17 #49)
-#47 := (iff #16 #45)
-#48 := [rewrite]: #47
-#51 := [monotonicity #48]: #50
-#44 := [asserted]: #17
-#54 := [mp #44 #51]: #49
-#9 := (:var 0 S2)
-#10 := (f3 f4 #9)
-#11 := (pattern #10)
-#38 := (= #9 #10)
-#41 := (forall (vars (?v0 S2)) (:pat #11) #38)
-#62 := (~ #41 #41)
-#60 := (~ #38 #38)
-#61 := [refl]: #60
-#63 := [nnf-pos #61]: #62
-#12 := (= #10 #9)
-#13 := (forall (vars (?v0 S2)) (:pat #11) #12)
-#42 := (iff #13 #41)
-#39 := (iff #12 #38)
-#40 := [rewrite]: #39
-#43 := [quant-intro #40]: #42
-#37 := [asserted]: #13
-#46 := [mp #37 #43]: #41
-#53 := [mp~ #46 #63]: #41
-#117 := (not #41)
-#204 := (or #117 #45)
-#118 := [quant-inst #14]: #204
-[unit-resolution #118 #53 #54]: false
-unsat
-6406bec77481f36eeae30a26a0091f3d105ae5e6 38 0
+#7 := f4
+#14 := (f3 f4 f5)
+#15 := (= #14 f5)
+#16 := (not #15)
+#19 := [asserted]: #16
+#8 := (:var 0 S2)
+#9 := (f3 f4 #8)
+#10 := (pattern #9)
+#11 := (= #9 #8)
+#12 := (forall (vars (?v0 S2)) (:pat #10) #11)
+#46 := (~ #12 #12)
+#44 := (~ #11 #11)
+#45 := [refl]: #44
+#47 := [nnf-pos #45]: #46
+#18 := [asserted]: #12
+#42 := [mp~ #18 #47]: #12
+#134 := (not #12)
+#127 := (or #134 #15)
+#138 := [quant-inst #13]: #127
+[unit-resolution #138 #42 #19]: false
+fcd8f166db037b8608ae35e66521fd11e6030072 30 0
+unsat
 #2 := false
 decl f4 :: (-> S3 S4)
-decl f6 :: (-> S5 Int S3)
-decl f8 :: (-> Int Int)
-decl f9 :: (-> Int Int)
-decl f10 :: Int
-#18 := f10
-#19 := (f9 f10)
-#20 := (f8 #19)
-decl f7 :: S5
-#17 := f7
-#21 := (f6 f7 #20)
-#22 := (f4 #21)
+decl f6 :: S3
+#16 := f6
+#17 := (f4 f6)
 decl f3 :: (-> S2 S4)
 decl f5 :: S2
+#14 := f5
+#15 := (f3 f5)
+#18 := (= #15 #17)
+#19 := (not #18)
+#22 := [asserted]: #19
+#9 := (:var 0 S3)
+#10 := (f4 #9)
+#7 := (:var 1 S2)
+#8 := (f3 #7)
+#11 := (pattern #8 #10)
+#12 := (= #8 #10)
+#13 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #11) #12)
+#49 := (~ #13 #13)
+#47 := (~ #12 #12)
+#48 := [refl]: #47
+#50 := [nnf-pos #48]: #49
+#21 := [asserted]: #13
+#45 := [mp~ #21 #50]: #13
+#53 := (not #13)
+#138 := (or #53 #18)
+#46 := [quant-inst #14 #16]: #138
+[unit-resolution #46 #45 #22]: false
+c7511e2629c4356cab2cf09d9c82407aa7fe6d05 47 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: (-> S2 S1)
+decl f5 :: S2
 #15 := f5
+#18 := (f4 f5)
+#19 := (= #18 f1)
+#20 := (not #19)
+#24 := [asserted]: #20
+decl f3 :: (-> S2 S1)
 #16 := (f3 f5)
-#23 := (= #16 #22)
-#24 := (not #23)
-#45 := [asserted]: #24
-#10 := (:var 0 S3)
-#11 := (f4 #10)
-#8 := (:var 1 S2)
-#9 := (f3 #8)
-#12 := (pattern #9 #11)
-#13 := (= #9 #11)
-#14 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #12) #13)
-#55 := (~ #14 #14)
-#53 := (~ #13 #13)
-#54 := [refl]: #53
-#56 := [nnf-pos #54]: #55
-#44 := [asserted]: #14
-#47 := [mp~ #44 #56]: #14
-#110 := (not #14)
-#197 := (or #110 #23)
-#111 := [quant-inst #15 #21]: #197
-[unit-resolution #111 #47 #45]: false
-unsat
-2e896cd9a2fe5bb207857c1a092e502ece669e01 16 0
-#2 := false
-#1 := true
-#8 := (implies true true)
-#9 := (not #8)
-#37 := (iff #9 false)
-#32 := (not true)
-#35 := (iff #32 false)
-#36 := [rewrite]: #35
-#33 := (iff #9 #32)
-#30 := (iff #8 true)
+#17 := (= #16 f1)
+#23 := [asserted]: #17
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#9 := (pattern #8)
+#11 := (f4 #7)
+#12 := (= #11 f1)
+#10 := (= #8 f1)
+#28 := (not #10)
+#29 := (or #28 #12)
+#32 := (forall (vars (?v0 S2)) (:pat #9) #29)
+#57 := (~ #32 #32)
+#55 := (~ #29 #29)
+#56 := [refl]: #55
+#58 := [nnf-pos #56]: #57
+#13 := (implies #10 #12)
+#14 := (forall (vars (?v0 S2)) (:pat #9) #13)
+#33 := (iff #14 #32)
+#30 := (iff #13 #29)
 #31 := [rewrite]: #30
-#34 := [monotonicity #31]: #33
-#38 := [trans #34 #36]: #37
-#29 := [asserted]: #9
-[mp #29 #38]: false
-unsat
-a79bf9f4931711426a169989fc9caedc89cfa1a4 16 0
-#2 := false
-#8 := (implies false false)
-#9 := (not #8)
-#37 := (iff #9 false)
-#1 := true
-#32 := (not true)
-#35 := (iff #32 false)
-#36 := [rewrite]: #35
-#33 := (iff #9 #32)
-#30 := (iff #8 true)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31]: #33
-#38 := [trans #34 #36]: #37
-#29 := [asserted]: #9
-[mp #29 #38]: false
-unsat
-1be840005f8a5d8a9ad842fa8ca7ecbce8bcb124 31 0
-#2 := false
-decl f1 :: S1
-#4 := f1
+#34 := [quant-intro #31]: #33
+#22 := [asserted]: #14
+#35 := [mp #22 #34]: #32
+#61 := [mp~ #35 #58]: #32
+#62 := (not #17)
+#60 := (not #32)
+#149 := (or #60 #62 #19)
+#147 := (or #62 #19)
+#140 := (or #60 #147)
+#152 := (iff #140 #149)
+#153 := [rewrite]: #152
+#151 := [quant-inst #15]: #140
+#150 := [mp #151 #153]: #149
+[unit-resolution #150 #61 #23 #24]: false
+a6270f81d5df8dfba370dfde937210f23b9d7a30 80 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f5 :: (-> S2 S1)
+decl f6 :: S2
+#18 := f6
+#23 := (f5 f6)
+#24 := (= #23 f1)
+#25 := (not #24)
+#30 := [asserted]: #25
+decl f4 :: (-> S2 S1)
+#21 := (f4 f6)
+#22 := (= #21 f1)
+#29 := [asserted]: #22
+decl f3 :: (-> S2 S1)
+#19 := (f3 f6)
+#20 := (= #19 f1)
+#28 := [asserted]: #20
+#7 := (:var 0 S2)
+#9 := (f4 #7)
+#8 := (f3 #7)
+#10 := (pattern #8 #9)
+#14 := (f5 #7)
+#15 := (= #14 f1)
+#12 := (= #9 f1)
+#65 := (not #12)
+#11 := (= #8 f1)
+#62 := (not #11)
+#82 := (or #62 #65 #15)
+#87 := (forall (vars (?v0 S2)) (:pat #10) #82)
+#13 := (and #11 #12)
+#34 := (not #13)
+#35 := (or #34 #15)
+#38 := (forall (vars (?v0 S2)) (:pat #10) #35)
+#88 := (iff #38 #87)
+#85 := (iff #35 #82)
+#68 := (or #62 #65)
+#79 := (or #68 #15)
+#83 := (iff #79 #82)
+#84 := [rewrite]: #83
+#80 := (iff #35 #79)
+#77 := (iff #34 #68)
+#61 := (not #68)
+#72 := (not #61)
+#75 := (iff #72 #68)
+#76 := [rewrite]: #75
+#73 := (iff #34 #72)
+#66 := (iff #13 #61)
+#71 := [rewrite]: #66
+#74 := [monotonicity #71]: #73
+#78 := [trans #74 #76]: #77
+#81 := [monotonicity #78]: #80
+#86 := [trans #81 #84]: #85
+#89 := [quant-intro #86]: #88
+#63 := (~ #38 #38)
+#69 := (~ #35 #35)
+#70 := [refl]: #69
+#64 := [nnf-pos #70]: #63
+#16 := (implies #13 #15)
+#17 := (forall (vars (?v0 S2)) (:pat #10) #16)
+#39 := (iff #17 #38)
+#36 := (iff #16 #35)
+#37 := [rewrite]: #36
+#40 := [quant-intro #37]: #39
+#27 := [asserted]: #17
+#41 := [mp #27 #40]: #38
+#67 := [mp~ #41 #64]: #38
+#90 := [mp #67 #89]: #87
+#178 := (not #22)
+#91 := (not #20)
+#180 := (not #87)
+#171 := (or #180 #91 #178 #24)
+#92 := (or #91 #178 #24)
+#182 := (or #180 #92)
+#184 := (iff #182 #171)
+#181 := [rewrite]: #184
+#183 := [quant-inst #18]: #182
+#185 := [mp #183 #181]: #171
+[unit-resolution #185 #90 #28 #29 #30]: false
+9a5dc5d34493dd61c515054a38ab88431b1114aa 94 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+decl f6 :: S2
+#20 := f6
+#21 := (f3 f6)
+#22 := (= #21 f1)
+#85 := (not #22)
+decl f5 :: (-> S2 S1)
+#26 := (f5 f6)
+#27 := (= #26 f1)
+#172 := (or #85 #27)
+decl f4 :: (-> S2 S1)
+#23 := (f4 f6)
+#24 := (= #23 f1)
+#173 := (not #24)
+#87 := (or #173 #27)
+#174 := (not #87)
+#86 := (not #172)
+#165 := (or #86 #174)
+#176 := (not #165)
+#177 := [hypothesis]: #165
+#7 := (:var 0 S2)
+#10 := (f4 #7)
+#11 := (pattern #10)
+#8 := (f3 #7)
+#9 := (pattern #8)
+#13 := (f5 #7)
+#14 := (= #13 f1)
+#16 := (= #10 f1)
+#40 := (not #16)
+#41 := (or #40 #14)
+#72 := (not #41)
+#12 := (= #8 f1)
+#36 := (not #12)
+#37 := (or #36 #14)
+#77 := (not #37)
+#73 := (or #77 #72)
+#78 := (not #73)
+#81 := (forall (vars (?v0 S2)) (:pat #9 #11) #78)
+#44 := (and #37 #41)
+#47 := (forall (vars (?v0 S2)) (:pat #9 #11) #44)
+#82 := (iff #47 #81)
+#79 := (iff #44 #78)
+#80 := [rewrite]: #79
+#83 := [quant-intro #80]: #82
+#70 := (~ #47 #47)
+#74 := (~ #44 #44)
+#75 := [refl]: #74
+#71 := [nnf-pos #75]: #70
+#17 := (implies #16 #14)
+#15 := (implies #12 #14)
+#18 := (and #15 #17)
+#19 := (forall (vars (?v0 S2)) (:pat #9 #11) #18)
+#48 := (iff #19 #47)
+#45 := (iff #18 #44)
+#42 := (iff #17 #41)
+#43 := [rewrite]: #42
+#38 := (iff #15 #37)
+#39 := [rewrite]: #38
+#46 := [monotonicity #39 #43]: #45
+#49 := [quant-intro #46]: #48
+#30 := [asserted]: #19
+#50 := [mp #30 #49]: #47
+#76 := [mp~ #50 #71]: #47
+#84 := [mp #76 #83]: #81
+#175 := (not #81)
+#179 := (or #175 #176)
+#158 := [quant-inst #20]: #179
+#178 := [unit-resolution #158 #84 #177]: false
+#493 := [lemma #178]: #176
+#501 := (or #165 #172)
+#491 := [def-axiom]: #501
+#135 := [unit-resolution #491 #493]: #172
+#477 := (or #86 #85)
+#28 := (not #27)
+#32 := [asserted]: #28
+#490 := (or #86 #85 #27)
+#163 := [def-axiom]: #490
+#139 := [unit-resolution #163 #32]: #477
+#140 := [unit-resolution #139 #135]: #85
+#150 := (or #165 #87)
+#155 := [def-axiom]: #150
+#141 := [unit-resolution #155 #493]: #87
+#142 := (or #174 #173)
+#500 := (or #174 #173 #27)
+#495 := [def-axiom]: #500
+#479 := [unit-resolution #495 #32]: #142
+#480 := [unit-resolution #479 #141]: #173
+#25 := (or #22 #24)
+#31 := [asserted]: #25
+[unit-resolution #31 #480 #140]: false
+0174e3da6a3b0d1b54444b41bf1d3bca92d15ce1 47 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: (-> S2 S1)
+decl f5 :: S2
+#16 := f5
+#19 := (f4 f5)
+#20 := (= #19 f1)
+#21 := (not #20)
+#25 := [asserted]: #21
 decl f3 :: (-> S2 S1)
-decl f4 :: S2
-#8 := f4
-#9 := (f3 f4)
+#17 := (f3 f5)
+#18 := (= #17 f1)
+#24 := [asserted]: #18
+#7 := (:var 0 S2)
+#8 := (f3 #7)
+#9 := (pattern #8)
+#12 := (f4 #7)
+#13 := (= #12 f1)
+#11 := (= #8 f1)
+#29 := (not #11)
+#30 := (or #29 #13)
+#33 := (forall (vars (?v0 S2)) (:pat #9) #30)
+#58 := (~ #33 #33)
+#56 := (~ #30 #30)
+#57 := [refl]: #56
+#59 := [nnf-pos #57]: #58
+#14 := (implies #11 #13)
+#15 := (forall (vars (?v0 S2)) (:pat #9) #14)
+#34 := (iff #15 #33)
+#31 := (iff #14 #30)
+#32 := [rewrite]: #31
+#35 := [quant-intro #32]: #34
+#23 := [asserted]: #15
+#36 := [mp #23 #35]: #33
+#62 := [mp~ #36 #59]: #33
+#63 := (not #18)
+#61 := (not #33)
+#150 := (or #61 #63 #20)
+#148 := (or #63 #20)
+#141 := (or #61 #148)
+#153 := (iff #141 #150)
+#154 := [rewrite]: #153
+#152 := [quant-inst #16]: #141
+#151 := [mp #152 #154]: #150
+[unit-resolution #151 #62 #24 #25]: false
+3cf2f5774e9cb53226a2180612e5e1ffeb96f030 54 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: (-> S2 S1)
+decl f5 :: S2
+#15 := f5
+#18 := (f4 f5)
+#19 := (= #18 f1)
+#20 := (not #19)
+#24 := [asserted]: #20
+decl f3 :: (-> S2 S1)
+#16 := (f3 f5)
+#17 := (= #16 f1)
+#23 := [asserted]: #17
+#8 := (:var 0 S2)
+#11 := (f4 #8)
+#477 := (pattern #11)
+#9 := (f3 #8)
+#476 := (pattern #9)
+#12 := (= #11 f1)
 #10 := (= #9 f1)
-#11 := (implies #10 #10)
-#12 := (not #11)
-#48 := (iff #12 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (iff #11 true)
-#33 := (= f1 #9)
-#36 := (implies #33 #33)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (iff #10 #33)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35 #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#32 := [asserted]: #12
-[mp #32 #49]: false
-unsat
-ff912d650aac3afb164b55e5753273823fac2c2b 48 0
-#2 := false
-decl f1 :: S1
-#4 := f1
+#28 := (not #10)
+#29 := (or #28 #12)
+#478 := (forall (vars (?v0 S2)) (:pat #476 #477) #29)
+#32 := (forall (vars (?v0 S2)) #29)
+#481 := (iff #32 #478)
+#479 := (iff #29 #29)
+#480 := [refl]: #479
+#482 := [quant-intro #480]: #481
+#61 := (~ #32 #32)
+#59 := (~ #29 #29)
+#60 := [refl]: #59
+#62 := [nnf-pos #60]: #61
+#13 := (implies #10 #12)
+#14 := (forall (vars (?v0 S2)) #13)
+#33 := (iff #14 #32)
+#30 := (iff #13 #29)
+#31 := [rewrite]: #30
+#34 := [quant-intro #31]: #33
+#22 := [asserted]: #14
+#35 := [mp #22 #34]: #32
+#57 := [mp~ #35 #62]: #32
+#483 := [mp #57 #482]: #478
+#58 := (not #17)
+#56 := (not #478)
+#148 := (or #56 #58 #19)
+#146 := (or #58 #19)
+#139 := (or #56 #146)
+#151 := (iff #139 #148)
+#152 := [rewrite]: #151
+#150 := [quant-inst #15]: #139
+#149 := [mp #150 #152]: #148
+[unit-resolution #149 #483 #23 #24]: false
+cb6801fac47863f5b3d24e889ecd9d6a4cb46df6 16 0
+unsat
+#2 := false
+#1 := true
+#7 := (implies true true)
+#8 := (not #7)
+#21 := (iff #8 false)
+#16 := (not true)
+#19 := (iff #16 false)
+#20 := [rewrite]: #19
+#17 := (iff #8 #16)
+#14 := (iff #7 true)
+#15 := [rewrite]: #14
+#18 := [monotonicity #15]: #17
+#22 := [trans #18 #20]: #21
+#10 := [asserted]: #8
+[mp #10 #22]: false
+16e1681a3c64ecd748e6c05bfb8e8c32bcbc7c22 16 0
+unsat
+#2 := false
+#7 := (implies false false)
+#8 := (not #7)
+#21 := (iff #8 false)
+#1 := true
+#16 := (not true)
+#19 := (iff #16 false)
+#20 := [rewrite]: #19
+#17 := (iff #8 #16)
+#14 := (iff #7 true)
+#15 := [rewrite]: #14
+#18 := [monotonicity #15]: #17
+#22 := [trans #18 #20]: #21
+#10 := [asserted]: #8
+[mp #10 #22]: false
+388e4d9b91ffb1a7279a22ad67a0af16108a59dd 23 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1)
+decl f4 :: S2
+#7 := f4
+#8 := (f3 f4)
+#9 := (= #8 f1)
+#10 := (implies #9 #9)
+#11 := (not #10)
+#24 := (iff #11 false)
+#1 := true
+#19 := (not true)
+#22 := (iff #19 false)
+#23 := [rewrite]: #22
+#20 := (iff #11 #19)
+#17 := (iff #10 true)
+#18 := [rewrite]: #17
+#21 := [monotonicity #18]: #20
+#25 := [trans #21 #23]: #24
+#13 := [asserted]: #11
+[mp #13 #25]: false
+8b861d903a9a1054060c90c6ae2af47fe5197810 25 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#11 := (or #8 #10)
+#12 := (implies #8 #11)
+#13 := (not #12)
+#26 := (iff #13 false)
+#1 := true
+#21 := (not true)
+#24 := (iff #21 false)
+#25 := [rewrite]: #24
+#22 := (iff #13 #21)
+#19 := (iff #12 true)
+#20 := [rewrite]: #19
+#23 := [monotonicity #20]: #22
+#27 := [trans #23 #25]: #26
+#15 := [asserted]: #13
+[mp #15 #27]: false
+25b3a4036a36c70240b5d9e2d0a1d55ba7cba9e7 25 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#11 := (or #10 #8)
+#12 := (implies #8 #11)
+#13 := (not #12)
+#26 := (iff #13 false)
+#1 := true
+#21 := (not true)
+#24 := (iff #21 false)
+#25 := [rewrite]: #24
+#22 := (iff #13 #21)
+#19 := (iff #12 true)
+#20 := [rewrite]: #19
+#23 := [monotonicity #20]: #22
+#27 := [trans #23 #25]: #26
+#15 := [asserted]: #13
+[mp #15 #27]: false
+4e6d14ef22716878d11f1de1592f873bbc16eb75 34 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
 decl f4 :: S1
 #10 := f4
 #11 := (= f4 f1)
 decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#12 := (or #9 #11)
-#13 := (implies #9 #12)
-#14 := (not #13)
-#65 := (iff #14 false)
-#38 := (= f1 f4)
-#35 := (= f1 f3)
-#41 := (or #35 #38)
-#47 := (not #35)
-#48 := (or #47 #41)
-#53 := (not #48)
-#63 := (iff #53 false)
-#1 := true
-#58 := (not true)
-#61 := (iff #58 false)
-#62 := [rewrite]: #61
-#59 := (iff #53 #58)
-#56 := (iff #48 true)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#54 := (iff #14 #53)
-#51 := (iff #13 #48)
-#44 := (implies #35 #41)
-#49 := (iff #44 #48)
-#50 := [rewrite]: #49
-#45 := (iff #13 #44)
-#42 := (iff #12 #41)
-#39 := (iff #11 #38)
-#40 := [rewrite]: #39
-#36 := (iff #9 #35)
-#37 := [rewrite]: #36
-#43 := [monotonicity #37 #40]: #42
-#46 := [monotonicity #37 #43]: #45
-#52 := [trans #46 #50]: #51
-#55 := [monotonicity #52]: #54
-#66 := [trans #55 #64]: #65
-#34 := [asserted]: #14
-[mp #34 #66]: false
-unsat
-4edc7ae478dc44e520d7e30a938c9581ab4e2a19 53 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-#12 := (or #11 #9)
+#7 := f3
+#8 := (= f3 f1)
+#12 := (implies #8 #11)
+#9 := (not #8)
 #13 := (implies #9 #12)
 #14 := (not #13)
-#70 := (iff #14 false)
-#38 := (= f1 f4)
-#35 := (= f1 f3)
-#44 := (or #35 #38)
-#52 := (not #35)
-#53 := (or #52 #44)
-#58 := (not #53)
-#68 := (iff #58 false)
-#1 := true
-#63 := (not true)
-#66 := (iff #63 false)
-#67 := [rewrite]: #66
-#64 := (iff #58 #63)
-#61 := (iff #53 true)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#69 := [trans #65 #67]: #68
-#59 := (iff #14 #58)
-#56 := (iff #13 #53)
-#49 := (implies #35 #44)
-#54 := (iff #49 #53)
-#55 := [rewrite]: #54
-#50 := (iff #13 #49)
-#47 := (iff #12 #44)
-#41 := (or #38 #35)
-#45 := (iff #41 #44)
-#46 := [rewrite]: #45
-#42 := (iff #12 #41)
-#36 := (iff #9 #35)
-#37 := [rewrite]: #36
-#39 := (iff #11 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40 #37]: #42
-#48 := [trans #43 #46]: #47
-#51 := [monotonicity #37 #48]: #50
-#57 := [trans #51 #55]: #56
-#60 := [monotonicity #57]: #59
-#71 := [trans #60 #69]: #70
-#34 := [asserted]: #14
-[mp #34 #71]: false
-unsat
-efb9f6518fd6418e28f5a875349db177d5fe4ceb 56 0
-#2 := false
-decl f1 :: S1
-#4 := f1
+#35 := (iff #14 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #14 #30)
+#28 := (iff #13 true)
+#20 := (or #9 #11)
+#23 := (implies #9 #20)
+#26 := (iff #23 true)
+#27 := [rewrite]: #26
+#24 := (iff #13 #23)
+#21 := (iff #12 #20)
+#22 := [rewrite]: #21
+#25 := [monotonicity #22]: #24
+#29 := [trans #25 #27]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#16 := [asserted]: #14
+[mp #16 #36]: false
+bcec35782699eb337715cce60af2a2265320a550 79 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
 decl f4 :: S1
-#11 := f4
-#12 := (= f4 f1)
+#9 := f4
+#10 := (= f4 f1)
+#11 := (not #10)
+#99 := (iff #11 false)
+#1 := true
+#78 := (not true)
+#81 := (iff #78 false)
+#82 := [rewrite]: #81
+#97 := (iff #11 #78)
+#95 := (iff #10 true)
+#71 := (= f1 f1)
+#74 := (iff #71 true)
+#75 := [rewrite]: #74
+#93 := (iff #10 #71)
 decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#13 := (implies #9 #12)
-#10 := (not #9)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#73 := (iff #15 false)
-#42 := (= f1 f4)
-#36 := (= f1 f3)
-#39 := (not #36)
-#48 := (or #39 #42)
-#56 := (or #36 #48)
-#61 := (not #56)
-#71 := (iff #61 false)
-#1 := true
-#66 := (not true)
-#69 := (iff #66 false)
-#70 := [rewrite]: #69
-#67 := (iff #61 #66)
-#64 := (iff #56 true)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#72 := [trans #68 #70]: #71
-#62 := (iff #15 #61)
-#59 := (iff #14 #56)
-#53 := (implies #39 #48)
-#57 := (iff #53 #56)
-#58 := [rewrite]: #57
-#54 := (iff #14 #53)
-#51 := (iff #13 #48)
-#45 := (implies #36 #42)
-#49 := (iff #45 #48)
-#50 := [rewrite]: #49
-#46 := (iff #13 #45)
-#43 := (iff #12 #42)
-#44 := [rewrite]: #43
-#37 := (iff #9 #36)
-#38 := [rewrite]: #37
-#47 := [monotonicity #38 #44]: #46
-#52 := [trans #47 #50]: #51
-#40 := (iff #10 #39)
-#41 := [monotonicity #38]: #40
-#55 := [monotonicity #41 #52]: #54
-#60 := [trans #55 #58]: #59
-#63 := [monotonicity #60]: #62
-#74 := [trans #63 #72]: #73
-#35 := [asserted]: #15
-[mp #35 #74]: false
-unsat
-741dce5f3cb8845f3e976710e82077b71b6e3b48 89 0
-#2 := false
-decl f4 :: S1
-#10 := f4
-decl f1 :: S1
-#4 := f1
-#41 := (= f1 f4)
-decl f3 :: S1
-#8 := f3
-#38 := (= f1 f3)
-#50 := (not #38)
-#51 := (or #50 #41)
-#109 := (iff #51 false)
-#104 := (or false false)
-#107 := (iff #104 false)
-#108 := [rewrite]: #107
-#105 := (iff #51 #104)
-#95 := (iff #41 false)
-#44 := (not #41)
-#56 := (not #51)
-#78 := (or #50 #41 #56)
-#81 := (not #78)
-#11 := (= f4 f1)
-#9 := (= f3 f1)
-#13 := (implies #9 #11)
+#7 := f3
+#8 := (= f3 f1)
+#22 := (not #8)
+#23 := (or #22 #10)
+#90 := (iff #23 #10)
+#85 := (or false #10)
+#88 := (iff #85 #10)
+#89 := [rewrite]: #88
+#86 := (iff #23 #85)
+#83 := (iff #22 false)
+#79 := (iff #22 #78)
+#76 := (iff #8 true)
+#72 := (iff #8 #71)
+#26 := (not #23)
+#40 := (or #22 #10 #26)
+#45 := (not #40)
+#12 := (implies #8 #10)
+#13 := (not #12)
+#14 := (implies #11 #13)
+#15 := (implies #8 #14)
+#16 := (not #15)
+#46 := (iff #16 #45)
+#43 := (iff #15 #40)
+#32 := (or #10 #26)
+#37 := (implies #8 #32)
+#41 := (iff #37 #40)
+#42 := [rewrite]: #41
+#38 := (iff #15 #37)
+#35 := (iff #14 #32)
+#29 := (implies #11 #26)
+#33 := (iff #29 #32)
+#34 := [rewrite]: #33
+#30 := (iff #14 #29)
+#27 := (iff #13 #26)
+#24 := (iff #12 #23)
+#25 := [rewrite]: #24
+#28 := [monotonicity #25]: #27
+#31 := [monotonicity #28]: #30
+#36 := [trans #31 #34]: #35
+#39 := [monotonicity #36]: #38
+#44 := [trans #39 #42]: #43
+#47 := [monotonicity #44]: #46
+#18 := [asserted]: #16
+#48 := [mp #18 #47]: #45
+#49 := [not-or-elim #48]: #8
+#73 := [monotonicity #49]: #72
+#77 := [trans #73 #75]: #76
+#80 := [monotonicity #77]: #79
+#84 := [trans #80 #82]: #83
+#87 := [monotonicity #84]: #86
+#91 := [trans #87 #89]: #90
+#51 := [not-or-elim #48]: #23
+#92 := [mp #51 #91]: #10
+#94 := [monotonicity #92]: #93
+#96 := [trans #94 #75]: #95
+#98 := [monotonicity #96]: #97
+#100 := [trans #98 #82]: #99
+#50 := [not-or-elim #48]: #11
+[mp #50 #100]: false
+760574e0ad704bb8f35577bec0aff7d25c63c601 58 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f5 :: (-> S2 S1)
+decl f4 :: S2
+#7 := f4
+#10 := (f5 f4)
+#11 := (= #10 f1)
+#57 := (not #11)
+#75 := [hypothesis]: #57
+decl f3 :: (-> S2 S1)
+#8 := (f3 f4)
+#9 := (= #8 f1)
+#20 := (not #9)
+#65 := (or #20 #11)
+#12 := (iff #9 #11)
+#21 := (iff #20 #11)
+#29 := (not #21)
+#52 := (iff #29 #12)
+#53 := [rewrite]: #52
+#22 := (or #21 #12)
+#25 := (not #22)
+#13 := (implies #12 #12)
 #14 := (not #13)
-#12 := (not #11)
-#15 := (implies #12 #14)
-#16 := (implies #9 #15)
-#17 := (not #16)
-#84 := (iff #17 #81)
-#62 := (or #41 #56)
-#70 := (or #50 #62)
-#75 := (not #70)
-#82 := (iff #75 #81)
-#79 := (iff #70 #78)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#76 := (iff #17 #75)
-#73 := (iff #16 #70)
-#67 := (implies #38 #62)
-#71 := (iff #67 #70)
-#72 := [rewrite]: #71
-#68 := (iff #16 #67)
-#65 := (iff #15 #62)
-#59 := (implies #44 #56)
-#63 := (iff #59 #62)
-#64 := [rewrite]: #63
-#60 := (iff #15 #59)
-#57 := (iff #14 #56)
-#54 := (iff #13 #51)
-#47 := (implies #38 #41)
-#52 := (iff #47 #51)
-#53 := [rewrite]: #52
-#48 := (iff #13 #47)
-#42 := (iff #11 #41)
-#43 := [rewrite]: #42
-#39 := (iff #9 #38)
-#40 := [rewrite]: #39
-#49 := [monotonicity #40 #43]: #48
-#55 := [trans #49 #53]: #54
-#58 := [monotonicity #55]: #57
-#45 := (iff #12 #44)
-#46 := [monotonicity #43]: #45
-#61 := [monotonicity #46 #58]: #60
-#66 := [trans #61 #64]: #65
-#69 := [monotonicity #40 #66]: #68
-#74 := [trans #69 #72]: #73
-#77 := [monotonicity #74]: #76
-#85 := [trans #77 #83]: #84
-#37 := [asserted]: #17
-#86 := [mp #37 #85]: #81
-#88 := [not-or-elim #86]: #44
-#96 := [iff-false #88]: #95
-#102 := (iff #50 false)
-#1 := true
-#97 := (not true)
-#100 := (iff #97 false)
-#101 := [rewrite]: #100
-#98 := (iff #50 #97)
-#93 := (iff #38 true)
-#87 := [not-or-elim #86]: #38
-#94 := [iff-true #87]: #93
-#99 := [monotonicity #94]: #98
-#103 := [trans #99 #101]: #102
-#106 := [monotonicity #103 #96]: #105
-#110 := [trans #106 #108]: #109
-#89 := [not-or-elim #86]: #51
-[mp #89 #110]: false
-unsat
-0f2e31d8ce8759346cad7c733d7f6d64c22635fd 57 0
-#2 := false
-decl f3 :: (-> S2 S1)
-decl f4 :: S2
-#8 := f4
-#9 := (f3 f4)
-decl f1 :: S1
-#4 := f1
-#36 := (= f1 #9)
-#48 := (not #36)
-decl f5 :: (-> S2 S1)
-#11 := (f5 f4)
-#39 := (= f1 #11)
-#49 := (iff #39 #48)
-#61 := (not #49)
-#76 := (iff #61 false)
-#1 := true
-#71 := (not true)
-#74 := (iff #71 false)
-#75 := [rewrite]: #74
-#72 := (iff #61 #71)
-#69 := (iff #49 true)
-#42 := (iff #36 #39)
-#58 := (not #42)
-#66 := (iff #58 #49)
-#67 := [rewrite]: #66
-#50 := (or #42 #49)
-#55 := (not #50)
-#12 := (= #11 f1)
-#10 := (= #9 f1)
-#13 := (iff #10 #12)
-#14 := (implies #13 #13)
-#15 := (not #14)
-#56 := (iff #15 #55)
-#53 := (iff #14 #50)
-#45 := (implies #42 #42)
-#51 := (iff #45 #50)
-#52 := [rewrite]: #51
-#46 := (iff #14 #45)
-#43 := (iff #13 #42)
-#40 := (iff #12 #39)
-#41 := [rewrite]: #40
-#37 := (iff #10 #36)
-#38 := [rewrite]: #37
-#44 := [monotonicity #38 #41]: #43
-#47 := [monotonicity #44 #44]: #46
-#54 := [trans #47 #52]: #53
-#57 := [monotonicity #54]: #56
-#35 := [asserted]: #15
-#60 := [mp #35 #57]: #55
-#59 := [not-or-elim #60]: #58
-#68 := [mp #59 #67]: #49
-#70 := [iff-true #68]: #69
-#73 := [monotonicity #70]: #72
-#77 := [trans #73 #75]: #76
-#62 := [not-or-elim #60]: #61
-[mp #62 #77]: false
-unsat
-1f5e449bae0893dc762768fde0ab33c8f0ed64d8 50 0
+#26 := (iff #14 #25)
+#23 := (iff #13 #22)
+#24 := [rewrite]: #23
+#27 := [monotonicity #24]: #26
+#16 := [asserted]: #14
+#28 := [mp #16 #27]: #25
+#30 := [not-or-elim #28]: #29
+#56 := [mp #30 #53]: #12
+#31 := (not #12)
+#63 := (or #20 #11 #31)
+#64 := [def-axiom]: #63
+#66 := [unit-resolution #64 #56]: #65
+#76 := [unit-resolution #66 #75]: #20
+#73 := (or #9 #11)
+#54 := (iff #31 #21)
+#55 := [rewrite]: #54
+#32 := [not-or-elim #28]: #31
+#59 := [mp #32 #55]: #21
+#71 := (or #9 #11 #29)
+#72 := [def-axiom]: #71
+#74 := [unit-resolution #72 #59]: #73
+#77 := [unit-resolution #74 #76 #75]: false
+#78 := [lemma #77]: #11
+#61 := (or #9 #57)
+#58 := (or #9 #57 #31)
+#60 := [def-axiom]: #58
+#62 := [unit-resolution #60 #56]: #61
+#79 := [unit-resolution #62 #78]: #9
+#69 := (or #20 #57)
+#67 := (or #20 #57 #29)
+#68 := [def-axiom]: #67
+#70 := [unit-resolution #68 #59]: #69
+[unit-resolution #70 #79 #78]: false
+b7a3c12d014ca4816865d67abe41008844e852f3 53 0
+unsat
 #2 := false
 decl f5 :: S2
-#11 := f5
-decl f3 :: S2
-#8 := f3
-#13 := (= f3 f5)
-decl f4 :: S2
-#9 := f4
-#12 := (= f4 f5)
-#77 := (iff #12 #13)
-#75 := (iff #13 #12)
-#10 := (= f3 f4)
-#37 := (not #12)
-#44 := (not #10)
-#53 := (or #44 #37 #13)
-#56 := (not #53)
-#14 := (implies #12 #13)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#59 := (iff #16 #56)
-#38 := (or #37 #13)
-#45 := (or #44 #38)
-#50 := (not #45)
-#57 := (iff #50 #56)
-#54 := (iff #45 #53)
-#55 := [rewrite]: #54
-#58 := [monotonicity #55]: #57
-#51 := (iff #16 #50)
-#48 := (iff #15 #45)
-#41 := (implies #10 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#60 := [trans #52 #58]: #59
-#36 := [asserted]: #16
-#61 := [mp #36 #60]: #56
-#62 := [not-or-elim #61]: #10
-#76 := [monotonicity #62]: #75
-#78 := [symm #76]: #77
-#63 := [not-or-elim #61]: #12
-#73 := [mp #63 #78]: #13
-#64 := (not #13)
-#65 := [not-or-elim #61]: #64
-[unit-resolution #65 #73]: false
-unsat
-4e0b37ec3c792ee4a851a10d652496a1aab77e5d 27 0
-#2 := false
-decl f5 :: (-> S2 S3)
-decl f4 :: S2
-#9 := f4
-#12 := (f5 f4)
+#10 := f5
 decl f3 :: S2
-#8 := f3
-#11 := (f5 f3)
-#13 := (= #11 #12)
-#10 := (= f3 f4)
-#36 := (not #10)
-#37 := (or #36 #13)
-#40 := (not #37)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#41 := (iff #15 #40)
-#38 := (iff #14 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#35 := [asserted]: #15
-#45 := [mp #35 #42]: #40
-#43 := [not-or-elim #45]: #10
-#54 := [monotonicity #43]: #13
-#44 := (not #13)
-#46 := [not-or-elim #45]: #44
-[unit-resolution #46 #54]: false
-unsat
-4dde6baa3718fc0e77a819f22fb6fcabd08b0613 75 0
-#2 := false
-decl f3 :: (-> S2 S1 S1)
-decl f5 :: S1
-#13 := f5
-decl f4 :: S2
-#8 := f4
-#14 := (f3 f4 f5)
-decl f1 :: S1
-#4 := f1
-#46 := (= f1 #14)
-#77 := (not #46)
-#49 := (= f1 f5)
-#9 := (:var 0 S1)
-#10 := (f3 f4 #9)
-#40 := (= f1 #10)
-#43 := (forall (vars (?v0 S1)) #40)
-#58 := (not #43)
-#67 := (or #58 #46 #49)
-#70 := (not #67)
-#16 := (= f5 f1)
-#15 := (= #14 f1)
-#17 := (or #15 #16)
-#11 := (= #10 f1)
-#12 := (forall (vars (?v0 S1)) #11)
-#18 := (implies #12 #17)
-#19 := (not #18)
-#73 := (iff #19 #70)
-#52 := (or #46 #49)
-#59 := (or #58 #52)
-#64 := (not #59)
-#71 := (iff #64 #70)
-#68 := (iff #59 #67)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#65 := (iff #19 #64)
-#62 := (iff #18 #59)
-#55 := (implies #43 #52)
-#60 := (iff #55 #59)
-#61 := [rewrite]: #60
-#56 := (iff #18 #55)
-#53 := (iff #17 #52)
-#50 := (iff #16 #49)
-#51 := [rewrite]: #50
-#47 := (iff #15 #46)
-#48 := [rewrite]: #47
-#54 := [monotonicity #48 #51]: #53
-#44 := (iff #12 #43)
-#41 := (iff #11 #40)
-#42 := [rewrite]: #41
-#45 := [quant-intro #42]: #44
-#57 := [monotonicity #45 #54]: #56
-#63 := [trans #57 #61]: #62
-#66 := [monotonicity #63]: #65
-#74 := [trans #66 #72]: #73
-#39 := [asserted]: #19
-#75 := [mp #39 #74]: #70
-#78 := [not-or-elim #75]: #77
-#562 := (pattern #10)
-#563 := (forall (vars (?v0 S1)) (:pat #562) #40)
-#566 := (iff #43 #563)
-#564 := (iff #40 #40)
-#565 := [refl]: #564
-#567 := [quant-intro #565]: #566
-#92 := (~ #43 #43)
-#90 := (~ #40 #40)
-#91 := [refl]: #90
-#93 := [nnf-pos #91]: #92
-#76 := [not-or-elim #75]: #43
-#82 := [mp~ #76 #93]: #43
-#568 := [mp #82 #567]: #563
-#145 := (not #563)
-#232 := (or #145 #46)
-#146 := [quant-inst #13]: #232
-[unit-resolution #146 #568 #78]: false
-unsat
-58e0c0ea4309865900675d68ad0e58b939e134fe 106 0
-#2 := false
-decl f3 :: (-> S2 S2 S1)
-decl ?v0!0 :: S2
-#77 := ?v0!0
-#86 := (f3 ?v0!0 ?v0!0)
-decl f1 :: S1
-#4 := f1
-#78 := (= f1 #86)
-#79 := (not #78)
-#9 := (:var 0 S2)
-#16 := (f3 #9 #9)
-#53 := (= f1 #16)
-#56 := (forall (vars (?v0 S2)) #53)
-#72 := (not #56)
-#87 := (~ #72 #79)
-#88 := [sk]: #87
-#8 := (:var 1 S2)
-#12 := (f3 #9 #8)
-#44 := (= f1 #12)
-#10 := (f3 #8 #9)
-#41 := (= f1 #10)
-#47 := (and #41 #44)
-#50 := (forall (vars (?v0 S2) (?v1 S2)) #47)
-#62 := (not #50)
-#63 := (or #62 #56)
-#68 := (not #63)
-#17 := (= #16 f1)
-#18 := (forall (vars (?v0 S2)) #17)
-#13 := (= #12 f1)
-#11 := (= #10 f1)
-#14 := (and #11 #13)
-#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
-#19 := (implies #15 #18)
-#20 := (not #19)
-#69 := (iff #20 #68)
-#66 := (iff #19 #63)
-#59 := (implies #50 #56)
-#64 := (iff #59 #63)
-#65 := [rewrite]: #64
-#60 := (iff #19 #59)
-#57 := (iff #18 #56)
-#54 := (iff #17 #53)
-#55 := [rewrite]: #54
-#58 := [quant-intro #55]: #57
-#51 := (iff #15 #50)
-#48 := (iff #14 #47)
-#45 := (iff #13 #44)
-#46 := [rewrite]: #45
-#42 := (iff #11 #41)
-#43 := [rewrite]: #42
-#49 := [monotonicity #43 #46]: #48
-#52 := [quant-intro #49]: #51
-#61 := [monotonicity #52 #58]: #60
-#67 := [trans #61 #65]: #66
-#70 := [monotonicity #67]: #69
-#40 := [asserted]: #20
-#73 := [mp #40 #70]: #68
-#74 := [not-or-elim #73]: #72
-#91 := [mp~ #74 #88]: #79
-#576 := (pattern #12)
-#575 := (pattern #10)
-#90 := (not #44)
-#89 := (not #41)
-#92 := (or #89 #90)
-#93 := (not #92)
-#577 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #575 #576) #93)
-#96 := (forall (vars (?v0 S2) (?v1 S2)) #93)
-#580 := (iff #96 #577)
-#578 := (iff #93 #93)
-#579 := [refl]: #578
-#581 := [quant-intro #579]: #580
-#97 := (iff #50 #96)
-#94 := (iff #47 #93)
-#95 := [rewrite]: #94
-#98 := [quant-intro #95]: #97
-#84 := (~ #50 #50)
-#82 := (~ #47 #47)
-#83 := [refl]: #82
-#85 := [nnf-pos #83]: #84
-#71 := [not-or-elim #73]: #50
-#76 := [mp~ #71 #85]: #50
-#99 := [mp #76 #98]: #96
-#582 := [mp #99 #581]: #577
-#247 := (not #577)
-#251 := (or #247 #78)
-#157 := (or #79 #79)
-#244 := (not #157)
-#230 := (or #247 #244)
-#569 := (iff #230 #251)
-#356 := (iff #251 #251)
-#563 := [rewrite]: #356
-#177 := (iff #244 #78)
-#159 := (not #79)
-#248 := (iff #159 #78)
-#249 := [rewrite]: #248
-#246 := (iff #244 #159)
-#158 := (iff #157 #79)
-#245 := [rewrite]: #158
-#237 := [monotonicity #245]: #246
-#250 := [trans #237 #249]: #177
-#224 := [monotonicity #250]: #569
-#235 := [trans #224 #563]: #569
-#567 := [quant-inst #77 #77]: #230
-#236 := [mp #567 #235]: #251
-[unit-resolution #236 #582 #91]: false
-unsat
-6f5c195ed8186ea009f805e2f8ea8ad3b1ee6432 66 0
-#2 := false
-decl f4 :: S1
-#10 := f4
-decl f1 :: S1
-#4 := f1
-#40 := (= f1 f4)
-decl f3 :: S1
-#8 := f3
-#37 := (= f1 f3)
-#43 := (or #37 #40)
-#87 := (iff #43 false)
-#82 := (or false false)
-#85 := (iff #82 false)
-#86 := [rewrite]: #85
-#83 := (iff #43 #82)
-#78 := (iff #40 false)
-#69 := (not #40)
-#46 := (not #37)
-#52 := (and #46 #43)
-#60 := (not #52)
-#61 := (or #40 #60)
-#66 := (not #61)
-#11 := (= f4 f1)
-#9 := (= f3 f1)
-#13 := (not #9)
-#12 := (or #9 #11)
-#14 := (and #12 #13)
-#15 := (implies #14 #11)
-#16 := (not #15)
-#67 := (iff #16 #66)
-#64 := (iff #15 #61)
-#57 := (implies #52 #40)
-#62 := (iff #57 #61)
-#63 := [rewrite]: #62
-#58 := (iff #15 #57)
-#41 := (iff #11 #40)
-#42 := [rewrite]: #41
-#55 := (iff #14 #52)
-#49 := (and #43 #46)
-#53 := (iff #49 #52)
-#54 := [rewrite]: #53
-#50 := (iff #14 #49)
-#47 := (iff #13 #46)
-#38 := (iff #9 #37)
-#39 := [rewrite]: #38
-#48 := [monotonicity #39]: #47
-#44 := (iff #12 #43)
-#45 := [monotonicity #39 #42]: #44
-#51 := [monotonicity #45 #48]: #50
-#56 := [trans #51 #54]: #55
-#59 := [monotonicity #56 #42]: #58
-#65 := [trans #59 #63]: #64
-#68 := [monotonicity #65]: #67
-#36 := [asserted]: #16
-#71 := [mp #36 #68]: #66
-#70 := [not-or-elim #71]: #69
-#79 := [iff-false #70]: #78
-#80 := (iff #37 false)
-#72 := [not-or-elim #71]: #52
-#73 := [and-elim #72]: #46
-#81 := [iff-false #73]: #80
-#84 := [monotonicity #81 #79]: #83
-#88 := [trans #84 #86]: #87
-#74 := [and-elim #72]: #43
-[mp #74 #88]: false
-unsat
-bc6de36d6c86b416e91711bb23067cc8250ac153 59 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f6 :: S1
-#15 := f6
-#16 := (= f6 f1)
-decl f5 :: S1
-#13 := f5
-#14 := (= f5 f1)
-#17 := (and #14 #16)
-decl f4 :: S1
-#10 := f4
-#11 := (= f4 f1)
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#12 := (and #9 #11)
-#18 := (or #12 #17)
-#19 := (implies #18 #18)
-#20 := (not #19)
-#74 := (iff #20 false)
+#7 := f3
+#12 := (= f3 f5)
+#40 := (not #12)
+#74 := (iff #40 false)
 #1 := true
 #69 := (not true)
 #72 := (iff #69 false)
 #73 := [rewrite]: #72
-#70 := (iff #20 #69)
-#67 := (iff #19 true)
-#53 := (= f1 f6)
-#50 := (= f1 f5)
-#56 := (and #50 #53)
-#44 := (= f1 f4)
-#41 := (= f1 f3)
-#47 := (and #41 #44)
-#59 := (or #47 #56)
-#62 := (implies #59 #59)
-#65 := (iff #62 true)
-#66 := [rewrite]: #65
-#63 := (iff #19 #62)
-#60 := (iff #18 #59)
-#57 := (iff #17 #56)
-#54 := (iff #16 #53)
-#55 := [rewrite]: #54
-#51 := (iff #14 #50)
-#52 := [rewrite]: #51
-#58 := [monotonicity #52 #55]: #57
-#48 := (iff #12 #47)
-#45 := (iff #11 #44)
-#46 := [rewrite]: #45
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#49 := [monotonicity #43 #46]: #48
-#61 := [monotonicity #49 #58]: #60
-#64 := [monotonicity #61 #61]: #63
-#68 := [trans #64 #66]: #67
+#70 := (iff #40 #69)
+#67 := (iff #12 true)
+#64 := (= f5 f5)
+#62 := (iff #64 true)
+#63 := [rewrite]: #62
+#65 := (iff #12 #64)
+decl f4 :: S2
+#8 := f4
+#11 := (= f4 f5)
+#21 := (not #11)
+#9 := (= f3 f4)
+#28 := (not #9)
+#29 := (or #28 #21 #12)
+#34 := (not #29)
+#13 := (implies #11 #12)
+#14 := (implies #9 #13)
+#15 := (not #14)
+#35 := (iff #15 #34)
+#32 := (iff #14 #29)
+#22 := (or #21 #12)
+#25 := (implies #9 #22)
+#30 := (iff #25 #29)
+#31 := [rewrite]: #30
+#26 := (iff #14 #25)
+#23 := (iff #13 #22)
+#24 := [rewrite]: #23
+#27 := [monotonicity #24]: #26
+#33 := [trans #27 #31]: #32
+#36 := [monotonicity #33]: #35
+#17 := [asserted]: #15
+#37 := [mp #17 #36]: #34
+#39 := [not-or-elim #37]: #11
+#38 := [not-or-elim #37]: #9
+#61 := [trans #38 #39]: #12
+#66 := [monotonicity #61]: #65
+#68 := [trans #66 #63]: #67
 #71 := [monotonicity #68]: #70
 #75 := [trans #71 #73]: #74
-#40 := [asserted]: #20
-[mp #40 #75]: false
-unsat
-2d4ae4bcfab81366c725be4feb5f77df1b3a121a 21 0
+#41 := [not-or-elim #37]: #40
+[mp #41 #75]: false
+7b6d64f8e2fad3aa032b79fa9487b8cccfe3a0a4 42 0
+unsat
+#2 := false
+decl f5 :: (-> S2 S3)
+decl f4 :: S2
+#8 := f4
+#11 := (f5 f4)
+decl f3 :: S2
+#7 := f3
+#10 := (f5 f3)
+#12 := (= #10 #11)
+#29 := (not #12)
+#63 := (iff #29 false)
+#1 := true
+#58 := (not true)
+#61 := (iff #58 false)
+#62 := [rewrite]: #61
+#59 := (iff #29 #58)
+#56 := (iff #12 true)
+#51 := (= #11 #11)
+#54 := (iff #51 true)
+#55 := [rewrite]: #54
+#52 := (iff #12 #51)
+#9 := (= f3 f4)
+#20 := (not #9)
+#21 := (or #20 #12)
+#24 := (not #21)
+#13 := (implies #9 #12)
+#14 := (not #13)
+#25 := (iff #14 #24)
+#22 := (iff #13 #21)
+#23 := [rewrite]: #22
+#26 := [monotonicity #23]: #25
+#16 := [asserted]: #14
+#27 := [mp #16 #26]: #24
+#28 := [not-or-elim #27]: #9
+#50 := [monotonicity #28]: #12
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#30 := [not-or-elim #27]: #29
+[mp #30 #64]: false
+f511fb1b0e8a27977d86f256b0e8ec93254257bd 47 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S1 S1)
+decl f5 :: S1
+#12 := f5
+decl f4 :: S2
+#7 := f4
+#13 := (f3 f4 f5)
+#14 := (= #13 f1)
+#33 := (not #14)
+#15 := (= f5 f1)
+#8 := (:var 0 S1)
+#9 := (f3 f4 #8)
+#10 := (= #9 f1)
+#11 := (forall (vars (?v0 S1)) #10)
+#24 := (not #11)
+#25 := (or #24 #14 #15)
+#28 := (not #25)
+#16 := (or #14 #15)
+#17 := (implies #11 #16)
+#18 := (not #17)
+#29 := (iff #18 #28)
+#26 := (iff #17 #25)
+#27 := [rewrite]: #26
+#30 := [monotonicity #27]: #29
+#20 := [asserted]: #18
+#31 := [mp #20 #30]: #28
+#34 := [not-or-elim #31]: #33
+#478 := (pattern #9)
+#479 := (forall (vars (?v0 S1)) (:pat #478) #10)
+#482 := (iff #11 #479)
+#480 := (iff #10 #10)
+#481 := [refl]: #480
+#483 := [quant-intro #481]: #482
+#58 := (~ #11 #11)
+#56 := (~ #10 #10)
+#57 := [refl]: #56
+#59 := [nnf-pos #57]: #58
+#32 := [not-or-elim #31]: #11
+#62 := [mp~ #32 #59]: #11
+#484 := [mp #62 #483]: #479
+#148 := (not #479)
+#149 := (or #148 #14)
+#141 := [quant-inst #12]: #149
+[unit-resolution #141 #484 #34]: false
+c24e42c8de71d8f3805a038868f7d2820e47f725 83 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S2 S1)
+decl ?v0!0 :: S2
+#60 := ?v0!0
+#61 := (f3 ?v0!0 ?v0!0)
+#62 := (= #61 f1)
+#63 := (not #62)
+#8 := (:var 0 S2)
+#15 := (f3 #8 #8)
+#16 := (= #15 f1)
+#17 := (forall (vars (?v0 S2)) #16)
+#34 := (not #17)
+#64 := (~ #34 #63)
+#65 := [sk]: #64
+#7 := (:var 1 S2)
+#11 := (f3 #8 #7)
+#12 := (= #11 f1)
+#9 := (f3 #7 #8)
+#10 := (= #9 f1)
+#13 := (and #10 #12)
+#14 := (forall (vars (?v0 S2) (?v1 S2)) #13)
+#25 := (not #14)
+#26 := (or #25 #17)
+#29 := (not #26)
+#18 := (implies #14 #17)
+#19 := (not #18)
+#30 := (iff #19 #29)
+#27 := (iff #18 #26)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#21 := [asserted]: #19
+#32 := [mp #21 #31]: #29
+#35 := [not-or-elim #32]: #34
+#66 := [mp~ #35 #65]: #63
+#495 := (pattern #11)
+#494 := (pattern #9)
+#68 := (not #12)
+#67 := (not #10)
+#69 := (or #67 #68)
+#70 := (not #69)
+#496 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #494 #495) #70)
+#73 := (forall (vars (?v0 S2) (?v1 S2)) #70)
+#499 := (iff #73 #496)
+#497 := (iff #70 #70)
+#498 := [refl]: #497
+#500 := [quant-intro #498]: #499
+#74 := (iff #14 #73)
+#71 := (iff #13 #70)
+#72 := [rewrite]: #71
+#75 := [quant-intro #72]: #74
+#57 := (~ #14 #14)
+#55 := (~ #13 #13)
+#56 := [refl]: #55
+#58 := [nnf-pos #56]: #57
+#33 := [not-or-elim #32]: #14
+#59 := [mp~ #33 #58]: #14
+#76 := [mp #59 #75]: #73
+#501 := [mp #76 #500]: #496
+#171 := (not #496)
+#150 := (or #171 #62)
+#77 := (or #63 #63)
+#164 := (not #77)
+#486 := (or #171 #164)
+#144 := (iff #486 #150)
+#482 := (iff #150 #150)
+#155 := [rewrite]: #482
+#170 := (iff #164 #62)
+#79 := (not #63)
+#168 := (iff #79 #62)
+#169 := [rewrite]: #168
+#166 := (iff #164 #79)
+#78 := (iff #77 #63)
+#165 := [rewrite]: #78
+#157 := [monotonicity #165]: #166
+#167 := [trans #157 #169]: #170
+#275 := [monotonicity #167]: #144
+#156 := [trans #275 #155]: #144
+#488 := [quant-inst #60 #60]: #486
+#489 := [mp #488 #156]: #150
+[unit-resolution #489 #501 #66]: false
+d4525927e0ca94e2a8cd999f8854bd810a0a45a9 30 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#12 := (not #8)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#11 := (or #8 #10)
+#13 := (and #11 #12)
+#21 := (not #13)
+#22 := (or #21 #10)
+#25 := (not #22)
+#14 := (implies #13 #10)
+#15 := (not #14)
+#26 := (iff #15 #25)
+#23 := (iff #14 #22)
+#24 := [rewrite]: #23
+#27 := [monotonicity #24]: #26
+#17 := [asserted]: #15
+#28 := [mp #17 #27]: #25
+#29 := [not-or-elim #28]: #13
+#31 := [and-elim #29]: #12
+#32 := (not #10)
+#33 := [not-or-elim #28]: #32
+#30 := [and-elim #29]: #11
+[unit-resolution #30 #33 #31]: false
+55b7bd861df00e9621f738450037b0df80372741 84 0
+unsat
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f5 :: S1
+#12 := f5
+#13 := (= f5 f1)
+decl f6 :: S1
+#14 := f6
+#15 := (= f6 f1)
+#64 := (not #15)
+#63 := (not #13)
+#65 := (or #63 #64)
+#66 := (not #65)
+decl f4 :: S1
+#9 := f4
+#10 := (= f4 f1)
+#58 := (not #10)
+decl f3 :: S1
+#7 := f3
+#8 := (= f3 f1)
+#57 := (not #8)
+#59 := (or #57 #58)
+#60 := (not #59)
+#101 := [hypothesis]: #60
+#89 := (or #59 #8)
+#90 := [def-axiom]: #89
+#102 := [unit-resolution #90 #101]: #8
+#91 := (or #59 #10)
+#92 := [def-axiom]: #91
+#103 := [unit-resolution #92 #101]: #10
+#11 := (and #8 #10)
+#34 := (not #11)
+#78 := (iff #34 #59)
+#73 := (not #60)
+#76 := (iff #73 #59)
+#77 := [rewrite]: #76
+#74 := (iff #34 #73)
+#61 := (iff #11 #60)
+#62 := [rewrite]: #61
+#75 := [monotonicity #62]: #74
+#79 := [trans #75 #77]: #78
+#16 := (and #13 #15)
+#17 := (or #11 #16)
+#25 := (not #17)
+#26 := (or #25 #11 #16)
+#29 := (not #26)
+#18 := (implies #17 #17)
+#19 := (not #18)
+#30 := (iff #19 #29)
+#27 := (iff #18 #26)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#21 := [asserted]: #19
+#32 := [mp #21 #31]: #29
+#35 := [not-or-elim #32]: #34
+#80 := [mp #35 #79]: #59
+#104 := [unit-resolution #80 #103 #102]: false
+#105 := [lemma #104]: #59
+#69 := (or #60 #66)
+#70 := (iff #17 #69)
+#67 := (iff #16 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #62 #68]: #70
+#33 := [not-or-elim #32]: #17
+#72 := [mp #33 #71]: #69
+#106 := [unit-resolution #72 #105]: #66
+#95 := (or #65 #13)
+#96 := [def-axiom]: #95
+#107 := [unit-resolution #96 #106]: #13
+#97 := (or #65 #15)
+#98 := [def-axiom]: #97
+#108 := [unit-resolution #98 #106]: #15
+#36 := (not #16)
+#86 := (iff #36 #65)
+#81 := (not #66)
+#84 := (iff #81 #65)
+#85 := [rewrite]: #84
+#82 := (iff #36 #81)
+#83 := [monotonicity #68]: #82
+#87 := [trans #83 #85]: #86
+#37 := [not-or-elim #32]: #36
+#88 := [mp #37 #87]: #65
+[unit-resolution #88 #108 #107]: false
+b837a165a2820c577cec1ceb0af63b70266981a2 21 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int S3)
-#9 := 0::Int
-decl f4 :: S2
-#8 := f4
-#10 := (f3 f4 0::Int)
-#11 := (= #10 #10)
-#12 := (not #11)
-#57 := (iff #12 false)
-#1 := true
-#52 := (not true)
-#55 := (iff #52 false)
-#56 := [rewrite]: #55
-#53 := (iff #12 #52)
-#50 := (iff #11 true)
-#51 := [rewrite]: #50
-#54 := [monotonicity #51]: #53
-#58 := [trans #54 #56]: #57
-#49 := [asserted]: #12
-[mp #49 #58]: false
-unsat
-1237b209e2d4ddd9117dc897ef6936e3505b22b6 21 0
+#8 := 0::Int
+decl f4 :: S2
+#7 := f4
+#9 := (f3 f4 0::Int)
+#10 := (= #9 #9)
+#11 := (not #10)
+#44 := (iff #11 false)
+#1 := true
+#39 := (not true)
+#42 := (iff #39 false)
+#43 := [rewrite]: #42
+#40 := (iff #11 #39)
+#37 := (iff #10 true)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#30 := [asserted]: #11
+[mp #30 #45]: false
+02dc6935c407b4ef97754e97998a7b070a0b59ca 21 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int S3)
+#8 := 1::Int
+decl f4 :: S2
+#7 := f4
+#9 := (f3 f4 1::Int)
+#10 := (= #9 #9)
+#11 := (not #10)
+#45 := (iff #11 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #11 #40)
+#38 := (iff #10 true)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#31 := [asserted]: #11
+[mp #31 #46]: false
+44ca1520d643e1582af61ce0d7aa9f785f2ec009 31 0
+unsat
+#2 := false
+#8 := 1::Int
+#7 := 0::Int
+#9 := (< 0::Int 1::Int)
+#10 := (not #9)
+#36 := (iff #10 false)
+#1 := true
+#31 := (not true)
+#34 := (iff #31 false)
+#35 := [rewrite]: #34
+#32 := (iff #10 #31)
+#29 := (iff #9 true)
+#16 := (<= 1::Int 0::Int)
+#17 := (not #16)
+#27 := (iff #17 true)
+#22 := (not false)
+#25 := (iff #22 true)
+#26 := [rewrite]: #25
+#23 := (iff #17 #22)
+#20 := (iff #16 false)
+#21 := [rewrite]: #20
+#24 := [monotonicity #21]: #23
+#28 := [trans #24 #26]: #27
+#18 := (iff #9 #17)
+#19 := [rewrite]: #18
+#30 := [trans #19 #28]: #29
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#12 := [asserted]: #10
+[mp #12 #37]: false
+805b06e44b11919f00a075b70915715352398ed7 18 0
+unsat
+#2 := false
+#8 := 1::Int
+#7 := 0::Int
+#9 := (<= 0::Int 1::Int)
+#10 := (not #9)
+#23 := (iff #10 false)
+#1 := true
+#18 := (not true)
+#21 := (iff #18 false)
+#22 := [rewrite]: #21
+#19 := (iff #10 #18)
+#16 := (iff #9 true)
+#17 := [rewrite]: #16
+#20 := [monotonicity #17]: #19
+#24 := [trans #20 #22]: #23
+#12 := [asserted]: #10
+[mp #12 #24]: false
+cb23173094fd6f97948421b52674d05e743e64af 31 0
+unsat
+#2 := false
+#8 := 2345678901::Int
+#7 := 123456789::Int
+#9 := (< 123456789::Int 2345678901::Int)
+#10 := (not #9)
+#37 := (iff #10 false)
+#1 := true
+#32 := (not true)
+#35 := (iff #32 false)
+#36 := [rewrite]: #35
+#33 := (iff #10 #32)
+#30 := (iff #9 true)
+#16 := (<= 2345678901::Int 123456789::Int)
+#17 := (not #16)
+#28 := (iff #17 true)
+#23 := (not false)
+#26 := (iff #23 true)
+#27 := [rewrite]: #26
+#24 := (iff #17 #23)
+#20 := (iff #16 false)
+#22 := [rewrite]: #20
+#25 := [monotonicity #22]: #24
+#29 := [trans #25 #27]: #28
+#18 := (iff #9 #17)
+#19 := [rewrite]: #18
+#31 := [trans #19 #29]: #30
+#34 := [monotonicity #31]: #33
+#38 := [trans #34 #36]: #37
+#12 := [asserted]: #10
+[mp #12 #38]: false
+57796d4943fee61a1421439bead7ffbccb1f7332 32 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int S3)
 #9 := 1::Int
 decl f4 :: S2
-#8 := f4
-#10 := (f3 f4 1::Int)
-#11 := (= #10 #10)
-#12 := (not #11)
-#58 := (iff #12 false)
-#1 := true
-#53 := (not true)
-#56 := (iff #53 false)
-#57 := [rewrite]: #56
-#54 := (iff #12 #53)
-#51 := (iff #11 true)
-#52 := [rewrite]: #51
-#55 := [monotonicity #52]: #54
-#59 := [trans #55 #57]: #58
-#50 := [asserted]: #12
-[mp #50 #59]: false
-unsat
-fb370925ef9917dad66e0244200f67eedf11b6cf 18 0
-#2 := false
-#9 := 1::Int
+#7 := f4
+#12 := (f3 f4 1::Int)
 #8 := 0::Int
-#10 := (< 0::Int 1::Int)
-#11 := (not #10)
-#41 := (iff #11 false)
-#1 := true
-#36 := (not true)
-#39 := (iff #36 false)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (iff #10 true)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#31 := [asserted]: #11
-[mp #31 #42]: false
-unsat
-3e975ce36aa1bd6d92c534a802e4e9206e497829 18 0
-#2 := false
-#9 := 1::Int
-#8 := 0::Int
-#10 := (<= 0::Int 1::Int)
-#11 := (not #10)
-#41 := (iff #11 false)
-#1 := true
-#36 := (not true)
-#39 := (iff #36 false)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (iff #10 true)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#31 := [asserted]: #11
-[mp #31 #42]: false
-unsat
-a8dfb9a9f38e5293ee803fd471ebee346a686963 18 0
-#2 := false
-#9 := 2345678901::Int
-#8 := 123456789::Int
-#10 := (< 123456789::Int 2345678901::Int)
-#11 := (not #10)
-#41 := (iff #11 false)
-#1 := true
-#36 := (not true)
-#39 := (iff #36 false)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (iff #10 true)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#31 := [asserted]: #11
-[mp #31 #42]: false
-unsat
-aff64a9b452534297441f7fa34b8b94b4f3e56c4 32 0
+#10 := (+ 0::Int 1::Int)
+#11 := (f3 f4 #10)
+#13 := (= #11 #12)
+#14 := (not #13)
+#55 := (iff #14 false)
+#1 := true
+#50 := (not true)
+#53 := (iff #50 false)
+#54 := [rewrite]: #53
+#51 := (iff #14 #50)
+#48 := (iff #13 true)
+#43 := (= #12 #12)
+#46 := (iff #43 true)
+#47 := [rewrite]: #46
+#44 := (iff #13 #43)
+#40 := (= #10 1::Int)
+#41 := [rewrite]: #40
+#42 := [monotonicity #41]: #13
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#52 := [monotonicity #49]: #51
+#56 := [trans #52 #54]: #55
+#33 := [asserted]: #14
+[mp #33 #56]: false
+94bb208fb4bd74ca4a0d2702fe8efdee4ab2e9da 39 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int S3)
+#11 := 1::Int
+decl f5 :: (-> S4 S3 Int)
+decl f7 :: S3
+#9 := f7
+decl f6 :: S4
+#8 := f6
+#10 := (f5 f6 f7)
+#12 := (+ #10 1::Int)
+decl f4 :: S2
+#7 := f4
+#13 := (f3 f4 #12)
+#14 := (= #13 #13)
+#15 := (not #14)
+#59 := (iff #15 false)
+#1 := true
+#54 := (not true)
+#57 := (iff #54 false)
+#58 := [rewrite]: #57
+#55 := (iff #15 #54)
+#52 := (iff #14 true)
+#41 := (+ 1::Int #10)
+#44 := (f3 f4 #41)
+#47 := (= #44 #44)
+#50 := (iff #47 true)
+#51 := [rewrite]: #50
+#48 := (iff #14 #47)
+#45 := (= #13 #44)
+#42 := (= #12 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#49 := [monotonicity #46 #46]: #48
+#53 := [trans #49 #51]: #52
+#56 := [monotonicity #53]: #55
+#60 := [trans #56 #58]: #59
+#34 := [asserted]: #15
+[mp #34 #60]: false
+c089e88f20d062979d8a0b72e27bcc2d6ec57d80 45 0
+unsat
+#2 := false
 #10 := 1::Int
-decl f4 :: S2
-#8 := f4
-#13 := (f3 f4 1::Int)
-#9 := 0::Int
-#11 := (+ 0::Int 1::Int)
-#12 := (f3 f4 #11)
-#14 := (= #12 #13)
-#15 := (not #14)
-#68 := (iff #15 false)
+decl f3 :: (-> S2 S3 Int)
+decl f5 :: S3
+#8 := f5
+decl f4 :: S2
+#7 := f4
+#9 := (f3 f4 f5)
+#11 := (+ #9 1::Int)
+#12 := (< #9 #11)
+#13 := (not #12)
+#68 := (iff #13 false)
 #1 := true
 #63 := (not true)
 #66 := (iff #63 false)
 #67 := [rewrite]: #66
-#64 := (iff #15 #63)
-#61 := (iff #14 true)
-#56 := (= #13 #13)
-#59 := (iff #56 true)
-#60 := [rewrite]: #59
-#57 := (iff #14 #56)
-#53 := (= #11 1::Int)
-#54 := [rewrite]: #53
-#55 := [monotonicity #54]: #14
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
+#64 := (iff #13 #63)
+#61 := (iff #12 true)
+#40 := (+ 1::Int #9)
+#46 := (<= #40 #9)
+#47 := (not #46)
+#59 := (iff #47 true)
+#54 := (not false)
+#57 := (iff #54 true)
+#58 := [rewrite]: #57
+#55 := (iff #47 #54)
+#52 := (iff #46 false)
+#53 := [rewrite]: #52
+#56 := [monotonicity #53]: #55
+#60 := [trans #56 #58]: #59
+#50 := (iff #12 #47)
+#43 := (< #9 #40)
+#48 := (iff #43 #47)
+#49 := [rewrite]: #48
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#42 := [rewrite]: #41
+#45 := [monotonicity #42]: #44
+#51 := [trans #45 #49]: #50
+#62 := [trans #51 #60]: #61
 #65 := [monotonicity #62]: #64
 #69 := [trans #65 #67]: #68
-#52 := [asserted]: #15
-[mp #52 #69]: false
-unsat
-188a62b171c1839a04b3ae9512b9928709991d32 39 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#12 := 1::Int
-decl f5 :: (-> S4 S3 Int)
-decl f7 :: S3
-#10 := f7
-decl f6 :: S4
-#9 := f6
-#11 := (f5 f6 f7)
-#13 := (+ #11 1::Int)
-decl f4 :: S2
-#8 := f4
-#14 := (f3 f4 #13)
-#15 := (= #14 #14)
-#16 := (not #15)
-#72 := (iff #16 false)
-#1 := true
-#67 := (not true)
-#70 := (iff #67 false)
-#71 := [rewrite]: #70
-#68 := (iff #16 #67)
-#65 := (iff #15 true)
-#54 := (+ 1::Int #11)
-#57 := (f3 f4 #54)
-#60 := (= #57 #57)
-#63 := (iff #60 true)
-#64 := [rewrite]: #63
-#61 := (iff #15 #60)
-#58 := (= #14 #57)
-#55 := (= #13 #54)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#62 := [monotonicity #59 #59]: #61
-#66 := [trans #62 #64]: #65
-#69 := [monotonicity #66]: #68
-#73 := [trans #69 #71]: #72
-#53 := [asserted]: #16
-[mp #53 #73]: false
-unsat
-4bb4300ae1fd273267e574c22bf6d893fc16ad07 35 0
-#2 := false
-#11 := 1::Int
-decl f3 :: (-> S2 S3 Int)
-decl f5 :: S3
-#9 := f5
-decl f4 :: S2
-#8 := f4
-#10 := (f3 f4 f5)
-#12 := (+ #10 1::Int)
-#13 := (< #10 #12)
-#14 := (not #13)
-#71 := (iff #14 false)
-#53 := (+ 1::Int #10)
-#56 := (< #10 #53)
-#59 := (not #56)
-#69 := (iff #59 false)
-#1 := true
-#64 := (not true)
-#67 := (iff #64 false)
-#68 := [rewrite]: #67
-#65 := (iff #59 #64)
-#62 := (iff #56 true)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#70 := [trans #66 #68]: #69
-#60 := (iff #14 #59)
-#57 := (iff #13 #56)
-#54 := (= #12 #53)
-#55 := [rewrite]: #54
-#58 := [monotonicity #55]: #57
-#61 := [monotonicity #58]: #60
-#72 := [trans #61 #70]: #71
-#52 := [asserted]: #14
-[mp #52 #72]: false
-unsat
-093b78ef584eedb2da5a266465d4fa39b0cfdf4f 491 0
+#33 := [asserted]: #13
+[mp #33 #69]: false
+ff72406b31ddd8b52ba835673c07232596ff0a01 438 0
+unsat
 #2 := false
 decl f5 :: (-> S4 S3 Int)
 decl f8 :: S3
-#15 := f8
+#14 := f8
+decl f6 :: S4
+#8 := f6
+#15 := (f5 f6 f8)
+#11 := 1::Int
+#53 := (+ 1::Int #15)
+decl f7 :: S3
+#9 := f7
+#10 := (f5 f6 f7)
+#47 := (+ 1::Int #10)
+#342 := (= #47 #53)
+#309 := (not #342)
+decl f3 :: (-> S2 Int S3)
+decl f4 :: S2
+#7 := f4
+#56 := (f3 f4 #53)
+#50 := (f3 f4 #47)
+#59 := (= #50 #56)
+#571 := (f5 f6 #50)
+#388 := (f3 f4 #571)
+#326 := (= #388 #56)
+#320 := (= #56 #388)
+#316 := (= #53 #571)
+#333 := (= #47 #571)
+#250 := -1::Int
+#210 := (* -1::Int #571)
+#211 := (+ #10 #210)
+#560 := (<= #211 -1::Int)
+#548 := (= #211 -1::Int)
+#562 := (>= #10 -1::Int)
+#27 := 0::Int
+#409 := (>= #10 0::Int)
+#387 := (= #10 0::Int)
+#229 := (f3 f4 #10)
+#402 := (f5 f6 #229)
+#410 := (= #402 0::Int)
+#373 := (not #409)
+#389 := [hypothesis]: #373
+#411 := (or #409 #410)
+#28 := (:var 0 Int)
+#30 := (f3 f4 #28)
+#580 := (pattern #30)
+#31 := (f5 f6 #30)
+#36 := (= #31 0::Int)
+#127 := (>= #28 0::Int)
+#138 := (or #127 #36)
+#587 := (forall (vars (?v0 Int)) (:pat #580) #138)
+#141 := (forall (vars (?v0 Int)) #138)
+#590 := (iff #141 #587)
+#588 := (iff #138 #138)
+#589 := [refl]: #588
+#591 := [quant-intro #589]: #590
+#155 := (~ #141 #141)
+#153 := (~ #138 #138)
+#154 := [refl]: #153
+#156 := [nnf-pos #154]: #155
+#29 := (<= 0::Int #28)
+#96 := (or #29 #36)
+#101 := (forall (vars (?v0 Int)) #96)
+#142 := (iff #101 #141)
+#139 := (iff #96 #138)
+#125 := (iff #29 #127)
+#126 := [rewrite]: #125
+#140 := [monotonicity #126]: #139
+#143 := [quant-intro #140]: #142
+#35 := (< #28 0::Int)
+#37 := (implies #35 #36)
+#38 := (forall (vars (?v0 Int)) #37)
+#102 := (iff #38 #101)
+#99 := (iff #37 #96)
+#79 := (not #29)
+#93 := (implies #79 #36)
+#97 := (iff #93 #96)
+#98 := [rewrite]: #97
+#94 := (iff #37 #93)
+#88 := (iff #35 #79)
+#90 := (iff #79 #79)
+#75 := (iff #29 #29)
+#76 := [rewrite]: #75
+#91 := [monotonicity #76]: #90
+#89 := [rewrite]: #88
+#92 := [trans #89 #91]: #88
+#95 := [monotonicity #92]: #94
+#100 := [trans #95 #98]: #99
+#103 := [quant-intro #100]: #102
+#43 := [asserted]: #38
+#104 := [mp #43 #103]: #101
+#144 := [mp #104 #143]: #141
+#157 := [mp~ #144 #156]: #141
+#592 := [mp #157 #591]: #587
+#272 := (not #587)
+#414 := (or #272 #409 #410)
+#507 := (or #272 #411)
+#508 := (iff #507 #414)
+#495 := [rewrite]: #508
+#504 := [quant-inst #10]: #507
+#497 := [mp #504 #495]: #414
+#350 := [unit-resolution #497 #592]: #411
+#351 := [unit-resolution #350 #389]: #410
+#358 := (= #10 #402)
+#416 := (= f7 #229)
+#565 := (= #229 f7)
+#22 := (:var 0 S3)
+#23 := (f5 f6 #22)
+#573 := (pattern #23)
+#24 := (f3 f4 #23)
+#25 := (= #24 #22)
+#574 := (forall (vars (?v0 S3)) (:pat #573) #25)
+#26 := (forall (vars (?v0 S3)) #25)
+#577 := (iff #26 #574)
+#575 := (iff #25 #25)
+#576 := [refl]: #575
+#578 := [quant-intro #576]: #577
+#147 := (~ #26 #26)
+#151 := (~ #25 #25)
+#152 := [refl]: #151
+#148 := [nnf-pos #152]: #147
+#41 := [asserted]: #26
+#149 := [mp~ #41 #148]: #26
+#579 := [mp #149 #578]: #574
+#354 := (not #574)
+#561 := (or #354 #565)
+#234 := [quant-inst #9]: #561
+#395 := [unit-resolution #234 #579]: #565
+#371 := [symm #395]: #416
+#360 := [monotonicity #371]: #358
+#361 := [trans #360 #351]: #387
+#362 := (not #387)
+#364 := (or #362 #409)
+#365 := [th-lemma arith triangle-eq]: #364
+#366 := [unit-resolution #365 #389 #361]: false
+#367 := [lemma #366]: #409
+#338 := (or #373 #562)
+#336 := [th-lemma arith farkas 1 1]: #338
+#339 := [unit-resolution #336 #367]: #562
+#563 := (not #562)
+#213 := (or #563 #548)
+#32 := (= #31 #28)
+#128 := (not #127)
+#131 := (or #128 #32)
+#581 := (forall (vars (?v0 Int)) (:pat #580) #131)
+#134 := (forall (vars (?v0 Int)) #131)
+#584 := (iff #134 #581)
+#582 := (iff #131 #131)
+#583 := [refl]: #582
+#585 := [quant-intro #583]: #584
+#124 := (~ #134 #134)
+#150 := (~ #131 #131)
+#123 := [refl]: #150
+#145 := [nnf-pos #123]: #124
+#80 := (or #79 #32)
+#84 := (forall (vars (?v0 Int)) #80)
+#135 := (iff #84 #134)
+#132 := (iff #80 #131)
+#129 := (iff #79 #128)
+#130 := [monotonicity #126]: #129
+#133 := [monotonicity #130]: #132
+#136 := [quant-intro #133]: #135
+#33 := (implies #29 #32)
+#34 := (forall (vars (?v0 Int)) #33)
+#85 := (iff #34 #84)
+#81 := (iff #33 #80)
+#82 := [rewrite]: #81
+#77 := (iff #33 #33)
+#78 := [monotonicity #76]: #77
+#83 := [trans #78 #82]: #81
+#86 := [quant-intro #83]: #85
+#42 := [asserted]: #34
+#87 := [mp #42 #86]: #84
+#137 := [mp #87 #136]: #134
+#146 := [mp~ #137 #145]: #134
+#586 := [mp #146 #585]: #581
+#552 := (not #581)
+#553 := (or #552 #563 #548)
+#566 := (= #571 #47)
+#235 := (>= #47 0::Int)
+#568 := (not #235)
+#572 := (or #568 #566)
+#554 := (or #552 #572)
+#198 := (iff #554 #553)
+#555 := (or #552 #213)
+#558 := (iff #555 #553)
+#197 := [rewrite]: #558
+#192 := (iff #554 #555)
+#550 := (iff #572 #213)
+#206 := (iff #566 #548)
+#212 := [rewrite]: #206
+#222 := (iff #568 #563)
+#221 := (iff #235 #562)
+#226 := [rewrite]: #221
+#564 := [monotonicity #226]: #222
+#551 := [monotonicity #564 #212]: #550
+#556 := [monotonicity #551]: #192
+#559 := [trans #556 #197]: #198
+#549 := [quant-inst #47]: #554
+#557 := [mp #549 #559]: #553
+#393 := [unit-resolution #557 #586]: #213
+#327 := [unit-resolution #393 #339]: #548
+#359 := (not #548)
+#390 := (or #359 #560)
+#392 := [th-lemma arith triangle-eq]: #390
+#330 := [unit-resolution #392 #327]: #560
+#546 := (>= #211 -1::Int)
+#401 := (or #359 #546)
+#403 := [th-lemma arith triangle-eq]: #401
+#332 := [unit-resolution #403 #327]: #546
+#329 := [th-lemma arith eq-propagate -1 -1 #332 #330]: #333
+#324 := (= #53 #47)
+#334 := [hypothesis]: #342
+#314 := [symm #334]: #324
+#317 := [trans #314 #329]: #316
+#321 := [monotonicity #317]: #320
+#319 := [symm #321]: #326
+#325 := (= #50 #388)
+#368 := (= #388 #50)
+#370 := (or #354 #368)
+#340 := [quant-inst #50]: #370
+#337 := [unit-resolution #340 #579]: #368
+#318 := [symm #337]: #325
+#322 := [trans #318 #319]: #59
+#68 := (not #59)
+#19 := (= f7 f8)
+#567 := (f3 f4 #15)
+#223 := (= #567 f8)
+#569 := (or #354 #223)
+#570 := [quant-inst #14]: #569
+#458 := [unit-resolution #570 #579]: #223
+#378 := (= f7 #567)
+#372 := (= #229 #567)
+#405 := (= #10 #15)
+#251 := (f5 f6 #56)
+#532 := (* -1::Int #251)
+#527 := (+ #15 #532)
+#355 := (<= #527 -1::Int)
+#531 := (= #527 -1::Int)
+#535 := (>= #15 -1::Int)
+#412 := (>= #15 0::Int)
+#488 := (= #15 0::Int)
+#413 := (f5 f6 #567)
+#489 := (= #413 0::Int)
+#492 := (not #412)
+#493 := [hypothesis]: #492
+#486 := (or #412 #489)
+#499 := (or #272 #412 #489)
+#500 := (or #272 #486)
+#501 := (iff #500 #499)
+#490 := [rewrite]: #501
+#496 := [quant-inst #15]: #500
+#491 := [mp #496 #490]: #499
+#477 := [unit-resolution #491 #592]: #486
+#457 := [unit-resolution #477 #493]: #489
+#462 := (= #15 #413)
+#460 := (= f8 #567)
+#461 := [symm #458]: #460
+#463 := [monotonicity #461]: #462
+#464 := [trans #463 #457]: #488
+#465 := (not #488)
+#466 := (or #465 #412)
+#467 := [th-lemma arith triangle-eq]: #466
+#468 := [unit-resolution #467 #493 #464]: false
+#469 := [lemma #468]: #412
+#455 := (or #492 #535)
+#450 := [th-lemma arith farkas 1 1]: #455
+#456 := [unit-resolution #450 #469]: #535
+#529 := (not #535)
+#374 := (or #529 #531)
+#518 := (or #552 #529 #531)
+#534 := (= #251 #53)
+#536 := (>= #53 0::Int)
+#537 := (not #536)
+#538 := (or #537 #534)
+#519 := (or #552 #538)
+#517 := (iff #519 #518)
+#521 := (or #552 #374)
+#522 := (iff #521 #518)
+#523 := [rewrite]: #522
+#515 := (iff #519 #521)
+#375 := (iff #538 #374)
+#526 := (iff #534 #531)
+#533 := [rewrite]: #526
+#530 := (iff #537 #529)
+#539 := (iff #536 #535)
+#528 := [rewrite]: #539
+#525 := [monotonicity #528]: #530
+#376 := [monotonicity #525 #533]: #375
+#516 := [monotonicity #376]: #515
+#524 := [trans #516 #523]: #517
+#520 := [quant-inst #53]: #519
+#353 := [mp #520 #524]: #518
+#480 := [unit-resolution #353 #586]: #374
+#442 := [unit-resolution #480 #456]: #531
+#471 := (not #531)
+#472 := (or #471 #355)
+#474 := [th-lemma arith triangle-eq]: #472
+#438 := [unit-resolution #474 #442]: #355
+#356 := (>= #527 -1::Int)
+#439 := (or #471 #356)
+#440 := [th-lemma arith triangle-eq]: #439
+#443 := [unit-resolution #440 #442]: #356
+#448 := (+ #251 #210)
+#452 := (<= #448 0::Int)
+#470 := (= #251 #571)
+#445 := (= #571 #251)
+#158 := (not #19)
+#454 := [hypothesis]: #158
+#249 := (or #59 #19)
+#69 := (iff #68 #19)
+#16 := (+ #15 1::Int)
+#17 := (f3 f4 #16)
+#12 := (+ #10 1::Int)
+#13 := (f3 f4 #12)
+#18 := (= #13 #17)
+#20 := (iff #18 #19)
+#21 := (not #20)
+#72 := (iff #21 #69)
+#62 := (iff #59 #19)
+#65 := (not #62)
+#70 := (iff #65 #69)
+#71 := [rewrite]: #70
+#66 := (iff #21 #65)
+#63 := (iff #20 #62)
+#60 := (iff #18 #59)
+#57 := (= #17 #56)
+#54 := (= #16 #53)
+#55 := [rewrite]: #54
+#58 := [monotonicity #55]: #57
+#51 := (= #13 #50)
+#48 := (= #12 #47)
+#49 := [rewrite]: #48
+#52 := [monotonicity #49]: #51
+#61 := [monotonicity #52 #58]: #60
+#64 := [monotonicity #61]: #63
+#67 := [monotonicity #64]: #66
+#73 := [trans #67 #71]: #72
+#40 := [asserted]: #21
+#74 := [mp #40 #73]: #69
+#243 := (not #69)
+#247 := (or #59 #19 #243)
+#248 := [def-axiom]: #247
+#246 := [unit-resolution #248 #74]: #249
+#444 := [unit-resolution #246 #454]: #59
+#446 := [monotonicity #444]: #445
+#441 := [symm #446]: #470
+#447 := (not #470)
+#420 := (or #447 #452)
+#421 := [th-lemma arith triangle-eq]: #420
+#422 := [unit-resolution #421 #441]: #452
+#453 := (>= #448 0::Int)
+#315 := (or #447 #453)
+#426 := [th-lemma arith triangle-eq]: #315
+#427 := [unit-resolution #426 #441]: #453
+#547 := (= #571 0::Int)
+#418 := (not #547)
+#509 := (= #251 0::Int)
+#478 := (not #509)
+#399 := (iff #478 #418)
+#417 := (iff #509 #547)
+#432 := (iff #547 #509)
+#437 := [monotonicity #446]: #432
+#363 := [symm #437]: #417
+#423 := [monotonicity #363]: #399
+#406 := (<= #251 0::Int)
+#428 := (not #406)
+#433 := (not #355)
+#429 := (or #428 #492 #433)
+#430 := [th-lemma arith assign-bounds -1 1]: #429
+#431 := [unit-resolution #430 #438 #469]: #428
+#434 := (or #478 #406)
+#435 := [th-lemma arith triangle-eq]: #434
+#436 := [unit-resolution #435 #431]: #478
+#424 := [mp #436 #423]: #418
+#269 := (or #562 #547)
+#165 := (or #272 #562 #547)
+#254 := (or #235 #547)
+#542 := (or #272 #254)
+#545 := (iff #542 #165)
+#265 := (or #272 #269)
+#544 := (iff #265 #165)
+#541 := [rewrite]: #544
+#266 := (iff #542 #265)
+#270 := (iff #254 #269)
+#271 := [monotonicity #226]: #270
+#540 := [monotonicity #271]: #266
+#255 := [trans #540 #541]: #545
+#543 := [quant-inst #47]: #542
+#256 := [mp #543 #255]: #165
+#419 := [unit-resolution #256 #592]: #269
+#425 := [unit-resolution #419 #424]: #562
+#400 := [unit-resolution #393 #425]: #548
+#394 := [unit-resolution #392 #400]: #560
+#404 := [unit-resolution #403 #400]: #546
+#415 := [th-lemma arith eq-propagate -1 -1 1 1 1 1 #404 #394 #427 #422 #443 #438]: #405
+#377 := [monotonicity #415]: #372
+#379 := [trans #371 #377]: #378
+#380 := [trans #379 #458]: #19
+#381 := [unit-resolution #454 #380]: false
+#382 := [lemma #381]: #19
+#245 := (or #68 #158)
+#159 := (or #68 #158 #243)
+#244 := [def-axiom]: #159
+#236 := [unit-resolution #244 #74]: #245
+#335 := [unit-resolution #236 #382]: #68
+#323 := [unit-resolution #335 #322]: false
+#311 := [lemma #323]: #309
+#343 := (* -1::Int #53)
+#349 := (+ #47 #343)
+#328 := (<= #349 0::Int)
+#383 := (* -1::Int #15)
+#384 := (+ #10 #383)
+#385 := (<= #384 0::Int)
+#312 := [monotonicity #382]: #405
+#310 := (not #405)
+#313 := (or #310 #385)
+#295 := [th-lemma arith triangle-eq]: #313
+#297 := [unit-resolution #295 #312]: #385
+#298 := (not #385)
+#299 := (or #328 #298)
+#300 := [th-lemma arith assign-bounds -1]: #299
+#301 := [unit-resolution #300 #297]: #328
+#331 := (>= #349 0::Int)
+#386 := (>= #384 0::Int)
+#302 := (or #310 #386)
+#303 := [th-lemma arith triangle-eq]: #302
+#304 := [unit-resolution #303 #312]: #386
+#305 := (not #386)
+#306 := (or #331 #305)
+#307 := [th-lemma arith assign-bounds -1]: #306
+#296 := [unit-resolution #307 #304]: #331
+#285 := (not #331)
+#308 := (not #328)
+#287 := (or #342 #308 #285)
+#288 := [th-lemma arith triangle-eq]: #287
+#289 := [unit-resolution #288 #296 #301]: #342
+[unit-resolution #289 #311]: false
+cca0c63f74b94d280921e8468e9a688b21297a96 67 0
+unsat
+#2 := false
+#13 := 1::Int
+decl f3 :: (-> S2 S3 Int)
+decl f6 :: S3
+#10 := f6
+decl f4 :: S2
+#7 := f4
+#11 := (f3 f4 f6)
+#16 := (+ #11 1::Int)
+decl f5 :: S3
+#8 := f5
+#9 := (f3 f4 f5)
+#15 := (+ #9 1::Int)
+#17 := (+ #15 #16)
+#12 := (+ #9 #11)
+#14 := (+ #12 1::Int)
+#18 := (< #14 #17)
+#19 := (not #18)
+#89 := (iff #19 false)
+#1 := true
+#84 := (not true)
+#87 := (iff #84 false)
+#88 := [rewrite]: #87
+#85 := (iff #19 #84)
+#82 := (iff #18 true)
+#46 := (+ 1::Int #9 #11)
+#58 := 2::Int
+#59 := (+ 2::Int #9 #11)
+#67 := (<= #59 #46)
+#68 := (not #67)
+#80 := (iff #68 true)
+#75 := (not false)
+#78 := (iff #75 true)
+#79 := [rewrite]: #78
+#76 := (iff #68 #75)
+#73 := (iff #67 false)
+#74 := [rewrite]: #73
+#77 := [monotonicity #74]: #76
+#81 := [trans #77 #79]: #80
+#71 := (iff #18 #68)
+#64 := (< #46 #59)
+#69 := (iff #64 #68)
+#70 := [rewrite]: #69
+#65 := (iff #18 #64)
+#62 := (= #17 #59)
+#52 := (+ 1::Int #11)
+#49 := (+ 1::Int #9)
+#55 := (+ #49 #52)
+#60 := (= #55 #59)
+#61 := [rewrite]: #60
+#56 := (= #17 #55)
+#53 := (= #16 #52)
+#54 := [rewrite]: #53
+#50 := (= #15 #49)
+#51 := [rewrite]: #50
+#57 := [monotonicity #51 #54]: #56
+#63 := [trans #57 #61]: #62
+#47 := (= #14 #46)
+#48 := [rewrite]: #47
+#66 := [monotonicity #48 #63]: #65
+#72 := [trans #66 #70]: #71
+#83 := [trans #72 #81]: #82
+#86 := [monotonicity #83]: #85
+#90 := [trans #86 #88]: #89
+#39 := [asserted]: #19
+[mp #39 #90]: false
+4be683229ab203b6ad6e1365fb0baa3afc13e7f9 51 0
+unsat
+#2 := false
+decl f5 :: (-> S4 S3 Int)
+#16 := (:var 0 S3)
+decl f6 :: S4
+#8 := f6
+#17 := (f5 f6 #16)
+#551 := (pattern #17)
+decl f3 :: (-> S2 Int S3)
+decl f4 :: S2
+#7 := f4
+#18 := (f3 f4 #17)
+#19 := (= #18 #16)
+#552 := (forall (vars (?v0 S3)) (:pat #551) #19)
+#20 := (forall (vars (?v0 S3)) #19)
+#555 := (iff #20 #552)
+#553 := (iff #19 #19)
+#554 := [refl]: #553
+#556 := [quant-intro #554]: #555
+#124 := (~ #20 #20)
+#128 := (~ #19 #19)
+#129 := [refl]: #128
+#125 := [nnf-pos #129]: #124
+#34 := [asserted]: #20
+#126 := [mp~ #34 #125]: #20
+#557 := [mp #126 #556]: #552
+decl f7 :: S3
+#9 := f7
+#10 := (f5 f6 f7)
+#42 := (f3 f4 #10)
+#45 := (= #42 f7)
+#48 := (not #45)
+#11 := 0::Int
+#12 := (+ #10 0::Int)
+#13 := (f3 f4 #12)
+#14 := (= #13 f7)
+#15 := (not #14)
+#49 := (iff #15 #48)
+#46 := (iff #14 #45)
+#43 := (= #13 #42)
+#40 := (= #12 #10)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#47 := [monotonicity #44]: #46
+#50 := [monotonicity #47]: #49
+#33 := [asserted]: #15
+#51 := [mp #33 #50]: #48
+#222 := (not #552)
+#223 := (or #222 #45)
+#214 := [quant-inst #9]: #223
+[unit-resolution #214 #51 #557]: false
+36b449ec06f74f034486ed7a3a374426eb6148a7 51 0
+unsat
+#2 := false
+decl f5 :: (-> S4 S3 Int)
+#16 := (:var 0 S3)
 decl f6 :: S4
 #9 := f6
-#16 := (f5 f6 f8)
-#12 := 1::Int
-#66 := (+ 1::Int #16)
+#17 := (f5 f6 #16)
+#551 := (pattern #17)
+decl f3 :: (-> S2 Int S3)
+decl f4 :: S2
+#7 := f4
+#18 := (f3 f4 #17)
+#19 := (= #18 #16)
+#552 := (forall (vars (?v0 S3)) (:pat #551) #19)
+#20 := (forall (vars (?v0 S3)) #19)
+#555 := (iff #20 #552)
+#553 := (iff #19 #19)
+#554 := [refl]: #553
+#556 := [quant-intro #554]: #555
+#124 := (~ #20 #20)
+#128 := (~ #19 #19)
+#129 := [refl]: #128
+#125 := [nnf-pos #129]: #124
+#34 := [asserted]: #20
+#126 := [mp~ #34 #125]: #20
+#557 := [mp #126 #556]: #552
 decl f7 :: S3
 #10 := f7
 #11 := (f5 f6 f7)
-#60 := (+ 1::Int #11)
-#416 := (= #60 #66)
-#384 := (not #416)
+#42 := (f3 f4 #11)
+#45 := (= #42 f7)
+#48 := (not #45)
+#8 := 0::Int
+#12 := (+ 0::Int #11)
+#13 := (f3 f4 #12)
+#14 := (= #13 f7)
+#15 := (not #14)
+#49 := (iff #15 #48)
+#46 := (iff #14 #45)
+#43 := (= #13 #42)
+#40 := (= #12 #11)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#47 := [monotonicity #44]: #46
+#50 := [monotonicity #47]: #49
+#33 := [asserted]: #15
+#51 := [mp #33 #50]: #48
+#222 := (not #552)
+#223 := (or #222 #45)
+#214 := [quant-inst #10]: #223
+[unit-resolution #214 #51 #557]: false
+6876f4e575b0c8bc3fe85299f4bf8864b5f3e6ce 41 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int S3)
+decl f5 :: (-> S4 S3 Int)
+decl f7 :: S3
+#9 := f7
+decl f6 :: S4
+#8 := f6
+#10 := (f5 f6 f7)
+decl f8 :: S3
+#11 := f8
+#12 := (f5 f6 f8)
+#15 := (+ #12 #10)
+decl f4 :: S2
+#7 := f4
+#16 := (f3 f4 #15)
+#13 := (+ #10 #12)
+#14 := (f3 f4 #13)
+#17 := (= #14 #16)
+#18 := (not #17)
+#108 := (iff #18 false)
+#1 := true
+#103 := (not true)
+#106 := (iff #103 false)
+#107 := [rewrite]: #106
+#104 := (iff #18 #103)
+#101 := (iff #17 true)
+#96 := (= #14 #14)
+#99 := (iff #96 true)
+#100 := [rewrite]: #99
+#97 := (iff #17 #96)
+#94 := (= #16 #14)
+#92 := (= #15 #13)
+#93 := [rewrite]: #92
+#95 := [monotonicity #93]: #94
+#98 := [monotonicity #95]: #97
+#102 := [trans #98 #100]: #101
+#105 := [monotonicity #102]: #104
+#109 := [trans #105 #107]: #108
+#37 := [asserted]: #18
+[mp #37 #109]: false
+b54b0a8e9089b1fc3a30b6ccbd0b1a995d0b98ef 52 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int S3)
+decl f5 :: (-> S4 S3 Int)
+decl f9 :: S3
+#13 := f9
+decl f6 :: S4
+#8 := f6
+#14 := (f5 f6 f9)
+decl f8 :: S3
+#11 := f8
+#12 := (f5 f6 f8)
+decl f7 :: S3
+#9 := f7
+#10 := (f5 f6 f7)
+#18 := (+ #10 #12)
+#19 := (+ #18 #14)
+decl f4 :: S2
+#7 := f4
+#20 := (f3 f4 #19)
+#15 := (+ #12 #14)
+#16 := (+ #10 #15)
+#17 := (f3 f4 #16)
+#21 := (= #17 #20)
+#22 := (not #21)
+#70 := (iff #22 false)
+#1 := true
+#65 := (not true)
+#68 := (iff #65 false)
+#69 := [rewrite]: #68
+#66 := (iff #22 #65)
+#63 := (iff #21 true)
+#48 := (+ #10 #12 #14)
+#51 := (f3 f4 #48)
+#58 := (= #51 #51)
+#61 := (iff #58 true)
+#62 := [rewrite]: #61
+#59 := (iff #21 #58)
+#56 := (= #20 #51)
+#54 := (= #19 #48)
+#55 := [rewrite]: #54
+#57 := [monotonicity #55]: #56
+#52 := (= #17 #51)
+#49 := (= #16 #48)
+#50 := [rewrite]: #49
+#53 := [monotonicity #50]: #52
+#60 := [monotonicity #53 #57]: #59
+#64 := [trans #60 #62]: #63
+#67 := [monotonicity #64]: #66
+#71 := [trans #67 #69]: #70
+#41 := [asserted]: #22
+[mp #41 #71]: false
+dc4471261a7af4fe9cbee9553569694766037bc0 408 0
+unsat
+#2 := false
+#15 := 0::Int
+decl f5 :: (-> S4 S3 Int)
+decl f7 :: S3
+#9 := f7
+decl f6 :: S4
+#8 := f6
+#10 := (f5 f6 f7)
+#385 := (= #10 0::Int)
 decl f3 :: (-> S2 Int S3)
 decl f4 :: S2
-#8 := f4
-#69 := (f3 f4 #66)
-#63 := (f3 f4 #60)
-#72 := (= #63 #69)
-#663 := (f5 f6 #63)
-#435 := (f3 f4 #663)
-#380 := (= #435 #69)
-#401 := (= #69 #435)
-#399 := (= #66 #663)
-#664 := (= #60 #663)
-#665 := -1::Int
-#655 := (* -1::Int #663)
-#314 := (+ #11 #655)
-#653 := (<= #314 -1::Int)
-#319 := (= #314 -1::Int)
-#657 := (>= #11 -1::Int)
-#28 := 0::Int
-#506 := (>= #11 0::Int)
-#434 := (= #11 0::Int)
-#343 := (f3 f4 #11)
-#507 := (f5 f6 #343)
-#600 := (= #507 0::Int)
-#436 := (not #506)
-#438 := [hypothesis]: #436
-#601 := (or #506 #600)
-#29 := (:var 0 Int)
-#31 := (f3 f4 #29)
-#673 := (pattern #31)
-#119 := (>= #29 0::Int)
-#32 := (f5 f6 #31)
-#37 := (= #32 0::Int)
-#167 := (or #37 #119)
-#680 := (forall (vars (?v0 Int)) (:pat #673) #167)
-#172 := (forall (vars (?v0 Int)) #167)
-#683 := (iff #172 #680)
-#681 := (iff #167 #167)
-#682 := [refl]: #681
-#684 := [quant-intro #682]: #683
-#185 := (~ #172 #172)
-#193 := (~ #167 #167)
-#194 := [refl]: #193
-#186 := [nnf-pos #194]: #185
-#36 := (< #29 0::Int)
-#38 := (implies #36 #37)
-#39 := (forall (vars (?v0 Int)) #38)
-#175 := (iff #39 #172)
-#138 := (= 0::Int #32)
-#144 := (not #36)
-#145 := (or #144 #138)
-#150 := (forall (vars (?v0 Int)) #145)
-#173 := (iff #150 #172)
-#170 := (iff #145 #167)
-#164 := (or #119 #37)
-#168 := (iff #164 #167)
-#169 := [rewrite]: #168
-#165 := (iff #145 #164)
-#162 := (iff #138 #37)
-#163 := [rewrite]: #162
-#160 := (iff #144 #119)
-#120 := (not #119)
-#155 := (not #120)
-#158 := (iff #155 #119)
-#159 := [rewrite]: #158
-#156 := (iff #144 #155)
-#153 := (iff #36 #120)
-#154 := [rewrite]: #153
-#157 := [monotonicity #154]: #156
-#161 := [trans #157 #159]: #160
-#166 := [monotonicity #161 #163]: #165
-#171 := [trans #166 #169]: #170
-#174 := [quant-intro #171]: #173
-#151 := (iff #39 #150)
-#148 := (iff #38 #145)
-#141 := (implies #36 #138)
-#146 := (iff #141 #145)
-#147 := [rewrite]: #146
-#142 := (iff #38 #141)
-#139 := (iff #37 #138)
+#7 := f4
+#554 := (f3 f4 #10)
+#348 := (f5 f6 #554)
+#349 := (= #348 0::Int)
+decl f8 :: S3
+#11 := f8
+#12 := (f5 f6 f8)
+#228 := (f3 f4 #12)
+#505 := (f5 f6 #228)
+#350 := (= #505 0::Int)
+#346 := (>= #10 0::Int)
+#408 := (not #349)
+#364 := [hypothesis]: #408
+#502 := (or #346 #349)
+#28 := (:var 0 Int)
+#30 := (f3 f4 #28)
+#573 := (pattern #30)
+#31 := (f5 f6 #30)
+#36 := (= #31 0::Int)
+#104 := (>= #28 0::Int)
+#115 := (or #104 #36)
+#580 := (forall (vars (?v0 Int)) (:pat #573) #115)
+#118 := (forall (vars (?v0 Int)) #115)
+#583 := (iff #118 #580)
+#581 := (iff #115 #115)
+#582 := [refl]: #581
+#584 := [quant-intro #582]: #583
+#132 := (~ #118 #118)
+#130 := (~ #115 #115)
+#131 := [refl]: #130
+#133 := [nnf-pos #131]: #132
+#29 := (<= 0::Int #28)
+#73 := (or #29 #36)
+#78 := (forall (vars (?v0 Int)) #73)
+#119 := (iff #78 #118)
+#116 := (iff #73 #115)
+#102 := (iff #29 #104)
+#103 := [rewrite]: #102
+#117 := [monotonicity #103]: #116
+#120 := [quant-intro #117]: #119
+#35 := (< #28 0::Int)
+#37 := (implies #35 #36)
+#38 := (forall (vars (?v0 Int)) #37)
+#79 := (iff #38 #78)
+#76 := (iff #37 #73)
+#56 := (not #29)
+#70 := (implies #56 #36)
+#74 := (iff #70 #73)
+#75 := [rewrite]: #74
+#71 := (iff #37 #70)
+#65 := (iff #35 #56)
+#67 := (iff #56 #56)
+#52 := (iff #29 #29)
+#53 := [rewrite]: #52
+#68 := [monotonicity #53]: #67
+#66 := [rewrite]: #65
+#69 := [trans #66 #68]: #65
+#72 := [monotonicity #69]: #71
+#77 := [trans #72 #75]: #76
+#80 := [quant-intro #77]: #79
+#43 := [asserted]: #38
+#81 := [mp #43 #80]: #78
+#121 := [mp #81 #120]: #118
+#134 := [mp~ #121 #133]: #118
+#585 := [mp #134 #584]: #580
+#263 := (not #580)
+#506 := (or #263 #346 #349)
+#504 := (or #263 #502)
+#389 := (iff #504 #506)
+#390 := [rewrite]: #389
+#507 := [quant-inst #10]: #504
+#391 := [mp #507 #390]: #506
+#365 := [unit-resolution #391 #585]: #502
+#370 := [unit-resolution #365 #364]: #346
+#448 := (not #346)
+#392 := (or #448 #350)
+#400 := (= #12 0::Int)
+#13 := (+ #10 #12)
+#14 := (f3 f4 #13)
+#219 := (f5 f6 #14)
+#347 := -1::Int
+#203 := (* -1::Int #219)
+#204 := (+ #10 #12 #203)
+#550 := (<= #204 0::Int)
+#541 := (= #204 0::Int)
+#559 := (>= #13 0::Int)
+#503 := (>= #12 0::Int)
+#453 := (not #350)
+#435 := [hypothesis]: #453
+#498 := (or #503 #350)
+#496 := (or #263 #503 #350)
+#499 := (or #263 #498)
+#399 := (iff #499 #496)
+#401 := [rewrite]: #399
+#384 := [quant-inst #12]: #499
+#402 := [mp #384 #401]: #496
+#431 := [unit-resolution #402 #585]: #498
+#432 := [unit-resolution #431 #435]: #503
+#457 := [hypothesis]: #346
+#433 := (not #503)
+#436 := (or #559 #448 #433)
+#437 := [th-lemma arith assign-bounds -1 -1]: #436
+#438 := [unit-resolution #437 #457 #432]: #559
+#565 := (not #559)
+#205 := (or #565 #541)
+#32 := (= #31 #28)
+#105 := (not #104)
+#108 := (or #105 #32)
+#574 := (forall (vars (?v0 Int)) (:pat #573) #108)
+#111 := (forall (vars (?v0 Int)) #108)
+#577 := (iff #111 #574)
+#575 := (iff #108 #108)
+#576 := [refl]: #575
+#578 := [quant-intro #576]: #577
+#123 := (~ #111 #111)
+#125 := (~ #108 #108)
+#122 := [refl]: #125
+#126 := [nnf-pos #122]: #123
+#57 := (or #56 #32)
+#61 := (forall (vars (?v0 Int)) #57)
+#112 := (iff #61 #111)
+#109 := (iff #57 #108)
+#106 := (iff #56 #105)
+#107 := [monotonicity #103]: #106
+#110 := [monotonicity #107]: #109
+#113 := [quant-intro #110]: #112
+#33 := (implies #29 #32)
+#34 := (forall (vars (?v0 Int)) #33)
+#62 := (iff #34 #61)
+#58 := (iff #33 #57)
+#59 := [rewrite]: #58
+#54 := (iff #33 #33)
+#55 := [monotonicity #53]: #54
+#60 := [trans #55 #59]: #58
+#63 := [quant-intro #60]: #62
+#42 := [asserted]: #34
+#64 := [mp #42 #63]: #61
+#114 := [mp #64 #113]: #111
+#127 := [mp~ #114 #126]: #111
+#579 := [mp #127 #578]: #574
+#544 := (not #574)
+#545 := (or #544 #565 #541)
+#556 := (= #219 #13)
+#215 := (or #565 #556)
+#546 := (or #544 #215)
+#190 := (iff #546 #545)
+#542 := (or #544 #205)
+#549 := (iff #542 #545)
+#551 := [rewrite]: #549
+#548 := (iff #546 #542)
+#206 := (iff #215 #205)
+#199 := (iff #556 #541)
+#557 := [rewrite]: #199
+#543 := [monotonicity #557]: #206
+#185 := [monotonicity #543]: #548
+#191 := [trans #185 #551]: #190
+#547 := [quant-inst #13]: #546
+#552 := [mp #547 #191]: #545
+#439 := [unit-resolution #552 #579]: #205
+#434 := [unit-resolution #439 #438]: #541
+#440 := (not #541)
+#413 := (or #440 #550)
+#414 := [th-lemma arith triangle-eq]: #413
+#415 := [unit-resolution #414 #434]: #550
+#553 := (>= #204 0::Int)
+#259 := (<= #219 0::Int)
+#539 := (= #219 0::Int)
+#16 := (f3 f4 0::Int)
+#537 := (f5 f6 #16)
+#534 := (= #537 0::Int)
+#524 := (or #544 #534)
+#247 := (>= 0::Int 0::Int)
+#262 := (not #247)
+#538 := (or #262 #534)
+#525 := (or #544 #538)
+#526 := (iff #525 #524)
+#368 := (iff #524 #524)
+#369 := [rewrite]: #368
+#518 := (iff #538 #534)
+#528 := (or false #534)
+#522 := (iff #528 #534)
+#523 := [rewrite]: #522
+#532 := (iff #538 #528)
+#527 := (iff #262 false)
+#1 := true
+#250 := (not true)
+#530 := (iff #250 false)
+#244 := [rewrite]: #530
+#251 := (iff #262 #250)
+#248 := (iff #247 true)
+#249 := [rewrite]: #248
+#529 := [monotonicity #249]: #251
+#531 := [trans #529 #244]: #527
+#521 := [monotonicity #531]: #532
+#519 := [trans #521 #523]: #518
+#367 := [monotonicity #519]: #526
+#511 := [trans #367 #369]: #526
+#520 := [quant-inst #15]: #525
+#512 := [mp #520 #511]: #524
+#497 := [unit-resolution #512 #579]: #534
+#462 := (= #219 #537)
+#17 := (= #14 #16)
+#19 := (= f8 #16)
+#136 := (not #19)
+#18 := (= f7 #16)
+#135 := (not #18)
+#137 := (or #135 #136)
+#464 := (= #13 0::Int)
+#473 := (= #13 #537)
+#491 := (= #12 #537)
+#138 := (not #137)
+#407 := [hypothesis]: #138
+#151 := (or #137 #19)
+#237 := [def-axiom]: #151
+#501 := [unit-resolution #237 #407]: #19
+#492 := [monotonicity #501]: #491
+#476 := (= #13 #12)
+#395 := (= #10 #12)
+#479 := (= f7 f8)
+#488 := (= #16 f8)
+#490 := [symm #501]: #488
+#150 := (or #137 #18)
+#236 := [def-axiom]: #150
+#482 := [unit-resolution #236 #407]: #18
+#481 := [trans #482 #490]: #479
+#475 := [monotonicity #481]: #395
+#472 := (= #13 #10)
+#487 := (= #10 #13)
+#495 := (<= #12 0::Int)
+#493 := [trans #492 #497]: #400
+#489 := (not #400)
+#494 := (or #489 #495)
+#483 := [th-lemma arith triangle-eq]: #494
+#484 := [unit-resolution #483 #493]: #495
+#485 := (or #489 #503)
+#486 := [th-lemma arith triangle-eq]: #485
+#480 := [unit-resolution #486 #493]: #503
+#471 := [th-lemma arith eq-propagate -1 -1 #480 #484]: #487
+#474 := [symm #471]: #472
+#477 := [trans #474 #475]: #476
+#478 := [trans #477 #492]: #473
+#465 := [trans #478 #497]: #464
+#467 := [monotonicity #465]: #17
+#47 := (not #17)
+#560 := (or #47 #137)
+#144 := (iff #17 #137)
+#20 := (and #18 #19)
+#48 := (iff #47 #20)
+#147 := (iff #48 #144)
+#141 := (iff #47 #138)
+#145 := (iff #141 #144)
+#146 := [rewrite]: #145
+#142 := (iff #48 #141)
+#139 := (iff #20 #138)
 #140 := [rewrite]: #139
 #143 := [monotonicity #140]: #142
-#149 := [trans #143 #147]: #148
-#152 := [quant-intro #149]: #151
-#176 := [trans #152 #174]: #175
-#137 := [asserted]: #39
-#177 := [mp #137 #176]: #172
-#195 := [mp~ #177 #186]: #172
-#685 := [mp #195 #684]: #680
-#365 := (not #680)
-#582 := (or #365 #506 #600)
-#597 := (or #600 #506)
-#579 := (or #365 #597)
-#583 := (iff #579 #582)
-#591 := (or #365 #601)
-#589 := (iff #591 #582)
-#594 := [rewrite]: #589
-#592 := (iff #579 #591)
-#588 := (iff #597 #601)
-#590 := [rewrite]: #588
-#593 := [monotonicity #590]: #592
-#584 := [trans #593 #594]: #583
-#581 := [quant-inst #11]: #579
-#585 := [mp #581 #584]: #582
-#439 := [unit-resolution #585 #685]: #601
-#440 := [unit-resolution #439 #438]: #600
-#437 := (= #11 #507)
-#322 := (= f7 #343)
+#148 := [trans #143 #146]: #147
+#21 := (iff #17 #20)
+#22 := (not #21)
+#49 := (iff #22 #48)
+#50 := [rewrite]: #49
+#40 := [asserted]: #22
+#51 := [mp #40 #50]: #48
+#149 := [mp #51 #148]: #144
+#240 := (not #144)
+#222 := (or #47 #137 #240)
+#558 := [def-axiom]: #222
+#216 := [unit-resolution #558 #149]: #560
+#500 := [unit-resolution #216 #407]: #47
+#468 := [unit-resolution #500 #467]: false
+#469 := [lemma #468]: #137
+#239 := (or #17 #138)
+#241 := (or #17 #138 #240)
+#242 := [def-axiom]: #241
+#243 := [unit-resolution #242 #149]: #239
+#461 := [unit-resolution #243 #469]: #17
+#452 := [monotonicity #461]: #462
+#463 := [trans #452 #497]: #539
+#441 := (not #539)
+#442 := (or #441 #259)
+#444 := [th-lemma arith triangle-eq]: #442
+#445 := [unit-resolution #444 #463]: #259
+#308 := (not #259)
+#419 := (or #553 #448 #433 #308)
+#420 := [th-lemma arith assign-bounds -1 -1 1]: #419
+#421 := [unit-resolution #420 #457 #445 #432]: #553
+#533 := (>= #219 0::Int)
+#426 := (or #441 #533)
+#422 := [th-lemma arith triangle-eq]: #426
+#423 := [unit-resolution #422 #463]: #533
+#403 := (* -1::Int #12)
+#404 := (+ #10 #403)
+#456 := (<= #404 0::Int)
+#447 := (not #550)
+#424 := (or #456 #433 #308 #447)
+#427 := [th-lemma arith assign-bounds 1 -1/2 -1/2]: #424
+#428 := [unit-resolution #427 #415 #432 #445]: #456
+#406 := (>= #404 0::Int)
+#443 := (or #406 #447 #448)
+#458 := (not #406)
+#459 := [hypothesis]: #458
+#460 := [hypothesis]: #550
+#446 := [th-lemma arith farkas -1/2 -1/2 -1/2 1 #445 #460 #459 #457]: false
+#449 := [lemma #446]: #443
+#429 := [unit-resolution #449 #415 #457]: #406
+#425 := [th-lemma arith eq-propagate 1/2 1/2 -1/2 -1/2 -1/2 -1/2 #429 #428 #423 #445 #421 #415]: #400
+#430 := (= #505 #12)
+#561 := (= #228 f8)
+#23 := (:var 0 S3)
+#24 := (f5 f6 #23)
+#566 := (pattern #24)
+#25 := (f3 f4 #24)
+#26 := (= #25 #23)
+#567 := (forall (vars (?v0 S3)) (:pat #566) #26)
+#27 := (forall (vars (?v0 S3)) #26)
+#570 := (iff #27 #567)
+#568 := (iff #26 #26)
+#569 := [refl]: #568
+#571 := [quant-intro #569]: #570
+#128 := (~ #27 #27)
+#100 := (~ #26 #26)
+#101 := [refl]: #100
+#129 := [nnf-pos #101]: #128
+#41 := [asserted]: #27
+#124 := [mp~ #41 #129]: #27
+#572 := [mp #124 #571]: #567
+#562 := (not #567)
+#555 := (or #562 #561)
+#214 := [quant-inst #11]: #555
+#509 := [unit-resolution #214 #572]: #561
+#410 := [monotonicity #509]: #430
+#356 := [trans #410 #425]: #350
+#411 := [unit-resolution #435 #356]: false
+#416 := [lemma #411]: #392
+#371 := [unit-resolution #416 #370]: #350
+#353 := (= #348 #505)
+#510 := (= #12 #505)
+#515 := (= f8 #228)
+#516 := [symm #509]: #515
+#517 := [monotonicity #516]: #510
+#344 := (= #348 #12)
+#372 := [trans #517 #371]: #400
+#373 := [unit-resolution #486 #372]: #503
+#374 := [unit-resolution #437 #373 #370]: #559
+#375 := [unit-resolution #439 #374]: #541
+#376 := [unit-resolution #414 #375]: #550
+#377 := [unit-resolution #427 #376 #373 #445]: #456
+#378 := [unit-resolution #449 #376 #370]: #406
+#379 := (not #456)
+#380 := (or #395 #379 #458)
+#381 := [th-lemma arith triangle-eq]: #380
+#366 := [unit-resolution #381 #378 #377]: #395
+#382 := (= #348 #10)
+#227 := (= #554 f7)
+#563 := (or #562 #227)
+#564 := [quant-inst #9]: #563
+#418 := [unit-resolution #564 #572]: #227
+#343 := [monotonicity #418]: #382
+#351 := [trans #343 #366]: #344
+#354 := [trans #351 #517]: #353
+#355 := [trans #354 #371]: #349
+#357 := [unit-resolution #364 #355]: false
+#358 := [lemma #357]: #349
+#352 := (= #10 #348)
+#386 := (= f7 #554)
+#393 := [symm #418]: #386
+#383 := [monotonicity #393]: #352
+#360 := [trans #383 #358]: #385
+#388 := (or #408 #18)
+#394 := (= #554 #16)
+#412 := [hypothesis]: #349
+#387 := [trans #383 #412]: #385
+#396 := [monotonicity #387]: #394
+#397 := [trans #393 #396]: #18
+#417 := [hypothesis]: #135
+#398 := [unit-resolution #417 #397]: false
+#409 := [lemma #398]: #388
+#361 := [unit-resolution #409 #358]: #18
+#238 := (or #138 #135 #136)
+#229 := [def-axiom]: #238
+#362 := [unit-resolution #229 #361 #469]: #136
+#454 := (or #453 #19)
+#466 := (= #228 #16)
+#508 := [hypothesis]: #350
+#405 := [trans #517 #508]: #400
+#470 := [monotonicity #405]: #466
+#450 := [trans #516 #470]: #19
+#514 := [hypothesis]: #136
+#451 := [unit-resolution #514 #450]: false
+#455 := [lemma #451]: #454
+#345 := [unit-resolution #455 #362]: #453
+#363 := [unit-resolution #416 #345]: #448
+#333 := (not #385)
+#334 := (or #333 #346)
+#335 := [th-lemma arith triangle-eq]: #334
+[unit-resolution #335 #363 #360]: false
+3c81c3713e9b37bc83515c2cd6394e0a05b5171d 65 0
+unsat
+#2 := false
+decl f5 :: (-> S4 S3 Int)
+#16 := (:var 0 S3)
+decl f6 :: S4
+#8 := f6
+#17 := (f5 f6 #16)
+#564 := (pattern #17)
+decl f3 :: (-> S2 Int S3)
+decl f4 :: S2
+#7 := f4
+#18 := (f3 f4 #17)
+#19 := (= #18 #16)
+#565 := (forall (vars (?v0 S3)) (:pat #564) #19)
+#20 := (forall (vars (?v0 S3)) #19)
+#568 := (iff #20 #565)
+#566 := (iff #19 #19)
+#567 := [refl]: #566
+#569 := [quant-intro #567]: #568
+#138 := (~ #20 #20)
+#142 := (~ #19 #19)
+#143 := [refl]: #142
+#139 := [nnf-pos #143]: #138
+#34 := [asserted]: #20
+#140 := [mp~ #34 #139]: #20
+#570 := [mp #140 #569]: #565
+decl f7 :: S3
+#9 := f7
+#10 := (f5 f6 f7)
+#56 := (f3 f4 #10)
+#59 := (= #56 f7)
+#62 := (not #59)
+#11 := 0::Int
+#12 := (- #10 0::Int)
+#13 := (f3 f4 #12)
+#14 := (= #13 f7)
+#15 := (not #14)
+#63 := (iff #15 #62)
+#60 := (iff #14 #59)
+#57 := (= #13 #56)
+#54 := (= #12 #10)
+#40 := -1::Int
+#41 := (* -1::Int 0::Int)
+#42 := (+ #10 #41)
+#52 := (= #42 #10)
+#47 := (+ #10 0::Int)
+#50 := (= #47 #10)
+#51 := [rewrite]: #50
+#48 := (= #42 #47)
+#45 := (= #41 0::Int)
+#46 := [rewrite]: #45
+#49 := [monotonicity #46]: #48
+#53 := [trans #49 #51]: #52
+#43 := (= #12 #42)
+#44 := [rewrite]: #43
+#55 := [trans #44 #53]: #54
+#58 := [monotonicity #55]: #57
+#61 := [monotonicity #58]: #60
+#64 := [monotonicity #61]: #63
+#33 := [asserted]: #15
+#65 := [mp #33 #64]: #62
+#150 := (not #565)
+#236 := (or #150 #59)
+#237 := [quant-inst #9]: #236
+[unit-resolution #237 #65 #570]: false
+7a1aee105dba714bf6a08b99cf3f498e052aeddf 156 0
+unsat
+#2 := false
+decl f7 :: (-> S4 Int S3)
+#16 := 0::Int
+decl f8 :: S4
+#13 := f8
+#17 := (f7 f8 0::Int)
+decl f3 :: (-> S2 S3 Int)
+decl f6 :: S3
+#10 := f6
+decl f4 :: S2
+#7 := f4
+#11 := (f3 f4 f6)
+#49 := -1::Int
+#50 := (* -1::Int #11)
+decl f5 :: S3
+#8 := f5
+#9 := (f3 f4 f5)
+#51 := (+ #9 #50)
+#54 := (f7 f8 #51)
+#57 := (= #54 #17)
+#256 := (f3 f4 #54)
+#530 := (f7 f8 #256)
+#509 := (= #530 #17)
+#405 := (= #17 #530)
+#403 := (= 0::Int #256)
+#219 := (= #256 0::Int)
+#26 := (:var 0 Int)
+#28 := (f7 f8 #26)
+#587 := (pattern #28)
+#29 := (f3 f4 #28)
+#34 := (= #29 0::Int)
+#133 := (>= #26 0::Int)
+#145 := (or #133 #34)
+#594 := (forall (vars (?v0 Int)) (:pat #587) #145)
+#148 := (forall (vars (?v0 Int)) #145)
+#597 := (iff #148 #594)
+#595 := (iff #145 #145)
+#596 := [refl]: #595
+#598 := [quant-intro #596]: #597
+#162 := (~ #148 #148)
+#158 := (~ #145 #145)
+#159 := [refl]: #158
+#163 := [nnf-pos #159]: #162
+#27 := (<= 0::Int #26)
+#96 := (or #27 #34)
+#101 := (forall (vars (?v0 Int)) #96)
+#149 := (iff #101 #148)
+#146 := (iff #96 #145)
+#132 := (iff #27 #133)
+#134 := [rewrite]: #132
+#147 := [monotonicity #134]: #146
+#150 := [quant-intro #147]: #149
+#33 := (< #26 0::Int)
+#35 := (implies #33 #34)
+#36 := (forall (vars (?v0 Int)) #35)
+#102 := (iff #36 #101)
+#99 := (iff #35 #96)
+#79 := (not #27)
+#93 := (implies #79 #34)
+#97 := (iff #93 #96)
+#98 := [rewrite]: #97
+#94 := (iff #35 #93)
+#88 := (iff #33 #79)
+#90 := (iff #79 #79)
+#75 := (iff #27 #27)
+#76 := [rewrite]: #75
+#91 := [monotonicity #76]: #90
+#89 := [rewrite]: #88
+#92 := [trans #89 #91]: #88
+#95 := [monotonicity #92]: #94
+#100 := [trans #95 #98]: #99
+#103 := [quant-intro #100]: #102
+#41 := [asserted]: #36
+#104 := [mp #41 #103]: #101
+#151 := [mp #104 #150]: #148
+#164 := [mp~ #151 #163]: #148
+#599 := [mp #164 #598]: #594
+#126 := (>= #51 0::Int)
+#128 := (not #126)
+#45 := (<= #11 #9)
+#46 := (not #45)
+#129 := (iff #46 #128)
+#125 := (iff #45 #126)
+#127 := [rewrite]: #125
+#130 := [monotonicity #127]: #129
+#63 := (or #45 #57)
+#68 := (not #63)
+#14 := (- #9 #11)
+#15 := (f7 f8 #14)
+#18 := (= #15 #17)
+#12 := (< #9 #11)
+#19 := (implies #12 #18)
+#20 := (not #19)
+#69 := (iff #20 #68)
+#66 := (iff #19 #63)
+#60 := (implies #46 #57)
+#64 := (iff #60 #63)
+#65 := [rewrite]: #64
+#61 := (iff #19 #60)
+#58 := (iff #18 #57)
+#55 := (= #15 #54)
+#52 := (= #14 #51)
+#53 := [rewrite]: #52
+#56 := [monotonicity #53]: #55
+#59 := [monotonicity #56]: #58
+#47 := (iff #12 #46)
+#48 := [rewrite]: #47
+#62 := [monotonicity #48 #59]: #61
+#67 := [trans #62 #65]: #66
+#70 := [monotonicity #67]: #69
+#38 := [asserted]: #20
+#71 := [mp #38 #70]: #68
+#72 := [not-or-elim #71]: #46
+#131 := [mp #72 #130]: #128
+#558 := (not #594)
+#559 := (or #558 #126 #219)
+#220 := (or #126 #219)
+#560 := (or #558 #220)
+#556 := (iff #560 #559)
+#562 := [rewrite]: #556
+#561 := [quant-inst #51]: #560
+#200 := [mp #561 #562]: #559
+#520 := [unit-resolution #200 #131 #599]: #219
+#404 := [symm #520]: #403
+#364 := [monotonicity #404]: #405
+#510 := [symm #364]: #509
+#512 := (= #54 #530)
+#524 := (= #530 #54)
+#21 := (:var 0 S3)
+#22 := (f3 f4 #21)
+#580 := (pattern #22)
+#23 := (f7 f8 #22)
+#24 := (= #23 #21)
+#581 := (forall (vars (?v0 S3)) (:pat #580) #24)
+#25 := (forall (vars (?v0 S3)) #24)
+#584 := (iff #25 #581)
+#582 := (iff #24 #24)
+#583 := [refl]: #582
+#585 := [quant-intro #583]: #584
+#156 := (~ #25 #25)
+#154 := (~ #24 #24)
+#155 := [refl]: #154
+#157 := [nnf-pos #155]: #156
+#39 := [asserted]: #25
+#123 := [mp~ #39 #157]: #25
+#586 := [mp #123 #585]: #581
+#253 := (not #581)
+#518 := (or #253 #524)
+#521 := [quant-inst #54]: #518
+#519 := [unit-resolution #521 #586]: #524
+#414 := [symm #519]: #512
+#513 := [trans #414 #510]: #57
+#73 := (not #57)
+#74 := [not-or-elim #71]: #73
+[unit-resolution #74 #513]: false
+18cfec257bf09c7e04f15e4363ab463f93e36d3c 297 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int S3)
+#15 := 0::Int
+decl f4 :: S2
+#7 := f4
+#16 := (f3 f4 0::Int)
+decl f5 :: (-> S4 S3 Int)
+decl f8 :: S3
+#11 := f8
+decl f6 :: S4
+#8 := f6
+#12 := (f5 f6 f8)
+#51 := -1::Int
+#52 := (* -1::Int #12)
+decl f7 :: S3
+#9 := f7
+#10 := (f5 f6 f7)
+#53 := (+ #10 #52)
+#56 := (f3 f4 #53)
+#59 := (= #56 #16)
+#248 := (f5 f6 #56)
+#490 := (f3 f4 #248)
+#435 := (= #490 #16)
+#453 := (= #16 #490)
+#449 := (= 0::Int #248)
+#232 := (= #248 0::Int)
+#267 := (>= #53 0::Int)
+#268 := (not #267)
+#66 := (* -1::Int #10)
+#128 := (+ #66 #12)
+#131 := (f3 f4 #128)
+#392 := (f5 f6 #131)
+#515 := (<= #392 0::Int)
+#463 := (not #515)
+#521 := (= #392 0::Int)
+#477 := (not #521)
+#134 := (= #131 #16)
+#497 := (f3 f4 #392)
+#484 := (= #497 #16)
+#480 := (= #16 #497)
+#478 := (= 0::Int #392)
+#495 := [hypothesis]: #521
+#479 := [symm #495]: #478
+#481 := [monotonicity #479]: #480
+#485 := [symm #481]: #484
+#482 := (= #131 #497)
+#499 := (= #497 #131)
 #23 := (:var 0 S3)
 #24 := (f5 f6 #23)
-#666 := (pattern #24)
+#591 := (pattern #24)
 #25 := (f3 f4 #24)
-#93 := (= #23 #25)
-#667 := (forall (vars (?v0 S3)) (:pat #666) #93)
-#97 := (forall (vars (?v0 S3)) #93)
-#670 := (iff #97 #667)
-#668 := (iff #93 #93)
-#669 := [refl]: #668
-#671 := [quant-intro #669]: #670
-#191 := (~ #97 #97)
-#189 := (~ #93 #93)
-#190 := [refl]: #189
-#192 := [nnf-pos #190]: #191
 #26 := (= #25 #23)
+#592 := (forall (vars (?v0 S3)) (:pat #591) #26)
 #27 := (forall (vars (?v0 S3)) #26)
-#98 := (iff #27 #97)
-#95 := (iff #26 #93)
-#96 := [rewrite]: #95
-#99 := [quant-intro #96]: #98
-#92 := [asserted]: #27
-#102 := [mp #92 #99]: #97
-#181 := [mp~ #102 #192]: #97
-#672 := [mp #181 #671]: #667
-#316 := (not #667)
-#447 := (or #316 #322)
-#654 := [quant-inst #10]: #447
-#444 := [unit-resolution #654 #672]: #322
-#442 := [monotonicity #444]: #437
-#421 := [trans #442 #440]: #434
-#424 := (not #434)
-#428 := (or #424 #506)
-#430 := [th-lemma arith triangle-eq]: #428
-#431 := [unit-resolution #430 #438 #421]: false
-#429 := [lemma #431]: #506
-#388 := (or #436 #657)
-#390 := [th-lemma arith farkas 1 1]: #388
-#391 := [unit-resolution #390 #429]: #657
-#303 := (not #657)
-#306 := (or #319 #303)
-#101 := (= #29 #32)
-#126 := (or #101 #120)
-#674 := (forall (vars (?v0 Int)) (:pat #673) #126)
-#131 := (forall (vars (?v0 Int)) #126)
-#677 := (iff #131 #674)
-#675 := (iff #126 #126)
-#676 := [refl]: #675
-#678 := [quant-intro #676]: #677
-#183 := (~ #131 #131)
-#182 := (~ #126 #126)
-#179 := [refl]: #182
-#184 := [nnf-pos #179]: #183
-#33 := (= #32 #29)
-#30 := (<= 0::Int #29)
-#34 := (implies #30 #33)
-#35 := (forall (vars (?v0 Int)) #34)
-#134 := (iff #35 #131)
-#108 := (not #30)
-#109 := (or #108 #101)
-#114 := (forall (vars (?v0 Int)) #109)
-#132 := (iff #114 #131)
-#129 := (iff #109 #126)
-#123 := (or #120 #101)
-#127 := (iff #123 #126)
-#128 := [rewrite]: #127
-#124 := (iff #109 #123)
-#121 := (iff #108 #120)
-#117 := (iff #30 #119)
-#118 := [rewrite]: #117
-#122 := [monotonicity #118]: #121
-#125 := [monotonicity #122]: #124
-#130 := [trans #125 #128]: #129
-#133 := [quant-intro #130]: #132
-#115 := (iff #35 #114)
-#112 := (iff #34 #109)
-#105 := (implies #30 #101)
-#110 := (iff #105 #109)
-#111 := [rewrite]: #110
-#106 := (iff #34 #105)
-#103 := (iff #33 #101)
-#104 := [rewrite]: #103
-#107 := [monotonicity #104]: #106
-#113 := [trans #107 #111]: #112
-#116 := [quant-intro #113]: #115
-#135 := [trans #116 #133]: #134
-#100 := [asserted]: #35
-#136 := [mp #100 #135]: #131
-#180 := [mp~ #136 #184]: #131
-#679 := [mp #180 #678]: #674
-#645 := (not #674)
-#646 := (or #645 #319 #303)
-#327 := (>= #60 0::Int)
-#328 := (not #327)
-#659 := (or #664 #328)
-#647 := (or #645 #659)
-#291 := (iff #647 #646)
-#648 := (or #645 #306)
-#651 := (iff #648 #646)
-#290 := [rewrite]: #651
-#285 := (iff #647 #648)
-#643 := (iff #659 #306)
-#304 := (iff #328 #303)
-#299 := (iff #327 #657)
-#641 := [rewrite]: #299
-#305 := [monotonicity #641]: #304
-#656 := (iff #664 #319)
-#315 := [rewrite]: #656
-#644 := [monotonicity #315 #305]: #643
-#649 := [monotonicity #644]: #285
-#652 := [trans #649 #290]: #291
-#642 := [quant-inst #60]: #647
-#650 := [mp #642 #652]: #646
-#474 := [unit-resolution #650 #679]: #306
-#392 := [unit-resolution #474 #391]: #319
-#476 := (not #319)
-#477 := (or #476 #653)
-#478 := [th-lemma arith triangle-eq]: #477
-#393 := [unit-resolution #478 #392]: #653
-#639 := (>= #314 -1::Int)
-#480 := (or #476 #639)
-#481 := [th-lemma arith triangle-eq]: #480
-#394 := [unit-resolution #481 #392]: #639
-#395 := [th-lemma arith eq-propagate -1 -1 #394 #393]: #664
-#397 := (= #66 #60)
-#396 := [hypothesis]: #416
-#398 := [symm #396]: #397
-#400 := [trans #398 #395]: #399
-#378 := [monotonicity #400]: #401
-#381 := [symm #378]: #380
-#282 := (= #63 #435)
-#420 := (or #316 #282)
-#423 := [quant-inst #63]: #420
-#389 := [unit-resolution #423 #672]: #282
-#382 := [trans #389 #381]: #72
-#329 := (not #72)
-#20 := (= f7 f8)
-#658 := (f3 f4 #16)
-#454 := (= #658 f8)
-#660 := (= f8 #658)
-#661 := (or #316 #660)
-#662 := [quant-inst #15]: #661
-#549 := [unit-resolution #662 #672]: #660
-#455 := [symm #549]: #454
-#457 := (= f7 #658)
-#451 := (= #343 #658)
-#482 := (= #11 #16)
-#344 := (f5 f6 #69)
-#628 := (* -1::Int #344)
-#632 := (+ #16 #628)
-#606 := (<= #632 -1::Int)
-#621 := (= #632 -1::Int)
-#618 := (>= #16 -1::Int)
-#586 := (>= #16 0::Int)
-#550 := (= #16 0::Int)
-#580 := (f5 f6 #658)
-#587 := (= #580 0::Int)
-#553 := (not #586)
-#554 := [hypothesis]: #553
-#572 := (or #586 #587)
-#576 := (or #365 #586 #587)
-#571 := (or #587 #586)
-#577 := (or #365 #571)
-#569 := (iff #577 #576)
-#578 := (or #365 #572)
-#567 := (iff #578 #576)
-#568 := [rewrite]: #567
-#564 := (iff #577 #578)
-#574 := (iff #571 #572)
-#575 := [rewrite]: #574
-#565 := [monotonicity #575]: #564
-#566 := [trans #565 #568]: #569
-#573 := [quant-inst #16]: #577
-#570 := [mp #573 #566]: #576
-#548 := [unit-resolution #570 #685]: #572
-#543 := [unit-resolution #548 #554]: #587
-#535 := (= #16 #580)
-#531 := [monotonicity #549]: #535
-#532 := [trans #531 #543]: #550
-#533 := (not #550)
-#536 := (or #533 #586)
-#537 := [th-lemma arith triangle-eq]: #536
-#538 := [unit-resolution #537 #554 #532]: false
-#539 := [lemma #538]: #586
-#521 := (or #553 #618)
-#526 := [th-lemma arith farkas 1 1]: #521
-#522 := [unit-resolution #526 #539]: #618
-#625 := (not #618)
-#611 := (or #625 #621)
-#609 := (or #645 #625 #621)
-#629 := (>= #66 0::Int)
-#630 := (not #629)
-#627 := (= #66 #344)
-#631 := (or #627 #630)
-#615 := (or #645 #631)
-#602 := (iff #615 #609)
-#610 := (or #645 #611)
-#448 := (iff #610 #609)
-#449 := [rewrite]: #448
-#617 := (iff #615 #610)
-#614 := (iff #631 #611)
-#467 := (or #621 #625)
-#612 := (iff #467 #611)
-#613 := [rewrite]: #612
-#468 := (iff #631 #467)
-#620 := (iff #630 #625)
-#619 := (iff #629 #618)
-#624 := [rewrite]: #619
-#626 := [monotonicity #624]: #620
-#622 := (iff #627 #621)
-#623 := [rewrite]: #622
-#469 := [monotonicity #623 #626]: #468
-#608 := [trans #469 #613]: #614
-#446 := [monotonicity #608]: #617
-#603 := [trans #446 #449]: #602
-#616 := [quant-inst #66]: #615
-#605 := [mp #616 #603]: #609
-#552 := [unit-resolution #605 #679]: #611
-#523 := [unit-resolution #552 #522]: #621
-#541 := (not #621)
-#542 := (or #541 #606)
-#544 := [th-lemma arith triangle-eq]: #542
-#524 := [unit-resolution #544 #523]: #606
-#604 := (>= #632 -1::Int)
-#527 := (or #541 #604)
-#528 := [th-lemma arith triangle-eq]: #527
-#529 := [unit-resolution #528 #523]: #604
-#513 := (+ #344 #655)
-#408 := (<= #513 0::Int)
-#540 := (= #344 #663)
-#530 := (= #663 #344)
-#86 := (not #20)
-#520 := [hypothesis]: #86
-#337 := (or #72 #20)
-#87 := (iff #72 #86)
-#17 := (+ #16 1::Int)
-#18 := (f3 f4 #17)
-#13 := (+ #11 1::Int)
+#595 := (iff #27 #592)
+#593 := (iff #26 #26)
+#594 := [refl]: #593
+#596 := [quant-intro #594]: #595
+#171 := (~ #27 #27)
+#167 := (~ #26 #26)
+#168 := [refl]: #167
+#172 := [nnf-pos #168]: #171
+#45 := [asserted]: #27
+#169 := [mp~ #45 #172]: #27
+#597 := [mp #169 #596]: #592
+#264 := (not #592)
+#493 := (or #264 #499)
+#494 := [quant-inst #131]: #493
+#491 := [unit-resolution #494 #597]: #499
+#483 := [symm #491]: #482
+#486 := [trans #483 #485]: #134
+#137 := (not #134)
+#67 := (+ #12 #66)
+#70 := (f3 f4 #67)
+#73 := (= #70 #16)
+#76 := (not #73)
+#138 := (iff #76 #137)
+#135 := (iff #73 #134)
+#132 := (= #70 #131)
+#129 := (= #67 #128)
+#130 := [rewrite]: #129
+#133 := [monotonicity #130]: #132
+#136 := [monotonicity #133]: #135
+#139 := [monotonicity #136]: #138
+#18 := (- #12 #10)
+#19 := (f3 f4 #18)
+#20 := (= #19 #16)
+#43 := (not #20)
+#77 := (iff #43 #76)
+#74 := (iff #20 #73)
+#71 := (= #19 #70)
+#68 := (= #18 #67)
+#69 := [rewrite]: #68
+#72 := [monotonicity #69]: #71
+#75 := [monotonicity #72]: #74
+#78 := [monotonicity #75]: #77
+#13 := (- #10 #12)
+#14 := (f3 f4 #13)
+#17 := (= #14 #16)
+#21 := (or #17 #20)
+#22 := (not #21)
+#40 := [asserted]: #22
+#44 := [not-or-elim #40]: #43
+#79 := [mp #44 #78]: #76
+#142 := [mp #79 #139]: #137
+#487 := [unit-resolution #142 #486]: false
+#488 := [lemma #487]: #477
+#507 := (>= #392 0::Int)
+#536 := (<= #53 0::Int)
+#409 := (or #536 #521)
+#28 := (:var 0 Int)
+#30 := (f3 f4 #28)
+#598 := (pattern #30)
+#31 := (f5 f6 #30)
+#36 := (= #31 0::Int)
+#144 := (>= #28 0::Int)
+#156 := (or #144 #36)
+#605 := (forall (vars (?v0 Int)) (:pat #598) #156)
+#159 := (forall (vars (?v0 Int)) #156)
+#608 := (iff #159 #605)
+#606 := (iff #156 #156)
+#607 := [refl]: #606
+#609 := [quant-intro #607]: #608
+#173 := (~ #159 #159)
+#165 := (~ #156 #156)
+#166 := [refl]: #165
+#174 := [nnf-pos #166]: #173
+#29 := (<= 0::Int #28)
+#101 := (or #29 #36)
+#106 := (forall (vars (?v0 Int)) #101)
+#160 := (iff #106 #159)
+#157 := (iff #101 #156)
+#143 := (iff #29 #144)
+#145 := [rewrite]: #143
+#158 := [monotonicity #145]: #157
+#161 := [quant-intro #158]: #160
+#35 := (< #28 0::Int)
+#37 := (implies #35 #36)
+#38 := (forall (vars (?v0 Int)) #37)
+#107 := (iff #38 #106)
+#104 := (iff #37 #101)
+#84 := (not #29)
+#98 := (implies #84 #36)
+#102 := (iff #98 #101)
+#103 := [rewrite]: #102
+#99 := (iff #37 #98)
+#93 := (iff #35 #84)
+#95 := (iff #84 #84)
+#80 := (iff #29 #29)
+#81 := [rewrite]: #80
+#96 := [monotonicity #81]: #95
+#94 := [rewrite]: #93
+#97 := [trans #94 #96]: #93
+#100 := [monotonicity #97]: #99
+#105 := [trans #100 #103]: #104
+#108 := [quant-intro #105]: #107
+#47 := [asserted]: #38
+#109 := [mp #47 #108]: #106
+#162 := [mp #109 #161]: #159
+#175 := [mp~ #162 #174]: #159
+#610 := [mp #175 #609]: #605
+#571 := (not #605)
+#427 := (or #571 #536 #521)
+#545 := (>= #128 0::Int)
+#524 := (or #545 #521)
+#420 := (or #571 #524)
+#522 := (iff #420 #427)
+#429 := (or #571 #409)
+#432 := (iff #429 #427)
+#525 := [rewrite]: #432
+#430 := (iff #420 #429)
+#424 := (iff #524 #409)
+#537 := (iff #545 #536)
+#538 := [rewrite]: #537
+#426 := [monotonicity #538]: #424
+#431 := [monotonicity #426]: #430
+#526 := [trans #431 #525]: #522
+#428 := [quant-inst #128]: #420
+#513 := [mp #428 #526]: #427
+#544 := [unit-resolution #513 #610]: #409
+#471 := [unit-resolution #544 #488]: #536
+#540 := (+ #10 #52 #392)
+#520 := (>= #540 0::Int)
+#541 := (= #540 0::Int)
+#539 := (not #536)
+#371 := (or #539 #541)
+#32 := (= #31 #28)
+#146 := (not #144)
+#149 := (or #146 #32)
+#599 := (forall (vars (?v0 Int)) (:pat #598) #149)
+#152 := (forall (vars (?v0 Int)) #149)
+#602 := (iff #152 #599)
+#600 := (iff #149 #149)
+#601 := [refl]: #600
+#603 := [quant-intro #601]: #602
+#141 := (~ #152 #152)
+#170 := (~ #149 #149)
+#140 := [refl]: #170
+#163 := [nnf-pos #140]: #141
+#85 := (or #84 #32)
+#89 := (forall (vars (?v0 Int)) #85)
+#153 := (iff #89 #152)
+#150 := (iff #85 #149)
+#147 := (iff #84 #146)
+#148 := [monotonicity #145]: #147
+#151 := [monotonicity #148]: #150
+#154 := [quant-intro #151]: #153
+#33 := (implies #29 #32)
+#34 := (forall (vars (?v0 Int)) #33)
+#90 := (iff #34 #89)
+#86 := (iff #33 #85)
+#87 := [rewrite]: #86
+#82 := (iff #33 #33)
+#83 := [monotonicity #81]: #82
+#88 := [trans #83 #87]: #86
+#91 := [quant-intro #88]: #90
+#46 := [asserted]: #34
+#92 := [mp #46 #91]: #89
+#155 := [mp #92 #154]: #152
+#164 := [mp~ #155 #163]: #152
+#604 := [mp #164 #603]: #599
+#589 := (not #599)
+#527 := (or #589 #539 #541)
+#393 := (= #392 #128)
+#551 := (not #545)
+#394 := (or #551 #393)
+#528 := (or #589 #394)
+#416 := (iff #528 #527)
+#531 := (or #589 #371)
+#414 := (iff #531 #527)
+#415 := [rewrite]: #414
+#529 := (iff #528 #531)
+#373 := (iff #394 #371)
+#535 := (iff #393 #541)
+#542 := [rewrite]: #535
+#533 := (iff #551 #539)
+#534 := [monotonicity #538]: #533
+#374 := [monotonicity #534 #542]: #373
+#532 := [monotonicity #374]: #529
+#375 := [trans #532 #415]: #416
+#530 := [quant-inst #128]: #528
+#523 := [mp #530 #375]: #527
+#472 := [unit-resolution #523 #604]: #371
+#473 := [unit-resolution #472 #471]: #541
+#468 := (not #541)
+#474 := (or #468 #520)
+#460 := [th-lemma arith triangle-eq]: #474
+#456 := [unit-resolution #460 #473]: #520
+#457 := (not #520)
+#458 := (or #507 #457 #539)
+#461 := [th-lemma arith assign-bounds 1 -1]: #458
+#462 := [unit-resolution #461 #456 #471]: #507
+#464 := (not #507)
+#459 := (or #521 #463 #464)
+#465 := [th-lemma arith triangle-eq]: #459
+#438 := [unit-resolution #465 #462 #488]: #463
+#425 := (<= #540 0::Int)
+#439 := (or #468 #425)
+#440 := [th-lemma arith triangle-eq]: #439
+#333 := [unit-resolution #440 #473]: #425
+#444 := (not #425)
+#445 := (or #268 #515 #444)
+#446 := [th-lemma arith assign-bounds 1 -1]: #445
+#451 := [unit-resolution #446 #333 #438]: #268
+#568 := (or #267 #232)
+#572 := (or #571 #267 #232)
+#567 := (or #571 #568)
+#211 := (iff #567 #572)
+#574 := [rewrite]: #211
+#573 := [quant-inst #53]: #567
+#576 := [mp #573 #574]: #572
+#447 := [unit-resolution #576 #610]: #568
+#448 := [unit-resolution #447 #451]: #232
+#452 := [symm #448]: #449
+#454 := [monotonicity #452]: #453
+#381 := [symm #454]: #435
+#450 := (= #56 #490)
+#492 := (= #490 #56)
+#469 := (or #264 #492)
+#470 := [quant-inst #56]: #469
+#543 := [unit-resolution #470 #597]: #492
+#455 := [symm #543]: #450
+#436 := [trans #455 #381]: #59
+#62 := (not #59)
+#41 := (not #17)
+#63 := (iff #41 #62)
+#60 := (iff #17 #59)
+#57 := (= #14 #56)
+#54 := (= #13 #53)
+#55 := [rewrite]: #54
+#58 := [monotonicity #55]: #57
+#61 := [monotonicity #58]: #60
+#64 := [monotonicity #61]: #63
+#42 := [not-or-elim #40]: #41
+#65 := [mp #42 #64]: #62
+[unit-resolution #65 #436]: false
+1bebcd25606d258ac04a776ceb5aa65b98a4cfcc 287 0
+unsat
+#2 := false
+decl f8 :: S3
+#11 := f8
+decl f7 :: S3
+#9 := f7
+#27 := 0::Int
+decl f5 :: (-> S4 S3 Int)
+decl f6 :: S4
+#8 := f6
+#12 := (f5 f6 f8)
+#47 := -1::Int
+#48 := (* -1::Int #12)
+#10 := (f5 f6 f7)
+#49 := (+ #10 #48)
+#144 := (>= #49 0::Int)
+#146 := (if #144 f7 f8)
+decl f3 :: (-> S2 Int S3)
+decl f4 :: S2
+#7 := f4
+#52 := (f3 f4 #49)
+#55 := (f5 f6 #52)
+#131 := (+ #12 #55)
+#134 := (f3 f4 #131)
+#149 := (= #134 #146)
+#279 := (= f8 #146)
+#194 := (not #144)
+#193 := (= f7 #146)
+#446 := [hypothesis]: #144
+#280 := (or #194 #193)
+#281 := [def-axiom]: #280
+#447 := [unit-resolution #281 #446]: #193
+#477 := (= #134 f7)
+#282 := (f3 f4 #10)
+#286 := (= #282 f7)
+#22 := (:var 0 S3)
+#23 := (f5 f6 #22)
+#608 := (pattern #23)
+#24 := (f3 f4 #23)
+#25 := (= #24 #22)
+#609 := (forall (vars (?v0 S3)) (:pat #608) #25)
+#26 := (forall (vars (?v0 S3)) #25)
+#612 := (iff #26 #609)
+#610 := (iff #25 #25)
+#611 := [refl]: #610
+#613 := [quant-intro #611]: #612
+#180 := (~ #26 #26)
+#186 := (~ #25 #25)
+#187 := [refl]: #186
+#181 := [nnf-pos #187]: #180
+#41 := [asserted]: #26
+#158 := [mp~ #41 #181]: #26
+#614 := [mp #158 #613]: #609
+#265 := (not #609)
+#596 := (or #265 #286)
+#270 := [quant-inst #9]: #596
+#533 := [unit-resolution #270 #614]: #286
+#489 := (= #134 #282)
+#506 := (= #131 #10)
+#536 := (= #10 #131)
+#607 := (* -1::Int #55)
+#597 := (+ #10 #48 #607)
+#584 := (<= #597 0::Int)
+#601 := (= #597 0::Int)
+#262 := (or #194 #601)
+#28 := (:var 0 Int)
+#30 := (f3 f4 #28)
+#615 := (pattern #30)
+#31 := (f5 f6 #30)
+#32 := (= #31 #28)
+#161 := (>= #28 0::Int)
+#163 := (not #161)
+#166 := (or #163 #32)
+#616 := (forall (vars (?v0 Int)) (:pat #615) #166)
+#169 := (forall (vars (?v0 Int)) #166)
+#619 := (iff #169 #616)
+#617 := (iff #166 #166)
+#618 := [refl]: #617
+#620 := [quant-intro #618]: #619
+#185 := (~ #169 #169)
+#159 := (~ #166 #166)
+#184 := [refl]: #159
+#182 := [nnf-pos #184]: #185
+#29 := (<= 0::Int #28)
+#87 := (not #29)
+#88 := (or #87 #32)
+#92 := (forall (vars (?v0 Int)) #88)
+#170 := (iff #92 #169)
+#167 := (iff #88 #166)
+#164 := (iff #87 #163)
+#160 := (iff #29 #161)
+#162 := [rewrite]: #160
+#165 := [monotonicity #162]: #164
+#168 := [monotonicity #165]: #167
+#171 := [quant-intro #168]: #170
+#33 := (implies #29 #32)
+#34 := (forall (vars (?v0 Int)) #33)
+#93 := (iff #34 #92)
+#89 := (iff #33 #88)
+#90 := [rewrite]: #89
+#85 := (iff #33 #33)
+#83 := (iff #29 #29)
+#84 := [rewrite]: #83
+#86 := [monotonicity #84]: #85
+#91 := [trans #86 #90]: #89
+#94 := [quant-intro #91]: #93
+#42 := [asserted]: #34
+#95 := [mp #42 #94]: #92
+#172 := [mp #95 #171]: #169
+#183 := [mp~ #172 #182]: #169
+#621 := [mp #183 #620]: #616
+#599 := (not #616)
+#242 := (or #599 #194 #601)
+#271 := (= #55 #49)
+#603 := (or #194 #271)
+#583 := (or #599 #603)
+#587 := (iff #583 #242)
+#247 := (or #599 #262)
+#585 := (iff #247 #242)
+#586 := [rewrite]: #585
+#248 := (iff #583 #247)
+#598 := (iff #603 #262)
+#606 := (iff #271 #601)
+#257 := [rewrite]: #606
+#258 := [monotonicity #257]: #598
+#249 := [monotonicity #258]: #248
+#588 := [trans #249 #586]: #587
+#246 := [quant-inst #49]: #583
+#589 := [mp #246 #588]: #242
+#501 := [unit-resolution #589 #621]: #262
+#502 := [unit-resolution #501 #446]: #601
+#503 := (not #601)
+#504 := (or #503 #584)
+#494 := [th-lemma arith triangle-eq]: #504
+#505 := [unit-resolution #494 #502]: #584
+#590 := (>= #597 0::Int)
+#483 := (or #503 #590)
+#484 := [th-lemma arith triangle-eq]: #483
+#486 := [unit-resolution #484 #502]: #590
+#487 := [th-lemma arith eq-propagate -1 -1 #486 #505]: #536
+#488 := [symm #487]: #506
+#490 := [monotonicity #488]: #489
+#473 := [trans #490 #533]: #477
+#474 := [trans #473 #447]: #149
+#152 := (not #149)
+#64 := (<= #12 #10)
+#71 := (if #64 f7 f8)
+#58 := (+ #55 #12)
+#61 := (f3 f4 #58)
+#76 := (= #61 #71)
+#79 := (not #76)
+#155 := (iff #79 #152)
+#137 := (= #134 #71)
+#140 := (not #137)
+#153 := (iff #140 #152)
+#150 := (iff #137 #149)
+#147 := (= #71 #146)
+#143 := (iff #64 #144)
+#145 := [rewrite]: #143
+#148 := [monotonicity #145]: #147
+#151 := [monotonicity #148]: #150
+#154 := [monotonicity #151]: #153
+#141 := (iff #79 #140)
+#138 := (iff #76 #137)
+#135 := (= #61 #134)
+#132 := (= #58 #131)
+#133 := [rewrite]: #132
+#136 := [monotonicity #133]: #135
+#139 := [monotonicity #136]: #138
+#142 := [monotonicity #139]: #141
+#156 := [trans #142 #154]: #155
+#18 := (< #10 #12)
+#19 := (if #18 f8 f7)
+#13 := (- #10 #12)
 #14 := (f3 f4 #13)
-#19 := (= #14 #18)
-#21 := (iff #19 #20)
-#22 := (not #21)
-#90 := (iff #22 #87)
-#78 := (iff #20 #72)
-#83 := (not #78)
-#88 := (iff #83 #87)
-#89 := [rewrite]: #88
-#84 := (iff #22 #83)
-#81 := (iff #21 #78)
-#75 := (iff #72 #20)
-#79 := (iff #75 #78)
-#80 := [rewrite]: #79
-#76 := (iff #21 #75)
-#73 := (iff #19 #72)
-#70 := (= #18 #69)
-#67 := (= #17 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#64 := (= #14 #63)
-#61 := (= #13 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#74 := [monotonicity #65 #71]: #73
-#77 := [monotonicity #74]: #76
-#82 := [trans #77 #80]: #81
-#85 := [monotonicity #82]: #84
-#91 := [trans #85 #89]: #90
-#59 := [asserted]: #22
-#94 := [mp #59 #91]: #87
-#251 := (not #87)
-#336 := (or #72 #20 #251)
-#252 := [def-axiom]: #336
-#338 := [unit-resolution #252 #94]: #337
-#525 := [unit-resolution #338 #520]: #72
-#510 := [monotonicity #525]: #530
-#456 := [symm #510]: #540
-#511 := (not #540)
-#492 := (or #511 #408)
-#516 := [th-lemma arith triangle-eq]: #492
-#517 := [unit-resolution #516 #456]: #408
-#519 := (>= #513 0::Int)
-#512 := (or #511 #519)
-#518 := [th-lemma arith triangle-eq]: #512
-#486 := [unit-resolution #518 #456]: #519
-#640 := (= #663 0::Int)
-#464 := (not #640)
-#607 := (= #344 0::Int)
-#557 := (not #607)
-#465 := (iff #557 #464)
-#488 := (iff #607 #640)
-#498 := (iff #640 #607)
-#508 := [monotonicity #510]: #498
-#509 := [symm #508]: #488
-#470 := [monotonicity #509]: #465
-#504 := (<= #344 0::Int)
-#493 := (not #504)
-#452 := (not #606)
-#483 := (or #493 #553 #452)
-#485 := [th-lemma arith assign-bounds -1 1]: #483
-#487 := [unit-resolution #485 #524 #539]: #493
-#494 := (or #557 #504)
-#496 := [th-lemma arith triangle-eq]: #494
-#497 := [unit-resolution #496 #487]: #557
-#471 := [mp #497 #470]: #464
-#362 := (or #640 #657)
-#258 := (or #365 #640 #657)
-#347 := (or #640 #327)
-#635 := (or #365 #347)
-#638 := (iff #635 #258)
-#358 := (or #365 #362)
-#637 := (iff #358 #258)
-#634 := [rewrite]: #637
-#359 := (iff #635 #358)
-#363 := (iff #347 #362)
-#364 := [monotonicity #641]: #363
-#633 := [monotonicity #364]: #359
-#348 := [trans #633 #634]: #638
-#636 := [quant-inst #60]: #635
-#349 := [mp #636 #348]: #258
-#472 := [unit-resolution #349 #685]: #362
-#473 := [unit-resolution #472 #471]: #657
-#475 := [unit-resolution #474 #473]: #319
-#479 := [unit-resolution #478 #475]: #653
-#466 := [unit-resolution #481 #475]: #639
-#443 := [th-lemma arith eq-propagate -1 -1 1 1 1 1 #466 #479 #486 #517 #529 #524]: #482
-#453 := [monotonicity #443]: #451
-#458 := [trans #444 #453]: #457
-#459 := [trans #458 #455]: #20
-#460 := [unit-resolution #520 #459]: false
-#461 := [lemma #460]: #20
-#342 := (or #329 #86)
-#340 := (or #329 #86 #251)
-#341 := [def-axiom]: #340
-#339 := [unit-resolution #341 #94]: #342
-#406 := [unit-resolution #339 #461]: #329
-#383 := [unit-resolution #406 #382]: false
-#385 := [lemma #383]: #384
-#402 := (* -1::Int #66)
-#404 := (+ #60 #402)
-#405 := (<= #404 0::Int)
-#462 := (* -1::Int #16)
-#445 := (+ #11 #462)
-#463 := (<= #445 0::Int)
-#386 := [monotonicity #461]: #482
-#379 := (not #482)
-#387 := (or #379 #463)
-#372 := [th-lemma arith triangle-eq]: #387
-#373 := [unit-resolution #372 #386]: #463
-#374 := (not #463)
-#376 := (or #405 #374)
-#375 := [th-lemma arith assign-bounds -1]: #376
-#377 := [unit-resolution #375 #373]: #405
-#403 := (>= #404 0::Int)
-#433 := (>= #445 0::Int)
-#366 := (or #379 #433)
-#367 := [th-lemma arith triangle-eq]: #366
-#368 := [unit-resolution #367 #386]: #433
-#360 := (not #433)
-#369 := (or #403 #360)
-#370 := [th-lemma arith assign-bounds -1]: #369
-#361 := [unit-resolution #370 #368]: #403
-#352 := (not #403)
-#371 := (not #405)
-#353 := (or #416 #371 #352)
-#354 := [th-lemma arith triangle-eq]: #353
-#345 := [unit-resolution #354 #361 #377]: #416
-[unit-resolution #345 #385]: false
-unsat
-34ccedc923aa27667e2d2f840ae4550b6d0b2c97 57 0
-#2 := false
-#14 := 1::Int
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#11 := f6
-decl f4 :: S2
-#8 := f4
-#12 := (f3 f4 f6)
-#17 := (+ #12 1::Int)
-decl f5 :: S3
-#9 := f5
-#10 := (f3 f4 f5)
-#16 := (+ #10 1::Int)
-#18 := (+ #16 #17)
-#13 := (+ #10 #12)
-#15 := (+ #13 1::Int)
-#19 := (< #15 #18)
-#20 := (not #19)
-#92 := (iff #20 false)
-#71 := 2::Int
-#72 := (+ 2::Int #13)
-#59 := (+ 1::Int #13)
-#77 := (< #59 #72)
-#80 := (not #77)
-#90 := (iff #80 false)
-#1 := true
-#84 := (not true)
-#88 := (iff #84 false)
-#89 := [rewrite]: #88
-#86 := (iff #80 #84)
-#83 := (iff #77 true)
-#85 := [rewrite]: #83
-#87 := [monotonicity #85]: #86
-#91 := [trans #87 #89]: #90
-#81 := (iff #20 #80)
-#78 := (iff #19 #77)
-#75 := (= #18 #72)
-#65 := (+ 1::Int #12)
-#62 := (+ 1::Int #10)
-#68 := (+ #62 #65)
-#73 := (= #68 #72)
-#74 := [rewrite]: #73
-#69 := (= #18 #68)
-#66 := (= #17 #65)
+#15 := (f5 f6 #14)
+#16 := (+ #15 #12)
+#17 := (f3 f4 #16)
+#20 := (= #17 #19)
+#21 := (not #20)
+#80 := (iff #21 #79)
+#77 := (iff #20 #76)
+#74 := (= #19 #71)
+#65 := (not #64)
+#68 := (if #65 f8 f7)
+#72 := (= #68 #71)
+#73 := [rewrite]: #72
+#69 := (= #19 #68)
+#66 := (iff #18 #65)
 #67 := [rewrite]: #66
-#63 := (= #16 #62)
-#64 := [rewrite]: #63
-#70 := [monotonicity #64 #67]: #69
-#76 := [trans #70 #74]: #75
-#60 := (= #15 #59)
-#61 := [rewrite]: #60
-#79 := [monotonicity #61 #76]: #78
-#82 := [monotonicity #79]: #81
-#93 := [trans #82 #91]: #92
-#58 := [asserted]: #20
-[mp #58 #93]: false
-unsat
-06547da4b6900b96251643835237282d4f034d2d 63 0
-#2 := false
+#70 := [monotonicity #67]: #69
+#75 := [trans #70 #73]: #74
+#62 := (= #17 #61)
+#59 := (= #16 #58)
+#56 := (= #15 #55)
+#53 := (= #14 #52)
+#50 := (= #13 #49)
+#51 := [rewrite]: #50
+#54 := [monotonicity #51]: #53
+#57 := [monotonicity #54]: #56
+#60 := [monotonicity #57]: #59
+#63 := [monotonicity #60]: #62
+#78 := [monotonicity #63 #75]: #77
+#81 := [monotonicity #78]: #80
+#40 := [asserted]: #21
+#82 := [mp #40 #81]: #79
+#157 := [mp #82 #156]: #152
+#475 := [unit-resolution #157 #474]: false
+#478 := [lemma #475]: #194
+#272 := (or #144 #279)
+#283 := [def-axiom]: #272
+#499 := [unit-resolution #283 #478]: #279
+#466 := (= #134 f8)
+#284 := (f3 f4 #12)
+#285 := (= #284 f8)
+#600 := (or #265 #285)
+#602 := [quant-inst #11]: #600
+#500 := [unit-resolution #602 #614]: #285
+#463 := (= #134 #284)
+#461 := (= #131 #12)
+#457 := (= #12 #131)
+#305 := (<= #55 0::Int)
+#228 := (= #55 0::Int)
+#591 := (or #144 #228)
+#36 := (= #31 0::Int)
+#173 := (or #161 #36)
+#622 := (forall (vars (?v0 Int)) (:pat #615) #173)
+#176 := (forall (vars (?v0 Int)) #173)
+#625 := (iff #176 #622)
+#623 := (iff #173 #173)
+#624 := [refl]: #623
+#626 := [quant-intro #624]: #625
+#190 := (~ #176 #176)
+#188 := (~ #173 #173)
+#189 := [refl]: #188
+#191 := [nnf-pos #189]: #190
+#104 := (or #29 #36)
+#109 := (forall (vars (?v0 Int)) #104)
+#177 := (iff #109 #176)
+#174 := (iff #104 #173)
+#175 := [monotonicity #162]: #174
+#178 := [quant-intro #175]: #177
+#35 := (< #28 0::Int)
+#37 := (implies #35 #36)
+#38 := (forall (vars (?v0 Int)) #37)
+#110 := (iff #38 #109)
+#107 := (iff #37 #104)
+#101 := (implies #87 #36)
+#105 := (iff #101 #104)
+#106 := [rewrite]: #105
+#102 := (iff #37 #101)
+#96 := (iff #35 #87)
+#98 := (iff #87 #87)
+#99 := [monotonicity #84]: #98
+#97 := [rewrite]: #96
+#100 := [trans #97 #99]: #96
+#103 := [monotonicity #100]: #102
+#108 := [trans #103 #106]: #107
+#111 := [quant-intro #108]: #110
+#43 := [asserted]: #38
+#112 := [mp #43 #111]: #109
+#179 := [mp #112 #178]: #176
+#192 := [mp~ #179 #191]: #176
+#627 := [mp #192 #626]: #622
+#234 := (not #622)
+#594 := (or #234 #144 #228)
+#592 := (or #234 #591)
+#581 := (iff #592 #594)
+#582 := [rewrite]: #581
+#595 := [quant-inst #49]: #592
+#304 := [mp #595 #582]: #594
+#485 := [unit-resolution #304 #627]: #591
+#491 := [unit-resolution #485 #478]: #228
+#479 := (not #228)
+#480 := (or #479 #305)
+#481 := [th-lemma arith triangle-eq]: #480
+#476 := [unit-resolution #481 #491]: #305
+#306 := (>= #55 0::Int)
+#482 := (or #479 #306)
+#455 := [th-lemma arith triangle-eq]: #482
+#456 := [unit-resolution #455 #491]: #306
+#350 := [th-lemma arith eq-propagate 1 1 #456 #476]: #457
+#462 := [symm #350]: #461
+#468 := [monotonicity #462]: #463
+#469 := [trans #468 #500]: #466
+#470 := [trans #469 #499]: #149
+[unit-resolution #157 #470]: false
+f4628a2370e422e0b0b89be90bd88f22cd742f4d 493 0
+unsat
+#2 := false
+#30 := 0::Int
 decl f5 :: (-> S4 S3 Int)
-#17 := (:var 0 S3)
+decl f3 :: (-> S2 Int S3)
+decl f8 :: S3
+#11 := f8
 decl f6 :: S4
-#9 := f6
-#18 := (f5 f6 #17)
-#644 := (pattern #18)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#8 := f4
+#8 := f6
+#12 := (f5 f6 f8)
+#50 := -1::Int
+#51 := (* -1::Int #12)
+decl f7 :: S3
+#9 := f7
+#10 := (f5 f6 f7)
+#52 := (+ #10 #51)
+decl f4 :: S2
+#7 := f4
+#55 := (f3 f4 #52)
+#58 := (f5 f6 #55)
+#604 := (* -1::Int #58)
+#610 := (+ #10 #51 #604)
+#609 := (= #610 0::Int)
+#455 := (not #609)
+#587 := (>= #610 0::Int)
+#330 := (not #587)
+decl f9 :: S3
+#16 := f9
+#17 := (f5 f6 f9)
+#64 := (* -1::Int #17)
+#83 := (+ #10 #51 #64)
+#548 := (>= #83 0::Int)
+#550 := (not #548)
+#90 := (f3 f4 #83)
+#148 := (+ #64 #58)
+#151 := (f3 f4 #148)
+#154 := (= #151 #90)
+#551 := (f5 f6 #90)
+#492 := (f3 f4 #551)
+#493 := (= #492 #90)
+#25 := (:var 0 S3)
+#26 := (f5 f6 #25)
+#611 := (pattern #26)
+#27 := (f3 f4 #26)
+#28 := (= #27 #25)
+#612 := (forall (vars (?v0 S3)) (:pat #611) #28)
+#29 := (forall (vars (?v0 S3)) #28)
+#615 := (iff #29 #612)
+#613 := (iff #28 #28)
+#614 := [refl]: #613
+#616 := [quant-intro #614]: #615
+#185 := (~ #29 #29)
+#160 := (~ #28 #28)
+#161 := [refl]: #160
+#186 := [nnf-pos #161]: #185
+#44 := [asserted]: #29
+#189 := [mp~ #44 #186]: #29
+#617 := [mp #189 #616]: #612
+#284 := (not #612)
+#441 := (or #284 #493)
+#442 := [quant-inst #90]: #441
+#410 := [unit-resolution #442 #617]: #493
+#423 := (= #151 #492)
+#335 := (= #148 #551)
+#436 := (* -1::Int #551)
+#395 := (+ #10 #51 #64 #436)
+#545 := (<= #395 0::Int)
+#435 := (= #395 0::Int)
+#381 := [hypothesis]: #548
+#445 := (or #550 #435)
+#31 := (:var 0 Int)
+#33 := (f3 f4 #31)
+#618 := (pattern #33)
+#34 := (f5 f6 #33)
+#35 := (= #34 #31)
+#164 := (>= #31 0::Int)
+#166 := (not #164)
+#169 := (or #166 #35)
+#619 := (forall (vars (?v0 Int)) (:pat #618) #169)
+#172 := (forall (vars (?v0 Int)) #169)
+#622 := (iff #172 #619)
+#620 := (iff #169 #169)
+#621 := [refl]: #620
+#623 := [quant-intro #621]: #622
+#184 := (~ #172 #172)
+#190 := (~ #169 #169)
+#183 := [refl]: #190
+#187 := [nnf-pos #183]: #184
+#32 := (<= 0::Int #31)
+#104 := (not #32)
+#105 := (or #104 #35)
+#109 := (forall (vars (?v0 Int)) #105)
+#173 := (iff #109 #172)
+#170 := (iff #105 #169)
+#167 := (iff #104 #166)
+#163 := (iff #32 #164)
+#165 := [rewrite]: #163
+#168 := [monotonicity #165]: #167
+#171 := [monotonicity #168]: #170
+#174 := [quant-intro #171]: #173
+#36 := (implies #32 #35)
+#37 := (forall (vars (?v0 Int)) #36)
+#110 := (iff #37 #109)
+#106 := (iff #36 #105)
+#107 := [rewrite]: #106
+#102 := (iff #36 #36)
+#100 := (iff #32 #32)
+#101 := [rewrite]: #100
+#103 := [monotonicity #101]: #102
+#108 := [trans #103 #107]: #106
+#111 := [quant-intro #108]: #110
+#45 := [asserted]: #37
+#112 := [mp #45 #111]: #109
+#175 := [mp #112 #174]: #172
+#188 := [mp~ #175 #187]: #172
+#624 := [mp #188 #623]: #619
+#261 := (not #619)
+#544 := (or #261 #550 #435)
+#549 := (= #551 #83)
+#552 := (or #550 #549)
+#429 := (or #261 #552)
+#450 := (iff #429 #544)
+#446 := (or #261 #445)
+#448 := (iff #446 #544)
+#449 := [rewrite]: #448
+#447 := (iff #429 #446)
+#540 := (iff #552 #445)
+#434 := (iff #549 #435)
+#543 := [rewrite]: #434
+#541 := [monotonicity #543]: #540
+#440 := [monotonicity #541]: #447
+#451 := [trans #440 #449]: #450
+#444 := [quant-inst #83]: #429
+#452 := [mp #444 #451]: #544
+#464 := [unit-resolution #452 #624]: #445
+#352 := [unit-resolution #464 #381]: #435
+#466 := (not #435)
+#399 := (or #466 #545)
+#400 := [th-lemma arith triangle-eq]: #399
+#354 := [unit-resolution #400 #352]: #545
+#542 := (>= #395 0::Int)
+#471 := (or #466 #542)
+#467 := [th-lemma arith triangle-eq]: #471
+#355 := [unit-resolution #467 #352]: #542
+#592 := (<= #610 0::Int)
+#392 := (>= #52 0::Int)
+#528 := (>= #551 0::Int)
+#358 := (not #545)
+#359 := (or #528 #358 #550)
+#363 := [th-lemma arith assign-bounds 1 -1]: #359
+#356 := [unit-resolution #363 #354 #381]: #528
+#473 := (not #542)
+#472 := (not #528)
+#360 := (or #392 #472 #473)
+#535 := (>= #17 0::Int)
+#380 := (= #17 0::Int)
+#196 := (f3 f4 #17)
+#527 := (f5 f6 #196)
+#529 := (= #527 0::Int)
+#387 := (not #535)
+#366 := [hypothesis]: #387
+#530 := (or #535 #529)
+#39 := (= #34 0::Int)
+#176 := (or #164 #39)
+#625 := (forall (vars (?v0 Int)) (:pat #618) #176)
+#179 := (forall (vars (?v0 Int)) #176)
+#628 := (iff #179 #625)
+#626 := (iff #176 #176)
+#627 := [refl]: #626
+#629 := [quant-intro #627]: #628
+#193 := (~ #179 #179)
+#191 := (~ #176 #176)
+#192 := [refl]: #191
+#194 := [nnf-pos #192]: #193
+#121 := (or #32 #39)
+#126 := (forall (vars (?v0 Int)) #121)
+#180 := (iff #126 #179)
+#177 := (iff #121 #176)
+#178 := [monotonicity #165]: #177
+#181 := [quant-intro #178]: #180
+#38 := (< #31 0::Int)
+#40 := (implies #38 #39)
+#41 := (forall (vars (?v0 Int)) #40)
+#127 := (iff #41 #126)
+#124 := (iff #40 #121)
+#118 := (implies #104 #39)
+#122 := (iff #118 #121)
+#123 := [rewrite]: #122
+#119 := (iff #40 #118)
+#113 := (iff #38 #104)
+#115 := (iff #104 #104)
+#116 := [monotonicity #101]: #115
+#114 := [rewrite]: #113
+#117 := [trans #114 #116]: #113
+#120 := [monotonicity #117]: #119
+#125 := [trans #120 #123]: #124
+#128 := [quant-intro #125]: #127
+#46 := [asserted]: #41
+#129 := [mp #46 #128]: #126
+#182 := [mp #129 #181]: #179
+#195 := [mp~ #182 #194]: #179
+#630 := [mp #195 #629]: #625
+#236 := (not #625)
+#532 := (or #236 #535 #529)
+#516 := (or #236 #530)
+#519 := (iff #516 #532)
+#520 := [rewrite]: #519
+#517 := [quant-inst #17]: #516
+#521 := [mp #517 #520]: #532
+#369 := [unit-resolution #521 #630]: #530
+#373 := [unit-resolution #369 #366]: #529
+#377 := (= #17 #527)
+#376 := (= f9 #196)
+#282 := (= #196 f9)
+#275 := (or #284 #282)
+#286 := [quant-inst #16]: #275
+#375 := [unit-resolution #286 #617]: #282
+#374 := [symm #375]: #376
+#365 := [monotonicity #374]: #377
+#368 := [trans #365 #373]: #380
+#370 := (not #380)
+#371 := (or #370 #535)
+#367 := [th-lemma arith triangle-eq]: #371
+#372 := [unit-resolution #367 #366 #368]: false
+#362 := [lemma #372]: #535
+#364 := (or #387 #392 #472 #473)
+#357 := [th-lemma arith assign-bounds 1 1 1]: #364
+#361 := [unit-resolution #357 #362]: #360
+#347 := [unit-resolution #361 #356 #355]: #392
+#599 := (not #392)
+#260 := (or #599 #609)
+#602 := (or #261 #599 #609)
+#606 := (= #58 #52)
+#607 := (or #599 #606)
+#245 := (or #261 #607)
+#589 := (iff #245 #602)
+#249 := (or #261 #260)
+#252 := (iff #249 #602)
+#588 := [rewrite]: #252
+#250 := (iff #245 #249)
+#265 := (iff #607 #260)
+#608 := (iff #606 #609)
+#600 := [rewrite]: #608
+#601 := [monotonicity #600]: #265
+#251 := [monotonicity #601]: #250
+#590 := [trans #251 #588]: #589
+#586 := [quant-inst #52]: #245
+#591 := [mp #586 #590]: #602
+#461 := [unit-resolution #591 #624]: #260
+#349 := [unit-resolution #461 #347]: #609
+#401 := (or #455 #592)
+#456 := [th-lemma arith triangle-eq]: #401
+#350 := [unit-resolution #456 #349]: #592
+#348 := (or #455 #587)
+#351 := [th-lemma arith triangle-eq]: #348
+#333 := [unit-resolution #351 #349]: #587
+#336 := [th-lemma arith eq-propagate 1 1 -1 -1 #333 #350 #355 #354]: #335
+#337 := [monotonicity #336]: #423
+#338 := [trans #337 #410]: #154
+#157 := (not #154)
+#65 := (+ #58 #64)
+#70 := (f3 f4 #65)
+#93 := (= #70 #90)
+#96 := (not #93)
+#158 := (iff #96 #157)
+#155 := (iff #93 #154)
+#152 := (= #70 #151)
+#149 := (= #65 #148)
+#150 := [rewrite]: #149
+#153 := [monotonicity #150]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#20 := (+ #12 #17)
+#21 := (- #10 #20)
+#22 := (f3 f4 #21)
+#13 := (- #10 #12)
+#14 := (f3 f4 #13)
+#15 := (f5 f6 #14)
+#18 := (- #15 #17)
 #19 := (f3 f4 #18)
-#70 := (= #17 #19)
-#645 := (forall (vars (?v0 S3)) (:pat #644) #70)
-#74 := (forall (vars (?v0 S3)) #70)
-#648 := (iff #74 #645)
-#646 := (iff #70 #70)
-#647 := [refl]: #646
-#649 := [quant-intro #647]: #648
-#168 := (~ #74 #74)
-#166 := (~ #70 #70)
-#167 := [refl]: #166
-#169 := [nnf-pos #167]: #168
-#20 := (= #19 #17)
-#21 := (forall (vars (?v0 S3)) #20)
-#75 := (iff #21 #74)
-#72 := (iff #20 #70)
-#73 := [rewrite]: #72
-#76 := [quant-intro #73]: #75
-#69 := [asserted]: #21
-#79 := [mp #69 #76]: #74
-#158 := [mp~ #79 #169]: #74
-#650 := [mp #158 #649]: #645
-decl f7 :: S3
-#10 := f7
-#11 := (f5 f6 f7)
-#55 := (f3 f4 #11)
-#61 := (= f7 #55)
-#66 := (not #61)
-#12 := 0::Int
-#13 := (+ #11 0::Int)
-#14 := (f3 f4 #13)
-#15 := (= #14 f7)
-#16 := (not #15)
-#67 := (iff #16 #66)
-#64 := (iff #15 #61)
-#58 := (= #55 f7)
-#62 := (iff #58 #61)
-#63 := [rewrite]: #62
-#59 := (iff #15 #58)
+#23 := (= #19 #22)
+#24 := (not #23)
+#97 := (iff #24 #96)
+#94 := (iff #23 #93)
+#91 := (= #22 #90)
+#88 := (= #21 #83)
+#73 := (* -1::Int #20)
+#74 := (+ #10 #73)
+#86 := (= #74 #83)
+#77 := (+ #51 #64)
+#80 := (+ #10 #77)
+#84 := (= #80 #83)
+#85 := [rewrite]: #84
+#81 := (= #74 #80)
+#78 := (= #73 #77)
+#79 := [rewrite]: #78
+#82 := [monotonicity #79]: #81
+#87 := [trans #82 #85]: #86
+#75 := (= #21 #74)
+#76 := [rewrite]: #75
+#89 := [trans #76 #87]: #88
+#92 := [monotonicity #89]: #91
+#71 := (= #19 #70)
+#68 := (= #18 #65)
+#61 := (- #58 #17)
+#66 := (= #61 #65)
+#67 := [rewrite]: #66
+#62 := (= #18 #61)
+#59 := (= #15 #58)
 #56 := (= #14 #55)
-#53 := (= #13 #11)
+#53 := (= #13 #52)
 #54 := [rewrite]: #53
 #57 := [monotonicity #54]: #56
 #60 := [monotonicity #57]: #59
-#65 := [trans #60 #63]: #64
-#68 := [monotonicity #65]: #67
-#52 := [asserted]: #16
-#71 := [mp #52 #68]: #66
-#229 := (not #645)
-#315 := (or #229 #61)
-#316 := [quant-inst #10]: #315
-[unit-resolution #316 #71 #650]: false
-unsat
-2e6c64dc1fed5f8593a680fedc292cfd0c92d82b 63 0
-#2 := false
-decl f5 :: (-> S4 S3 Int)
-#17 := (:var 0 S3)
-decl f6 :: S4
-#10 := f6
-#18 := (f5 f6 #17)
-#644 := (pattern #18)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#8 := f4
-#19 := (f3 f4 #18)
-#70 := (= #17 #19)
-#645 := (forall (vars (?v0 S3)) (:pat #644) #70)
-#74 := (forall (vars (?v0 S3)) #70)
-#648 := (iff #74 #645)
-#646 := (iff #70 #70)
-#647 := [refl]: #646
-#649 := [quant-intro #647]: #648
-#168 := (~ #74 #74)
-#166 := (~ #70 #70)
-#167 := [refl]: #166
-#169 := [nnf-pos #167]: #168
-#20 := (= #19 #17)
-#21 := (forall (vars (?v0 S3)) #20)
-#75 := (iff #21 #74)
-#72 := (iff #20 #70)
-#73 := [rewrite]: #72
-#76 := [quant-intro #73]: #75
-#69 := [asserted]: #21
-#79 := [mp #69 #76]: #74
-#158 := [mp~ #79 #169]: #74
-#650 := [mp #158 #649]: #645
-decl f7 :: S3
-#11 := f7
-#12 := (f5 f6 f7)
-#55 := (f3 f4 #12)
-#61 := (= f7 #55)
-#66 := (not #61)
-#9 := 0::Int
-#13 := (+ 0::Int #12)
-#14 := (f3 f4 #13)
-#15 := (= #14 f7)
-#16 := (not #15)
-#67 := (iff #16 #66)
-#64 := (iff #15 #61)
-#58 := (= #55 f7)
-#62 := (iff #58 #61)
-#63 := [rewrite]: #62
-#59 := (iff #15 #58)
-#56 := (= #14 #55)
-#53 := (= #13 #12)
-#54 := [rewrite]: #53
-#57 := [monotonicity #54]: #56
-#60 := [monotonicity #57]: #59
-#65 := [trans #60 #63]: #64
-#68 := [monotonicity #65]: #67
-#52 := [asserted]: #16
-#71 := [mp #52 #68]: #66
-#229 := (not #645)
-#315 := (or #229 #61)
-#316 := [quant-inst #11]: #315
-[unit-resolution #316 #71 #650]: false
-unsat
-37591ff5dbc8460fa182050d7f7cc90ee27bcacc 41 0
+#63 := [monotonicity #60]: #62
+#69 := [trans #63 #67]: #68
+#72 := [monotonicity #69]: #71
+#95 := [monotonicity #72 #92]: #94
+#98 := [monotonicity #95]: #97
+#43 := [asserted]: #24
+#99 := [mp #43 #98]: #96
+#162 := [mp #99 #159]: #157
+#339 := [unit-resolution #162 #338]: false
+#340 := [lemma #339]: #550
+#309 := (f5 f6 #151)
+#547 := (>= #309 0::Int)
+#580 := (+ #17 #604)
+#581 := (<= #580 0::Int)
+#546 := (= #551 0::Int)
+#479 := (not #546)
+#571 := (= #309 0::Int)
+#578 := (not #581)
+#484 := [hypothesis]: #578
+#413 := (or #581 #571)
+#557 := (or #236 #581 #571)
+#594 := (>= #148 0::Int)
+#412 := (or #594 #571)
+#558 := (or #236 #412)
+#562 := (iff #558 #557)
+#553 := (or #236 #413)
+#561 := (iff #553 #557)
+#555 := [rewrite]: #561
+#554 := (iff #558 #553)
+#414 := (iff #412 #413)
+#303 := (iff #594 #581)
+#304 := [rewrite]: #303
+#556 := [monotonicity #304]: #414
+#560 := [monotonicity #556]: #554
+#391 := [trans #560 #555]: #562
+#559 := [quant-inst #148]: #558
+#393 := [mp #559 #391]: #557
+#415 := [unit-resolution #393 #630]: #413
+#416 := [unit-resolution #415 #484]: #571
+#411 := (not #571)
+#427 := (or #479 #411)
+#507 := (f3 f4 #309)
+#421 := (= #507 #492)
+#417 := (= #492 #507)
+#454 := (= #551 #309)
+#453 := (= 0::Int #309)
+#478 := [hypothesis]: #571
+#433 := [symm #478]: #453
+#443 := [hypothesis]: #546
+#409 := [trans #443 #433]: #454
+#418 := [monotonicity #409]: #417
+#422 := [symm #418]: #421
+#419 := (= #151 #507)
+#497 := (= #507 #151)
+#488 := (or #284 #497)
+#494 := [quant-inst #151]: #488
+#477 := [unit-resolution #494 #617]: #497
+#420 := [symm #477]: #419
+#424 := [trans #420 #422]: #423
+#425 := [trans #424 #410]: #154
+#426 := [unit-resolution #162 #425]: false
+#388 := [lemma #426]: #427
+#389 := [unit-resolution #388 #416]: #479
+#533 := (or #548 #546)
+#524 := (or #236 #548 #546)
+#526 := (or #236 #533)
+#537 := (iff #526 #524)
+#538 := [rewrite]: #537
+#536 := [quant-inst #83]: #526
+#534 := [mp #536 #538]: #524
+#460 := [unit-resolution #534 #630]: #533
+#396 := [unit-resolution #460 #389]: #548
+#398 := [unit-resolution #464 #396]: #435
+#402 := [unit-resolution #400 #398]: #545
+#539 := (<= #551 0::Int)
+#432 := (or #539 #581)
+#308 := (>= #58 0::Int)
+#593 := (= #58 0::Int)
+#469 := (not #592)
+#480 := (not #539)
+#476 := [hypothesis]: #480
+#481 := (or #528 #539)
+#482 := [th-lemma arith farkas 1 1]: #481
+#483 := [unit-resolution #482 #476]: #528
+#485 := (or #479 #539)
+#458 := [th-lemma arith triangle-eq]: #485
+#459 := [unit-resolution #458 #476]: #479
+#353 := [unit-resolution #460 #459]: #548
+#465 := [unit-resolution #464 #353]: #435
+#468 := [unit-resolution #467 #465]: #542
+#474 := (or #469 #581 #472 #473)
+#470 := [th-lemma arith assign-bounds 1 1 -1]: #474
+#475 := [unit-resolution #470 #468 #484 #483]: #469
+#437 := [unit-resolution #456 #475]: #455
+#462 := [unit-resolution #461 #437]: #599
+#231 := (or #392 #593)
+#237 := (or #236 #392 #593)
+#597 := (or #236 #231)
+#598 := (iff #597 #237)
+#584 := [rewrite]: #598
+#595 := [quant-inst #52]: #597
+#585 := [mp #595 #584]: #237
+#457 := [unit-resolution #585 #630]: #231
+#463 := [unit-resolution #457 #462]: #593
+#431 := (not #593)
+#438 := (or #431 #308)
+#397 := [th-lemma arith triangle-eq]: #438
+#428 := [unit-resolution #397 #463]: #308
+#430 := [th-lemma arith farkas 1 1 1 1 1 #484 #462 #483 #468 #428]: false
+#439 := [lemma #430]: #432
+#403 := [unit-resolution #439 #484]: #539
+#404 := (or #546 #480 #472)
+#405 := [th-lemma arith triangle-eq]: #404
+#406 := [unit-resolution #405 #389 #403]: #472
+#407 := [th-lemma arith farkas 1 -1 1 #406 #396 #402]: false
+#390 := [lemma #407]: #581
+#583 := (+ #17 #604 #309)
+#565 := (>= #583 0::Int)
+#293 := (= #583 0::Int)
+#296 := (or #578 #293)
+#290 := (or #261 #578 #293)
+#310 := (= #309 #148)
+#596 := (not #594)
+#203 := (or #596 #310)
+#572 := (or #261 #203)
+#563 := (iff #572 #290)
+#573 := (or #261 #296)
+#567 := (iff #573 #290)
+#568 := [rewrite]: #567
+#577 := (iff #572 #573)
+#574 := (iff #203 #296)
+#294 := (iff #310 #293)
+#295 := [rewrite]: #294
+#582 := (iff #596 #578)
+#579 := [monotonicity #304]: #582
+#575 := [monotonicity #579 #295]: #574
+#566 := [monotonicity #575]: #577
+#564 := [trans #566 #568]: #563
+#576 := [quant-inst #148]: #572
+#569 := [mp #576 #564]: #290
+#341 := [unit-resolution #569 #624]: #296
+#342 := [unit-resolution #341 #390]: #293
+#343 := (not #293)
+#344 := (or #343 #565)
+#345 := [th-lemma arith triangle-eq]: #344
+#334 := [unit-resolution #345 #342]: #565
+#346 := (not #565)
+#323 := (or #547 #346 #578)
+#325 := [th-lemma arith assign-bounds 1 -1]: #323
+#326 := [unit-resolution #325 #334 #390]: #547
+#570 := (<= #583 0::Int)
+#327 := (or #343 #570)
+#328 := [th-lemma arith triangle-eq]: #327
+#329 := [unit-resolution #328 #342]: #570
+#324 := (not #570)
+#331 := (not #547)
+#332 := (or #330 #548 #331 #324)
+#317 := [th-lemma arith assign-bounds 1 1 -1]: #332
+#318 := [unit-resolution #317 #329 #326 #340]: #330
+#319 := [unit-resolution #351 #318]: #455
+#307 := (<= #58 0::Int)
+#315 := (not #307)
+#394 := (<= #309 0::Int)
+#322 := (not #394)
+#321 := [unit-resolution #460 #340]: #546
+#320 := [unit-resolution #388 #321]: #411
+#313 := (or #571 #322)
+#311 := (or #571 #322 #331)
+#312 := [th-lemma arith triangle-eq]: #311
+#305 := [unit-resolution #312 #326]: #313
+#314 := [unit-resolution #305 #320]: #322
+#306 := (or #315 #387 #394 #324)
+#316 := [th-lemma arith assign-bounds -1 -1 1]: #306
+#297 := [unit-resolution #316 #329 #314 #362]: #315
+#298 := (or #431 #307)
+#299 := [th-lemma arith triangle-eq]: #298
+#291 := [unit-resolution #299 #297]: #431
+#300 := [unit-resolution #457 #291]: #392
+[unit-resolution #461 #300 #319]: false
+9dcff463b5dde1dc69fdd0a078b0bc4466ce47fc 37 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int S3)
+#11 := 0::Int
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 0::Int)
+decl f5 :: (-> S4 S3 Int)
+decl f7 :: S3
+#9 := f7
+decl f6 :: S4
+#8 := f6
+#10 := (f5 f6 f7)
+#12 := (* #10 0::Int)
+#13 := (f3 f4 #12)
+#15 := (= #13 #14)
+#16 := (not #15)
+#56 := (iff #16 false)
+#1 := true
+#51 := (not true)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #16 #51)
+#49 := (iff #15 true)
+#44 := (= #14 #14)
+#47 := (iff #44 true)
+#48 := [rewrite]: #47
+#45 := (iff #15 #44)
+#41 := (= #12 0::Int)
+#42 := [rewrite]: #41
+#43 := [monotonicity #42]: #15
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#34 := [asserted]: #16
+[mp #34 #57]: false
+7af90292232e0f0b0c8c0c4509e0eab106814f00 37 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int S3)
+#8 := 0::Int
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 0::Int)
 decl f5 :: (-> S4 S3 Int)
 decl f7 :: S3
 #10 := f7
 decl f6 :: S4
 #9 := f6
 #11 := (f5 f6 f7)
-decl f8 :: S3
-#12 := f8
-#13 := (f5 f6 f8)
-#16 := (+ #13 #11)
-decl f4 :: S2
-#8 := f4
-#17 := (f3 f4 #16)
-#14 := (+ #11 #13)
-#15 := (f3 f4 #14)
-#18 := (= #15 #17)
-#19 := (not #18)
-#73 := (iff #19 false)
-#1 := true
-#68 := (not true)
-#71 := (iff #68 false)
-#72 := [rewrite]: #71
-#69 := (iff #19 #68)
-#66 := (iff #18 true)
-#61 := (= #15 #15)
-#64 := (iff #61 true)
-#65 := [rewrite]: #64
-#62 := (iff #18 #61)
-#59 := (= #17 #15)
-#57 := (= #16 #14)
-#58 := [rewrite]: #57
-#60 := [monotonicity #58]: #59
-#63 := [monotonicity #60]: #62
-#67 := [trans #63 #65]: #66
-#70 := [monotonicity #67]: #69
-#74 := [trans #70 #72]: #73
-#56 := [asserted]: #19
-[mp #56 #74]: false
-unsat
-cd71619977b1d23166ca99b7b8abcdf70eddab9e 46 0
-#2 := false
+#12 := (* 0::Int #11)
+#13 := (f3 f4 #12)
+#15 := (= #13 #14)
+#16 := (not #15)
+#56 := (iff #16 false)
+#1 := true
+#51 := (not true)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #16 #51)
+#49 := (iff #15 true)
+#44 := (= #14 #14)
+#47 := (iff #44 true)
+#48 := [rewrite]: #47
+#45 := (iff #15 #44)
+#41 := (= #12 0::Int)
+#42 := [rewrite]: #41
+#43 := [monotonicity #42]: #15
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#34 := [asserted]: #16
+[mp #34 #57]: false
+96ea1637fc28c7299348496b50b04624bb54bbca 51 0
+unsat
+#2 := false
+decl f5 :: (-> S4 S3 Int)
+#16 := (:var 0 S3)
+decl f6 :: S4
+#8 := f6
+#17 := (f5 f6 #16)
+#551 := (pattern #17)
 decl f3 :: (-> S2 Int S3)
+decl f4 :: S2
+#7 := f4
+#18 := (f3 f4 #17)
+#19 := (= #18 #16)
+#552 := (forall (vars (?v0 S3)) (:pat #551) #19)
+#20 := (forall (vars (?v0 S3)) #19)
+#555 := (iff #20 #552)
+#553 := (iff #19 #19)
+#554 := [refl]: #553
+#556 := [quant-intro #554]: #555
+#125 := (~ #20 #20)
+#129 := (~ #19 #19)
+#130 := [refl]: #129
+#126 := [nnf-pos #130]: #125
+#35 := [asserted]: #20
+#127 := [mp~ #35 #126]: #20
+#557 := [mp #127 #556]: #552
+decl f7 :: S3
+#9 := f7
+#10 := (f5 f6 f7)
+#43 := (f3 f4 #10)
+#46 := (= #43 f7)
+#49 := (not #46)
+#11 := 1::Int
+#12 := (* #10 1::Int)
+#13 := (f3 f4 #12)
+#14 := (= #13 f7)
+#15 := (not #14)
+#50 := (iff #15 #49)
+#47 := (iff #14 #46)
+#44 := (= #13 #43)
+#41 := (= #12 #10)
+#42 := [rewrite]: #41
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#51 := [monotonicity #48]: #50
+#34 := [asserted]: #15
+#52 := [mp #34 #51]: #49
+#222 := (not #552)
+#223 := (or #222 #46)
+#214 := [quant-inst #9]: #223
+[unit-resolution #214 #52 #557]: false
+7f2d30410f583c1a05e491b41f4eb605721a63ed 51 0
+unsat
+#2 := false
 decl f5 :: (-> S4 S3 Int)
-decl f9 :: S3
-#14 := f9
+#16 := (:var 0 S3)
 decl f6 :: S4
 #9 := f6
-#15 := (f5 f6 f9)
-decl f8 :: S3
-#12 := f8
-#13 := (f5 f6 f8)
+#17 := (f5 f6 #16)
+#551 := (pattern #17)
+decl f3 :: (-> S2 Int S3)
+decl f4 :: S2
+#7 := f4
+#18 := (f3 f4 #17)
+#19 := (= #18 #16)
+#552 := (forall (vars (?v0 S3)) (:pat #551) #19)
+#20 := (forall (vars (?v0 S3)) #19)
+#555 := (iff #20 #552)
+#553 := (iff #19 #19)
+#554 := [refl]: #553
+#556 := [quant-intro #554]: #555
+#125 := (~ #20 #20)
+#129 := (~ #19 #19)
+#130 := [refl]: #129
+#126 := [nnf-pos #130]: #125
+#35 := [asserted]: #20
+#127 := [mp~ #35 #126]: #20
+#557 := [mp #127 #556]: #552
 decl f7 :: S3
 #10 := f7
 #11 := (f5 f6 f7)
-#19 := (+ #11 #13)
-#20 := (+ #19 #15)
-decl f4 :: S2
-#8 := f4
-#21 := (f3 f4 #20)
-#16 := (+ #13 #15)
-#17 := (+ #11 #16)
-#18 := (f3 f4 #17)
-#22 := (= #18 #21)
-#23 := (not #22)
-#77 := (iff #23 false)
-#1 := true
-#72 := (not true)
-#75 := (iff #72 false)
-#76 := [rewrite]: #75
-#73 := (iff #23 #72)
-#70 := (iff #22 true)
-#65 := (= #18 #18)
-#68 := (iff #65 true)
-#69 := [rewrite]: #68
-#66 := (iff #22 #65)
-#63 := (= #21 #18)
-#61 := (= #20 #17)
-#62 := [rewrite]: #61
-#64 := [monotonicity #62]: #63
-#67 := [monotonicity #64]: #66
-#71 := [trans #67 #69]: #70
-#74 := [monotonicity #71]: #73
-#78 := [trans #74 #76]: #77
-#60 := [asserted]: #23
-[mp #60 #78]: false
-unsat
-813a6c8e0ab3abb6bf8ce17a0ae6b4b02be63190 465 0
-#2 := false
-#16 := 0::Int
+#43 := (f3 f4 #11)
+#46 := (= #43 f7)
+#49 := (not #46)
+#8 := 1::Int
+#12 := (* 1::Int #11)
+#13 := (f3 f4 #12)
+#14 := (= #13 f7)
+#15 := (not #14)
+#50 := (iff #15 #49)
+#47 := (iff #14 #46)
+#44 := (= #13 #43)
+#41 := (= #12 #11)
+#42 := [rewrite]: #41
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#51 := [monotonicity #48]: #50
+#34 := [asserted]: #15
+#52 := [mp #34 #51]: #49
+#222 := (not #552)
+#223 := (or #222 #46)
+#214 := [quant-inst #10]: #223
+[unit-resolution #214 #52 #557]: false
+0f3423719873455ea9f7115fd0d9b716e38c9561 39 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int S3)
+#8 := 3::Int
 decl f5 :: (-> S4 S3 Int)
 decl f7 :: S3
 #10 := f7
 decl f6 :: S4
 #9 := f6
 #11 := (f5 f6 f7)
-#475 := (= #11 0::Int)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#8 := f4
-#309 := (f3 f4 #11)
-#596 := (f5 f6 #309)
-#598 := (= #596 0::Int)
-decl f8 :: S3
-#12 := f8
-#13 := (f5 f6 f8)
-#647 := (f3 f4 #13)
-#488 := (f5 f6 #647)
-#496 := (= #488 0::Int)
-#595 := (>= #11 0::Int)
-#448 := (not #598)
-#452 := [hypothesis]: #448
-#597 := (or #595 #598)
-#29 := (:var 0 Int)
-#31 := (f3 f4 #29)
-#666 := (pattern #31)
-#91 := (>= #29 0::Int)
-#32 := (f5 f6 #31)
-#37 := (= #32 0::Int)
-#139 := (or #37 #91)
-#673 := (forall (vars (?v0 Int)) (:pat #666) #139)
-#144 := (forall (vars (?v0 Int)) #139)
-#676 := (iff #144 #673)
-#674 := (iff #139 #139)
-#675 := [refl]: #674
-#677 := [quant-intro #675]: #676
-#157 := (~ #144 #144)
-#165 := (~ #139 #139)
-#166 := [refl]: #165
-#158 := [nnf-pos #166]: #157
-#36 := (< #29 0::Int)
-#38 := (implies #36 #37)
-#39 := (forall (vars (?v0 Int)) #38)
-#147 := (iff #39 #144)
-#110 := (= 0::Int #32)
-#116 := (not #36)
-#117 := (or #116 #110)
-#122 := (forall (vars (?v0 Int)) #117)
-#145 := (iff #122 #144)
-#142 := (iff #117 #139)
-#136 := (or #91 #37)
-#140 := (iff #136 #139)
-#141 := [rewrite]: #140
-#137 := (iff #117 #136)
-#134 := (iff #110 #37)
-#135 := [rewrite]: #134
-#132 := (iff #116 #91)
-#92 := (not #91)
-#127 := (not #92)
-#130 := (iff #127 #91)
-#131 := [rewrite]: #130
-#128 := (iff #116 #127)
-#125 := (iff #36 #92)
-#126 := [rewrite]: #125
-#129 := [monotonicity #126]: #128
-#133 := [trans #129 #131]: #132
-#138 := [monotonicity #133 #135]: #137
-#143 := [trans #138 #141]: #142
-#146 := [quant-intro #143]: #145
-#123 := (iff #39 #122)
-#120 := (iff #38 #117)
-#113 := (implies #36 #110)
-#118 := (iff #113 #117)
-#119 := [rewrite]: #118
-#114 := (iff #38 #113)
-#111 := (iff #37 #110)
-#112 := [rewrite]: #111
-#115 := [monotonicity #112]: #114
-#121 := [trans #115 #119]: #120
-#124 := [quant-intro #121]: #123
-#148 := [trans #124 #146]: #147
-#109 := [asserted]: #39
-#149 := [mp #109 #148]: #144
-#167 := [mp~ #149 #158]: #144
-#678 := [mp #167 #677]: #673
-#356 := (not #673)
-#483 := (or #356 #595 #598)
-#599 := (or #598 #595)
-#484 := (or #356 #599)
-#477 := (iff #484 #483)
-#591 := (or #356 #597)
-#589 := (iff #591 #483)
-#592 := [rewrite]: #589
-#493 := (iff #484 #591)
-#600 := (iff #599 #597)
-#482 := [rewrite]: #600
-#588 := [monotonicity #482]: #493
-#492 := [trans #588 #592]: #477
-#443 := [quant-inst #11]: #484
-#494 := [mp #443 #492]: #483
-#453 := [unit-resolution #494 #678]: #597
-#454 := [unit-resolution #453 #452]: #595
-#520 := (not #595)
-#469 := (or #520 #496)
-#582 := (= #13 0::Int)
-#14 := (+ #11 #13)
-#15 := (f3 f4 #14)
-#648 := (f5 f6 #15)
-#649 := -1::Int
-#308 := (* -1::Int #648)
-#650 := (+ #13 #308)
-#292 := (+ #11 #650)
-#643 := (<= #292 0::Int)
-#634 := (= #292 0::Int)
-#656 := (>= #14 0::Int)
-#495 := (>= #13 0::Int)
-#526 := (not #496)
-#518 := [hypothesis]: #526
-#498 := (or #495 #496)
-#593 := (or #356 #495 #496)
-#497 := (or #496 #495)
-#590 := (or #356 #497)
-#584 := (iff #590 #593)
-#581 := (or #356 #498)
-#572 := (iff #581 #593)
-#574 := [rewrite]: #572
-#583 := (iff #590 #581)
-#499 := (iff #497 #498)
-#500 := [rewrite]: #499
-#575 := [monotonicity #500]: #583
-#585 := [trans #575 #574]: #584
-#594 := [quant-inst #13]: #590
-#586 := [mp #594 #585]: #593
-#523 := [unit-resolution #586 #678]: #498
-#503 := [unit-resolution #523 #518]: #495
-#532 := [hypothesis]: #595
-#449 := (not #495)
-#504 := (or #656 #520 #449)
-#485 := [th-lemma arith assign-bounds -1 -1]: #504
-#509 := [unit-resolution #485 #532 #503]: #656
-#657 := (not #656)
-#298 := (or #634 #657)
-#73 := (= #29 #32)
-#98 := (or #73 #92)
-#667 := (forall (vars (?v0 Int)) (:pat #666) #98)
-#103 := (forall (vars (?v0 Int)) #98)
-#670 := (iff #103 #667)
-#668 := (iff #98 #98)
-#669 := [refl]: #668
-#671 := [quant-intro #669]: #670
-#155 := (~ #103 #103)
-#154 := (~ #98 #98)
-#151 := [refl]: #154
-#156 := [nnf-pos #151]: #155
-#33 := (= #32 #29)
-#30 := (<= 0::Int #29)
-#34 := (implies #30 #33)
-#35 := (forall (vars (?v0 Int)) #34)
-#106 := (iff #35 #103)
-#80 := (not #30)
-#81 := (or #80 #73)
-#86 := (forall (vars (?v0 Int)) #81)
-#104 := (iff #86 #103)
-#101 := (iff #81 #98)
-#95 := (or #92 #73)
-#99 := (iff #95 #98)
-#100 := [rewrite]: #99
-#96 := (iff #81 #95)
-#93 := (iff #80 #92)
-#89 := (iff #30 #91)
-#90 := [rewrite]: #89
-#94 := [monotonicity #90]: #93
-#97 := [monotonicity #94]: #96
-#102 := [trans #97 #100]: #101
-#105 := [quant-intro #102]: #104
-#87 := (iff #35 #86)
-#84 := (iff #34 #81)
-#77 := (implies #30 #73)
-#82 := (iff #77 #81)
-#83 := [rewrite]: #82
-#78 := (iff #34 #77)
-#75 := (iff #33 #73)
-#76 := [rewrite]: #75
-#79 := [monotonicity #76]: #78
-#85 := [trans #79 #83]: #84
-#88 := [quant-intro #85]: #87
-#107 := [trans #88 #105]: #106
-#72 := [asserted]: #35
-#108 := [mp #72 #107]: #103
-#152 := [mp~ #108 #156]: #103
-#672 := [mp #152 #671]: #667
-#637 := (not #667)
-#638 := (or #637 #634 #657)
-#307 := (= #14 #648)
-#312 := (or #307 #657)
-#639 := (or #637 #312)
-#283 := (iff #639 #638)
-#635 := (or #637 #298)
-#642 := (iff #635 #638)
-#644 := [rewrite]: #642
-#641 := (iff #639 #635)
-#299 := (iff #312 #298)
-#296 := (iff #307 #634)
-#297 := [rewrite]: #296
-#636 := [monotonicity #297]: #299
-#278 := [monotonicity #636]: #641
-#284 := [trans #278 #644]: #283
-#640 := [quant-inst #14]: #639
-#645 := [mp #640 #284]: #638
-#510 := [unit-resolution #645 #672]: #298
-#505 := [unit-resolution #510 #509]: #634
-#511 := (not #634)
-#479 := (or #511 #643)
-#486 := [th-lemma arith triangle-eq]: #479
-#445 := [unit-resolution #486 #505]: #643
-#646 := (>= #292 0::Int)
-#352 := (<= #648 0::Int)
-#632 := (= #648 0::Int)
-#17 := (f3 f4 0::Int)
-#630 := (f5 f6 #17)
-#342 := (= #630 0::Int)
-#619 := (or #637 #342)
-#340 := (>= 0::Int 0::Int)
-#355 := (not #340)
-#627 := (= 0::Int #630)
-#631 := (or #627 #355)
-#460 := (or #637 #631)
-#462 := (iff #460 #619)
-#605 := (iff #619 #619)
-#606 := [rewrite]: #605
-#618 := (iff #631 #342)
-#615 := (or #342 false)
-#612 := (iff #615 #342)
-#617 := [rewrite]: #612
-#616 := (iff #631 #615)
-#625 := (iff #355 false)
-#1 := true
-#623 := (not true)
-#624 := (iff #623 false)
-#621 := [rewrite]: #624
-#337 := (iff #355 #623)
-#344 := (iff #340 true)
-#622 := [rewrite]: #344
-#620 := [monotonicity #622]: #337
-#614 := [trans #620 #621]: #625
-#341 := (iff #627 #342)
-#343 := [rewrite]: #341
-#611 := [monotonicity #343 #614]: #616
-#613 := [trans #611 #617]: #618
-#604 := [monotonicity #613]: #462
-#607 := [trans #604 #606]: #462
-#461 := [quant-inst #16]: #460
-#601 := [mp #461 #607]: #619
-#565 := [unit-resolution #601 #672]: #342
-#508 := (= #648 #630)
-#18 := (= #15 #17)
-#20 := (= f8 #17)
-#169 := (not #20)
-#19 := (= f7 #17)
-#168 := (not #19)
-#159 := (or #168 #169)
-#545 := (= #14 0::Int)
-#554 := (= #14 #630)
-#557 := (= #13 #630)
-#160 := (not #159)
-#580 := [hypothesis]: #160
-#244 := (or #159 #20)
-#330 := [def-axiom]: #244
-#567 := [unit-resolution #330 #580]: #20
-#558 := [monotonicity #567]: #557
-#552 := (= #14 #13)
-#576 := (= #11 #13)
-#566 := (= f7 f8)
-#568 := (= #17 f8)
-#569 := [symm #567]: #568
-#243 := (or #159 #19)
-#329 := [def-axiom]: #243
-#570 := [unit-resolution #329 #580]: #19
-#571 := [trans #570 #569]: #566
-#551 := [monotonicity #571]: #576
-#549 := (= #14 #11)
-#547 := (= #11 #14)
-#587 := (<= #13 0::Int)
-#560 := [trans #558 #565]: #582
-#561 := (not #582)
-#562 := (or #561 #587)
-#559 := [th-lemma arith triangle-eq]: #562
-#563 := [unit-resolution #559 #560]: #587
-#543 := (or #561 #495)
-#544 := [th-lemma arith triangle-eq]: #543
-#546 := [unit-resolution #544 #560]: #495
-#548 := [th-lemma arith eq-propagate -1 -1 #546 #563]: #547
-#550 := [symm #548]: #549
-#553 := [trans #550 #551]: #552
-#555 := [trans #553 #558]: #554
-#556 := [trans #555 #565]: #545
-#534 := [monotonicity #556]: #18
-#60 := (not #18)
-#651 := (or #60 #159)
-#180 := (iff #18 #159)
-#21 := (and #19 #20)
-#61 := (iff #21 #60)
-#183 := (iff #61 #180)
-#175 := (iff #159 #18)
-#181 := (iff #175 #180)
-#182 := [rewrite]: #181
-#178 := (iff #61 #175)
-#172 := (iff #160 #60)
-#176 := (iff #172 #175)
-#177 := [rewrite]: #176
-#173 := (iff #61 #172)
-#170 := (iff #21 #160)
-#171 := [rewrite]: #170
-#174 := [monotonicity #171]: #173
-#179 := [trans #174 #177]: #178
-#184 := [trans #179 #182]: #183
-#22 := (iff #18 #21)
-#23 := (not #22)
-#62 := (iff #23 #61)
-#63 := [rewrite]: #62
-#59 := [asserted]: #23
-#66 := [mp #59 #63]: #61
-#185 := [mp #66 #184]: #180
-#333 := (not #180)
-#336 := (or #60 #159 #333)
-#315 := [def-axiom]: #336
-#653 := [unit-resolution #315 #185]: #651
-#564 := [unit-resolution #653 #580]: #60
-#535 := [unit-resolution #564 #534]: false
-#537 := [lemma #535]: #159
-#335 := (or #18 #160)
-#334 := (or #18 #160 #333)
-#262 := [def-axiom]: #334
-#332 := [unit-resolution #262 #185]: #335
-#507 := [unit-resolution #332 #537]: #18
-#401 := [monotonicity #507]: #508
-#512 := [trans #401 #565]: #632
-#513 := (not #632)
-#514 := (or #513 #352)
-#519 := [th-lemma arith triangle-eq]: #514
-#515 := [unit-resolution #519 #512]: #352
-#476 := (not #352)
-#478 := (or #646 #520 #449 #476)
-#480 := [th-lemma arith assign-bounds -1 -1 1]: #478
-#487 := [unit-resolution #480 #532 #515 #503]: #646
-#626 := (>= #648 0::Int)
-#489 := (or #513 #626)
-#490 := [th-lemma arith triangle-eq]: #489
-#491 := [unit-resolution #490 #512]: #626
-#577 := (* -1::Int #13)
-#578 := (+ #11 #577)
-#531 := (<= #578 0::Int)
-#517 := (not #643)
-#501 := (or #531 #449 #476 #517)
-#481 := [th-lemma arith assign-bounds 1 -1/2 -1/2]: #501
-#502 := [unit-resolution #481 #445 #503 #515]: #531
-#573 := (>= #578 0::Int)
-#521 := (or #573 #517 #520)
-#527 := (not #573)
-#533 := [hypothesis]: #527
-#506 := [hypothesis]: #643
-#516 := [th-lemma arith farkas -1/2 -1/2 -1/2 1 #515 #506 #533 #532]: false
-#522 := [lemma #516]: #521
-#457 := [unit-resolution #522 #445 #532]: #573
-#458 := [th-lemma arith eq-propagate 1/2 1/2 -1/2 -1/2 -1/2 -1/2 #457 #502 #491 #515 #487 #445]: #582
-#465 := (= #488 #13)
-#463 := (= #647 f8)
-#320 := (= f8 #647)
-#24 := (:var 0 S3)
-#25 := (f5 f6 #24)
-#659 := (pattern #25)
-#26 := (f3 f4 #25)
-#65 := (= #24 #26)
-#660 := (forall (vars (?v0 S3)) (:pat #659) #65)
-#69 := (forall (vars (?v0 S3)) #65)
-#663 := (iff #69 #660)
-#661 := (iff #65 #65)
-#662 := [refl]: #661
-#664 := [quant-intro #662]: #663
-#163 := (~ #69 #69)
-#161 := (~ #65 #65)
-#162 := [refl]: #161
-#164 := [nnf-pos #162]: #163
-#27 := (= #26 #24)
-#28 := (forall (vars (?v0 S3)) #27)
-#70 := (iff #28 #69)
-#67 := (iff #27 #65)
-#68 := [rewrite]: #67
-#71 := [quant-intro #68]: #70
-#64 := [asserted]: #28
-#74 := [mp #64 #71]: #69
-#153 := [mp~ #74 #164]: #69
-#665 := [mp #153 #664]: #660
-#321 := (not #660)
-#652 := (or #321 #320)
-#658 := [quant-inst #12]: #652
-#539 := [unit-resolution #658 #665]: #320
-#464 := [symm #539]: #463
-#466 := [monotonicity #464]: #465
-#467 := [trans #466 #458]: #496
-#468 := [unit-resolution #518 #467]: false
-#470 := [lemma #468]: #469
-#455 := [unit-resolution #470 #454]: #496
-#424 := (= #596 #488)
-#540 := (= #13 #488)
-#541 := [monotonicity #539]: #540
-#421 := (= #596 #13)
-#438 := [trans #541 #455]: #582
-#456 := [unit-resolution #544 #438]: #495
-#426 := [unit-resolution #485 #456 #454]: #656
-#427 := [unit-resolution #510 #426]: #634
-#428 := [unit-resolution #486 #427]: #643
-#429 := [unit-resolution #481 #428 #456 #515]: #531
-#431 := [unit-resolution #522 #428 #454]: #573
-#432 := (not #531)
-#433 := (or #576 #432 #527)
-#275 := [th-lemma arith triangle-eq]: #433
-#434 := [unit-resolution #275 #431 #429]: #576
-#414 := (= #596 #11)
-#430 := (= #309 f7)
-#440 := (= f7 #309)
-#654 := (or #321 #440)
-#655 := [quant-inst #10]: #654
-#473 := [unit-resolution #655 #665]: #440
-#435 := [symm #473]: #430
-#417 := [monotonicity #435]: #414
-#423 := [trans #417 #434]: #421
-#422 := [trans #423 #541]: #424
-#425 := [trans #422 #455]: #598
-#413 := [unit-resolution #452 #425]: false
-#416 := [lemma #413]: #598
-#474 := (= #11 #596)
-#459 := [monotonicity #473]: #474
-#419 := [trans #459 #416]: #475
-#450 := (or #448 #19)
-#437 := (= #309 #17)
-#472 := [hypothesis]: #598
-#436 := [trans #459 #472]: #475
-#444 := [monotonicity #436]: #437
-#446 := [trans #473 #444]: #19
-#471 := [hypothesis]: #168
-#447 := [unit-resolution #471 #446]: false
-#451 := [lemma #447]: #450
-#415 := [unit-resolution #451 #416]: #19
-#331 := (or #160 #168 #169)
-#322 := [def-axiom]: #331
-#420 := [unit-resolution #322 #415 #537]: #169
-#529 := (or #526 #20)
-#542 := (= #647 #17)
-#538 := [hypothesis]: #496
-#536 := [trans #541 #538]: #582
-#528 := [monotonicity #536]: #542
-#524 := [trans #539 #528]: #20
-#579 := [hypothesis]: #169
-#525 := [unit-resolution #579 #524]: false
-#530 := [lemma #525]: #529
-#410 := [unit-resolution #530 #420]: #526
-#400 := [unit-resolution #470 #410]: #520
-#402 := (not #475)
-#403 := (or #402 #595)
-#406 := [th-lemma arith triangle-eq]: #403
-[unit-resolution #406 #400 #419]: false
-unsat
-c410ff5449a3f410ed451a7af1fea3b3810fa300 63 0
-#2 := false
-decl f5 :: (-> S4 S3 Int)
-#17 := (:var 0 S3)
-decl f6 :: S4
-#9 := f6
-#18 := (f5 f6 #17)
-#644 := (pattern #18)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#8 := f4
-#19 := (f3 f4 #18)
-#70 := (= #17 #19)
-#645 := (forall (vars (?v0 S3)) (:pat #644) #70)
-#74 := (forall (vars (?v0 S3)) #70)
-#648 := (iff #74 #645)
-#646 := (iff #70 #70)
-#647 := [refl]: #646
-#649 := [quant-intro #647]: #648
-#168 := (~ #74 #74)
-#166 := (~ #70 #70)
-#167 := [refl]: #166
-#169 := [nnf-pos #167]: #168
-#20 := (= #19 #17)
-#21 := (forall (vars (?v0 S3)) #20)
-#75 := (iff #21 #74)
-#72 := (iff #20 #70)
-#73 := [rewrite]: #72
-#76 := [quant-intro #73]: #75
-#69 := [asserted]: #21
-#79 := [mp #69 #76]: #74
-#158 := [mp~ #79 #169]: #74
-#650 := [mp #158 #649]: #645
-decl f7 :: S3
-#10 := f7
-#11 := (f5 f6 f7)
-#55 := (f3 f4 #11)
-#61 := (= f7 #55)
-#66 := (not #61)
-#12 := 0::Int
-#13 := (- #11 0::Int)
-#14 := (f3 f4 #13)
-#15 := (= #14 f7)
-#16 := (not #15)
-#67 := (iff #16 #66)
-#64 := (iff #15 #61)
-#58 := (= #55 f7)
-#62 := (iff #58 #61)
-#63 := [rewrite]: #62
-#59 := (iff #15 #58)
-#56 := (= #14 #55)
-#53 := (= #13 #11)
-#54 := [rewrite]: #53
-#57 := [monotonicity #54]: #56
-#60 := [monotonicity #57]: #59
-#65 := [trans #60 #63]: #64
-#68 := [monotonicity #65]: #67
-#52 := [asserted]: #16
-#71 := [mp #52 #68]: #66
-#229 := (not #645)
-#315 := (or #229 #61)
-#316 := [quant-inst #10]: #315
-[unit-resolution #316 #71 #650]: false
-unsat
-0deb4c7d00f3565760ed39501cec28af0e51f83b 199 0
-#2 := false
-decl f7 :: (-> S4 Int S3)
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#11 := f6
-decl f4 :: S2
-#8 := f4
-#12 := (f3 f4 f6)
-#58 := -1::Int
-#59 := (* -1::Int #12)
-decl f5 :: S3
-#9 := f5
-#10 := (f3 f4 f5)
-#60 := (+ #10 #59)
-decl f8 :: S4
-#14 := f8
-#63 := (f7 f8 #60)
-#17 := 0::Int
-#18 := (f7 f8 0::Int)
-#69 := (= #18 #63)
-#671 := (f3 f4 #63)
-#619 := (f7 f8 #671)
-#618 := (= #619 #63)
-#521 := (= #63 #619)
-#22 := (:var 0 S3)
-#23 := (f3 f4 #22)
-#687 := (pattern #23)
-#24 := (f7 f8 #23)
-#115 := (= #22 #24)
-#688 := (forall (vars (?v0 S3)) (:pat #687) #115)
-#118 := (forall (vars (?v0 S3)) #115)
-#691 := (iff #118 #688)
-#689 := (iff #115 #115)
-#690 := [refl]: #689
-#692 := [quant-intro #690]: #691
-#214 := (~ #118 #118)
-#212 := (~ #115 #115)
-#213 := [refl]: #212
-#215 := [nnf-pos #213]: #214
-#25 := (= #24 #22)
-#26 := (forall (vars (?v0 S3)) #25)
-#119 := (iff #26 #118)
-#116 := (iff #25 #115)
-#117 := [rewrite]: #116
-#120 := [quant-intro #117]: #119
-#114 := [asserted]: #26
-#123 := [mp #114 #120]: #118
-#204 := [mp~ #123 #215]: #118
-#693 := [mp #204 #692]: #688
-#360 := (not #688)
-#524 := (or #360 #521)
-#525 := [quant-inst #63]: #524
-#523 := [unit-resolution #525 #693]: #521
-#622 := [symm #523]: #618
-#528 := (= #18 #619)
-#526 := (= 0::Int #671)
-#644 := (= #671 0::Int)
-#27 := (:var 0 Int)
-#29 := (f7 f8 #27)
-#694 := (pattern #29)
-#139 := (>= #27 0::Int)
-#30 := (f3 f4 #29)
-#35 := (= #30 0::Int)
-#188 := (or #35 #139)
-#701 := (forall (vars (?v0 Int)) (:pat #694) #188)
-#193 := (forall (vars (?v0 Int)) #188)
-#704 := (iff #193 #701)
-#702 := (iff #188 #188)
-#703 := [refl]: #702
-#705 := [quant-intro #703]: #704
-#208 := (~ #193 #193)
-#200 := (~ #188 #188)
-#201 := [refl]: #200
-#209 := [nnf-pos #201]: #208
-#34 := (< #27 0::Int)
-#36 := (implies #34 #35)
-#37 := (forall (vars (?v0 Int)) #36)
-#196 := (iff #37 #193)
-#159 := (= 0::Int #30)
-#165 := (not #34)
-#166 := (or #165 #159)
-#171 := (forall (vars (?v0 Int)) #166)
-#194 := (iff #171 #193)
-#191 := (iff #166 #188)
-#185 := (or #139 #35)
-#189 := (iff #185 #188)
-#190 := [rewrite]: #189
-#186 := (iff #166 #185)
-#183 := (iff #159 #35)
-#184 := [rewrite]: #183
-#181 := (iff #165 #139)
-#141 := (not #139)
-#176 := (not #141)
-#179 := (iff #176 #139)
-#180 := [rewrite]: #179
-#177 := (iff #165 #176)
-#174 := (iff #34 #141)
-#175 := [rewrite]: #174
-#178 := [monotonicity #175]: #177
-#182 := [trans #178 #180]: #181
-#187 := [monotonicity #182 #184]: #186
-#192 := [trans #187 #190]: #191
-#195 := [quant-intro #192]: #194
-#172 := (iff #37 #171)
-#169 := (iff #36 #166)
-#162 := (implies #34 #159)
-#167 := (iff #162 #166)
-#168 := [rewrite]: #167
-#163 := (iff #36 #162)
-#160 := (iff #35 #159)
-#161 := [rewrite]: #160
-#164 := [monotonicity #161]: #163
-#170 := [trans #164 #168]: #169
-#173 := [quant-intro #170]: #172
-#197 := [trans #173 #195]: #196
-#158 := [asserted]: #37
-#198 := [mp #158 #197]: #193
-#216 := [mp~ #198 #209]: #193
-#706 := [mp #216 #705]: #701
-#87 := (>= #60 0::Int)
-#86 := (not #87)
-#100 := (or #69 #87)
-#105 := (not #100)
-#15 := (- #10 #12)
-#16 := (f7 f8 #15)
-#19 := (= #16 #18)
-#13 := (< #10 #12)
-#20 := (implies #13 #19)
-#21 := (not #20)
-#108 := (iff #21 #105)
-#77 := (not #13)
-#78 := (or #77 #69)
-#83 := (not #78)
-#106 := (iff #83 #105)
-#103 := (iff #78 #100)
-#97 := (or #87 #69)
-#101 := (iff #97 #100)
-#102 := [rewrite]: #101
-#98 := (iff #78 #97)
-#95 := (iff #77 #87)
-#90 := (not #86)
-#93 := (iff #90 #87)
-#94 := [rewrite]: #93
-#91 := (iff #77 #90)
-#88 := (iff #13 #86)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#96 := [trans #92 #94]: #95
-#99 := [monotonicity #96]: #98
-#104 := [trans #99 #102]: #103
-#107 := [monotonicity #104]: #106
-#84 := (iff #21 #83)
-#81 := (iff #20 #78)
-#74 := (implies #13 #69)
-#79 := (iff #74 #78)
-#80 := [rewrite]: #79
-#75 := (iff #20 #74)
-#72 := (iff #19 #69)
-#66 := (= #63 #18)
-#70 := (iff #66 #69)
-#71 := [rewrite]: #70
-#67 := (iff #19 #66)
-#64 := (= #16 #63)
-#61 := (= #15 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#68 := [monotonicity #65]: #67
-#73 := [trans #68 #71]: #72
-#76 := [monotonicity #73]: #75
-#82 := [trans #76 #80]: #81
-#85 := [monotonicity #82]: #84
-#109 := [trans #85 #107]: #108
-#57 := [asserted]: #21
-#110 := [mp #57 #109]: #105
-#113 := [not-or-elim #110]: #86
-#641 := (not #701)
-#647 := (or #641 #87 #644)
-#639 := (or #644 #87)
-#488 := (or #641 #639)
-#629 := (iff #488 #647)
-#640 := (or #87 #644)
-#490 := (or #641 #640)
-#634 := (iff #490 #647)
-#635 := [rewrite]: #634
-#632 := (iff #488 #490)
-#645 := (iff #639 #640)
-#646 := [rewrite]: #645
-#633 := [monotonicity #646]: #632
-#630 := [trans #633 #635]: #629
-#489 := [quant-inst #60]: #488
-#636 := [mp #489 #630]: #647
-#516 := [unit-resolution #636 #113 #706]: #644
-#527 := [symm #516]: #526
-#621 := [monotonicity #527]: #528
-#609 := [trans #621 #622]: #69
-#111 := (not #69)
-#112 := [not-or-elim #110]: #111
-[unit-resolution #112 #609]: false
-unsat
-0ecccf24805faeb34fe64234048355611a56c8f8 322 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-decl f5 :: (-> S4 S3 Int)
-decl f8 :: S3
-#12 := f8
-decl f6 :: S4
-#9 := f6
-#13 := (f5 f6 f8)
-#60 := -1::Int
-#61 := (* -1::Int #13)
-decl f7 :: S3
-#10 := f7
-#11 := (f5 f6 f7)
-#62 := (+ #11 #61)
-decl f4 :: S2
-#8 := f4
-#65 := (f3 f4 #62)
-#16 := 0::Int
-#17 := (f3 f4 0::Int)
-#71 := (= #17 #65)
-#648 := (f5 f6 #65)
-#550 := (f3 f4 #648)
-#479 := (= #550 #65)
-#551 := (= #65 #550)
-#24 := (:var 0 S3)
-#25 := (f5 f6 #24)
-#675 := (pattern #25)
-#26 := (f3 f4 #25)
-#103 := (= #24 #26)
-#676 := (forall (vars (?v0 S3)) (:pat #675) #103)
-#106 := (forall (vars (?v0 S3)) #103)
-#679 := (iff #106 #676)
-#677 := (iff #103 #103)
-#678 := [refl]: #677
-#680 := [quant-intro #678]: #679
-#202 := (~ #106 #106)
-#200 := (~ #103 #103)
-#201 := [refl]: #200
-#203 := [nnf-pos #201]: #202
-#27 := (= #26 #24)
-#28 := (forall (vars (?v0 S3)) #27)
-#107 := (iff #28 #106)
-#104 := (iff #27 #103)
-#105 := [rewrite]: #104
-#108 := [quant-intro #105]: #107
-#102 := [asserted]: #28
-#111 := [mp #102 #108]: #106
-#192 := [mp~ #111 #203]: #106
-#681 := [mp #192 #680]: #676
-#348 := (not #676)
-#531 := (or #348 #551)
-#532 := [quant-inst #65]: #531
-#522 := [unit-resolution #532 #681]: #551
-#480 := [symm #522]: #479
-#473 := (= #17 #550)
-#497 := (= 0::Int #648)
-#641 := (= #648 0::Int)
-#659 := (>= #62 0::Int)
-#662 := (not #659)
-#76 := (* -1::Int #11)
-#77 := (+ #76 #13)
-#80 := (f3 f4 #77)
-#620 := (f5 f6 #80)
-#600 := (<= #620 0::Int)
-#526 := (not #600)
-#510 := (= #620 0::Int)
-#548 := (not #510)
-#86 := (= #17 #80)
-#561 := (f3 f4 #620)
-#542 := (= #561 #80)
-#572 := (= #80 #561)
-#553 := (or #348 #572)
-#554 := [quant-inst #80]: #553
-#555 := [unit-resolution #554 #681]: #572
-#545 := [symm #555]: #542
-#540 := (= #17 #561)
-#558 := (= 0::Int #620)
-#556 := [hypothesis]: #510
-#544 := [symm #556]: #558
-#541 := [monotonicity #544]: #540
-#546 := [trans #541 #545]: #86
-#100 := (not #86)
-#91 := (or #71 #86)
-#94 := (not #91)
-#19 := (- #13 #11)
-#20 := (f3 f4 #19)
-#21 := (= #20 #17)
-#14 := (- #11 #13)
+#14 := (* #11 3::Int)
+decl f4 :: S2
+#7 := f4
 #15 := (f3 f4 #14)
-#18 := (= #15 #17)
-#22 := (or #18 #21)
-#23 := (not #22)
-#95 := (iff #23 #94)
-#92 := (iff #22 #91)
-#89 := (iff #21 #86)
-#83 := (= #80 #17)
-#87 := (iff #83 #86)
-#88 := [rewrite]: #87
-#84 := (iff #21 #83)
-#81 := (= #20 #80)
-#78 := (= #19 #77)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#85 := [monotonicity #82]: #84
-#90 := [trans #85 #88]: #89
-#74 := (iff #18 #71)
-#68 := (= #65 #17)
-#72 := (iff #68 #71)
-#73 := [rewrite]: #72
-#69 := (iff #18 #68)
-#66 := (= #15 #65)
-#63 := (= #14 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#70 := [monotonicity #67]: #69
-#75 := [trans #70 #73]: #74
-#93 := [monotonicity #75 #90]: #92
-#96 := [monotonicity #93]: #95
-#59 := [asserted]: #23
-#99 := [mp #59 #96]: #94
-#101 := [not-or-elim #99]: #100
-#547 := [unit-resolution #101 #546]: false
-#543 := [lemma #547]: #548
-#601 := (>= #620 0::Int)
-#624 := (+ #61 #620)
-#625 := (+ #11 #624)
-#508 := (>= #625 0::Int)
-#617 := (= #625 0::Int)
-#619 := (<= #62 0::Int)
-#504 := (or #510 #619)
-#29 := (:var 0 Int)
-#31 := (f3 f4 #29)
-#682 := (pattern #31)
-#127 := (>= #29 0::Int)
-#32 := (f5 f6 #31)
-#37 := (= #32 0::Int)
-#176 := (or #37 #127)
-#689 := (forall (vars (?v0 Int)) (:pat #682) #176)
-#181 := (forall (vars (?v0 Int)) #176)
-#692 := (iff #181 #689)
-#690 := (iff #176 #176)
-#691 := [refl]: #690
-#693 := [quant-intro #691]: #692
-#196 := (~ #181 #181)
-#188 := (~ #176 #176)
-#189 := [refl]: #188
-#197 := [nnf-pos #189]: #196
-#36 := (< #29 0::Int)
-#38 := (implies #36 #37)
-#39 := (forall (vars (?v0 Int)) #38)
-#184 := (iff #39 #181)
-#147 := (= 0::Int #32)
-#153 := (not #36)
-#154 := (or #153 #147)
-#159 := (forall (vars (?v0 Int)) #154)
-#182 := (iff #159 #181)
-#179 := (iff #154 #176)
-#173 := (or #127 #37)
-#177 := (iff #173 #176)
-#178 := [rewrite]: #177
-#174 := (iff #154 #173)
-#171 := (iff #147 #37)
-#172 := [rewrite]: #171
-#169 := (iff #153 #127)
-#129 := (not #127)
-#164 := (not #129)
-#167 := (iff #164 #127)
-#168 := [rewrite]: #167
-#165 := (iff #153 #164)
-#162 := (iff #36 #129)
-#163 := [rewrite]: #162
-#166 := [monotonicity #163]: #165
-#170 := [trans #166 #168]: #169
-#175 := [monotonicity #170 #172]: #174
-#180 := [trans #175 #178]: #179
-#183 := [quant-intro #180]: #182
-#160 := (iff #39 #159)
-#157 := (iff #38 #154)
-#150 := (implies #36 #147)
-#155 := (iff #150 #154)
-#156 := [rewrite]: #155
-#151 := (iff #38 #150)
-#148 := (iff #37 #147)
-#149 := [rewrite]: #148
-#152 := [monotonicity #149]: #151
-#158 := [trans #152 #156]: #157
-#161 := [quant-intro #158]: #160
-#185 := [trans #161 #183]: #184
-#146 := [asserted]: #39
-#186 := [mp #146 #185]: #181
-#204 := [mp~ #186 #197]: #181
-#694 := [mp #204 #693]: #689
-#627 := (not #689)
-#514 := (or #627 #510 #619)
-#631 := (>= #77 0::Int)
-#511 := (or #510 #631)
-#515 := (or #627 #511)
-#591 := (iff #515 #514)
-#609 := (or #627 #504)
-#597 := (iff #609 #514)
-#599 := [rewrite]: #597
-#606 := (iff #515 #609)
-#512 := (iff #511 #504)
-#626 := (iff #631 #619)
-#455 := [rewrite]: #626
-#513 := [monotonicity #455]: #512
-#610 := [monotonicity #513]: #606
-#588 := [trans #610 #599]: #591
-#516 := [quant-inst #77]: #515
-#590 := [mp #516 #588]: #514
-#523 := [unit-resolution #590 #694]: #504
-#533 := [unit-resolution #523 #543]: #619
-#457 := (not #619)
-#612 := (or #617 #457)
-#110 := (= #29 #32)
-#135 := (or #110 #129)
-#683 := (forall (vars (?v0 Int)) (:pat #682) #135)
-#140 := (forall (vars (?v0 Int)) #135)
-#686 := (iff #140 #683)
-#684 := (iff #135 #135)
-#685 := [refl]: #684
-#687 := [quant-intro #685]: #686
-#194 := (~ #140 #140)
-#193 := (~ #135 #135)
-#190 := [refl]: #193
-#195 := [nnf-pos #190]: #194
-#33 := (= #32 #29)
-#30 := (<= 0::Int #29)
-#34 := (implies #30 #33)
-#35 := (forall (vars (?v0 Int)) #34)
-#143 := (iff #35 #140)
-#117 := (not #30)
-#118 := (or #117 #110)
-#123 := (forall (vars (?v0 Int)) #118)
-#141 := (iff #123 #140)
-#138 := (iff #118 #135)
-#132 := (or #129 #110)
-#136 := (iff #132 #135)
-#137 := [rewrite]: #136
-#133 := (iff #118 #132)
-#130 := (iff #117 #129)
-#126 := (iff #30 #127)
-#128 := [rewrite]: #126
-#131 := [monotonicity #128]: #130
-#134 := [monotonicity #131]: #133
-#139 := [trans #134 #137]: #138
-#142 := [quant-intro #139]: #141
-#124 := (iff #35 #123)
-#121 := (iff #34 #118)
-#114 := (implies #30 #110)
-#119 := (iff #114 #118)
-#120 := [rewrite]: #119
-#115 := (iff #34 #114)
-#112 := (iff #33 #110)
-#113 := [rewrite]: #112
-#116 := [monotonicity #113]: #115
-#122 := [trans #116 #120]: #121
-#125 := [quant-intro #122]: #124
-#144 := [trans #125 #142]: #143
-#109 := [asserted]: #35
-#145 := [mp #109 #144]: #140
-#191 := [mp~ #145 #195]: #140
-#688 := [mp #191 #687]: #683
-#650 := (not #683)
-#613 := (or #650 #617 #457)
-#632 := (not #631)
-#621 := (= #77 #620)
-#622 := (or #621 #632)
-#616 := (or #650 #622)
-#604 := (iff #616 #613)
-#499 := (or #650 #612)
-#607 := (iff #499 #613)
-#509 := [rewrite]: #607
-#500 := (iff #616 #499)
-#614 := (iff #622 #612)
-#458 := (iff #632 #457)
-#611 := [monotonicity #455]: #458
-#623 := (iff #621 #617)
-#618 := [rewrite]: #623
-#615 := [monotonicity #618 #611]: #614
-#459 := [monotonicity #615]: #500
-#605 := [trans #459 #509]: #604
-#498 := [quant-inst #77]: #616
-#608 := [mp #498 #605]: #613
-#536 := [unit-resolution #608 #688]: #612
-#537 := [unit-resolution #536 #533]: #617
-#538 := (not #617)
-#534 := (or #538 #508)
-#539 := [th-lemma arith triangle-eq]: #534
-#519 := [unit-resolution #539 #537]: #508
-#465 := (not #508)
-#520 := (or #601 #465 #457)
-#501 := [th-lemma arith assign-bounds 1 -1]: #520
-#525 := [unit-resolution #501 #533 #519]: #601
-#521 := (not #601)
-#527 := (or #510 #526 #521)
-#495 := [th-lemma arith triangle-eq]: #527
-#502 := [unit-resolution #495 #525 #543]: #526
-#493 := (<= #625 0::Int)
-#461 := (or #538 #493)
-#492 := [th-lemma arith triangle-eq]: #461
-#494 := [unit-resolution #492 #537]: #493
-#496 := (not #493)
-#503 := (or #662 #600 #496)
-#505 := [th-lemma arith assign-bounds 1 -1]: #503
-#506 := [unit-resolution #505 #494 #502]: #662
-#630 := (or #641 #659)
-#628 := (or #627 #641 #659)
-#633 := (or #627 #630)
-#629 := (iff #633 #628)
-#635 := [rewrite]: #629
-#634 := [quant-inst #62]: #633
-#476 := [mp #634 #635]: #628
-#507 := [unit-resolution #476 #694]: #630
-#517 := [unit-resolution #507 #506]: #641
-#518 := [symm #517]: #497
-#474 := [monotonicity #518]: #473
-#481 := [trans #474 #480]: #71
-#97 := (not #71)
-#98 := [not-or-elim #99]: #97
-[unit-resolution #98 #481]: false
-unsat
-2040d7605c8194d6e392f4c62e64beaa6bc5c29d 332 0
-#2 := false
-decl f8 :: S3
-#12 := f8
-decl f7 :: S3
-#10 := f7
-#28 := 0::Int
-decl f5 :: (-> S4 S3 Int)
-decl f6 :: S4
-#9 := f6
-#13 := (f5 f6 f8)
-#60 := -1::Int
-#61 := (* -1::Int #13)
-#11 := (f5 f6 f7)
-#62 := (+ #11 #61)
-#94 := (>= #62 0::Int)
-#100 := (ite #94 f7 f8)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#8 := f4
-#65 := (f3 f4 #62)
-#68 := (f5 f6 #65)
-#74 := (+ #13 #68)
-#79 := (f3 f4 #74)
-#108 := (= #79 #100)
-#363 := (= f8 #100)
-#93 := (not #94)
-#277 := (= f7 #100)
-#594 := [hypothesis]: #94
-#278 := (or #93 #277)
-#364 := [def-axiom]: #278
-#595 := [unit-resolution #364 #594]: #277
-#512 := (= #79 f7)
-#296 := (f3 f4 #11)
-#538 := (= #296 f7)
-#369 := (= f7 #296)
-#23 := (:var 0 S3)
-#24 := (f5 f6 #23)
-#692 := (pattern #24)
-#25 := (f3 f4 #24)
-#120 := (= #23 #25)
-#693 := (forall (vars (?v0 S3)) (:pat #692) #120)
-#123 := (forall (vars (?v0 S3)) #120)
-#696 := (iff #123 #693)
-#694 := (iff #120 #120)
-#695 := [refl]: #694
-#697 := [quant-intro #695]: #696
-#217 := (~ #123 #123)
-#215 := (~ #120 #120)
-#216 := [refl]: #215
-#218 := [nnf-pos #216]: #217
-#26 := (= #25 #23)
-#27 := (forall (vars (?v0 S3)) #26)
-#124 := (iff #27 #123)
-#121 := (iff #26 #120)
-#122 := [rewrite]: #121
-#125 := [quant-intro #122]: #124
-#119 := [asserted]: #27
-#128 := [mp #119 #125]: #123
-#207 := [mp~ #128 #218]: #123
-#698 := [mp #207 #697]: #693
-#366 := (not #693)
-#343 := (or #366 #369)
-#473 := [quant-inst #10]: #343
-#585 := [unit-resolution #473 #698]: #369
-#544 := [symm #585]: #538
-#537 := (= #79 #296)
-#558 := (= #74 #11)
-#587 := (= #11 #74)
-#688 := (* -1::Int #68)
-#689 := (+ #61 #688)
-#690 := (+ #11 #689)
-#677 := (<= #690 0::Int)
-#685 := (= #690 0::Int)
-#342 := (or #93 #685)
-#29 := (:var 0 Int)
-#31 := (f3 f4 #29)
-#699 := (pattern #31)
-#144 := (>= #29 0::Int)
-#146 := (not #144)
-#32 := (f5 f6 #31)
-#127 := (= #29 #32)
-#152 := (or #127 #146)
-#700 := (forall (vars (?v0 Int)) (:pat #699) #152)
-#157 := (forall (vars (?v0 Int)) #152)
-#703 := (iff #157 #700)
-#701 := (iff #152 #152)
-#702 := [refl]: #701
-#704 := [quant-intro #702]: #703
-#209 := (~ #157 #157)
-#208 := (~ #152 #152)
-#205 := [refl]: #208
-#210 := [nnf-pos #205]: #209
-#33 := (= #32 #29)
-#30 := (<= 0::Int #29)
-#34 := (implies #30 #33)
-#35 := (forall (vars (?v0 Int)) #34)
-#160 := (iff #35 #157)
-#134 := (not #30)
-#135 := (or #134 #127)
-#140 := (forall (vars (?v0 Int)) #135)
-#158 := (iff #140 #157)
-#155 := (iff #135 #152)
-#149 := (or #146 #127)
-#153 := (iff #149 #152)
-#154 := [rewrite]: #153
-#150 := (iff #135 #149)
-#147 := (iff #134 #146)
-#143 := (iff #30 #144)
-#145 := [rewrite]: #143
-#148 := [monotonicity #145]: #147
-#151 := [monotonicity #148]: #150
-#156 := [trans #151 #154]: #155
-#159 := [quant-intro #156]: #158
-#141 := (iff #35 #140)
-#138 := (iff #34 #135)
-#131 := (implies #30 #127)
-#136 := (iff #131 #135)
-#137 := [rewrite]: #136
-#132 := (iff #34 #131)
-#129 := (iff #33 #127)
-#130 := [rewrite]: #129
-#133 := [monotonicity #130]: #132
-#139 := [trans #133 #137]: #138
-#142 := [quant-intro #139]: #141
-#161 := [trans #142 #159]: #160
-#126 := [asserted]: #35
-#162 := [mp #126 #161]: #157
-#206 := [mp~ #162 #210]: #157
-#705 := [mp #206 #704]: #700
-#331 := (not #700)
-#332 := (or #331 #93 #685)
-#680 := (= #62 #68)
-#354 := (or #680 #93)
-#333 := (or #331 #354)
-#674 := (iff #333 #332)
-#670 := (or #331 #342)
-#673 := (iff #670 #332)
-#668 := [rewrite]: #673
-#671 := (iff #333 #670)
-#667 := (iff #354 #342)
-#341 := (or #685 #93)
-#683 := (iff #341 #342)
-#326 := [rewrite]: #683
-#346 := (iff #354 #341)
-#691 := (iff #680 #685)
-#681 := [rewrite]: #691
-#682 := [monotonicity #681]: #346
-#330 := [trans #682 #326]: #667
-#672 := [monotonicity #330]: #671
-#312 := [trans #672 #668]: #674
-#669 := [quant-inst #62]: #333
-#675 := [mp #669 #312]: #332
-#552 := [unit-resolution #675 #705]: #342
-#548 := [unit-resolution #552 #594]: #685
-#549 := (not #685)
-#550 := (or #549 #677)
-#553 := [th-lemma arith triangle-eq]: #550
-#554 := [unit-resolution #553 #548]: #677
-#317 := (>= #690 0::Int)
-#555 := (or #549 #317)
-#551 := [th-lemma arith triangle-eq]: #555
-#556 := [unit-resolution #551 #548]: #317
-#536 := [th-lemma arith eq-propagate -1 -1 #556 #554]: #587
-#482 := [symm #536]: #558
-#518 := [monotonicity #482]: #537
-#519 := [trans #518 #544]: #512
-#478 := [trans #519 #595]: #108
-#113 := (not #108)
-#19 := (< #11 #13)
-#20 := (ite #19 f8 f7)
-#14 := (- #11 #13)
-#15 := (f3 f4 #14)
-#16 := (f5 f6 #15)
-#17 := (+ #16 #13)
-#18 := (f3 f4 #17)
-#21 := (= #18 #20)
-#22 := (not #21)
-#116 := (iff #22 #113)
-#85 := (= #20 #79)
-#90 := (not #85)
-#114 := (iff #90 #113)
-#111 := (iff #85 #108)
-#105 := (= #100 #79)
-#109 := (iff #105 #108)
-#110 := [rewrite]: #109
-#106 := (iff #85 #105)
-#103 := (= #20 #100)
-#97 := (ite #93 f8 f7)
-#101 := (= #97 #100)
-#102 := [rewrite]: #101
-#98 := (= #20 #97)
-#95 := (iff #19 #93)
-#96 := [rewrite]: #95
-#99 := [monotonicity #96]: #98
-#104 := [trans #99 #102]: #103
-#107 := [monotonicity #104]: #106
-#112 := [trans #107 #110]: #111
-#115 := [monotonicity #112]: #114
-#91 := (iff #22 #90)
-#88 := (iff #21 #85)
-#82 := (= #79 #20)
-#86 := (iff #82 #85)
-#87 := [rewrite]: #86
-#83 := (iff #21 #82)
-#80 := (= #18 #79)
-#77 := (= #17 #74)
-#71 := (+ #68 #13)
-#75 := (= #71 #74)
-#76 := [rewrite]: #75
-#72 := (= #17 #71)
-#69 := (= #16 #68)
-#66 := (= #15 #65)
-#63 := (= #14 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#70 := [monotonicity #67]: #69
-#73 := [monotonicity #70]: #72
-#78 := [trans #73 #76]: #77
-#81 := [monotonicity #78]: #80
-#84 := [monotonicity #81]: #83
-#89 := [trans #84 #87]: #88
-#92 := [monotonicity #89]: #91
-#117 := [trans #92 #115]: #116
-#59 := [asserted]: #22
-#118 := [mp #59 #117]: #113
-#509 := [unit-resolution #118 #478]: false
-#511 := [lemma #509]: #93
-#365 := (or #94 #363)
-#356 := [def-axiom]: #365
-#547 := [unit-resolution #356 #511]: #363
-#503 := (= #79 f8)
-#367 := (f3 f4 #13)
-#501 := (= #367 f8)
-#368 := (= f8 #367)
-#370 := (or #366 #368)
-#349 := [quant-inst #12]: #370
-#546 := [unit-resolution #349 #698]: #368
-#502 := [symm #546]: #501
-#497 := (= #79 #367)
-#491 := (= #74 #13)
-#535 := (= #13 #74)
-#660 := (<= #68 0::Int)
-#318 := (= #68 0::Int)
-#676 := (or #94 #318)
-#37 := (= #32 0::Int)
-#193 := (or #37 #144)
-#706 := (forall (vars (?v0 Int)) (:pat #699) #193)
-#198 := (forall (vars (?v0 Int)) #193)
-#709 := (iff #198 #706)
-#707 := (iff #193 #193)
-#708 := [refl]: #707
-#710 := [quant-intro #708]: #709
-#211 := (~ #198 #198)
-#219 := (~ #193 #193)
-#220 := [refl]: #219
-#212 := [nnf-pos #220]: #211
-#36 := (< #29 0::Int)
-#38 := (implies #36 #37)
-#39 := (forall (vars (?v0 Int)) #38)
-#201 := (iff #39 #198)
-#164 := (= 0::Int #32)
-#170 := (not #36)
-#171 := (or #170 #164)
-#176 := (forall (vars (?v0 Int)) #171)
-#199 := (iff #176 #198)
-#196 := (iff #171 #193)
-#190 := (or #144 #37)
-#194 := (iff #190 #193)
-#195 := [rewrite]: #194
-#191 := (iff #171 #190)
-#188 := (iff #164 #37)
-#189 := [rewrite]: #188
-#186 := (iff #170 #144)
-#181 := (not #146)
-#184 := (iff #181 #144)
-#185 := [rewrite]: #184
-#182 := (iff #170 #181)
-#179 := (iff #36 #146)
-#180 := [rewrite]: #179
-#183 := [monotonicity #180]: #182
-#187 := [trans #183 #185]: #186
-#192 := [monotonicity #187 #189]: #191
-#197 := [trans #192 #195]: #196
-#200 := [quant-intro #197]: #199
-#177 := (iff #39 #176)
-#174 := (iff #38 #171)
-#167 := (implies #36 #164)
-#172 := (iff #167 #171)
-#173 := [rewrite]: #172
-#168 := (iff #38 #167)
-#165 := (iff #37 #164)
-#166 := [rewrite]: #165
-#169 := [monotonicity #166]: #168
-#175 := [trans #169 #173]: #174
-#178 := [quant-intro #175]: #177
-#202 := [trans #178 #200]: #201
-#163 := [asserted]: #39
-#203 := [mp #163 #202]: #198
-#221 := [mp~ #203 #212]: #198
-#711 := [mp #221 #710]: #706
-#666 := (not #706)
-#388 := (or #666 #94 #318)
-#678 := (or #318 #94)
-#389 := (or #666 #678)
-#385 := (iff #389 #388)
-#391 := (or #666 #676)
-#662 := (iff #391 #388)
-#384 := [rewrite]: #662
-#284 := (iff #389 #391)
-#679 := (iff #678 #676)
-#665 := [rewrite]: #679
-#661 := [monotonicity #665]: #284
-#659 := [trans #661 #384]: #385
-#390 := [quant-inst #62]: #389
-#663 := [mp #390 #659]: #388
-#542 := [unit-resolution #663 #711]: #676
-#543 := [unit-resolution #542 #511]: #318
-#513 := (not #318)
-#520 := (or #513 #660)
-#522 := [th-lemma arith triangle-eq]: #520
-#523 := [unit-resolution #522 #543]: #660
-#664 := (>= #68 0::Int)
-#524 := (or #513 #664)
-#534 := [th-lemma arith triangle-eq]: #524
-#514 := [unit-resolution #534 #543]: #664
-#490 := [th-lemma arith eq-propagate 1 1 #514 #523]: #535
-#496 := [symm #490]: #491
-#498 := [monotonicity #496]: #497
-#504 := [trans #498 #502]: #503
-#505 := [trans #504 #547]: #108
-[unit-resolution #118 #505]: false
-unsat
-ec17b7c3a16edeb0d8d580fab6cc5b716941df1a 537 0
-#2 := false
-#31 := 0::Int
-decl f5 :: (-> S4 S3 Int)
-decl f3 :: (-> S2 Int S3)
-decl f8 :: S3
-#12 := f8
-decl f6 :: S4
-#9 := f6
-#13 := (f5 f6 f8)
-#63 := -1::Int
-#64 := (* -1::Int #13)
-decl f7 :: S3
-#10 := f7
-#11 := (f5 f6 f7)
-#65 := (+ #11 #64)
-decl f4 :: S2
-#8 := f4
-#68 := (f3 f4 #65)
-#71 := (f5 f6 #68)
-#669 := (* -1::Int #71)
-#670 := (+ #64 #669)
-#671 := (+ #11 #670)
-#666 := (= #671 0::Int)
-#468 := (not #666)
-#298 := (>= #671 0::Int)
-#318 := (not #298)
-decl f9 :: S3
-#17 := f9
-#18 := (f5 f6 f9)
-#77 := (* -1::Int #18)
-#86 := (+ #64 #77)
-#87 := (+ #11 #86)
-#508 := (>= #87 0::Int)
-#509 := (not #508)
-#90 := (f3 f4 #87)
-#78 := (+ #77 #71)
-#83 := (f3 f4 #78)
-#93 := (= #83 #90)
-#502 := (f5 f6 #90)
-#505 := (f3 f4 #502)
-#434 := (= #505 #90)
-#515 := (= #90 #505)
-#26 := (:var 0 S3)
-#27 := (f5 f6 #26)
-#673 := (pattern #27)
-#28 := (f3 f4 #27)
-#100 := (= #26 #28)
-#674 := (forall (vars (?v0 S3)) (:pat #673) #100)
-#104 := (forall (vars (?v0 S3)) #100)
-#677 := (iff #104 #674)
-#675 := (iff #100 #100)
-#676 := [refl]: #675
-#678 := [quant-intro #676]: #677
-#198 := (~ #104 #104)
-#196 := (~ #100 #100)
-#197 := [refl]: #196
-#199 := [nnf-pos #197]: #198
-#29 := (= #28 #26)
-#30 := (forall (vars (?v0 S3)) #29)
-#105 := (iff #30 #104)
-#102 := (iff #29 #100)
-#103 := [rewrite]: #102
-#106 := [quant-intro #103]: #105
-#99 := [asserted]: #30
-#109 := [mp #99 #106]: #104
-#188 := [mp~ #109 #199]: #104
-#679 := [mp #188 #678]: #674
-#346 := (not #674)
-#428 := (or #346 #515)
-#431 := [quant-inst #90]: #428
-#439 := [unit-resolution #431 #679]: #515
-#424 := [symm #439]: #434
-#414 := (= #83 #505)
-#331 := (= #78 #502)
-#512 := (* -1::Int #502)
-#513 := (+ #77 #512)
-#514 := (+ #64 #513)
-#607 := (+ #11 #514)
-#583 := (<= #607 0::Int)
-#604 := (= #607 0::Int)
-#405 := [hypothesis]: #508
-#588 := (or #509 #604)
-#32 := (:var 0 Int)
-#34 := (f3 f4 #32)
-#680 := (pattern #34)
-#125 := (>= #32 0::Int)
-#127 := (not #125)
-#35 := (f5 f6 #34)
-#108 := (= #32 #35)
-#133 := (or #108 #127)
-#681 := (forall (vars (?v0 Int)) (:pat #680) #133)
-#138 := (forall (vars (?v0 Int)) #133)
-#684 := (iff #138 #681)
-#682 := (iff #133 #133)
-#683 := [refl]: #682
-#685 := [quant-intro #683]: #684
-#190 := (~ #138 #138)
-#189 := (~ #133 #133)
-#186 := [refl]: #189
-#191 := [nnf-pos #186]: #190
-#36 := (= #35 #32)
-#33 := (<= 0::Int #32)
-#37 := (implies #33 #36)
-#38 := (forall (vars (?v0 Int)) #37)
-#141 := (iff #38 #138)
-#115 := (not #33)
-#116 := (or #115 #108)
-#121 := (forall (vars (?v0 Int)) #116)
-#139 := (iff #121 #138)
-#136 := (iff #116 #133)
-#130 := (or #127 #108)
-#134 := (iff #130 #133)
-#135 := [rewrite]: #134
-#131 := (iff #116 #130)
-#128 := (iff #115 #127)
-#124 := (iff #33 #125)
-#126 := [rewrite]: #124
-#129 := [monotonicity #126]: #128
-#132 := [monotonicity #129]: #131
-#137 := [trans #132 #135]: #136
-#140 := [quant-intro #137]: #139
-#122 := (iff #38 #121)
-#119 := (iff #37 #116)
-#112 := (implies #33 #108)
-#117 := (iff #112 #116)
-#118 := [rewrite]: #117
-#113 := (iff #37 #112)
-#110 := (iff #36 #108)
-#111 := [rewrite]: #110
-#114 := [monotonicity #111]: #113
-#120 := [trans #114 #118]: #119
-#123 := [quant-intro #120]: #122
-#142 := [trans #123 #140]: #141
-#107 := [asserted]: #38
-#143 := [mp #107 #142]: #138
-#187 := [mp~ #143 #191]: #138
-#686 := [mp #187 #685]: #681
-#312 := (not #681)
-#601 := (or #312 #509 #604)
-#510 := (= #87 #502)
-#511 := (or #510 #509)
-#590 := (or #312 #511)
-#579 := (iff #590 #601)
-#592 := (or #312 #588)
-#594 := (iff #592 #601)
-#578 := [rewrite]: #594
-#593 := (iff #590 #592)
-#600 := (iff #511 #588)
-#597 := (or #604 #509)
-#598 := (iff #597 #588)
-#599 := [rewrite]: #598
-#589 := (iff #511 #597)
-#608 := (iff #510 #604)
-#595 := [rewrite]: #608
-#586 := [monotonicity #595]: #589
-#596 := [trans #586 #599]: #600
-#587 := [monotonicity #596]: #593
-#581 := [trans #587 #578]: #579
-#591 := [quant-inst #87]: #590
-#582 := [mp #591 #581]: #601
-#473 := [unit-resolution #582 #686]: #588
-#384 := [unit-resolution #473 #405]: #604
-#450 := (not #604)
-#411 := (or #450 #583)
-#412 := [th-lemma arith triangle-eq]: #411
-#373 := [unit-resolution #412 #384]: #583
-#584 := (>= #607 0::Int)
-#451 := (or #450 #584)
-#458 := [th-lemma arith triangle-eq]: #451
-#374 := [unit-resolution #458 #384]: #584
-#658 := (<= #671 0::Int)
-#324 := (>= #65 0::Int)
-#566 := (>= #502 0::Int)
-#375 := (not #583)
-#367 := (or #566 #375 #509)
-#376 := [th-lemma arith assign-bounds 1 -1]: #367
-#377 := [unit-resolution #376 #373 #405]: #566
-#464 := (not #584)
-#462 := (not #566)
-#359 := (or #324 #462 #464)
-#567 := (>= #18 0::Int)
-#404 := (= #18 0::Int)
-#258 := (f3 f4 #18)
-#568 := (f5 f6 #258)
-#569 := (= #568 0::Int)
-#388 := (not #567)
-#389 := [hypothesis]: #388
-#570 := (or #567 #569)
-#40 := (= #35 0::Int)
-#174 := (or #40 #125)
-#687 := (forall (vars (?v0 Int)) (:pat #680) #174)
-#179 := (forall (vars (?v0 Int)) #174)
-#690 := (iff #179 #687)
-#688 := (iff #174 #174)
-#689 := [refl]: #688
-#691 := [quant-intro #689]: #690
-#192 := (~ #179 #179)
-#200 := (~ #174 #174)
-#201 := [refl]: #200
-#193 := [nnf-pos #201]: #192
-#39 := (< #32 0::Int)
-#41 := (implies #39 #40)
-#42 := (forall (vars (?v0 Int)) #41)
-#182 := (iff #42 #179)
-#145 := (= 0::Int #35)
-#151 := (not #39)
-#152 := (or #151 #145)
-#157 := (forall (vars (?v0 Int)) #152)
-#180 := (iff #157 #179)
-#177 := (iff #152 #174)
-#171 := (or #125 #40)
-#175 := (iff #171 #174)
-#176 := [rewrite]: #175
-#172 := (iff #152 #171)
-#169 := (iff #145 #40)
-#170 := [rewrite]: #169
-#167 := (iff #151 #125)
-#162 := (not #127)
-#165 := (iff #162 #125)
-#166 := [rewrite]: #165
-#163 := (iff #151 #162)
-#160 := (iff #39 #127)
-#161 := [rewrite]: #160
-#164 := [monotonicity #161]: #163
-#168 := [trans #164 #166]: #167
-#173 := [monotonicity #168 #170]: #172
-#178 := [trans #173 #176]: #177
-#181 := [quant-intro #178]: #180
-#158 := (iff #42 #157)
-#155 := (iff #41 #152)
-#148 := (implies #39 #145)
-#153 := (iff #148 #152)
-#154 := [rewrite]: #153
-#149 := (iff #41 #148)
-#146 := (iff #40 #145)
-#147 := [rewrite]: #146
-#150 := [monotonicity #147]: #149
-#156 := [trans #150 #154]: #155
-#159 := [quant-intro #156]: #158
-#183 := [trans #159 #181]: #182
-#144 := [asserted]: #42
-#184 := [mp #144 #183]: #179
-#202 := [mp~ #184 #193]: #179
-#692 := [mp #202 #691]: #687
-#646 := (not #687)
-#551 := (or #646 #567 #569)
-#559 := (or #569 #567)
-#552 := (or #646 #559)
-#538 := (iff #552 #551)
-#554 := (or #646 #570)
-#556 := (iff #554 #551)
-#542 := [rewrite]: #556
-#555 := (iff #552 #554)
-#548 := (iff #559 #570)
-#549 := [rewrite]: #548
-#550 := [monotonicity #549]: #555
-#539 := [trans #550 #542]: #538
-#553 := [quant-inst #18]: #552
-#540 := [mp #553 #539]: #551
-#390 := [unit-resolution #540 #692]: #570
-#391 := [unit-resolution #390 #389]: #569
-#393 := (= #18 #568)
-#344 := (= f9 #258)
-#337 := (or #346 #344)
-#348 := [quant-inst #17]: #337
-#392 := [unit-resolution #348 #679]: #344
-#386 := [monotonicity #392]: #393
-#394 := [trans #386 #391]: #404
-#379 := (not #404)
-#380 := (or #379 #567)
-#381 := [th-lemma arith triangle-eq]: #380
-#383 := [unit-resolution #381 #389 #394]: false
-#382 := [lemma #383]: #567
-#368 := (or #388 #324 #462 #464)
-#378 := [th-lemma arith assign-bounds 1 1 1]: #368
-#360 := [unit-resolution #378 #382]: #359
-#361 := [unit-resolution #360 #377 #374]: #324
-#454 := (not #324)
-#323 := (or #454 #666)
-#313 := (or #312 #454 #666)
-#336 := (= #65 #71)
-#668 := (or #336 #454)
-#314 := (or #312 #668)
-#655 := (iff #314 #313)
-#651 := (or #312 #323)
-#654 := (iff #651 #313)
-#649 := [rewrite]: #654
-#652 := (iff #314 #651)
-#648 := (iff #668 #323)
-#322 := (or #666 #454)
-#664 := (iff #322 #323)
-#307 := [rewrite]: #664
-#327 := (iff #668 #322)
-#672 := (iff #336 #666)
-#662 := [rewrite]: #672
-#663 := [monotonicity #662]: #327
-#311 := [trans #663 #307]: #648
-#653 := [monotonicity #311]: #652
-#293 := [trans #653 #649]: #655
-#650 := [quant-inst #65]: #314
-#656 := [mp #650 #293]: #313
-#440 := [unit-resolution #656 #686]: #323
-#353 := [unit-resolution #440 #361]: #666
-#469 := (or #468 #658)
-#452 := [th-lemma arith triangle-eq]: #469
-#362 := [unit-resolution #452 #353]: #658
-#363 := (or #468 #298)
-#354 := [th-lemma arith triangle-eq]: #363
-#364 := [unit-resolution #354 #353]: #298
-#333 := [th-lemma arith eq-propagate 1 1 -1 -1 #364 #362 #374 #373]: #331
-#334 := [monotonicity #333]: #414
-#325 := [trans #334 #424]: #93
-#96 := (not #93)
-#21 := (+ #13 #18)
-#22 := (- #11 #21)
-#23 := (f3 f4 #22)
-#14 := (- #11 #13)
-#15 := (f3 f4 #14)
-#16 := (f5 f6 #15)
-#19 := (- #16 #18)
-#20 := (f3 f4 #19)
-#24 := (= #20 #23)
-#25 := (not #24)
-#97 := (iff #25 #96)
-#94 := (iff #24 #93)
-#91 := (= #23 #90)
-#88 := (= #22 #87)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#84 := (= #20 #83)
-#81 := (= #19 #78)
-#74 := (- #71 #18)
-#79 := (= #74 #78)
-#80 := [rewrite]: #79
-#75 := (= #19 #74)
-#72 := (= #16 #71)
-#69 := (= #15 #68)
-#66 := (= #14 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73]: #75
-#82 := [trans #76 #80]: #81
-#85 := [monotonicity #82]: #84
-#95 := [monotonicity #85 #92]: #94
-#98 := [monotonicity #95]: #97
-#62 := [asserted]: #25
-#101 := [mp #62 #98]: #96
-#338 := [unit-resolution #101 #325]: false
-#339 := [lemma #338]: #509
-#365 := (f5 f6 #83)
-#506 := (>= #365 0::Int)
-#357 := (+ #18 #669)
-#358 := (<= #357 0::Int)
-#580 := (= #502 0::Int)
-#483 := (not #580)
-#623 := (= #365 0::Int)
-#352 := (not #358)
-#482 := [hypothesis]: #352
-#456 := (or #358 #623)
-#611 := (or #646 #358 #623)
-#657 := (>= #78 0::Int)
-#617 := (or #623 #657)
-#614 := (or #646 #617)
-#602 := (iff #614 #611)
-#497 := (or #646 #456)
-#605 := (iff #497 #611)
-#507 := [rewrite]: #605
-#498 := (iff #614 #497)
-#612 := (iff #617 #456)
-#624 := (or #623 #358)
-#609 := (iff #624 #456)
-#610 := [rewrite]: #609
-#453 := (iff #617 #624)
-#636 := (iff #657 #358)
-#637 := [rewrite]: #636
-#455 := [monotonicity #637]: #453
-#613 := [trans #455 #610]: #612
-#457 := [monotonicity #613]: #498
-#603 := [trans #457 #507]: #602
-#496 := [quant-inst #78]: #614
-#606 := [mp #496 #603]: #611
-#426 := [unit-resolution #606 #692]: #456
-#419 := [unit-resolution #426 #482]: #623
-#421 := (not #623)
-#425 := (or #483 #421)
-#500 := (f3 f4 #365)
-#433 := (= #500 #505)
-#430 := (= #505 #500)
-#438 := (= #502 #365)
-#435 := (= 0::Int #365)
-#477 := [hypothesis]: #623
-#437 := [symm #477]: #435
-#478 := [hypothesis]: #580
-#436 := [trans #478 #437]: #438
-#432 := [monotonicity #436]: #430
-#429 := [symm #432]: #433
-#459 := (= #83 #500)
-#495 := (or #346 #459)
-#516 := [quant-inst #83]: #495
-#427 := [unit-resolution #516 #679]: #459
-#416 := [trans #427 #429]: #414
-#417 := [trans #416 #424]: #93
-#420 := [unit-resolution #101 #417]: false
-#418 := [lemma #420]: #425
-#422 := [unit-resolution #418 #419]: #483
-#571 := (or #508 #580)
-#575 := (or #646 #508 #580)
-#585 := (or #580 #508)
-#576 := (or #646 #585)
-#562 := (iff #576 #575)
-#577 := (or #646 #571)
-#560 := (iff #577 #575)
-#561 := [rewrite]: #560
-#557 := (iff #576 #577)
-#572 := (iff #585 #571)
-#574 := [rewrite]: #572
-#558 := [monotonicity #574]: #557
-#563 := [trans #558 #561]: #562
-#573 := [quant-inst #87]: #576
-#564 := [mp #573 #563]: #575
-#487 := [unit-resolution #564 #692]: #571
-#423 := [unit-resolution #487 #422]: #508
-#409 := [unit-resolution #473 #423]: #604
-#410 := [unit-resolution #412 #409]: #583
-#565 := (<= #502 0::Int)
-#444 := (or #565 #358)
-#643 := (>= #71 0::Int)
-#299 := (= #71 0::Int)
-#461 := (not #658)
-#471 := (not #565)
-#472 := [hypothesis]: #471
-#479 := (or #566 #565)
-#480 := [th-lemma arith farkas 1 1]: #479
-#481 := [unit-resolution #480 #472]: #566
-#484 := (or #483 #565)
-#485 := [th-lemma arith triangle-eq]: #484
-#486 := [unit-resolution #485 #472]: #483
-#488 := [unit-resolution #487 #486]: #508
-#489 := [unit-resolution #473 #488]: #604
-#460 := [unit-resolution #458 #489]: #584
-#465 := (or #461 #358 #462 #464)
-#466 := [th-lemma arith assign-bounds 1 1 -1]: #465
-#467 := [unit-resolution #466 #460 #482 #481]: #461
-#470 := [unit-resolution #452 #467]: #468
-#441 := [unit-resolution #440 #470]: #454
-#659 := (or #299 #324)
-#647 := (or #646 #299 #324)
-#369 := (or #646 #659)
-#371 := (iff #369 #647)
-#372 := [rewrite]: #371
-#370 := [quant-inst #65]: #369
-#265 := [mp #370 #372]: #647
-#442 := [unit-resolution #265 #692]: #659
-#443 := [unit-resolution #442 #441]: #299
-#445 := (not #299)
-#446 := (or #445 #643)
-#447 := [th-lemma arith triangle-eq]: #446
-#290 := [unit-resolution #447 #443]: #643
-#448 := [th-lemma arith farkas 1 1 1 1 1 #482 #441 #481 #460 #290]: false
-#449 := [lemma #448]: #444
-#413 := [unit-resolution #449 #482]: #565
-#395 := (or #580 #471 #462)
-#397 := [th-lemma arith triangle-eq]: #395
-#398 := [unit-resolution #397 #422 #413]: #462
-#399 := [th-lemma arith farkas 1 -1 1 #398 #423 #410]: false
-#400 := [lemma #399]: #358
-#355 := (+ #669 #365)
-#356 := (+ #18 #355)
-#622 := (>= #356 0::Int)
-#641 := (= #356 0::Int)
-#629 := (or #352 #641)
-#632 := (or #312 #352 #641)
-#660 := (not #657)
-#366 := (= #78 #365)
-#640 := (or #366 #660)
-#627 := (or #312 #640)
-#620 := (iff #627 #632)
-#474 := (or #312 #629)
-#618 := (iff #474 #632)
-#619 := [rewrite]: #618
-#475 := (iff #627 #474)
-#626 := (iff #640 #629)
-#635 := (or #641 #352)
-#630 := (iff #635 #629)
-#625 := [rewrite]: #630
-#639 := (iff #640 #635)
-#634 := (iff #660 #352)
-#638 := [monotonicity #637]: #634
-#644 := (iff #366 #641)
-#645 := [rewrite]: #644
-#628 := [monotonicity #645 #638]: #639
-#631 := [trans #628 #625]: #626
-#476 := [monotonicity #631]: #475
-#621 := [trans #476 #619]: #620
-#633 := [quant-inst #78]: #627
-#615 := [mp #633 #621]: #632
-#340 := [unit-resolution #615 #686]: #629
-#341 := [unit-resolution #340 #400]: #641
-#342 := (not #641)
-#332 := (or #342 #622)
-#343 := [th-lemma arith triangle-eq]: #332
-#326 := [unit-resolution #343 #341]: #622
-#328 := (not #622)
-#329 := (or #506 #328 #352)
-#308 := [th-lemma arith assign-bounds 1 -1]: #329
-#310 := [unit-resolution #308 #326 #400]: #506
-#616 := (<= #356 0::Int)
-#315 := (or #342 #616)
-#316 := [th-lemma arith triangle-eq]: #315
-#317 := [unit-resolution #316 #341]: #616
-#320 := (not #616)
-#319 := (not #506)
-#309 := (or #318 #508 #319 #320)
-#321 := [th-lemma arith assign-bounds 1 1 -1]: #309
-#302 := [unit-resolution #321 #317 #310 #339]: #318
-#304 := [unit-resolution #354 #302]: #468
-#642 := (<= #71 0::Int)
-#301 := (not #642)
-#491 := (<= #365 0::Int)
-#306 := (not #491)
-#305 := [unit-resolution #487 #339]: #580
-#303 := [unit-resolution #418 #305]: #421
-#297 := (or #623 #306)
-#294 := (or #623 #306 #319)
-#296 := [th-lemma arith triangle-eq]: #294
-#300 := [unit-resolution #296 #310]: #297
-#295 := [unit-resolution #300 #303]: #306
-#275 := (or #301 #388 #491 #320)
-#280 := [th-lemma arith assign-bounds -1 -1 1]: #275
-#281 := [unit-resolution #280 #317 #295 #382]: #301
-#286 := (or #445 #642)
-#288 := [th-lemma arith triangle-eq]: #286
-#289 := [unit-resolution #288 #281]: #445
-#291 := [unit-resolution #442 #289]: #324
-[unit-resolution #440 #291 #304]: false
-unsat
-ab89ff5ea26d6edebe4b09181b1bc1f04912fd23 37 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#12 := 0::Int
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 0::Int)
-decl f5 :: (-> S4 S3 Int)
-decl f7 :: S3
-#10 := f7
-decl f6 :: S4
-#9 := f6
-#11 := (f5 f6 f7)
-#13 := (* #11 0::Int)
-#14 := (f3 f4 #13)
-#16 := (= #14 #15)
+#12 := (* 3::Int #11)
+#13 := (f3 f4 #12)
+#16 := (= #13 #15)
 #17 := (not #16)
-#69 := (iff #17 false)
-#1 := true
-#64 := (not true)
-#67 := (iff #64 false)
-#68 := [rewrite]: #67
-#65 := (iff #17 #64)
-#62 := (iff #16 true)
-#57 := (= #15 #15)
-#60 := (iff #57 true)
-#61 := [rewrite]: #60
-#58 := (iff #16 #57)
-#54 := (= #13 0::Int)
-#55 := [rewrite]: #54
-#56 := [monotonicity #55]: #16
-#59 := [monotonicity #56]: #58
-#63 := [trans #59 #61]: #62
-#66 := [monotonicity #63]: #65
-#70 := [trans #66 #68]: #69
-#53 := [asserted]: #17
-[mp #53 #70]: false
-unsat
-b41254f53c1c7293071acdd08e77aef8fc6b2a43 37 0
+#59 := (iff #17 false)
+#1 := true
+#54 := (not true)
+#57 := (iff #54 false)
+#58 := [rewrite]: #57
+#55 := (iff #17 #54)
+#52 := (iff #16 true)
+#47 := (= #13 #13)
+#50 := (iff #47 true)
+#51 := [rewrite]: #50
+#48 := (iff #16 #47)
+#45 := (= #15 #13)
+#43 := (= #14 #12)
+#44 := [rewrite]: #43
+#46 := [monotonicity #44]: #45
+#49 := [monotonicity #46]: #48
+#53 := [trans #49 #51]: #52
+#56 := [monotonicity #53]: #55
+#60 := [trans #56 #58]: #59
+#36 := [asserted]: #17
+[mp #36 #60]: false
+f8dca01b17d79b25cc840adcb38387a94d6a160a 262 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int S3)
 #9 := 0::Int
 decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 0::Int)
-decl f5 :: (-> S4 S3 Int)
-decl f7 :: S3
-#11 := f7
-decl f6 :: S4
-#10 := f6
-#12 := (f5 f6 f7)
-#13 := (* 0::Int #12)
-#14 := (f3 f4 #13)
-#16 := (= #14 #15)
-#17 := (not #16)
-#69 := (iff #17 false)
-#1 := true
-#64 := (not true)
-#67 := (iff #64 false)
-#68 := [rewrite]: #67
-#65 := (iff #17 #64)
-#62 := (iff #16 true)
-#57 := (= #15 #15)
-#60 := (iff #57 true)
-#61 := [rewrite]: #60
-#58 := (iff #16 #57)
-#54 := (= #13 0::Int)
-#55 := [rewrite]: #54
-#56 := [monotonicity #55]: #16
-#59 := [monotonicity #56]: #58
-#63 := [trans #59 #61]: #62
-#66 := [monotonicity #63]: #65
-#70 := [trans #66 #68]: #69
-#53 := [asserted]: #17
-[mp #53 #70]: false
-unsat
-cc02b658321764bb4d18c203df49b67755d56924 63 0
-#2 := false
-decl f5 :: (-> S4 S3 Int)
-#17 := (:var 0 S3)
-decl f6 :: S4
-#9 := f6
-#18 := (f5 f6 #17)
-#644 := (pattern #18)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#8 := f4
-#19 := (f3 f4 #18)
-#71 := (= #17 #19)
-#645 := (forall (vars (?v0 S3)) (:pat #644) #71)
-#75 := (forall (vars (?v0 S3)) #71)
-#648 := (iff #75 #645)
-#646 := (iff #71 #71)
-#647 := [refl]: #646
-#649 := [quant-intro #647]: #648
-#169 := (~ #75 #75)
-#167 := (~ #71 #71)
-#168 := [refl]: #167
-#170 := [nnf-pos #168]: #169
-#20 := (= #19 #17)
-#21 := (forall (vars (?v0 S3)) #20)
-#76 := (iff #21 #75)
-#73 := (iff #20 #71)
-#74 := [rewrite]: #73
-#77 := [quant-intro #74]: #76
-#70 := [asserted]: #21
-#80 := [mp #70 #77]: #75
-#159 := [mp~ #80 #170]: #75
-#650 := [mp #159 #649]: #645
-decl f7 :: S3
-#10 := f7
-#11 := (f5 f6 f7)
-#56 := (f3 f4 #11)
-#62 := (= f7 #56)
-#67 := (not #62)
-#12 := 1::Int
-#13 := (* #11 1::Int)
-#14 := (f3 f4 #13)
-#15 := (= #14 f7)
-#16 := (not #15)
-#68 := (iff #16 #67)
-#65 := (iff #15 #62)
-#59 := (= #56 f7)
-#63 := (iff #59 #62)
-#64 := [rewrite]: #63
-#60 := (iff #15 #59)
-#57 := (= #14 #56)
-#54 := (= #13 #11)
-#55 := [rewrite]: #54
-#58 := [monotonicity #55]: #57
-#61 := [monotonicity #58]: #60
-#66 := [trans #61 #64]: #65
-#69 := [monotonicity #66]: #68
-#53 := [asserted]: #16
-#72 := [mp #53 #69]: #67
-#230 := (not #645)
-#315 := (or #230 #62)
-#316 := [quant-inst #10]: #315
-[unit-resolution #316 #72 #650]: false
-unsat
-7e233a0f8e38e4c371798a2d4c4445220456e627 63 0
-#2 := false
-decl f5 :: (-> S4 S3 Int)
-#17 := (:var 0 S3)
-decl f6 :: S4
-#10 := f6
-#18 := (f5 f6 #17)
-#644 := (pattern #18)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#8 := f4
-#19 := (f3 f4 #18)
-#71 := (= #17 #19)
-#645 := (forall (vars (?v0 S3)) (:pat #644) #71)
-#75 := (forall (vars (?v0 S3)) #71)
-#648 := (iff #75 #645)
-#646 := (iff #71 #71)
-#647 := [refl]: #646
-#649 := [quant-intro #647]: #648
-#169 := (~ #75 #75)
-#167 := (~ #71 #71)
-#168 := [refl]: #167
-#170 := [nnf-pos #168]: #169
-#20 := (= #19 #17)
-#21 := (forall (vars (?v0 S3)) #20)
-#76 := (iff #21 #75)
-#73 := (iff #20 #71)
-#74 := [rewrite]: #73
-#77 := [quant-intro #74]: #76
-#70 := [asserted]: #21
-#80 := [mp #70 #77]: #75
-#159 := [mp~ #80 #170]: #75
-#650 := [mp #159 #649]: #645
-decl f7 :: S3
-#11 := f7
-#12 := (f5 f6 f7)
-#56 := (f3 f4 #12)
-#62 := (= f7 #56)
-#67 := (not #62)
-#9 := 1::Int
-#13 := (* 1::Int #12)
-#14 := (f3 f4 #13)
-#15 := (= #14 f7)
-#16 := (not #15)
-#68 := (iff #16 #67)
-#65 := (iff #15 #62)
-#59 := (= #56 f7)
-#63 := (iff #59 #62)
-#64 := [rewrite]: #63
-#60 := (iff #15 #59)
-#57 := (= #14 #56)
-#54 := (= #13 #12)
-#55 := [rewrite]: #54
-#58 := [monotonicity #55]: #57
-#61 := [monotonicity #58]: #60
-#66 := [trans #61 #64]: #65
-#69 := [monotonicity #66]: #68
-#53 := [asserted]: #16
-#72 := [mp #53 #69]: #67
-#230 := (not #645)
-#315 := (or #230 #62)
-#316 := [quant-inst #11]: #315
-[unit-resolution #316 #72 #650]: false
-unsat
-86a82c10cd25f6f1fdba21944f486b50661e3300 39 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#9 := 3::Int
-decl f5 :: (-> S4 S3 Int)
-decl f7 :: S3
-#11 := f7
-decl f6 :: S4
-#10 := f6
-#12 := (f5 f6 f7)
-#15 := (* #12 3::Int)
-decl f4 :: S2
-#8 := f4
-#16 := (f3 f4 #15)
-#13 := (* 3::Int #12)
-#14 := (f3 f4 #13)
-#17 := (= #14 #16)
-#18 := (not #17)
-#72 := (iff #18 false)
-#1 := true
-#67 := (not true)
-#70 := (iff #67 false)
-#71 := [rewrite]: #70
-#68 := (iff #18 #67)
-#65 := (iff #17 true)
-#60 := (= #14 #14)
-#63 := (iff #60 true)
-#64 := [rewrite]: #63
-#61 := (iff #17 #60)
-#58 := (= #16 #14)
-#56 := (= #15 #13)
-#57 := [rewrite]: #56
-#59 := [monotonicity #57]: #58
-#62 := [monotonicity #59]: #61
-#66 := [trans #62 #64]: #65
-#69 := [monotonicity #66]: #68
-#73 := [trans #69 #71]: #72
-#55 := [asserted]: #18
-[mp #55 #73]: false
-unsat
-d3aa3ddfc691a1e97ab763a8c849657ed90534ad 267 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#10 := 0::Int
-decl f4 :: S2
-#8 := f4
-#14 := (f3 f4 0::Int)
+#7 := f4
+#13 := (f3 f4 0::Int)
 decl f5 :: (-> S4 Int Int)
 decl f6 :: (-> S5 Int S4)
 decl f7 :: S5
-#9 := f7
-#11 := (f6 f7 0::Int)
-#12 := (f5 #11 0::Int)
+#8 := f7
+#10 := (f6 f7 0::Int)
+#11 := (f5 #10 0::Int)
+#12 := (f3 f4 #11)
+#14 := (= #12 #13)
+#462 := (= #11 0::Int)
+#22 := (:var 0 Int)
+#33 := (:var 1 Int)
+#34 := (f6 f7 #33)
+#35 := (f5 #34 #22)
+#789 := (pattern #35)
+#130 := -1::Int
+#134 := (* -1::Int #22)
+#131 := (* -1::Int #33)
+#137 := (div #131 #134)
+#328 := (* -1::Int #137)
+#329 := (+ #35 #328)
+#330 := (= #329 0::Int)
+#45 := (div #33 #22)
+#325 := (* -1::Int #45)
+#326 := (+ #35 #325)
+#327 := (= #326 0::Int)
+#108 := (<= #22 0::Int)
+#220 := (>= #33 0::Int)
+#288 := (or #220 #108)
+#289 := (not #288)
+#104 := (<= #33 0::Int)
+#284 := (or #104 #108)
+#285 := (not #284)
+#292 := (or #285 #289)
+#331 := (if #292 #327 #330)
+#324 := (= #35 0::Int)
+#37 := (= #22 0::Int)
+#36 := (= #33 0::Int)
+#38 := (or #36 #37)
+#332 := (if #38 #324 #331)
+#790 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #789) #332)
+#335 := (forall (vars (?v0 Int) (?v1 Int)) #332)
+#793 := (iff #335 #790)
+#791 := (iff #332 #332)
+#792 := [refl]: #791
+#794 := [quant-intro #792]: #793
+#295 := (if #292 #45 #137)
+#298 := (if #38 0::Int #295)
+#301 := (= #35 #298)
+#304 := (forall (vars (?v0 Int) (?v1 Int)) #301)
+#336 := (iff #304 #335)
+#333 := (iff #301 #332)
+#334 := [rewrite]: #333
+#337 := [quant-intro #334]: #336
+#109 := (not #108)
+#223 := (not #220)
+#226 := (and #223 #109)
+#105 := (not #104)
+#112 := (and #105 #109)
+#229 := (or #112 #226)
+#232 := (if #229 #45 #137)
+#235 := (if #38 0::Int #232)
+#238 := (= #35 #235)
+#241 := (forall (vars (?v0 Int) (?v1 Int)) #238)
+#305 := (iff #241 #304)
+#302 := (iff #238 #301)
+#299 := (= #235 #298)
+#296 := (= #232 #295)
+#293 := (iff #229 #292)
+#290 := (iff #226 #289)
+#291 := [rewrite]: #290
+#286 := (iff #112 #285)
+#287 := [rewrite]: #286
+#294 := [monotonicity #287 #291]: #293
+#297 := [monotonicity #294]: #296
+#300 := [monotonicity #297]: #299
+#303 := [monotonicity #300]: #302
+#306 := [quant-intro #303]: #305
+#276 := (~ #241 #241)
+#274 := (~ #238 #238)
+#275 := [refl]: #274
+#277 := [nnf-pos #275]: #276
+#115 := (<= 0::Int #33)
+#116 := (not #115)
+#124 := (and #116 #109)
+#127 := (or #112 #124)
+#140 := (if #127 #45 #137)
+#143 := (if #38 0::Int #140)
+#146 := (= #35 #143)
+#149 := (forall (vars (?v0 Int) (?v1 Int)) #146)
+#242 := (iff #149 #241)
+#239 := (iff #146 #238)
+#236 := (= #143 #235)
+#233 := (= #140 #232)
+#230 := (iff #127 #229)
+#227 := (iff #124 #226)
+#224 := (iff #116 #223)
+#221 := (iff #115 #220)
+#222 := [rewrite]: #221
+#225 := [monotonicity #222]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [monotonicity #234]: #236
+#240 := [monotonicity #237]: #239
+#243 := [quant-intro #240]: #242
+#47 := (- #22)
+#46 := (- #33)
+#48 := (div #46 #47)
+#40 := (< 0::Int #22)
+#42 := (< #33 0::Int)
+#43 := (and #42 #40)
+#39 := (< 0::Int #33)
+#41 := (and #39 #40)
+#44 := (or #41 #43)
+#49 := (if #44 #45 #48)
+#50 := (if #38 0::Int #49)
+#51 := (= #35 #50)
+#52 := (forall (vars (?v0 Int) (?v1 Int)) #51)
+#150 := (iff #52 #149)
+#147 := (iff #51 #146)
+#144 := (= #50 #143)
+#141 := (= #49 #140)
+#138 := (= #48 #137)
+#135 := (= #47 #134)
+#136 := [rewrite]: #135
+#132 := (= #46 #131)
+#133 := [rewrite]: #132
+#139 := [monotonicity #133 #136]: #138
+#128 := (iff #44 #127)
+#125 := (iff #43 #124)
+#110 := (iff #40 #109)
+#111 := [rewrite]: #110
+#117 := (iff #42 #116)
+#121 := (iff #116 #116)
+#119 := (iff #115 #115)
+#120 := [rewrite]: #119
+#122 := [monotonicity #120]: #121
+#118 := [rewrite]: #117
+#123 := [trans #118 #122]: #117
+#126 := [monotonicity #123 #111]: #125
+#113 := (iff #41 #112)
+#106 := (iff #39 #105)
+#107 := [rewrite]: #106
+#114 := [monotonicity #107 #111]: #113
+#129 := [monotonicity #114 #126]: #128
+#142 := [monotonicity #129 #139]: #141
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#151 := [quant-intro #148]: #150
+#69 := [asserted]: #52
+#152 := [mp #69 #151]: #149
+#244 := [mp #152 #243]: #241
+#278 := [mp~ #244 #277]: #241
+#307 := [mp #278 #306]: #304
+#338 := [mp #307 #337]: #335
+#795 := [mp #338 #794]: #790
+#696 := (not #790)
+#692 := (or #696 #462)
+#448 := (* -1::Int 0::Int)
+#730 := (div #448 #448)
+#734 := (* -1::Int #730)
+#731 := (+ #11 #734)
+#735 := (= #731 0::Int)
+#453 := (div 0::Int 0::Int)
+#454 := (* -1::Int #453)
+#732 := (+ #11 #454)
+#733 := (= #732 0::Int)
+#736 := (<= 0::Int 0::Int)
+#550 := (>= 0::Int 0::Int)
+#741 := (or #550 #736)
+#451 := (not #741)
+#740 := (or #736 #736)
+#737 := (not #740)
+#452 := (or #737 #451)
+#724 := (if #452 #733 #735)
+#739 := (= 0::Int 0::Int)
+#461 := (or #739 #739)
+#725 := (if #461 #462 #724)
+#697 := (or #696 #725)
+#687 := (iff #697 #692)
+#689 := (iff #692 #692)
+#683 := [rewrite]: #689
+#694 := (iff #725 #462)
+#1 := true
+#691 := (if true #462 #733)
+#682 := (iff #691 #462)
+#684 := [rewrite]: #682
+#693 := (iff #725 #691)
+#700 := (iff #724 #733)
+#607 := (if false #733 #733)
+#610 := (iff #607 #733)
+#703 := [rewrite]: #610
+#608 := (iff #724 #607)
+#598 := (iff #735 #733)
+#604 := (= #731 #732)
+#587 := (= #734 #454)
+#699 := (= #730 #453)
+#603 := (= #448 0::Int)
+#698 := [rewrite]: #603
+#702 := [monotonicity #698 #698]: #699
+#602 := [monotonicity #702]: #587
+#605 := [monotonicity #602]: #604
+#606 := [monotonicity #605]: #598
+#553 := (iff #452 false)
+#707 := (or false false)
+#593 := (iff #707 false)
+#594 := [rewrite]: #593
+#710 := (iff #452 #707)
+#708 := (iff #451 false)
+#419 := (not true)
+#744 := (iff #419 false)
+#407 := [rewrite]: #744
+#705 := (iff #451 #419)
+#551 := (iff #741 true)
+#722 := (or true true)
+#723 := (iff #722 true)
+#729 := [rewrite]: #723
+#720 := (iff #741 #722)
+#572 := (iff #736 true)
+#714 := [rewrite]: #572
+#423 := (iff #550 true)
+#759 := [rewrite]: #423
+#549 := [monotonicity #759 #714]: #720
+#552 := [trans #549 #729]: #551
+#706 := [monotonicity #552]: #705
+#709 := [trans #706 #407]: #708
+#719 := (iff #737 false)
+#712 := (iff #737 #419)
+#717 := (iff #740 true)
+#715 := (iff #740 #722)
+#716 := [monotonicity #714 #714]: #715
+#711 := [trans #716 #729]: #717
+#718 := [monotonicity #711]: #712
+#713 := [trans #718 #407]: #719
+#592 := [monotonicity #713 #709]: #710
+#701 := [trans #592 #594]: #553
+#609 := [monotonicity #701 #606]: #608
+#704 := [trans #609 #703]: #700
+#570 := (iff #461 true)
+#727 := (iff #461 #722)
+#726 := (iff #739 true)
+#721 := [rewrite]: #726
+#728 := [monotonicity #721 #721]: #727
+#571 := [trans #728 #729]: #570
+#685 := [monotonicity #571 #704]: #693
+#695 := [trans #685 #684]: #694
+#688 := [monotonicity #695]: #687
+#690 := [trans #688 #683]: #687
+#686 := [quant-inst #9 #9]: #697
+#674 := [mp #686 #690]: #692
+#677 := [unit-resolution #674 #795]: #462
+#678 := [monotonicity #677]: #14
+#15 := (not #14)
+#65 := [asserted]: #15
+[unit-resolution #65 #678]: false
+c5e05aa748f8c52496e5b5ccde5700a56e70c1ef 279 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int S3)
+#13 := 0::Int
+decl f4 :: S2
+#7 := f4
+#16 := (f3 f4 0::Int)
+decl f5 :: (-> S4 Int Int)
+decl f6 :: (-> S5 Int S4)
+decl f8 :: (-> S6 S3 Int)
+decl f10 :: S3
+#10 := f10
+decl f9 :: S6
+#9 := f9
+#11 := (f8 f9 f10)
+decl f7 :: S5
+#8 := f7
+#12 := (f6 f7 #11)
+#14 := (f5 #12 0::Int)
+#15 := (f3 f4 #14)
+#17 := (= #15 #16)
+#454 := (= #14 0::Int)
+#24 := (:var 0 Int)
+#35 := (:var 1 Int)
+#36 := (f6 f7 #35)
+#37 := (f5 #36 #24)
+#791 := (pattern #37)
+#132 := -1::Int
+#136 := (* -1::Int #24)
+#133 := (* -1::Int #35)
+#139 := (div #133 #136)
+#330 := (* -1::Int #139)
+#331 := (+ #37 #330)
+#332 := (= #331 0::Int)
+#47 := (div #35 #24)
+#327 := (* -1::Int #47)
+#328 := (+ #37 #327)
+#329 := (= #328 0::Int)
+#110 := (<= #24 0::Int)
+#222 := (>= #35 0::Int)
+#290 := (or #222 #110)
+#291 := (not #290)
+#106 := (<= #35 0::Int)
+#286 := (or #106 #110)
+#287 := (not #286)
+#294 := (or #287 #291)
+#333 := (if #294 #329 #332)
+#326 := (= #37 0::Int)
+#39 := (= #24 0::Int)
+#38 := (= #35 0::Int)
+#40 := (or #38 #39)
+#334 := (if #40 #326 #333)
+#792 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #791) #334)
+#337 := (forall (vars (?v0 Int) (?v1 Int)) #334)
+#795 := (iff #337 #792)
+#793 := (iff #334 #334)
+#794 := [refl]: #793
+#796 := [quant-intro #794]: #795
+#297 := (if #294 #47 #139)
+#300 := (if #40 0::Int #297)
+#303 := (= #37 #300)
+#306 := (forall (vars (?v0 Int) (?v1 Int)) #303)
+#338 := (iff #306 #337)
+#335 := (iff #303 #334)
+#336 := [rewrite]: #335
+#339 := [quant-intro #336]: #338
+#111 := (not #110)
+#225 := (not #222)
+#228 := (and #225 #111)
+#107 := (not #106)
+#114 := (and #107 #111)
+#231 := (or #114 #228)
+#234 := (if #231 #47 #139)
+#237 := (if #40 0::Int #234)
+#240 := (= #37 #237)
+#243 := (forall (vars (?v0 Int) (?v1 Int)) #240)
+#307 := (iff #243 #306)
+#304 := (iff #240 #303)
+#301 := (= #237 #300)
+#298 := (= #234 #297)
+#295 := (iff #231 #294)
+#292 := (iff #228 #291)
+#293 := [rewrite]: #292
+#288 := (iff #114 #287)
+#289 := [rewrite]: #288
+#296 := [monotonicity #289 #293]: #295
+#299 := [monotonicity #296]: #298
+#302 := [monotonicity #299]: #301
+#305 := [monotonicity #302]: #304
+#308 := [quant-intro #305]: #307
+#278 := (~ #243 #243)
+#276 := (~ #240 #240)
+#277 := [refl]: #276
+#279 := [nnf-pos #277]: #278
+#117 := (<= 0::Int #35)
+#118 := (not #117)
+#126 := (and #118 #111)
+#129 := (or #114 #126)
+#142 := (if #129 #47 #139)
+#145 := (if #40 0::Int #142)
+#148 := (= #37 #145)
+#151 := (forall (vars (?v0 Int) (?v1 Int)) #148)
+#244 := (iff #151 #243)
+#241 := (iff #148 #240)
+#238 := (= #145 #237)
+#235 := (= #142 #234)
+#232 := (iff #129 #231)
+#229 := (iff #126 #228)
+#226 := (iff #118 #225)
+#223 := (iff #117 #222)
+#224 := [rewrite]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [monotonicity #233]: #235
+#239 := [monotonicity #236]: #238
+#242 := [monotonicity #239]: #241
+#245 := [quant-intro #242]: #244
+#49 := (- #24)
+#48 := (- #35)
+#50 := (div #48 #49)
+#42 := (< 0::Int #24)
+#44 := (< #35 0::Int)
+#45 := (and #44 #42)
+#41 := (< 0::Int #35)
+#43 := (and #41 #42)
+#46 := (or #43 #45)
+#51 := (if #46 #47 #50)
+#52 := (if #40 0::Int #51)
+#53 := (= #37 #52)
+#54 := (forall (vars (?v0 Int) (?v1 Int)) #53)
+#152 := (iff #54 #151)
+#149 := (iff #53 #148)
+#146 := (= #52 #145)
+#143 := (= #51 #142)
+#140 := (= #50 #139)
+#137 := (= #49 #136)
+#138 := [rewrite]: #137
+#134 := (= #48 #133)
+#135 := [rewrite]: #134
+#141 := [monotonicity #135 #138]: #140
+#130 := (iff #46 #129)
+#127 := (iff #45 #126)
+#112 := (iff #42 #111)
+#113 := [rewrite]: #112
+#119 := (iff #44 #118)
+#123 := (iff #118 #118)
+#121 := (iff #117 #117)
+#122 := [rewrite]: #121
+#124 := [monotonicity #122]: #123
+#120 := [rewrite]: #119
+#125 := [trans #120 #124]: #119
+#128 := [monotonicity #125 #113]: #127
+#115 := (iff #43 #114)
+#108 := (iff #41 #107)
+#109 := [rewrite]: #108
+#116 := [monotonicity #109 #113]: #115
+#131 := [monotonicity #116 #128]: #130
+#144 := [monotonicity #131 #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [monotonicity #147]: #149
+#153 := [quant-intro #150]: #152
+#71 := [asserted]: #54
+#154 := [mp #71 #153]: #151
+#246 := [mp #154 #245]: #243
+#280 := [mp~ #246 #279]: #243
+#309 := [mp #280 #308]: #306
+#340 := [mp #309 #339]: #337
+#797 := [mp #340 #796]: #792
+#672 := (not #792)
+#673 := (or #672 #454)
+#724 := (* -1::Int 0::Int)
+#723 := (* -1::Int #11)
+#729 := (div #723 #724)
+#730 := (* -1::Int #729)
+#725 := (+ #14 #730)
+#731 := (= #725 0::Int)
+#737 := (div #11 0::Int)
+#726 := (* -1::Int #737)
+#727 := (+ #14 #726)
+#728 := (= #727 0::Int)
+#456 := (<= 0::Int 0::Int)
+#450 := (>= #11 0::Int)
+#732 := (or #450 #456)
+#736 := (not #732)
+#455 := (<= #11 0::Int)
+#734 := (or #455 #456)
+#735 := (not #734)
+#733 := (or #735 #736)
+#572 := (if #733 #728 #731)
+#743 := (= 0::Int 0::Int)
+#739 := (= #11 0::Int)
+#453 := (or #739 #743)
+#573 := (if #453 #454 #572)
+#674 := (or #672 #573)
+#675 := (iff #674 #673)
+#656 := (iff #673 #673)
+#658 := [rewrite]: #656
+#669 := (iff #573 #454)
+#693 := (div #723 0::Int)
+#684 := (* -1::Int #693)
+#697 := (+ #14 #684)
+#699 := (= #697 0::Int)
+#1 := true
+#680 := (if true #454 #699)
+#678 := (iff #680 #454)
+#683 := [rewrite]: #678
+#681 := (iff #573 #680)
+#677 := (iff #572 #699)
+#690 := (if false #728 #699)
+#692 := (iff #690 #699)
+#676 := [rewrite]: #692
+#691 := (iff #572 #690)
+#688 := (iff #731 #699)
+#698 := (= #725 #697)
+#686 := (= #730 #684)
+#695 := (= #729 #693)
+#702 := (= #724 0::Int)
+#706 := [rewrite]: #702
+#687 := [monotonicity #706]: #695
+#696 := [monotonicity #687]: #686
+#694 := [monotonicity #696]: #698
+#689 := [monotonicity #694]: #688
+#612 := (iff #733 false)
+#600 := (or false false)
+#610 := (iff #600 false)
+#611 := [rewrite]: #610
+#608 := (iff #733 #600)
+#606 := (iff #736 false)
+#410 := (not true)
+#748 := (iff #410 false)
+#749 := [rewrite]: #748
+#589 := (iff #736 #410)
+#701 := (iff #732 true)
+#596 := (or #450 true)
+#605 := (iff #596 true)
+#700 := [rewrite]: #605
+#555 := (iff #732 #596)
+#715 := (iff #456 true)
+#722 := [rewrite]: #715
+#703 := [monotonicity #722]: #555
+#704 := [trans #703 #700]: #701
+#604 := [monotonicity #704]: #589
+#607 := [trans #604 #749]: #606
+#594 := (iff #735 false)
+#709 := (iff #735 #410)
+#710 := (iff #734 true)
+#551 := (or #455 true)
+#707 := (iff #551 true)
+#708 := [rewrite]: #707
+#553 := (iff #734 #551)
+#554 := [monotonicity #722]: #553
+#711 := [trans #554 #708]: #710
+#712 := [monotonicity #711]: #709
+#595 := [trans #712 #749]: #594
+#609 := [monotonicity #595 #607]: #608
+#705 := [trans #609 #611]: #612
+#685 := [monotonicity #705 #689]: #691
+#679 := [trans #685 #676]: #677
+#720 := (iff #453 true)
+#717 := (or #739 true)
+#713 := (iff #717 true)
+#714 := [rewrite]: #713
+#718 := (iff #453 #717)
+#574 := (iff #743 true)
+#716 := [rewrite]: #574
+#719 := [monotonicity #716]: #718
+#721 := [trans #719 #714]: #720
+#682 := [monotonicity #721 #679]: #681
+#670 := [trans #682 #683]: #669
+#655 := [monotonicity #670]: #675
+#659 := [trans #655 #658]: #675
+#671 := [quant-inst #11 #13]: #674
+#660 := [mp #671 #659]: #673
+#662 := [unit-resolution #660 #797]: #454
+#663 := [monotonicity #662]: #17
+#18 := (not #17)
+#67 := [asserted]: #18
+[unit-resolution #67 #663]: false
+471141abc1c5de0524559d60a8710dc5938c99dd 296 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int S3)
+#9 := 0::Int
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 0::Int)
+decl f5 :: (-> S4 Int Int)
+#11 := 1::Int
+decl f6 :: (-> S5 Int S4)
+decl f7 :: S5
+#8 := f7
+#10 := (f6 f7 0::Int)
+#12 := (f5 #10 1::Int)
 #13 := (f3 f4 #12)
 #15 := (= #13 #14)
-#805 := (= #12 0::Int)
+#736 := (= #12 0::Int)
 #23 := (:var 0 Int)
 #34 := (:var 1 Int)
 #35 := (f6 f7 #34)
 #36 := (f5 #35 #23)
-#883 := (pattern #36)
-#186 := -1::Int
-#190 := (* -1::Int #23)
-#187 := (* -1::Int #34)
-#193 := (div #187 #190)
-#365 := (* -1::Int #193)
-#366 := (+ #36 #365)
-#367 := (= #366 0::Int)
+#789 := (pattern #36)
+#131 := -1::Int
+#135 := (* -1::Int #23)
+#132 := (* -1::Int #34)
+#138 := (div #132 #135)
+#329 := (* -1::Int #138)
+#330 := (+ #36 #329)
+#331 := (= #330 0::Int)
 #46 := (div #34 #23)
-#362 := (* -1::Int #46)
-#363 := (+ #36 #362)
-#364 := (= #363 0::Int)
-#225 := (>= #34 0::Int)
-#218 := (<= #23 0::Int)
-#325 := (or #218 #225)
-#326 := (not #325)
-#214 := (<= #34 0::Int)
-#323 := (or #214 #218)
-#324 := (not #323)
-#329 := (or #324 #326)
-#368 := (ite #329 #364 #367)
-#361 := (= #36 0::Int)
+#326 := (* -1::Int #46)
+#327 := (+ #36 #326)
+#328 := (= #327 0::Int)
+#109 := (<= #23 0::Int)
+#221 := (>= #34 0::Int)
+#289 := (or #221 #109)
+#290 := (not #289)
+#105 := (<= #34 0::Int)
+#285 := (or #105 #109)
+#286 := (not #285)
+#293 := (or #286 #290)
+#332 := (if #293 #328 #331)
+#325 := (= #36 0::Int)
 #38 := (= #23 0::Int)
 #37 := (= #34 0::Int)
 #39 := (or #37 #38)
-#369 := (ite #39 #361 #368)
-#884 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #883) #369)
-#372 := (forall (vars (?v0 Int) (?v1 Int)) #369)
-#887 := (iff #372 #884)
-#885 := (iff #369 #369)
-#886 := [refl]: #885
-#888 := [quant-intro #886]: #887
-#332 := (ite #329 #46 #193)
-#335 := (ite #39 0::Int #332)
-#338 := (= #36 #335)
-#341 := (forall (vars (?v0 Int) (?v1 Int)) #338)
-#373 := (iff #341 #372)
-#370 := (iff #338 #369)
-#371 := [rewrite]: #370
-#374 := [quant-intro #371]: #373
-#226 := (not #225)
-#219 := (not #218)
-#229 := (and #219 #226)
-#215 := (not #214)
-#222 := (and #215 #219)
-#232 := (or #222 #229)
-#235 := (ite #232 #46 #193)
-#238 := (ite #39 0::Int #235)
-#241 := (= #36 #238)
-#244 := (forall (vars (?v0 Int) (?v1 Int)) #241)
-#342 := (iff #244 #341)
-#339 := (iff #241 #338)
-#336 := (= #238 #335)
-#333 := (= #235 #332)
-#330 := (iff #232 #329)
-#327 := (iff #229 #326)
-#328 := [rewrite]: #327
-#308 := (iff #222 #324)
-#309 := [rewrite]: #308
-#331 := [monotonicity #309 #328]: #330
-#334 := [monotonicity #331]: #333
-#337 := [monotonicity #334]: #336
-#340 := [monotonicity #337]: #339
-#343 := [quant-intro #340]: #342
-#304 := (~ #244 #244)
-#317 := (~ #241 #241)
-#318 := [refl]: #317
-#305 := [nnf-pos #318]: #304
+#333 := (if #39 #325 #332)
+#790 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #789) #333)
+#336 := (forall (vars (?v0 Int) (?v1 Int)) #333)
+#793 := (iff #336 #790)
+#791 := (iff #333 #333)
+#792 := [refl]: #791
+#794 := [quant-intro #792]: #793
+#296 := (if #293 #46 #138)
+#299 := (if #39 0::Int #296)
+#302 := (= #36 #299)
+#305 := (forall (vars (?v0 Int) (?v1 Int)) #302)
+#337 := (iff #305 #336)
+#334 := (iff #302 #333)
+#335 := [rewrite]: #334
+#338 := [quant-intro #335]: #337
+#110 := (not #109)
+#224 := (not #221)
+#227 := (and #224 #110)
+#106 := (not #105)
+#113 := (and #106 #110)
+#230 := (or #113 #227)
+#233 := (if #230 #46 #138)
+#236 := (if #39 0::Int #233)
+#239 := (= #36 #236)
+#242 := (forall (vars (?v0 Int) (?v1 Int)) #239)
+#306 := (iff #242 #305)
+#303 := (iff #239 #302)
+#300 := (= #236 #299)
+#297 := (= #233 #296)
+#294 := (iff #230 #293)
+#291 := (iff #227 #290)
+#292 := [rewrite]: #291
+#287 := (iff #113 #286)
+#288 := [rewrite]: #287
+#295 := [monotonicity #288 #292]: #294
+#298 := [monotonicity #295]: #297
+#301 := [monotonicity #298]: #300
+#304 := [monotonicity #301]: #303
+#307 := [quant-intro #304]: #306
+#277 := (~ #242 #242)
+#275 := (~ #239 #239)
+#276 := [refl]: #275
+#278 := [nnf-pos #276]: #277
+#116 := (<= 0::Int #34)
+#117 := (not #116)
+#125 := (and #117 #110)
+#128 := (or #113 #125)
+#141 := (if #128 #46 #138)
+#144 := (if #39 0::Int #141)
+#147 := (= #36 #144)
+#150 := (forall (vars (?v0 Int) (?v1 Int)) #147)
+#243 := (iff #150 #242)
+#240 := (iff #147 #239)
+#237 := (= #144 #236)
+#234 := (= #141 #233)
+#231 := (iff #128 #230)
+#228 := (iff #125 #227)
+#225 := (iff #117 #224)
+#222 := (iff #116 #221)
+#223 := [rewrite]: #222
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#235 := [monotonicity #232]: #234
+#238 := [monotonicity #235]: #237
+#241 := [monotonicity #238]: #240
+#244 := [quant-intro #241]: #243
 #48 := (- #23)
 #47 := (- #34)
 #49 := (div #47 #48)
@@ -13349,856 +13336,595 @@
 #40 := (< 0::Int #34)
 #42 := (and #40 #41)
 #45 := (or #42 #44)
-#50 := (ite #45 #46 #49)
-#51 := (ite #39 0::Int #50)
+#50 := (if #45 #46 #49)
+#51 := (if #39 0::Int #50)
 #52 := (= #36 #51)
 #53 := (forall (vars (?v0 Int) (?v1 Int)) #52)
-#247 := (iff #53 #244)
-#180 := (and #41 #43)
-#183 := (or #42 #180)
-#196 := (ite #183 #46 #193)
-#174 := (= 0::Int #23)
-#171 := (= 0::Int #34)
-#177 := (or #171 #174)
-#199 := (ite #177 0::Int #196)
-#202 := (= #36 #199)
-#205 := (forall (vars (?v0 Int) (?v1 Int)) #202)
-#245 := (iff #205 #244)
-#242 := (iff #202 #241)
-#239 := (= #199 #238)
-#236 := (= #196 #235)
-#233 := (iff #183 #232)
-#230 := (iff #180 #229)
-#227 := (iff #43 #226)
-#228 := [rewrite]: #227
-#220 := (iff #41 #219)
-#221 := [rewrite]: #220
-#231 := [monotonicity #221 #228]: #230
-#223 := (iff #42 #222)
-#216 := (iff #40 #215)
-#217 := [rewrite]: #216
-#224 := [monotonicity #217 #221]: #223
-#234 := [monotonicity #224 #231]: #233
-#237 := [monotonicity #234]: #236
-#212 := (iff #177 #39)
-#210 := (iff #174 #38)
-#211 := [rewrite]: #210
-#208 := (iff #171 #37)
-#209 := [rewrite]: #208
-#213 := [monotonicity #209 #211]: #212
-#240 := [monotonicity #213 #237]: #239
-#243 := [monotonicity #240]: #242
-#246 := [quant-intro #243]: #245
-#206 := (iff #53 #205)
-#203 := (iff #52 #202)
-#200 := (= #51 #199)
-#197 := (= #50 #196)
-#194 := (= #49 #193)
-#191 := (= #48 #190)
-#192 := [rewrite]: #191
-#188 := (= #47 #187)
-#189 := [rewrite]: #188
-#195 := [monotonicity #189 #192]: #194
-#184 := (iff #45 #183)
-#181 := (iff #44 #180)
-#182 := [rewrite]: #181
-#185 := [monotonicity #182]: #184
-#198 := [monotonicity #185 #195]: #197
-#178 := (iff #39 #177)
-#175 := (iff #38 #174)
-#176 := [rewrite]: #175
-#172 := (iff #37 #171)
-#173 := [rewrite]: #172
-#179 := [monotonicity #173 #176]: #178
-#201 := [monotonicity #179 #198]: #200
-#204 := [monotonicity #201]: #203
-#207 := [quant-intro #204]: #206
-#248 := [trans #207 #246]: #247
-#170 := [asserted]: #53
-#249 := [mp #170 #248]: #244
-#319 := [mp~ #249 #305]: #244
-#344 := [mp #319 #343]: #341
-#375 := [mp #344 #374]: #372
-#889 := [mp #375 #888]: #884
-#762 := (not #884)
-#764 := (or #762 #805)
-#818 := (* -1::Int 0::Int)
-#819 := (div #818 #818)
-#820 := (* -1::Int #819)
-#815 := (+ #12 #820)
-#816 := (= #815 0::Int)
-#821 := (div 0::Int 0::Int)
-#822 := (* -1::Int #821)
-#817 := (+ #12 #822)
-#823 := (= #817 0::Int)
-#840 := (>= 0::Int 0::Int)
-#664 := (<= 0::Int 0::Int)
-#665 := (or #664 #840)
-#666 := (not #665)
-#808 := (or #664 #664)
-#809 := (not #808)
-#810 := (or #809 #666)
-#811 := (ite #810 #823 #816)
-#806 := (= 0::Int 0::Int)
-#812 := (or #806 #806)
-#813 := (ite #812 #805 #811)
-#765 := (or #762 #813)
-#763 := (iff #765 #764)
-#747 := (iff #764 #764)
-#748 := [rewrite]: #747
-#775 := (iff #813 #805)
-#1 := true
-#771 := (ite true #805 #823)
-#774 := (iff #771 #805)
-#770 := [rewrite]: #774
-#772 := (iff #813 #771)
-#768 := (iff #811 #823)
-#781 := (ite false #823 #823)
-#777 := (iff #781 #823)
-#784 := [rewrite]: #777
-#782 := (iff #811 #781)
-#791 := (iff #816 #823)
-#790 := (= #815 #817)
-#788 := (= #820 #822)
-#776 := (= #819 #821)
-#787 := (= #818 0::Int)
-#779 := [rewrite]: #787
-#778 := [monotonicity #779 #779]: #776
-#789 := [monotonicity #778]: #788
-#786 := [monotonicity #789]: #790
-#780 := [monotonicity #786]: #791
-#798 := (iff #810 false)
-#702 := (or false false)
-#797 := (iff #702 false)
-#794 := [rewrite]: #797
-#703 := (iff #810 #702)
-#700 := (iff #666 false)
-#488 := (not true)
-#847 := (iff #488 false)
-#850 := [rewrite]: #847
-#699 := (iff #666 #488)
-#696 := (iff #665 true)
-#643 := (or true true)
-#799 := (iff #643 true)
-#800 := [rewrite]: #799
-#796 := (iff #665 #643)
-#846 := (iff #840 true)
-#848 := [rewrite]: #846
-#801 := (iff #664 true)
-#804 := [rewrite]: #801
-#681 := [monotonicity #804 #848]: #796
-#698 := [trans #681 #800]: #696
-#692 := [monotonicity #698]: #699
-#701 := [trans #692 #850]: #700
-#792 := (iff #809 false)
-#795 := (iff #809 #488)
-#688 := (iff #808 true)
-#686 := (iff #808 #643)
-#687 := [monotonicity #804 #804]: #686
-#647 := [trans #687 #800]: #688
-#697 := [monotonicity #647]: #795
-#793 := [trans #697 #850]: #792
-#704 := [monotonicity #793 #701]: #703
-#785 := [trans #704 #794]: #798
-#783 := [monotonicity #785 #780]: #782
-#769 := [trans #783 #784]: #768
-#802 := (iff #812 true)
-#645 := (iff #812 #643)
-#807 := (iff #806 true)
-#814 := [rewrite]: #807
-#646 := [monotonicity #814 #814]: #645
-#803 := [trans #646 #800]: #802
-#773 := [monotonicity #803 #769]: #772
-#761 := [trans #773 #770]: #775
-#767 := [monotonicity #761]: #763
-#750 := [trans #767 #748]: #763
-#766 := [quant-inst #10 #10]: #765
-#751 := [mp #766 #750]: #764
-#753 := [unit-resolution #751 #889]: #805
-#754 := [monotonicity #753]: #15
+#151 := (iff #53 #150)
+#148 := (iff #52 #147)
+#145 := (= #51 #144)
+#142 := (= #50 #141)
+#139 := (= #49 #138)
+#136 := (= #48 #135)
+#137 := [rewrite]: #136
+#133 := (= #47 #132)
+#134 := [rewrite]: #133
+#140 := [monotonicity #134 #137]: #139
+#129 := (iff #45 #128)
+#126 := (iff #44 #125)
+#111 := (iff #41 #110)
+#112 := [rewrite]: #111
+#118 := (iff #43 #117)
+#122 := (iff #117 #117)
+#120 := (iff #116 #116)
+#121 := [rewrite]: #120
+#123 := [monotonicity #121]: #122
+#119 := [rewrite]: #118
+#124 := [trans #119 #123]: #118
+#127 := [monotonicity #124 #112]: #126
+#114 := (iff #42 #113)
+#107 := (iff #40 #106)
+#108 := [rewrite]: #107
+#115 := [monotonicity #108 #112]: #114
+#130 := [monotonicity #115 #127]: #129
+#143 := [monotonicity #130 #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [monotonicity #146]: #148
+#152 := [quant-intro #149]: #151
+#70 := [asserted]: #53
+#153 := [mp #70 #152]: #150
+#245 := [mp #153 #244]: #242
+#279 := [mp~ #245 #278]: #242
+#308 := [mp #279 #307]: #305
+#339 := [mp #308 #338]: #336
+#795 := [mp #339 #794]: #790
+#663 := (not #790)
+#664 := (or #663 #736)
+#731 := (* -1::Int 1::Int)
+#734 := (* -1::Int 0::Int)
+#735 := (div #734 #731)
+#724 := (* -1::Int #735)
+#725 := (+ #12 #724)
+#726 := (= #725 0::Int)
+#732 := (div 0::Int 1::Int)
+#733 := (* -1::Int #732)
+#448 := (+ #12 #733)
+#730 := (= #448 0::Int)
+#737 := (<= 1::Int 0::Int)
+#550 := (>= 0::Int 0::Int)
+#452 := (or #550 #737)
+#453 := (not #452)
+#740 := (<= 0::Int 0::Int)
+#741 := (or #740 #737)
+#451 := (not #741)
+#454 := (or #451 #453)
+#721 := (if #454 #730 #726)
+#461 := (= 1::Int 0::Int)
+#739 := (= 0::Int 0::Int)
+#462 := (or #739 #461)
+#722 := (if #462 #736 #721)
+#665 := (or #663 #722)
+#666 := (iff #665 #664)
+#645 := (iff #664 #664)
+#647 := [rewrite]: #645
+#661 := (iff #722 #736)
+#1 := true
+#656 := (if true #736 #736)
+#659 := (iff #656 #736)
+#660 := [rewrite]: #659
+#657 := (iff #722 #656)
+#653 := (iff #721 #736)
+#670 := (if false #736 #736)
+#669 := (iff #670 #736)
+#673 := [rewrite]: #669
+#671 := (iff #721 #670)
+#667 := (iff #726 #736)
+#676 := (= #725 #12)
+#700 := (+ #12 0::Int)
+#693 := (= #700 #12)
+#685 := [rewrite]: #693
+#679 := (= #725 #700)
+#677 := (= #724 0::Int)
+#608 := (= #734 0::Int)
+#609 := [rewrite]: #608
+#674 := (= #724 #734)
+#683 := (= #735 0::Int)
+#697 := (div 0::Int -1::Int)
+#688 := (= #697 0::Int)
+#689 := [rewrite]: #688
+#686 := (= #735 #697)
+#696 := (= #731 -1::Int)
+#692 := [rewrite]: #696
+#687 := [monotonicity #609 #692]: #686
+#690 := [trans #687 #689]: #683
+#675 := [monotonicity #690]: #674
+#678 := [trans #675 #609]: #677
+#680 := [monotonicity #678]: #679
+#681 := [trans #680 #685]: #676
+#668 := [monotonicity #681]: #667
+#694 := (iff #730 #736)
+#682 := (= #448 #12)
+#704 := (= #448 #700)
+#610 := (= #733 0::Int)
+#606 := (= #733 #734)
+#605 := (= #732 0::Int)
+#598 := [rewrite]: #605
+#607 := [monotonicity #598]: #606
+#703 := [trans #607 #609]: #610
+#691 := [monotonicity #703]: #704
+#684 := [trans #691 #685]: #682
+#695 := [monotonicity #684]: #694
+#602 := (iff #454 false)
+#603 := (or false false)
+#702 := (iff #603 false)
+#587 := [rewrite]: #702
+#698 := (iff #454 #603)
+#553 := (iff #453 false)
+#419 := (not true)
+#744 := (iff #419 false)
+#407 := [rewrite]: #744
+#593 := (iff #453 #419)
+#710 := (iff #452 true)
+#570 := (or true false)
+#714 := (iff #570 true)
+#715 := [rewrite]: #714
+#709 := (iff #452 #570)
+#718 := (iff #737 false)
+#719 := [rewrite]: #718
+#423 := (iff #550 true)
+#759 := [rewrite]: #423
+#707 := [monotonicity #759 #719]: #709
+#592 := [trans #707 #715]: #710
+#594 := [monotonicity #592]: #593
+#701 := [trans #594 #407]: #553
+#706 := (iff #451 false)
+#552 := (iff #451 #419)
+#549 := (iff #741 true)
+#713 := (iff #741 #570)
+#711 := (iff #740 true)
+#712 := [rewrite]: #711
+#720 := [monotonicity #712 #719]: #713
+#551 := [trans #720 #715]: #549
+#705 := [monotonicity #551]: #552
+#708 := [trans #705 #407]: #706
+#699 := [monotonicity #708 #701]: #698
+#604 := [trans #699 #587]: #602
+#672 := [monotonicity #604 #695 #668]: #671
+#654 := [trans #672 #673]: #653
+#716 := (iff #462 true)
+#571 := (iff #462 #570)
+#723 := (iff #461 false)
+#729 := [rewrite]: #723
+#727 := (iff #739 true)
+#728 := [rewrite]: #727
+#572 := [monotonicity #728 #729]: #571
+#717 := [trans #572 #715]: #716
+#658 := [monotonicity #717 #654]: #657
+#662 := [trans #658 #660]: #661
+#644 := [monotonicity #662]: #666
+#648 := [trans #644 #647]: #666
+#655 := [quant-inst #9 #11]: #665
+#649 := [mp #655 #648]: #664
+#651 := [unit-resolution #649 #795]: #736
+#646 := [monotonicity #651]: #15
 #16 := (not #15)
-#84 := [asserted]: #16
-[unit-resolution #84 #754]: false
-unsat
-30453646d0803ed6c97ad5b92ef57ecbbc2d5650 284 0
+#66 := [asserted]: #16
+[unit-resolution #66 #646]: false
+5f4a21ddc8bb410dbf2483dc973cb115e8b16b3c 299 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int S3)
-#14 := 0::Int
-decl f4 :: S2
-#8 := f4
-#17 := (f3 f4 0::Int)
+#9 := 1::Int
+decl f4 :: S2
+#7 := f4
+#13 := (f3 f4 1::Int)
 decl f5 :: (-> S4 Int Int)
 decl f6 :: (-> S5 Int S4)
-decl f8 :: (-> S6 S3 Int)
-decl f10 :: S3
-#11 := f10
-decl f9 :: S6
-#10 := f9
-#12 := (f8 f9 f10)
 decl f7 :: S5
-#9 := f7
-#13 := (f6 f7 #12)
-#15 := (f5 #13 0::Int)
-#16 := (f3 f4 #15)
-#18 := (= #16 #17)
-#648 := (= #15 0::Int)
-#25 := (:var 0 Int)
-#36 := (:var 1 Int)
-#37 := (f6 f7 #36)
-#38 := (f5 #37 #25)
-#885 := (pattern #38)
-#188 := -1::Int
-#192 := (* -1::Int #25)
-#189 := (* -1::Int #36)
-#195 := (div #189 #192)
-#367 := (* -1::Int #195)
-#368 := (+ #38 #367)
-#369 := (= #368 0::Int)
-#48 := (div #36 #25)
-#364 := (* -1::Int #48)
-#365 := (+ #38 #364)
-#366 := (= #365 0::Int)
-#227 := (>= #36 0::Int)
-#220 := (<= #25 0::Int)
-#327 := (or #220 #227)
-#328 := (not #327)
-#216 := (<= #36 0::Int)
-#325 := (or #216 #220)
-#326 := (not #325)
-#331 := (or #326 #328)
-#370 := (ite #331 #366 #369)
-#363 := (= #38 0::Int)
-#40 := (= #25 0::Int)
-#39 := (= #36 0::Int)
-#41 := (or #39 #40)
-#371 := (ite #41 #363 #370)
-#886 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #885) #371)
-#374 := (forall (vars (?v0 Int) (?v1 Int)) #371)
-#889 := (iff #374 #886)
-#887 := (iff #371 #371)
-#888 := [refl]: #887
-#890 := [quant-intro #888]: #889
-#334 := (ite #331 #48 #195)
-#337 := (ite #41 0::Int #334)
-#340 := (= #38 #337)
-#343 := (forall (vars (?v0 Int) (?v1 Int)) #340)
-#375 := (iff #343 #374)
-#372 := (iff #340 #371)
-#373 := [rewrite]: #372
-#376 := [quant-intro #373]: #375
-#228 := (not #227)
-#221 := (not #220)
-#231 := (and #221 #228)
-#217 := (not #216)
-#224 := (and #217 #221)
-#234 := (or #224 #231)
-#237 := (ite #234 #48 #195)
-#240 := (ite #41 0::Int #237)
-#243 := (= #38 #240)
-#246 := (forall (vars (?v0 Int) (?v1 Int)) #243)
-#344 := (iff #246 #343)
-#341 := (iff #243 #340)
-#338 := (= #240 #337)
-#335 := (= #237 #334)
-#332 := (iff #234 #331)
-#329 := (iff #231 #328)
-#330 := [rewrite]: #329
-#310 := (iff #224 #326)
-#311 := [rewrite]: #310
-#333 := [monotonicity #311 #330]: #332
-#336 := [monotonicity #333]: #335
-#339 := [monotonicity #336]: #338
-#342 := [monotonicity #339]: #341
-#345 := [quant-intro #342]: #344
-#306 := (~ #246 #246)
-#319 := (~ #243 #243)
-#320 := [refl]: #319
-#307 := [nnf-pos #320]: #306
-#50 := (- #25)
-#49 := (- #36)
-#51 := (div #49 #50)
-#43 := (< 0::Int #25)
-#45 := (< #36 0::Int)
-#46 := (and #45 #43)
-#42 := (< 0::Int #36)
-#44 := (and #42 #43)
-#47 := (or #44 #46)
-#52 := (ite #47 #48 #51)
-#53 := (ite #41 0::Int #52)
-#54 := (= #38 #53)
-#55 := (forall (vars (?v0 Int) (?v1 Int)) #54)
-#249 := (iff #55 #246)
-#182 := (and #43 #45)
-#185 := (or #44 #182)
-#198 := (ite #185 #48 #195)
-#176 := (= 0::Int #25)
-#173 := (= 0::Int #36)
-#179 := (or #173 #176)
-#201 := (ite #179 0::Int #198)
-#204 := (= #38 #201)
-#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
-#247 := (iff #207 #246)
-#244 := (iff #204 #243)
-#241 := (= #201 #240)
-#238 := (= #198 #237)
-#235 := (iff #185 #234)
-#232 := (iff #182 #231)
-#229 := (iff #45 #228)
-#230 := [rewrite]: #229
-#222 := (iff #43 #221)
+#8 := f7
+#10 := (f6 f7 1::Int)
+#11 := (f5 #10 1::Int)
+#12 := (f3 f4 #11)
+#14 := (= #12 #13)
+#695 := (= #11 1::Int)
+#23 := (:var 0 Int)
+#34 := (:var 1 Int)
+#35 := (f6 f7 #34)
+#36 := (f5 #35 #23)
+#789 := (pattern #36)
+#22 := 0::Int
+#131 := -1::Int
+#135 := (* -1::Int #23)
+#132 := (* -1::Int #34)
+#138 := (div #132 #135)
+#329 := (* -1::Int #138)
+#330 := (+ #36 #329)
+#331 := (= #330 0::Int)
+#46 := (div #34 #23)
+#326 := (* -1::Int #46)
+#327 := (+ #36 #326)
+#328 := (= #327 0::Int)
+#109 := (<= #23 0::Int)
+#221 := (>= #34 0::Int)
+#289 := (or #221 #109)
+#290 := (not #289)
+#105 := (<= #34 0::Int)
+#285 := (or #105 #109)
+#286 := (not #285)
+#293 := (or #286 #290)
+#332 := (if #293 #328 #331)
+#325 := (= #36 0::Int)
+#38 := (= #23 0::Int)
+#37 := (= #34 0::Int)
+#39 := (or #37 #38)
+#333 := (if #39 #325 #332)
+#790 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #789) #333)
+#336 := (forall (vars (?v0 Int) (?v1 Int)) #333)
+#793 := (iff #336 #790)
+#791 := (iff #333 #333)
+#792 := [refl]: #791
+#794 := [quant-intro #792]: #793
+#296 := (if #293 #46 #138)
+#299 := (if #39 0::Int #296)
+#302 := (= #36 #299)
+#305 := (forall (vars (?v0 Int) (?v1 Int)) #302)
+#337 := (iff #305 #336)
+#334 := (iff #302 #333)
+#335 := [rewrite]: #334
+#338 := [quant-intro #335]: #337
+#110 := (not #109)
+#224 := (not #221)
+#227 := (and #224 #110)
+#106 := (not #105)
+#113 := (and #106 #110)
+#230 := (or #113 #227)
+#233 := (if #230 #46 #138)
+#236 := (if #39 0::Int #233)
+#239 := (= #36 #236)
+#242 := (forall (vars (?v0 Int) (?v1 Int)) #239)
+#306 := (iff #242 #305)
+#303 := (iff #239 #302)
+#300 := (= #236 #299)
+#297 := (= #233 #296)
+#294 := (iff #230 #293)
+#291 := (iff #227 #290)
+#292 := [rewrite]: #291
+#287 := (iff #113 #286)
+#288 := [rewrite]: #287
+#295 := [monotonicity #288 #292]: #294
+#298 := [monotonicity #295]: #297
+#301 := [monotonicity #298]: #300
+#304 := [monotonicity #301]: #303
+#307 := [quant-intro #304]: #306
+#277 := (~ #242 #242)
+#275 := (~ #239 #239)
+#276 := [refl]: #275
+#278 := [nnf-pos #276]: #277
+#116 := (<= 0::Int #34)
+#117 := (not #116)
+#125 := (and #117 #110)
+#128 := (or #113 #125)
+#141 := (if #128 #46 #138)
+#144 := (if #39 0::Int #141)
+#147 := (= #36 #144)
+#150 := (forall (vars (?v0 Int) (?v1 Int)) #147)
+#243 := (iff #150 #242)
+#240 := (iff #147 #239)
+#237 := (= #144 #236)
+#234 := (= #141 #233)
+#231 := (iff #128 #230)
+#228 := (iff #125 #227)
+#225 := (iff #117 #224)
+#222 := (iff #116 #221)
 #223 := [rewrite]: #222
-#233 := [monotonicity #223 #230]: #232
-#225 := (iff #44 #224)
-#218 := (iff #42 #217)
-#219 := [rewrite]: #218
-#226 := [monotonicity #219 #223]: #225
-#236 := [monotonicity #226 #233]: #235
-#239 := [monotonicity #236]: #238
-#214 := (iff #179 #41)
-#212 := (iff #176 #40)
-#213 := [rewrite]: #212
-#210 := (iff #173 #39)
-#211 := [rewrite]: #210
-#215 := [monotonicity #211 #213]: #214
-#242 := [monotonicity #215 #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [quant-intro #245]: #247
-#208 := (iff #55 #207)
-#205 := (iff #54 #204)
-#202 := (= #53 #201)
-#199 := (= #52 #198)
-#196 := (= #51 #195)
-#193 := (= #50 #192)
-#194 := [rewrite]: #193
-#190 := (= #49 #189)
-#191 := [rewrite]: #190
-#197 := [monotonicity #191 #194]: #196
-#186 := (iff #47 #185)
-#183 := (iff #46 #182)
-#184 := [rewrite]: #183
-#187 := [monotonicity #184]: #186
-#200 := [monotonicity #187 #197]: #199
-#180 := (iff #41 #179)
-#177 := (iff #40 #176)
-#178 := [rewrite]: #177
-#174 := (iff #39 #173)
-#175 := [rewrite]: #174
-#181 := [monotonicity #175 #178]: #180
-#203 := [monotonicity #181 #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [quant-intro #206]: #208
-#250 := [trans #209 #248]: #249
-#172 := [asserted]: #55
-#251 := [mp #172 #250]: #246
-#321 := [mp~ #251 #307]: #246
-#346 := [mp #321 #345]: #343
-#377 := [mp #346 #376]: #374
-#891 := [mp #377 #890]: #886
-#762 := (not #886)
-#740 := (or #762 #648)
-#823 := (* -1::Int 0::Int)
-#824 := (* -1::Int #12)
-#819 := (div #824 #823)
-#825 := (* -1::Int #819)
-#666 := (+ #15 #825)
-#667 := (= #666 0::Int)
-#668 := (div #12 0::Int)
-#810 := (* -1::Int #668)
-#811 := (+ #15 #810)
-#812 := (= #811 0::Int)
-#813 := (>= #12 0::Int)
-#807 := (<= 0::Int 0::Int)
-#808 := (or #807 #813)
-#814 := (not #808)
-#815 := (<= #12 0::Int)
-#809 := (or #815 #807)
-#816 := (not #809)
-#645 := (or #816 #814)
-#647 := (ite #645 #812 #667)
-#801 := (= 0::Int 0::Int)
-#802 := (= #12 0::Int)
-#804 := (or #802 #801)
-#805 := (ite #804 #648 #647)
-#741 := (or #762 #805)
-#744 := (iff #741 #740)
-#746 := (iff #740 #740)
-#747 := [rewrite]: #746
-#761 := (iff #805 #648)
-#773 := (div #824 0::Int)
-#776 := (* -1::Int #773)
-#763 := (+ #15 #776)
-#767 := (= #763 0::Int)
-#1 := true
-#756 := (ite true #648 #767)
-#759 := (iff #756 #648)
-#760 := [rewrite]: #759
-#757 := (iff #805 #756)
-#754 := (iff #647 #767)
-#769 := (ite false #812 #767)
-#752 := (iff #769 #767)
-#753 := [rewrite]: #752
-#749 := (iff #647 #769)
-#768 := (iff #667 #767)
-#764 := (= #666 #763)
-#772 := (= #825 #776)
-#774 := (= #819 #773)
-#770 := (= #823 0::Int)
-#771 := [rewrite]: #770
-#775 := [monotonicity #771]: #774
-#777 := [monotonicity #775]: #772
-#766 := [monotonicity #777]: #764
-#765 := [monotonicity #766]: #768
-#779 := (iff #645 false)
-#793 := (or false false)
-#784 := (iff #793 false)
-#785 := [rewrite]: #784
-#782 := (iff #645 #793)
-#792 := (iff #814 false)
-#838 := (not true)
-#562 := (iff #838 false)
-#563 := [rewrite]: #562
-#790 := (iff #814 #838)
-#778 := (iff #808 true)
-#796 := (or true #813)
-#789 := (iff #796 true)
-#781 := [rewrite]: #789
-#800 := (iff #808 #796)
-#795 := (iff #807 true)
-#798 := [rewrite]: #795
-#787 := [monotonicity #798]: #800
-#780 := [trans #787 #781]: #778
-#791 := [monotonicity #780]: #790
-#788 := [trans #791 #563]: #792
-#706 := (iff #816 false)
-#704 := (iff #816 #838)
-#702 := (iff #809 true)
-#683 := (or #815 true)
-#701 := (iff #683 true)
-#694 := [rewrite]: #701
-#698 := (iff #809 #683)
-#700 := [monotonicity #798]: #698
-#703 := [trans #700 #694]: #702
-#705 := [monotonicity #703]: #704
-#799 := [trans #705 #563]: #706
-#783 := [monotonicity #799 #788]: #782
-#786 := [trans #783 #785]: #779
-#750 := [monotonicity #786 #765]: #749
-#755 := [trans #750 #753]: #754
-#699 := (iff #804 true)
-#688 := (or #802 true)
-#649 := (iff #688 true)
-#797 := [rewrite]: #649
-#689 := (iff #804 #688)
-#803 := (iff #801 true)
-#806 := [rewrite]: #803
-#690 := [monotonicity #806]: #689
-#794 := [trans #690 #797]: #699
-#758 := [monotonicity #794 #755]: #757
-#751 := [trans #758 #760]: #761
-#745 := [monotonicity #751]: #744
-#742 := [trans #745 #747]: #744
-#743 := [quant-inst #12 #14]: #741
-#748 := [mp #743 #742]: #740
-#730 := [unit-resolution #748 #891]: #648
-#731 := [monotonicity #730]: #18
-#19 := (not #18)
-#86 := [asserted]: #19
-[unit-resolution #86 #731]: false
-unsat
-008b16baa059bf8db3712b63abb197cb3108389b 304 0
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#235 := [monotonicity #232]: #234
+#238 := [monotonicity #235]: #237
+#241 := [monotonicity #238]: #240
+#244 := [quant-intro #241]: #243
+#48 := (- #23)
+#47 := (- #34)
+#49 := (div #47 #48)
+#41 := (< 0::Int #23)
+#43 := (< #34 0::Int)
+#44 := (and #43 #41)
+#40 := (< 0::Int #34)
+#42 := (and #40 #41)
+#45 := (or #42 #44)
+#50 := (if #45 #46 #49)
+#51 := (if #39 0::Int #50)
+#52 := (= #36 #51)
+#53 := (forall (vars (?v0 Int) (?v1 Int)) #52)
+#151 := (iff #53 #150)
+#148 := (iff #52 #147)
+#145 := (= #51 #144)
+#142 := (= #50 #141)
+#139 := (= #49 #138)
+#136 := (= #48 #135)
+#137 := [rewrite]: #136
+#133 := (= #47 #132)
+#134 := [rewrite]: #133
+#140 := [monotonicity #134 #137]: #139
+#129 := (iff #45 #128)
+#126 := (iff #44 #125)
+#111 := (iff #41 #110)
+#112 := [rewrite]: #111
+#118 := (iff #43 #117)
+#122 := (iff #117 #117)
+#120 := (iff #116 #116)
+#121 := [rewrite]: #120
+#123 := [monotonicity #121]: #122
+#119 := [rewrite]: #118
+#124 := [trans #119 #123]: #118
+#127 := [monotonicity #124 #112]: #126
+#114 := (iff #42 #113)
+#107 := (iff #40 #106)
+#108 := [rewrite]: #107
+#115 := [monotonicity #108 #112]: #114
+#130 := [monotonicity #115 #127]: #129
+#143 := [monotonicity #130 #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [monotonicity #146]: #148
+#152 := [quant-intro #149]: #151
+#70 := [asserted]: #53
+#153 := [mp #70 #152]: #150
+#245 := [mp #153 #244]: #242
+#279 := [mp~ #245 #278]: #242
+#308 := [mp #279 #307]: #305
+#339 := [mp #308 #338]: #336
+#795 := [mp #339 #794]: #790
+#666 := (not #790)
+#644 := (or #666 #695)
+#730 := (* -1::Int 1::Int)
+#734 := (div #730 #730)
+#731 := (* -1::Int #734)
+#735 := (+ #11 #731)
+#724 := (= #735 0::Int)
+#454 := (div 1::Int 1::Int)
+#732 := (* -1::Int #454)
+#733 := (+ #11 #732)
+#448 := (= #733 0::Int)
+#740 := (<= 1::Int 0::Int)
+#550 := (>= 1::Int 0::Int)
+#451 := (or #550 #740)
+#452 := (not #451)
+#737 := (or #740 #740)
+#741 := (not #737)
+#453 := (or #741 #452)
+#725 := (if #453 #448 #724)
+#736 := (= #11 0::Int)
+#461 := (= 1::Int 0::Int)
+#462 := (or #461 #461)
+#726 := (if #462 #736 #725)
+#645 := (or #666 #726)
+#648 := (iff #645 #644)
+#650 := (iff #644 #644)
+#651 := [rewrite]: #650
+#665 := (iff #726 #695)
+#660 := (if false #736 #695)
+#663 := (iff #660 #695)
+#664 := [rewrite]: #663
+#661 := (iff #726 #660)
+#658 := (iff #725 #695)
+#1 := true
+#673 := (if true #695 #695)
+#656 := (iff #673 #695)
+#657 := [rewrite]: #656
+#653 := (iff #725 #673)
+#672 := (iff #724 #695)
+#700 := (+ -1::Int #11)
+#682 := (= #700 0::Int)
+#696 := (iff #682 #695)
+#692 := [rewrite]: #696
+#670 := (iff #724 #682)
+#667 := (= #735 #700)
+#609 := (+ #11 -1::Int)
+#704 := (= #609 #700)
+#691 := [rewrite]: #704
+#676 := (= #735 #609)
+#679 := (= #731 -1::Int)
+#598 := (= #730 -1::Int)
+#606 := [rewrite]: #598
+#677 := (= #731 #730)
+#674 := (= #734 1::Int)
+#687 := (div -1::Int -1::Int)
+#683 := (= #687 1::Int)
+#690 := [rewrite]: #683
+#688 := (= #734 #687)
+#689 := [monotonicity #606 #606]: #688
+#675 := [trans #689 #690]: #674
+#678 := [monotonicity #675]: #677
+#680 := [trans #678 #606]: #679
+#681 := [monotonicity #680]: #676
+#668 := [trans #681 #691]: #667
+#671 := [monotonicity #668]: #670
+#669 := [trans #671 #692]: #672
+#697 := (iff #448 #695)
+#684 := (iff #448 #682)
+#693 := (= #733 #700)
+#610 := (= #733 #609)
+#607 := (= #732 -1::Int)
+#604 := (= #732 #730)
+#587 := (= #454 1::Int)
+#602 := [rewrite]: #587
+#605 := [monotonicity #602]: #604
+#608 := [trans #605 #606]: #607
+#703 := [monotonicity #608]: #610
+#685 := [trans #703 #691]: #693
+#694 := [monotonicity #685]: #684
+#686 := [trans #694 #692]: #697
+#699 := (iff #453 true)
+#705 := (or true false)
+#709 := (iff #705 true)
+#707 := [rewrite]: #709
+#603 := (iff #453 #705)
+#553 := (iff #452 false)
+#419 := (not true)
+#744 := (iff #419 false)
+#407 := [rewrite]: #744
+#593 := (iff #452 #419)
+#710 := (iff #451 true)
+#706 := (iff #451 #705)
+#714 := (iff #740 false)
+#715 := [rewrite]: #714
+#423 := (iff #550 true)
+#759 := [rewrite]: #423
+#708 := [monotonicity #759 #715]: #706
+#592 := [trans #708 #707]: #710
+#594 := [monotonicity #592]: #593
+#701 := [trans #594 #407]: #553
+#551 := (iff #741 true)
+#718 := (not false)
+#720 := (iff #718 true)
+#549 := [rewrite]: #720
+#719 := (iff #741 #718)
+#711 := (iff #737 false)
+#727 := (or false false)
+#729 := (iff #727 false)
+#570 := [rewrite]: #729
+#716 := (iff #737 #727)
+#717 := [monotonicity #715 #715]: #716
+#712 := [trans #717 #570]: #711
+#713 := [monotonicity #712]: #719
+#552 := [trans #713 #549]: #551
+#698 := [monotonicity #552 #701]: #603
+#702 := [trans #698 #707]: #699
+#654 := [monotonicity #702 #686 #669]: #653
+#659 := [trans #654 #657]: #658
+#571 := (iff #462 false)
+#728 := (iff #462 #727)
+#721 := (iff #461 false)
+#722 := [rewrite]: #721
+#723 := [monotonicity #722 #722]: #728
+#572 := [trans #723 #570]: #571
+#662 := [monotonicity #572 #659]: #661
+#655 := [trans #662 #664]: #665
+#649 := [monotonicity #655]: #648
+#646 := [trans #649 #651]: #648
+#647 := [quant-inst #9 #9]: #645
+#652 := [mp #647 #646]: #644
+#635 := [unit-resolution #652 #795]: #695
+#636 := [monotonicity #635]: #14
+#15 := (not #14)
+#66 := [asserted]: #15
+[unit-resolution #66 #636]: false
+68e6a38048a26ed5e2cde0fce9122240abdb6e8c 310 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int S3)
-#10 := 0::Int
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 0::Int)
+#9 := 3::Int
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 3::Int)
 decl f5 :: (-> S4 Int Int)
-#12 := 1::Int
+#11 := 1::Int
 decl f6 :: (-> S5 Int S4)
 decl f7 :: S5
-#9 := f7
-#11 := (f6 f7 0::Int)
-#13 := (f5 #11 1::Int)
-#14 := (f3 f4 #13)
-#16 := (= #14 #15)
-#813 := (= #13 0::Int)
+#8 := f7
+#10 := (f6 f7 3::Int)
+#12 := (f5 #10 1::Int)
+#13 := (f3 f4 #12)
+#15 := (= #13 #14)
+#684 := (= #12 3::Int)
 #24 := (:var 0 Int)
 #35 := (:var 1 Int)
 #36 := (f6 f7 #35)
 #37 := (f5 #36 #24)
-#883 := (pattern #37)
-#187 := -1::Int
-#191 := (* -1::Int #24)
-#188 := (* -1::Int #35)
-#194 := (div #188 #191)
-#366 := (* -1::Int #194)
-#367 := (+ #37 #366)
-#368 := (= #367 0::Int)
+#790 := (pattern #37)
+#23 := 0::Int
+#132 := -1::Int
+#136 := (* -1::Int #24)
+#133 := (* -1::Int #35)
+#139 := (div #133 #136)
+#330 := (* -1::Int #139)
+#331 := (+ #37 #330)
+#332 := (= #331 0::Int)
 #47 := (div #35 #24)
-#363 := (* -1::Int #47)
-#364 := (+ #37 #363)
-#365 := (= #364 0::Int)
-#226 := (>= #35 0::Int)
-#219 := (<= #24 0::Int)
-#326 := (or #219 #226)
-#327 := (not #326)
-#215 := (<= #35 0::Int)
-#324 := (or #215 #219)
-#325 := (not #324)
-#330 := (or #325 #327)
-#369 := (ite #330 #365 #368)
-#362 := (= #37 0::Int)
+#327 := (* -1::Int #47)
+#328 := (+ #37 #327)
+#329 := (= #328 0::Int)
+#110 := (<= #24 0::Int)
+#222 := (>= #35 0::Int)
+#290 := (or #222 #110)
+#291 := (not #290)
+#106 := (<= #35 0::Int)
+#286 := (or #106 #110)
+#287 := (not #286)
+#294 := (or #287 #291)
+#333 := (if #294 #329 #332)
+#326 := (= #37 0::Int)
 #39 := (= #24 0::Int)
 #38 := (= #35 0::Int)
 #40 := (or #38 #39)
-#370 := (ite #40 #362 #369)
-#884 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #883) #370)
-#373 := (forall (vars (?v0 Int) (?v1 Int)) #370)
-#887 := (iff #373 #884)
-#885 := (iff #370 #370)
-#886 := [refl]: #885
-#888 := [quant-intro #886]: #887
-#333 := (ite #330 #47 #194)
-#336 := (ite #40 0::Int #333)
-#339 := (= #37 #336)
-#342 := (forall (vars (?v0 Int) (?v1 Int)) #339)
-#374 := (iff #342 #373)
-#371 := (iff #339 #370)
-#372 := [rewrite]: #371
-#375 := [quant-intro #372]: #374
-#227 := (not #226)
-#220 := (not #219)
-#230 := (and #220 #227)
-#216 := (not #215)
-#223 := (and #216 #220)
-#233 := (or #223 #230)
-#236 := (ite #233 #47 #194)
-#239 := (ite #40 0::Int #236)
-#242 := (= #37 #239)
-#245 := (forall (vars (?v0 Int) (?v1 Int)) #242)
-#343 := (iff #245 #342)
-#340 := (iff #242 #339)
-#337 := (= #239 #336)
-#334 := (= #236 #333)
-#331 := (iff #233 #330)
-#328 := (iff #230 #327)
-#329 := [rewrite]: #328
-#309 := (iff #223 #325)
-#310 := [rewrite]: #309
-#332 := [monotonicity #310 #329]: #331
-#335 := [monotonicity #332]: #334
-#338 := [monotonicity #335]: #337
-#341 := [monotonicity #338]: #340
-#344 := [quant-intro #341]: #343
-#305 := (~ #245 #245)
-#318 := (~ #242 #242)
-#319 := [refl]: #318
-#306 := [nnf-pos #319]: #305
-#49 := (- #24)
-#48 := (- #35)
-#50 := (div #48 #49)
-#42 := (< 0::Int #24)
-#44 := (< #35 0::Int)
-#45 := (and #44 #42)
-#41 := (< 0::Int #35)
-#43 := (and #41 #42)
-#46 := (or #43 #45)
-#51 := (ite #46 #47 #50)
-#52 := (ite #40 0::Int #51)
-#53 := (= #37 #52)
-#54 := (forall (vars (?v0 Int) (?v1 Int)) #53)
-#248 := (iff #54 #245)
-#181 := (and #42 #44)
-#184 := (or #43 #181)
-#197 := (ite #184 #47 #194)
-#175 := (= 0::Int #24)
-#172 := (= 0::Int #35)
-#178 := (or #172 #175)
-#200 := (ite #178 0::Int #197)
-#203 := (= #37 #200)
-#206 := (forall (vars (?v0 Int) (?v1 Int)) #203)
-#246 := (iff #206 #245)
-#243 := (iff #203 #242)
-#240 := (= #200 #239)
-#237 := (= #197 #236)
-#234 := (iff #184 #233)
-#231 := (iff #181 #230)
-#228 := (iff #44 #227)
-#229 := [rewrite]: #228
-#221 := (iff #42 #220)
-#222 := [rewrite]: #221
-#232 := [monotonicity #222 #229]: #231
-#224 := (iff #43 #223)
-#217 := (iff #41 #216)
-#218 := [rewrite]: #217
-#225 := [monotonicity #218 #222]: #224
-#235 := [monotonicity #225 #232]: #234
-#238 := [monotonicity #235]: #237
-#213 := (iff #178 #40)
-#211 := (iff #175 #39)
-#212 := [rewrite]: #211
-#209 := (iff #172 #38)
-#210 := [rewrite]: #209
-#214 := [monotonicity #210 #212]: #213
-#241 := [monotonicity #214 #238]: #240
-#244 := [monotonicity #241]: #243
-#247 := [quant-intro #244]: #246
-#207 := (iff #54 #206)
-#204 := (iff #53 #203)
-#201 := (= #52 #200)
-#198 := (= #51 #197)
-#195 := (= #50 #194)
-#192 := (= #49 #191)
-#193 := [rewrite]: #192
-#189 := (= #48 #188)
-#190 := [rewrite]: #189
-#196 := [monotonicity #190 #193]: #195
-#185 := (iff #46 #184)
-#182 := (iff #45 #181)
-#183 := [rewrite]: #182
-#186 := [monotonicity #183]: #185
-#199 := [monotonicity #186 #196]: #198
-#179 := (iff #40 #178)
-#176 := (iff #39 #175)
-#177 := [rewrite]: #176
-#173 := (iff #38 #172)
-#174 := [rewrite]: #173
-#180 := [monotonicity #174 #177]: #179
-#202 := [monotonicity #180 #199]: #201
-#205 := [monotonicity #202]: #204
-#208 := [quant-intro #205]: #207
-#249 := [trans #208 #247]: #248
-#171 := [asserted]: #54
-#250 := [mp #171 #249]: #245
-#320 := [mp~ #250 #306]: #245
-#345 := [mp #320 #344]: #342
-#376 := [mp #345 #375]: #373
-#889 := [mp #376 #888]: #884
-#731 := (not #884)
-#737 := (or #731 #813)
-#819 := (* -1::Int 1::Int)
-#820 := (* -1::Int 0::Int)
-#815 := (div #820 #819)
-#816 := (* -1::Int #815)
-#821 := (+ #13 #816)
-#822 := (= #821 0::Int)
-#817 := (div 0::Int 1::Int)
-#823 := (* -1::Int #817)
-#664 := (+ #13 #823)
-#665 := (= #664 0::Int)
-#841 := (>= 0::Int 0::Int)
-#666 := (<= 1::Int 0::Int)
-#808 := (or #666 #841)
-#809 := (not #808)
-#810 := (<= 0::Int 0::Int)
-#811 := (or #810 #666)
-#805 := (not #811)
-#806 := (or #805 #809)
-#812 := (ite #806 #665 #822)
-#807 := (= 1::Int 0::Int)
-#814 := (= 0::Int 0::Int)
-#643 := (or #814 #807)
-#645 := (ite #643 #813 #812)
-#710 := (or #731 #645)
-#712 := (iff #710 #737)
-#716 := (iff #737 #737)
-#717 := [rewrite]: #716
-#735 := (iff #645 #813)
-#1 := true
-#728 := (ite true #813 #813)
-#733 := (iff #728 #813)
-#734 := [rewrite]: #733
-#729 := (iff #645 #728)
-#746 := (iff #812 #813)
-#742 := (ite false #813 #813)
-#745 := (iff #742 #813)
-#740 := [rewrite]: #745
-#743 := (iff #812 #742)
-#739 := (iff #822 #813)
-#760 := (= #821 #13)
-#773 := (+ #13 0::Int)
-#775 := (= #773 #13)
-#761 := [rewrite]: #775
-#759 := (= #821 #773)
-#757 := (= #816 0::Int)
-#768 := (= #820 0::Int)
-#769 := [rewrite]: #768
-#755 := (= #816 #820)
-#753 := (= #815 0::Int)
-#747 := (div 0::Int -1::Int)
-#751 := (= #747 0::Int)
-#752 := [rewrite]: #751
-#748 := (= #815 #747)
-#763 := (= #819 -1::Int)
-#767 := [rewrite]: #763
-#750 := [monotonicity #769 #767]: #748
-#754 := [trans #750 #752]: #753
-#756 := [monotonicity #754]: #755
-#758 := [trans #756 #769]: #757
-#749 := [monotonicity #758]: #759
-#738 := [trans #749 #761]: #760
-#741 := [monotonicity #738]: #739
-#765 := (iff #665 #813)
-#762 := (= #664 #13)
-#774 := (= #664 #773)
-#771 := (= #823 0::Int)
-#777 := (= #823 #820)
-#782 := (= #817 0::Int)
-#783 := [rewrite]: #782
-#784 := [monotonicity #783]: #777
-#772 := [trans #784 #769]: #771
-#770 := [monotonicity #772]: #774
-#764 := [trans #770 #761]: #762
-#766 := [monotonicity #764]: #765
-#780 := (iff #806 false)
-#788 := (or false false)
-#786 := (iff #788 false)
-#791 := [rewrite]: #786
-#789 := (iff #806 #788)
-#776 := (iff #809 false)
-#489 := (not true)
-#850 := (iff #489 false)
-#836 := [rewrite]: #850
-#787 := (iff #809 #489)
-#798 := (iff #808 true)
-#702 := (or false true)
-#797 := (iff #702 true)
-#794 := [rewrite]: #797
-#703 := (iff #808 #702)
-#848 := (iff #841 true)
-#488 := [rewrite]: #848
-#792 := (iff #666 false)
-#793 := [rewrite]: #792
-#704 := [monotonicity #793 #488]: #703
-#785 := [trans #704 #794]: #798
-#779 := [monotonicity #785]: #787
-#778 := [trans #779 #836]: #776
-#700 := (iff #805 false)
-#699 := (iff #805 #489)
-#696 := (iff #811 true)
-#803 := (or true false)
-#686 := (iff #803 true)
-#687 := [rewrite]: #686
-#796 := (iff #811 #803)
-#795 := (iff #810 true)
-#697 := [rewrite]: #795
-#681 := [monotonicity #697 #793]: #796
-#698 := [trans #681 #687]: #696
-#692 := [monotonicity #698]: #699
-#701 := [trans #692 #836]: #700
-#790 := [monotonicity #701 #778]: #789
-#781 := [trans #790 #791]: #780
-#744 := [monotonicity #781 #766 #741]: #743
-#732 := [trans #744 #740]: #746
-#688 := (iff #643 true)
-#801 := (iff #643 #803)
-#800 := (iff #807 false)
-#802 := [rewrite]: #800
-#646 := (iff #814 true)
-#799 := [rewrite]: #646
-#804 := [monotonicity #799 #802]: #801
-#647 := [trans #804 #687]: #688
-#730 := [monotonicity #647 #732]: #729
-#736 := [trans #730 #734]: #735
-#605 := [monotonicity #736]: #712
-#718 := [trans #605 #717]: #712
-#711 := [quant-inst #10 #12]: #710
-#723 := [mp #711 #718]: #737
-#720 := [unit-resolution #723 #889]: #813
-#721 := [monotonicity #720]: #16
-#17 := (not #16)
-#85 := [asserted]: #17
-[unit-resolution #85 #721]: false
-unsat
-b427c6e1aa7e8efb75c28eb2c11cd0d7fd389271 307 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#10 := 1::Int
-decl f4 :: S2
-#8 := f4
-#14 := (f3 f4 1::Int)
-decl f5 :: (-> S4 Int Int)
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#9 := f7
-#11 := (f6 f7 1::Int)
-#12 := (f5 #11 1::Int)
-#13 := (f3 f4 #12)
-#15 := (= #13 #14)
-#766 := (= #12 1::Int)
-#24 := (:var 0 Int)
-#35 := (:var 1 Int)
-#36 := (f6 f7 #35)
-#37 := (f5 #36 #24)
-#883 := (pattern #37)
-#23 := 0::Int
-#187 := -1::Int
-#191 := (* -1::Int #24)
-#188 := (* -1::Int #35)
-#194 := (div #188 #191)
-#366 := (* -1::Int #194)
-#367 := (+ #37 #366)
-#368 := (= #367 0::Int)
-#47 := (div #35 #24)
-#363 := (* -1::Int #47)
-#364 := (+ #37 #363)
-#365 := (= #364 0::Int)
-#226 := (>= #35 0::Int)
-#219 := (<= #24 0::Int)
-#326 := (or #219 #226)
-#327 := (not #326)
-#215 := (<= #35 0::Int)
-#324 := (or #215 #219)
-#325 := (not #324)
-#330 := (or #325 #327)
-#369 := (ite #330 #365 #368)
-#362 := (= #37 0::Int)
-#39 := (= #24 0::Int)
-#38 := (= #35 0::Int)
-#40 := (or #38 #39)
-#370 := (ite #40 #362 #369)
-#884 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #883) #370)
-#373 := (forall (vars (?v0 Int) (?v1 Int)) #370)
-#887 := (iff #373 #884)
-#885 := (iff #370 #370)
-#886 := [refl]: #885
-#888 := [quant-intro #886]: #887
-#333 := (ite #330 #47 #194)
-#336 := (ite #40 0::Int #333)
-#339 := (= #37 #336)
-#342 := (forall (vars (?v0 Int) (?v1 Int)) #339)
-#374 := (iff #342 #373)
-#371 := (iff #339 #370)
-#372 := [rewrite]: #371
-#375 := [quant-intro #372]: #374
-#227 := (not #226)
-#220 := (not #219)
-#230 := (and #220 #227)
-#216 := (not #215)
-#223 := (and #216 #220)
-#233 := (or #223 #230)
-#236 := (ite #233 #47 #194)
-#239 := (ite #40 0::Int #236)
-#242 := (= #37 #239)
-#245 := (forall (vars (?v0 Int) (?v1 Int)) #242)
-#343 := (iff #245 #342)
-#340 := (iff #242 #339)
-#337 := (= #239 #336)
-#334 := (= #236 #333)
-#331 := (iff #233 #330)
-#328 := (iff #230 #327)
-#329 := [rewrite]: #328
-#309 := (iff #223 #325)
-#310 := [rewrite]: #309
-#332 := [monotonicity #310 #329]: #331
-#335 := [monotonicity #332]: #334
-#338 := [monotonicity #335]: #337
-#341 := [monotonicity #338]: #340
-#344 := [quant-intro #341]: #343
-#305 := (~ #245 #245)
-#318 := (~ #242 #242)
-#319 := [refl]: #318
-#306 := [nnf-pos #319]: #305
+#334 := (if #40 #326 #333)
+#791 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #790) #334)
+#337 := (forall (vars (?v0 Int) (?v1 Int)) #334)
+#794 := (iff #337 #791)
+#792 := (iff #334 #334)
+#793 := [refl]: #792
+#795 := [quant-intro #793]: #794
+#297 := (if #294 #47 #139)
+#300 := (if #40 0::Int #297)
+#303 := (= #37 #300)
+#306 := (forall (vars (?v0 Int) (?v1 Int)) #303)
+#338 := (iff #306 #337)
+#335 := (iff #303 #334)
+#336 := [rewrite]: #335
+#339 := [quant-intro #336]: #338
+#111 := (not #110)
+#225 := (not #222)
+#228 := (and #225 #111)
+#107 := (not #106)
+#114 := (and #107 #111)
+#231 := (or #114 #228)
+#234 := (if #231 #47 #139)
+#237 := (if #40 0::Int #234)
+#240 := (= #37 #237)
+#243 := (forall (vars (?v0 Int) (?v1 Int)) #240)
+#307 := (iff #243 #306)
+#304 := (iff #240 #303)
+#301 := (= #237 #300)
+#298 := (= #234 #297)
+#295 := (iff #231 #294)
+#292 := (iff #228 #291)
+#293 := [rewrite]: #292
+#288 := (iff #114 #287)
+#289 := [rewrite]: #288
+#296 := [monotonicity #289 #293]: #295
+#299 := [monotonicity #296]: #298
+#302 := [monotonicity #299]: #301
+#305 := [monotonicity #302]: #304
+#308 := [quant-intro #305]: #307
+#278 := (~ #243 #243)
+#276 := (~ #240 #240)
+#277 := [refl]: #276
+#279 := [nnf-pos #277]: #278
+#117 := (<= 0::Int #35)
+#118 := (not #117)
+#126 := (and #118 #111)
+#129 := (or #114 #126)
+#142 := (if #129 #47 #139)
+#145 := (if #40 0::Int #142)
+#148 := (= #37 #145)
+#151 := (forall (vars (?v0 Int) (?v1 Int)) #148)
+#244 := (iff #151 #243)
+#241 := (iff #148 #240)
+#238 := (= #145 #237)
+#235 := (= #142 #234)
+#232 := (iff #129 #231)
+#229 := (iff #126 #228)
+#226 := (iff #118 #225)
+#223 := (iff #117 #222)
+#224 := [rewrite]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [monotonicity #233]: #235
+#239 := [monotonicity #236]: #238
+#242 := [monotonicity #239]: #241
+#245 := [quant-intro #242]: #244
 #49 := (- #24)
 #48 := (- #35)
 #50 := (div #48 #49)
@@ -14208,1011 +13934,966 @@
 #41 := (< 0::Int #35)
 #43 := (and #41 #42)
 #46 := (or #43 #45)
-#51 := (ite #46 #47 #50)
-#52 := (ite #40 0::Int #51)
+#51 := (if #46 #47 #50)
+#52 := (if #40 0::Int #51)
 #53 := (= #37 #52)
 #54 := (forall (vars (?v0 Int) (?v1 Int)) #53)
-#248 := (iff #54 #245)
-#181 := (and #42 #44)
-#184 := (or #43 #181)
-#197 := (ite #184 #47 #194)
-#175 := (= 0::Int #24)
-#172 := (= 0::Int #35)
-#178 := (or #172 #175)
-#200 := (ite #178 0::Int #197)
-#203 := (= #37 #200)
-#206 := (forall (vars (?v0 Int) (?v1 Int)) #203)
-#246 := (iff #206 #245)
-#243 := (iff #203 #242)
-#240 := (= #200 #239)
-#237 := (= #197 #236)
-#234 := (iff #184 #233)
-#231 := (iff #181 #230)
-#228 := (iff #44 #227)
-#229 := [rewrite]: #228
-#221 := (iff #42 #220)
-#222 := [rewrite]: #221
-#232 := [monotonicity #222 #229]: #231
-#224 := (iff #43 #223)
-#217 := (iff #41 #216)
-#218 := [rewrite]: #217
-#225 := [monotonicity #218 #222]: #224
-#235 := [monotonicity #225 #232]: #234
-#238 := [monotonicity #235]: #237
-#213 := (iff #178 #40)
-#211 := (iff #175 #39)
-#212 := [rewrite]: #211
-#209 := (iff #172 #38)
-#210 := [rewrite]: #209
-#214 := [monotonicity #210 #212]: #213
-#241 := [monotonicity #214 #238]: #240
-#244 := [monotonicity #241]: #243
-#247 := [quant-intro #244]: #246
-#207 := (iff #54 #206)
-#204 := (iff #53 #203)
-#201 := (= #52 #200)
-#198 := (= #51 #197)
-#195 := (= #50 #194)
-#192 := (= #49 #191)
-#193 := [rewrite]: #192
-#189 := (= #48 #188)
-#190 := [rewrite]: #189
-#196 := [monotonicity #190 #193]: #195
-#185 := (iff #46 #184)
-#182 := (iff #45 #181)
-#183 := [rewrite]: #182
-#186 := [monotonicity #183]: #185
-#199 := [monotonicity #186 #196]: #198
-#179 := (iff #40 #178)
-#176 := (iff #39 #175)
-#177 := [rewrite]: #176
-#173 := (iff #38 #172)
-#174 := [rewrite]: #173
-#180 := [monotonicity #174 #177]: #179
-#202 := [monotonicity #180 #199]: #201
-#205 := [monotonicity #202]: #204
-#208 := [quant-intro #205]: #207
-#249 := [trans #208 #247]: #248
-#171 := [asserted]: #54
-#250 := [mp #171 #249]: #245
-#320 := [mp~ #250 #306]: #245
-#345 := [mp #320 #344]: #342
-#376 := [mp #345 #375]: #373
-#889 := [mp #376 #888]: #884
-#712 := (not #884)
-#605 := (or #712 #766)
-#820 := (* -1::Int 1::Int)
-#815 := (div #820 #820)
-#816 := (* -1::Int #815)
-#821 := (+ #12 #816)
-#822 := (= #821 0::Int)
-#817 := (div 1::Int 1::Int)
-#823 := (* -1::Int #817)
-#664 := (+ #12 #823)
-#665 := (= #664 0::Int)
-#841 := (>= 1::Int 0::Int)
-#666 := (<= 1::Int 0::Int)
-#808 := (or #666 #841)
-#809 := (not #808)
-#810 := (or #666 #666)
-#811 := (not #810)
-#805 := (or #811 #809)
-#806 := (ite #805 #665 #822)
-#812 := (= #12 0::Int)
-#813 := (= 1::Int 0::Int)
-#807 := (or #813 #813)
-#814 := (ite #807 #812 #806)
-#716 := (or #712 #814)
-#718 := (iff #716 #605)
-#719 := (iff #605 #605)
-#720 := [rewrite]: #719
-#710 := (iff #814 #766)
-#734 := (ite false #812 #766)
-#731 := (iff #734 #766)
-#737 := [rewrite]: #731
-#735 := (iff #814 #734)
-#730 := (iff #806 #766)
-#1 := true
-#740 := (ite true #766 #766)
-#728 := (iff #740 #766)
-#729 := [rewrite]: #728
-#746 := (iff #806 #740)
-#744 := (iff #822 #766)
-#773 := (+ -1::Int #12)
-#762 := (= #773 0::Int)
-#763 := (iff #762 #766)
-#767 := [rewrite]: #763
-#742 := (iff #822 #762)
-#739 := (= #821 #773)
-#769 := (+ #12 -1::Int)
-#774 := (= #769 #773)
-#770 := [rewrite]: #774
-#760 := (= #821 #769)
-#759 := (= #816 -1::Int)
-#783 := (= #820 -1::Int)
-#777 := [rewrite]: #783
-#757 := (= #816 #820)
-#755 := (= #815 1::Int)
-#750 := (div -1::Int -1::Int)
-#753 := (= #750 1::Int)
-#754 := [rewrite]: #753
-#751 := (= #815 #750)
-#752 := [monotonicity #777 #777]: #751
-#756 := [trans #752 #754]: #755
-#758 := [monotonicity #756]: #757
-#749 := [trans #758 #777]: #759
-#738 := [monotonicity #749]: #760
-#741 := [trans #738 #770]: #739
-#743 := [monotonicity #741]: #742
-#745 := [trans #743 #767]: #744
-#747 := (iff #665 #766)
-#764 := (iff #665 #762)
-#775 := (= #664 #773)
-#771 := (= #664 #769)
-#784 := (= #823 -1::Int)
-#781 := (= #823 #820)
-#791 := (= #817 1::Int)
-#780 := [rewrite]: #791
-#782 := [monotonicity #780]: #781
-#768 := [trans #782 #777]: #784
-#772 := [monotonicity #768]: #771
-#761 := [trans #772 #770]: #775
-#765 := [monotonicity #761]: #764
-#748 := [trans #765 #767]: #747
-#790 := (iff #805 true)
-#779 := (or true false)
-#788 := (iff #779 true)
-#789 := [rewrite]: #788
-#776 := (iff #805 #779)
-#785 := (iff #809 false)
-#489 := (not true)
-#850 := (iff #489 false)
-#836 := [rewrite]: #850
-#794 := (iff #809 #489)
-#704 := (iff #808 true)
-#692 := (or false true)
-#702 := (iff #692 true)
-#703 := [rewrite]: #702
-#700 := (iff #808 #692)
-#848 := (iff #841 true)
-#488 := [rewrite]: #848
-#686 := (iff #666 false)
-#687 := [rewrite]: #686
-#701 := [monotonicity #687 #488]: #700
-#797 := [trans #701 #703]: #704
-#798 := [monotonicity #797]: #794
-#787 := [trans #798 #836]: #785
-#698 := (iff #811 true)
-#792 := (not false)
-#681 := (iff #792 true)
-#696 := [rewrite]: #681
-#793 := (iff #811 #792)
-#795 := (iff #810 false)
-#646 := (or false false)
-#802 := (iff #646 false)
-#803 := [rewrite]: #802
-#688 := (iff #810 #646)
-#647 := [monotonicity #687 #687]: #688
-#697 := [trans #647 #803]: #795
-#796 := [monotonicity #697]: #793
-#699 := [trans #796 #696]: #698
-#778 := [monotonicity #699 #787]: #776
-#786 := [trans #778 #789]: #790
-#732 := [monotonicity #786 #748 #745]: #746
-#733 := [trans #732 #729]: #730
-#801 := (iff #807 false)
-#799 := (iff #807 #646)
-#643 := (iff #813 false)
-#645 := [rewrite]: #643
-#800 := [monotonicity #645 #645]: #799
-#804 := [trans #800 #803]: #801
-#736 := [monotonicity #804 #733]: #735
-#711 := [trans #736 #737]: #710
-#723 := [monotonicity #711]: #718
-#721 := [trans #723 #720]: #718
-#717 := [quant-inst #10 #10]: #716
-#724 := [mp #717 #721]: #605
-#722 := [unit-resolution #724 #889]: #766
-#727 := [monotonicity #722]: #15
+#152 := (iff #54 #151)
+#149 := (iff #53 #148)
+#146 := (= #52 #145)
+#143 := (= #51 #142)
+#140 := (= #50 #139)
+#137 := (= #49 #136)
+#138 := [rewrite]: #137
+#134 := (= #48 #133)
+#135 := [rewrite]: #134
+#141 := [monotonicity #135 #138]: #140
+#130 := (iff #46 #129)
+#127 := (iff #45 #126)
+#112 := (iff #42 #111)
+#113 := [rewrite]: #112
+#119 := (iff #44 #118)
+#123 := (iff #118 #118)
+#121 := (iff #117 #117)
+#122 := [rewrite]: #121
+#124 := [monotonicity #122]: #123
+#120 := [rewrite]: #119
+#125 := [trans #120 #124]: #119
+#128 := [monotonicity #125 #113]: #127
+#115 := (iff #43 #114)
+#108 := (iff #41 #107)
+#109 := [rewrite]: #108
+#116 := [monotonicity #109 #113]: #115
+#131 := [monotonicity #116 #128]: #130
+#144 := [monotonicity #131 #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [monotonicity #147]: #149
+#153 := [quant-intro #150]: #152
+#71 := [asserted]: #54
+#154 := [mp #71 #153]: #151
+#246 := [mp #154 #245]: #243
+#280 := [mp~ #246 #279]: #243
+#309 := [mp #280 #308]: #306
+#340 := [mp #309 #339]: #337
+#796 := [mp #340 #795]: #791
+#639 := (not #791)
+#635 := (or #639 #684)
+#736 := (* -1::Int 1::Int)
+#732 := (* -1::Int 3::Int)
+#725 := (div #732 #736)
+#726 := (* -1::Int #725)
+#727 := (+ #12 #726)
+#722 := (= #727 0::Int)
+#734 := (div 3::Int 1::Int)
+#449 := (* -1::Int #734)
+#731 := (+ #12 #449)
+#735 := (= #731 0::Int)
+#742 := (<= 1::Int 0::Int)
+#551 := (>= 3::Int 0::Int)
+#454 := (or #551 #742)
+#455 := (not #454)
+#738 := (<= 3::Int 0::Int)
+#452 := (or #738 #742)
+#453 := (not #452)
+#733 := (or #453 #455)
+#723 := (if #733 #735 #722)
+#741 := (= #12 0::Int)
+#463 := (= 1::Int 0::Int)
+#462 := (= 3::Int 0::Int)
+#737 := (or #462 #463)
+#728 := (if #737 #741 #723)
+#636 := (or #639 #728)
+#640 := (iff #636 #635)
+#642 := (iff #635 #635)
+#643 := [rewrite]: #642
+#647 := (iff #728 #684)
+#648 := (if false #741 #684)
+#651 := (iff #648 #684)
+#652 := [rewrite]: #651
+#649 := (iff #728 #648)
+#645 := (iff #723 #684)
+#1 := true
+#664 := (if true #684 #684)
+#656 := (iff #664 #684)
+#667 := [rewrite]: #656
+#665 := (iff #723 #664)
+#662 := (iff #722 #684)
+#701 := -3::Int
+#696 := (+ -3::Int #12)
+#688 := (= #696 0::Int)
+#691 := (iff #688 #684)
+#675 := [rewrite]: #691
+#660 := (iff #722 #688)
+#658 := (= #727 #696)
+#683 := (+ #12 -3::Int)
+#697 := (= #683 #696)
+#693 := [rewrite]: #697
+#655 := (= #727 #683)
+#674 := (= #726 -3::Int)
+#705 := (= #732 -3::Int)
+#692 := [rewrite]: #705
+#673 := (= #726 #732)
+#671 := (= #725 3::Int)
+#681 := (div -3::Int -1::Int)
+#668 := (= #681 3::Int)
+#669 := [rewrite]: #668
+#677 := (= #725 #681)
+#679 := (= #736 -1::Int)
+#680 := [rewrite]: #679
+#682 := [monotonicity #692 #680]: #677
+#672 := [trans #682 #669]: #671
+#670 := [monotonicity #672]: #673
+#654 := [trans #670 #692]: #674
+#657 := [monotonicity #654]: #655
+#659 := [trans #657 #693]: #658
+#661 := [monotonicity #659]: #660
+#663 := [trans #661 #675]: #662
+#676 := (iff #735 #684)
+#689 := (iff #735 #688)
+#698 := (= #731 #696)
+#685 := (= #731 #683)
+#694 := (= #449 -3::Int)
+#611 := (= #449 #732)
+#609 := (= #734 3::Int)
+#610 := [rewrite]: #609
+#704 := [monotonicity #610]: #611
+#686 := [trans #704 #692]: #694
+#695 := [monotonicity #686]: #685
+#687 := [trans #695 #693]: #698
+#690 := [monotonicity #687]: #689
+#678 := [trans #690 #675]: #676
+#607 := (iff #733 true)
+#594 := (or true false)
+#702 := (iff #594 true)
+#604 := [rewrite]: #702
+#606 := (iff #733 #594)
+#603 := (iff #455 false)
+#420 := (not true)
+#745 := (iff #420 false)
+#408 := [rewrite]: #745
+#703 := (iff #455 #420)
+#699 := (iff #454 true)
+#595 := (iff #454 #594)
+#720 := (iff #742 false)
+#714 := [rewrite]: #720
+#424 := (iff #551 true)
+#760 := [rewrite]: #424
+#554 := [monotonicity #760 #714]: #595
+#700 := [trans #554 #604]: #699
+#588 := [monotonicity #700]: #703
+#605 := [trans #588 #408]: #603
+#711 := (iff #453 true)
+#706 := (not false)
+#710 := (iff #706 true)
+#708 := [rewrite]: #710
+#707 := (iff #453 #706)
+#552 := (iff #452 false)
+#572 := (or false false)
+#716 := (iff #572 false)
+#717 := [rewrite]: #716
+#721 := (iff #452 #572)
+#713 := (iff #738 false)
+#719 := [rewrite]: #713
+#550 := [monotonicity #719 #714]: #721
+#553 := [trans #550 #717]: #552
+#709 := [monotonicity #553]: #707
+#593 := [trans #709 #708]: #711
+#599 := [monotonicity #593 #605]: #606
+#608 := [trans #599 #604]: #607
+#666 := [monotonicity #608 #678 #663]: #665
+#646 := [trans #666 #667]: #645
+#718 := (iff #737 false)
+#573 := (iff #737 #572)
+#730 := (iff #463 false)
+#571 := [rewrite]: #730
+#729 := (iff #462 false)
+#724 := [rewrite]: #729
+#715 := [monotonicity #724 #571]: #573
+#712 := [trans #715 #717]: #718
+#650 := [monotonicity #712 #646]: #649
+#653 := [trans #650 #652]: #647
+#641 := [monotonicity #653]: #640
+#638 := [trans #641 #643]: #640
+#637 := [quant-inst #9 #11]: #636
+#644 := [mp #637 #638]: #635
+#619 := [unit-resolution #644 #796]: #684
+#512 := [monotonicity #619]: #15
 #16 := (not #15)
-#85 := [asserted]: #16
-[unit-resolution #85 #727]: false
-unsat
-0a93bcd756c41eafe5e87939721bc016585791fd 318 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#10 := 3::Int
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 3::Int)
-decl f5 :: (-> S4 Int Int)
-#12 := 1::Int
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#9 := f7
-#11 := (f6 f7 3::Int)
-#13 := (f5 #11 1::Int)
-#14 := (f3 f4 #13)
-#16 := (= #14 #15)
-#754 := (= #13 3::Int)
-#25 := (:var 0 Int)
-#36 := (:var 1 Int)
-#37 := (f6 f7 #36)
-#38 := (f5 #37 #25)
-#884 := (pattern #38)
-#24 := 0::Int
-#188 := -1::Int
-#192 := (* -1::Int #25)
-#189 := (* -1::Int #36)
-#195 := (div #189 #192)
-#367 := (* -1::Int #195)
-#368 := (+ #38 #367)
-#369 := (= #368 0::Int)
-#48 := (div #36 #25)
-#364 := (* -1::Int #48)
-#365 := (+ #38 #364)
-#366 := (= #365 0::Int)
-#227 := (>= #36 0::Int)
-#220 := (<= #25 0::Int)
-#327 := (or #220 #227)
-#328 := (not #327)
-#216 := (<= #36 0::Int)
-#325 := (or #216 #220)
-#326 := (not #325)
-#331 := (or #326 #328)
-#370 := (ite #331 #366 #369)
-#363 := (= #38 0::Int)
-#40 := (= #25 0::Int)
-#39 := (= #36 0::Int)
-#41 := (or #39 #40)
-#371 := (ite #41 #363 #370)
-#885 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #884) #371)
-#374 := (forall (vars (?v0 Int) (?v1 Int)) #371)
-#888 := (iff #374 #885)
-#886 := (iff #371 #371)
-#887 := [refl]: #886
-#889 := [quant-intro #887]: #888
-#334 := (ite #331 #48 #195)
-#337 := (ite #41 0::Int #334)
-#340 := (= #38 #337)
-#343 := (forall (vars (?v0 Int) (?v1 Int)) #340)
-#375 := (iff #343 #374)
-#372 := (iff #340 #371)
-#373 := [rewrite]: #372
-#376 := [quant-intro #373]: #375
-#228 := (not #227)
-#221 := (not #220)
-#231 := (and #221 #228)
-#217 := (not #216)
-#224 := (and #217 #221)
-#234 := (or #224 #231)
-#237 := (ite #234 #48 #195)
-#240 := (ite #41 0::Int #237)
-#243 := (= #38 #240)
-#246 := (forall (vars (?v0 Int) (?v1 Int)) #243)
-#344 := (iff #246 #343)
-#341 := (iff #243 #340)
-#338 := (= #240 #337)
-#335 := (= #237 #334)
-#332 := (iff #234 #331)
-#329 := (iff #231 #328)
-#330 := [rewrite]: #329
-#310 := (iff #224 #326)
-#311 := [rewrite]: #310
-#333 := [monotonicity #311 #330]: #332
-#336 := [monotonicity #333]: #335
-#339 := [monotonicity #336]: #338
-#342 := [monotonicity #339]: #341
-#345 := [quant-intro #342]: #344
-#306 := (~ #246 #246)
-#319 := (~ #243 #243)
-#320 := [refl]: #319
-#307 := [nnf-pos #320]: #306
-#50 := (- #25)
-#49 := (- #36)
-#51 := (div #49 #50)
-#43 := (< 0::Int #25)
-#45 := (< #36 0::Int)
-#46 := (and #45 #43)
-#42 := (< 0::Int #36)
-#44 := (and #42 #43)
-#47 := (or #44 #46)
-#52 := (ite #47 #48 #51)
-#53 := (ite #41 0::Int #52)
-#54 := (= #38 #53)
-#55 := (forall (vars (?v0 Int) (?v1 Int)) #54)
-#249 := (iff #55 #246)
-#182 := (and #43 #45)
-#185 := (or #44 #182)
-#198 := (ite #185 #48 #195)
-#176 := (= 0::Int #25)
-#173 := (= 0::Int #36)
-#179 := (or #173 #176)
-#201 := (ite #179 0::Int #198)
-#204 := (= #38 #201)
-#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
-#247 := (iff #207 #246)
-#244 := (iff #204 #243)
-#241 := (= #201 #240)
-#238 := (= #198 #237)
-#235 := (iff #185 #234)
-#232 := (iff #182 #231)
-#229 := (iff #45 #228)
-#230 := [rewrite]: #229
-#222 := (iff #43 #221)
-#223 := [rewrite]: #222
-#233 := [monotonicity #223 #230]: #232
-#225 := (iff #44 #224)
-#218 := (iff #42 #217)
-#219 := [rewrite]: #218
-#226 := [monotonicity #219 #223]: #225
-#236 := [monotonicity #226 #233]: #235
-#239 := [monotonicity #236]: #238
-#214 := (iff #179 #41)
-#212 := (iff #176 #40)
-#213 := [rewrite]: #212
-#210 := (iff #173 #39)
-#211 := [rewrite]: #210
-#215 := [monotonicity #211 #213]: #214
-#242 := [monotonicity #215 #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [quant-intro #245]: #247
-#208 := (iff #55 #207)
-#205 := (iff #54 #204)
-#202 := (= #53 #201)
-#199 := (= #52 #198)
-#196 := (= #51 #195)
-#193 := (= #50 #192)
-#194 := [rewrite]: #193
-#190 := (= #49 #189)
-#191 := [rewrite]: #190
-#197 := [monotonicity #191 #194]: #196
-#186 := (iff #47 #185)
-#183 := (iff #46 #182)
-#184 := [rewrite]: #183
-#187 := [monotonicity #184]: #186
-#200 := [monotonicity #187 #197]: #199
-#180 := (iff #41 #179)
-#177 := (iff #40 #176)
-#178 := [rewrite]: #177
-#174 := (iff #39 #173)
-#175 := [rewrite]: #174
-#181 := [monotonicity #175 #178]: #180
-#203 := [monotonicity #181 #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [quant-intro #206]: #208
-#250 := [trans #209 #248]: #249
-#172 := [asserted]: #55
-#251 := [mp #172 #250]: #246
-#321 := [mp~ #251 #307]: #246
-#346 := [mp #321 #345]: #343
-#377 := [mp #346 #376]: #374
-#890 := [mp #377 #889]: #885
-#726 := (not #885)
-#727 := (or #726 #754)
-#821 := (* -1::Int 1::Int)
-#816 := (* -1::Int 3::Int)
-#817 := (div #816 #821)
-#822 := (* -1::Int #817)
-#823 := (+ #13 #822)
-#818 := (= #823 0::Int)
-#824 := (div 3::Int 1::Int)
-#665 := (* -1::Int #824)
-#666 := (+ #13 #665)
-#667 := (= #666 0::Int)
-#842 := (>= 3::Int 0::Int)
-#809 := (<= 1::Int 0::Int)
-#810 := (or #809 #842)
-#811 := (not #810)
-#812 := (<= 3::Int 0::Int)
-#806 := (or #812 #809)
-#807 := (not #806)
-#813 := (or #807 #811)
-#814 := (ite #813 #667 #818)
-#808 := (= #13 0::Int)
-#815 := (= 1::Int 0::Int)
-#644 := (= 3::Int 0::Int)
-#646 := (or #644 #815)
-#647 := (ite #646 #808 #814)
-#723 := (or #726 #647)
-#708 := (iff #723 #727)
-#709 := (iff #727 #727)
-#690 := [rewrite]: #709
-#722 := (iff #647 #754)
-#718 := (ite false #808 #754)
-#720 := (iff #718 #754)
-#721 := [rewrite]: #720
-#719 := (iff #647 #718)
-#606 := (iff #814 #754)
-#1 := true
-#732 := (ite true #754 #754)
-#712 := (iff #732 #754)
-#713 := [rewrite]: #712
-#738 := (iff #814 #732)
-#736 := (iff #818 #754)
-#774 := -3::Int
-#767 := (+ -3::Int #13)
-#751 := (= #767 0::Int)
-#755 := (iff #751 #754)
-#756 := [rewrite]: #755
-#734 := (iff #818 #751)
-#730 := (= #823 #767)
-#763 := (+ #13 -3::Int)
-#764 := (= #763 #767)
-#768 := [rewrite]: #764
-#733 := (= #823 #763)
-#741 := (= #822 -3::Int)
-#775 := (= #816 -3::Int)
-#771 := [rewrite]: #775
-#745 := (= #822 #816)
-#743 := (= #817 3::Int)
-#750 := (div -3::Int -1::Int)
-#740 := (= #750 3::Int)
-#742 := [rewrite]: #740
-#761 := (= #817 #750)
-#759 := (= #821 -1::Int)
-#760 := [rewrite]: #759
-#739 := [monotonicity #771 #760]: #761
-#744 := [trans #739 #742]: #743
-#746 := [monotonicity #744]: #745
-#747 := [trans #746 #771]: #741
-#729 := [monotonicity #747]: #733
-#731 := [trans #729 #768]: #730
-#735 := [monotonicity #731]: #734
-#737 := [trans #735 #756]: #736
-#757 := (iff #667 #754)
-#752 := (iff #667 #751)
-#748 := (= #666 #767)
-#765 := (= #666 #763)
-#776 := (= #665 -3::Int)
-#772 := (= #665 #816)
-#769 := (= #824 3::Int)
-#770 := [rewrite]: #769
-#773 := [monotonicity #770]: #772
-#762 := [trans #773 #771]: #776
-#766 := [monotonicity #762]: #765
-#749 := [trans #766 #768]: #748
-#753 := [monotonicity #749]: #752
-#758 := [trans #753 #756]: #757
-#778 := (iff #813 true)
-#792 := (or true false)
-#783 := (iff #792 true)
-#784 := [rewrite]: #783
-#781 := (iff #813 #792)
-#791 := (iff #811 false)
-#490 := (not true)
-#851 := (iff #490 false)
-#837 := [rewrite]: #851
-#789 := (iff #811 #490)
-#777 := (iff #810 true)
-#795 := (or false true)
-#788 := (iff #795 true)
-#780 := [rewrite]: #788
-#799 := (iff #810 #795)
-#849 := (iff #842 true)
-#489 := [rewrite]: #849
-#794 := (iff #809 false)
-#797 := [rewrite]: #794
-#786 := [monotonicity #797 #489]: #799
-#779 := [trans #786 #780]: #777
-#790 := [monotonicity #779]: #789
-#787 := [trans #790 #837]: #791
-#705 := (iff #807 true)
-#693 := (not false)
-#703 := (iff #693 true)
-#704 := [rewrite]: #703
-#701 := (iff #807 #693)
-#699 := (iff #806 false)
-#802 := (or false false)
-#688 := (iff #802 false)
-#689 := [rewrite]: #688
-#682 := (iff #806 #802)
-#698 := (iff #812 false)
-#793 := [rewrite]: #698
-#697 := [monotonicity #793 #797]: #682
-#700 := [trans #697 #689]: #699
-#702 := [monotonicity #700]: #701
-#798 := [trans #702 #704]: #705
-#782 := [monotonicity #798 #787]: #781
-#785 := [trans #782 #784]: #778
-#711 := [monotonicity #785 #758 #737]: #738
-#717 := [trans #711 #713]: #606
-#648 := (iff #646 false)
-#805 := (iff #646 #802)
-#803 := (iff #815 false)
-#804 := [rewrite]: #803
-#800 := (iff #644 false)
-#801 := [rewrite]: #800
-#687 := [monotonicity #801 #804]: #805
-#796 := [trans #687 #689]: #648
-#724 := [monotonicity #796 #717]: #719
-#725 := [trans #724 #721]: #722
-#654 := [monotonicity #725]: #708
-#714 := [trans #654 #690]: #708
-#728 := [quant-inst #10 #12]: #723
-#715 := [mp #728 #714]: #727
-#684 := [unit-resolution #715 #890]: #754
-#691 := [monotonicity #684]: #16
-#17 := (not #16)
-#86 := [asserted]: #17
-[unit-resolution #86 #691]: false
-unsat
-a120f065741062bd8358dab2e8b4f52695deae0b 386 0
-#2 := false
+#67 := [asserted]: #16
+[unit-resolution #67 #512]: false
+d21ca909bb9fdc349bb51970eb9c0a08bd158bb5 359 0
+unsat
+#2 := false
+decl f10 :: S3
+#10 := f10
 decl f3 :: (-> S2 Int S3)
 decl f5 :: (-> S4 Int Int)
-#14 := 1::Int
+#13 := 1::Int
 decl f6 :: (-> S5 Int S4)
 decl f8 :: (-> S6 S3 Int)
-decl f10 :: S3
-#11 := f10
 decl f9 :: S6
-#10 := f9
-#12 := (f8 f9 f10)
+#9 := f9
+#11 := (f8 f9 f10)
 decl f7 :: S5
-#9 := f7
-#13 := (f6 f7 #12)
-#15 := (f5 #13 1::Int)
-decl f4 :: S2
-#8 := f4
-#16 := (f3 f4 #15)
-#87 := (= f10 #16)
-#458 := (f3 f4 #12)
-#676 := (= #458 #16)
-#670 := (= #16 #458)
-#738 := (= #15 #12)
-#852 := (div #12 1::Int)
-#667 := (= #852 #12)
-#605 := (= #12 #852)
-#24 := 0::Int
-#195 := -1::Int
-#847 := (* -1::Int #852)
-#639 := (+ #12 #847)
-#645 := (<= #639 0::Int)
-#638 := (= #639 0::Int)
-#1 := true
-#84 := [true-axiom]: true
-#595 := (or false #638)
-#596 := [th-lemma arith]: #595
-#597 := [unit-resolution #596 #84]: #638
-#598 := (not #638)
-#599 := (or #598 #645)
-#600 := [th-lemma arith triangle-eq]: #599
-#601 := [unit-resolution #600 #597]: #645
-#488 := (>= #639 0::Int)
-#602 := (or #598 #488)
-#603 := [th-lemma arith triangle-eq]: #602
-#604 := [unit-resolution #603 #597]: #488
-#594 := [th-lemma arith eq-propagate 1 1 #604 #601]: #605
-#585 := [symm #594]: #667
-#611 := (= #15 #852)
-#853 := (+ #15 #847)
-#797 := (<= #853 0::Int)
-#491 := (= #853 0::Int)
-#569 := (= #12 0::Int)
-#783 := (not #569)
-#722 := (= 0::Int #12)
-#661 := [hypothesis]: #569
-#737 := [symm #661]: #722
-#567 := (= #15 0::Int)
-#716 := (or #783 #567)
-#521 := (* -1::Int #12)
-#651 := (div #521 -1::Int)
-#807 := (* -1::Int #651)
-#811 := (+ #15 #807)
-#694 := (= #811 0::Int)
-#857 := (<= #12 0::Int)
-#837 := (not #857)
-#854 := (>= #12 0::Int)
-#672 := (not #854)
-#819 := (or #672 #837)
-#655 := (ite #819 #491 #694)
-#800 := (ite #569 #567 #655)
-#25 := (:var 0 Int)
-#36 := (:var 1 Int)
-#37 := (f6 f7 #36)
-#38 := (f5 #37 #25)
-#891 := (pattern #38)
-#199 := (* -1::Int #25)
-#196 := (* -1::Int #36)
-#202 := (div #196 #199)
-#374 := (* -1::Int #202)
-#375 := (+ #38 #374)
-#376 := (= #375 0::Int)
-#48 := (div #36 #25)
-#371 := (* -1::Int #48)
-#372 := (+ #38 #371)
-#373 := (= #372 0::Int)
-#234 := (>= #36 0::Int)
-#227 := (<= #25 0::Int)
-#334 := (or #227 #234)
-#335 := (not #334)
-#223 := (<= #36 0::Int)
-#332 := (or #223 #227)
-#333 := (not #332)
-#338 := (or #333 #335)
-#377 := (ite #338 #373 #376)
-#370 := (= #38 0::Int)
-#40 := (= #25 0::Int)
-#39 := (= #36 0::Int)
-#41 := (or #39 #40)
-#378 := (ite #41 #370 #377)
-#892 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #891) #378)
-#381 := (forall (vars (?v0 Int) (?v1 Int)) #378)
-#895 := (iff #381 #892)
-#893 := (iff #378 #378)
-#894 := [refl]: #893
-#896 := [quant-intro #894]: #895
-#341 := (ite #338 #48 #202)
-#344 := (ite #41 0::Int #341)
-#347 := (= #38 #344)
-#350 := (forall (vars (?v0 Int) (?v1 Int)) #347)
-#382 := (iff #350 #381)
-#379 := (iff #347 #378)
-#380 := [rewrite]: #379
-#383 := [quant-intro #380]: #382
-#235 := (not #234)
-#228 := (not #227)
-#238 := (and #228 #235)
-#224 := (not #223)
-#231 := (and #224 #228)
-#241 := (or #231 #238)
-#244 := (ite #241 #48 #202)
-#247 := (ite #41 0::Int #244)
-#250 := (= #38 #247)
-#253 := (forall (vars (?v0 Int) (?v1 Int)) #250)
-#351 := (iff #253 #350)
-#348 := (iff #250 #347)
-#345 := (= #247 #344)
-#342 := (= #244 #341)
-#339 := (iff #241 #338)
-#336 := (iff #238 #335)
-#337 := [rewrite]: #336
-#317 := (iff #231 #333)
-#318 := [rewrite]: #317
-#340 := [monotonicity #318 #337]: #339
-#343 := [monotonicity #340]: #342
-#346 := [monotonicity #343]: #345
-#349 := [monotonicity #346]: #348
-#352 := [quant-intro #349]: #351
-#313 := (~ #253 #253)
-#326 := (~ #250 #250)
-#327 := [refl]: #326
-#314 := [nnf-pos #327]: #313
-#50 := (- #25)
-#49 := (- #36)
-#51 := (div #49 #50)
-#43 := (< 0::Int #25)
-#45 := (< #36 0::Int)
-#46 := (and #45 #43)
-#42 := (< 0::Int #36)
-#44 := (and #42 #43)
-#47 := (or #44 #46)
-#52 := (ite #47 #48 #51)
-#53 := (ite #41 0::Int #52)
-#54 := (= #38 #53)
-#55 := (forall (vars (?v0 Int) (?v1 Int)) #54)
-#256 := (iff #55 #253)
-#189 := (and #43 #45)
-#192 := (or #44 #189)
-#205 := (ite #192 #48 #202)
-#183 := (= 0::Int #25)
-#180 := (= 0::Int #36)
-#186 := (or #180 #183)
-#208 := (ite #186 0::Int #205)
-#211 := (= #38 #208)
-#214 := (forall (vars (?v0 Int) (?v1 Int)) #211)
-#254 := (iff #214 #253)
-#251 := (iff #211 #250)
-#248 := (= #208 #247)
-#245 := (= #205 #244)
-#242 := (iff #192 #241)
-#239 := (iff #189 #238)
-#236 := (iff #45 #235)
-#237 := [rewrite]: #236
-#229 := (iff #43 #228)
-#230 := [rewrite]: #229
-#240 := [monotonicity #230 #237]: #239
-#232 := (iff #44 #231)
-#225 := (iff #42 #224)
-#226 := [rewrite]: #225
-#233 := [monotonicity #226 #230]: #232
-#243 := [monotonicity #233 #240]: #242
-#246 := [monotonicity #243]: #245
-#221 := (iff #186 #41)
-#219 := (iff #183 #40)
-#220 := [rewrite]: #219
-#217 := (iff #180 #39)
-#218 := [rewrite]: #217
-#222 := [monotonicity #218 #220]: #221
-#249 := [monotonicity #222 #246]: #248
-#252 := [monotonicity #249]: #251
-#255 := [quant-intro #252]: #254
-#215 := (iff #55 #214)
-#212 := (iff #54 #211)
-#209 := (= #53 #208)
-#206 := (= #52 #205)
-#203 := (= #51 #202)
-#200 := (= #50 #199)
-#201 := [rewrite]: #200
-#197 := (= #49 #196)
-#198 := [rewrite]: #197
-#204 := [monotonicity #198 #201]: #203
-#193 := (iff #47 #192)
-#190 := (iff #46 #189)
-#191 := [rewrite]: #190
-#194 := [monotonicity #191]: #193
-#207 := [monotonicity #194 #204]: #206
-#187 := (iff #41 #186)
-#184 := (iff #40 #183)
-#185 := [rewrite]: #184
-#181 := (iff #39 #180)
-#182 := [rewrite]: #181
-#188 := [monotonicity #182 #185]: #187
-#210 := [monotonicity #188 #207]: #209
-#213 := [monotonicity #210]: #212
-#216 := [quant-intro #213]: #215
-#257 := [trans #216 #255]: #256
-#179 := [asserted]: #55
-#258 := [mp #179 #257]: #253
-#328 := [mp~ #258 #314]: #253
-#353 := [mp #328 #352]: #350
-#384 := [mp #353 #383]: #381
-#897 := [mp #384 #896]: #892
-#689 := (not #892)
-#704 := (or #689 #800)
-#861 := (* -1::Int 1::Int)
-#848 := (div #521 #861)
-#849 := (* -1::Int #848)
-#850 := (+ #15 #849)
-#851 := (= #850 0::Int)
-#856 := (<= 1::Int 0::Int)
-#496 := (or #856 #854)
-#497 := (not #496)
-#855 := (or #857 #856)
-#858 := (not #855)
-#844 := (or #858 #497)
-#845 := (ite #844 #491 #851)
-#568 := (= 1::Int 0::Int)
-#570 := (or #569 #568)
-#464 := (ite #570 #567 #845)
-#706 := (or #689 #464)
-#700 := (iff #706 #704)
-#709 := (iff #704 #704)
-#710 := [rewrite]: #709
-#801 := (iff #464 #800)
-#803 := (iff #845 #655)
-#695 := (iff #851 #694)
-#809 := (= #850 #811)
-#808 := (= #849 #807)
-#653 := (= #848 #651)
-#815 := (= #861 -1::Int)
-#822 := [rewrite]: #815
-#654 := [monotonicity #822]: #653
-#810 := [monotonicity #654]: #808
-#812 := [monotonicity #810]: #809
-#696 := [monotonicity #812]: #695
-#820 := (iff #844 #819)
-#816 := (or #837 #672)
-#813 := (iff #816 #819)
-#814 := [rewrite]: #813
-#817 := (iff #844 #816)
-#673 := (iff #497 #672)
-#825 := (iff #496 #854)
-#828 := (or false #854)
-#829 := (iff #828 #854)
-#830 := [rewrite]: #829
-#823 := (iff #496 #828)
-#554 := (iff #856 false)
-#555 := [rewrite]: #554
-#824 := [monotonicity #555]: #823
-#831 := [trans #824 #830]: #825
-#674 := [monotonicity #831]: #673
-#826 := (iff #858 #837)
-#836 := (iff #855 #857)
-#556 := (or #857 false)
-#550 := (iff #556 #857)
-#832 := [rewrite]: #550
-#834 := (iff #855 #556)
-#835 := [monotonicity #555]: #834
-#833 := [trans #835 #832]: #836
-#827 := [monotonicity #833]: #826
-#818 := [monotonicity #827 #674]: #817
-#821 := [trans #818 #814]: #820
-#705 := [monotonicity #821 #696]: #803
-#843 := (iff #570 #569)
-#563 := (or #569 false)
-#842 := (iff #563 #569)
-#839 := [rewrite]: #842
-#564 := (iff #570 #563)
-#840 := (iff #568 false)
-#841 := [rewrite]: #840
-#838 := [monotonicity #841]: #564
-#553 := [trans #838 #839]: #843
-#804 := [monotonicity #553 #705]: #801
-#708 := [monotonicity #804]: #700
-#711 := [trans #708 #710]: #700
-#707 := [quant-inst #12 #14]: #706
-#712 := [mp #707 #711]: #704
-#691 := [unit-resolution #712 #897]: #800
-#778 := (not #800)
-#769 := (or #778 #783 #567)
-#770 := [def-axiom]: #769
-#697 := [unit-resolution #770 #691]: #716
-#721 := [unit-resolution #697 #661]: #567
-#714 := [trans #721 #737]: #738
-#675 := [monotonicity #714]: #670
-#677 := [symm #675]: #676
-#542 := (= f10 #458)
-#19 := (:var 0 S3)
-#20 := (f8 f9 #19)
-#871 := (pattern #20)
-#21 := (f3 f4 #20)
-#94 := (= #19 #21)
-#872 := (forall (vars (?v0 S3)) (:pat #871) #94)
-#98 := (forall (vars (?v0 S3)) #94)
-#875 := (iff #98 #872)
-#873 := (iff #94 #94)
-#874 := [refl]: #873
-#876 := [quant-intro #874]: #875
-#321 := (~ #98 #98)
-#319 := (~ #94 #94)
-#320 := [refl]: #319
-#322 := [nnf-pos #320]: #321
-#22 := (= #21 #19)
-#23 := (forall (vars (?v0 S3)) #22)
-#99 := (iff #23 #98)
-#96 := (iff #22 #94)
-#97 := [rewrite]: #96
-#100 := [quant-intro #97]: #99
-#93 := [asserted]: #23
-#103 := [mp #93 #100]: #98
-#307 := [mp~ #103 #322]: #98
-#877 := [mp #307 #876]: #872
-#535 := (not #872)
-#546 := (or #535 #542)
-#547 := [quant-inst #11]: #546
-#669 := [unit-resolution #547 #877]: #542
-#678 := [trans #669 #677]: #87
-#90 := (not #87)
-#17 := (= #16 f10)
-#18 := (not #17)
-#91 := (iff #18 #90)
-#88 := (iff #17 #87)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#86 := [asserted]: #18
-#95 := [mp #86 #92]: #90
-#679 := [unit-resolution #95 #678]: false
-#680 := [lemma #679]: #783
-#713 := (or #569 #491)
-#787 := (not #819)
-#776 := (not #491)
-#717 := [hypothesis]: #776
-#723 := [hypothesis]: #783
-#698 := (or #569 #655)
-#772 := (or #778 #569 #655)
-#773 := [def-axiom]: #772
-#657 := [unit-resolution #773 #691]: #698
-#688 := [unit-resolution #657 #723]: #655
-#789 := (not #655)
-#790 := (or #789 #787 #491)
-#791 := [def-axiom]: #790
-#690 := [unit-resolution #791 #688 #717]: #787
-#793 := (or #819 #857)
-#795 := [def-axiom]: #793
-#692 := [unit-resolution #795 #690]: #857
-#802 := (or #819 #854)
-#806 := [def-axiom]: #802
-#699 := [unit-resolution #806 #690]: #854
-#701 := (or #569 #837 #672)
-#702 := [th-lemma arith triangle-eq]: #701
-#703 := [unit-resolution #702 #723 #699 #692]: false
-#693 := [lemma #703]: #713
-#617 := [unit-resolution #693 #680]: #491
-#620 := (or #776 #797)
-#621 := [th-lemma arith triangle-eq]: #620
-#607 := [unit-resolution #621 #617]: #797
-#798 := (>= #853 0::Int)
-#609 := (or #776 #798)
-#610 := [th-lemma arith triangle-eq]: #609
-#608 := [unit-resolution #610 #617]: #798
-#593 := [th-lemma arith eq-propagate 1 1 #608 #607]: #611
-#586 := [trans #593 #585]: #738
-#587 := [monotonicity #586]: #670
-#588 := [symm #587]: #676
-#589 := [trans #669 #588]: #87
-[unit-resolution #95 #589]: false
-unsat
-fa7182dc645244698a32bbbaa9910ba3ddf6ee99 305 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#10 := 0::Int
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 0::Int)
-decl f5 :: (-> S4 Int Int)
-#12 := 3::Int
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#9 := f7
-#11 := (f6 f7 0::Int)
-#13 := (f5 #11 3::Int)
-#14 := (f3 f4 #13)
-#16 := (= #14 #15)
-#813 := (= #13 0::Int)
+#8 := f7
+#12 := (f6 f7 #11)
+#14 := (f5 #12 1::Int)
+decl f4 :: S2
+#7 := f4
+#15 := (f3 f4 #14)
+#16 := (= #15 f10)
+#357 := (f3 f4 #11)
+#441 := (= #357 f10)
+#18 := (:var 0 S3)
+#19 := (f8 f9 #18)
+#770 := (pattern #19)
+#20 := (f3 f4 #19)
+#21 := (= #20 #18)
+#771 := (forall (vars (?v0 S3)) (:pat #770) #21)
+#22 := (forall (vars (?v0 S3)) #21)
+#774 := (iff #22 #771)
+#772 := (iff #21 #21)
+#773 := [refl]: #772
+#775 := [quant-intro #773]: #774
+#265 := (~ #22 #22)
+#271 := (~ #21 #21)
+#272 := [refl]: #271
+#266 := [nnf-pos #272]: #265
+#68 := [asserted]: #22
+#273 := [mp~ #68 #266]: #22
+#776 := [mp #273 #775]: #771
+#434 := (not #771)
+#445 := (or #434 #441)
+#446 := [quant-inst #10]: #445
+#663 := [unit-resolution #446 #776]: #441
+#645 := (= #15 #357)
+#665 := (= #14 #11)
+#749 := (div #11 1::Int)
+#636 := (= #749 #11)
+#537 := (= #11 #749)
+#23 := 0::Int
+#132 := -1::Int
+#750 := (* -1::Int #749)
+#641 := (+ #11 #750)
+#617 := (<= #641 0::Int)
+#660 := (= #641 0::Int)
+#1 := true
+#199 := [true-axiom]: true
+#558 := (or false #660)
+#559 := [th-lemma arith]: #558
+#561 := [unit-resolution #559 #199]: #660
+#562 := (not #660)
+#563 := (or #562 #617)
+#564 := [th-lemma arith triangle-eq]: #563
+#565 := [unit-resolution #564 #561]: #617
+#618 := (>= #641 0::Int)
+#566 := (or #562 #618)
+#549 := [th-lemma arith triangle-eq]: #566
+#567 := [unit-resolution #549 #561]: #618
+#538 := [th-lemma arith eq-propagate 1 1 #567 #565]: #537
+#542 := [symm #538]: #636
+#555 := (= #14 #749)
+#751 := (+ #14 #750)
+#608 := (<= #751 0::Int)
+#746 := (= #751 0::Int)
+#766 := (= #11 0::Int)
+#687 := (not #766)
+#659 := (= 0::Int #11)
+#664 := [hypothesis]: #766
+#655 := [symm #664]: #659
+#761 := (= #14 0::Int)
+#657 := (or #687 #761)
+#752 := (* -1::Int #11)
+#571 := (div #752 -1::Int)
+#715 := (* -1::Int #571)
+#718 := (+ #14 #715)
+#719 := (= #718 0::Int)
+#410 := (>= #11 0::Int)
+#726 := (not #410)
+#404 := (<= #11 0::Int)
+#454 := (not #404)
+#723 := (or #454 #726)
+#721 := (if #723 #746 #719)
+#553 := (if #766 #761 #721)
 #24 := (:var 0 Int)
 #35 := (:var 1 Int)
 #36 := (f6 f7 #35)
 #37 := (f5 #36 #24)
-#884 := (pattern #37)
-#187 := -1::Int
-#191 := (* -1::Int #24)
-#188 := (* -1::Int #35)
-#194 := (div #188 #191)
-#366 := (* -1::Int #194)
-#367 := (+ #37 #366)
-#368 := (= #367 0::Int)
+#790 := (pattern #37)
+#136 := (* -1::Int #24)
+#133 := (* -1::Int #35)
+#139 := (div #133 #136)
+#330 := (* -1::Int #139)
+#331 := (+ #37 #330)
+#332 := (= #331 0::Int)
 #47 := (div #35 #24)
-#363 := (* -1::Int #47)
-#364 := (+ #37 #363)
-#365 := (= #364 0::Int)
-#226 := (>= #35 0::Int)
-#219 := (<= #24 0::Int)
-#326 := (or #219 #226)
-#327 := (not #326)
-#215 := (<= #35 0::Int)
-#324 := (or #215 #219)
-#325 := (not #324)
-#330 := (or #325 #327)
-#369 := (ite #330 #365 #368)
-#362 := (= #37 0::Int)
+#327 := (* -1::Int #47)
+#328 := (+ #37 #327)
+#329 := (= #328 0::Int)
+#110 := (<= #24 0::Int)
+#222 := (>= #35 0::Int)
+#290 := (or #222 #110)
+#291 := (not #290)
+#106 := (<= #35 0::Int)
+#286 := (or #106 #110)
+#287 := (not #286)
+#294 := (or #287 #291)
+#333 := (if #294 #329 #332)
+#326 := (= #37 0::Int)
 #39 := (= #24 0::Int)
 #38 := (= #35 0::Int)
 #40 := (or #38 #39)
-#370 := (ite #40 #362 #369)
-#885 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #884) #370)
-#373 := (forall (vars (?v0 Int) (?v1 Int)) #370)
-#888 := (iff #373 #885)
-#886 := (iff #370 #370)
-#887 := [refl]: #886
-#889 := [quant-intro #887]: #888
-#333 := (ite #330 #47 #194)
-#336 := (ite #40 0::Int #333)
-#339 := (= #37 #336)
-#342 := (forall (vars (?v0 Int) (?v1 Int)) #339)
-#374 := (iff #342 #373)
-#371 := (iff #339 #370)
-#372 := [rewrite]: #371
-#375 := [quant-intro #372]: #374
-#227 := (not #226)
-#220 := (not #219)
-#230 := (and #220 #227)
-#216 := (not #215)
-#223 := (and #216 #220)
-#233 := (or #223 #230)
-#236 := (ite #233 #47 #194)
-#239 := (ite #40 0::Int #236)
-#242 := (= #37 #239)
-#245 := (forall (vars (?v0 Int) (?v1 Int)) #242)
-#343 := (iff #245 #342)
-#340 := (iff #242 #339)
-#337 := (= #239 #336)
-#334 := (= #236 #333)
-#331 := (iff #233 #330)
-#328 := (iff #230 #327)
-#329 := [rewrite]: #328
-#309 := (iff #223 #325)
-#310 := [rewrite]: #309
-#332 := [monotonicity #310 #329]: #331
-#335 := [monotonicity #332]: #334
-#338 := [monotonicity #335]: #337
-#341 := [monotonicity #338]: #340
-#344 := [quant-intro #341]: #343
-#305 := (~ #245 #245)
-#318 := (~ #242 #242)
-#319 := [refl]: #318
-#306 := [nnf-pos #319]: #305
+#334 := (if #40 #326 #333)
+#791 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #790) #334)
+#337 := (forall (vars (?v0 Int) (?v1 Int)) #334)
+#794 := (iff #337 #791)
+#792 := (iff #334 #334)
+#793 := [refl]: #792
+#795 := [quant-intro #793]: #794
+#297 := (if #294 #47 #139)
+#300 := (if #40 0::Int #297)
+#303 := (= #37 #300)
+#306 := (forall (vars (?v0 Int) (?v1 Int)) #303)
+#338 := (iff #306 #337)
+#335 := (iff #303 #334)
+#336 := [rewrite]: #335
+#339 := [quant-intro #336]: #338
+#111 := (not #110)
+#225 := (not #222)
+#228 := (and #225 #111)
+#107 := (not #106)
+#114 := (and #107 #111)
+#231 := (or #114 #228)
+#234 := (if #231 #47 #139)
+#237 := (if #40 0::Int #234)
+#240 := (= #37 #237)
+#243 := (forall (vars (?v0 Int) (?v1 Int)) #240)
+#307 := (iff #243 #306)
+#304 := (iff #240 #303)
+#301 := (= #237 #300)
+#298 := (= #234 #297)
+#295 := (iff #231 #294)
+#292 := (iff #228 #291)
+#293 := [rewrite]: #292
+#288 := (iff #114 #287)
+#289 := [rewrite]: #288
+#296 := [monotonicity #289 #293]: #295
+#299 := [monotonicity #296]: #298
+#302 := [monotonicity #299]: #301
+#305 := [monotonicity #302]: #304
+#308 := [quant-intro #305]: #307
+#278 := (~ #243 #243)
+#276 := (~ #240 #240)
+#277 := [refl]: #276
+#279 := [nnf-pos #277]: #278
+#117 := (<= 0::Int #35)
+#118 := (not #117)
+#126 := (and #118 #111)
+#129 := (or #114 #126)
+#142 := (if #129 #47 #139)
+#145 := (if #40 0::Int #142)
+#148 := (= #37 #145)
+#151 := (forall (vars (?v0 Int) (?v1 Int)) #148)
+#244 := (iff #151 #243)
+#241 := (iff #148 #240)
+#238 := (= #145 #237)
+#235 := (= #142 #234)
+#232 := (iff #129 #231)
+#229 := (iff #126 #228)
+#226 := (iff #118 #225)
+#223 := (iff #117 #222)
+#224 := [rewrite]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [monotonicity #233]: #235
+#239 := [monotonicity #236]: #238
+#242 := [monotonicity #239]: #241
+#245 := [quant-intro #242]: #244
+#49 := (- #24)
+#48 := (- #35)
+#50 := (div #48 #49)
+#42 := (< 0::Int #24)
+#44 := (< #35 0::Int)
+#45 := (and #44 #42)
+#41 := (< 0::Int #35)
+#43 := (and #41 #42)
+#46 := (or #43 #45)
+#51 := (if #46 #47 #50)
+#52 := (if #40 0::Int #51)
+#53 := (= #37 #52)
+#54 := (forall (vars (?v0 Int) (?v1 Int)) #53)
+#152 := (iff #54 #151)
+#149 := (iff #53 #148)
+#146 := (= #52 #145)
+#143 := (= #51 #142)
+#140 := (= #50 #139)
+#137 := (= #49 #136)
+#138 := [rewrite]: #137
+#134 := (= #48 #133)
+#135 := [rewrite]: #134
+#141 := [monotonicity #135 #138]: #140
+#130 := (iff #46 #129)
+#127 := (iff #45 #126)
+#112 := (iff #42 #111)
+#113 := [rewrite]: #112
+#119 := (iff #44 #118)
+#123 := (iff #118 #118)
+#121 := (iff #117 #117)
+#122 := [rewrite]: #121
+#124 := [monotonicity #122]: #123
+#120 := [rewrite]: #119
+#125 := [trans #120 #124]: #119
+#128 := [monotonicity #125 #113]: #127
+#115 := (iff #43 #114)
+#108 := (iff #41 #107)
+#109 := [rewrite]: #108
+#116 := [monotonicity #109 #113]: #115
+#131 := [monotonicity #116 #128]: #130
+#144 := [monotonicity #131 #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [monotonicity #147]: #149
+#153 := [quant-intro #150]: #152
+#71 := [asserted]: #54
+#154 := [mp #71 #153]: #151
+#246 := [mp #154 #245]: #243
+#280 := [mp~ #246 #279]: #243
+#309 := [mp #280 #308]: #306
+#340 := [mp #309 #339]: #337
+#796 := [mp #340 #795]: #791
+#709 := (not #791)
+#710 := (or #709 #553)
+#390 := (* -1::Int 1::Int)
+#753 := (div #752 #390)
+#755 := (* -1::Int #753)
+#395 := (+ #14 #755)
+#396 := (= #395 0::Int)
+#745 := (<= 1::Int 0::Int)
+#411 := (or #410 #745)
+#747 := (not #411)
+#408 := (or #404 #745)
+#409 := (not #408)
+#748 := (or #409 #747)
+#756 := (if #748 #746 #396)
+#767 := (= 1::Int 0::Int)
+#420 := (or #766 #767)
+#754 := (if #420 #761 #756)
+#708 := (or #709 #754)
+#593 := (iff #708 #710)
+#595 := (iff #710 #710)
+#554 := [rewrite]: #595
+#706 := (iff #754 #553)
+#550 := (iff #756 #721)
+#720 := (iff #396 #719)
+#712 := (= #395 #718)
+#716 := (= #755 #715)
+#572 := (= #753 #571)
+#724 := (= #390 -1::Int)
+#730 := [rewrite]: #724
+#573 := [monotonicity #730]: #572
+#717 := [monotonicity #573]: #716
+#713 := [monotonicity #717]: #712
+#714 := [monotonicity #713]: #720
+#728 := (iff #748 #723)
+#727 := (iff #747 #726)
+#736 := (iff #411 #410)
+#734 := (or #410 false)
+#735 := (iff #734 #410)
+#732 := [rewrite]: #735
+#449 := (iff #411 #734)
+#740 := (iff #745 false)
+#462 := [rewrite]: #740
+#731 := [monotonicity #462]: #449
+#725 := [trans #731 #732]: #736
+#722 := [monotonicity #725]: #727
+#455 := (iff #409 #454)
+#452 := (iff #408 #404)
+#463 := (or #404 false)
+#738 := (iff #463 #404)
+#742 := [rewrite]: #738
+#737 := (iff #408 #463)
+#741 := [monotonicity #462]: #737
+#453 := [trans #741 #742]: #452
+#733 := [monotonicity #453]: #455
+#729 := [monotonicity #733 #722]: #728
+#552 := [monotonicity #729 #714]: #550
+#363 := (iff #420 #766)
+#744 := (or #766 false)
+#468 := (iff #744 #766)
+#469 := [rewrite]: #468
+#466 := (iff #420 #744)
+#757 := (iff #767 false)
+#743 := [rewrite]: #757
+#467 := [monotonicity #743]: #466
+#739 := [trans #467 #469]: #363
+#707 := [monotonicity #739 #552]: #706
+#594 := [monotonicity #707]: #593
+#702 := [trans #594 #554]: #593
+#711 := [quant-inst #11 #13]: #708
+#604 := [mp #711 #702]: #710
+#631 := [unit-resolution #604 #796]: #553
+#698 := (not #553)
+#688 := (or #698 #687 #761)
+#689 := [def-axiom]: #688
+#658 := [unit-resolution #689 #631]: #657
+#646 := [unit-resolution #658 #664]: #761
+#666 := [trans #646 #655]: #665
+#648 := [monotonicity #666]: #645
+#661 := [trans #648 #663]: #16
+#17 := (not #16)
+#67 := [asserted]: #17
+#662 := [unit-resolution #67 #661]: false
+#623 := [lemma #662]: #687
+#621 := (or #766 #746)
+#605 := (not #723)
+#683 := (not #746)
+#627 := [hypothesis]: #683
+#628 := [hypothesis]: #687
+#632 := (or #766 #721)
+#690 := (or #698 #766 #721)
+#684 := [def-axiom]: #690
+#633 := [unit-resolution #684 #631]: #632
+#629 := [unit-resolution #633 #628]: #721
+#701 := (not #721)
+#705 := (or #701 #605 #746)
+#692 := [def-axiom]: #705
+#634 := [unit-resolution #692 #629 #627]: #605
+#588 := (or #723 #410)
+#603 := [def-axiom]: #588
+#614 := [unit-resolution #603 #634]: #410
+#700 := (or #723 #404)
+#703 := [def-axiom]: #700
+#560 := [unit-resolution #703 #634]: #404
+#615 := (or #766 #454 #726)
+#596 := [th-lemma arith triangle-eq]: #615
+#620 := [unit-resolution #596 #628 #560 #614]: false
+#616 := [lemma #620]: #621
+#583 := [unit-resolution #616 #623]: #746
+#584 := (or #683 #608)
+#585 := [th-lemma arith triangle-eq]: #584
+#570 := [unit-resolution #585 #583]: #608
+#609 := (>= #751 0::Int)
+#586 := (or #683 #609)
+#547 := [th-lemma arith triangle-eq]: #586
+#548 := [unit-resolution #547 #583]: #609
+#557 := [th-lemma arith eq-propagate 1 1 #548 #570]: #555
+#543 := [trans #557 #542]: #665
+#544 := [monotonicity #543]: #645
+#387 := [trans #544 #663]: #16
+[unit-resolution #67 #387]: false
+6833c76ab94aad24a4f35a6e42e2cc121c836709 297 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int S3)
+#9 := 0::Int
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 0::Int)
+decl f5 :: (-> S4 Int Int)
+#11 := 3::Int
+decl f6 :: (-> S5 Int S4)
+decl f7 :: S5
+#8 := f7
+#10 := (f6 f7 0::Int)
+#12 := (f5 #10 3::Int)
+#13 := (f3 f4 #12)
+#15 := (= #13 #14)
+#737 := (= #12 0::Int)
+#23 := (:var 0 Int)
+#34 := (:var 1 Int)
+#35 := (f6 f7 #34)
+#36 := (f5 #35 #23)
+#790 := (pattern #36)
+#131 := -1::Int
+#135 := (* -1::Int #23)
+#132 := (* -1::Int #34)
+#138 := (div #132 #135)
+#329 := (* -1::Int #138)
+#330 := (+ #36 #329)
+#331 := (= #330 0::Int)
+#46 := (div #34 #23)
+#326 := (* -1::Int #46)
+#327 := (+ #36 #326)
+#328 := (= #327 0::Int)
+#109 := (<= #23 0::Int)
+#221 := (>= #34 0::Int)
+#289 := (or #221 #109)
+#290 := (not #289)
+#105 := (<= #34 0::Int)
+#285 := (or #105 #109)
+#286 := (not #285)
+#293 := (or #286 #290)
+#332 := (if #293 #328 #331)
+#325 := (= #36 0::Int)
+#38 := (= #23 0::Int)
+#37 := (= #34 0::Int)
+#39 := (or #37 #38)
+#333 := (if #39 #325 #332)
+#791 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #790) #333)
+#336 := (forall (vars (?v0 Int) (?v1 Int)) #333)
+#794 := (iff #336 #791)
+#792 := (iff #333 #333)
+#793 := [refl]: #792
+#795 := [quant-intro #793]: #794
+#296 := (if #293 #46 #138)
+#299 := (if #39 0::Int #296)
+#302 := (= #36 #299)
+#305 := (forall (vars (?v0 Int) (?v1 Int)) #302)
+#337 := (iff #305 #336)
+#334 := (iff #302 #333)
+#335 := [rewrite]: #334
+#338 := [quant-intro #335]: #337
+#110 := (not #109)
+#224 := (not #221)
+#227 := (and #224 #110)
+#106 := (not #105)
+#113 := (and #106 #110)
+#230 := (or #113 #227)
+#233 := (if #230 #46 #138)
+#236 := (if #39 0::Int #233)
+#239 := (= #36 #236)
+#242 := (forall (vars (?v0 Int) (?v1 Int)) #239)
+#306 := (iff #242 #305)
+#303 := (iff #239 #302)
+#300 := (= #236 #299)
+#297 := (= #233 #296)
+#294 := (iff #230 #293)
+#291 := (iff #227 #290)
+#292 := [rewrite]: #291
+#287 := (iff #113 #286)
+#288 := [rewrite]: #287
+#295 := [monotonicity #288 #292]: #294
+#298 := [monotonicity #295]: #297
+#301 := [monotonicity #298]: #300
+#304 := [monotonicity #301]: #303
+#307 := [quant-intro #304]: #306
+#277 := (~ #242 #242)
+#275 := (~ #239 #239)
+#276 := [refl]: #275
+#278 := [nnf-pos #276]: #277
+#116 := (<= 0::Int #34)
+#117 := (not #116)
+#125 := (and #117 #110)
+#128 := (or #113 #125)
+#141 := (if #128 #46 #138)
+#144 := (if #39 0::Int #141)
+#147 := (= #36 #144)
+#150 := (forall (vars (?v0 Int) (?v1 Int)) #147)
+#243 := (iff #150 #242)
+#240 := (iff #147 #239)
+#237 := (= #144 #236)
+#234 := (= #141 #233)
+#231 := (iff #128 #230)
+#228 := (iff #125 #227)
+#225 := (iff #117 #224)
+#222 := (iff #116 #221)
+#223 := [rewrite]: #222
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#235 := [monotonicity #232]: #234
+#238 := [monotonicity #235]: #237
+#241 := [monotonicity #238]: #240
+#244 := [quant-intro #241]: #243
+#48 := (- #23)
+#47 := (- #34)
+#49 := (div #47 #48)
+#41 := (< 0::Int #23)
+#43 := (< #34 0::Int)
+#44 := (and #43 #41)
+#40 := (< 0::Int #34)
+#42 := (and #40 #41)
+#45 := (or #42 #44)
+#50 := (if #45 #46 #49)
+#51 := (if #39 0::Int #50)
+#52 := (= #36 #51)
+#53 := (forall (vars (?v0 Int) (?v1 Int)) #52)
+#151 := (iff #53 #150)
+#148 := (iff #52 #147)
+#145 := (= #51 #144)
+#142 := (= #50 #141)
+#139 := (= #49 #138)
+#136 := (= #48 #135)
+#137 := [rewrite]: #136
+#133 := (= #47 #132)
+#134 := [rewrite]: #133
+#140 := [monotonicity #134 #137]: #139
+#129 := (iff #45 #128)
+#126 := (iff #44 #125)
+#111 := (iff #41 #110)
+#112 := [rewrite]: #111
+#118 := (iff #43 #117)
+#122 := (iff #117 #117)
+#120 := (iff #116 #116)
+#121 := [rewrite]: #120
+#123 := [monotonicity #121]: #122
+#119 := [rewrite]: #118
+#124 := [trans #119 #123]: #118
+#127 := [monotonicity #124 #112]: #126
+#114 := (iff #42 #113)
+#107 := (iff #40 #106)
+#108 := [rewrite]: #107
+#115 := [monotonicity #108 #112]: #114
+#130 := [monotonicity #115 #127]: #129
+#143 := [monotonicity #130 #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [monotonicity #146]: #148
+#152 := [quant-intro #149]: #151
+#70 := [asserted]: #53
+#153 := [mp #70 #152]: #150
+#245 := [mp #153 #244]: #242
+#279 := [mp~ #245 #278]: #242
+#308 := [mp #279 #307]: #305
+#339 := [mp #308 #338]: #336
+#796 := [mp #339 #795]: #791
+#665 := (not #791)
+#666 := (or #665 #737)
+#732 := (* -1::Int 3::Int)
+#735 := (* -1::Int 0::Int)
+#736 := (div #735 #732)
+#725 := (* -1::Int #736)
+#726 := (+ #12 #725)
+#727 := (= #726 0::Int)
+#733 := (div 0::Int 3::Int)
+#734 := (* -1::Int #733)
+#449 := (+ #12 #734)
+#731 := (= #449 0::Int)
+#738 := (<= 3::Int 0::Int)
+#551 := (>= 0::Int 0::Int)
+#453 := (or #551 #738)
+#454 := (not #453)
+#741 := (<= 0::Int 0::Int)
+#742 := (or #741 #738)
+#452 := (not #742)
+#455 := (or #452 #454)
+#722 := (if #455 #731 #727)
+#462 := (= 3::Int 0::Int)
+#740 := (= 0::Int 0::Int)
+#463 := (or #740 #462)
+#723 := (if #463 #737 #722)
+#656 := (or #665 #723)
+#645 := (iff #656 #666)
+#648 := (iff #666 #666)
+#649 := [rewrite]: #648
+#663 := (iff #723 #737)
+#1 := true
+#658 := (if true #737 #737)
+#661 := (iff #658 #737)
+#662 := [rewrite]: #661
+#659 := (iff #723 #658)
+#655 := (iff #722 #737)
+#672 := (if false #737 #737)
+#674 := (iff #672 #737)
+#654 := [rewrite]: #674
+#673 := (iff #722 #672)
+#669 := (iff #727 #737)
+#682 := (= #726 #12)
+#701 := (+ #12 0::Int)
+#694 := (= #701 #12)
+#686 := [rewrite]: #694
+#681 := (= #726 #701)
+#679 := (= #725 0::Int)
+#609 := (= #735 0::Int)
+#610 := [rewrite]: #609
+#676 := (= #725 #735)
+#691 := (= #736 0::Int)
+#697 := -3::Int
+#687 := (div 0::Int -3::Int)
+#690 := (= #687 0::Int)
+#684 := [rewrite]: #690
+#688 := (= #736 #687)
+#693 := (= #732 -3::Int)
+#698 := [rewrite]: #693
+#689 := [monotonicity #610 #698]: #688
+#675 := [trans #689 #684]: #691
+#678 := [monotonicity #675]: #676
+#680 := [trans #678 #610]: #679
+#677 := [monotonicity #680]: #681
+#668 := [trans #677 #686]: #682
+#671 := [monotonicity #668]: #669
+#695 := (iff #731 #737)
+#683 := (= #449 #12)
+#705 := (= #449 #701)
+#611 := (= #734 0::Int)
+#607 := (= #734 #735)
+#606 := (= #733 0::Int)
+#599 := [rewrite]: #606
+#608 := [monotonicity #599]: #607
+#704 := [trans #608 #610]: #611
+#692 := [monotonicity #704]: #705
+#685 := [trans #692 #686]: #683
+#696 := [monotonicity #685]: #695
+#603 := (iff #455 false)
+#604 := (or false false)
+#703 := (iff #604 false)
+#588 := [rewrite]: #703
+#699 := (iff #455 #604)
+#554 := (iff #454 false)
+#420 := (not true)
+#745 := (iff #420 false)
+#408 := [rewrite]: #745
+#594 := (iff #454 #420)
+#711 := (iff #453 true)
+#571 := (or true false)
+#715 := (iff #571 true)
+#716 := [rewrite]: #715
+#710 := (iff #453 #571)
+#719 := (iff #738 false)
+#720 := [rewrite]: #719
+#424 := (iff #551 true)
+#760 := [rewrite]: #424
+#708 := [monotonicity #760 #720]: #710
+#593 := [trans #708 #716]: #711
+#595 := [monotonicity #593]: #594
+#702 := [trans #595 #408]: #554
+#707 := (iff #452 false)
+#553 := (iff #452 #420)
+#550 := (iff #742 true)
+#714 := (iff #742 #571)
+#712 := (iff #741 true)
+#713 := [rewrite]: #712
+#721 := [monotonicity #713 #720]: #714
+#552 := [trans #721 #716]: #550
+#706 := [monotonicity #552]: #553
+#709 := [trans #706 #408]: #707
+#700 := [monotonicity #709 #702]: #699
+#605 := [trans #700 #588]: #603
+#670 := [monotonicity #605 #696 #671]: #673
+#657 := [trans #670 #654]: #655
+#717 := (iff #463 true)
+#572 := (iff #463 #571)
+#724 := (iff #462 false)
+#730 := [rewrite]: #724
+#728 := (iff #740 true)
+#729 := [rewrite]: #728
+#573 := [monotonicity #729 #730]: #572
+#718 := [trans #573 #716]: #717
+#660 := [monotonicity #718 #657]: #659
+#664 := [trans #660 #662]: #663
+#646 := [monotonicity #664]: #645
+#650 := [trans #646 #649]: #645
+#667 := [quant-inst #9 #11]: #656
+#651 := [mp #667 #650]: #666
+#647 := [unit-resolution #651 #796]: #737
+#653 := [monotonicity #647]: #15
+#16 := (not #15)
+#66 := [asserted]: #16
+[unit-resolution #66 #653]: false
+3a5431ba2dda9bb93e22830a67e761b1aca1ace1 314 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int S3)
+#14 := 0::Int
+decl f4 :: S2
+#7 := f4
+#15 := (f3 f4 0::Int)
+decl f5 :: (-> S4 Int Int)
+#11 := 3::Int
+decl f6 :: (-> S5 Int S4)
+#9 := 1::Int
+decl f7 :: S5
+#8 := f7
+#10 := (f6 f7 1::Int)
+#12 := (f5 #10 3::Int)
+#13 := (f3 f4 #12)
+#16 := (= #13 #15)
+#737 := (= #12 0::Int)
+#24 := (:var 0 Int)
+#35 := (:var 1 Int)
+#36 := (f6 f7 #35)
+#37 := (f5 #36 #24)
+#790 := (pattern #37)
+#132 := -1::Int
+#136 := (* -1::Int #24)
+#133 := (* -1::Int #35)
+#139 := (div #133 #136)
+#330 := (* -1::Int #139)
+#331 := (+ #37 #330)
+#332 := (= #331 0::Int)
+#47 := (div #35 #24)
+#327 := (* -1::Int #47)
+#328 := (+ #37 #327)
+#329 := (= #328 0::Int)
+#110 := (<= #24 0::Int)
+#222 := (>= #35 0::Int)
+#290 := (or #222 #110)
+#291 := (not #290)
+#106 := (<= #35 0::Int)
+#286 := (or #106 #110)
+#287 := (not #286)
+#294 := (or #287 #291)
+#333 := (if #294 #329 #332)
+#326 := (= #37 0::Int)
+#39 := (= #24 0::Int)
+#38 := (= #35 0::Int)
+#40 := (or #38 #39)
+#334 := (if #40 #326 #333)
+#791 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #790) #334)
+#337 := (forall (vars (?v0 Int) (?v1 Int)) #334)
+#794 := (iff #337 #791)
+#792 := (iff #334 #334)
+#793 := [refl]: #792
+#795 := [quant-intro #793]: #794
+#297 := (if #294 #47 #139)
+#300 := (if #40 0::Int #297)
+#303 := (= #37 #300)
+#306 := (forall (vars (?v0 Int) (?v1 Int)) #303)
+#338 := (iff #306 #337)
+#335 := (iff #303 #334)
+#336 := [rewrite]: #335
+#339 := [quant-intro #336]: #338
+#111 := (not #110)
+#225 := (not #222)
+#228 := (and #225 #111)
+#107 := (not #106)
+#114 := (and #107 #111)
+#231 := (or #114 #228)
+#234 := (if #231 #47 #139)
+#237 := (if #40 0::Int #234)
+#240 := (= #37 #237)
+#243 := (forall (vars (?v0 Int) (?v1 Int)) #240)
+#307 := (iff #243 #306)
+#304 := (iff #240 #303)
+#301 := (= #237 #300)
+#298 := (= #234 #297)
+#295 := (iff #231 #294)
+#292 := (iff #228 #291)
+#293 := [rewrite]: #292
+#288 := (iff #114 #287)
+#289 := [rewrite]: #288
+#296 := [monotonicity #289 #293]: #295
+#299 := [monotonicity #296]: #298
+#302 := [monotonicity #299]: #301
+#305 := [monotonicity #302]: #304
+#308 := [quant-intro #305]: #307
+#278 := (~ #243 #243)
+#276 := (~ #240 #240)
+#277 := [refl]: #276
+#279 := [nnf-pos #277]: #278
+#117 := (<= 0::Int #35)
+#118 := (not #117)
+#126 := (and #118 #111)
+#129 := (or #114 #126)
+#142 := (if #129 #47 #139)
+#145 := (if #40 0::Int #142)
+#148 := (= #37 #145)
+#151 := (forall (vars (?v0 Int) (?v1 Int)) #148)
+#244 := (iff #151 #243)
+#241 := (iff #148 #240)
+#238 := (= #145 #237)
+#235 := (= #142 #234)
+#232 := (iff #129 #231)
+#229 := (iff #126 #228)
+#226 := (iff #118 #225)
+#223 := (iff #117 #222)
+#224 := [rewrite]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [monotonicity #233]: #235
+#239 := [monotonicity #236]: #238
+#242 := [monotonicity #239]: #241
+#245 := [quant-intro #242]: #244
 #49 := (- #24)
 #48 := (- #35)
 #50 := (div #48 #49)
@@ -15222,991 +14903,312 @@
 #41 := (< 0::Int #35)
 #43 := (and #41 #42)
 #46 := (or #43 #45)
-#51 := (ite #46 #47 #50)
-#52 := (ite #40 0::Int #51)
+#51 := (if #46 #47 #50)
+#52 := (if #40 0::Int #51)
 #53 := (= #37 #52)
 #54 := (forall (vars (?v0 Int) (?v1 Int)) #53)
-#248 := (iff #54 #245)
-#181 := (and #42 #44)
-#184 := (or #43 #181)
-#197 := (ite #184 #47 #194)
-#175 := (= 0::Int #24)
-#172 := (= 0::Int #35)
-#178 := (or #172 #175)
-#200 := (ite #178 0::Int #197)
-#203 := (= #37 #200)
-#206 := (forall (vars (?v0 Int) (?v1 Int)) #203)
-#246 := (iff #206 #245)
-#243 := (iff #203 #242)
-#240 := (= #200 #239)
-#237 := (= #197 #236)
-#234 := (iff #184 #233)
-#231 := (iff #181 #230)
-#228 := (iff #44 #227)
-#229 := [rewrite]: #228
-#221 := (iff #42 #220)
-#222 := [rewrite]: #221
-#232 := [monotonicity #222 #229]: #231
-#224 := (iff #43 #223)
-#217 := (iff #41 #216)
-#218 := [rewrite]: #217
-#225 := [monotonicity #218 #222]: #224
-#235 := [monotonicity #225 #232]: #234
-#238 := [monotonicity #235]: #237
-#213 := (iff #178 #40)
-#211 := (iff #175 #39)
-#212 := [rewrite]: #211
-#209 := (iff #172 #38)
-#210 := [rewrite]: #209
-#214 := [monotonicity #210 #212]: #213
-#241 := [monotonicity #214 #238]: #240
-#244 := [monotonicity #241]: #243
-#247 := [quant-intro #244]: #246
-#207 := (iff #54 #206)
-#204 := (iff #53 #203)
-#201 := (= #52 #200)
-#198 := (= #51 #197)
-#195 := (= #50 #194)
-#192 := (= #49 #191)
-#193 := [rewrite]: #192
-#189 := (= #48 #188)
-#190 := [rewrite]: #189
-#196 := [monotonicity #190 #193]: #195
-#185 := (iff #46 #184)
-#182 := (iff #45 #181)
-#183 := [rewrite]: #182
-#186 := [monotonicity #183]: #185
-#199 := [monotonicity #186 #196]: #198
-#179 := (iff #40 #178)
-#176 := (iff #39 #175)
-#177 := [rewrite]: #176
-#173 := (iff #38 #172)
-#174 := [rewrite]: #173
-#180 := [monotonicity #174 #177]: #179
-#202 := [monotonicity #180 #199]: #201
-#205 := [monotonicity #202]: #204
-#208 := [quant-intro #205]: #207
-#249 := [trans #208 #247]: #248
-#171 := [asserted]: #54
-#250 := [mp #171 #249]: #245
-#320 := [mp~ #250 #306]: #245
-#345 := [mp #320 #344]: #342
-#376 := [mp #345 #375]: #373
-#890 := [mp #376 #889]: #885
-#732 := (not #885)
-#738 := (or #732 #813)
-#819 := (* -1::Int 3::Int)
-#820 := (* -1::Int 0::Int)
-#821 := (div #820 #819)
-#816 := (* -1::Int #821)
-#817 := (+ #13 #816)
-#822 := (= #817 0::Int)
-#823 := (div 0::Int 3::Int)
-#818 := (* -1::Int #823)
-#824 := (+ #13 #818)
-#665 := (= #824 0::Int)
-#841 := (>= 0::Int 0::Int)
-#666 := (<= 3::Int 0::Int)
-#667 := (or #666 #841)
-#809 := (not #667)
-#810 := (<= 0::Int 0::Int)
-#811 := (or #810 #666)
-#812 := (not #811)
-#806 := (or #812 #809)
-#807 := (ite #806 #665 #822)
-#814 := (= 3::Int 0::Int)
-#808 := (= 0::Int 0::Int)
-#815 := (or #808 #814)
-#644 := (ite #815 #813 #807)
-#711 := (or #732 #644)
-#713 := (iff #711 #738)
-#717 := (iff #738 #738)
-#718 := [rewrite]: #717
-#736 := (iff #644 #813)
-#1 := true
-#729 := (ite true #813 #813)
-#734 := (iff #729 #813)
-#735 := [rewrite]: #734
-#730 := (iff #644 #729)
-#747 := (iff #807 #813)
-#743 := (ite false #813 #813)
-#746 := (iff #743 #813)
-#741 := [rewrite]: #746
-#744 := (iff #807 #743)
-#740 := (iff #822 #813)
-#761 := (= #817 #13)
-#773 := (+ #13 0::Int)
-#771 := (= #773 #13)
-#776 := [rewrite]: #771
-#760 := (= #817 #773)
-#758 := (= #816 0::Int)
-#785 := (= #820 0::Int)
-#769 := [rewrite]: #785
-#756 := (= #816 #820)
-#754 := (= #821 0::Int)
-#767 := -3::Int
-#748 := (div 0::Int -3::Int)
-#752 := (= #748 0::Int)
-#753 := [rewrite]: #752
-#749 := (= #821 #748)
-#764 := (= #819 -3::Int)
-#768 := [rewrite]: #764
-#751 := [monotonicity #769 #768]: #749
-#755 := [trans #751 #753]: #754
-#757 := [monotonicity #755]: #756
-#759 := [trans #757 #769]: #758
-#750 := [monotonicity #759]: #760
-#739 := [trans #750 #776]: #761
-#742 := [monotonicity #739]: #740
-#765 := (iff #665 #813)
-#762 := (= #824 #13)
-#774 := (= #824 #773)
-#770 := (= #818 0::Int)
-#784 := (= #818 #820)
-#782 := (= #823 0::Int)
-#783 := [rewrite]: #782
-#778 := [monotonicity #783]: #784
-#772 := [trans #778 #769]: #770
-#775 := [monotonicity #772]: #774
-#763 := [trans #775 #776]: #762
-#766 := [monotonicity #763]: #765
-#792 := (iff #806 false)
-#779 := (or false false)
-#791 := (iff #779 false)
-#787 := [rewrite]: #791
-#789 := (iff #806 #779)
-#780 := (iff #809 false)
-#489 := (not true)
-#848 := (iff #489 false)
-#851 := [rewrite]: #848
-#786 := (iff #809 #489)
-#795 := (iff #667 true)
-#702 := (or false true)
-#705 := (iff #702 true)
-#798 := [rewrite]: #705
-#703 := (iff #667 #702)
-#847 := (iff #841 true)
-#849 := [rewrite]: #847
-#698 := (iff #666 false)
-#793 := [rewrite]: #698
-#704 := [monotonicity #793 #849]: #703
-#799 := [trans #704 #798]: #795
-#788 := [monotonicity #799]: #786
-#777 := [trans #788 #851]: #780
-#693 := (iff #812 false)
-#699 := (iff #812 #489)
-#682 := (iff #811 true)
-#803 := (or true false)
-#805 := (iff #803 true)
-#687 := [rewrite]: #805
-#794 := (iff #811 #803)
-#648 := (iff #810 true)
-#796 := [rewrite]: #648
-#797 := [monotonicity #796 #793]: #794
-#697 := [trans #797 #687]: #682
-#700 := [monotonicity #697]: #699
-#701 := [trans #700 #851]: #693
-#790 := [monotonicity #701 #777]: #789
-#781 := [trans #790 #787]: #792
-#745 := [monotonicity #781 #766 #742]: #744
-#733 := [trans #745 #741]: #747
-#688 := (iff #815 true)
-#804 := (iff #815 #803)
-#800 := (iff #814 false)
-#801 := [rewrite]: #800
-#646 := (iff #808 true)
-#647 := [rewrite]: #646
-#802 := [monotonicity #647 #801]: #804
-#689 := [trans #802 #687]: #688
-#731 := [monotonicity #689 #733]: #730
-#737 := [trans #731 #735]: #736
-#606 := [monotonicity #737]: #713
-#719 := [trans #606 #718]: #713
-#712 := [quant-inst #10 #12]: #711
-#724 := [mp #712 #719]: #738
-#721 := [unit-resolution #724 #890]: #813
-#722 := [monotonicity #721]: #16
+#152 := (iff #54 #151)
+#149 := (iff #53 #148)
+#146 := (= #52 #145)
+#143 := (= #51 #142)
+#140 := (= #50 #139)
+#137 := (= #49 #136)
+#138 := [rewrite]: #137
+#134 := (= #48 #133)
+#135 := [rewrite]: #134
+#141 := [monotonicity #135 #138]: #140
+#130 := (iff #46 #129)
+#127 := (iff #45 #126)
+#112 := (iff #42 #111)
+#113 := [rewrite]: #112
+#119 := (iff #44 #118)
+#123 := (iff #118 #118)
+#121 := (iff #117 #117)
+#122 := [rewrite]: #121
+#124 := [monotonicity #122]: #123
+#120 := [rewrite]: #119
+#125 := [trans #120 #124]: #119
+#128 := [monotonicity #125 #113]: #127
+#115 := (iff #43 #114)
+#108 := (iff #41 #107)
+#109 := [rewrite]: #108
+#116 := [monotonicity #109 #113]: #115
+#131 := [monotonicity #116 #128]: #130
+#144 := [monotonicity #131 #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [monotonicity #147]: #149
+#153 := [quant-intro #150]: #152
+#71 := [asserted]: #54
+#154 := [mp #71 #153]: #151
+#246 := [mp #154 #245]: #243
+#280 := [mp~ #246 #279]: #243
+#309 := [mp #280 #308]: #306
+#340 := [mp #309 #339]: #337
+#796 := [mp #340 #795]: #791
+#642 := (not #791)
+#643 := (or #642 #737)
+#736 := (* -1::Int 3::Int)
+#732 := (* -1::Int 1::Int)
+#725 := (div #732 #736)
+#726 := (* -1::Int #725)
+#727 := (+ #12 #726)
+#722 := (= #727 0::Int)
+#734 := (div 1::Int 3::Int)
+#449 := (* -1::Int #734)
+#731 := (+ #12 #449)
+#735 := (= #731 0::Int)
+#738 := (<= 3::Int 0::Int)
+#453 := (>= 1::Int 0::Int)
+#454 := (or #453 #738)
+#455 := (not #454)
+#741 := (<= 1::Int 0::Int)
+#742 := (or #741 #738)
+#452 := (not #742)
+#733 := (or #452 #455)
+#723 := (if #733 #735 #722)
+#462 := (= 3::Int 0::Int)
+#740 := (= 1::Int 0::Int)
+#463 := (or #740 #462)
+#728 := (if #463 #737 #723)
+#638 := (or #642 #728)
+#617 := (iff #638 #643)
+#619 := (iff #643 #643)
+#512 := [rewrite]: #619
+#640 := (iff #728 #737)
+#653 := (if false #737 #737)
+#636 := (iff #653 #737)
+#637 := [rewrite]: #636
+#639 := (iff #728 #653)
+#652 := (iff #723 #737)
+#665 := (= #12 1::Int)
+#1 := true
+#646 := (if true #737 #665)
+#650 := (iff #646 #737)
+#651 := [rewrite]: #650
+#648 := (iff #723 #646)
+#667 := (iff #722 #665)
+#657 := (+ -1::Int #12)
+#662 := (= #657 0::Int)
+#666 := (iff #662 #665)
+#656 := [rewrite]: #666
+#663 := (iff #722 #662)
+#660 := (= #727 #657)
+#674 := (+ #12 -1::Int)
+#658 := (= #674 #657)
+#659 := [rewrite]: #658
+#654 := (= #727 #674)
+#673 := (= #726 -1::Int)
+#684 := (= #732 -1::Int)
+#691 := [rewrite]: #684
+#671 := (= #726 #732)
+#668 := (= #725 1::Int)
+#675 := -3::Int
+#679 := (div -1::Int -3::Int)
+#677 := (= #679 1::Int)
+#682 := [rewrite]: #677
+#680 := (= #725 #679)
+#676 := (= #736 -3::Int)
+#678 := [rewrite]: #676
+#681 := [monotonicity #691 #678]: #680
+#669 := [trans #681 #682]: #668
+#672 := [monotonicity #669]: #671
+#670 := [trans #672 #691]: #673
+#655 := [monotonicity #670]: #654
+#661 := [trans #655 #659]: #660
+#664 := [monotonicity #661]: #663
+#645 := [trans #664 #656]: #667
+#689 := (iff #735 #737)
+#687 := (= #731 #12)
+#695 := (+ #12 0::Int)
+#693 := (= #695 #12)
+#698 := [rewrite]: #693
+#696 := (= #731 #695)
+#683 := (= #449 0::Int)
+#701 := (* -1::Int 0::Int)
+#694 := (= #701 0::Int)
+#686 := [rewrite]: #694
+#705 := (= #449 #701)
+#611 := (= #734 0::Int)
+#704 := [rewrite]: #611
+#692 := [monotonicity #704]: #705
+#685 := [trans #692 #686]: #683
+#697 := [monotonicity #685]: #696
+#688 := [trans #697 #698]: #687
+#690 := [monotonicity #688]: #689
+#609 := (iff #733 true)
+#554 := (or true false)
+#699 := (iff #554 true)
+#700 := [rewrite]: #699
+#607 := (iff #733 #554)
+#606 := (iff #455 false)
+#420 := (not true)
+#745 := (iff #420 false)
+#408 := [rewrite]: #745
+#603 := (iff #455 #420)
+#703 := (iff #454 true)
+#702 := (iff #454 #554)
+#720 := (iff #738 false)
+#714 := [rewrite]: #720
+#594 := (iff #453 true)
+#595 := [rewrite]: #594
+#604 := [monotonicity #595 #714]: #702
+#588 := [trans #604 #700]: #703
+#605 := [monotonicity #588]: #603
+#599 := [trans #605 #408]: #606
+#711 := (iff #452 true)
+#706 := (not false)
+#710 := (iff #706 true)
+#708 := [rewrite]: #710
+#707 := (iff #452 #706)
+#552 := (iff #742 false)
+#572 := (or false false)
+#716 := (iff #572 false)
+#717 := [rewrite]: #716
+#721 := (iff #742 #572)
+#713 := (iff #741 false)
+#719 := [rewrite]: #713
+#550 := [monotonicity #719 #714]: #721
+#553 := [trans #550 #717]: #552
+#709 := [monotonicity #553]: #707
+#593 := [trans #709 #708]: #711
+#608 := [monotonicity #593 #599]: #607
+#610 := [trans #608 #700]: #609
+#649 := [monotonicity #610 #690 #645]: #648
+#647 := [trans #649 #651]: #652
+#718 := (iff #463 false)
+#573 := (iff #463 #572)
+#730 := (iff #462 false)
+#571 := [rewrite]: #730
+#729 := (iff #740 false)
+#724 := [rewrite]: #729
+#715 := [monotonicity #724 #571]: #573
+#712 := [trans #715 #717]: #718
+#635 := [monotonicity #712 #647]: #639
+#641 := [trans #635 #637]: #640
+#618 := [monotonicity #641]: #617
+#623 := [trans #618 #512]: #617
+#644 := [quant-inst #9 #11]: #638
+#624 := [mp #644 #623]: #643
+#630 := [unit-resolution #624 #796]: #737
+#626 := [monotonicity #630]: #16
 #17 := (not #16)
-#85 := [asserted]: #17
-[unit-resolution #85 #722]: false
-unsat
-30b8b8c7c2003682f026b61d7ed1d6dcdfdd31f7 322 0
+#67 := [asserted]: #17
+[unit-resolution #67 #626]: false
+68d1ad7f70142308c629f42d1199c9a3061f756d 304 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int S3)
-#15 := 0::Int
-decl f4 :: S2
-#8 := f4
-#16 := (f3 f4 0::Int)
+#13 := 1::Int
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 1::Int)
 decl f5 :: (-> S4 Int Int)
-#12 := 3::Int
-decl f6 :: (-> S5 Int S4)
-#10 := 1::Int
-decl f7 :: S5
-#9 := f7
-#11 := (f6 f7 1::Int)
-#13 := (f5 #11 3::Int)
-#14 := (f3 f4 #13)
-#17 := (= #14 #16)
-#808 := (= #13 0::Int)
-#25 := (:var 0 Int)
-#36 := (:var 1 Int)
-#37 := (f6 f7 #36)
-#38 := (f5 #37 #25)
-#884 := (pattern #38)
-#188 := -1::Int
-#192 := (* -1::Int #25)
-#189 := (* -1::Int #36)
-#195 := (div #189 #192)
-#367 := (* -1::Int #195)
-#368 := (+ #38 #367)
-#369 := (= #368 0::Int)
-#48 := (div #36 #25)
-#364 := (* -1::Int #48)
-#365 := (+ #38 #364)
-#366 := (= #365 0::Int)
-#227 := (>= #36 0::Int)
-#220 := (<= #25 0::Int)
-#327 := (or #220 #227)
-#328 := (not #327)
-#216 := (<= #36 0::Int)
-#325 := (or #216 #220)
-#326 := (not #325)
-#331 := (or #326 #328)
-#370 := (ite #331 #366 #369)
-#363 := (= #38 0::Int)
-#40 := (= #25 0::Int)
-#39 := (= #36 0::Int)
-#41 := (or #39 #40)
-#371 := (ite #41 #363 #370)
-#885 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #884) #371)
-#374 := (forall (vars (?v0 Int) (?v1 Int)) #371)
-#888 := (iff #374 #885)
-#886 := (iff #371 #371)
-#887 := [refl]: #886
-#889 := [quant-intro #887]: #888
-#334 := (ite #331 #48 #195)
-#337 := (ite #41 0::Int #334)
-#340 := (= #38 #337)
-#343 := (forall (vars (?v0 Int) (?v1 Int)) #340)
-#375 := (iff #343 #374)
-#372 := (iff #340 #371)
-#373 := [rewrite]: #372
-#376 := [quant-intro #373]: #375
-#228 := (not #227)
-#221 := (not #220)
-#231 := (and #221 #228)
-#217 := (not #216)
-#224 := (and #217 #221)
-#234 := (or #224 #231)
-#237 := (ite #234 #48 #195)
-#240 := (ite #41 0::Int #237)
-#243 := (= #38 #240)
-#246 := (forall (vars (?v0 Int) (?v1 Int)) #243)
-#344 := (iff #246 #343)
-#341 := (iff #243 #340)
-#338 := (= #240 #337)
-#335 := (= #237 #334)
-#332 := (iff #234 #331)
-#329 := (iff #231 #328)
-#330 := [rewrite]: #329
-#310 := (iff #224 #326)
-#311 := [rewrite]: #310
-#333 := [monotonicity #311 #330]: #332
-#336 := [monotonicity #333]: #335
-#339 := [monotonicity #336]: #338
-#342 := [monotonicity #339]: #341
-#345 := [quant-intro #342]: #344
-#306 := (~ #246 #246)
-#319 := (~ #243 #243)
-#320 := [refl]: #319
-#307 := [nnf-pos #320]: #306
-#50 := (- #25)
-#49 := (- #36)
-#51 := (div #49 #50)
-#43 := (< 0::Int #25)
-#45 := (< #36 0::Int)
-#46 := (and #45 #43)
-#42 := (< 0::Int #36)
-#44 := (and #42 #43)
-#47 := (or #44 #46)
-#52 := (ite #47 #48 #51)
-#53 := (ite #41 0::Int #52)
-#54 := (= #38 #53)
-#55 := (forall (vars (?v0 Int) (?v1 Int)) #54)
-#249 := (iff #55 #246)
-#182 := (and #43 #45)
-#185 := (or #44 #182)
-#198 := (ite #185 #48 #195)
-#176 := (= 0::Int #25)
-#173 := (= 0::Int #36)
-#179 := (or #173 #176)
-#201 := (ite #179 0::Int #198)
-#204 := (= #38 #201)
-#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
-#247 := (iff #207 #246)
-#244 := (iff #204 #243)
-#241 := (= #201 #240)
-#238 := (= #198 #237)
-#235 := (iff #185 #234)
-#232 := (iff #182 #231)
-#229 := (iff #45 #228)
-#230 := [rewrite]: #229
-#222 := (iff #43 #221)
-#223 := [rewrite]: #222
-#233 := [monotonicity #223 #230]: #232
-#225 := (iff #44 #224)
-#218 := (iff #42 #217)
-#219 := [rewrite]: #218
-#226 := [monotonicity #219 #223]: #225
-#236 := [monotonicity #226 #233]: #235
-#239 := [monotonicity #236]: #238
-#214 := (iff #179 #41)
-#212 := (iff #176 #40)
-#213 := [rewrite]: #212
-#210 := (iff #173 #39)
-#211 := [rewrite]: #210
-#215 := [monotonicity #211 #213]: #214
-#242 := [monotonicity #215 #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [quant-intro #245]: #247
-#208 := (iff #55 #207)
-#205 := (iff #54 #204)
-#202 := (= #53 #201)
-#199 := (= #52 #198)
-#196 := (= #51 #195)
-#193 := (= #50 #192)
-#194 := [rewrite]: #193
-#190 := (= #49 #189)
-#191 := [rewrite]: #190
-#197 := [monotonicity #191 #194]: #196
-#186 := (iff #47 #185)
-#183 := (iff #46 #182)
-#184 := [rewrite]: #183
-#187 := [monotonicity #184]: #186
-#200 := [monotonicity #187 #197]: #199
-#180 := (iff #41 #179)
-#177 := (iff #40 #176)
-#178 := [rewrite]: #177
-#174 := (iff #39 #173)
-#175 := [rewrite]: #174
-#181 := [monotonicity #175 #178]: #180
-#203 := [monotonicity #181 #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [quant-intro #206]: #208
-#250 := [trans #209 #248]: #249
-#172 := [asserted]: #55
-#251 := [mp #172 #250]: #246
-#321 := [mp~ #251 #307]: #246
-#346 := [mp #321 #345]: #343
-#377 := [mp #346 #376]: #374
-#890 := [mp #377 #889]: #885
-#709 := (not #885)
-#690 := (or #709 #808)
-#820 := (* -1::Int 3::Int)
-#821 := (* -1::Int 1::Int)
-#816 := (div #821 #820)
-#817 := (* -1::Int #816)
-#822 := (+ #13 #817)
-#823 := (= #822 0::Int)
-#818 := (div 1::Int 3::Int)
-#824 := (* -1::Int #818)
-#665 := (+ #13 #824)
-#666 := (= #665 0::Int)
-#667 := (>= 1::Int 0::Int)
-#809 := (<= 3::Int 0::Int)
-#810 := (or #809 #667)
-#811 := (not #810)
-#812 := (<= 1::Int 0::Int)
-#806 := (or #812 #809)
-#807 := (not #806)
-#813 := (or #807 #811)
-#814 := (ite #813 #666 #823)
-#815 := (= 3::Int 0::Int)
-#644 := (= 1::Int 0::Int)
-#646 := (or #644 #815)
-#647 := (ite #646 #808 #814)
-#714 := (or #709 #647)
-#710 := (iff #714 #690)
-#684 := (iff #690 #690)
-#691 := [rewrite]: #684
-#708 := (iff #647 #808)
-#725 := (ite false #808 #808)
-#723 := (iff #725 #808)
-#728 := [rewrite]: #723
-#726 := (iff #647 #725)
-#721 := (iff #814 #808)
-#738 := (= #13 1::Int)
-#1 := true
-#717 := (ite true #808 #738)
-#724 := (iff #717 #808)
-#720 := [rewrite]: #724
-#718 := (iff #814 #717)
-#713 := (iff #823 #738)
-#729 := (+ -1::Int #13)
-#736 := (= #729 0::Int)
-#711 := (iff #736 #738)
-#712 := [rewrite]: #711
-#737 := (iff #823 #736)
-#734 := (= #822 #729)
-#741 := (+ #13 -1::Int)
-#730 := (= #741 #729)
-#731 := [rewrite]: #730
-#747 := (= #822 #741)
-#745 := (= #817 -1::Int)
-#754 := (= #821 -1::Int)
-#755 := [rewrite]: #754
-#743 := (= #817 #821)
-#740 := (= #816 1::Int)
-#756 := -3::Int
-#759 := (div -1::Int -3::Int)
-#761 := (= #759 1::Int)
-#739 := [rewrite]: #761
-#760 := (= #816 #759)
-#757 := (= #820 -3::Int)
-#758 := [rewrite]: #757
-#750 := [monotonicity #755 #758]: #760
-#742 := [trans #750 #739]: #740
-#744 := [monotonicity #742]: #743
-#746 := [trans #744 #755]: #745
-#733 := [monotonicity #746]: #747
-#735 := [trans #733 #731]: #734
-#732 := [monotonicity #735]: #737
-#606 := [trans #732 #712]: #713
-#752 := (iff #666 #808)
-#749 := (= #665 #13)
-#766 := (+ #13 0::Int)
-#768 := (= #766 #13)
-#748 := [rewrite]: #768
-#767 := (= #665 #766)
-#763 := (= #824 0::Int)
-#774 := (* -1::Int 0::Int)
-#776 := (= #774 0::Int)
-#762 := [rewrite]: #776
-#775 := (= #824 #774)
-#772 := (= #818 0::Int)
-#773 := [rewrite]: #772
-#771 := [monotonicity #773]: #775
-#765 := [trans #771 #762]: #763
-#764 := [monotonicity #765]: #767
-#751 := [trans #764 #748]: #749
-#753 := [monotonicity #751]: #752
-#769 := (iff #813 true)
-#782 := (or true false)
-#778 := (iff #782 true)
-#785 := [rewrite]: #778
-#783 := (iff #813 #782)
-#792 := (iff #811 false)
-#490 := (not true)
-#851 := (iff #490 false)
-#837 := [rewrite]: #851
-#791 := (iff #811 #490)
-#789 := (iff #810 true)
-#786 := (or false true)
-#777 := (iff #786 true)
-#779 := [rewrite]: #777
-#788 := (iff #810 #786)
-#795 := (iff #667 true)
-#799 := [rewrite]: #795
-#794 := (iff #809 false)
-#797 := [rewrite]: #794
-#780 := [monotonicity #797 #799]: #788
-#790 := [trans #780 #779]: #789
-#787 := [monotonicity #790]: #791
-#781 := [trans #787 #837]: #792
-#705 := (iff #807 true)
-#693 := (not false)
-#703 := (iff #693 true)
-#704 := [rewrite]: #703
-#701 := (iff #807 #693)
-#699 := (iff #806 false)
-#802 := (or false false)
-#688 := (iff #802 false)
-#689 := [rewrite]: #688
-#682 := (iff #806 #802)
-#698 := (iff #812 false)
-#793 := [rewrite]: #698
-#697 := [monotonicity #793 #797]: #682
-#700 := [trans #697 #689]: #699
-#702 := [monotonicity #700]: #701
-#798 := [trans #702 #704]: #705
-#784 := [monotonicity #798 #781]: #783
-#770 := [trans #784 #785]: #769
-#719 := [monotonicity #770 #753 #606]: #718
-#722 := [trans #719 #720]: #721
-#648 := (iff #646 false)
-#805 := (iff #646 #802)
-#803 := (iff #815 false)
-#804 := [rewrite]: #803
-#800 := (iff #644 false)
-#801 := [rewrite]: #800
-#687 := [monotonicity #801 #804]: #805
-#796 := [trans #687 #689]: #648
-#727 := [monotonicity #796 #722]: #726
-#654 := [trans #727 #728]: #708
-#716 := [monotonicity #654]: #710
-#650 := [trans #716 #691]: #710
-#715 := [quant-inst #10 #12]: #714
-#681 := [mp #715 #650]: #690
-#685 := [unit-resolution #681 #890]: #808
-#692 := [monotonicity #685]: #17
-#18 := (not #17)
-#86 := [asserted]: #18
-[unit-resolution #86 #692]: false
-unsat
-eed23a962a9be5f7206f850271a55f051364feed 312 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#14 := 1::Int
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 1::Int)
-decl f5 :: (-> S4 Int Int)
-#10 := 3::Int
+#9 := 3::Int
 decl f6 :: (-> S5 Int S4)
 decl f7 :: S5
-#9 := f7
-#11 := (f6 f7 3::Int)
-#12 := (f5 #11 3::Int)
-#13 := (f3 f4 #12)
-#16 := (= #13 #15)
-#749 := (= #12 1::Int)
-#25 := (:var 0 Int)
-#36 := (:var 1 Int)
-#37 := (f6 f7 #36)
-#38 := (f5 #37 #25)
-#884 := (pattern #38)
-#24 := 0::Int
-#188 := -1::Int
-#192 := (* -1::Int #25)
-#189 := (* -1::Int #36)
-#195 := (div #189 #192)
-#367 := (* -1::Int #195)
-#368 := (+ #38 #367)
-#369 := (= #368 0::Int)
-#48 := (div #36 #25)
-#364 := (* -1::Int #48)
-#365 := (+ #38 #364)
-#366 := (= #365 0::Int)
-#227 := (>= #36 0::Int)
-#220 := (<= #25 0::Int)
-#327 := (or #220 #227)
-#328 := (not #327)
-#216 := (<= #36 0::Int)
-#325 := (or #216 #220)
-#326 := (not #325)
-#331 := (or #326 #328)
-#370 := (ite #331 #366 #369)
-#363 := (= #38 0::Int)
-#40 := (= #25 0::Int)
-#39 := (= #36 0::Int)
-#41 := (or #39 #40)
-#371 := (ite #41 #363 #370)
-#885 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #884) #371)
-#374 := (forall (vars (?v0 Int) (?v1 Int)) #371)
-#888 := (iff #374 #885)
-#886 := (iff #371 #371)
-#887 := [refl]: #886
-#889 := [quant-intro #887]: #888
-#334 := (ite #331 #48 #195)
-#337 := (ite #41 0::Int #334)
-#340 := (= #38 #337)
-#343 := (forall (vars (?v0 Int) (?v1 Int)) #340)
-#375 := (iff #343 #374)
-#372 := (iff #340 #371)
-#373 := [rewrite]: #372
-#376 := [quant-intro #373]: #375
-#228 := (not #227)
-#221 := (not #220)
-#231 := (and #221 #228)
-#217 := (not #216)
-#224 := (and #217 #221)
-#234 := (or #224 #231)
-#237 := (ite #234 #48 #195)
-#240 := (ite #41 0::Int #237)
-#243 := (= #38 #240)
-#246 := (forall (vars (?v0 Int) (?v1 Int)) #243)
-#344 := (iff #246 #343)
-#341 := (iff #243 #340)
-#338 := (= #240 #337)
-#335 := (= #237 #334)
-#332 := (iff #234 #331)
-#329 := (iff #231 #328)
-#330 := [rewrite]: #329
-#310 := (iff #224 #326)
-#311 := [rewrite]: #310
-#333 := [monotonicity #311 #330]: #332
-#336 := [monotonicity #333]: #335
-#339 := [monotonicity #336]: #338
-#342 := [monotonicity #339]: #341
-#345 := [quant-intro #342]: #344
-#306 := (~ #246 #246)
-#319 := (~ #243 #243)
-#320 := [refl]: #319
-#307 := [nnf-pos #320]: #306
-#50 := (- #25)
-#49 := (- #36)
-#51 := (div #49 #50)
-#43 := (< 0::Int #25)
-#45 := (< #36 0::Int)
-#46 := (and #45 #43)
-#42 := (< 0::Int #36)
-#44 := (and #42 #43)
-#47 := (or #44 #46)
-#52 := (ite #47 #48 #51)
-#53 := (ite #41 0::Int #52)
-#54 := (= #38 #53)
-#55 := (forall (vars (?v0 Int) (?v1 Int)) #54)
-#249 := (iff #55 #246)
-#182 := (and #43 #45)
-#185 := (or #44 #182)
-#198 := (ite #185 #48 #195)
-#176 := (= 0::Int #25)
-#173 := (= 0::Int #36)
-#179 := (or #173 #176)
-#201 := (ite #179 0::Int #198)
-#204 := (= #38 #201)
-#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
-#247 := (iff #207 #246)
-#244 := (iff #204 #243)
-#241 := (= #201 #240)
-#238 := (= #198 #237)
-#235 := (iff #185 #234)
-#232 := (iff #182 #231)
-#229 := (iff #45 #228)
-#230 := [rewrite]: #229
-#222 := (iff #43 #221)
-#223 := [rewrite]: #222
-#233 := [monotonicity #223 #230]: #232
-#225 := (iff #44 #224)
-#218 := (iff #42 #217)
-#219 := [rewrite]: #218
-#226 := [monotonicity #219 #223]: #225
-#236 := [monotonicity #226 #233]: #235
-#239 := [monotonicity #236]: #238
-#214 := (iff #179 #41)
-#212 := (iff #176 #40)
-#213 := [rewrite]: #212
-#210 := (iff #173 #39)
-#211 := [rewrite]: #210
-#215 := [monotonicity #211 #213]: #214
-#242 := [monotonicity #215 #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [quant-intro #245]: #247
-#208 := (iff #55 #207)
-#205 := (iff #54 #204)
-#202 := (= #53 #201)
-#199 := (= #52 #198)
-#196 := (= #51 #195)
-#193 := (= #50 #192)
-#194 := [rewrite]: #193
-#190 := (= #49 #189)
-#191 := [rewrite]: #190
-#197 := [monotonicity #191 #194]: #196
-#186 := (iff #47 #185)
-#183 := (iff #46 #182)
-#184 := [rewrite]: #183
-#187 := [monotonicity #184]: #186
-#200 := [monotonicity #187 #197]: #199
-#180 := (iff #41 #179)
-#177 := (iff #40 #176)
-#178 := [rewrite]: #177
-#174 := (iff #39 #173)
-#175 := [rewrite]: #174
-#181 := [monotonicity #175 #178]: #180
-#203 := [monotonicity #181 #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [quant-intro #206]: #208
-#250 := [trans #209 #248]: #249
-#172 := [asserted]: #55
-#251 := [mp #172 #250]: #246
-#321 := [mp~ #251 #307]: #246
-#346 := [mp #321 #345]: #343
-#377 := [mp #346 #376]: #374
-#890 := [mp #377 #889]: #885
-#721 := (not #885)
-#722 := (or #721 #749)
-#821 := (* -1::Int 3::Int)
-#816 := (div #821 #821)
-#817 := (* -1::Int #816)
-#822 := (+ #12 #817)
-#823 := (= #822 0::Int)
-#818 := (div 3::Int 3::Int)
-#824 := (* -1::Int #818)
-#665 := (+ #12 #824)
-#666 := (= #665 0::Int)
-#667 := (>= 3::Int 0::Int)
-#809 := (<= 3::Int 0::Int)
-#810 := (or #809 #667)
-#811 := (not #810)
-#812 := (or #809 #809)
-#806 := (not #812)
-#807 := (or #806 #811)
-#813 := (ite #807 #666 #823)
-#814 := (= #12 0::Int)
-#808 := (= 3::Int 0::Int)
-#815 := (or #808 #808)
-#644 := (ite #815 #814 #813)
-#725 := (or #721 #644)
-#727 := (iff #725 #722)
-#728 := (iff #722 #722)
-#708 := [rewrite]: #728
-#724 := (iff #644 #749)
-#713 := (ite false #814 #749)
-#718 := (iff #713 #749)
-#719 := [rewrite]: #718
-#606 := (iff #644 #713)
-#711 := (iff #813 #749)
-#1 := true
-#735 := (ite true #749 #749)
-#732 := (iff #735 #749)
-#738 := [rewrite]: #732
-#736 := (iff #813 #735)
-#731 := (iff #823 #749)
-#762 := (+ -1::Int #12)
-#764 := (= #762 0::Int)
-#751 := (iff #764 #749)
-#752 := [rewrite]: #751
-#729 := (iff #823 #764)
-#747 := (= #822 #762)
-#775 := (+ #12 -1::Int)
-#763 := (= #775 #762)
-#765 := [rewrite]: #763
-#746 := (= #822 #775)
-#744 := (= #817 -1::Int)
-#778 := (* -1::Int 1::Int)
-#770 := (= #778 -1::Int)
-#772 := [rewrite]: #770
-#742 := (= #817 #778)
-#739 := (= #816 1::Int)
-#755 := -3::Int
-#758 := (div -3::Int -3::Int)
-#750 := (= #758 1::Int)
-#761 := [rewrite]: #750
-#759 := (= #816 #758)
-#756 := (= #821 -3::Int)
-#757 := [rewrite]: #756
-#760 := [monotonicity #757 #757]: #759
-#740 := [trans #760 #761]: #739
-#743 := [monotonicity #740]: #742
-#745 := [trans #743 #772]: #744
-#741 := [monotonicity #745]: #746
-#733 := [trans #741 #765]: #747
-#730 := [monotonicity #733]: #729
-#734 := [trans #730 #752]: #731
-#753 := (iff #666 #749)
-#768 := (iff #666 #764)
-#766 := (= #665 #762)
-#771 := (= #665 #775)
-#773 := (= #824 -1::Int)
-#785 := (= #824 #778)
-#783 := (= #818 1::Int)
-#784 := [rewrite]: #783
-#769 := [monotonicity #784]: #785
-#774 := [trans #769 #772]: #773
-#776 := [monotonicity #774]: #771
-#767 := [trans #776 #765]: #766
-#748 := [monotonicity #767]: #768
-#754 := [trans #748 #752]: #753
-#781 := (iff #807 true)
-#789 := (or true false)
-#787 := (iff #789 true)
-#792 := [rewrite]: #787
-#790 := (iff #807 #789)
-#777 := (iff #811 false)
-#490 := (not true)
-#851 := (iff #490 false)
-#837 := [rewrite]: #851
-#788 := (iff #811 #490)
-#799 := (iff #810 true)
-#703 := (or false true)
-#798 := (iff #703 true)
-#795 := [rewrite]: #798
-#704 := (iff #810 #703)
-#701 := (iff #667 true)
-#702 := [rewrite]: #701
-#688 := (iff #809 false)
-#689 := [rewrite]: #688
-#705 := [monotonicity #689 #702]: #704
-#786 := [trans #705 #795]: #799
-#780 := [monotonicity #786]: #788
-#779 := [trans #780 #837]: #777
-#700 := (iff #806 true)
-#794 := (not false)
-#697 := (iff #794 true)
-#699 := [rewrite]: #697
-#797 := (iff #806 #794)
-#698 := (iff #812 false)
-#800 := (or false false)
-#804 := (iff #800 false)
-#802 := [rewrite]: #804
-#648 := (iff #812 #800)
-#796 := [monotonicity #689 #689]: #648
-#793 := [trans #796 #802]: #698
-#682 := [monotonicity #793]: #797
-#693 := [trans #682 #699]: #700
-#791 := [monotonicity #693 #779]: #790
-#782 := [trans #791 #792]: #781
-#737 := [monotonicity #782 #754 #734]: #736
-#712 := [trans #737 #738]: #711
-#805 := (iff #815 false)
-#801 := (iff #815 #800)
-#646 := (iff #808 false)
-#647 := [rewrite]: #646
-#803 := [monotonicity #647 #647]: #801
-#687 := [trans #803 #802]: #805
-#717 := [monotonicity #687 #712]: #606
-#720 := [trans #717 #719]: #724
-#723 := [monotonicity #720]: #727
-#654 := [trans #723 #708]: #727
-#726 := [quant-inst #10 #10]: #725
-#709 := [mp #726 #654]: #722
-#715 := [unit-resolution #709 #890]: #749
-#710 := [monotonicity #715]: #16
-#17 := (not #16)
-#86 := [asserted]: #17
-[unit-resolution #86 #710]: false
-unsat
-14f833dd4fb04a0cdd005cf364c1d2d23fdad718 467 0
-#2 := false
-#23 := 0::Int
-#13 := 3::Int
-decl f6 :: (-> S4 S5 Int)
-decl f8 :: S5
-#10 := f8
-decl f7 :: S4
-#9 := f7
-#11 := (f6 f7 f8)
-#814 := (mod #11 3::Int)
-#88 := -1::Int
-#760 := (* -1::Int #814)
-#530 := (div #11 3::Int)
-#556 := -3::Int
-#758 := (* -3::Int #530)
-#761 := (+ #758 #760)
-#762 := (+ #11 #761)
-#757 := (= #762 0::Int)
-#1 := true
-#83 := [true-axiom]: true
-#726 := (or false #757)
-#727 := [th-lemma arith]: #726
-#728 := [unit-resolution #727 #83]: #757
-#766 := (>= #762 0::Int)
-#669 := (not #766)
-#767 := (>= #814 0::Int)
-#671 := (or false #767)
-#672 := [th-lemma arith]: #671
-#677 := [unit-resolution #672 #83]: #767
-decl f3 :: (-> S2 Int Int)
-decl f4 :: (-> S3 Int S2)
-decl f5 :: S3
-#8 := f5
-#12 := (f4 f5 #11)
-#14 := (f3 #12 3::Int)
-#91 := (* -1::Int #14)
-#92 := (+ #11 #91)
-#90 := (>= #92 0::Int)
-#94 := (not #90)
-#15 := (<= #14 #11)
-#16 := (not #15)
-#95 := (iff #16 #94)
-#89 := (iff #15 #90)
-#93 := [rewrite]: #89
-#96 := [monotonicity #93]: #95
-#85 := [asserted]: #16
-#97 := [mp #85 #96]: #94
-#865 := (* -1::Int #530)
-#867 := (+ #14 #865)
-#696 := (<= #867 0::Int)
-#524 := (= #867 0::Int)
-#546 := (* -1::Int #11)
-#836 := (div #546 -3::Int)
-#834 := (* -1::Int #836)
-#839 := (+ #14 #834)
-#830 := (= #839 0::Int)
-#868 := (<= #11 0::Int)
-#498 := (not #868)
-#654 := (>= #11 0::Int)
-#572 := (not #654)
-#840 := (or #572 #498)
-#831 := (ite #840 #524 #830)
-#522 := (= #11 0::Int)
-#713 := (not #522)
-#824 := (<= #14 0::Int)
-#872 := (= #14 0::Int)
-#747 := [hypothesis]: #522
-#720 := (or #713 #872)
-#833 := (ite #522 #872 #831)
+#8 := f7
+#10 := (f6 f7 3::Int)
+#11 := (f5 #10 3::Int)
+#12 := (f3 f4 #11)
+#15 := (= #12 #14)
+#687 := (= #11 1::Int)
 #24 := (:var 0 Int)
 #35 := (:var 1 Int)
-#36 := (f4 f5 #35)
-#37 := (f3 #36 #24)
-#893 := (pattern #37)
-#200 := (* -1::Int #24)
-#197 := (* -1::Int #35)
-#203 := (div #197 #200)
-#375 := (* -1::Int #203)
-#376 := (+ #37 #375)
-#377 := (= #376 0::Int)
+#36 := (f6 f7 #35)
+#37 := (f5 #36 #24)
+#790 := (pattern #37)
+#23 := 0::Int
+#132 := -1::Int
+#136 := (* -1::Int #24)
+#133 := (* -1::Int #35)
+#139 := (div #133 #136)
+#330 := (* -1::Int #139)
+#331 := (+ #37 #330)
+#332 := (= #331 0::Int)
 #47 := (div #35 #24)
-#372 := (* -1::Int #47)
-#373 := (+ #37 #372)
-#374 := (= #373 0::Int)
-#235 := (>= #35 0::Int)
-#228 := (<= #24 0::Int)
-#335 := (or #228 #235)
-#336 := (not #335)
-#224 := (<= #35 0::Int)
-#333 := (or #224 #228)
-#334 := (not #333)
-#339 := (or #334 #336)
-#378 := (ite #339 #374 #377)
-#371 := (= #37 0::Int)
+#327 := (* -1::Int #47)
+#328 := (+ #37 #327)
+#329 := (= #328 0::Int)
+#110 := (<= #24 0::Int)
+#222 := (>= #35 0::Int)
+#290 := (or #222 #110)
+#291 := (not #290)
+#106 := (<= #35 0::Int)
+#286 := (or #106 #110)
+#287 := (not #286)
+#294 := (or #287 #291)
+#333 := (if #294 #329 #332)
+#326 := (= #37 0::Int)
 #39 := (= #24 0::Int)
 #38 := (= #35 0::Int)
 #40 := (or #38 #39)
-#379 := (ite #40 #371 #378)
-#894 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #893) #379)
-#382 := (forall (vars (?v0 Int) (?v1 Int)) #379)
-#897 := (iff #382 #894)
-#895 := (iff #379 #379)
-#896 := [refl]: #895
-#898 := [quant-intro #896]: #897
-#342 := (ite #339 #47 #203)
-#345 := (ite #40 0::Int #342)
-#348 := (= #37 #345)
-#351 := (forall (vars (?v0 Int) (?v1 Int)) #348)
-#383 := (iff #351 #382)
-#380 := (iff #348 #379)
-#381 := [rewrite]: #380
-#384 := [quant-intro #381]: #383
-#236 := (not #235)
-#229 := (not #228)
-#239 := (and #229 #236)
-#225 := (not #224)
-#232 := (and #225 #229)
-#242 := (or #232 #239)
-#245 := (ite #242 #47 #203)
-#248 := (ite #40 0::Int #245)
-#251 := (= #37 #248)
-#254 := (forall (vars (?v0 Int) (?v1 Int)) #251)
-#352 := (iff #254 #351)
-#349 := (iff #251 #348)
-#346 := (= #248 #345)
-#343 := (= #245 #342)
-#340 := (iff #242 #339)
-#337 := (iff #239 #336)
-#338 := [rewrite]: #337
-#318 := (iff #232 #334)
-#319 := [rewrite]: #318
-#341 := [monotonicity #319 #338]: #340
-#344 := [monotonicity #341]: #343
-#347 := [monotonicity #344]: #346
-#350 := [monotonicity #347]: #349
-#353 := [quant-intro #350]: #352
-#314 := (~ #254 #254)
-#327 := (~ #251 #251)
-#328 := [refl]: #327
-#315 := [nnf-pos #328]: #314
+#334 := (if #40 #326 #333)
+#791 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #790) #334)
+#337 := (forall (vars (?v0 Int) (?v1 Int)) #334)
+#794 := (iff #337 #791)
+#792 := (iff #334 #334)
+#793 := [refl]: #792
+#795 := [quant-intro #793]: #794
+#297 := (if #294 #47 #139)
+#300 := (if #40 0::Int #297)
+#303 := (= #37 #300)
+#306 := (forall (vars (?v0 Int) (?v1 Int)) #303)
+#338 := (iff #306 #337)
+#335 := (iff #303 #334)
+#336 := [rewrite]: #335
+#339 := [quant-intro #336]: #338
+#111 := (not #110)
+#225 := (not #222)
+#228 := (and #225 #111)
+#107 := (not #106)
+#114 := (and #107 #111)
+#231 := (or #114 #228)
+#234 := (if #231 #47 #139)
+#237 := (if #40 0::Int #234)
+#240 := (= #37 #237)
+#243 := (forall (vars (?v0 Int) (?v1 Int)) #240)
+#307 := (iff #243 #306)
+#304 := (iff #240 #303)
+#301 := (= #237 #300)
+#298 := (= #234 #297)
+#295 := (iff #231 #294)
+#292 := (iff #228 #291)
+#293 := [rewrite]: #292
+#288 := (iff #114 #287)
+#289 := [rewrite]: #288
+#296 := [monotonicity #289 #293]: #295
+#299 := [monotonicity #296]: #298
+#302 := [monotonicity #299]: #301
+#305 := [monotonicity #302]: #304
+#308 := [quant-intro #305]: #307
+#278 := (~ #243 #243)
+#276 := (~ #240 #240)
+#277 := [refl]: #276
+#279 := [nnf-pos #277]: #278
+#117 := (<= 0::Int #35)
+#118 := (not #117)
+#126 := (and #118 #111)
+#129 := (or #114 #126)
+#142 := (if #129 #47 #139)
+#145 := (if #40 0::Int #142)
+#148 := (= #37 #145)
+#151 := (forall (vars (?v0 Int) (?v1 Int)) #148)
+#244 := (iff #151 #243)
+#241 := (iff #148 #240)
+#238 := (= #145 #237)
+#235 := (= #142 #234)
+#232 := (iff #129 #231)
+#229 := (iff #126 #228)
+#226 := (iff #118 #225)
+#223 := (iff #117 #222)
+#224 := [rewrite]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [monotonicity #233]: #235
+#239 := [monotonicity #236]: #238
+#242 := [monotonicity #239]: #241
+#245 := [quant-intro #242]: #244
 #49 := (- #24)
 #48 := (- #35)
 #50 := (div #48 #49)
@@ -16216,1062 +15218,1629 @@
 #41 := (< 0::Int #35)
 #43 := (and #41 #42)
 #46 := (or #43 #45)
-#51 := (ite #46 #47 #50)
-#52 := (ite #40 0::Int #51)
+#51 := (if #46 #47 #50)
+#52 := (if #40 0::Int #51)
 #53 := (= #37 #52)
 #54 := (forall (vars (?v0 Int) (?v1 Int)) #53)
-#257 := (iff #54 #254)
-#191 := (and #42 #44)
-#194 := (or #43 #191)
-#206 := (ite #194 #47 #203)
-#185 := (= 0::Int #24)
-#182 := (= 0::Int #35)
-#188 := (or #182 #185)
-#209 := (ite #188 0::Int #206)
-#212 := (= #37 #209)
-#215 := (forall (vars (?v0 Int) (?v1 Int)) #212)
-#255 := (iff #215 #254)
-#252 := (iff #212 #251)
-#249 := (= #209 #248)
-#246 := (= #206 #245)
-#243 := (iff #194 #242)
-#240 := (iff #191 #239)
-#237 := (iff #44 #236)
-#238 := [rewrite]: #237
-#230 := (iff #42 #229)
-#231 := [rewrite]: #230
-#241 := [monotonicity #231 #238]: #240
-#233 := (iff #43 #232)
-#226 := (iff #41 #225)
-#227 := [rewrite]: #226
-#234 := [monotonicity #227 #231]: #233
-#244 := [monotonicity #234 #241]: #243
+#152 := (iff #54 #151)
+#149 := (iff #53 #148)
+#146 := (= #52 #145)
+#143 := (= #51 #142)
+#140 := (= #50 #139)
+#137 := (= #49 #136)
+#138 := [rewrite]: #137
+#134 := (= #48 #133)
+#135 := [rewrite]: #134
+#141 := [monotonicity #135 #138]: #140
+#130 := (iff #46 #129)
+#127 := (iff #45 #126)
+#112 := (iff #42 #111)
+#113 := [rewrite]: #112
+#119 := (iff #44 #118)
+#123 := (iff #118 #118)
+#121 := (iff #117 #117)
+#122 := [rewrite]: #121
+#124 := [monotonicity #122]: #123
+#120 := [rewrite]: #119
+#125 := [trans #120 #124]: #119
+#128 := [monotonicity #125 #113]: #127
+#115 := (iff #43 #114)
+#108 := (iff #41 #107)
+#109 := [rewrite]: #108
+#116 := [monotonicity #109 #113]: #115
+#131 := [monotonicity #116 #128]: #130
+#144 := [monotonicity #131 #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [monotonicity #147]: #149
+#153 := [quant-intro #150]: #152
+#71 := [asserted]: #54
+#154 := [mp #71 #153]: #151
+#246 := [mp #154 #245]: #243
+#280 := [mp~ #246 #279]: #243
+#309 := [mp #280 #308]: #306
+#340 := [mp #309 #339]: #337
+#796 := [mp #340 #795]: #791
+#652 := (not #791)
+#647 := (or #652 #687)
+#735 := (* -1::Int 3::Int)
+#732 := (div #735 #735)
+#736 := (* -1::Int #732)
+#725 := (+ #11 #736)
+#726 := (= #725 0::Int)
+#733 := (div 3::Int 3::Int)
+#734 := (* -1::Int #733)
+#449 := (+ #11 #734)
+#731 := (= #449 0::Int)
+#741 := (<= 3::Int 0::Int)
+#452 := (>= 3::Int 0::Int)
+#453 := (or #452 #741)
+#454 := (not #453)
+#738 := (or #741 #741)
+#742 := (not #738)
+#455 := (or #742 #454)
+#727 := (if #455 #731 #726)
+#737 := (= #11 0::Int)
+#462 := (= 3::Int 0::Int)
+#463 := (or #462 #462)
+#722 := (if #463 #737 #727)
+#653 := (or #652 #722)
+#635 := (iff #653 #647)
+#637 := (iff #647 #647)
+#640 := [rewrite]: #637
+#650 := (iff #722 #687)
+#667 := (if false #737 #687)
+#648 := (iff #667 #687)
+#649 := [rewrite]: #648
+#645 := (iff #722 #667)
+#666 := (iff #727 #687)
+#1 := true
+#661 := (if true #687 #687)
+#664 := (iff #661 #687)
+#665 := [rewrite]: #664
+#662 := (iff #727 #661)
+#659 := (iff #726 #687)
+#686 := (+ -1::Int #11)
+#697 := (= #686 0::Int)
+#688 := (iff #697 #687)
+#689 := [rewrite]: #688
+#657 := (iff #726 #697)
+#654 := (= #725 #686)
+#705 := (+ #11 -1::Int)
+#683 := (= #705 #686)
+#685 := [rewrite]: #683
+#670 := (= #725 #705)
+#672 := (= #736 -1::Int)
+#607 := (* -1::Int 1::Int)
+#610 := (= #607 -1::Int)
+#611 := [rewrite]: #610
+#669 := (= #736 #607)
+#682 := (= #732 1::Int)
+#691 := -3::Int
+#678 := (div -3::Int -3::Int)
+#681 := (= #678 1::Int)
+#677 := [rewrite]: #681
+#679 := (= #732 #678)
+#675 := (= #735 -3::Int)
+#676 := [rewrite]: #675
+#680 := [monotonicity #676 #676]: #679
+#668 := [trans #680 #677]: #682
+#671 := [monotonicity #668]: #669
+#673 := [trans #671 #611]: #672
+#674 := [monotonicity #673]: #670
+#655 := [trans #674 #685]: #654
+#658 := [monotonicity #655]: #657
+#660 := [trans #658 #689]: #659
+#690 := (iff #731 #687)
+#693 := (iff #731 #697)
+#695 := (= #449 #686)
+#692 := (= #449 #705)
+#704 := (= #734 -1::Int)
+#608 := (= #734 #607)
+#606 := (= #733 1::Int)
+#599 := [rewrite]: #606
+#609 := [monotonicity #599]: #608
+#701 := [trans #609 #611]: #704
+#694 := [monotonicity #701]: #692
+#696 := [trans #694 #685]: #695
+#698 := [monotonicity #696]: #693
+#684 := [trans #698 #689]: #690
+#603 := (iff #455 true)
+#710 := (or true false)
+#593 := (iff #710 true)
+#594 := [rewrite]: #593
+#703 := (iff #455 #710)
+#699 := (iff #454 false)
+#420 := (not true)
+#745 := (iff #420 false)
+#408 := [rewrite]: #745
+#702 := (iff #454 #420)
+#595 := (iff #453 true)
+#708 := (iff #453 #710)
+#716 := (iff #741 false)
+#717 := [rewrite]: #716
+#707 := (iff #452 true)
+#709 := [rewrite]: #707
+#711 := [monotonicity #709 #717]: #708
+#554 := [trans #711 #594]: #595
+#604 := [monotonicity #554]: #702
+#700 := [trans #604 #408]: #699
+#553 := (iff #742 true)
+#720 := (not false)
+#550 := (iff #720 true)
+#552 := [rewrite]: #550
+#714 := (iff #742 #720)
+#713 := (iff #738 false)
+#729 := (or false false)
+#571 := (iff #729 false)
+#572 := [rewrite]: #571
+#718 := (iff #738 #729)
+#712 := [monotonicity #717 #717]: #718
+#719 := [trans #712 #572]: #713
+#721 := [monotonicity #719]: #714
+#706 := [trans #721 #552]: #553
+#588 := [monotonicity #706 #700]: #703
+#605 := [trans #588 #594]: #603
+#663 := [monotonicity #605 #684 #660]: #662
+#656 := [trans #663 #665]: #666
+#573 := (iff #463 false)
+#724 := (iff #463 #729)
+#723 := (iff #462 false)
+#728 := [rewrite]: #723
+#730 := [monotonicity #728 #728]: #724
+#715 := [trans #730 #572]: #573
+#646 := [monotonicity #715 #656]: #645
+#651 := [trans #646 #649]: #650
+#636 := [monotonicity #651]: #635
+#641 := [trans #636 #640]: #635
+#639 := [quant-inst #9 #9]: #653
+#642 := [mp #639 #641]: #647
+#644 := [unit-resolution #642 #796]: #687
+#617 := [monotonicity #644]: #15
+#16 := (not #15)
+#67 := [asserted]: #16
+[unit-resolution #67 #617]: false
+c1d414123c29937a6ed9d7b6e1f766000d0e13e1 428 0
+unsat
+#2 := false
+#22 := 0::Int
+#12 := 3::Int
+decl f6 :: (-> S4 S5 Int)
+decl f8 :: S5
+#9 := f8
+decl f7 :: S4
+#8 := f7
+#10 := (f6 f7 f8)
+#716 := (mod #10 3::Int)
+#131 := -1::Int
+#690 := (* -1::Int #716)
+#442 := (div #10 3::Int)
+#750 := -3::Int
+#689 := (* -3::Int #442)
+#686 := (+ #10 #689 #690)
+#688 := (= #686 0::Int)
+#1 := true
+#198 := [true-axiom]: true
+#644 := (or false #688)
+#645 := [th-lemma arith]: #644
+#646 := [unit-resolution #645 #198]: #688
+#680 := (>= #686 0::Int)
+#593 := (not #680)
+#681 := (>= #716 0::Int)
+#625 := (or false #681)
+#631 := [th-lemma arith]: #625
+#599 := [unit-resolution #631 #198]: #681
+decl f3 :: (-> S2 Int Int)
+decl f4 :: (-> S3 Int S2)
+decl f5 :: S3
+#7 := f5
+#11 := (f4 f5 #10)
+#13 := (f3 #11 3::Int)
+#203 := (* -1::Int #13)
+#204 := (+ #10 #203)
+#202 := (>= #204 0::Int)
+#206 := (not #202)
+#14 := (<= #13 #10)
+#15 := (not #14)
+#207 := (iff #15 #206)
+#201 := (iff #14 #202)
+#205 := [rewrite]: #201
+#208 := [monotonicity #205]: #207
+#66 := [asserted]: #15
+#209 := [mp #66 #208]: #206
+#774 := (* -1::Int #442)
+#775 := (+ #13 #774)
+#718 := (<= #775 0::Int)
+#776 := (= #775 0::Int)
+#777 := (* -1::Int #10)
+#461 := (div #777 -3::Int)
+#464 := (* -1::Int #461)
+#458 := (+ #13 #464)
+#741 := (= #458 0::Int)
+#430 := (>= #10 0::Int)
+#371 := (not #430)
+#457 := (<= #10 0::Int)
+#405 := (not #457)
+#471 := (or #405 #371)
+#735 := (if #471 #776 #741)
+#451 := (= #10 0::Int)
+#608 := (not #451)
+#722 := (<= #13 0::Int)
+#453 := (= #13 0::Int)
+#693 := [hypothesis]: #451
+#700 := (or #608 #453)
+#732 := (if #451 #453 #735)
+#23 := (:var 0 Int)
+#34 := (:var 1 Int)
+#35 := (f4 f5 #34)
+#36 := (f3 #35 #23)
+#799 := (pattern #36)
+#135 := (* -1::Int #23)
+#132 := (* -1::Int #34)
+#138 := (div #132 #135)
+#338 := (* -1::Int #138)
+#339 := (+ #36 #338)
+#340 := (= #339 0::Int)
+#46 := (div #34 #23)
+#335 := (* -1::Int #46)
+#336 := (+ #36 #335)
+#337 := (= #336 0::Int)
+#109 := (<= #23 0::Int)
+#230 := (>= #34 0::Int)
+#298 := (or #230 #109)
+#299 := (not #298)
+#105 := (<= #34 0::Int)
+#294 := (or #105 #109)
+#295 := (not #294)
+#302 := (or #295 #299)
+#341 := (if #302 #337 #340)
+#334 := (= #36 0::Int)
+#38 := (= #23 0::Int)
+#37 := (= #34 0::Int)
+#39 := (or #37 #38)
+#342 := (if #39 #334 #341)
+#800 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #799) #342)
+#345 := (forall (vars (?v0 Int) (?v1 Int)) #342)
+#803 := (iff #345 #800)
+#801 := (iff #342 #342)
+#802 := [refl]: #801
+#804 := [quant-intro #802]: #803
+#305 := (if #302 #46 #138)
+#308 := (if #39 0::Int #305)
+#311 := (= #36 #308)
+#314 := (forall (vars (?v0 Int) (?v1 Int)) #311)
+#346 := (iff #314 #345)
+#343 := (iff #311 #342)
+#344 := [rewrite]: #343
+#347 := [quant-intro #344]: #346
+#110 := (not #109)
+#233 := (not #230)
+#236 := (and #233 #110)
+#106 := (not #105)
+#113 := (and #106 #110)
+#239 := (or #113 #236)
+#242 := (if #239 #46 #138)
+#245 := (if #39 0::Int #242)
+#248 := (= #36 #245)
+#251 := (forall (vars (?v0 Int) (?v1 Int)) #248)
+#315 := (iff #251 #314)
+#312 := (iff #248 #311)
+#309 := (= #245 #308)
+#306 := (= #242 #305)
+#303 := (iff #239 #302)
+#300 := (iff #236 #299)
+#301 := [rewrite]: #300
+#296 := (iff #113 #295)
+#297 := [rewrite]: #296
+#304 := [monotonicity #297 #301]: #303
+#307 := [monotonicity #304]: #306
+#310 := [monotonicity #307]: #309
+#313 := [monotonicity #310]: #312
+#316 := [quant-intro #313]: #315
+#286 := (~ #251 #251)
+#284 := (~ #248 #248)
+#285 := [refl]: #284
+#287 := [nnf-pos #285]: #286
+#116 := (<= 0::Int #34)
+#117 := (not #116)
+#125 := (and #117 #110)
+#128 := (or #113 #125)
+#141 := (if #128 #46 #138)
+#144 := (if #39 0::Int #141)
+#147 := (= #36 #144)
+#150 := (forall (vars (?v0 Int) (?v1 Int)) #147)
+#252 := (iff #150 #251)
+#249 := (iff #147 #248)
+#246 := (= #144 #245)
+#243 := (= #141 #242)
+#240 := (iff #128 #239)
+#237 := (iff #125 #236)
+#234 := (iff #117 #233)
+#231 := (iff #116 #230)
+#232 := [rewrite]: #231
+#235 := [monotonicity #232]: #234
+#238 := [monotonicity #235]: #237
+#241 := [monotonicity #238]: #240
+#244 := [monotonicity #241]: #243
 #247 := [monotonicity #244]: #246
-#222 := (iff #188 #40)
-#220 := (iff #185 #39)
-#221 := [rewrite]: #220
-#218 := (iff #182 #38)
-#219 := [rewrite]: #218
-#223 := [monotonicity #219 #221]: #222
-#250 := [monotonicity #223 #247]: #249
-#253 := [monotonicity #250]: #252
-#256 := [quant-intro #253]: #255
-#216 := (iff #54 #215)
-#213 := (iff #53 #212)
-#210 := (= #52 #209)
-#207 := (= #51 #206)
-#204 := (= #50 #203)
-#201 := (= #49 #200)
-#202 := [rewrite]: #201
-#198 := (= #48 #197)
-#199 := [rewrite]: #198
-#205 := [monotonicity #199 #202]: #204
-#195 := (iff #46 #194)
-#192 := (iff #45 #191)
-#193 := [rewrite]: #192
-#196 := [monotonicity #193]: #195
-#208 := [monotonicity #196 #205]: #207
-#189 := (iff #40 #188)
-#186 := (iff #39 #185)
-#187 := [rewrite]: #186
-#183 := (iff #38 #182)
-#184 := [rewrite]: #183
-#190 := [monotonicity #184 #187]: #189
-#211 := [monotonicity #190 #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [quant-intro #214]: #216
-#258 := [trans #217 #256]: #257
-#181 := [asserted]: #54
-#259 := [mp #181 #258]: #254
-#329 := [mp~ #259 #315]: #254
-#354 := [mp #329 #353]: #351
-#385 := [mp #354 #384]: #382
-#899 := [mp #385 #898]: #894
-#676 := (not #894)
-#818 := (or #676 #833)
-#545 := (* -1::Int 3::Int)
-#477 := (div #546 #545)
-#550 := (* -1::Int #477)
-#547 := (+ #14 #550)
-#551 := (= #547 0::Int)
-#861 := (<= 3::Int 0::Int)
-#535 := (or #861 #654)
-#536 := (not #535)
-#869 := (or #868 #861)
-#870 := (not #869)
-#871 := (or #870 #536)
-#866 := (ite #871 #524 #551)
-#862 := (= 3::Int 0::Int)
-#527 := (or #522 #862)
-#863 := (ite #527 #872 #866)
-#819 := (or #676 #863)
-#821 := (iff #819 #818)
-#816 := (iff #818 #818)
-#822 := [rewrite]: #816
-#674 := (iff #863 #833)
-#832 := (iff #866 #831)
-#825 := (iff #551 #830)
-#828 := (= #547 #839)
-#838 := (= #550 #834)
-#837 := (= #477 #836)
-#557 := (= #545 -3::Int)
-#558 := [rewrite]: #557
-#552 := [monotonicity #558]: #837
-#835 := [monotonicity #552]: #838
-#829 := [monotonicity #835]: #828
-#826 := [monotonicity #829]: #825
-#845 := (iff #871 #840)
-#843 := (or #498 #572)
-#844 := (iff #843 #840)
-#841 := [rewrite]: #844
-#565 := (iff #871 #843)
-#465 := (iff #536 #572)
-#570 := (iff #535 #654)
-#857 := (or false #654)
-#847 := (iff #857 #654)
-#569 := [rewrite]: #847
-#860 := (iff #535 #857)
-#851 := (iff #861 false)
-#852 := [rewrite]: #851
-#846 := [monotonicity #852]: #860
-#571 := [trans #846 #569]: #570
-#842 := [monotonicity #571]: #465
-#499 := (iff #870 #498)
-#856 := (iff #869 #868)
-#853 := (or #868 false)
-#855 := (iff #853 #868)
-#493 := [rewrite]: #855
-#854 := (iff #869 #853)
-#849 := [monotonicity #852]: #854
-#858 := [trans #849 #493]: #856
-#859 := [monotonicity #858]: #499
-#566 := [monotonicity #859 #842]: #565
-#555 := [trans #566 #841]: #845
-#827 := [monotonicity #555 #826]: #832
-#514 := (iff #527 #522)
-#507 := (or #522 false)
-#512 := (iff #507 #522)
-#513 := [rewrite]: #512
-#848 := (iff #527 #507)
-#523 := (iff #862 false)
-#864 := [rewrite]: #523
-#511 := [monotonicity #864]: #848
-#850 := [trans #511 #513]: #514
-#675 := [monotonicity #850 #827]: #674
-#815 := [monotonicity #675]: #821
-#823 := [trans #815 #822]: #821
-#820 := [quant-inst #11 #13]: #819
-#817 := [mp #820 #823]: #818
-#735 := [unit-resolution #817 #899]: #833
-#712 := (not #833)
-#714 := (or #712 #713 #872)
-#807 := [def-axiom]: #714
-#721 := [unit-resolution #807 #735]: #720
-#722 := [unit-resolution #721 #747]: #872
-#795 := (not #872)
-#615 := (or #795 #824)
-#765 := [th-lemma arith triangle-eq]: #615
-#681 := [unit-resolution #765 #722]: #824
-#682 := (or #713 #654)
-#683 := [th-lemma arith triangle-eq]: #682
-#684 := [unit-resolution #683 #747]: #654
-#685 := [th-lemma arith farkas -1 1 1 #684 #97 #681]: false
-#686 := [lemma #685]: #713
-#736 := (or #522 #831)
-#804 := (or #712 #522 #831)
-#808 := [def-axiom]: #804
-#732 := [unit-resolution #808 #735]: #736
-#658 := [unit-resolution #732 #686]: #831
+#250 := [monotonicity #247]: #249
+#253 := [quant-intro #250]: #252
+#48 := (- #23)
+#47 := (- #34)
+#49 := (div #47 #48)
+#41 := (< 0::Int #23)
+#43 := (< #34 0::Int)
+#44 := (and #43 #41)
+#40 := (< 0::Int #34)
+#42 := (and #40 #41)
+#45 := (or #42 #44)
+#50 := (if #45 #46 #49)
+#51 := (if #39 0::Int #50)
+#52 := (= #36 #51)
+#53 := (forall (vars (?v0 Int) (?v1 Int)) #52)
+#151 := (iff #53 #150)
+#148 := (iff #52 #147)
+#145 := (= #51 #144)
+#142 := (= #50 #141)
+#139 := (= #49 #138)
+#136 := (= #48 #135)
+#137 := [rewrite]: #136
+#133 := (= #47 #132)
+#134 := [rewrite]: #133
+#140 := [monotonicity #134 #137]: #139
+#129 := (iff #45 #128)
+#126 := (iff #44 #125)
+#111 := (iff #41 #110)
+#112 := [rewrite]: #111
+#118 := (iff #43 #117)
+#122 := (iff #117 #117)
+#120 := (iff #116 #116)
+#121 := [rewrite]: #120
+#123 := [monotonicity #121]: #122
+#119 := [rewrite]: #118
+#124 := [trans #119 #123]: #118
+#127 := [monotonicity #124 #112]: #126
+#114 := (iff #42 #113)
+#107 := (iff #40 #106)
+#108 := [rewrite]: #107
+#115 := [monotonicity #108 #112]: #114
+#130 := [monotonicity #115 #127]: #129
+#143 := [monotonicity #130 #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [monotonicity #146]: #148
+#152 := [quant-intro #149]: #151
+#70 := [asserted]: #53
+#153 := [mp #70 #152]: #150
+#254 := [mp #153 #253]: #251
+#288 := [mp~ #254 #287]: #251
+#317 := [mp #288 #316]: #314
+#348 := [mp #317 #347]: #345
+#805 := [mp #348 #804]: #800
+#733 := (not #800)
+#739 := (or #733 #732)
+#772 := (* -1::Int 3::Int)
+#778 := (div #777 #772)
+#768 := (* -1::Int #778)
+#428 := (+ #13 #768)
+#433 := (= #428 0::Int)
+#436 := (<= 3::Int 0::Int)
+#560 := (or #430 #436)
+#767 := (not #560)
+#771 := (or #457 #436)
+#773 := (not #771)
+#441 := (or #773 #767)
+#769 := (if #441 #776 #433)
+#452 := (= 3::Int 0::Int)
+#456 := (or #451 #452)
+#429 := (if #456 #453 #769)
+#580 := (or #733 #429)
+#582 := (iff #580 #739)
+#725 := (iff #739 #739)
+#726 := [rewrite]: #725
+#737 := (iff #429 #732)
+#736 := (iff #769 #735)
+#745 := (iff #433 #741)
+#740 := (= #428 #458)
+#742 := (= #768 #464)
+#462 := (= #778 #461)
+#747 := (= #772 -3::Int)
+#751 := [rewrite]: #747
+#463 := [monotonicity #751]: #462
+#743 := [monotonicity #463]: #742
+#744 := [monotonicity #743]: #740
+#734 := [monotonicity #744]: #745
+#472 := (iff #441 #471)
+#748 := (iff #767 #371)
+#477 := (iff #560 #430)
+#766 := (or #430 false)
+#475 := (iff #766 #430)
+#476 := [rewrite]: #475
+#752 := (iff #560 #766)
+#758 := (iff #436 false)
+#759 := [rewrite]: #758
+#753 := [monotonicity #759]: #752
+#478 := [trans #753 #476]: #477
+#749 := [monotonicity #478]: #748
+#765 := (iff #773 #405)
+#764 := (iff #771 #457)
+#760 := (or #457 false)
+#399 := (iff #760 #457)
+#762 := [rewrite]: #399
+#755 := (iff #771 #760)
+#761 := [monotonicity #759]: #755
+#404 := [trans #761 #762]: #764
+#763 := [monotonicity #404]: #765
+#746 := [monotonicity #763 #749]: #472
+#731 := [monotonicity #746 #734]: #736
+#756 := (iff #456 #451)
+#754 := (or #451 false)
+#419 := (iff #754 #451)
+#420 := [rewrite]: #419
+#417 := (iff #456 #754)
+#770 := (iff #452 false)
+#413 := [rewrite]: #770
+#418 := [monotonicity #413]: #417
+#757 := [trans #418 #420]: #756
+#738 := [monotonicity #757 #731]: #737
+#724 := [monotonicity #738]: #582
+#727 := [trans #724 #726]: #582
+#581 := [quant-inst #10 #12]: #580
+#721 := [mp #581 #727]: #739
+#653 := [unit-resolution #721 #805]: #732
+#615 := (not #732)
+#616 := (or #615 #608 #453)
+#617 := [def-axiom]: #616
+#684 := [unit-resolution #617 #653]: #700
+#685 := [unit-resolution #684 #693]: #453
+#620 := (not #453)
+#691 := (or #620 #722)
+#677 := [th-lemma arith triangle-eq]: #691
+#682 := [unit-resolution #677 #685]: #722
+#679 := (or #608 #430)
+#660 := [th-lemma arith triangle-eq]: #679
+#661 := [unit-resolution #660 #693]: #430
+#656 := [th-lemma arith farkas -1 1 1 #661 #209 #682]: false
+#662 := [lemma #656]: #608
+#626 := (or #451 #735)
+#618 := (or #615 #451 #735)
+#619 := [def-axiom]: #618
+#627 := [unit-resolution #619 #653]: #626
+#584 := [unit-resolution #627 #662]: #735
 decl f9 :: (-> S6 Int S5)
 decl f10 :: S6
-#17 := f10
-#459 := (f9 f10 #11)
-#798 := (f6 f7 #459)
-#799 := (= #798 0::Int)
-#703 := (not #799)
-#704 := (iff #713 #703)
-#694 := (iff #522 #799)
-#690 := (iff #799 #522)
-#700 := (= #798 #11)
-#725 := (= #459 f8)
-#544 := (= f8 #459)
-#18 := (:var 0 S5)
-#19 := (f6 f7 #18)
-#873 := (pattern #19)
-#20 := (f9 f10 #19)
-#87 := (= #18 #20)
-#874 := (forall (vars (?v0 S5)) (:pat #873) #87)
-#100 := (forall (vars (?v0 S5)) #87)
-#877 := (iff #100 #874)
-#875 := (iff #87 #87)
-#876 := [refl]: #875
-#878 := [quant-intro #876]: #877
-#322 := (~ #100 #100)
-#320 := (~ #87 #87)
-#321 := [refl]: #320
-#323 := [nnf-pos #321]: #322
-#21 := (= #20 #18)
-#22 := (forall (vars (?v0 S5)) #21)
-#101 := (iff #22 #100)
-#98 := (iff #21 #87)
-#99 := [rewrite]: #98
-#102 := [quant-intro #99]: #101
-#86 := [asserted]: #22
-#105 := [mp #86 #102]: #100
-#308 := [mp~ #105 #323]: #100
-#879 := [mp #308 #878]: #874
-#537 := (not #874)
-#548 := (or #537 #544)
-#549 := [quant-inst #10]: #548
-#719 := [unit-resolution #549 #879]: #544
-#693 := [symm #719]: #725
-#659 := [monotonicity #693]: #700
-#692 := [monotonicity #659]: #690
-#701 := [symm #692]: #694
-#705 := [monotonicity #701]: #704
-#660 := [mp #686 #705]: #703
-#796 := (or #654 #799)
-#26 := (f9 f10 #24)
-#880 := (pattern #26)
-#121 := (>= #24 0::Int)
-#27 := (f6 f7 #26)
-#32 := (= #27 0::Int)
-#170 := (or #32 #121)
-#887 := (forall (vars (?v0 Int)) (:pat #880) #170)
-#175 := (forall (vars (?v0 Int)) #170)
-#890 := (iff #175 #887)
-#888 := (iff #170 #170)
-#889 := [refl]: #888
-#891 := [quant-intro #889]: #890
-#312 := (~ #175 #175)
-#324 := (~ #170 #170)
-#325 := [refl]: #324
-#313 := [nnf-pos #325]: #312
-#31 := (< #24 0::Int)
-#33 := (implies #31 #32)
-#34 := (forall (vars (?v0 Int)) #33)
-#178 := (iff #34 #175)
-#141 := (= 0::Int #27)
-#147 := (not #31)
-#148 := (or #147 #141)
-#153 := (forall (vars (?v0 Int)) #148)
-#176 := (iff #153 #175)
-#173 := (iff #148 #170)
-#167 := (or #121 #32)
-#171 := (iff #167 #170)
-#172 := [rewrite]: #171
-#168 := (iff #148 #167)
-#165 := (iff #141 #32)
-#166 := [rewrite]: #165
-#163 := (iff #147 #121)
-#123 := (not #121)
-#158 := (not #123)
-#161 := (iff #158 #121)
-#162 := [rewrite]: #161
-#159 := (iff #147 #158)
-#156 := (iff #31 #123)
-#157 := [rewrite]: #156
-#160 := [monotonicity #157]: #159
-#164 := [trans #160 #162]: #163
-#169 := [monotonicity #164 #166]: #168
-#174 := [trans #169 #172]: #173
-#177 := [quant-intro #174]: #176
-#154 := (iff #34 #153)
-#151 := (iff #33 #148)
-#144 := (implies #31 #141)
-#149 := (iff #144 #148)
-#150 := [rewrite]: #149
-#145 := (iff #33 #144)
-#142 := (iff #32 #141)
-#143 := [rewrite]: #142
-#146 := [monotonicity #143]: #145
-#152 := [trans #146 #150]: #151
-#155 := [quant-intro #152]: #154
-#179 := [trans #155 #177]: #178
-#140 := [asserted]: #34
-#180 := [mp #140 #179]: #175
-#326 := [mp~ #180 #313]: #175
-#892 := [mp #326 #891]: #887
-#791 := (not #887)
-#792 := (or #791 #654 #799)
-#800 := (or #799 #654)
-#793 := (or #791 #800)
-#783 := (iff #793 #792)
-#794 := (or #791 #796)
-#781 := (iff #794 #792)
-#782 := [rewrite]: #781
-#778 := (iff #793 #794)
-#801 := (iff #800 #796)
-#790 := [rewrite]: #801
-#779 := [monotonicity #790]: #778
-#784 := [trans #779 #782]: #783
-#787 := [quant-inst #11]: #793
-#780 := [mp #787 #784]: #792
-#695 := [unit-resolution #780 #892]: #796
-#661 := [unit-resolution #695 #660]: #654
-#662 := (or #522 #498 #572)
-#664 := [th-lemma arith triangle-eq]: #662
-#665 := [unit-resolution #664 #661 #686]: #498
-#809 := (or #840 #868)
-#810 := [def-axiom]: #809
-#666 := [unit-resolution #810 #665]: #840
-#812 := (not #840)
-#707 := (not #831)
-#802 := (or #707 #812 #524)
-#803 := [def-axiom]: #802
-#667 := [unit-resolution #803 #666 #658]: #524
-#706 := (not #524)
-#699 := (or #706 #696)
-#723 := [th-lemma arith triangle-eq]: #699
-#668 := [unit-resolution #723 #667]: #696
-#670 := (not #696)
-#652 := (not #767)
-#640 := (or #669 #572 #652 #670 #90)
-#641 := [th-lemma arith assign-bounds 2 1 3 3]: #640
-#642 := [unit-resolution #641 #661 #668 #97 #677]: #669
-#733 := (not #757)
-#729 := (or #733 #766)
-#730 := [th-lemma arith triangle-eq]: #729
-[unit-resolution #730 #642 #728]: false
-unsat
-007f39662e30c666548c8884f07065be331edd50 644 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-decl f5 :: (-> S4 Int Int)
-#14 := 3::Int
-decl f6 :: (-> S5 Int S4)
-decl f8 :: (-> S6 S3 Int)
-decl f10 :: S3
-#11 := f10
-decl f9 :: S6
-#10 := f9
-#12 := (f8 f9 f10)
-decl f7 :: S5
-#9 := f7
-#13 := (f6 f7 #12)
-#15 := (f5 #13 3::Int)
-decl f4 :: S2
-#8 := f4
-#16 := (f3 f4 #15)
-#90 := (= f10 #16)
-#18 := 0::Int
-#19 := (f3 f4 0::Int)
-#938 := (= #19 #16)
-#936 := (= #16 #19)
-#826 := (= #15 0::Int)
-#829 := (= #12 0::Int)
-#874 := (f8 f9 #19)
-#873 := (= #874 0::Int)
-#28 := (:var 0 Int)
-#30 := (f3 f4 #28)
-#896 := (pattern #30)
-#137 := (>= #28 0::Int)
-#138 := (not #137)
-#31 := (f8 f9 #30)
-#119 := (= #28 #31)
-#144 := (or #119 #138)
-#897 := (forall (vars (?v0 Int)) (:pat #896) #144)
-#149 := (forall (vars (?v0 Int)) #144)
-#900 := (iff #149 #897)
-#898 := (iff #144 #144)
-#899 := [refl]: #898
-#901 := [quant-intro #899]: #900
-#326 := (~ #149 #149)
-#325 := (~ #144 #144)
-#322 := [refl]: #325
-#327 := [nnf-pos #322]: #326
-#32 := (= #31 #28)
-#29 := (<= 0::Int #28)
-#33 := (implies #29 #32)
-#34 := (forall (vars (?v0 Int)) #33)
-#152 := (iff #34 #149)
-#126 := (not #29)
-#127 := (or #126 #119)
-#132 := (forall (vars (?v0 Int)) #127)
-#150 := (iff #132 #149)
-#147 := (iff #127 #144)
-#141 := (or #138 #119)
-#145 := (iff #141 #144)
-#146 := [rewrite]: #145
-#142 := (iff #127 #141)
-#139 := (iff #126 #138)
-#135 := (iff #29 #137)
-#136 := [rewrite]: #135
-#140 := [monotonicity #136]: #139
-#143 := [monotonicity #140]: #142
-#148 := [trans #143 #146]: #147
-#151 := [quant-intro #148]: #150
-#133 := (iff #34 #132)
-#130 := (iff #33 #127)
-#123 := (implies #29 #119)
-#128 := (iff #123 #127)
-#129 := [rewrite]: #128
-#124 := (iff #33 #123)
-#121 := (iff #32 #119)
-#122 := [rewrite]: #121
-#125 := [monotonicity #122]: #124
-#131 := [trans #125 #129]: #130
-#134 := [quant-intro #131]: #133
-#153 := [trans #134 #151]: #152
-#118 := [asserted]: #34
-#154 := [mp #118 #153]: #149
-#323 := [mp~ #154 #327]: #149
-#902 := [mp #323 #901]: #897
-#887 := (not #897)
-#572 := (or #887 #873)
-#509 := (>= 0::Int 0::Int)
-#872 := (not #509)
-#514 := (= 0::Int #874)
-#515 := (or #514 #872)
-#573 := (or #887 #515)
-#852 := (iff #573 #572)
-#568 := (iff #572 #572)
-#850 := [rewrite]: #568
-#861 := (iff #515 #873)
-#581 := (or #873 false)
-#860 := (iff #581 #873)
-#857 := [rewrite]: #860
-#582 := (iff #515 #581)
-#858 := (iff #872 false)
-#1 := true
-#585 := (not true)
-#588 := (iff #585 false)
-#481 := [rewrite]: #588
-#586 := (iff #872 #585)
-#862 := (iff #509 true)
-#863 := [rewrite]: #862
-#587 := [monotonicity #863]: #586
-#859 := [trans #587 #481]: #858
-#875 := (iff #514 #873)
-#876 := [rewrite]: #875
-#856 := [monotonicity #876 #859]: #582
-#571 := [trans #856 #857]: #861
-#853 := [monotonicity #571]: #852
-#854 := [trans #853 #850]: #852
-#574 := [quant-inst #18]: #573
-#851 := [mp #574 #854]: #572
-#929 := [unit-resolution #851 #902]: #873
-#932 := (= #12 #874)
-#20 := (= f10 #19)
-#567 := (f3 f4 #12)
-#924 := (= #567 #19)
-#480 := (= #19 #567)
-#478 := (= 0::Int #12)
-#551 := (f8 f9 #16)
-#633 := (= #551 #12)
-#504 := (= #12 #551)
-#104 := (not #20)
-#577 := [hypothesis]: #104
-#562 := (or #90 #20)
-#105 := (iff #90 #104)
-#17 := (= #16 f10)
-#21 := (iff #17 #20)
-#22 := (not #21)
-#108 := (iff #22 #105)
-#96 := (iff #20 #90)
-#101 := (not #96)
-#106 := (iff #101 #105)
-#107 := [rewrite]: #106
-#102 := (iff #22 #101)
-#99 := (iff #21 #96)
-#93 := (iff #90 #20)
+#16 := f10
+#365 := (f9 f10 #10)
+#703 := (f6 f7 #365)
+#695 := (= #703 0::Int)
+#623 := (not #695)
+#569 := (iff #608 #623)
+#638 := (iff #451 #695)
+#641 := (iff #695 #451)
+#637 := (= #703 #10)
+#450 := (= #365 f8)
+#17 := (:var 0 S5)
+#18 := (f6 f7 #17)
+#779 := (pattern #18)
+#19 := (f9 f10 #18)
+#20 := (= #19 #17)
+#780 := (forall (vars (?v0 S5)) (:pat #779) #20)
+#21 := (forall (vars (?v0 S5)) #20)
+#783 := (iff #21 #780)
+#781 := (iff #20 #20)
+#782 := [refl]: #781
+#784 := [quant-intro #782]: #783
+#279 := (~ #21 #21)
+#273 := (~ #20 #20)
+#274 := [refl]: #273
+#280 := [nnf-pos #274]: #279
+#67 := [asserted]: #21
+#271 := [mp~ #67 #280]: #21
+#785 := [mp #271 #784]: #780
+#443 := (not #780)
+#454 := (or #443 #450)
+#455 := [quant-inst #9]: #454
+#636 := [unit-resolution #455 #785]: #450
+#640 := [monotonicity #636]: #637
+#642 := [monotonicity #640]: #641
+#643 := [symm #642]: #638
+#624 := [monotonicity #643]: #569
+#585 := [mp #662 #624]: #623
+#692 := (or #430 #695)
+#25 := (f9 f10 #23)
+#786 := (pattern #25)
+#26 := (f6 f7 #25)
+#31 := (= #26 0::Int)
+#210 := (>= #23 0::Int)
+#223 := (or #210 #31)
+#793 := (forall (vars (?v0 Int)) (:pat #786) #223)
+#226 := (forall (vars (?v0 Int)) #223)
+#796 := (iff #226 #793)
+#794 := (iff #223 #223)
+#795 := [refl]: #794
+#797 := [quant-intro #795]: #796
+#277 := (~ #226 #226)
+#199 := (~ #223 #223)
+#200 := [refl]: #199
+#278 := [nnf-pos #200]: #277
+#24 := (<= 0::Int #23)
+#96 := (or #24 #31)
+#101 := (forall (vars (?v0 Int)) #96)
+#227 := (iff #101 #226)
+#224 := (iff #96 #223)
+#211 := (iff #24 #210)
+#212 := [rewrite]: #211
+#225 := [monotonicity #212]: #224
+#228 := [quant-intro #225]: #227
+#30 := (< #23 0::Int)
+#32 := (implies #30 #31)
+#33 := (forall (vars (?v0 Int)) #32)
+#102 := (iff #33 #101)
+#99 := (iff #32 #96)
+#79 := (not #24)
+#93 := (implies #79 #31)
 #97 := (iff #93 #96)
 #98 := [rewrite]: #97
-#94 := (iff #21 #93)
-#91 := (iff #17 #90)
-#92 := [rewrite]: #91
+#94 := (iff #32 #93)
+#88 := (iff #30 #79)
+#90 := (iff #79 #79)
+#75 := (iff #24 #24)
+#76 := [rewrite]: #75
+#91 := [monotonicity #76]: #90
+#89 := [rewrite]: #88
+#92 := [trans #89 #91]: #88
 #95 := [monotonicity #92]: #94
 #100 := [trans #95 #98]: #99
-#103 := [monotonicity #100]: #102
-#109 := [trans #103 #107]: #108
-#89 := [asserted]: #22
-#112 := [mp #89 #109]: #105
-#475 := (not #105)
-#560 := (or #90 #20 #475)
-#561 := [def-axiom]: #560
-#553 := [unit-resolution #561 #112]: #562
-#569 := [unit-resolution #553 #577]: #90
-#505 := [monotonicity #569]: #504
-#484 := [symm #505]: #633
-#489 := (= 0::Int #551)
-#552 := (= #15 #551)
-#881 := (>= #15 0::Int)
-#564 := (not #90)
-#635 := (or #881 #564)
-#885 := (= #551 0::Int)
-#637 := (iff #885 #829)
-#630 := [hypothesis]: #90
-#632 := [symm #630]: #17
-#636 := [monotonicity #632]: #633
-#641 := [monotonicity #636]: #637
-#883 := (not #881)
-#654 := [hypothesis]: #883
-#539 := (or #881 #885)
-#36 := (= #31 0::Int)
-#185 := (or #36 #137)
-#903 := (forall (vars (?v0 Int)) (:pat #896) #185)
-#190 := (forall (vars (?v0 Int)) #185)
-#906 := (iff #190 #903)
-#904 := (iff #185 #185)
-#905 := [refl]: #904
-#907 := [quant-intro #905]: #906
-#328 := (~ #190 #190)
-#340 := (~ #185 #185)
-#341 := [refl]: #340
-#329 := [nnf-pos #341]: #328
-#35 := (< #28 0::Int)
-#37 := (implies #35 #36)
-#38 := (forall (vars (?v0 Int)) #37)
-#193 := (iff #38 #190)
-#156 := (= 0::Int #31)
-#162 := (not #35)
-#163 := (or #162 #156)
-#168 := (forall (vars (?v0 Int)) #163)
-#191 := (iff #168 #190)
-#188 := (iff #163 #185)
-#182 := (or #137 #36)
-#186 := (iff #182 #185)
-#187 := [rewrite]: #186
-#183 := (iff #163 #182)
-#180 := (iff #156 #36)
-#181 := [rewrite]: #180
-#178 := (iff #162 #137)
-#173 := (not #138)
-#176 := (iff #173 #137)
-#177 := [rewrite]: #176
-#174 := (iff #162 #173)
-#171 := (iff #35 #138)
-#172 := [rewrite]: #171
-#175 := [monotonicity #172]: #174
-#179 := [trans #175 #177]: #178
-#184 := [monotonicity #179 #181]: #183
-#189 := [trans #184 #187]: #188
-#192 := [quant-intro #189]: #191
-#169 := (iff #38 #168)
-#166 := (iff #37 #163)
-#159 := (implies #35 #156)
-#164 := (iff #159 #163)
-#165 := [rewrite]: #164
-#160 := (iff #37 #159)
-#157 := (iff #36 #156)
-#158 := [rewrite]: #157
-#161 := [monotonicity #158]: #160
-#167 := [trans #161 #165]: #166
-#170 := [quant-intro #167]: #169
-#194 := [trans #170 #192]: #193
-#155 := [asserted]: #38
-#195 := [mp #155 #194]: #190
-#342 := [mp~ #195 #329]: #190
-#908 := [mp #342 #907]: #903
-#864 := (not #903)
-#527 := (or #864 #881 #885)
-#886 := (or #885 #881)
-#528 := (or #864 #886)
-#870 := (iff #528 #527)
-#530 := (or #864 #539)
-#868 := (iff #530 #527)
-#869 := [rewrite]: #868
-#866 := (iff #528 #530)
-#880 := (iff #886 #539)
-#523 := [rewrite]: #880
-#867 := [monotonicity #523]: #866
-#865 := [trans #867 #869]: #870
-#529 := [quant-inst #15]: #528
-#871 := [mp #529 #865]: #527
-#650 := [unit-resolution #871 #908]: #539
-#640 := [unit-resolution #650 #654]: #885
-#634 := [mp #640 #641]: #829
-#747 := (not #829)
-#753 := (not #826)
-#652 := (or #753 #881)
-#655 := [th-lemma arith triangle-eq]: #652
-#643 := [unit-resolution #655 #654]: #753
-#648 := (or #747 #826)
-#795 := -3::Int
-#212 := -1::Int
-#849 := (* -1::Int #12)
-#799 := (div #849 -3::Int)
-#801 := (* -1::Int #799)
-#790 := (+ #15 #801)
-#789 := (= #790 0::Int)
-#835 := (div #12 3::Int)
-#836 := (* -1::Int #835)
-#837 := (+ #15 #836)
-#831 := (= #837 0::Int)
-#840 := (<= #12 0::Int)
-#730 := (not #840)
-#832 := (>= #12 0::Int)
-#815 := (not #832)
-#808 := (or #815 #730)
-#774 := (ite #808 #831 #789)
-#778 := (ite #829 #826 #774)
-#39 := (:var 1 Int)
-#40 := (f6 f7 #39)
-#41 := (f5 #40 #28)
-#909 := (pattern #41)
-#216 := (* -1::Int #28)
-#213 := (* -1::Int #39)
-#219 := (div #213 #216)
-#391 := (* -1::Int #219)
-#392 := (+ #41 #391)
-#393 := (= #392 0::Int)
-#51 := (div #39 #28)
-#388 := (* -1::Int #51)
-#389 := (+ #41 #388)
-#390 := (= #389 0::Int)
-#251 := (>= #39 0::Int)
-#244 := (<= #28 0::Int)
-#351 := (or #244 #251)
-#352 := (not #351)
-#240 := (<= #39 0::Int)
-#349 := (or #240 #244)
-#350 := (not #349)
-#355 := (or #350 #352)
-#394 := (ite #355 #390 #393)
-#387 := (= #41 0::Int)
-#43 := (= #28 0::Int)
-#42 := (= #39 0::Int)
-#44 := (or #42 #43)
-#395 := (ite #44 #387 #394)
-#910 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #909) #395)
-#398 := (forall (vars (?v0 Int) (?v1 Int)) #395)
-#913 := (iff #398 #910)
-#911 := (iff #395 #395)
-#912 := [refl]: #911
-#914 := [quant-intro #912]: #913
-#358 := (ite #355 #51 #219)
-#361 := (ite #44 0::Int #358)
-#364 := (= #41 #361)
-#367 := (forall (vars (?v0 Int) (?v1 Int)) #364)
-#399 := (iff #367 #398)
-#396 := (iff #364 #395)
-#397 := [rewrite]: #396
-#400 := [quant-intro #397]: #399
-#252 := (not #251)
-#245 := (not #244)
-#255 := (and #245 #252)
-#241 := (not #240)
-#248 := (and #241 #245)
-#258 := (or #248 #255)
-#261 := (ite #258 #51 #219)
-#264 := (ite #44 0::Int #261)
-#267 := (= #41 #264)
-#270 := (forall (vars (?v0 Int) (?v1 Int)) #267)
-#368 := (iff #270 #367)
-#365 := (iff #267 #364)
-#362 := (= #264 #361)
-#359 := (= #261 #358)
-#356 := (iff #258 #355)
-#353 := (iff #255 #352)
-#354 := [rewrite]: #353
-#334 := (iff #248 #350)
-#335 := [rewrite]: #334
-#357 := [monotonicity #335 #354]: #356
-#360 := [monotonicity #357]: #359
-#363 := [monotonicity #360]: #362
-#366 := [monotonicity #363]: #365
-#369 := [quant-intro #366]: #368
-#330 := (~ #270 #270)
-#343 := (~ #267 #267)
-#344 := [refl]: #343
-#331 := [nnf-pos #344]: #330
-#53 := (- #28)
-#52 := (- #39)
-#54 := (div #52 #53)
-#46 := (< 0::Int #28)
-#48 := (< #39 0::Int)
-#49 := (and #48 #46)
-#45 := (< 0::Int #39)
-#47 := (and #45 #46)
-#50 := (or #47 #49)
-#55 := (ite #50 #51 #54)
-#56 := (ite #44 0::Int #55)
-#57 := (= #41 #56)
-#58 := (forall (vars (?v0 Int) (?v1 Int)) #57)
-#273 := (iff #58 #270)
-#206 := (and #46 #48)
-#209 := (or #47 #206)
-#222 := (ite #209 #51 #219)
-#200 := (= 0::Int #28)
-#197 := (= 0::Int #39)
-#203 := (or #197 #200)
-#225 := (ite #203 0::Int #222)
-#228 := (= #41 #225)
-#231 := (forall (vars (?v0 Int) (?v1 Int)) #228)
-#271 := (iff #231 #270)
-#268 := (iff #228 #267)
-#265 := (= #225 #264)
-#262 := (= #222 #261)
-#259 := (iff #209 #258)
-#256 := (iff #206 #255)
-#253 := (iff #48 #252)
-#254 := [rewrite]: #253
-#246 := (iff #46 #245)
-#247 := [rewrite]: #246
-#257 := [monotonicity #247 #254]: #256
-#249 := (iff #47 #248)
-#242 := (iff #45 #241)
-#243 := [rewrite]: #242
-#250 := [monotonicity #243 #247]: #249
-#260 := [monotonicity #250 #257]: #259
-#263 := [monotonicity #260]: #262
-#238 := (iff #203 #44)
-#236 := (iff #200 #43)
-#237 := [rewrite]: #236
-#234 := (iff #197 #42)
-#235 := [rewrite]: #234
-#239 := [monotonicity #235 #237]: #238
-#266 := [monotonicity #239 #263]: #265
-#269 := [monotonicity #266]: #268
-#272 := [quant-intro #269]: #271
-#232 := (iff #58 #231)
-#229 := (iff #57 #228)
-#226 := (= #56 #225)
-#223 := (= #55 #222)
-#220 := (= #54 #219)
-#217 := (= #53 #216)
-#218 := [rewrite]: #217
-#214 := (= #52 #213)
-#215 := [rewrite]: #214
-#221 := [monotonicity #215 #218]: #220
-#210 := (iff #50 #209)
-#207 := (iff #49 #206)
-#208 := [rewrite]: #207
-#211 := [monotonicity #208]: #210
-#224 := [monotonicity #211 #221]: #223
-#204 := (iff #44 #203)
-#201 := (iff #43 #200)
-#202 := [rewrite]: #201
-#198 := (iff #42 #197)
-#199 := [rewrite]: #198
-#205 := [monotonicity #199 #202]: #204
-#227 := [monotonicity #205 #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [quant-intro #230]: #232
-#274 := [trans #233 #272]: #273
-#196 := [asserted]: #58
-#275 := [mp #196 #274]: #270
-#345 := [mp~ #275 #331]: #270
-#370 := [mp #345 #369]: #367
-#401 := [mp #370 #400]: #398
-#915 := [mp #401 #914]: #910
-#781 := (not #910)
-#782 := (or #781 #778)
-#843 := (* -1::Int 3::Int)
-#690 := (div #849 #843)
-#691 := (* -1::Int #690)
-#692 := (+ #15 #691)
-#834 := (= #692 0::Int)
-#838 := (<= 3::Int 0::Int)
-#839 := (or #838 #832)
-#833 := (not #839)
-#669 := (or #840 #838)
-#671 := (not #669)
-#672 := (or #671 #833)
-#825 := (ite #672 #831 #834)
-#828 := (= 3::Int 0::Int)
-#827 := (or #829 #828)
-#830 := (ite #827 #826 #825)
-#783 := (or #781 #830)
-#785 := (iff #783 #782)
-#786 := (iff #782 #782)
-#764 := [rewrite]: #786
-#779 := (iff #830 #778)
-#776 := (iff #825 #774)
-#793 := (iff #834 #789)
-#791 := (= #692 #790)
-#787 := (= #691 #801)
-#800 := (= #690 #799)
-#797 := (= #843 -3::Int)
-#798 := [rewrite]: #797
-#796 := [monotonicity #798]: #800
-#788 := [monotonicity #796]: #787
-#792 := [monotonicity #788]: #791
-#773 := [monotonicity #792]: #793
-#810 := (iff #672 #808)
-#817 := (or #730 #815)
-#809 := (iff #817 #808)
-#803 := [rewrite]: #809
-#806 := (iff #672 #817)
-#816 := (iff #833 #815)
-#804 := (iff #839 #832)
-#824 := (or false #832)
-#805 := (iff #824 #832)
-#802 := [rewrite]: #805
-#811 := (iff #839 #824)
-#707 := (iff #838 false)
-#722 := [rewrite]: #707
-#813 := [monotonicity #722]: #811
-#814 := [trans #813 #802]: #804
-#812 := [monotonicity #814]: #816
-#823 := (iff #671 #730)
-#728 := (iff #669 #840)
-#724 := (or #840 false)
-#726 := (iff #724 #840)
-#727 := [rewrite]: #726
-#725 := (iff #669 #724)
-#718 := [monotonicity #722]: #725
-#729 := [trans #718 #727]: #728
-#820 := [monotonicity #729]: #823
-#807 := [monotonicity #820 #812]: #806
-#794 := [trans #807 #803]: #810
-#777 := [monotonicity #794 #773]: #776
-#819 := (iff #827 #829)
-#714 := (or #829 false)
-#723 := (iff #714 #829)
-#818 := [rewrite]: #723
-#673 := (iff #827 #714)
-#712 := (iff #828 false)
-#713 := [rewrite]: #712
-#821 := [monotonicity #713]: #673
-#822 := [trans #821 #818]: #819
-#780 := [monotonicity #822 #777]: #779
-#775 := [monotonicity #780]: #785
-#765 := [trans #775 #764]: #785
-#784 := [quant-inst #12 #14]: #783
-#767 := [mp #784 #765]: #782
-#646 := [unit-resolution #767 #915]: #778
-#746 := (not #778)
-#750 := (or #746 #747 #826)
-#751 := [def-axiom]: #750
-#649 := [unit-resolution #751 #646]: #648
-#645 := [unit-resolution #649 #643]: #747
-#642 := [unit-resolution #645 #634]: false
-#638 := [lemma #642]: #635
-#578 := [unit-resolution #638 #569]: #881
-#884 := (or #552 #883)
-#882 := (or #887 #552 #883)
-#888 := (or #887 #884)
-#538 := (iff #888 #882)
-#543 := [rewrite]: #538
-#878 := [quant-inst #15]: #888
-#879 := [mp #878 #543]: #882
-#579 := [unit-resolution #879 #902]: #884
-#570 := [unit-resolution #579 #578]: #552
-#487 := (= 0::Int #15)
-#644 := (* -1::Int #15)
-#647 := (+ #12 #644)
-#653 := (>= #647 0::Int)
-#665 := (= #12 #15)
-#507 := (= #551 #15)
-#503 := [symm #570]: #507
-#508 := [trans #505 #503]: #665
-#490 := (not #665)
-#494 := (or #490 #653)
-#495 := [th-lemma arith triangle-eq]: #494
-#498 := [unit-resolution #495 #508]: #653
-#499 := (not #653)
-#500 := (or #832 #883 #499)
-#492 := [th-lemma arith assign-bounds 1 1]: #500
-#501 := [unit-resolution #492 #578 #498]: #832
-#651 := (<= #647 0::Int)
-#485 := (or #490 #651)
-#482 := [th-lemma arith triangle-eq]: #485
-#483 := [unit-resolution #482 #508]: #651
-#519 := (not #651)
-#496 := (or #826 #519 #815 #883)
-#620 := (* -3::Int #835)
-#755 := (mod #12 3::Int)
-#619 := (* -1::Int #755)
-#621 := (+ #619 #620)
-#622 := (+ #12 #621)
-#618 := (= #622 0::Int)
-#87 := [true-axiom]: true
-#580 := (or false #618)
-#547 := [th-lemma arith]: #580
-#549 := [unit-resolution #547 #87]: #618
-#604 := (>= #622 0::Int)
-#520 := (not #604)
-#605 := (>= #755 0::Int)
-#550 := (or false #605)
-#541 := [th-lemma arith]: #550
-#554 := [unit-resolution #541 #87]: #605
-#768 := (<= #15 0::Int)
-#557 := (not #768)
-#555 := [hypothesis]: #881
-#556 := [hypothesis]: #753
-#558 := (or #826 #557 #883)
-#548 := [th-lemma arith triangle-eq]: #558
-#559 := [unit-resolution #548 #556 #555]: #557
-#542 := [hypothesis]: #651
-#756 := (<= #837 0::Int)
-#544 := [unit-resolution #649 #556]: #747
-#545 := (or #829 #774)
-#752 := (or #746 #829 #774)
-#748 := [def-axiom]: #752
-#524 := [unit-resolution #748 #646]: #545
-#526 := [unit-resolution #524 #544]: #774
-#531 := [hypothesis]: #832
-#532 := (or #829 #730 #815)
-#533 := [th-lemma arith triangle-eq]: #532
-#534 := [unit-resolution #533 #544 #531]: #730
-#771 := (or #808 #840)
-#766 := [def-axiom]: #771
-#535 := [unit-resolution #766 #534]: #808
-#772 := (not #808)
-#757 := (not #774)
-#763 := (or #757 #772 #831)
-#736 := [def-axiom]: #763
-#536 := [unit-resolution #736 #535 #526]: #831
-#631 := (not #831)
-#525 := (or #631 #756)
-#537 := [th-lemma arith triangle-eq]: #525
-#518 := [unit-resolution #537 #536]: #756
-#522 := (not #756)
-#521 := (not #605)
-#510 := (or #520 #521 #768 #519 #522)
-#512 := [th-lemma arith assign-bounds 1 2 1 3]: #510
-#513 := [unit-resolution #512 #518 #542 #559 #554]: #520
-#516 := (not #618)
-#511 := (or #516 #604)
-#517 := [th-lemma arith triangle-eq]: #511
-#491 := [unit-resolution #517 #513 #549]: false
-#497 := [lemma #491]: #496
-#486 := [unit-resolution #497 #483 #501 #578]: #826
-#488 := [symm #486]: #487
-#476 := [trans #488 #570]: #489
-#479 := [trans #476 #484]: #478
-#923 := [monotonicity #479]: #480
-#925 := [symm #923]: #924
-#546 := (= f10 #567)
-#23 := (:var 0 S3)
-#24 := (f8 f9 #23)
-#889 := (pattern #24)
-#25 := (f3 f4 #24)
-#111 := (= #23 #25)
-#890 := (forall (vars (?v0 S3)) (:pat #889) #111)
-#115 := (forall (vars (?v0 S3)) #111)
-#893 := (iff #115 #890)
-#891 := (iff #111 #111)
-#892 := [refl]: #891
-#894 := [quant-intro #892]: #893
-#338 := (~ #115 #115)
-#336 := (~ #111 #111)
-#337 := [refl]: #336
-#339 := [nnf-pos #337]: #338
-#26 := (= #25 #23)
-#27 := (forall (vars (?v0 S3)) #26)
-#116 := (iff #27 #115)
-#113 := (iff #26 #111)
-#114 := [rewrite]: #113
-#117 := [quant-intro #114]: #116
-#110 := [asserted]: #27
-#120 := [mp #110 #117]: #115
-#324 := [mp~ #120 #339]: #115
-#895 := [mp #324 #894]: #890
-#540 := (not #890)
-#670 := (or #540 #546)
-#877 := [quant-inst #11]: #670
-#477 := [unit-resolution #877 #895]: #546
-#926 := [trans #477 #925]: #20
-#927 := [unit-resolution #577 #926]: false
-#928 := [lemma #927]: #20
-#933 := [monotonicity #928]: #932
-#934 := [trans #933 #929]: #829
-#935 := [unit-resolution #649 #934]: #826
-#937 := [monotonicity #935]: #936
-#939 := [symm #937]: #938
-#940 := [trans #928 #939]: #90
-#566 := (or #564 #104)
-#565 := (or #564 #104 #475)
-#493 := [def-axiom]: #565
-#563 := [unit-resolution #493 #112]: #566
-#502 := [unit-resolution #563 #928]: #564
-[unit-resolution #502 #940]: false
-unsat
-def579ba90bce689eaa18e94c9b7ab7ad2dc94d2 286 0
+#103 := [quant-intro #100]: #102
+#69 := [asserted]: #33
+#104 := [mp #69 #103]: #101
+#229 := [mp #104 #228]: #226
+#283 := [mp~ #229 #278]: #226
+#798 := [mp #283 #797]: #793
+#705 := (not #793)
+#706 := (or #705 #430 #695)
+#702 := (or #705 #692)
+#696 := (iff #702 #706)
+#697 := [rewrite]: #696
+#707 := [quant-inst #10]: #702
+#698 := [mp #707 #697]: #706
+#629 := [unit-resolution #698 #798]: #692
+#586 := [unit-resolution #629 #585]: #430
+#587 := (or #451 #405 #371)
+#588 := [th-lemma arith triangle-eq]: #587
+#589 := [unit-resolution #588 #586 #662]: #405
+#729 := (or #471 #457)
+#723 := [def-axiom]: #729
+#590 := [unit-resolution #723 #589]: #471
+#561 := (not #471)
+#603 := (not #735)
+#604 := (or #603 #561 #776)
+#563 := [def-axiom]: #604
+#591 := [unit-resolution #563 #590 #584]: #776
+#708 := (not #776)
+#634 := (or #708 #718)
+#639 := [th-lemma arith triangle-eq]: #634
+#592 := [unit-resolution #639 #591]: #718
+#579 := (not #718)
+#594 := (not #681)
+#595 := (or #593 #371 #594 #579 #202)
+#556 := [th-lemma arith assign-bounds 2 1 3 3]: #595
+#557 := [unit-resolution #556 #586 #592 #209 #599]: #593
+#649 := (not #688)
+#650 := (or #649 #680)
+#651 := [th-lemma arith triangle-eq]: #650
+[unit-resolution #651 #557 #646]: false
+397f4299b276d431a769b4b4686f5d15236336cb 577 0
+unsat
+#2 := false
+decl f10 :: S3
+#10 := f10
+decl f3 :: (-> S2 Int S3)
+decl f5 :: (-> S4 Int Int)
+#13 := 3::Int
+decl f6 :: (-> S5 Int S4)
+decl f8 :: (-> S6 S3 Int)
+decl f9 :: S6
+#9 := f9
+#11 := (f8 f9 f10)
+decl f7 :: S5
+#8 := f7
+#12 := (f6 f7 #11)
+#14 := (f5 #12 3::Int)
+decl f4 :: S2
+#7 := f4
+#15 := (f3 f4 #14)
+#16 := (= #15 f10)
+#17 := 0::Int
+#18 := (f3 f4 0::Int)
+#474 := (= #18 f10)
+#19 := (= f10 #18)
+#436 := (f3 f4 #11)
+#490 := (= #436 #18)
+#486 := (= #18 #436)
+#500 := (= 0::Int #11)
+#442 := (f8 f9 #15)
+#534 := (= #442 #11)
+#462 := (= #11 #442)
+#592 := (= f10 #15)
+#365 := (not #19)
+#630 := [hypothesis]: #365
+#453 := (or #16 #19)
+#79 := (not #16)
+#80 := (iff #79 #19)
+#20 := (iff #16 #19)
+#21 := (not #20)
+#81 := (iff #21 #80)
+#82 := [rewrite]: #81
+#70 := [asserted]: #21
+#83 := [mp #70 #82]: #80
+#450 := (not #80)
+#455 := (or #16 #19 #450)
+#456 := [def-axiom]: #455
+#457 := [unit-resolution #456 #83]: #453
+#599 := [unit-resolution #457 #630]: #16
+#593 := [symm #599]: #592
+#463 := [monotonicity #593]: #462
+#498 := [symm #463]: #534
+#499 := (= 0::Int #442)
+#496 := (= #14 #442)
+#774 := (= #442 #14)
+#773 := (>= #14 0::Int)
+#545 := (or #773 #79)
+#744 := (= #11 0::Int)
+#776 := (= #442 0::Int)
+#541 := (iff #776 #744)
+#555 := [hypothesis]: #16
+#537 := [monotonicity #555]: #534
+#543 := [monotonicity #537]: #541
+#430 := (not #773)
+#546 := [hypothesis]: #430
+#777 := (or #773 #776)
+#27 := (:var 0 Int)
+#29 := (f3 f4 #27)
+#786 := (pattern #29)
+#30 := (f8 f9 #29)
+#35 := (= #30 0::Int)
+#210 := (>= #27 0::Int)
+#223 := (or #210 #35)
+#793 := (forall (vars (?v0 Int)) (:pat #786) #223)
+#226 := (forall (vars (?v0 Int)) #223)
+#796 := (iff #226 #793)
+#794 := (iff #223 #223)
+#795 := [refl]: #794
+#797 := [quant-intro #795]: #796
+#271 := (~ #226 #226)
+#277 := (~ #223 #223)
+#278 := [refl]: #277
+#272 := [nnf-pos #278]: #271
+#28 := (<= 0::Int #27)
+#105 := (or #28 #35)
+#110 := (forall (vars (?v0 Int)) #105)
+#227 := (iff #110 #226)
+#224 := (iff #105 #223)
+#211 := (iff #28 #210)
+#212 := [rewrite]: #211
+#225 := [monotonicity #212]: #224
+#228 := [quant-intro #225]: #227
+#34 := (< #27 0::Int)
+#36 := (implies #34 #35)
+#37 := (forall (vars (?v0 Int)) #36)
+#111 := (iff #37 #110)
+#108 := (iff #36 #105)
+#88 := (not #28)
+#102 := (implies #88 #35)
+#106 := (iff #102 #105)
+#107 := [rewrite]: #106
+#103 := (iff #36 #102)
+#97 := (iff #34 #88)
+#99 := (iff #88 #88)
+#84 := (iff #28 #28)
+#85 := [rewrite]: #84
+#100 := [monotonicity #85]: #99
+#98 := [rewrite]: #97
+#101 := [trans #98 #100]: #97
+#104 := [monotonicity #101]: #103
+#109 := [trans #104 #107]: #108
+#112 := [quant-intro #109]: #111
+#73 := [asserted]: #37
+#113 := [mp #73 #112]: #110
+#229 := [mp #113 #228]: #226
+#283 := [mp~ #229 #272]: #226
+#798 := [mp #283 #797]: #793
+#754 := (not #793)
+#417 := (or #754 #773 #776)
+#418 := (or #754 #777)
+#420 := (iff #418 #417)
+#756 := [rewrite]: #420
+#419 := [quant-inst #14]: #418
+#757 := [mp #419 #756]: #417
+#554 := [unit-resolution #757 #798]: #777
+#550 := [unit-resolution #554 #546]: #776
+#544 := [mp #550 #543]: #744
+#650 := (not #744)
+#734 := (= #14 0::Int)
+#626 := (not #734)
+#547 := (or #626 #773)
+#548 := [th-lemma arith triangle-eq]: #547
+#549 := [unit-resolution #548 #546]: #626
+#552 := (or #650 #734)
+#695 := -3::Int
+#140 := -1::Int
+#725 := (* -1::Int #11)
+#704 := (div #725 -3::Int)
+#702 := (* -1::Int #704)
+#697 := (+ #14 #702)
+#693 := (= #697 0::Int)
+#580 := (div #11 3::Int)
+#581 := (* -1::Int #580)
+#582 := (+ #14 #581)
+#724 := (= #582 0::Int)
+#737 := (>= #11 0::Int)
+#620 := (not #737)
+#735 := (<= #11 0::Int)
+#712 := (not #735)
+#714 := (or #712 #620)
+#685 := (if #714 #724 #693)
+#689 := (if #744 #734 #685)
+#38 := (:var 1 Int)
+#39 := (f6 f7 #38)
+#40 := (f5 #39 #27)
+#799 := (pattern #40)
+#144 := (* -1::Int #27)
+#141 := (* -1::Int #38)
+#147 := (div #141 #144)
+#338 := (* -1::Int #147)
+#339 := (+ #40 #338)
+#340 := (= #339 0::Int)
+#50 := (div #38 #27)
+#335 := (* -1::Int #50)
+#336 := (+ #40 #335)
+#337 := (= #336 0::Int)
+#118 := (<= #27 0::Int)
+#230 := (>= #38 0::Int)
+#298 := (or #230 #118)
+#299 := (not #298)
+#114 := (<= #38 0::Int)
+#294 := (or #114 #118)
+#295 := (not #294)
+#302 := (or #295 #299)
+#341 := (if #302 #337 #340)
+#334 := (= #40 0::Int)
+#42 := (= #27 0::Int)
+#41 := (= #38 0::Int)
+#43 := (or #41 #42)
+#342 := (if #43 #334 #341)
+#800 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #799) #342)
+#345 := (forall (vars (?v0 Int) (?v1 Int)) #342)
+#803 := (iff #345 #800)
+#801 := (iff #342 #342)
+#802 := [refl]: #801
+#804 := [quant-intro #802]: #803
+#305 := (if #302 #50 #147)
+#308 := (if #43 0::Int #305)
+#311 := (= #40 #308)
+#314 := (forall (vars (?v0 Int) (?v1 Int)) #311)
+#346 := (iff #314 #345)
+#343 := (iff #311 #342)
+#344 := [rewrite]: #343
+#347 := [quant-intro #344]: #346
+#119 := (not #118)
+#233 := (not #230)
+#236 := (and #233 #119)
+#115 := (not #114)
+#122 := (and #115 #119)
+#239 := (or #122 #236)
+#242 := (if #239 #50 #147)
+#245 := (if #43 0::Int #242)
+#248 := (= #40 #245)
+#251 := (forall (vars (?v0 Int) (?v1 Int)) #248)
+#315 := (iff #251 #314)
+#312 := (iff #248 #311)
+#309 := (= #245 #308)
+#306 := (= #242 #305)
+#303 := (iff #239 #302)
+#300 := (iff #236 #299)
+#301 := [rewrite]: #300
+#296 := (iff #122 #295)
+#297 := [rewrite]: #296
+#304 := [monotonicity #297 #301]: #303
+#307 := [monotonicity #304]: #306
+#310 := [monotonicity #307]: #309
+#313 := [monotonicity #310]: #312
+#316 := [quant-intro #313]: #315
+#286 := (~ #251 #251)
+#284 := (~ #248 #248)
+#285 := [refl]: #284
+#287 := [nnf-pos #285]: #286
+#125 := (<= 0::Int #38)
+#126 := (not #125)
+#134 := (and #126 #119)
+#137 := (or #122 #134)
+#150 := (if #137 #50 #147)
+#153 := (if #43 0::Int #150)
+#156 := (= #40 #153)
+#159 := (forall (vars (?v0 Int) (?v1 Int)) #156)
+#252 := (iff #159 #251)
+#249 := (iff #156 #248)
+#246 := (= #153 #245)
+#243 := (= #150 #242)
+#240 := (iff #137 #239)
+#237 := (iff #134 #236)
+#234 := (iff #126 #233)
+#231 := (iff #125 #230)
+#232 := [rewrite]: #231
+#235 := [monotonicity #232]: #234
+#238 := [monotonicity #235]: #237
+#241 := [monotonicity #238]: #240
+#244 := [monotonicity #241]: #243
+#247 := [monotonicity #244]: #246
+#250 := [monotonicity #247]: #249
+#253 := [quant-intro #250]: #252
+#52 := (- #27)
+#51 := (- #38)
+#53 := (div #51 #52)
+#45 := (< 0::Int #27)
+#47 := (< #38 0::Int)
+#48 := (and #47 #45)
+#44 := (< 0::Int #38)
+#46 := (and #44 #45)
+#49 := (or #46 #48)
+#54 := (if #49 #50 #53)
+#55 := (if #43 0::Int #54)
+#56 := (= #40 #55)
+#57 := (forall (vars (?v0 Int) (?v1 Int)) #56)
+#160 := (iff #57 #159)
+#157 := (iff #56 #156)
+#154 := (= #55 #153)
+#151 := (= #54 #150)
+#148 := (= #53 #147)
+#145 := (= #52 #144)
+#146 := [rewrite]: #145
+#142 := (= #51 #141)
+#143 := [rewrite]: #142
+#149 := [monotonicity #143 #146]: #148
+#138 := (iff #49 #137)
+#135 := (iff #48 #134)
+#120 := (iff #45 #119)
+#121 := [rewrite]: #120
+#127 := (iff #47 #126)
+#131 := (iff #126 #126)
+#129 := (iff #125 #125)
+#130 := [rewrite]: #129
+#132 := [monotonicity #130]: #131
+#128 := [rewrite]: #127
+#133 := [trans #128 #132]: #127
+#136 := [monotonicity #133 #121]: #135
+#123 := (iff #46 #122)
+#116 := (iff #44 #115)
+#117 := [rewrite]: #116
+#124 := [monotonicity #117 #121]: #123
+#139 := [monotonicity #124 #136]: #138
+#152 := [monotonicity #139 #149]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [quant-intro #158]: #160
+#74 := [asserted]: #57
+#162 := [mp #74 #161]: #159
+#254 := [mp #162 #253]: #251
+#288 := [mp~ #254 #287]: #251
+#317 := [mp #288 #316]: #314
+#348 := [mp #317 #347]: #345
+#805 := [mp #348 #804]: #800
+#691 := (not #800)
+#677 := (or #691 #689)
+#726 := (* -1::Int 3::Int)
+#727 := (div #725 #726)
+#721 := (* -1::Int #727)
+#722 := (+ #14 #721)
+#728 := (= #722 0::Int)
+#736 := (<= 3::Int 0::Int)
+#738 := (or #737 #736)
+#733 := (not #738)
+#731 := (or #735 #736)
+#732 := (not #731)
+#739 := (or #732 #733)
+#729 := (if #739 #724 #728)
+#741 := (= 3::Int 0::Int)
+#745 := (or #744 #741)
+#723 := (if #745 #734 #729)
+#678 := (or #691 #723)
+#681 := (iff #678 #677)
+#679 := (iff #677 #677)
+#683 := [rewrite]: #679
+#690 := (iff #723 #689)
+#687 := (iff #729 #685)
+#700 := (iff #728 #693)
+#698 := (= #722 #697)
+#707 := (= #721 #702)
+#705 := (= #727 #704)
+#692 := (= #726 -3::Int)
+#694 := [rewrite]: #692
+#706 := [monotonicity #694]: #705
+#696 := [monotonicity #706]: #707
+#699 := [monotonicity #696]: #698
+#684 := [monotonicity #699]: #700
+#701 := (iff #739 #714)
+#713 := (iff #733 #620)
+#618 := (iff #738 #737)
+#614 := (or #737 false)
+#616 := (iff #614 #737)
+#617 := [rewrite]: #616
+#615 := (iff #738 #614)
+#720 := (iff #736 false)
+#602 := [rewrite]: #720
+#608 := [monotonicity #602]: #615
+#619 := [trans #608 #617]: #618
+#710 := [monotonicity #619]: #713
+#597 := (iff #732 #712)
+#708 := (iff #731 #735)
+#603 := (or #735 false)
+#711 := (iff #603 #735)
+#613 := [rewrite]: #711
+#604 := (iff #731 #603)
+#563 := [monotonicity #602]: #604
+#709 := [trans #563 #613]: #708
+#612 := [monotonicity #709]: #597
+#703 := [monotonicity #612 #710]: #701
+#688 := [monotonicity #703 #684]: #687
+#719 := (iff #745 #744)
+#561 := (or #744 false)
+#716 := (iff #561 #744)
+#718 := [rewrite]: #716
+#562 := (iff #745 #561)
+#730 := (iff #741 false)
+#559 := [rewrite]: #730
+#715 := [monotonicity #559]: #562
+#717 := [trans #715 #718]: #719
+#686 := [monotonicity #717 #688]: #690
+#682 := [monotonicity #686]: #681
+#663 := [trans #682 #683]: #681
+#680 := [quant-inst #11 #13]: #678
+#664 := [mp #680 #663]: #677
+#551 := [unit-resolution #664 #805]: #689
+#649 := (not #689)
+#651 := (or #649 #650 #734)
+#652 := [def-axiom]: #651
+#553 := [unit-resolution #652 #551]: #552
+#396 := [unit-resolution #553 #549]: #650
+#542 := [unit-resolution #396 #544]: false
+#533 := [lemma #542]: #545
+#565 := [unit-resolution #533 #599]: #773
+#775 := (or #430 #774)
+#31 := (= #30 #27)
+#213 := (not #210)
+#216 := (or #213 #31)
+#787 := (forall (vars (?v0 Int)) (:pat #786) #216)
+#219 := (forall (vars (?v0 Int)) #216)
+#790 := (iff #219 #787)
+#788 := (iff #216 #216)
+#789 := [refl]: #788
+#791 := [quant-intro #789]: #790
+#209 := (~ #219 #219)
+#282 := (~ #216 #216)
+#208 := [refl]: #282
+#275 := [nnf-pos #208]: #209
+#89 := (or #88 #31)
+#93 := (forall (vars (?v0 Int)) #89)
+#220 := (iff #93 #219)
+#217 := (iff #89 #216)
+#214 := (iff #88 #213)
+#215 := [monotonicity #212]: #214
+#218 := [monotonicity #215]: #217
+#221 := [quant-intro #218]: #220
+#32 := (implies #28 #31)
+#33 := (forall (vars (?v0 Int)) #32)
+#94 := (iff #33 #93)
+#90 := (iff #32 #89)
+#91 := [rewrite]: #90
+#86 := (iff #32 #32)
+#87 := [monotonicity #85]: #86
+#92 := [trans #87 #91]: #90
+#95 := [quant-intro #92]: #94
+#72 := [asserted]: #33
+#96 := [mp #72 #95]: #93
+#222 := [mp #96 #221]: #219
+#276 := [mp~ #222 #275]: #219
+#792 := [mp #276 #791]: #787
+#772 := (not #787)
+#778 := (or #772 #430 #774)
+#768 := (or #772 #775)
+#433 := (iff #768 #778)
+#769 := [rewrite]: #433
+#428 := [quant-inst #14]: #768
+#429 := [mp #428 #769]: #778
+#588 := [unit-resolution #429 #792]: #775
+#589 := [unit-resolution #588 #565]: #774
+#497 := [symm #589]: #496
+#494 := (= 0::Int #14)
+#624 := (* -1::Int #14)
+#609 := (+ #11 #624)
+#605 := (>= #609 0::Int)
+#569 := (= #11 #14)
+#464 := [trans #463 #589]: #569
+#742 := (not #569)
+#743 := (or #742 #605)
+#508 := [th-lemma arith triangle-eq]: #743
+#509 := [unit-resolution #508 #464]: #605
+#510 := (not #605)
+#511 := (or #737 #430 #510)
+#512 := [th-lemma arith assign-bounds 1 1]: #511
+#513 := [unit-resolution #512 #565 #509]: #737
+#610 := (<= #609 0::Int)
+#502 := (or #742 #610)
+#514 := [th-lemma arith triangle-eq]: #502
+#491 := [unit-resolution #514 #464]: #610
+#515 := (not #610)
+#506 := (or #734 #515 #620 #430)
+#674 := (mod #11 3::Int)
+#587 := (* -1::Int #674)
+#586 := (* -3::Int #580)
+#635 := (+ #11 #586 #587)
+#636 := (= #635 0::Int)
+#1 := true
+#207 := [true-axiom]: true
+#458 := (or false #636)
+#740 := [th-lemma arith]: #458
+#583 := [unit-resolution #740 #207]: #636
+#590 := (>= #635 0::Int)
+#528 := (not #590)
+#591 := (>= #674 0::Int)
+#585 := (or false #591)
+#573 := [th-lemma arith]: #585
+#574 := [unit-resolution #573 #207]: #591
+#666 := (<= #14 0::Int)
+#576 := (not #666)
+#575 := [hypothesis]: #773
+#558 := [hypothesis]: #626
+#577 := (or #734 #576 #430)
+#578 := [th-lemma arith triangle-eq]: #577
+#536 := [unit-resolution #578 #558 #575]: #576
+#538 := [hypothesis]: #610
+#675 := (<= #582 0::Int)
+#539 := [unit-resolution #553 #558]: #650
+#535 := (or #744 #685)
+#647 := (or #649 #744 #685)
+#653 := [def-axiom]: #647
+#540 := [unit-resolution #653 #551]: #535
+#530 := [unit-resolution #540 #539]: #685
+#520 := [hypothesis]: #737
+#522 := (or #744 #712 #620)
+#523 := [th-lemma arith triangle-eq]: #522
+#526 := [unit-resolution #523 #539 #520]: #712
+#667 := (or #714 #735)
+#668 := [def-axiom]: #667
+#527 := [unit-resolution #668 #526]: #714
+#671 := (not #714)
+#657 := (not #685)
+#658 := (or #657 #671 #724)
+#659 := [def-axiom]: #658
+#531 := [unit-resolution #659 #527 #530]: #724
+#656 := (not #724)
+#524 := (or #656 #675)
+#532 := [th-lemma arith triangle-eq]: #524
+#525 := [unit-resolution #532 #531]: #675
+#517 := (not #675)
+#529 := (not #591)
+#518 := (or #528 #529 #666 #515 #517)
+#516 := [th-lemma arith assign-bounds 1 2 1 3]: #518
+#519 := [unit-resolution #516 #525 #538 #536 #574]: #528
+#501 := (not #636)
+#503 := (or #501 #590)
+#504 := [th-lemma arith triangle-eq]: #503
+#505 := [unit-resolution #504 #519 #583]: false
+#507 := [lemma #505]: #506
+#493 := [unit-resolution #507 #491 #513 #565]: #734
+#495 := [symm #493]: #494
+#492 := [trans #495 #497]: #499
+#485 := [trans #492 #498]: #500
+#487 := [monotonicity #485]: #486
+#479 := [symm #487]: #490
+#489 := (= f10 #436)
+#771 := (= #436 f10)
+#22 := (:var 0 S3)
+#23 := (f8 f9 #22)
+#779 := (pattern #23)
+#24 := (f3 f4 #23)
+#25 := (= #24 #22)
+#780 := (forall (vars (?v0 S3)) (:pat #779) #25)
+#26 := (forall (vars (?v0 S3)) #25)
+#783 := (iff #26 #780)
+#781 := (iff #25 #25)
+#782 := [refl]: #781
+#784 := [quant-intro #782]: #783
+#273 := (~ #26 #26)
+#279 := (~ #25 #25)
+#280 := [refl]: #279
+#274 := [nnf-pos #280]: #273
+#71 := [asserted]: #26
+#281 := [mp~ #71 #274]: #26
+#785 := [mp #281 #784]: #780
+#560 := (not #780)
+#767 := (or #560 #771)
+#441 := [quant-inst #10]: #767
+#631 := [unit-resolution #441 #785]: #771
+#488 := [symm #631]: #489
+#480 := [trans #488 #479]: #19
+#481 := [unit-resolution #630 #480]: false
+#473 := [lemma #481]: #19
+#484 := [symm #473]: #474
+#468 := (= #15 #18)
+#758 := (f8 f9 #18)
+#759 := (= #758 0::Int)
+#371 := (or #772 #759)
+#770 := (>= 0::Int 0::Int)
+#413 := (not #770)
+#760 := (or #413 #759)
+#748 := (or #772 #760)
+#471 := (iff #748 #371)
+#746 := (iff #371 #371)
+#750 := [rewrite]: #746
+#477 := (iff #760 #759)
+#766 := (or false #759)
+#475 := (iff #766 #759)
+#476 := [rewrite]: #475
+#752 := (iff #760 #766)
+#765 := (iff #413 false)
+#399 := (not true)
+#404 := (iff #399 false)
+#405 := [rewrite]: #404
+#762 := (iff #413 #399)
+#755 := (iff #770 true)
+#761 := [rewrite]: #755
+#764 := [monotonicity #761]: #762
+#763 := [trans #764 #405]: #765
+#753 := [monotonicity #763]: #752
+#478 := [trans #753 #476]: #477
+#472 := [monotonicity #478]: #471
+#747 := [trans #472 #750]: #471
+#749 := [quant-inst #17]: #748
+#751 := [mp #749 #747]: #371
+#483 := [unit-resolution #751 #792]: #759
+#465 := (= #11 #758)
+#466 := [monotonicity #473]: #465
+#467 := [trans #466 #483]: #744
+#459 := [unit-resolution #553 #467]: #734
+#469 := [monotonicity #459]: #468
+#460 := [trans #469 #484]: #16
+#443 := (or #79 #365)
+#451 := (or #79 #365 #450)
+#452 := [def-axiom]: #451
+#454 := [unit-resolution #452 #83]: #443
+#482 := [unit-resolution #454 #473]: #79
+[unit-resolution #482 #460]: false
+1a7e6fb939840d6cef72226e157b39c6c463f1a1 283 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int S3)
-#10 := 0::Int
-decl f4 :: S2
-#8 := f4
-#14 := (f3 f4 0::Int)
+#9 := 0::Int
+decl f4 :: S2
+#7 := f4
+#13 := (f3 f4 0::Int)
 decl f5 :: (-> S4 Int Int)
 decl f6 :: (-> S5 Int S4)
 decl f7 :: S5
-#9 := f7
-#11 := (f6 f7 0::Int)
-#12 := (f5 #11 0::Int)
-#13 := (f3 f4 #12)
-#15 := (= #13 #14)
-#811 := (= #12 0::Int)
+#8 := f7
+#10 := (f6 f7 0::Int)
+#11 := (f5 #10 0::Int)
+#12 := (f3 f4 #11)
+#14 := (= #12 #13)
+#461 := (= #11 0::Int)
+#22 := (:var 0 Int)
+#34 := (:var 1 Int)
+#54 := (f6 f7 #34)
+#55 := (f5 #54 #22)
+#796 := (pattern #55)
+#130 := -1::Int
+#134 := (* -1::Int #22)
+#131 := (* -1::Int #34)
+#153 := (mod #131 #134)
+#344 := (+ #55 #153)
+#345 := (= #344 0::Int)
+#56 := (mod #34 #22)
+#341 := (* -1::Int #56)
+#342 := (+ #55 #341)
+#343 := (= #342 0::Int)
+#108 := (<= #22 0::Int)
+#220 := (>= #34 0::Int)
+#288 := (or #220 #108)
+#289 := (not #288)
+#104 := (<= #34 0::Int)
+#284 := (or #104 #108)
+#285 := (not #284)
+#292 := (or #285 #289)
+#346 := (if #292 #343 #345)
+#340 := (= #55 0::Int)
+#37 := (= #34 0::Int)
+#347 := (if #37 #340 #346)
+#339 := (= #55 #34)
+#38 := (= #22 0::Int)
+#348 := (if #38 #339 #347)
+#797 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #796) #348)
+#351 := (forall (vars (?v0 Int) (?v1 Int)) #348)
+#800 := (iff #351 #797)
+#798 := (iff #348 #348)
+#799 := [refl]: #798
+#801 := [quant-intro #799]: #800
+#159 := (* -1::Int #153)
+#308 := (if #292 #56 #159)
+#311 := (if #37 0::Int #308)
+#314 := (if #38 #34 #311)
+#317 := (= #55 #314)
+#320 := (forall (vars (?v0 Int) (?v1 Int)) #317)
+#352 := (iff #320 #351)
+#349 := (iff #317 #348)
+#350 := [rewrite]: #349
+#353 := [quant-intro #350]: #352
+#109 := (not #108)
+#223 := (not #220)
+#226 := (and #223 #109)
+#105 := (not #104)
+#112 := (and #105 #109)
+#229 := (or #112 #226)
+#245 := (if #229 #56 #159)
+#248 := (if #37 0::Int #245)
+#251 := (if #38 #34 #248)
+#254 := (= #55 #251)
+#257 := (forall (vars (?v0 Int) (?v1 Int)) #254)
+#321 := (iff #257 #320)
+#318 := (iff #254 #317)
+#315 := (= #251 #314)
+#312 := (= #248 #311)
+#309 := (= #245 #308)
+#293 := (iff #229 #292)
+#290 := (iff #226 #289)
+#291 := [rewrite]: #290
+#286 := (iff #112 #285)
+#287 := [rewrite]: #286
+#294 := [monotonicity #287 #291]: #293
+#310 := [monotonicity #294]: #309
+#313 := [monotonicity #310]: #312
+#316 := [monotonicity #313]: #315
+#319 := [monotonicity #316]: #318
+#322 := [quant-intro #319]: #321
+#281 := (~ #257 #257)
+#279 := (~ #254 #254)
+#280 := [refl]: #279
+#282 := [nnf-pos #280]: #281
+#115 := (<= 0::Int #34)
+#116 := (not #115)
+#124 := (and #116 #109)
+#127 := (or #112 #124)
+#164 := (if #127 #56 #159)
+#167 := (if #37 0::Int #164)
+#170 := (if #38 #34 #167)
+#173 := (= #55 #170)
+#176 := (forall (vars (?v0 Int) (?v1 Int)) #173)
+#258 := (iff #176 #257)
+#255 := (iff #173 #254)
+#252 := (= #170 #251)
+#249 := (= #167 #248)
+#246 := (= #164 #245)
+#230 := (iff #127 #229)
+#227 := (iff #124 #226)
+#224 := (iff #116 #223)
+#221 := (iff #115 #220)
+#222 := [rewrite]: #221
+#225 := [monotonicity #222]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#247 := [monotonicity #231]: #246
+#250 := [monotonicity #247]: #249
+#253 := [monotonicity #250]: #252
+#256 := [monotonicity #253]: #255
+#259 := [quant-intro #256]: #258
+#48 := (- #22)
+#47 := (- #34)
+#57 := (mod #47 #48)
+#58 := (- #57)
+#41 := (< 0::Int #22)
+#43 := (< #34 0::Int)
+#44 := (and #43 #41)
+#40 := (< 0::Int #34)
+#42 := (and #40 #41)
+#45 := (or #42 #44)
+#59 := (if #45 #56 #58)
+#60 := (if #37 0::Int #59)
+#61 := (if #38 #34 #60)
+#62 := (= #55 #61)
+#63 := (forall (vars (?v0 Int) (?v1 Int)) #62)
+#177 := (iff #63 #176)
+#174 := (iff #62 #173)
+#171 := (= #61 #170)
+#168 := (= #60 #167)
+#165 := (= #59 #164)
+#162 := (= #58 #159)
+#156 := (- #153)
+#160 := (= #156 #159)
+#161 := [rewrite]: #160
+#157 := (= #58 #156)
+#154 := (= #57 #153)
+#135 := (= #48 #134)
+#136 := [rewrite]: #135
+#132 := (= #47 #131)
+#133 := [rewrite]: #132
+#155 := [monotonicity #133 #136]: #154
+#158 := [monotonicity #155]: #157
+#163 := [trans #158 #161]: #162
+#128 := (iff #45 #127)
+#125 := (iff #44 #124)
+#110 := (iff #41 #109)
+#111 := [rewrite]: #110
+#117 := (iff #43 #116)
+#121 := (iff #116 #116)
+#119 := (iff #115 #115)
+#120 := [rewrite]: #119
+#122 := [monotonicity #120]: #121
+#118 := [rewrite]: #117
+#123 := [trans #118 #122]: #117
+#126 := [monotonicity #123 #111]: #125
+#113 := (iff #42 #112)
+#106 := (iff #40 #105)
+#107 := [rewrite]: #106
+#114 := [monotonicity #107 #111]: #113
+#129 := [monotonicity #114 #126]: #128
+#166 := [monotonicity #129 #163]: #165
+#169 := [monotonicity #166]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [quant-intro #175]: #177
+#70 := [asserted]: #63
+#179 := [mp #70 #178]: #176
+#260 := [mp #179 #259]: #257
+#283 := [mp~ #260 #282]: #257
+#323 := [mp #283 #322]: #320
+#354 := [mp #323 #353]: #351
+#802 := [mp #354 #801]: #797
+#697 := (not #797)
+#686 := (or #697 #461)
+#733 := (* -1::Int 0::Int)
+#448 := (mod #733 #733)
+#730 := (+ #11 #448)
+#734 := (= #730 0::Int)
+#452 := (mod 0::Int 0::Int)
+#453 := (* -1::Int #452)
+#454 := (+ #11 #453)
+#732 := (= #454 0::Int)
+#462 := (<= 0::Int 0::Int)
+#550 := (>= 0::Int 0::Int)
+#737 := (or #550 #462)
+#741 := (not #737)
+#736 := (or #462 #462)
+#740 := (not #736)
+#451 := (or #740 #741)
+#731 := (if #451 #732 #734)
+#739 := (= 0::Int 0::Int)
+#735 := (if #739 #461 #731)
+#724 := (if #739 #461 #735)
+#687 := (or #697 #724)
+#689 := (iff #687 #686)
+#690 := (iff #686 #686)
+#674 := [rewrite]: #690
+#696 := (iff #724 #461)
+#1 := true
+#685 := (if true #461 #461)
+#694 := (iff #685 #461)
+#695 := [rewrite]: #694
+#682 := (iff #724 #685)
+#691 := (iff #735 #461)
+#701 := (+ #11 #452)
+#699 := (= #701 0::Int)
+#609 := (if true #461 #699)
+#700 := (iff #609 #461)
+#704 := [rewrite]: #700
+#610 := (iff #735 #609)
+#607 := (iff #731 #699)
+#602 := (if false #732 #699)
+#598 := (iff #602 #699)
+#606 := [rewrite]: #598
+#604 := (iff #731 #602)
+#702 := (iff #734 #699)
+#603 := (= #730 #701)
+#594 := (= #448 #452)
+#592 := (= #733 0::Int)
+#593 := [rewrite]: #592
+#553 := [monotonicity #593 #593]: #594
+#698 := [monotonicity #553]: #603
+#587 := [monotonicity #698]: #702
+#707 := (iff #451 false)
+#552 := (or false false)
+#708 := (iff #552 false)
+#709 := [rewrite]: #708
+#705 := (iff #451 #552)
+#549 := (iff #741 false)
+#419 := (not true)
+#744 := (iff #419 false)
+#407 := [rewrite]: #744
+#713 := (iff #741 #419)
+#718 := (iff #737 true)
+#727 := (or true true)
+#729 := (iff #727 true)
+#570 := [rewrite]: #729
+#711 := (iff #737 #727)
+#721 := (iff #462 true)
+#722 := [rewrite]: #721
+#423 := (iff #550 true)
+#759 := [rewrite]: #423
+#712 := [monotonicity #759 #722]: #711
+#719 := [trans #712 #570]: #718
+#720 := [monotonicity #719]: #713
+#551 := [trans #720 #407]: #549
+#716 := (iff #740 false)
+#714 := (iff #740 #419)
+#571 := (iff #736 true)
+#728 := (iff #736 #727)
+#723 := [monotonicity #722 #722]: #728
+#572 := [trans #723 #570]: #571
+#715 := [monotonicity #572]: #714
+#717 := [trans #715 #407]: #716
+#706 := [monotonicity #717 #551]: #705
+#710 := [trans #706 #709]: #707
+#605 := [monotonicity #710 #587]: #604
+#608 := [trans #605 #606]: #607
+#725 := (iff #739 true)
+#726 := [rewrite]: #725
+#703 := [monotonicity #726 #608]: #610
+#693 := [trans #703 #704]: #691
+#684 := [monotonicity #726 #693]: #682
+#692 := [trans #684 #695]: #696
+#683 := [monotonicity #692]: #689
+#675 := [trans #683 #674]: #689
+#688 := [quant-inst #9 #9]: #687
+#677 := [mp #688 #675]: #686
+#679 := [unit-resolution #677 #802]: #461
+#680 := [monotonicity #679]: #14
+#15 := (not #14)
+#65 := [asserted]: #15
+[unit-resolution #65 #680]: false
+936a202ebc7a104f43c75b92a8828d52b8119be5 316 0
+unsat
+#2 := false
+decl f10 :: S3
+#10 := f10
+decl f3 :: (-> S2 Int S3)
+decl f5 :: (-> S4 Int Int)
+#13 := 0::Int
+decl f6 :: (-> S5 Int S4)
+decl f8 :: (-> S6 S3 Int)
+decl f9 :: S6
+#9 := f9
+#11 := (f8 f9 f10)
+decl f7 :: S5
+#8 := f7
+#12 := (f6 f7 #11)
+#14 := (f5 #12 0::Int)
+decl f4 :: S2
+#7 := f4
+#15 := (f3 f4 #14)
+#16 := (= #15 f10)
+#356 := (f3 f4 #11)
+#441 := (= #356 f10)
+#18 := (:var 0 S3)
+#19 := (f8 f9 #18)
+#770 := (pattern #19)
+#20 := (f3 f4 #19)
+#21 := (= #20 #18)
+#771 := (forall (vars (?v0 S3)) (:pat #770) #21)
+#22 := (forall (vars (?v0 S3)) #21)
+#774 := (iff #22 #771)
+#772 := (iff #21 #21)
+#773 := [refl]: #772
+#775 := [quant-intro #773]: #774
+#264 := (~ #22 #22)
+#199 := (~ #21 #21)
+#200 := [refl]: #199
+#265 := [nnf-pos #200]: #264
+#67 := [asserted]: #22
+#268 := [mp~ #67 #265]: #22
+#776 := [mp #268 #775]: #771
+#434 := (not #771)
+#445 := (or #434 #441)
+#446 := [quant-inst #10]: #445
+#609 := [unit-resolution #446 #776]: #441
+#611 := (= #15 #356)
+#767 := (= #14 #11)
 #23 := (:var 0 Int)
 #35 := (:var 1 Int)
 #55 := (f6 f7 #35)
 #56 := (f5 #55 #23)
-#890 := (pattern #56)
-#186 := -1::Int
-#190 := (* -1::Int #23)
-#187 := (* -1::Int #35)
-#251 := (mod #187 #190)
-#381 := (+ #56 #251)
-#382 := (= #381 0::Int)
+#797 := (pattern #56)
+#131 := -1::Int
+#135 := (* -1::Int #23)
+#132 := (* -1::Int #35)
+#154 := (mod #132 #135)
+#345 := (+ #56 #154)
+#346 := (= #345 0::Int)
 #57 := (mod #35 #23)
-#378 := (* -1::Int #57)
-#379 := (+ #56 #378)
-#380 := (= #379 0::Int)
-#225 := (>= #35 0::Int)
-#218 := (<= #23 0::Int)
-#325 := (or #218 #225)
-#326 := (not #325)
-#214 := (<= #35 0::Int)
-#323 := (or #214 #218)
-#324 := (not #323)
-#329 := (or #324 #326)
-#383 := (ite #329 #380 #382)
-#377 := (= #56 0::Int)
+#342 := (* -1::Int #57)
+#343 := (+ #56 #342)
+#344 := (= #343 0::Int)
+#109 := (<= #23 0::Int)
+#221 := (>= #35 0::Int)
+#289 := (or #221 #109)
+#290 := (not #289)
+#105 := (<= #35 0::Int)
+#285 := (or #105 #109)
+#286 := (not #285)
+#293 := (or #286 #290)
+#347 := (if #293 #344 #346)
+#341 := (= #56 0::Int)
 #38 := (= #35 0::Int)
-#384 := (ite #38 #377 #383)
-#376 := (= #35 #56)
+#348 := (if #38 #341 #347)
+#340 := (= #56 #35)
 #39 := (= #23 0::Int)
-#385 := (ite #39 #376 #384)
-#891 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #890) #385)
-#388 := (forall (vars (?v0 Int) (?v1 Int)) #385)
-#894 := (iff #388 #891)
-#892 := (iff #385 #385)
-#893 := [refl]: #892
-#895 := [quant-intro #893]: #894
-#257 := (* -1::Int #251)
-#345 := (ite #329 #57 #257)
-#348 := (ite #38 0::Int #345)
-#351 := (ite #39 #35 #348)
-#354 := (= #56 #351)
-#357 := (forall (vars (?v0 Int) (?v1 Int)) #354)
-#389 := (iff #357 #388)
-#386 := (iff #354 #385)
-#387 := [rewrite]: #386
-#390 := [quant-intro #387]: #389
-#226 := (not #225)
-#219 := (not #218)
-#229 := (and #219 #226)
-#215 := (not #214)
-#222 := (and #215 #219)
-#232 := (or #222 #229)
-#277 := (ite #232 #57 #257)
-#280 := (ite #38 0::Int #277)
-#283 := (ite #39 #35 #280)
-#286 := (= #56 #283)
-#289 := (forall (vars (?v0 Int) (?v1 Int)) #286)
-#358 := (iff #289 #357)
-#355 := (iff #286 #354)
-#352 := (= #283 #351)
-#349 := (= #280 #348)
-#346 := (= #277 #345)
-#330 := (iff #232 #329)
-#327 := (iff #229 #326)
-#328 := [rewrite]: #327
-#308 := (iff #222 #324)
-#309 := [rewrite]: #308
-#331 := [monotonicity #309 #328]: #330
-#347 := [monotonicity #331]: #346
-#350 := [monotonicity #347]: #349
-#353 := [monotonicity #350]: #352
-#356 := [monotonicity #353]: #355
-#359 := [quant-intro #356]: #358
-#306 := (~ #289 #289)
-#320 := (~ #286 #286)
-#321 := [refl]: #320
-#307 := [nnf-pos #321]: #306
+#349 := (if #39 #340 #348)
+#798 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #797) #349)
+#352 := (forall (vars (?v0 Int) (?v1 Int)) #349)
+#801 := (iff #352 #798)
+#799 := (iff #349 #349)
+#800 := [refl]: #799
+#802 := [quant-intro #800]: #801
+#160 := (* -1::Int #154)
+#309 := (if #293 #57 #160)
+#312 := (if #38 0::Int #309)
+#315 := (if #39 #35 #312)
+#318 := (= #56 #315)
+#321 := (forall (vars (?v0 Int) (?v1 Int)) #318)
+#353 := (iff #321 #352)
+#350 := (iff #318 #349)
+#351 := [rewrite]: #350
+#354 := [quant-intro #351]: #353
+#110 := (not #109)
+#224 := (not #221)
+#227 := (and #224 #110)
+#106 := (not #105)
+#113 := (and #106 #110)
+#230 := (or #113 #227)
+#246 := (if #230 #57 #160)
+#249 := (if #38 0::Int #246)
+#252 := (if #39 #35 #249)
+#255 := (= #56 #252)
+#258 := (forall (vars (?v0 Int) (?v1 Int)) #255)
+#322 := (iff #258 #321)
+#319 := (iff #255 #318)
+#316 := (= #252 #315)
+#313 := (= #249 #312)
+#310 := (= #246 #309)
+#294 := (iff #230 #293)
+#291 := (iff #227 #290)
+#292 := [rewrite]: #291
+#287 := (iff #113 #286)
+#288 := [rewrite]: #287
+#295 := [monotonicity #288 #292]: #294
+#311 := [monotonicity #295]: #310
+#314 := [monotonicity #311]: #313
+#317 := [monotonicity #314]: #316
+#320 := [monotonicity #317]: #319
+#323 := [quant-intro #320]: #322
+#282 := (~ #258 #258)
+#280 := (~ #255 #255)
+#281 := [refl]: #280
+#283 := [nnf-pos #281]: #282
+#116 := (<= 0::Int #35)
+#117 := (not #116)
+#125 := (and #117 #110)
+#128 := (or #113 #125)
+#165 := (if #128 #57 #160)
+#168 := (if #38 0::Int #165)
+#171 := (if #39 #35 #168)
+#174 := (= #56 #171)
+#177 := (forall (vars (?v0 Int) (?v1 Int)) #174)
+#259 := (iff #177 #258)
+#256 := (iff #174 #255)
+#253 := (= #171 #252)
+#250 := (= #168 #249)
+#247 := (= #165 #246)
+#231 := (iff #128 #230)
+#228 := (iff #125 #227)
+#225 := (iff #117 #224)
+#222 := (iff #116 #221)
+#223 := [rewrite]: #222
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#248 := [monotonicity #232]: #247
+#251 := [monotonicity #248]: #250
+#254 := [monotonicity #251]: #253
+#257 := [monotonicity #254]: #256
+#260 := [quant-intro #257]: #259
 #49 := (- #23)
 #48 := (- #35)
 #58 := (mod #48 #49)
@@ -17282,619 +16851,908 @@
 #41 := (< 0::Int #35)
 #43 := (and #41 #42)
 #46 := (or #43 #45)
-#60 := (ite #46 #57 #59)
-#61 := (ite #38 0::Int #60)
-#62 := (ite #39 #35 #61)
+#60 := (if #46 #57 #59)
+#61 := (if #38 0::Int #60)
+#62 := (if #39 #35 #61)
+#63 := (= #56 #62)
+#64 := (forall (vars (?v0 Int) (?v1 Int)) #63)
+#178 := (iff #64 #177)
+#175 := (iff #63 #174)
+#172 := (= #62 #171)
+#169 := (= #61 #168)
+#166 := (= #60 #165)
+#163 := (= #59 #160)
+#157 := (- #154)
+#161 := (= #157 #160)
+#162 := [rewrite]: #161
+#158 := (= #59 #157)
+#155 := (= #58 #154)
+#136 := (= #49 #135)
+#137 := [rewrite]: #136
+#133 := (= #48 #132)
+#134 := [rewrite]: #133
+#156 := [monotonicity #134 #137]: #155
+#159 := [monotonicity #156]: #158
+#164 := [trans #159 #162]: #163
+#129 := (iff #46 #128)
+#126 := (iff #45 #125)
+#111 := (iff #42 #110)
+#112 := [rewrite]: #111
+#118 := (iff #44 #117)
+#122 := (iff #117 #117)
+#120 := (iff #116 #116)
+#121 := [rewrite]: #120
+#123 := [monotonicity #121]: #122
+#119 := [rewrite]: #118
+#124 := [trans #119 #123]: #118
+#127 := [monotonicity #124 #112]: #126
+#114 := (iff #43 #113)
+#107 := (iff #41 #106)
+#108 := [rewrite]: #107
+#115 := [monotonicity #108 #112]: #114
+#130 := [monotonicity #115 #127]: #129
+#167 := [monotonicity #130 #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [monotonicity #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [quant-intro #176]: #178
+#71 := [asserted]: #64
+#180 := [mp #71 #179]: #177
+#261 := [mp #180 #260]: #258
+#284 := [mp~ #261 #283]: #258
+#324 := [mp #284 #323]: #321
+#355 := [mp #324 #354]: #352
+#803 := [mp #355 #802]: #798
+#699 := (not #798)
+#700 := (or #699 #767)
+#390 := (* -1::Int 0::Int)
+#752 := (* -1::Int #11)
+#753 := (mod #752 #390)
+#755 := (+ #14 #753)
+#395 := (= #755 0::Int)
+#749 := (mod #11 0::Int)
+#750 := (* -1::Int #749)
+#751 := (+ #14 #750)
+#746 := (= #751 0::Int)
+#745 := (<= 0::Int 0::Int)
+#410 := (>= #11 0::Int)
+#411 := (or #410 #745)
+#747 := (not #411)
+#404 := (<= #11 0::Int)
+#408 := (or #404 #745)
+#409 := (not #408)
+#748 := (or #409 #747)
+#396 := (if #748 #746 #395)
+#761 := (= #14 0::Int)
+#420 := (= #11 0::Int)
+#756 := (if #420 #761 #396)
+#766 := (= 0::Int 0::Int)
+#754 := (if #766 #767 #756)
+#703 := (or #699 #754)
+#603 := (iff #703 #700)
+#606 := (iff #700 #700)
+#599 := [rewrite]: #606
+#702 := (iff #754 #767)
+#573 := (mod #752 0::Int)
+#717 := (+ #14 #573)
+#713 := (= #717 0::Int)
+#709 := (if #420 #761 #713)
+#1 := true
+#711 := (if true #767 #709)
+#595 := (iff #711 #767)
+#554 := [rewrite]: #595
+#593 := (iff #754 #711)
+#710 := (iff #756 #709)
+#706 := (iff #396 #713)
+#714 := (if false #746 #713)
+#552 := (iff #714 #713)
+#553 := [rewrite]: #552
+#721 := (iff #396 #714)
+#719 := (iff #395 #713)
+#718 := (= #755 #717)
+#715 := (= #753 #573)
+#571 := (= #390 0::Int)
+#572 := [rewrite]: #571
+#716 := [monotonicity #572]: #715
+#712 := [monotonicity #716]: #718
+#720 := [monotonicity #712]: #719
+#724 := (iff #748 false)
+#727 := (or false false)
+#728 := (iff #727 false)
+#729 := [rewrite]: #728
+#722 := (iff #748 #727)
+#725 := (iff #747 false)
+#463 := (not true)
+#738 := (iff #463 false)
+#742 := [rewrite]: #738
+#732 := (iff #747 #463)
+#731 := (iff #411 true)
+#454 := (or #410 true)
+#734 := (iff #454 true)
+#449 := [rewrite]: #734
+#455 := (iff #411 #454)
+#744 := (iff #745 true)
+#466 := [rewrite]: #744
+#733 := [monotonicity #466]: #455
+#735 := [trans #733 #449]: #731
+#736 := [monotonicity #735]: #732
+#726 := [trans #736 #742]: #725
+#452 := (iff #409 false)
+#737 := (iff #409 #463)
+#740 := (iff #408 true)
+#467 := (or #404 true)
+#362 := (iff #467 true)
+#739 := [rewrite]: #362
+#468 := (iff #408 #467)
+#469 := [monotonicity #466]: #468
+#462 := [trans #469 #739]: #740
+#741 := [monotonicity #462]: #737
+#453 := [trans #741 #742]: #452
+#723 := [monotonicity #453 #726]: #722
+#730 := [trans #723 #729]: #724
+#550 := [monotonicity #730 #720]: #721
+#707 := [trans #550 #553]: #706
+#708 := [monotonicity #707]: #710
+#757 := (iff #766 true)
+#743 := [rewrite]: #757
+#594 := [monotonicity #743 #708]: #593
+#604 := [trans #594 #554]: #702
+#605 := [monotonicity #604]: #603
+#607 := [trans #605 #599]: #603
+#588 := [quant-inst #11 #13]: #703
+#608 := [mp #588 #607]: #700
+#610 := [unit-resolution #608 #803]: #767
+#704 := [monotonicity #610]: #611
+#701 := [trans #704 #609]: #16
+#17 := (not #16)
+#66 := [asserted]: #17
+[unit-resolution #66 #701]: false
+364659a809da594253b58b8a2b28d9516abee4db 310 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int S3)
+#9 := 0::Int
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 0::Int)
+decl f5 :: (-> S4 Int Int)
+#11 := 1::Int
+decl f6 :: (-> S5 Int S4)
+decl f7 :: S5
+#8 := f7
+#10 := (f6 f7 0::Int)
+#12 := (f5 #10 1::Int)
+#13 := (f3 f4 #12)
+#15 := (= #13 #14)
+#461 := (= #12 0::Int)
+#23 := (:var 0 Int)
+#35 := (:var 1 Int)
+#55 := (f6 f7 #35)
+#56 := (f5 #55 #23)
+#796 := (pattern #56)
+#131 := -1::Int
+#135 := (* -1::Int #23)
+#132 := (* -1::Int #35)
+#154 := (mod #132 #135)
+#345 := (+ #56 #154)
+#346 := (= #345 0::Int)
+#57 := (mod #35 #23)
+#342 := (* -1::Int #57)
+#343 := (+ #56 #342)
+#344 := (= #343 0::Int)
+#109 := (<= #23 0::Int)
+#221 := (>= #35 0::Int)
+#289 := (or #221 #109)
+#290 := (not #289)
+#105 := (<= #35 0::Int)
+#285 := (or #105 #109)
+#286 := (not #285)
+#293 := (or #286 #290)
+#347 := (if #293 #344 #346)
+#341 := (= #56 0::Int)
+#38 := (= #35 0::Int)
+#348 := (if #38 #341 #347)
+#340 := (= #56 #35)
+#39 := (= #23 0::Int)
+#349 := (if #39 #340 #348)
+#797 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #796) #349)
+#352 := (forall (vars (?v0 Int) (?v1 Int)) #349)
+#800 := (iff #352 #797)
+#798 := (iff #349 #349)
+#799 := [refl]: #798
+#801 := [quant-intro #799]: #800
+#160 := (* -1::Int #154)
+#309 := (if #293 #57 #160)
+#312 := (if #38 0::Int #309)
+#315 := (if #39 #35 #312)
+#318 := (= #56 #315)
+#321 := (forall (vars (?v0 Int) (?v1 Int)) #318)
+#353 := (iff #321 #352)
+#350 := (iff #318 #349)
+#351 := [rewrite]: #350
+#354 := [quant-intro #351]: #353
+#110 := (not #109)
+#224 := (not #221)
+#227 := (and #224 #110)
+#106 := (not #105)
+#113 := (and #106 #110)
+#230 := (or #113 #227)
+#246 := (if #230 #57 #160)
+#249 := (if #38 0::Int #246)
+#252 := (if #39 #35 #249)
+#255 := (= #56 #252)
+#258 := (forall (vars (?v0 Int) (?v1 Int)) #255)
+#322 := (iff #258 #321)
+#319 := (iff #255 #318)
+#316 := (= #252 #315)
+#313 := (= #249 #312)
+#310 := (= #246 #309)
+#294 := (iff #230 #293)
+#291 := (iff #227 #290)
+#292 := [rewrite]: #291
+#287 := (iff #113 #286)
+#288 := [rewrite]: #287
+#295 := [monotonicity #288 #292]: #294
+#311 := [monotonicity #295]: #310
+#314 := [monotonicity #311]: #313
+#317 := [monotonicity #314]: #316
+#320 := [monotonicity #317]: #319
+#323 := [quant-intro #320]: #322
+#282 := (~ #258 #258)
+#280 := (~ #255 #255)
+#281 := [refl]: #280
+#283 := [nnf-pos #281]: #282
+#116 := (<= 0::Int #35)
+#117 := (not #116)
+#125 := (and #117 #110)
+#128 := (or #113 #125)
+#165 := (if #128 #57 #160)
+#168 := (if #38 0::Int #165)
+#171 := (if #39 #35 #168)
+#174 := (= #56 #171)
+#177 := (forall (vars (?v0 Int) (?v1 Int)) #174)
+#259 := (iff #177 #258)
+#256 := (iff #174 #255)
+#253 := (= #171 #252)
+#250 := (= #168 #249)
+#247 := (= #165 #246)
+#231 := (iff #128 #230)
+#228 := (iff #125 #227)
+#225 := (iff #117 #224)
+#222 := (iff #116 #221)
+#223 := [rewrite]: #222
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#248 := [monotonicity #232]: #247
+#251 := [monotonicity #248]: #250
+#254 := [monotonicity #251]: #253
+#257 := [monotonicity #254]: #256
+#260 := [quant-intro #257]: #259
+#49 := (- #23)
+#48 := (- #35)
+#58 := (mod #48 #49)
+#59 := (- #58)
+#42 := (< 0::Int #23)
+#44 := (< #35 0::Int)
+#45 := (and #44 #42)
+#41 := (< 0::Int #35)
+#43 := (and #41 #42)
+#46 := (or #43 #45)
+#60 := (if #46 #57 #59)
+#61 := (if #38 0::Int #60)
+#62 := (if #39 #35 #61)
 #63 := (= #56 #62)
 #64 := (forall (vars (?v0 Int) (?v1 Int)) #63)
-#292 := (iff #64 #289)
-#180 := (and #42 #44)
-#183 := (or #43 #180)
-#262 := (ite #183 #57 #257)
-#171 := (= 0::Int #35)
-#265 := (ite #171 0::Int #262)
-#174 := (= 0::Int #23)
-#268 := (ite #174 #35 #265)
-#271 := (= #56 #268)
-#274 := (forall (vars (?v0 Int) (?v1 Int)) #271)
-#290 := (iff #274 #289)
-#287 := (iff #271 #286)
-#284 := (= #268 #283)
-#281 := (= #265 #280)
-#278 := (= #262 #277)
-#233 := (iff #183 #232)
-#230 := (iff #180 #229)
-#227 := (iff #44 #226)
-#228 := [rewrite]: #227
-#220 := (iff #42 #219)
-#221 := [rewrite]: #220
-#231 := [monotonicity #221 #228]: #230
-#223 := (iff #43 #222)
-#216 := (iff #41 #215)
-#217 := [rewrite]: #216
-#224 := [monotonicity #217 #221]: #223
-#234 := [monotonicity #224 #231]: #233
-#279 := [monotonicity #234]: #278
-#208 := (iff #171 #38)
-#209 := [rewrite]: #208
-#282 := [monotonicity #209 #279]: #281
-#210 := (iff #174 #39)
-#211 := [rewrite]: #210
-#285 := [monotonicity #211 #282]: #284
-#288 := [monotonicity #285]: #287
-#291 := [quant-intro #288]: #290
-#275 := (iff #64 #274)
-#272 := (iff #63 #271)
-#269 := (= #62 #268)
-#266 := (= #61 #265)
-#263 := (= #60 #262)
-#260 := (= #59 #257)
-#254 := (- #251)
-#258 := (= #254 #257)
-#259 := [rewrite]: #258
-#255 := (= #59 #254)
-#252 := (= #58 #251)
-#191 := (= #49 #190)
-#192 := [rewrite]: #191
-#188 := (= #48 #187)
-#189 := [rewrite]: #188
-#253 := [monotonicity #189 #192]: #252
-#256 := [monotonicity #253]: #255
-#261 := [trans #256 #259]: #260
-#184 := (iff #46 #183)
-#181 := (iff #45 #180)
-#182 := [rewrite]: #181
-#185 := [monotonicity #182]: #184
-#264 := [monotonicity #185 #261]: #263
-#172 := (iff #38 #171)
-#173 := [rewrite]: #172
-#267 := [monotonicity #173 #264]: #266
-#175 := (iff #39 #174)
-#176 := [rewrite]: #175
-#270 := [monotonicity #176 #267]: #269
-#273 := [monotonicity #270]: #272
-#276 := [quant-intro #273]: #275
-#293 := [trans #276 #291]: #292
-#250 := [asserted]: #64
-#294 := [mp #250 #293]: #289
-#322 := [mp~ #294 #307]: #289
-#360 := [mp #322 #359]: #357
-#391 := [mp #360 #390]: #388
-#896 := [mp #391 #895]: #891
-#767 := (not #891)
-#747 := (or #767 #811)
-#818 := (* -1::Int 0::Int)
-#819 := (mod #818 #818)
-#820 := (+ #12 #819)
-#815 := (= #820 0::Int)
-#816 := (mod 0::Int 0::Int)
-#821 := (* -1::Int #816)
-#822 := (+ #12 #821)
-#817 := (= #822 0::Int)
-#840 := (>= 0::Int 0::Int)
-#823 := (<= 0::Int 0::Int)
-#664 := (or #823 #840)
-#665 := (not #664)
-#666 := (or #823 #823)
-#808 := (not #666)
-#809 := (or #808 #665)
-#810 := (ite #809 #817 #815)
-#805 := (= 0::Int 0::Int)
-#806 := (ite #805 #811 #810)
-#812 := (= 0::Int #12)
-#813 := (ite #805 #812 #806)
-#748 := (or #767 #813)
-#751 := (iff #748 #747)
-#753 := (iff #747 #747)
-#754 := [rewrite]: #753
-#766 := (iff #813 #811)
-#1 := true
-#775 := (ite true #811 #811)
-#764 := (iff #775 #811)
-#765 := [rewrite]: #764
-#761 := (iff #813 #775)
-#774 := (iff #806 #811)
-#776 := (+ #12 #816)
-#789 := (= #776 0::Int)
-#768 := (ite true #811 #789)
-#772 := (iff #768 #811)
-#773 := [rewrite]: #772
-#769 := (iff #806 #768)
-#777 := (iff #810 #789)
-#791 := (ite false #817 #789)
-#782 := (iff #791 #789)
-#783 := [rewrite]: #782
-#780 := (iff #810 #791)
-#790 := (iff #815 #789)
-#778 := (= #820 #776)
-#787 := (= #819 #816)
-#798 := (= #818 0::Int)
-#785 := [rewrite]: #798
-#779 := [monotonicity #785 #785]: #787
-#788 := [monotonicity #779]: #778
-#786 := [monotonicity #788]: #790
-#797 := (iff #809 false)
-#700 := (or false false)
-#703 := (iff #700 false)
-#704 := [rewrite]: #703
-#701 := (iff #809 #700)
-#699 := (iff #665 false)
-#488 := (not true)
-#847 := (iff #488 false)
-#850 := [rewrite]: #847
-#696 := (iff #665 #488)
-#796 := (iff #664 true)
-#800 := (or true true)
-#801 := (iff #800 true)
-#804 := [rewrite]: #801
-#792 := (iff #664 #800)
-#846 := (iff #840 true)
-#848 := [rewrite]: #846
-#646 := (iff #823 true)
-#799 := [rewrite]: #646
-#793 := [monotonicity #799 #848]: #792
-#681 := [trans #793 #804]: #796
-#698 := [monotonicity #681]: #696
-#692 := [trans #698 #850]: #699
-#795 := (iff #808 false)
-#688 := (iff #808 #488)
-#686 := (iff #666 true)
-#802 := (iff #666 #800)
-#803 := [monotonicity #799 #799]: #802
-#687 := [trans #803 #804]: #686
-#647 := [monotonicity #687]: #688
-#697 := [trans #647 #850]: #795
-#702 := [monotonicity #697 #692]: #701
-#794 := [trans #702 #704]: #797
-#781 := [monotonicity #794 #786]: #780
-#784 := [trans #781 #783]: #777
-#807 := (iff #805 true)
-#814 := [rewrite]: #807
-#771 := [monotonicity #814 #784]: #769
-#770 := [trans #771 #773]: #774
-#643 := (iff #812 #811)
-#645 := [rewrite]: #643
-#762 := [monotonicity #814 #645 #770]: #761
-#763 := [trans #762 #765]: #766
-#752 := [monotonicity #763]: #751
-#755 := [trans #752 #754]: #751
-#750 := [quant-inst #10 #10]: #748
-#756 := [mp #750 #755]: #747
-#758 := [unit-resolution #756 #896]: #811
-#759 := [monotonicity #758]: #15
+#178 := (iff #64 #177)
+#175 := (iff #63 #174)
+#172 := (= #62 #171)
+#169 := (= #61 #168)
+#166 := (= #60 #165)
+#163 := (= #59 #160)
+#157 := (- #154)
+#161 := (= #157 #160)
+#162 := [rewrite]: #161
+#158 := (= #59 #157)
+#155 := (= #58 #154)
+#136 := (= #49 #135)
+#137 := [rewrite]: #136
+#133 := (= #48 #132)
+#134 := [rewrite]: #133
+#156 := [monotonicity #134 #137]: #155
+#159 := [monotonicity #156]: #158
+#164 := [trans #159 #162]: #163
+#129 := (iff #46 #128)
+#126 := (iff #45 #125)
+#111 := (iff #42 #110)
+#112 := [rewrite]: #111
+#118 := (iff #44 #117)
+#122 := (iff #117 #117)
+#120 := (iff #116 #116)
+#121 := [rewrite]: #120
+#123 := [monotonicity #121]: #122
+#119 := [rewrite]: #118
+#124 := [trans #119 #123]: #118
+#127 := [monotonicity #124 #112]: #126
+#114 := (iff #43 #113)
+#107 := (iff #41 #106)
+#108 := [rewrite]: #107
+#115 := [monotonicity #108 #112]: #114
+#130 := [monotonicity #115 #127]: #129
+#167 := [monotonicity #130 #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [monotonicity #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [quant-intro #176]: #178
+#71 := [asserted]: #64
+#180 := [mp #71 #179]: #177
+#261 := [mp #180 #260]: #258
+#284 := [mp~ #261 #283]: #258
+#324 := [mp #284 #323]: #321
+#355 := [mp #324 #354]: #352
+#802 := [mp #355 #801]: #797
+#658 := (not #797)
+#659 := (or #658 #461)
+#734 := (* -1::Int 1::Int)
+#730 := (* -1::Int 0::Int)
+#731 := (mod #730 #734)
+#735 := (+ #12 #731)
+#724 := (= #735 0::Int)
+#454 := (mod 0::Int 1::Int)
+#732 := (* -1::Int #454)
+#733 := (+ #12 #732)
+#448 := (= #733 0::Int)
+#740 := (<= 1::Int 0::Int)
+#550 := (>= 0::Int 0::Int)
+#451 := (or #550 #740)
+#452 := (not #451)
+#736 := (<= 0::Int 0::Int)
+#737 := (or #736 #740)
+#741 := (not #737)
+#453 := (or #741 #452)
+#725 := (if #453 #448 #724)
+#462 := (= 0::Int 0::Int)
+#726 := (if #462 #461 #725)
+#739 := (= 1::Int 0::Int)
+#721 := (if #739 #461 #726)
+#660 := (or #658 #721)
+#662 := (iff #660 #659)
+#664 := (iff #659 #659)
+#665 := [rewrite]: #664
+#656 := (iff #721 #461)
+#675 := (if false #461 #461)
+#679 := (iff #675 #461)
+#680 := [rewrite]: #679
+#653 := (iff #721 #675)
+#669 := (iff #726 #461)
+#1 := true
+#667 := (if true #461 #461)
+#671 := (iff #667 #461)
+#672 := [rewrite]: #671
+#668 := (iff #726 #667)
+#676 := (iff #725 #461)
+#677 := (iff #725 #675)
+#690 := (iff #724 #461)
+#689 := (= #735 #12)
+#607 := (+ #12 0::Int)
+#610 := (= #607 #12)
+#703 := [rewrite]: #610
+#687 := (= #735 #607)
+#697 := (= #731 0::Int)
+#684 := (mod 0::Int -1::Int)
+#696 := (= #684 0::Int)
+#692 := [rewrite]: #696
+#694 := (= #731 #684)
+#685 := (= #734 -1::Int)
+#682 := [rewrite]: #685
+#604 := (= #730 0::Int)
+#605 := [rewrite]: #604
+#695 := [monotonicity #605 #682]: #694
+#686 := [trans #695 #692]: #697
+#688 := [monotonicity #686]: #687
+#683 := [trans #688 #703]: #689
+#674 := [monotonicity #683]: #690
+#691 := (iff #448 #461)
+#700 := (= #733 #12)
+#608 := (= #733 #607)
+#598 := (= #732 0::Int)
+#587 := (= #732 #730)
+#699 := (= #454 0::Int)
+#702 := [rewrite]: #699
+#602 := [monotonicity #702]: #587
+#606 := [trans #602 #605]: #598
+#609 := [monotonicity #606]: #608
+#704 := [trans #609 #703]: #700
+#693 := [monotonicity #704]: #691
+#603 := (iff #453 false)
+#592 := (or false false)
+#553 := (iff #592 false)
+#701 := [rewrite]: #553
+#593 := (iff #453 #592)
+#707 := (iff #452 false)
+#419 := (not true)
+#744 := (iff #419 false)
+#407 := [rewrite]: #744
+#708 := (iff #452 #419)
+#705 := (iff #451 true)
+#714 := (or true false)
+#717 := (iff #714 true)
+#711 := [rewrite]: #717
+#551 := (iff #451 #714)
+#571 := (iff #740 false)
+#572 := [rewrite]: #571
+#423 := (iff #550 true)
+#759 := [rewrite]: #423
+#552 := [monotonicity #759 #572]: #551
+#706 := [trans #552 #711]: #705
+#709 := [monotonicity #706]: #708
+#710 := [trans #709 #407]: #707
+#720 := (iff #741 false)
+#719 := (iff #741 #419)
+#712 := (iff #737 true)
+#715 := (iff #737 #714)
+#729 := (iff #736 true)
+#570 := [rewrite]: #729
+#716 := [monotonicity #570 #572]: #715
+#718 := [trans #716 #711]: #712
+#713 := [monotonicity #718]: #719
+#549 := [trans #713 #407]: #720
+#594 := [monotonicity #549 #710]: #593
+#698 := [trans #594 #701]: #603
+#678 := [monotonicity #698 #693 #674]: #677
+#681 := [trans #678 #680]: #676
+#728 := (iff #462 true)
+#723 := [rewrite]: #728
+#670 := [monotonicity #723 #681]: #668
+#673 := [trans #670 #672]: #669
+#722 := (iff #739 false)
+#727 := [rewrite]: #722
+#654 := [monotonicity #727 #673]: #653
+#657 := [trans #654 #680]: #656
+#663 := [monotonicity #657]: #662
+#655 := [trans #663 #665]: #662
+#661 := [quant-inst #9 #11]: #660
+#666 := [mp #661 #655]: #659
+#645 := [unit-resolution #666 #802]: #461
+#647 := [monotonicity #645]: #15
 #16 := (not #15)
-#84 := [asserted]: #16
-[unit-resolution #84 #759]: false
-unsat
-4544bd7f1d69a8c650d4127827c1814d67919bb5 334 0
+#66 := [asserted]: #16
+[unit-resolution #66 #647]: false
+c3b392a5be27990617a5e1dba37905919a3d03ec 311 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int S3)
+#13 := 0::Int
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 0::Int)
 decl f5 :: (-> S4 Int Int)
-#14 := 0::Int
+#9 := 1::Int
 decl f6 :: (-> S5 Int S4)
-decl f8 :: (-> S6 S3 Int)
-decl f10 :: S3
-#11 := f10
-decl f9 :: S6
-#10 := f9
-#12 := (f8 f9 f10)
 decl f7 :: S5
-#9 := f7
-#13 := (f6 f7 #12)
-#15 := (f5 #13 0::Int)
-decl f4 :: S2
-#8 := f4
-#16 := (f3 f4 #15)
-#86 := (= f10 #16)
-#457 := (f3 f4 #12)
-#792 := (= #457 #16)
-#791 := (= #16 #457)
-#788 := (= #15 #12)
-#838 := (= #12 #15)
+#8 := f7
+#10 := (f6 f7 1::Int)
+#11 := (f5 #10 1::Int)
+#12 := (f3 f4 #11)
+#15 := (= #12 #14)
+#462 := (= #11 0::Int)
+#23 := (:var 0 Int)
+#35 := (:var 1 Int)
+#55 := (f6 f7 #35)
+#56 := (f5 #55 #23)
+#796 := (pattern #56)
+#131 := -1::Int
+#135 := (* -1::Int #23)
+#132 := (* -1::Int #35)
+#154 := (mod #132 #135)
+#345 := (+ #56 #154)
+#346 := (= #345 0::Int)
+#57 := (mod #35 #23)
+#342 := (* -1::Int #57)
+#343 := (+ #56 #342)
+#344 := (= #343 0::Int)
+#109 := (<= #23 0::Int)
+#221 := (>= #35 0::Int)
+#289 := (or #221 #109)
+#290 := (not #289)
+#105 := (<= #35 0::Int)
+#285 := (or #105 #109)
+#286 := (not #285)
+#293 := (or #286 #290)
+#347 := (if #293 #344 #346)
+#341 := (= #56 0::Int)
+#38 := (= #35 0::Int)
+#348 := (if #38 #341 #347)
+#340 := (= #56 #35)
+#39 := (= #23 0::Int)
+#349 := (if #39 #340 #348)
+#797 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #796) #349)
+#352 := (forall (vars (?v0 Int) (?v1 Int)) #349)
+#800 := (iff #352 #797)
+#798 := (iff #349 #349)
+#799 := [refl]: #798
+#801 := [quant-intro #799]: #800
+#160 := (* -1::Int #154)
+#309 := (if #293 #57 #160)
+#312 := (if #38 0::Int #309)
+#315 := (if #39 #35 #312)
+#318 := (= #56 #315)
+#321 := (forall (vars (?v0 Int) (?v1 Int)) #318)
+#353 := (iff #321 #352)
+#350 := (iff #318 #349)
+#351 := [rewrite]: #350
+#354 := [quant-intro #351]: #353
+#110 := (not #109)
+#224 := (not #221)
+#227 := (and #224 #110)
+#106 := (not #105)
+#113 := (and #106 #110)
+#230 := (or #113 #227)
+#246 := (if #230 #57 #160)
+#249 := (if #38 0::Int #246)
+#252 := (if #39 #35 #249)
+#255 := (= #56 #252)
+#258 := (forall (vars (?v0 Int) (?v1 Int)) #255)
+#322 := (iff #258 #321)
+#319 := (iff #255 #318)
+#316 := (= #252 #315)
+#313 := (= #249 #312)
+#310 := (= #246 #309)
+#294 := (iff #230 #293)
+#291 := (iff #227 #290)
+#292 := [rewrite]: #291
+#287 := (iff #113 #286)
+#288 := [rewrite]: #287
+#295 := [monotonicity #288 #292]: #294
+#311 := [monotonicity #295]: #310
+#314 := [monotonicity #311]: #313
+#317 := [monotonicity #314]: #316
+#320 := [monotonicity #317]: #319
+#323 := [quant-intro #320]: #322
+#282 := (~ #258 #258)
+#280 := (~ #255 #255)
+#281 := [refl]: #280
+#283 := [nnf-pos #281]: #282
+#116 := (<= 0::Int #35)
+#117 := (not #116)
+#125 := (and #117 #110)
+#128 := (or #113 #125)
+#165 := (if #128 #57 #160)
+#168 := (if #38 0::Int #165)
+#171 := (if #39 #35 #168)
+#174 := (= #56 #171)
+#177 := (forall (vars (?v0 Int) (?v1 Int)) #174)
+#259 := (iff #177 #258)
+#256 := (iff #174 #255)
+#253 := (= #171 #252)
+#250 := (= #168 #249)
+#247 := (= #165 #246)
+#231 := (iff #128 #230)
+#228 := (iff #125 #227)
+#225 := (iff #117 #224)
+#222 := (iff #116 #221)
+#223 := [rewrite]: #222
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#248 := [monotonicity #232]: #247
+#251 := [monotonicity #248]: #250
+#254 := [monotonicity #251]: #253
+#257 := [monotonicity #254]: #256
+#260 := [quant-intro #257]: #259
+#49 := (- #23)
+#48 := (- #35)
+#58 := (mod #48 #49)
+#59 := (- #58)
+#42 := (< 0::Int #23)
+#44 := (< #35 0::Int)
+#45 := (and #44 #42)
+#41 := (< 0::Int #35)
+#43 := (and #41 #42)
+#46 := (or #43 #45)
+#60 := (if #46 #57 #59)
+#61 := (if #38 0::Int #60)
+#62 := (if #39 #35 #61)
+#63 := (= #56 #62)
+#64 := (forall (vars (?v0 Int) (?v1 Int)) #63)
+#178 := (iff #64 #177)
+#175 := (iff #63 #174)
+#172 := (= #62 #171)
+#169 := (= #61 #168)
+#166 := (= #60 #165)
+#163 := (= #59 #160)
+#157 := (- #154)
+#161 := (= #157 #160)
+#162 := [rewrite]: #161
+#158 := (= #59 #157)
+#155 := (= #58 #154)
+#136 := (= #49 #135)
+#137 := [rewrite]: #136
+#133 := (= #48 #132)
+#134 := [rewrite]: #133
+#156 := [monotonicity #134 #137]: #155
+#159 := [monotonicity #156]: #158
+#164 := [trans #159 #162]: #163
+#129 := (iff #46 #128)
+#126 := (iff #45 #125)
+#111 := (iff #42 #110)
+#112 := [rewrite]: #111
+#118 := (iff #44 #117)
+#122 := (iff #117 #117)
+#120 := (iff #116 #116)
+#121 := [rewrite]: #120
+#123 := [monotonicity #121]: #122
+#119 := [rewrite]: #118
+#124 := [trans #119 #123]: #118
+#127 := [monotonicity #124 #112]: #126
+#114 := (iff #43 #113)
+#107 := (iff #41 #106)
+#108 := [rewrite]: #107
+#115 := [monotonicity #108 #112]: #114
+#130 := [monotonicity #115 #127]: #129
+#167 := [monotonicity #130 #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [monotonicity #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [quant-intro #176]: #178
+#71 := [asserted]: #64
+#180 := [mp #71 #179]: #177
+#261 := [mp #180 #260]: #258
+#284 := [mp~ #261 #283]: #258
+#324 := [mp #284 #323]: #321
+#355 := [mp #324 #354]: #352
+#802 := [mp #355 #801]: #797
+#662 := (not #797)
+#663 := (or #662 #462)
+#730 := (* -1::Int 1::Int)
+#734 := (mod #730 #730)
+#731 := (+ #11 #734)
+#735 := (= #731 0::Int)
+#454 := (mod 1::Int 1::Int)
+#732 := (* -1::Int #454)
+#733 := (+ #11 #732)
+#448 := (= #733 0::Int)
+#736 := (<= 1::Int 0::Int)
+#741 := (>= 1::Int 0::Int)
+#451 := (or #741 #736)
+#452 := (not #451)
+#740 := (or #736 #736)
+#737 := (not #740)
+#453 := (or #737 #452)
+#724 := (if #453 #448 #735)
+#739 := (= 1::Int 0::Int)
+#725 := (if #739 #462 #724)
+#461 := (= #11 1::Int)
+#726 := (if #739 #461 #725)
+#664 := (or #662 #726)
+#655 := (iff #664 #663)
+#644 := (iff #663 #663)
+#645 := [rewrite]: #644
+#660 := (iff #726 #462)
+#654 := (if false #461 #462)
+#658 := (iff #654 #462)
+#659 := [rewrite]: #658
+#656 := (iff #726 #654)
+#673 := (iff #725 #462)
+#668 := (if false #462 #462)
+#672 := (iff #668 #462)
+#669 := [rewrite]: #672
+#670 := (iff #725 #668)
+#681 := (iff #724 #462)
+#1 := true
+#677 := (if true #462 #462)
+#680 := (iff #677 #462)
+#676 := [rewrite]: #680
+#678 := (iff #724 #677)
+#674 := (iff #735 #462)
+#683 := (= #731 #11)
+#608 := (+ #11 0::Int)
+#703 := (= #608 #11)
+#700 := [rewrite]: #703
+#688 := (= #731 #608)
+#686 := (= #734 0::Int)
+#694 := (mod -1::Int -1::Int)
+#692 := (= #694 0::Int)
+#697 := [rewrite]: #692
+#695 := (= #734 #694)
+#682 := (= #730 -1::Int)
+#684 := [rewrite]: #682
+#696 := [monotonicity #684 #684]: #695
+#687 := [trans #696 #697]: #686
+#689 := [monotonicity #687]: #688
+#690 := [trans #689 #700]: #683
+#675 := [monotonicity #690]: #674
+#693 := (iff #448 #462)
+#704 := (= #733 #11)
+#609 := (= #733 #608)
+#606 := (= #732 0::Int)
+#587 := (* -1::Int 0::Int)
+#605 := (= #587 0::Int)
+#598 := [rewrite]: #605
+#602 := (= #732 #587)
+#699 := (= #454 0::Int)
+#702 := [rewrite]: #699
+#604 := [monotonicity #702]: #602
+#607 := [trans #604 #598]: #606
+#610 := [monotonicity #607]: #609
+#691 := [trans #610 #700]: #704
+#685 := [monotonicity #691]: #693
+#603 := (iff #453 true)
+#551 := (or true false)
+#706 := (iff #551 true)
+#708 := [rewrite]: #706
+#553 := (iff #453 #551)
+#593 := (iff #452 false)
+#419 := (not true)
+#744 := (iff #419 false)
+#407 := [rewrite]: #744
+#710 := (iff #452 #419)
+#709 := (iff #451 true)
+#552 := (iff #451 #551)
+#727 := (iff #736 false)
+#728 := [rewrite]: #727
+#720 := (iff #741 true)
+#549 := [rewrite]: #720
+#705 := [monotonicity #549 #728]: #552
+#707 := [trans #705 #708]: #709
+#592 := [monotonicity #707]: #710
+#594 := [trans #592 #407]: #593
+#719 := (iff #737 true)
+#716 := (not false)
+#712 := (iff #716 true)
+#718 := [rewrite]: #712
+#717 := (iff #737 #716)
+#714 := (iff #740 false)
+#723 := (or false false)
+#571 := (iff #723 false)
+#572 := [rewrite]: #571
+#729 := (iff #740 #723)
+#570 := [monotonicity #728 #728]: #729
+#715 := [trans #570 #572]: #714
+#711 := [monotonicity #715]: #717
+#713 := [trans #711 #718]: #719
+#701 := [monotonicity #713 #594]: #553
+#698 := [trans #701 #708]: #603
+#679 := [monotonicity #698 #685 #675]: #678
+#667 := [trans #679 #676]: #681
+#721 := (iff #739 false)
+#722 := [rewrite]: #721
+#671 := [monotonicity #722 #667]: #670
+#653 := [trans #671 #669]: #673
+#657 := [monotonicity #722 #653]: #656
+#661 := [trans #657 #659]: #660
+#666 := [monotonicity #661]: #655
+#647 := [trans #666 #645]: #655
+#665 := [quant-inst #9 #9]: #664
+#648 := [mp #665 #647]: #663
+#650 := [unit-resolution #648 #802]: #462
+#651 := [monotonicity #650]: #15
+#16 := (not #15)
+#66 := [asserted]: #16
+[unit-resolution #66 #651]: false
[phone]efc01fcf566cedf02a315f063404 322 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int S3)
+#14 := 0::Int
+decl f4 :: S2
+#7 := f4
+#15 := (f3 f4 0::Int)
+decl f5 :: (-> S4 Int Int)
+#11 := 1::Int
+decl f6 :: (-> S5 Int S4)
+#9 := 3::Int
+decl f7 :: S5
+#8 := f7
+#10 := (f6 f7 3::Int)
+#12 := (f5 #10 1::Int)
+#13 := (f3 f4 #12)
+#16 := (= #13 #15)
+#737 := (= #12 0::Int)
 #24 := (:var 0 Int)
 #36 := (:var 1 Int)
 #56 := (f6 f7 #36)
 #57 := (f5 #56 #24)
-#898 := (pattern #57)
-#194 := -1::Int
-#198 := (* -1::Int #24)
-#195 := (* -1::Int #36)
-#259 := (mod #195 #198)
-#389 := (+ #57 #259)
-#390 := (= #389 0::Int)
+#797 := (pattern #57)
+#132 := -1::Int
+#136 := (* -1::Int #24)
+#133 := (* -1::Int #36)
+#155 := (mod #133 #136)
+#346 := (+ #57 #155)
+#347 := (= #346 0::Int)
 #58 := (mod #36 #24)
-#386 := (* -1::Int #58)
-#387 := (+ #57 #386)
-#388 := (= #387 0::Int)
-#233 := (>= #36 0::Int)
-#226 := (<= #24 0::Int)
-#333 := (or #226 #233)
-#334 := (not #333)
-#222 := (<= #36 0::Int)
-#331 := (or #222 #226)
-#332 := (not #331)
-#337 := (or #332 #334)
-#391 := (ite #337 #388 #390)
-#385 := (= #57 0::Int)
+#343 := (* -1::Int #58)
+#344 := (+ #57 #343)
+#345 := (= #344 0::Int)
+#110 := (<= #24 0::Int)
+#222 := (>= #36 0::Int)
+#290 := (or #222 #110)
+#291 := (not #290)
+#106 := (<= #36 0::Int)
+#286 := (or #106 #110)
+#287 := (not #286)
+#294 := (or #287 #291)
+#348 := (if #294 #345 #347)
+#342 := (= #57 0::Int)
 #39 := (= #36 0::Int)
-#392 := (ite #39 #385 #391)
-#384 := (= #36 #57)
+#349 := (if #39 #342 #348)
+#341 := (= #57 #36)
 #40 := (= #24 0::Int)
-#393 := (ite #40 #384 #392)
-#899 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #898) #393)
-#396 := (forall (vars (?v0 Int) (?v1 Int)) #393)
-#902 := (iff #396 #899)
-#900 := (iff #393 #393)
-#901 := [refl]: #900
-#903 := [quant-intro #901]: #902
-#265 := (* -1::Int #259)
-#353 := (ite #337 #58 #265)
-#356 := (ite #39 0::Int #353)
-#359 := (ite #40 #36 #356)
-#362 := (= #57 #359)
-#365 := (forall (vars (?v0 Int) (?v1 Int)) #362)
-#397 := (iff #365 #396)
-#394 := (iff #362 #393)
-#395 := [rewrite]: #394
-#398 := [quant-intro #395]: #397
-#234 := (not #233)
-#227 := (not #226)
-#237 := (and #227 #234)
-#223 := (not #222)
-#230 := (and #223 #227)
-#240 := (or #230 #237)
-#285 := (ite #240 #58 #265)
-#288 := (ite #39 0::Int #285)
-#291 := (ite #40 #36 #288)
-#294 := (= #57 #291)
-#297 := (forall (vars (?v0 Int) (?v1 Int)) #294)
-#366 := (iff #297 #365)
-#363 := (iff #294 #362)
-#360 := (= #291 #359)
-#357 := (= #288 #356)
-#354 := (= #285 #353)
-#338 := (iff #240 #337)
-#335 := (iff #237 #334)
-#336 := [rewrite]: #335
-#316 := (iff #230 #332)
-#317 := [rewrite]: #316
-#339 := [monotonicity #317 #336]: #338
-#355 := [monotonicity #339]: #354
-#358 := [monotonicity #355]: #357
-#361 := [monotonicity #358]: #360
-#364 := [monotonicity #361]: #363
-#367 := [quant-intro #364]: #366
-#314 := (~ #297 #297)
-#328 := (~ #294 #294)
-#329 := [refl]: #328
-#315 := [nnf-pos #329]: #314
-#50 := (- #24)
-#49 := (- #36)
-#59 := (mod #49 #50)
-#60 := (- #59)
-#43 := (< 0::Int #24)
-#45 := (< #36 0::Int)
-#46 := (and #45 #43)
-#42 := (< 0::Int #36)
-#44 := (and #42 #43)
-#47 := (or #44 #46)
-#61 := (ite #47 #58 #60)
-#62 := (ite #39 0::Int #61)
-#63 := (ite #40 #36 #62)
-#64 := (= #57 #63)
-#65 := (forall (vars (?v0 Int) (?v1 Int)) #64)
-#300 := (iff #65 #297)
-#188 := (and #43 #45)
-#191 := (or #44 #188)
-#270 := (ite #191 #58 #265)
-#179 := (= 0::Int #36)
-#273 := (ite #179 0::Int #270)
-#182 := (= 0::Int #24)
-#276 := (ite #182 #36 #273)
-#279 := (= #57 #276)
-#282 := (forall (vars (?v0 Int) (?v1 Int)) #279)
-#298 := (iff #282 #297)
-#295 := (iff #279 #294)
-#292 := (= #276 #291)
-#289 := (= #273 #288)
-#286 := (= #270 #285)
-#241 := (iff #191 #240)
-#238 := (iff #188 #237)
-#235 := (iff #45 #234)
-#236 := [rewrite]: #235
-#228 := (iff #43 #227)
-#229 := [rewrite]: #228
-#239 := [monotonicity #229 #236]: #238
-#231 := (iff #44 #230)
-#224 := (iff #42 #223)
-#225 := [rewrite]: #224
-#232 := [monotonicity #225 #229]: #231
-#242 := [monotonicity #232 #239]: #241
-#287 := [monotonicity #242]: #286
-#216 := (iff #179 #39)
-#217 := [rewrite]: #216
-#290 := [monotonicity #217 #287]: #289
-#218 := (iff #182 #40)
-#219 := [rewrite]: #218
-#293 := [monotonicity #219 #290]: #292
-#296 := [monotonicity #293]: #295
-#299 := [quant-intro #296]: #298
-#283 := (iff #65 #282)
-#280 := (iff #64 #279)
-#277 := (= #63 #276)
-#274 := (= #62 #273)
-#271 := (= #61 #270)
-#268 := (= #60 #265)
-#262 := (- #259)
-#266 := (= #262 #265)
-#267 := [rewrite]: #266
-#263 := (= #60 #262)
-#260 := (= #59 #259)
-#199 := (= #50 #198)
-#200 := [rewrite]: #199
-#196 := (= #49 #195)
-#197 := [rewrite]: #196
-#261 := [monotonicity #197 #200]: #260
-#264 := [monotonicity #261]: #263
-#269 := [trans #264 #267]: #268
-#192 := (iff #47 #191)
-#189 := (iff #46 #188)
-#190 := [rewrite]: #189
-#193 := [monotonicity #190]: #192
-#272 := [monotonicity #193 #269]: #271
-#180 := (iff #39 #179)
-#181 := [rewrite]: #180
-#275 := [monotonicity #181 #272]: #274
-#183 := (iff #40 #182)
-#184 := [rewrite]: #183
-#278 := [monotonicity #184 #275]: #277
-#281 := [monotonicity #278]: #280
-#284 := [quant-intro #281]: #283
-#301 := [trans #284 #299]: #300
-#258 := [asserted]: #65
-#302 := [mp #258 #301]: #297
-#330 := [mp~ #302 #315]: #297
-#368 := [mp #330 #367]: #365
-#399 := [mp #368 #398]: #396
-#904 := [mp #399 #903]: #899
-#806 := (not #899)
-#793 := (or #806 #838)
-#847 := (* -1::Int 0::Int)
-#853 := (* -1::Int #12)
-#491 := (mod #853 #847)
-#854 := (+ #15 #491)
-#856 := (= #854 0::Int)
-#496 := (mod #12 0::Int)
-#497 := (* -1::Int #496)
-#857 := (+ #15 #497)
-#855 := (= #857 0::Int)
-#858 := (>= #12 0::Int)
-#844 := (<= 0::Int 0::Int)
-#845 := (or #844 #858)
-#567 := (not #845)
-#568 := (<= #12 0::Int)
-#569 := (or #568 #844)
-#570 := (not #569)
-#463 := (or #570 #567)
-#840 := (ite #463 #855 #856)
-#841 := (= #15 0::Int)
-#563 := (= #12 0::Int)
-#564 := (ite #563 #841 #840)
-#842 := (= 0::Int 0::Int)
-#839 := (ite #842 #838 #564)
-#795 := (or #806 #839)
-#784 := (iff #795 #793)
-#796 := (iff #793 #793)
-#797 := [rewrite]: #796
-#805 := (iff #839 #838)
-#808 := (mod #853 0::Int)
-#809 := (+ #15 #808)
-#695 := (= #809 0::Int)
-#706 := (ite #563 #841 #695)
-#1 := true
-#708 := (ite true #838 #706)
-#711 := (iff #708 #838)
-#712 := [rewrite]: #711
-#709 := (iff #839 #708)
-#707 := (iff #564 #706)
-#689 := (iff #840 #695)
-#803 := (ite false #855 #695)
-#801 := (iff #803 #695)
-#804 := [rewrite]: #801
-#705 := (iff #840 #803)
-#696 := (iff #856 #695)
-#812 := (= #854 #809)
-#810 := (= #491 #808)
-#654 := (= #847 0::Int)
-#807 := [rewrite]: #654
-#811 := [monotonicity #807]: #810
-#694 := [monotonicity #811]: #812
-#655 := [monotonicity #694]: #696
-#651 := (iff #463 false)
-#814 := (or false false)
-#815 := (iff #814 false)
-#822 := [rewrite]: #815
-#820 := (iff #463 #814)
-#819 := (iff #567 false)
-#837 := (not true)
-#828 := (iff #837 false)
-#823 := [rewrite]: #828
-#817 := (iff #567 #837)
-#674 := (iff #845 true)
-#830 := (or true #858)
-#672 := (iff #830 true)
-#673 := [rewrite]: #672
-#825 := (iff #845 #830)
-#554 := (iff #844 true)
-#555 := [rewrite]: #554
-#831 := [monotonicity #555]: #825
-#816 := [trans #831 #673]: #674
-#818 := [monotonicity #816]: #817
-#813 := [trans #818 #823]: #819
-#824 := (iff #570 false)
-#826 := (iff #570 #837)
-#836 := (iff #569 true)
-#556 := (or #568 true)
-#550 := (iff #556 true)
-#832 := [rewrite]: #550
-#834 := (iff #569 #556)
-#835 := [monotonicity #555]: #834
-#833 := [trans #835 #832]: #836
-#827 := [monotonicity #833]: #826
-#829 := [trans #827 #823]: #824
-#821 := [monotonicity #829 #813]: #820
-#653 := [trans #821 #822]: #651
-#800 := [monotonicity #653 #655]: #705
-#704 := [trans #800 #804]: #689
-#700 := [monotonicity #704]: #707
-#843 := (iff #842 true)
-#553 := [rewrite]: #843
-#710 := [monotonicity #553 #700]: #709
-#802 := [trans #710 #712]: #805
-#786 := [monotonicity #802]: #784
-#798 := [trans #786 #797]: #784
-#787 := [quant-inst #12 #14]: #795
-#794 := [mp #787 #798]: #793
-#799 := [unit-resolution #794 #904]: #838
-#789 := [symm #799]: #788
-#785 := [monotonicity #789]: #791
-#776 := [symm #785]: #792
-#542 := (= f10 #457)
-#19 := (:var 0 S3)
-#20 := (f8 f9 #19)
-#871 := (pattern #20)
-#21 := (f3 f4 #20)
-#93 := (= #19 #21)
-#872 := (forall (vars (?v0 S3)) (:pat #871) #93)
-#97 := (forall (vars (?v0 S3)) #93)
-#875 := (iff #97 #872)
-#873 := (iff #93 #93)
-#874 := [refl]: #873
-#876 := [quant-intro #874]: #875
-#320 := (~ #97 #97)
-#318 := (~ #93 #93)
-#319 := [refl]: #318
-#321 := [nnf-pos #319]: #320
-#22 := (= #21 #19)
-#23 := (forall (vars (?v0 S3)) #22)
-#98 := (iff #23 #97)
-#95 := (iff #22 #93)
-#96 := [rewrite]: #95
-#99 := [quant-intro #96]: #98
-#92 := [asserted]: #23
-#102 := [mp #92 #99]: #97
-#306 := [mp~ #102 #321]: #97
-#877 := [mp #306 #876]: #872
-#535 := (not #872)
-#546 := (or #535 #542)
-#547 := [quant-inst #11]: #546
-#790 := [unit-resolution #547 #877]: #542
-#777 := [trans #790 #776]: #86
-#89 := (not #86)
-#17 := (= #16 f10)
-#18 := (not #17)
-#90 := (iff #18 #89)
-#87 := (iff #17 #86)
-#88 := [rewrite]: #87
-#91 := [monotonicity #88]: #90
-#85 := [asserted]: #18
-#94 := [mp #85 #91]: #89
-[unit-resolution #94 #777]: false
-unsat
-a5014a162e416bc201fb7db6aadb8a2975a31d13 316 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#10 := 0::Int
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 0::Int)
-decl f5 :: (-> S4 Int Int)
-#12 := 1::Int
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#9 := f7
-#11 := (f6 f7 0::Int)
-#13 := (f5 #11 1::Int)
-#14 := (f3 f4 #13)
-#16 := (= #14 #15)
-#812 := (= #13 0::Int)
-#24 := (:var 0 Int)
-#36 := (:var 1 Int)
-#56 := (f6 f7 #36)
-#57 := (f5 #56 #24)
-#890 := (pattern #57)
-#187 := -1::Int
-#191 := (* -1::Int #24)
-#188 := (* -1::Int #36)
-#252 := (mod #188 #191)
-#382 := (+ #57 #252)
-#383 := (= #382 0::Int)
-#58 := (mod #36 #24)
-#379 := (* -1::Int #58)
-#380 := (+ #57 #379)
-#381 := (= #380 0::Int)
-#226 := (>= #36 0::Int)
-#219 := (<= #24 0::Int)
-#326 := (or #219 #226)
-#327 := (not #326)
-#215 := (<= #36 0::Int)
-#324 := (or #215 #219)
-#325 := (not #324)
-#330 := (or #325 #327)
-#384 := (ite #330 #381 #383)
-#378 := (= #57 0::Int)
-#39 := (= #36 0::Int)
-#385 := (ite #39 #378 #384)
-#377 := (= #36 #57)
-#40 := (= #24 0::Int)
-#386 := (ite #40 #377 #385)
-#891 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #890) #386)
-#389 := (forall (vars (?v0 Int) (?v1 Int)) #386)
-#894 := (iff #389 #891)
-#892 := (iff #386 #386)
-#893 := [refl]: #892
-#895 := [quant-intro #893]: #894
-#258 := (* -1::Int #252)
-#346 := (ite #330 #58 #258)
-#349 := (ite #39 0::Int #346)
-#352 := (ite #40 #36 #349)
-#355 := (= #57 #352)
-#358 := (forall (vars (?v0 Int) (?v1 Int)) #355)
-#390 := (iff #358 #389)
-#387 := (iff #355 #386)
-#388 := [rewrite]: #387
-#391 := [quant-intro #388]: #390
-#227 := (not #226)
-#220 := (not #219)
-#230 := (and #220 #227)
-#216 := (not #215)
-#223 := (and #216 #220)
-#233 := (or #223 #230)
-#278 := (ite #233 #58 #258)
-#281 := (ite #39 0::Int #278)
-#284 := (ite #40 #36 #281)
-#287 := (= #57 #284)
-#290 := (forall (vars (?v0 Int) (?v1 Int)) #287)
-#359 := (iff #290 #358)
-#356 := (iff #287 #355)
-#353 := (= #284 #352)
-#350 := (= #281 #349)
-#347 := (= #278 #346)
-#331 := (iff #233 #330)
-#328 := (iff #230 #327)
-#329 := [rewrite]: #328
-#309 := (iff #223 #325)
-#310 := [rewrite]: #309
-#332 := [monotonicity #310 #329]: #331
-#348 := [monotonicity #332]: #347
-#351 := [monotonicity #348]: #350
-#354 := [monotonicity #351]: #353
-#357 := [monotonicity #354]: #356
-#360 := [quant-intro #357]: #359
-#307 := (~ #290 #290)
-#321 := (~ #287 #287)
-#322 := [refl]: #321
-#308 := [nnf-pos #322]: #307
+#350 := (if #40 #341 #349)
+#798 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #797) #350)
+#353 := (forall (vars (?v0 Int) (?v1 Int)) #350)
+#801 := (iff #353 #798)
+#799 := (iff #350 #350)
+#800 := [refl]: #799
+#802 := [quant-intro #800]: #801
+#161 := (* -1::Int #155)
+#310 := (if #294 #58 #161)
+#313 := (if #39 0::Int #310)
+#316 := (if #40 #36 #313)
+#319 := (= #57 #316)
+#322 := (forall (vars (?v0 Int) (?v1 Int)) #319)
+#354 := (iff #322 #353)
+#351 := (iff #319 #350)
+#352 := [rewrite]: #351
+#355 := [quant-intro #352]: #354
+#111 := (not #110)
+#225 := (not #222)
+#228 := (and #225 #111)
+#107 := (not #106)
+#114 := (and #107 #111)
+#231 := (or #114 #228)
+#247 := (if #231 #58 #161)
+#250 := (if #39 0::Int #247)
+#253 := (if #40 #36 #250)
+#256 := (= #57 #253)
+#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
+#323 := (iff #259 #322)
+#320 := (iff #256 #319)
+#317 := (= #253 #316)
+#314 := (= #250 #313)
+#311 := (= #247 #310)
+#295 := (iff #231 #294)
+#292 := (iff #228 #291)
+#293 := [rewrite]: #292
+#288 := (iff #114 #287)
+#289 := [rewrite]: #288
+#296 := [monotonicity #289 #293]: #295
+#312 := [monotonicity #296]: #311
+#315 := [monotonicity #312]: #314
+#318 := [monotonicity #315]: #317
+#321 := [monotonicity #318]: #320
+#324 := [quant-intro #321]: #323
+#283 := (~ #259 #259)
+#281 := (~ #256 #256)
+#282 := [refl]: #281
+#284 := [nnf-pos #282]: #283
+#117 := (<= 0::Int #36)
+#118 := (not #117)
+#126 := (and #118 #111)
+#129 := (or #114 #126)
+#166 := (if #129 #58 #161)
+#169 := (if #39 0::Int #166)
+#172 := (if #40 #36 #169)
+#175 := (= #57 #172)
+#178 := (forall (vars (?v0 Int) (?v1 Int)) #175)
+#260 := (iff #178 #259)
+#257 := (iff #175 #256)
+#254 := (= #172 #253)
+#251 := (= #169 #250)
+#248 := (= #166 #247)
+#232 := (iff #129 #231)
+#229 := (iff #126 #228)
+#226 := (iff #118 #225)
+#223 := (iff #117 #222)
+#224 := [rewrite]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#249 := [monotonicity #233]: #248
+#252 := [monotonicity #249]: #251
+#255 := [monotonicity #252]: #254
+#258 := [monotonicity #255]: #257
+#261 := [quant-intro #258]: #260
 #50 := (- #24)
 #49 := (- #36)
 #59 := (mod #49 #50)
@@ -17905,632 +17763,346 @@
 #42 := (< 0::Int #36)
 #44 := (and #42 #43)
 #47 := (or #44 #46)
-#61 := (ite #47 #58 #60)
-#62 := (ite #39 0::Int #61)
-#63 := (ite #40 #36 #62)
+#61 := (if #47 #58 #60)
+#62 := (if #39 0::Int #61)
+#63 := (if #40 #36 #62)
 #64 := (= #57 #63)
 #65 := (forall (vars (?v0 Int) (?v1 Int)) #64)
-#293 := (iff #65 #290)
-#181 := (and #43 #45)
-#184 := (or #44 #181)
-#263 := (ite #184 #58 #258)
-#172 := (= 0::Int #36)
-#266 := (ite #172 0::Int #263)
-#175 := (= 0::Int #24)
-#269 := (ite #175 #36 #266)
-#272 := (= #57 #269)
-#275 := (forall (vars (?v0 Int) (?v1 Int)) #272)
-#291 := (iff #275 #290)
-#288 := (iff #272 #287)
-#285 := (= #269 #284)
-#282 := (= #266 #281)
-#279 := (= #263 #278)
-#234 := (iff #184 #233)
-#231 := (iff #181 #230)
-#228 := (iff #45 #227)
-#229 := [rewrite]: #228
-#221 := (iff #43 #220)
-#222 := [rewrite]: #221
-#232 := [monotonicity #222 #229]: #231
-#224 := (iff #44 #223)
-#217 := (iff #42 #216)
-#218 := [rewrite]: #217
-#225 := [monotonicity #218 #222]: #224
-#235 := [monotonicity #225 #232]: #234
-#280 := [monotonicity #235]: #279
-#209 := (iff #172 #39)
-#210 := [rewrite]: #209
-#283 := [monotonicity #210 #280]: #282
-#211 := (iff #175 #40)
-#212 := [rewrite]: #211
-#286 := [monotonicity #212 #283]: #285
-#289 := [monotonicity #286]: #288
-#292 := [quant-intro #289]: #291
-#276 := (iff #65 #275)
-#273 := (iff #64 #272)
-#270 := (= #63 #269)
-#267 := (= #62 #266)
-#264 := (= #61 #263)
-#261 := (= #60 #258)
-#255 := (- #252)
-#259 := (= #255 #258)
-#260 := [rewrite]: #259
-#256 := (= #60 #255)
-#253 := (= #59 #252)
-#192 := (= #50 #191)
-#193 := [rewrite]: #192
-#189 := (= #49 #188)
-#190 := [rewrite]: #189
-#254 := [monotonicity #190 #193]: #253
-#257 := [monotonicity #254]: #256
-#262 := [trans #257 #260]: #261
-#185 := (iff #47 #184)
-#182 := (iff #46 #181)
-#183 := [rewrite]: #182
-#186 := [monotonicity #183]: #185
-#265 := [monotonicity #186 #262]: #264
-#173 := (iff #39 #172)
-#174 := [rewrite]: #173
-#268 := [monotonicity #174 #265]: #267
-#176 := (iff #40 #175)
-#177 := [rewrite]: #176
-#271 := [monotonicity #177 #268]: #270
-#274 := [monotonicity #271]: #273
-#277 := [quant-intro #274]: #276
-#294 := [trans #277 #292]: #293
-#251 := [asserted]: #65
-#295 := [mp #251 #294]: #290
-#323 := [mp~ #295 #308]: #290
-#361 := [mp #323 #360]: #358
-#392 := [mp #361 #391]: #389
-#896 := [mp #392 #895]: #891
-#735 := (not #891)
-#736 := (or #735 #812)
-#819 := (* -1::Int 1::Int)
-#820 := (* -1::Int 0::Int)
-#815 := (mod #820 #819)
-#816 := (+ #13 #815)
-#821 := (= #816 0::Int)
-#822 := (mod 0::Int 1::Int)
-#817 := (* -1::Int #822)
-#823 := (+ #13 #817)
-#664 := (= #823 0::Int)
-#841 := (>= 0::Int 0::Int)
-#665 := (<= 1::Int 0::Int)
-#666 := (or #665 #841)
-#808 := (not #666)
-#809 := (<= 0::Int 0::Int)
-#810 := (or #809 #665)
-#811 := (not #810)
-#805 := (or #811 #808)
-#806 := (ite #805 #664 #821)
-#813 := (= 0::Int 0::Int)
-#807 := (ite #813 #812 #806)
-#814 := (= 0::Int #13)
-#643 := (= 1::Int 0::Int)
-#645 := (ite #643 #814 #807)
-#731 := (or #735 #645)
-#710 := (iff #731 #736)
-#712 := (iff #736 #736)
-#605 := [rewrite]: #712
-#733 := (iff #645 #812)
-#759 := (ite false #812 #812)
-#738 := (iff #759 #812)
-#739 := [rewrite]: #738
-#729 := (iff #645 #759)
-#732 := (iff #807 #812)
-#1 := true
-#743 := (ite true #812 #812)
-#740 := (iff #743 #812)
-#746 := [rewrite]: #740
-#744 := (iff #807 #743)
-#741 := (iff #806 #812)
-#749 := (iff #806 #759)
-#757 := (iff #821 #812)
-#755 := (= #816 #13)
-#771 := (+ #13 0::Int)
-#774 := (= #771 #13)
-#770 := [rewrite]: #774
-#753 := (= #816 #771)
-#751 := (= #815 0::Int)
-#763 := (mod 0::Int -1::Int)
-#748 := (= #763 0::Int)
-#750 := [rewrite]: #748
-#767 := (= #815 #763)
-#765 := (= #819 -1::Int)
-#766 := [rewrite]: #765
-#777 := (= #820 0::Int)
-#784 := [rewrite]: #777
-#747 := [monotonicity #784 #766]: #767
-#752 := [trans #747 #750]: #751
-#754 := [monotonicity #752]: #753
-#756 := [trans #754 #770]: #755
-#758 := [monotonicity #756]: #757
-#762 := (iff #664 #812)
-#775 := (= #823 #13)
-#772 := (= #823 #771)
-#768 := (= #817 0::Int)
-#782 := (= #817 #820)
-#780 := (= #822 0::Int)
-#781 := [rewrite]: #780
-#783 := [monotonicity #781]: #782
-#769 := [trans #783 #784]: #768
-#773 := [monotonicity #769]: #772
-#761 := [trans #773 #770]: #775
-#764 := [monotonicity #761]: #762
-#786 := (iff #805 false)
-#776 := (or false false)
-#789 := (iff #776 false)
-#790 := [rewrite]: #789
-#778 := (iff #805 #776)
-#787 := (iff #808 false)
-#489 := (not true)
-#850 := (iff #489 false)
-#836 := [rewrite]: #850
-#798 := (iff #808 #489)
-#797 := (iff #666 true)
-#700 := (or false true)
-#703 := (iff #700 true)
-#704 := [rewrite]: #703
-#701 := (iff #666 #700)
-#848 := (iff #841 true)
-#488 := [rewrite]: #848
-#687 := (iff #665 false)
-#688 := [rewrite]: #687
-#702 := [monotonicity #688 #488]: #701
-#794 := [trans #702 #704]: #797
-#785 := [monotonicity #794]: #798
-#779 := [trans #785 #836]: #787
-#699 := (iff #811 false)
-#696 := (iff #811 #489)
-#796 := (iff #810 true)
-#647 := (or true false)
-#792 := (iff #647 true)
-#793 := [rewrite]: #792
-#795 := (iff #810 #647)
-#804 := (iff #809 true)
-#686 := [rewrite]: #804
-#697 := [monotonicity #686 #688]: #795
-#681 := [trans #697 #793]: #796
-#698 := [monotonicity #681]: #696
-#692 := [trans #698 #836]: #699
-#788 := [monotonicity #692 #779]: #778
-#791 := [trans #788 #790]: #786
-#760 := [monotonicity #791 #764 #758]: #749
-#742 := [trans #760 #739]: #741
-#803 := (iff #813 true)
-#801 := [rewrite]: #803
-#745 := [monotonicity #801 #742]: #744
-#728 := [trans #745 #746]: #732
-#800 := (iff #814 #812)
-#802 := [rewrite]: #800
-#646 := (iff #643 false)
-#799 := [rewrite]: #646
-#730 := [monotonicity #799 #802 #728]: #729
-#734 := [trans #730 #739]: #733
-#711 := [monotonicity #734]: #710
-#716 := [trans #711 #605]: #710
-#737 := [quant-inst #10 #12]: #731
-#717 := [mp #737 #716]: #736
-#723 := [unit-resolution #717 #896]: #812
-#719 := [monotonicity #723]: #16
+#179 := (iff #65 #178)
+#176 := (iff #64 #175)
+#173 := (= #63 #172)
+#170 := (= #62 #169)
+#167 := (= #61 #166)
+#164 := (= #60 #161)
+#158 := (- #155)
+#162 := (= #158 #161)
+#163 := [rewrite]: #162
+#159 := (= #60 #158)
+#156 := (= #59 #155)
+#137 := (= #50 #136)
+#138 := [rewrite]: #137
+#134 := (= #49 #133)
+#135 := [rewrite]: #134
+#157 := [monotonicity #135 #138]: #156
+#160 := [monotonicity #157]: #159
+#165 := [trans #160 #163]: #164
+#130 := (iff #47 #129)
+#127 := (iff #46 #126)
+#112 := (iff #43 #111)
+#113 := [rewrite]: #112
+#119 := (iff #45 #118)
+#123 := (iff #118 #118)
+#121 := (iff #117 #117)
+#122 := [rewrite]: #121
+#124 := [monotonicity #122]: #123
+#120 := [rewrite]: #119
+#125 := [trans #120 #124]: #119
+#128 := [monotonicity #125 #113]: #127
+#115 := (iff #44 #114)
+#108 := (iff #42 #107)
+#109 := [rewrite]: #108
+#116 := [monotonicity #109 #113]: #115
+#131 := [monotonicity #116 #128]: #130
+#168 := [monotonicity #131 #165]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#180 := [quant-intro #177]: #179
+#72 := [asserted]: #65
+#181 := [mp #72 #180]: #178
+#262 := [mp #181 #261]: #259
+#285 := [mp~ #262 #284]: #259
+#325 := [mp #285 #324]: #322
+#356 := [mp #325 #355]: #353
+#803 := [mp #356 #802]: #798
+#650 := (not #798)
+#651 := (or #650 #737)
+#736 := (* -1::Int 1::Int)
+#732 := (* -1::Int 3::Int)
+#725 := (mod #732 #736)
+#726 := (+ #12 #725)
+#727 := (= #726 0::Int)
+#734 := (mod 3::Int 1::Int)
+#449 := (* -1::Int #734)
+#731 := (+ #12 #449)
+#735 := (= #731 0::Int)
+#738 := (<= 1::Int 0::Int)
+#453 := (>= 3::Int 0::Int)
+#454 := (or #453 #738)
+#455 := (not #454)
+#741 := (<= 3::Int 0::Int)
+#742 := (or #741 #738)
+#452 := (not #742)
+#733 := (or #452 #455)
+#722 := (if #733 #735 #727)
+#463 := (= 3::Int 0::Int)
+#723 := (if #463 #737 #722)
+#462 := (= #12 3::Int)
+#740 := (= 1::Int 0::Int)
+#728 := (if #740 #462 #723)
+#652 := (or #650 #728)
+#653 := (iff #652 #651)
+#635 := (iff #651 #651)
+#636 := [rewrite]: #635
+#648 := (iff #728 #737)
+#666 := (if false #462 #737)
+#645 := (iff #666 #737)
+#646 := [rewrite]: #645
+#656 := (iff #728 #666)
+#664 := (iff #723 #737)
+#659 := (if false #737 #737)
+#662 := (iff #659 #737)
+#663 := [rewrite]: #662
+#660 := (iff #723 #659)
+#657 := (iff #722 #737)
+#1 := true
+#673 := (if true #737 #737)
+#654 := (iff #673 #737)
+#655 := [rewrite]: #654
+#670 := (iff #722 #673)
+#671 := (iff #727 #737)
+#668 := (= #726 #12)
+#694 := (+ #12 0::Int)
+#685 := (= #694 #12)
+#695 := [rewrite]: #685
+#677 := (= #726 #694)
+#680 := (= #725 0::Int)
+#687 := -3::Int
+#691 := (mod -3::Int -1::Int)
+#678 := (= #691 0::Int)
+#679 := [rewrite]: #678
+#675 := (= #725 #691)
+#690 := (= #736 -1::Int)
+#684 := [rewrite]: #690
+#688 := (= #732 -3::Int)
+#689 := [rewrite]: #688
+#676 := [monotonicity #689 #684]: #675
+#681 := [trans #676 #679]: #680
+#682 := [monotonicity #681]: #677
+#669 := [trans #682 #695]: #668
+#672 := [monotonicity #669]: #671
+#693 := (iff #735 #737)
+#696 := (= #731 #12)
+#686 := (= #731 #694)
+#705 := (= #449 0::Int)
+#609 := (* -1::Int 0::Int)
+#704 := (= #609 0::Int)
+#701 := [rewrite]: #704
+#610 := (= #449 #609)
+#607 := (= #734 0::Int)
+#608 := [rewrite]: #607
+#611 := [monotonicity #608]: #610
+#692 := [trans #611 #701]: #705
+#683 := [monotonicity #692]: #686
+#697 := [trans #683 #695]: #696
+#698 := [monotonicity #697]: #693
+#606 := (iff #733 true)
+#711 := (or true false)
+#595 := (iff #711 true)
+#554 := [rewrite]: #595
+#603 := (iff #733 #711)
+#703 := (iff #455 false)
+#420 := (not true)
+#745 := (iff #420 false)
+#408 := [rewrite]: #745
+#699 := (iff #455 #420)
+#702 := (iff #454 true)
+#593 := (iff #454 #711)
+#715 := (iff #738 false)
+#716 := [rewrite]: #715
+#710 := (iff #453 true)
+#708 := [rewrite]: #710
+#594 := [monotonicity #708 #716]: #593
+#604 := [trans #594 #554]: #702
+#700 := [monotonicity #604]: #699
+#588 := [trans #700 #408]: #703
+#707 := (iff #452 true)
+#721 := (not false)
+#553 := (iff #721 true)
+#706 := [rewrite]: #553
+#550 := (iff #452 #721)
+#720 := (iff #742 false)
+#717 := (or false false)
+#713 := (iff #717 false)
+#719 := [rewrite]: #713
+#718 := (iff #742 #717)
+#572 := (iff #741 false)
+#573 := [rewrite]: #572
+#712 := [monotonicity #573 #716]: #718
+#714 := [trans #712 #719]: #720
+#552 := [monotonicity #714]: #550
+#709 := [trans #552 #706]: #707
+#605 := [monotonicity #709 #588]: #603
+#599 := [trans #605 #554]: #606
+#674 := [monotonicity #599 #698 #672]: #670
+#658 := [trans #674 #655]: #657
+#730 := (iff #463 false)
+#571 := [rewrite]: #730
+#661 := [monotonicity #571 #658]: #660
+#665 := [trans #661 #663]: #664
+#729 := (iff #740 false)
+#724 := [rewrite]: #729
+#667 := [monotonicity #724 #665]: #656
+#649 := [trans #667 #646]: #648
+#639 := [monotonicity #649]: #653
+#637 := [trans #639 #636]: #653
+#647 := [quant-inst #9 #11]: #652
+#640 := [mp #647 #637]: #651
+#642 := [unit-resolution #640 #803]: #737
+#643 := [monotonicity #642]: #16
 #17 := (not #16)
-#85 := [asserted]: #17
-[unit-resolution #85 #719]: false
-unsat
-7d3574c960626fe960bfda1798915870024d0a96 317 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#14 := 0::Int
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 0::Int)
+#67 := [asserted]: #17
+[unit-resolution #67 #643]: false
+27d83ae74f367979c88ed057145dc22d3bf30f3d 325 0
+unsat
+#2 := false
+#16 := 0::Int
+decl f8 :: (-> S6 S3 Int)
+decl f10 :: S3
+#10 := f10
+decl f9 :: S6
+#9 := f9
+#11 := (f8 f9 f10)
+#450 := (>= #11 0::Int)
+#595 := (not #450)
+#455 := (<= #11 0::Int)
+#551 := (not #455)
+#703 := (or #551 #595)
+#667 := (not #703)
 decl f5 :: (-> S4 Int Int)
-#10 := 1::Int
+#13 := 1::Int
 decl f6 :: (-> S5 Int S4)
 decl f7 :: S5
-#9 := f7
-#11 := (f6 f7 1::Int)
-#12 := (f5 #11 1::Int)
-#13 := (f3 f4 #12)
-#16 := (= #13 #15)
-#806 := (= #12 0::Int)
-#24 := (:var 0 Int)
-#36 := (:var 1 Int)
-#56 := (f6 f7 #36)
-#57 := (f5 #56 #24)
-#890 := (pattern #57)
-#187 := -1::Int
-#191 := (* -1::Int #24)
-#188 := (* -1::Int #36)
-#252 := (mod #188 #191)
-#382 := (+ #57 #252)
-#383 := (= #382 0::Int)
-#58 := (mod #36 #24)
-#379 := (* -1::Int #58)
-#380 := (+ #57 #379)
-#381 := (= #380 0::Int)
-#226 := (>= #36 0::Int)
-#219 := (<= #24 0::Int)
-#326 := (or #219 #226)
-#327 := (not #326)
-#215 := (<= #36 0::Int)
-#324 := (or #215 #219)
-#325 := (not #324)
-#330 := (or #325 #327)
-#384 := (ite #330 #381 #383)
-#378 := (= #57 0::Int)
-#39 := (= #36 0::Int)
-#385 := (ite #39 #378 #384)
-#377 := (= #36 #57)
-#40 := (= #24 0::Int)
-#386 := (ite #40 #377 #385)
-#891 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #890) #386)
-#389 := (forall (vars (?v0 Int) (?v1 Int)) #386)
-#894 := (iff #389 #891)
-#892 := (iff #386 #386)
-#893 := [refl]: #892
-#895 := [quant-intro #893]: #894
-#258 := (* -1::Int #252)
-#346 := (ite #330 #58 #258)
-#349 := (ite #39 0::Int #346)
-#352 := (ite #40 #36 #349)
-#355 := (= #57 #352)
-#358 := (forall (vars (?v0 Int) (?v1 Int)) #355)
-#390 := (iff #358 #389)
-#387 := (iff #355 #386)
-#388 := [rewrite]: #387
-#391 := [quant-intro #388]: #390
-#227 := (not #226)
-#220 := (not #219)
-#230 := (and #220 #227)
-#216 := (not #215)
-#223 := (and #216 #220)
-#233 := (or #223 #230)
-#278 := (ite #233 #58 #258)
-#281 := (ite #39 0::Int #278)
-#284 := (ite #40 #36 #281)
-#287 := (= #57 #284)
-#290 := (forall (vars (?v0 Int) (?v1 Int)) #287)
-#359 := (iff #290 #358)
-#356 := (iff #287 #355)
-#353 := (= #284 #352)
-#350 := (= #281 #349)
-#347 := (= #278 #346)
-#331 := (iff #233 #330)
-#328 := (iff #230 #327)
-#329 := [rewrite]: #328
-#309 := (iff #223 #325)
-#310 := [rewrite]: #309
-#332 := [monotonicity #310 #329]: #331
-#348 := [monotonicity #332]: #347
-#351 := [monotonicity #348]: #350
-#354 := [monotonicity #351]: #353
-#357 := [monotonicity #354]: #356
-#360 := [quant-intro #357]: #359
-#307 := (~ #290 #290)
-#321 := (~ #287 #287)
-#322 := [refl]: #321
-#308 := [nnf-pos #322]: #307
-#50 := (- #24)
-#49 := (- #36)
-#59 := (mod #49 #50)
-#60 := (- #59)
-#43 := (< 0::Int #24)
-#45 := (< #36 0::Int)
-#46 := (and #45 #43)
-#42 := (< 0::Int #36)
-#44 := (and #42 #43)
-#47 := (or #44 #46)
-#61 := (ite #47 #58 #60)
-#62 := (ite #39 0::Int #61)
-#63 := (ite #40 #36 #62)
-#64 := (= #57 #63)
-#65 := (forall (vars (?v0 Int) (?v1 Int)) #64)
-#293 := (iff #65 #290)
-#181 := (and #43 #45)
-#184 := (or #44 #181)
-#263 := (ite #184 #58 #258)
-#172 := (= 0::Int #36)
-#266 := (ite #172 0::Int #263)
-#175 := (= 0::Int #24)
-#269 := (ite #175 #36 #266)
-#272 := (= #57 #269)
-#275 := (forall (vars (?v0 Int) (?v1 Int)) #272)
-#291 := (iff #275 #290)
-#288 := (iff #272 #287)
-#285 := (= #269 #284)
-#282 := (= #266 #281)
-#279 := (= #263 #278)
-#234 := (iff #184 #233)
-#231 := (iff #181 #230)
-#228 := (iff #45 #227)
-#229 := [rewrite]: #228
-#221 := (iff #43 #220)
-#222 := [rewrite]: #221
-#232 := [monotonicity #222 #229]: #231
-#224 := (iff #44 #223)
-#217 := (iff #42 #216)
-#218 := [rewrite]: #217
-#225 := [monotonicity #218 #222]: #224
-#235 := [monotonicity #225 #232]: #234
-#280 := [monotonicity #235]: #279
-#209 := (iff #172 #39)
-#210 := [rewrite]: #209
-#283 := [monotonicity #210 #280]: #282
-#211 := (iff #175 #40)
-#212 := [rewrite]: #211
-#286 := [monotonicity #212 #283]: #285
-#289 := [monotonicity #286]: #288
-#292 := [quant-intro #289]: #291
-#276 := (iff #65 #275)
-#273 := (iff #64 #272)
-#270 := (= #63 #269)
-#267 := (= #62 #266)
-#264 := (= #61 #263)
-#261 := (= #60 #258)
-#255 := (- #252)
-#259 := (= #255 #258)
-#260 := [rewrite]: #259
-#256 := (= #60 #255)
-#253 := (= #59 #252)
-#192 := (= #50 #191)
-#193 := [rewrite]: #192
-#189 := (= #49 #188)
-#190 := [rewrite]: #189
-#254 := [monotonicity #190 #193]: #253
-#257 := [monotonicity #254]: #256
-#262 := [trans #257 #260]: #261
-#185 := (iff #47 #184)
-#182 := (iff #46 #181)
-#183 := [rewrite]: #182
-#186 := [monotonicity #183]: #185
-#265 := [monotonicity #186 #262]: #264
-#173 := (iff #39 #172)
-#174 := [rewrite]: #173
-#268 := [monotonicity #174 #265]: #267
-#176 := (iff #40 #175)
-#177 := [rewrite]: #176
-#271 := [monotonicity #177 #268]: #270
-#274 := [monotonicity #271]: #273
-#277 := [quant-intro #274]: #276
-#294 := [trans #277 #292]: #293
-#251 := [asserted]: #65
-#295 := [mp #251 #294]: #290
-#323 := [mp~ #295 #308]: #290
-#361 := [mp #323 #360]: #358
-#392 := [mp #361 #391]: #389
-#896 := [mp #392 #895]: #891
-#710 := (not #891)
-#711 := (or #710 #806)
-#819 := (* -1::Int 1::Int)
-#820 := (mod #819 #819)
-#815 := (+ #12 #820)
-#816 := (= #815 0::Int)
-#821 := (mod 1::Int 1::Int)
-#822 := (* -1::Int #821)
-#817 := (+ #12 #822)
-#823 := (= #817 0::Int)
-#664 := (>= 1::Int 0::Int)
-#665 := (<= 1::Int 0::Int)
-#666 := (or #665 #664)
-#808 := (not #666)
-#809 := (or #665 #665)
-#810 := (not #809)
-#811 := (or #810 #808)
-#805 := (ite #811 #823 #816)
-#812 := (= 1::Int 0::Int)
-#813 := (ite #812 #806 #805)
-#807 := (= 1::Int #12)
-#814 := (ite #812 #807 #813)
-#712 := (or #710 #814)
-#716 := (iff #712 #711)
-#718 := (iff #711 #711)
-#723 := [rewrite]: #718
-#731 := (iff #814 #806)
-#799 := (= #12 1::Int)
-#730 := (ite false #799 #806)
-#735 := (iff #730 #806)
-#736 := [rewrite]: #735
-#733 := (iff #814 #730)
-#728 := (iff #813 #806)
-#744 := (ite false #806 #806)
-#746 := (iff #744 #806)
-#732 := [rewrite]: #746
-#745 := (iff #813 #744)
-#742 := (iff #805 #806)
-#1 := true
-#749 := (ite true #806 #806)
-#739 := (iff #749 #806)
-#741 := [rewrite]: #739
-#760 := (iff #805 #749)
-#758 := (iff #816 #806)
-#756 := (= #815 #12)
-#772 := (+ #12 0::Int)
-#770 := (= #772 #12)
-#775 := [rewrite]: #770
-#754 := (= #815 #772)
-#752 := (= #820 0::Int)
-#767 := (mod -1::Int -1::Int)
-#750 := (= #767 0::Int)
-#751 := [rewrite]: #750
-#747 := (= #820 #767)
-#766 := (= #819 -1::Int)
-#763 := [rewrite]: #766
-#748 := [monotonicity #763 #763]: #747
-#753 := [trans #748 #751]: #752
-#755 := [monotonicity #753]: #754
-#757 := [trans #755 #775]: #756
-#759 := [monotonicity #757]: #758
-#764 := (iff #823 #806)
-#761 := (= #817 #12)
-#773 := (= #817 #772)
-#769 := (= #822 0::Int)
-#782 := (* -1::Int 0::Int)
-#784 := (= #782 0::Int)
-#768 := [rewrite]: #784
-#783 := (= #822 #782)
-#780 := (= #821 0::Int)
-#781 := [rewrite]: #780
-#777 := [monotonicity #781]: #783
-#771 := [trans #777 #768]: #769
-#774 := [monotonicity #771]: #773
-#762 := [trans #774 #775]: #761
-#765 := [monotonicity #762]: #764
-#786 := (iff #811 true)
-#776 := (or true false)
-#789 := (iff #776 true)
-#790 := [rewrite]: #789
-#778 := (iff #811 #776)
-#787 := (iff #808 false)
-#489 := (not true)
-#850 := (iff #489 false)
-#836 := [rewrite]: #850
-#798 := (iff #808 #489)
-#797 := (iff #666 true)
-#700 := (or false true)
-#703 := (iff #700 true)
-#704 := [rewrite]: #703
-#701 := (iff #666 #700)
-#699 := (iff #664 true)
-#692 := [rewrite]: #699
-#802 := (iff #665 false)
-#803 := [rewrite]: #802
-#702 := [monotonicity #803 #692]: #701
-#794 := [trans #702 #704]: #797
-#785 := [monotonicity #794]: #798
-#779 := [trans #785 #836]: #787
-#696 := (iff #810 true)
-#697 := (not false)
-#796 := (iff #697 true)
-#681 := [rewrite]: #796
-#792 := (iff #810 #697)
-#647 := (iff #809 false)
-#801 := (or false false)
-#687 := (iff #801 false)
-#688 := [rewrite]: #687
-#804 := (iff #809 #801)
-#686 := [monotonicity #803 #803]: #804
-#795 := [trans #686 #688]: #647
-#793 := [monotonicity #795]: #792
-#698 := [trans #793 #681]: #696
-#788 := [monotonicity #698 #779]: #778
-#791 := [trans #788 #790]: #786
-#738 := [monotonicity #791 #765 #759]: #760
-#743 := [trans #738 #741]: #742
-#643 := (iff #812 false)
-#645 := [rewrite]: #643
-#740 := [monotonicity #645 #743]: #745
-#729 := [trans #740 #732]: #728
-#646 := (iff #807 #799)
-#800 := [rewrite]: #646
-#734 := [monotonicity #645 #800 #729]: #733
-#737 := [trans #734 #736]: #731
-#717 := [monotonicity #737]: #716
-#719 := [trans #717 #723]: #716
-#605 := [quant-inst #10 #10]: #712
-#720 := [mp #605 #719]: #711
-#724 := [unit-resolution #720 #896]: #806
-#725 := [monotonicity #724]: #16
-#17 := (not #16)
-#85 := [asserted]: #17
-[unit-resolution #85 #725]: false
-unsat
-e9cdda2176e690083a382501d00feb100ad9b5ea 328 0
-#2 := false
+#8 := f7
+#12 := (f6 f7 #11)
+#14 := (f5 #12 1::Int)
+#454 := (= #14 0::Int)
+#648 := (not #454)
 decl f3 :: (-> S2 Int S3)
-#15 := 0::Int
-decl f4 :: S2
-#8 := f4
-#16 := (f3 f4 0::Int)
-decl f5 :: (-> S4 Int Int)
-#12 := 1::Int
-decl f6 :: (-> S5 Int S4)
-#10 := 3::Int
-decl f7 :: S5
-#9 := f7
-#11 := (f6 f7 3::Int)
-#13 := (f5 #11 1::Int)
-#14 := (f3 f4 #13)
-#17 := (= #14 #16)
-#814 := (= #13 0::Int)
+decl f4 :: S2
+#7 := f4
+#17 := (f3 f4 0::Int)
+#15 := (f3 f4 #14)
+#18 := (= #15 #17)
+#364 := [hypothesis]: #454
+#740 := [monotonicity #364]: #18
+#19 := (not #18)
+#68 := [asserted]: #19
+#741 := [unit-resolution #68 #740]: false
+#463 := [lemma #741]: #648
+#133 := -1::Int
+#723 := (* -1::Int #11)
+#696 := (mod #723 -1::Int)
+#694 := (+ #14 #696)
+#689 := (= #694 0::Int)
+#685 := (if #703 #454 #689)
+#453 := (= #11 0::Int)
+#642 := (not #453)
+#635 := (or #642 #454)
+#677 := (if #453 #454 #685)
 #25 := (:var 0 Int)
 #37 := (:var 1 Int)
 #57 := (f6 f7 #37)
 #58 := (f5 #57 #25)
-#891 := (pattern #58)
-#188 := -1::Int
-#192 := (* -1::Int #25)
-#189 := (* -1::Int #37)
-#253 := (mod #189 #192)
-#383 := (+ #58 #253)
-#384 := (= #383 0::Int)
+#798 := (pattern #58)
+#137 := (* -1::Int #25)
+#134 := (* -1::Int #37)
+#156 := (mod #134 #137)
+#347 := (+ #58 #156)
+#348 := (= #347 0::Int)
 #59 := (mod #37 #25)
-#380 := (* -1::Int #59)
-#381 := (+ #58 #380)
-#382 := (= #381 0::Int)
-#227 := (>= #37 0::Int)
-#220 := (<= #25 0::Int)
-#327 := (or #220 #227)
-#328 := (not #327)
-#216 := (<= #37 0::Int)
-#325 := (or #216 #220)
-#326 := (not #325)
-#331 := (or #326 #328)
-#385 := (ite #331 #382 #384)
-#379 := (= #58 0::Int)
+#344 := (* -1::Int #59)
+#345 := (+ #58 #344)
+#346 := (= #345 0::Int)
+#111 := (<= #25 0::Int)
+#223 := (>= #37 0::Int)
+#291 := (or #223 #111)
+#292 := (not #291)
+#107 := (<= #37 0::Int)
+#287 := (or #107 #111)
+#288 := (not #287)
+#295 := (or #288 #292)
+#349 := (if #295 #346 #348)
+#343 := (= #58 0::Int)
 #40 := (= #37 0::Int)
-#386 := (ite #40 #379 #385)
-#378 := (= #37 #58)
+#350 := (if #40 #343 #349)
+#342 := (= #58 #37)
 #41 := (= #25 0::Int)
-#387 := (ite #41 #378 #386)
-#892 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #891) #387)
-#390 := (forall (vars (?v0 Int) (?v1 Int)) #387)
-#895 := (iff #390 #892)
-#893 := (iff #387 #387)
-#894 := [refl]: #893
-#896 := [quant-intro #894]: #895
-#259 := (* -1::Int #253)
-#347 := (ite #331 #59 #259)
-#350 := (ite #40 0::Int #347)
-#353 := (ite #41 #37 #350)
-#356 := (= #58 #353)
-#359 := (forall (vars (?v0 Int) (?v1 Int)) #356)
-#391 := (iff #359 #390)
-#388 := (iff #356 #387)
-#389 := [rewrite]: #388
-#392 := [quant-intro #389]: #391
-#228 := (not #227)
-#221 := (not #220)
-#231 := (and #221 #228)
-#217 := (not #216)
-#224 := (and #217 #221)
-#234 := (or #224 #231)
-#279 := (ite #234 #59 #259)
-#282 := (ite #40 0::Int #279)
-#285 := (ite #41 #37 #282)
-#288 := (= #58 #285)
-#291 := (forall (vars (?v0 Int) (?v1 Int)) #288)
-#360 := (iff #291 #359)
-#357 := (iff #288 #356)
-#354 := (= #285 #353)
-#351 := (= #282 #350)
-#348 := (= #279 #347)
-#332 := (iff #234 #331)
-#329 := (iff #231 #328)
-#330 := [rewrite]: #329
-#310 := (iff #224 #326)
-#311 := [rewrite]: #310
-#333 := [monotonicity #311 #330]: #332
-#349 := [monotonicity #333]: #348
-#352 := [monotonicity #349]: #351
-#355 := [monotonicity #352]: #354
-#358 := [monotonicity #355]: #357
-#361 := [quant-intro #358]: #360
-#308 := (~ #291 #291)
-#322 := (~ #288 #288)
-#323 := [refl]: #322
-#309 := [nnf-pos #323]: #308
+#351 := (if #41 #342 #350)
+#799 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #798) #351)
+#354 := (forall (vars (?v0 Int) (?v1 Int)) #351)
+#802 := (iff #354 #799)
+#800 := (iff #351 #351)
+#801 := [refl]: #800
+#803 := [quant-intro #801]: #802
+#162 := (* -1::Int #156)
+#311 := (if #295 #59 #162)
+#314 := (if #40 0::Int #311)
+#317 := (if #41 #37 #314)
+#320 := (= #58 #317)
+#323 := (forall (vars (?v0 Int) (?v1 Int)) #320)
+#355 := (iff #323 #354)
+#352 := (iff #320 #351)
+#353 := [rewrite]: #352
+#356 := [quant-intro #353]: #355
+#112 := (not #111)
+#226 := (not #223)
+#229 := (and #226 #112)
+#108 := (not #107)
+#115 := (and #108 #112)
+#232 := (or #115 #229)
+#248 := (if #232 #59 #162)
+#251 := (if #40 0::Int #248)
+#254 := (if #41 #37 #251)
+#257 := (= #58 #254)
+#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
+#324 := (iff #260 #323)
+#321 := (iff #257 #320)
+#318 := (= #254 #317)
+#315 := (= #251 #314)
+#312 := (= #248 #311)
+#296 := (iff #232 #295)
+#293 := (iff #229 #292)
+#294 := [rewrite]: #293
+#289 := (iff #115 #288)
+#290 := [rewrite]: #289
+#297 := [monotonicity #290 #294]: #296
+#313 := [monotonicity #297]: #312
+#316 := [monotonicity #313]: #315
+#319 := [monotonicity #316]: #318
+#322 := [monotonicity #319]: #321
+#325 := [quant-intro #322]: #324
+#284 := (~ #260 #260)
+#282 := (~ #257 #257)
+#283 := [refl]: #282
+#285 := [nnf-pos #283]: #284
+#118 := (<= 0::Int #37)
+#119 := (not #118)
+#127 := (and #119 #112)
+#130 := (or #115 #127)
+#167 := (if #130 #59 #162)
+#170 := (if #40 0::Int #167)
+#173 := (if #41 #37 #170)
+#176 := (= #58 #173)
+#179 := (forall (vars (?v0 Int) (?v1 Int)) #176)
+#261 := (iff #179 #260)
+#258 := (iff #176 #257)
+#255 := (= #173 #254)
+#252 := (= #170 #251)
+#249 := (= #167 #248)
+#233 := (iff #130 #232)
+#230 := (iff #127 #229)
+#227 := (iff #119 #226)
+#224 := (iff #118 #223)
+#225 := [rewrite]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#250 := [monotonicity #234]: #249
+#253 := [monotonicity #250]: #252
+#256 := [monotonicity #253]: #255
+#259 := [monotonicity #256]: #258
+#262 := [quant-intro #259]: #261
 #51 := (- #25)
 #50 := (- #37)
 #60 := (mod #50 #51)
@@ -18541,1664 +18113,607 @@
 #43 := (< 0::Int #37)
 #45 := (and #43 #44)
 #48 := (or #45 #47)
-#62 := (ite #48 #59 #61)
-#63 := (ite #40 0::Int #62)
-#64 := (ite #41 #37 #63)
+#62 := (if #48 #59 #61)
+#63 := (if #40 0::Int #62)
+#64 := (if #41 #37 #63)
 #65 := (= #58 #64)
 #66 := (forall (vars (?v0 Int) (?v1 Int)) #65)
-#294 := (iff #66 #291)
-#182 := (and #44 #46)
-#185 := (or #45 #182)
-#264 := (ite #185 #59 #259)
-#173 := (= 0::Int #37)
-#267 := (ite #173 0::Int #264)
-#176 := (= 0::Int #25)
-#270 := (ite #176 #37 #267)
-#273 := (= #58 #270)
-#276 := (forall (vars (?v0 Int) (?v1 Int)) #273)
-#292 := (iff #276 #291)
-#289 := (iff #273 #288)
-#286 := (= #270 #285)
-#283 := (= #267 #282)
-#280 := (= #264 #279)
-#235 := (iff #185 #234)
-#232 := (iff #182 #231)
-#229 := (iff #46 #228)
-#230 := [rewrite]: #229
-#222 := (iff #44 #221)
-#223 := [rewrite]: #222
-#233 := [monotonicity #223 #230]: #232
-#225 := (iff #45 #224)
-#218 := (iff #43 #217)
-#219 := [rewrite]: #218
-#226 := [monotonicity #219 #223]: #225
-#236 := [monotonicity #226 #233]: #235
-#281 := [monotonicity #236]: #280
-#210 := (iff #173 #40)
-#211 := [rewrite]: #210
-#284 := [monotonicity #211 #281]: #283
-#212 := (iff #176 #41)
-#213 := [rewrite]: #212
-#287 := [monotonicity #213 #284]: #286
-#290 := [monotonicity #287]: #289
-#293 := [quant-intro #290]: #292
-#277 := (iff #66 #276)
-#274 := (iff #65 #273)
-#271 := (= #64 #270)
-#268 := (= #63 #267)
-#265 := (= #62 #264)
-#262 := (= #61 #259)
-#256 := (- #253)
-#260 := (= #256 #259)
-#261 := [rewrite]: #260
-#257 := (= #61 #256)
-#254 := (= #60 #253)
-#193 := (= #51 #192)
-#194 := [rewrite]: #193
-#190 := (= #50 #189)
-#191 := [rewrite]: #190
-#255 := [monotonicity #191 #194]: #254
-#258 := [monotonicity #255]: #257
-#263 := [trans #258 #261]: #262
-#186 := (iff #48 #185)
-#183 := (iff #47 #182)
-#184 := [rewrite]: #183
-#187 := [monotonicity #184]: #186
-#266 := [monotonicity #187 #263]: #265
-#174 := (iff #40 #173)
-#175 := [rewrite]: #174
-#269 := [monotonicity #175 #266]: #268
-#177 := (iff #41 #176)
-#178 := [rewrite]: #177
-#272 := [monotonicity #178 #269]: #271
-#275 := [monotonicity #272]: #274
-#278 := [quant-intro #275]: #277
-#295 := [trans #278 #293]: #294
-#252 := [asserted]: #66
-#296 := [mp #252 #295]: #291
-#324 := [mp~ #296 #309]: #291
-#362 := [mp #324 #361]: #359
-#393 := [mp #362 #392]: #390
-#897 := [mp #393 #896]: #892
-#722 := (not #892)
-#725 := (or #722 #814)
-#820 := (* -1::Int 1::Int)
-#821 := (* -1::Int 3::Int)
-#816 := (mod #821 #820)
-#817 := (+ #13 #816)
-#822 := (= #817 0::Int)
-#823 := (mod 3::Int 1::Int)
-#818 := (* -1::Int #823)
-#824 := (+ #13 #818)
-#665 := (= #824 0::Int)
-#666 := (>= 3::Int 0::Int)
-#667 := (<= 1::Int 0::Int)
-#809 := (or #667 #666)
-#810 := (not #809)
-#811 := (<= 3::Int 0::Int)
-#812 := (or #811 #667)
-#806 := (not #812)
-#807 := (or #806 #810)
-#813 := (ite #807 #665 #822)
-#808 := (= 3::Int 0::Int)
-#815 := (ite #808 #814 #813)
-#644 := (= 3::Int #13)
-#646 := (= 1::Int 0::Int)
-#647 := (ite #646 #644 #815)
-#726 := (or #722 #647)
-#723 := (iff #726 #725)
-#708 := (iff #725 #725)
-#654 := [rewrite]: #708
-#720 := (iff #647 #814)
-#804 := (= #13 3::Int)
-#606 := (ite false #804 #814)
-#719 := (iff #606 #814)
-#724 := [rewrite]: #719
-#717 := (iff #647 #606)
-#712 := (iff #815 #814)
-#736 := (ite false #814 #814)
-#738 := (iff #736 #814)
-#711 := [rewrite]: #738
-#737 := (iff #815 #736)
-#734 := (iff #813 #814)
-#1 := true
-#747 := (ite true #814 #814)
-#730 := (iff #747 #814)
-#731 := [rewrite]: #730
-#733 := (iff #813 #747)
-#746 := (iff #822 #814)
-#744 := (= #817 #13)
-#765 := (+ #13 0::Int)
-#764 := (= #765 #13)
-#768 := [rewrite]: #764
-#742 := (= #817 #765)
-#739 := (= #816 0::Int)
-#753 := -3::Int
-#758 := (mod -3::Int -1::Int)
-#750 := (= #758 0::Int)
-#761 := [rewrite]: #750
-#759 := (= #816 #758)
-#756 := (= #820 -1::Int)
-#757 := [rewrite]: #756
-#754 := (= #821 -3::Int)
-#755 := [rewrite]: #754
-#760 := [monotonicity #755 #757]: #759
-#740 := [trans #760 #761]: #739
-#743 := [monotonicity #740]: #742
-#745 := [trans #743 #768]: #744
-#741 := [monotonicity #745]: #746
-#751 := (iff #665 #814)
-#748 := (= #824 #13)
-#766 := (= #824 #765)
-#762 := (= #818 0::Int)
-#773 := (* -1::Int 0::Int)
-#771 := (= #773 0::Int)
-#776 := [rewrite]: #771
-#774 := (= #818 #773)
-#770 := (= #823 0::Int)
-#772 := [rewrite]: #770
-#775 := [monotonicity #772]: #774
-#763 := [trans #775 #776]: #762
-#767 := [monotonicity #763]: #766
-#749 := [trans #767 #768]: #748
-#752 := [monotonicity #749]: #751
-#785 := (iff #807 true)
-#781 := (or true false)
-#784 := (iff #781 true)
-#778 := [rewrite]: #784
-#782 := (iff #807 #781)
-#787 := (iff #810 false)
-#490 := (not true)
-#851 := (iff #490 false)
-#837 := [rewrite]: #851
-#790 := (iff #810 #490)
-#779 := (iff #809 true)
-#799 := (or false true)
-#780 := (iff #799 true)
-#777 := [rewrite]: #780
-#786 := (iff #809 #799)
-#798 := (iff #666 true)
-#795 := [rewrite]: #798
-#648 := (iff #667 false)
-#796 := [rewrite]: #648
-#788 := [monotonicity #796 #795]: #786
-#789 := [trans #788 #777]: #779
-#791 := [monotonicity #789]: #790
-#792 := [trans #791 #837]: #787
-#704 := (iff #806 true)
-#700 := (not false)
-#702 := (iff #700 true)
-#703 := [rewrite]: #702
-#693 := (iff #806 #700)
-#697 := (iff #812 false)
-#698 := (or false false)
-#797 := (iff #698 false)
-#682 := [rewrite]: #797
-#793 := (iff #812 #698)
-#688 := (iff #811 false)
-#689 := [rewrite]: #688
-#794 := [monotonicity #689 #796]: #793
-#699 := [trans #794 #682]: #697
-#701 := [monotonicity #699]: #693
-#705 := [trans #701 #703]: #704
-#783 := [monotonicity #705 #792]: #782
-#769 := [trans #783 #778]: #785
-#729 := [monotonicity #769 #752 #741]: #733
-#735 := [trans #729 #731]: #734
-#805 := (iff #808 false)
-#687 := [rewrite]: #805
-#732 := [monotonicity #687 #735]: #737
-#713 := [trans #732 #711]: #712
-#803 := (iff #644 #804)
-#802 := [rewrite]: #803
-#800 := (iff #646 false)
-#801 := [rewrite]: #800
-#718 := [monotonicity #801 #802 #713]: #717
-#721 := [trans #718 #724]: #720
-#728 := [monotonicity #721]: #723
-#709 := [trans #728 #654]: #723
-#727 := [quant-inst #10 #12]: #726
-#690 := [mp #727 #709]: #725
-#715 := [unit-resolution #690 #897]: #814
-#710 := [monotonicity #715]: #17
-#18 := (not #17)
-#86 := [asserted]: #18
-[unit-resolution #86 #710]: false
-unsat
-498414bdbc142ee84fb4637170090b972b5222e7 333 0
-#2 := false
-#17 := 0::Int
-decl f8 :: (-> S6 S3 Int)
-decl f10 :: S3
-#11 := f10
-decl f9 :: S6
-#10 := f9
-#12 := (f8 f9 f10)
-#819 := (>= #12 0::Int)
-#701 := (not #819)
-#808 := (= #12 0::Int)
-#668 := (<= #12 0::Int)
-#690 := (not #668)
-#762 := (or #690 #808 #701)
-#719 := (not #762)
+#180 := (iff #66 #179)
+#177 := (iff #65 #176)
+#174 := (= #64 #173)
+#171 := (= #63 #170)
+#168 := (= #62 #167)
+#165 := (= #61 #162)
+#159 := (- #156)
+#163 := (= #159 #162)
+#164 := [rewrite]: #163
+#160 := (= #61 #159)
+#157 := (= #60 #156)
+#138 := (= #51 #137)
+#139 := [rewrite]: #138
+#135 := (= #50 #134)
+#136 := [rewrite]: #135
+#158 := [monotonicity #136 #139]: #157
+#161 := [monotonicity #158]: #160
+#166 := [trans #161 #164]: #165
+#131 := (iff #48 #130)
+#128 := (iff #47 #127)
+#113 := (iff #44 #112)
+#114 := [rewrite]: #113
+#120 := (iff #46 #119)
+#124 := (iff #119 #119)
+#122 := (iff #118 #118)
+#123 := [rewrite]: #122
+#125 := [monotonicity #123]: #124
+#121 := [rewrite]: #120
+#126 := [trans #121 #125]: #120
+#129 := [monotonicity #126 #114]: #128
+#116 := (iff #45 #115)
+#109 := (iff #43 #108)
+#110 := [rewrite]: #109
+#117 := [monotonicity #110 #114]: #116
+#132 := [monotonicity #117 #129]: #131
+#169 := [monotonicity #132 #166]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [quant-intro #178]: #180
+#73 := [asserted]: #66
+#182 := [mp #73 #181]: #179
+#263 := [mp #182 #262]: #260
+#286 := [mp~ #263 #285]: #260
+#326 := [mp #286 #325]: #323
+#357 := [mp #326 #356]: #354
+#804 := [mp #357 #803]: #799
+#673 := (not #799)
+#674 := (or #673 #677)
+#724 := (* -1::Int 1::Int)
+#729 := (mod #723 #724)
+#730 := (+ #14 #729)
+#725 := (= #730 0::Int)
+#737 := (mod #11 1::Int)
+#726 := (* -1::Int #737)
+#727 := (+ #14 #726)
+#728 := (= #727 0::Int)
+#456 := (<= 1::Int 0::Int)
+#732 := (or #450 #456)
+#736 := (not #732)
+#734 := (or #455 #456)
+#735 := (not #734)
+#733 := (or #735 #736)
+#731 := (if #733 #728 #725)
+#572 := (if #453 #454 #731)
+#743 := (= #14 #11)
+#739 := (= 1::Int 0::Int)
+#573 := (if #739 #743 #572)
+#671 := (or #673 #573)
+#655 := (iff #671 #674)
+#658 := (iff #674 #674)
+#659 := [rewrite]: #658
+#670 := (iff #573 #677)
+#681 := (if false #743 #677)
+#683 := (iff #681 #677)
+#669 := [rewrite]: #683
+#682 := (iff #573 #681)
+#679 := (iff #572 #677)
+#692 := (iff #731 #685)
+#690 := (iff #725 #689)
+#699 := (= #730 #694)
+#697 := (= #729 #696)
+#684 := (= #724 -1::Int)
+#686 := [rewrite]: #684
+#698 := [monotonicity #686]: #697
+#688 := [monotonicity #698]: #699
+#691 := [monotonicity #688]: #690
+#695 := (iff #728 #454)
+#706 := (= #727 #14)
+#610 := (+ #14 0::Int)
+#705 := (= #610 #14)
+#702 := [rewrite]: #705
+#611 := (= #727 #610)
+#608 := (= #726 0::Int)
+#589 := (* -1::Int 0::Int)
+#607 := (= #589 0::Int)
+#600 := [rewrite]: #607
+#604 := (= #726 #589)
+#701 := (= #737 0::Int)
+#704 := [rewrite]: #701
+#606 := [monotonicity #704]: #604
+#609 := [trans #606 #600]: #608
+#612 := [monotonicity #609]: #611
+#693 := [trans #612 #702]: #706
+#687 := [monotonicity #693]: #695
+#605 := (iff #733 #703)
+#596 := (iff #736 #595)
+#712 := (iff #732 #450)
+#707 := (or #450 false)
+#711 := (iff #707 #450)
+#709 := [rewrite]: #711
+#708 := (iff #732 #707)
+#717 := (iff #456 false)
+#718 := [rewrite]: #717
+#710 := [monotonicity #718]: #708
+#594 := [trans #710 #709]: #712
+#555 := [monotonicity #594]: #596
+#553 := (iff #735 #551)
+#715 := (iff #734 #455)
+#719 := (or #455 false)
+#720 := (iff #719 #455)
+#721 := [rewrite]: #720
+#713 := (iff #734 #719)
+#714 := [monotonicity #718]: #713
+#722 := [trans #714 #721]: #715
+#554 := [monotonicity #722]: #553
+#700 := [monotonicity #554 #555]: #605
+#676 := [monotonicity #700 #687 #691]: #692
+#680 := [monotonicity #676]: #679
+#574 := (iff #739 false)
+#716 := [rewrite]: #574
+#678 := [monotonicity #716 #680]: #682
+#672 := [trans #678 #669]: #670
+#656 := [monotonicity #672]: #655
+#660 := [trans #656 #659]: #655
+#675 := [quant-inst #11 #13]: #671
+#661 := [mp #675 #660]: #674
+#627 := [unit-resolution #661 #804]: #677
+#641 := (not #677)
+#643 := (or #641 #642 #454)
+#644 := [def-axiom]: #643
+#615 := [unit-resolution #644 #627]: #635
+#540 := [unit-resolution #615 #463]: #642
+#616 := (or #453 #685)
+#639 := (or #641 #453 #685)
+#645 := [def-axiom]: #639
+#597 := [unit-resolution #645 #627]: #616
+#541 := [unit-resolution #597 #540]: #685
+#649 := (not #685)
+#650 := (or #649 #667 #454)
+#651 := [def-axiom]: #650
+#543 := [unit-resolution #651 #541 #463]: #667
+#665 := (or #703 #450)
+#666 := [def-axiom]: #665
+#544 := [unit-resolution #666 #543]: #450
+#663 := (or #703 #455)
+#664 := [def-axiom]: #663
+#545 := [unit-resolution #664 #543]: #455
+#388 := (or #453 #551 #595)
+#546 := [th-lemma arith triangle-eq]: #388
+[unit-resolution #546 #540 #545 #544]: false
+33c9f7f66858ac0e41501cb38daaa8a8b9d12fcd 311 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int S3)
+#9 := 0::Int
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 0::Int)
 decl f5 :: (-> S4 Int Int)
-#14 := 1::Int
+#11 := 3::Int
 decl f6 :: (-> S5 Int S4)
 decl f7 :: S5
-#9 := f7
-#13 := (f6 f7 #12)
-#15 := (f5 #13 1::Int)
-#807 := (= #15 0::Int)
-#709 := (not #807)
-decl f3 :: (-> S2 Int S3)
-decl f4 :: S2
-#8 := f4
-#18 := (f3 f4 0::Int)
-#16 := (f3 f4 #15)
-#19 := (= #16 #18)
-#692 := [hypothesis]: #807
-#651 := [monotonicity #692]: #19
-#20 := (not #19)
-#87 := [asserted]: #20
-#697 := [unit-resolution #87 #651]: false
-#707 := [lemma #697]: #709
-#708 := (or #719 #807)
-#189 := -1::Int
-#831 := (* -1::Int #12)
-#770 := (mod #831 -1::Int)
-#774 := (+ #15 #770)
-#772 := (= #774 0::Int)
-#743 := (ite #762 #807 #772)
-#26 := (:var 0 Int)
-#38 := (:var 1 Int)
-#58 := (f6 f7 #38)
-#59 := (f5 #58 #26)
-#892 := (pattern #59)
-#193 := (* -1::Int #26)
-#190 := (* -1::Int #38)
-#254 := (mod #190 #193)
-#384 := (+ #59 #254)
-#385 := (= #384 0::Int)
-#60 := (mod #38 #26)
-#381 := (* -1::Int #60)
-#382 := (+ #59 #381)
-#383 := (= #382 0::Int)
-#228 := (>= #38 0::Int)
-#221 := (<= #26 0::Int)
-#328 := (or #221 #228)
-#329 := (not #328)
-#217 := (<= #38 0::Int)
-#326 := (or #217 #221)
-#327 := (not #326)
-#332 := (or #327 #329)
-#386 := (ite #332 #383 #385)
-#380 := (= #59 0::Int)
-#41 := (= #38 0::Int)
-#387 := (ite #41 #380 #386)
-#379 := (= #38 #59)
-#42 := (= #26 0::Int)
-#388 := (ite #42 #379 #387)
-#893 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #892) #388)
-#391 := (forall (vars (?v0 Int) (?v1 Int)) #388)
-#896 := (iff #391 #893)
-#894 := (iff #388 #388)
-#895 := [refl]: #894
-#897 := [quant-intro #895]: #896
-#260 := (* -1::Int #254)
-#348 := (ite #332 #60 #260)
-#351 := (ite #41 0::Int #348)
-#354 := (ite #42 #38 #351)
-#357 := (= #59 #354)
-#360 := (forall (vars (?v0 Int) (?v1 Int)) #357)
-#392 := (iff #360 #391)
-#389 := (iff #357 #388)
-#390 := [rewrite]: #389
-#393 := [quant-intro #390]: #392
-#229 := (not #228)
-#222 := (not #221)
-#232 := (and #222 #229)
-#218 := (not #217)
-#225 := (and #218 #222)
-#235 := (or #225 #232)
-#280 := (ite #235 #60 #260)
-#283 := (ite #41 0::Int #280)
-#286 := (ite #42 #38 #283)
-#289 := (= #59 #286)
-#292 := (forall (vars (?v0 Int) (?v1 Int)) #289)
-#361 := (iff #292 #360)
-#358 := (iff #289 #357)
-#355 := (= #286 #354)
-#352 := (= #283 #351)
-#349 := (= #280 #348)
-#333 := (iff #235 #332)
-#330 := (iff #232 #329)
-#331 := [rewrite]: #330
-#311 := (iff #225 #327)
-#312 := [rewrite]: #311
-#334 := [monotonicity #312 #331]: #333
-#350 := [monotonicity #334]: #349
-#353 := [monotonicity #350]: #352
-#356 := [monotonicity #353]: #355
-#359 := [monotonicity #356]: #358
-#362 := [quant-intro #359]: #361
-#309 := (~ #292 #292)
-#323 := (~ #289 #289)
-#324 := [refl]: #323
-#310 := [nnf-pos #324]: #309
-#52 := (- #26)
-#51 := (- #38)
-#61 := (mod #51 #52)
-#62 := (- #61)
-#45 := (< 0::Int #26)
-#47 := (< #38 0::Int)
-#48 := (and #47 #45)
-#44 := (< 0::Int #38)
-#46 := (and #44 #45)
-#49 := (or #46 #48)
-#63 := (ite #49 #60 #62)
-#64 := (ite #41 0::Int #63)
-#65 := (ite #42 #38 #64)
-#66 := (= #59 #65)
-#67 := (forall (vars (?v0 Int) (?v1 Int)) #66)
-#295 := (iff #67 #292)
-#183 := (and #45 #47)
-#186 := (or #46 #183)
-#265 := (ite #186 #60 #260)
-#174 := (= 0::Int #38)
-#268 := (ite #174 0::Int #265)
-#177 := (= 0::Int #26)
-#271 := (ite #177 #38 #268)
-#274 := (= #59 #271)
-#277 := (forall (vars (?v0 Int) (?v1 Int)) #274)
-#293 := (iff #277 #292)
-#290 := (iff #274 #289)
-#287 := (= #271 #286)
-#284 := (= #268 #283)
-#281 := (= #265 #280)
-#236 := (iff #186 #235)
-#233 := (iff #183 #232)
-#230 := (iff #47 #229)
-#231 := [rewrite]: #230
-#223 := (iff #45 #222)
-#224 := [rewrite]: #223
-#234 := [monotonicity #224 #231]: #233
-#226 := (iff #46 #225)
-#219 := (iff #44 #218)
-#220 := [rewrite]: #219
-#227 := [monotonicity #220 #224]: #226
-#237 := [monotonicity #227 #234]: #236
-#282 := [monotonicity #237]: #281
-#211 := (iff #174 #41)
-#212 := [rewrite]: #211
-#285 := [monotonicity #212 #282]: #284
-#213 := (iff #177 #42)
-#214 := [rewrite]: #213
-#288 := [monotonicity #214 #285]: #287
-#291 := [monotonicity #288]: #290
-#294 := [quant-intro #291]: #293
-#278 := (iff #67 #277)
-#275 := (iff #66 #274)
-#272 := (= #65 #271)
-#269 := (= #64 #268)
-#266 := (= #63 #265)
-#263 := (= #62 #260)
-#257 := (- #254)
-#261 := (= #257 #260)
-#262 := [rewrite]: #261
-#258 := (= #62 #257)
-#255 := (= #61 #254)
-#194 := (= #52 #193)
-#195 := [rewrite]: #194
-#191 := (= #51 #190)
-#192 := [rewrite]: #191
-#256 := [monotonicity #192 #195]: #255
-#259 := [monotonicity #256]: #258
-#264 := [trans #259 #262]: #263
-#187 := (iff #49 #186)
-#184 := (iff #48 #183)
-#185 := [rewrite]: #184
-#188 := [monotonicity #185]: #187
-#267 := [monotonicity #188 #264]: #266
-#175 := (iff #41 #174)
-#176 := [rewrite]: #175
-#270 := [monotonicity #176 #267]: #269
-#178 := (iff #42 #177)
-#179 := [rewrite]: #178
-#273 := [monotonicity #179 #270]: #272
-#276 := [monotonicity #273]: #275
-#279 := [quant-intro #276]: #278
-#296 := [trans #279 #294]: #295
-#253 := [asserted]: #67
-#297 := [mp #253 #296]: #292
-#325 := [mp~ #297 #310]: #292
-#363 := [mp #325 #362]: #360
-#394 := [mp #363 #393]: #391
-#898 := [mp #394 #897]: #893
-#742 := (not #893)
-#748 := (or #742 #743)
-#827 := (* -1::Int 1::Int)
-#820 := (mod #831 #827)
-#821 := (+ #15 #820)
-#822 := (= #821 0::Int)
-#817 := (mod #12 1::Int)
-#818 := (* -1::Int #817)
-#823 := (+ #15 #818)
-#824 := (= #823 0::Int)
-#825 := (<= 1::Int 0::Int)
-#666 := (or #825 #819)
-#667 := (not #666)
-#810 := (or #668 #825)
-#811 := (not #810)
-#812 := (or #811 #667)
-#813 := (ite #812 #824 #822)
-#814 := (ite #808 #807 #813)
-#815 := (= #12 #15)
-#809 := (= 1::Int 0::Int)
-#816 := (ite #809 #815 #814)
-#734 := (or #742 #816)
-#731 := (iff #734 #748)
-#735 := (iff #748 #748)
-#736 := [rewrite]: #735
-#746 := (iff #816 #743)
-#703 := (or #690 #701)
-#749 := (or #703 #808)
-#750 := (ite #749 #807 #772)
-#744 := (iff #750 #743)
-#740 := (iff #749 #762)
-#741 := [rewrite]: #740
-#745 := [monotonicity #741]: #744
-#761 := (iff #816 #750)
-#756 := (ite false #815 #750)
-#759 := (iff #756 #750)
-#760 := [rewrite]: #759
-#757 := (iff #816 #756)
-#754 := (iff #814 #750)
-#764 := (ite #703 #807 #772)
-#768 := (ite #808 #807 #764)
-#752 := (iff #768 #750)
-#753 := [rewrite]: #752
-#765 := (iff #814 #768)
-#766 := (iff #813 #764)
-#777 := (iff #822 #772)
-#775 := (= #821 #774)
-#771 := (= #820 #770)
-#779 := (= #827 -1::Int)
-#786 := [rewrite]: #779
-#773 := [monotonicity #786]: #771
-#776 := [monotonicity #773]: #775
-#763 := [monotonicity #776]: #777
-#784 := (iff #824 #807)
-#782 := (= #823 #15)
-#790 := (+ #15 0::Int)
-#788 := (= #790 #15)
-#793 := [rewrite]: #788
-#791 := (= #823 #790)
-#778 := (= #818 0::Int)
-#796 := (* -1::Int 0::Int)
-#789 := (= #796 0::Int)
-#781 := [rewrite]: #789
-#800 := (= #818 #796)
-#706 := (= #817 0::Int)
-#799 := [rewrite]: #706
-#787 := [monotonicity #799]: #800
-#780 := [trans #787 #781]: #778
-#792 := [monotonicity #780]: #791
-#783 := [trans #792 #793]: #782
-#785 := [monotonicity #783]: #784
-#704 := (iff #812 #703)
-#694 := (iff #667 #701)
-#698 := (iff #666 #819)
-#699 := (or false #819)
-#798 := (iff #699 #819)
-#683 := [rewrite]: #798
-#794 := (iff #666 #699)
-#648 := (iff #825 false)
-#801 := [rewrite]: #648
-#795 := [monotonicity #801]: #794
-#700 := [trans #795 #683]: #698
-#702 := [monotonicity #700]: #694
-#649 := (iff #811 #690)
-#688 := (iff #810 #668)
-#802 := (or #668 false)
-#803 := (iff #802 #668)
-#806 := [rewrite]: #803
-#804 := (iff #810 #802)
-#805 := [monotonicity #801]: #804
-#689 := [trans #805 #806]: #688
-#797 := [monotonicity #689]: #649
-#705 := [monotonicity #797 #702]: #704
-#767 := [monotonicity #705 #785 #763]: #766
-#769 := [monotonicity #767]: #765
-#755 := [trans #769 #753]: #754
-#645 := (iff #809 false)
-#647 := [rewrite]: #645
-#758 := [monotonicity #647 #755]: #757
-#751 := [trans #758 #760]: #761
-#747 := [trans #751 #745]: #746
-#732 := [monotonicity #747]: #731
-#737 := [trans #732 #736]: #731
-#730 := [quant-inst #12 #14]: #734
-#738 := [mp #730 #737]: #748
-#687 := [unit-resolution #738 #898]: #743
-#726 := (not #743)
-#727 := (or #726 #719 #807)
-#728 := [def-axiom]: #727
-#663 := [unit-resolution #728 #687]: #708
-#664 := [unit-resolution #663 #707]: #719
-#607 := (or #762 #819)
-#718 := [def-axiom]: #607
-#669 := [unit-resolution #718 #664]: #819
-#733 := (or #762 #668)
-#739 := [def-axiom]: #733
-#670 := [unit-resolution #739 #664]: #668
-#712 := (not #808)
-#713 := (or #762 #712)
-#714 := [def-axiom]: #713
-#671 := [unit-resolution #714 #664]: #712
-#672 := (or #808 #690 #701)
-#673 := [th-lemma arith triangle-eq]: #672
-[unit-resolution #673 #671 #670 #669]: false
-unsat
-dd78f268b55a55e93289d874a56aaf5db4a02d03 317 0
+#8 := f7
+#10 := (f6 f7 0::Int)
+#12 := (f5 #10 3::Int)
+#13 := (f3 f4 #12)
+#15 := (= #13 #14)
+#462 := (= #12 0::Int)
+#23 := (:var 0 Int)
+#35 := (:var 1 Int)
+#55 := (f6 f7 #35)
+#56 := (f5 #55 #23)
+#797 := (pattern #56)
+#131 := -1::Int
+#135 := (* -1::Int #23)
+#132 := (* -1::Int #35)
+#154 := (mod #132 #135)
+#345 := (+ #56 #154)
+#346 := (= #345 0::Int)
+#57 := (mod #35 #23)
+#342 := (* -1::Int #57)
+#343 := (+ #56 #342)
+#344 := (= #343 0::Int)
+#109 := (<= #23 0::Int)
+#221 := (>= #35 0::Int)
+#289 := (or #221 #109)
+#290 := (not #289)
+#105 := (<= #35 0::Int)
+#285 := (or #105 #109)
+#286 := (not #285)
+#293 := (or #286 #290)
+#347 := (if #293 #344 #346)
+#341 := (= #56 0::Int)
+#38 := (= #35 0::Int)
+#348 := (if #38 #341 #347)
+#340 := (= #56 #35)
+#39 := (= #23 0::Int)
+#349 := (if #39 #340 #348)
+#798 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #797) #349)
+#352 := (forall (vars (?v0 Int) (?v1 Int)) #349)
+#801 := (iff #352 #798)
+#799 := (iff #349 #349)
+#800 := [refl]: #799
+#802 := [quant-intro #800]: #801
+#160 := (* -1::Int #154)
+#309 := (if #293 #57 #160)
+#312 := (if #38 0::Int #309)
+#315 := (if #39 #35 #312)
+#318 := (= #56 #315)
+#321 := (forall (vars (?v0 Int) (?v1 Int)) #318)
+#353 := (iff #321 #352)
+#350 := (iff #318 #349)
+#351 := [rewrite]: #350
+#354 := [quant-intro #351]: #353
+#110 := (not #109)
+#224 := (not #221)
+#227 := (and #224 #110)
+#106 := (not #105)
+#113 := (and #106 #110)
+#230 := (or #113 #227)
+#246 := (if #230 #57 #160)
+#249 := (if #38 0::Int #246)
+#252 := (if #39 #35 #249)
+#255 := (= #56 #252)
+#258 := (forall (vars (?v0 Int) (?v1 Int)) #255)
+#322 := (iff #258 #321)
+#319 := (iff #255 #318)
+#316 := (= #252 #315)
+#313 := (= #249 #312)
+#310 := (= #246 #309)
+#294 := (iff #230 #293)
+#291 := (iff #227 #290)
+#292 := [rewrite]: #291
+#287 := (iff #113 #286)
+#288 := [rewrite]: #287
+#295 := [monotonicity #288 #292]: #294
+#311 := [monotonicity #295]: #310
+#314 := [monotonicity #311]: #313
+#317 := [monotonicity #314]: #316
+#320 := [monotonicity #317]: #319
+#323 := [quant-intro #320]: #322
+#282 := (~ #258 #258)
+#280 := (~ #255 #255)
+#281 := [refl]: #280
+#283 := [nnf-pos #281]: #282
+#116 := (<= 0::Int #35)
+#117 := (not #116)
+#125 := (and #117 #110)
+#128 := (or #113 #125)
+#165 := (if #128 #57 #160)
+#168 := (if #38 0::Int #165)
+#171 := (if #39 #35 #168)
+#174 := (= #56 #171)
+#177 := (forall (vars (?v0 Int) (?v1 Int)) #174)
+#259 := (iff #177 #258)
+#256 := (iff #174 #255)
+#253 := (= #171 #252)
+#250 := (= #168 #249)
+#247 := (= #165 #246)
+#231 := (iff #128 #230)
+#228 := (iff #125 #227)
+#225 := (iff #117 #224)
+#222 := (iff #116 #221)
+#223 := [rewrite]: #222
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#248 := [monotonicity #232]: #247
+#251 := [monotonicity #248]: #250
+#254 := [monotonicity #251]: #253
+#257 := [monotonicity #254]: #256
+#260 := [quant-intro #257]: #259
+#49 := (- #23)
+#48 := (- #35)
+#58 := (mod #48 #49)
+#59 := (- #58)
+#42 := (< 0::Int #23)
+#44 := (< #35 0::Int)
+#45 := (and #44 #42)
+#41 := (< 0::Int #35)
+#43 := (and #41 #42)
+#46 := (or #43 #45)
+#60 := (if #46 #57 #59)
+#61 := (if #38 0::Int #60)
+#62 := (if #39 #35 #61)
+#63 := (= #56 #62)
+#64 := (forall (vars (?v0 Int) (?v1 Int)) #63)
+#178 := (iff #64 #177)
+#175 := (iff #63 #174)
+#172 := (= #62 #171)
+#169 := (= #61 #168)
+#166 := (= #60 #165)
+#163 := (= #59 #160)
+#157 := (- #154)
+#161 := (= #157 #160)
+#162 := [rewrite]: #161
+#158 := (= #59 #157)
+#155 := (= #58 #154)
+#136 := (= #49 #135)
+#137 := [rewrite]: #136
+#133 := (= #48 #132)
+#134 := [rewrite]: #133
+#156 := [monotonicity #134 #137]: #155
+#159 := [monotonicity #156]: #158
+#164 := [trans #159 #162]: #163
+#129 := (iff #46 #128)
+#126 := (iff #45 #125)
+#111 := (iff #42 #110)
+#112 := [rewrite]: #111
+#118 := (iff #44 #117)
+#122 := (iff #117 #117)
+#120 := (iff #116 #116)
+#121 := [rewrite]: #120
+#123 := [monotonicity #121]: #122
+#119 := [rewrite]: #118
+#124 := [trans #119 #123]: #118
+#127 := [monotonicity #124 #112]: #126
+#114 := (iff #43 #113)
+#107 := (iff #41 #106)
+#108 := [rewrite]: #107
+#115 := [monotonicity #108 #112]: #114
+#130 := [monotonicity #115 #127]: #129
+#167 := [monotonicity #130 #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [monotonicity #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [quant-intro #176]: #178
+#71 := [asserted]: #64
+#180 := [mp #71 #179]: #177
+#261 := [mp #180 #260]: #258
+#284 := [mp~ #261 #283]: #258
+#324 := [mp #284 #323]: #321
+#355 := [mp #324 #354]: #352
+#803 := [mp #355 #802]: #798
+#660 := (not #798)
+#661 := (or #660 #462)
+#735 := (* -1::Int 3::Int)
+#731 := (* -1::Int 0::Int)
+#732 := (mod #731 #735)
+#736 := (+ #12 #732)
+#725 := (= #736 0::Int)
+#455 := (mod 0::Int 3::Int)
+#733 := (* -1::Int #455)
+#734 := (+ #12 #733)
+#449 := (= #734 0::Int)
+#741 := (<= 3::Int 0::Int)
+#551 := (>= 0::Int 0::Int)
+#452 := (or #551 #741)
+#453 := (not #452)
+#737 := (<= 0::Int 0::Int)
+#738 := (or #737 #741)
+#742 := (not #738)
+#454 := (or #742 #453)
+#726 := (if #454 #449 #725)
+#463 := (= 0::Int 0::Int)
+#727 := (if #463 #462 #726)
+#740 := (= 3::Int 0::Int)
+#722 := (if #740 #462 #727)
+#662 := (or #660 #722)
+#664 := (iff #662 #661)
+#666 := (iff #661 #661)
+#656 := [rewrite]: #666
+#658 := (iff #722 #462)
+#678 := (if false #462 #462)
+#681 := (iff #678 #462)
+#677 := [rewrite]: #681
+#655 := (iff #722 #678)
+#674 := (iff #727 #462)
+#1 := true
+#669 := (if true #462 #462)
+#673 := (iff #669 #462)
+#670 := [rewrite]: #673
+#671 := (iff #727 #669)
+#682 := (iff #726 #462)
+#679 := (iff #726 #678)
+#675 := (iff #725 #462)
+#684 := (= #736 #12)
+#608 := (+ #12 0::Int)
+#611 := (= #608 #12)
+#704 := [rewrite]: #611
+#689 := (= #736 #608)
+#687 := (= #732 0::Int)
+#686 := -3::Int
+#695 := (mod 0::Int -3::Int)
+#693 := (= #695 0::Int)
+#698 := [rewrite]: #693
+#696 := (= #732 #695)
+#683 := (= #735 -3::Int)
+#685 := [rewrite]: #683
+#605 := (= #731 0::Int)
+#606 := [rewrite]: #605
+#697 := [monotonicity #606 #685]: #696
+#688 := [trans #697 #698]: #687
+#690 := [monotonicity #688]: #689
+#691 := [trans #690 #704]: #684
+#676 := [monotonicity #691]: #675
+#692 := (iff #449 #462)
+#701 := (= #734 #12)
+#609 := (= #734 #608)
+#599 := (= #733 0::Int)
+#588 := (= #733 #731)
+#700 := (= #455 0::Int)
+#703 := [rewrite]: #700
+#603 := [monotonicity #703]: #588
+#607 := [trans #603 #606]: #599
+#610 := [monotonicity #607]: #609
+#705 := [trans #610 #704]: #701
+#694 := [monotonicity #705]: #692
+#604 := (iff #454 false)
+#593 := (or false false)
+#554 := (iff #593 false)
+#702 := [rewrite]: #554
+#594 := (iff #454 #593)
+#708 := (iff #453 false)
+#420 := (not true)
+#745 := (iff #420 false)
+#408 := [rewrite]: #745
+#709 := (iff #453 #420)
+#706 := (iff #452 true)
+#715 := (or true false)
+#718 := (iff #715 true)
+#712 := [rewrite]: #718
+#552 := (iff #452 #715)
+#572 := (iff #741 false)
+#573 := [rewrite]: #572
+#424 := (iff #551 true)
+#760 := [rewrite]: #424
+#553 := [monotonicity #760 #573]: #552
+#707 := [trans #553 #712]: #706
+#710 := [monotonicity #707]: #709
+#711 := [trans #710 #408]: #708
+#721 := (iff #742 false)
+#720 := (iff #742 #420)
+#713 := (iff #738 true)
+#716 := (iff #738 #715)
+#730 := (iff #737 true)
+#571 := [rewrite]: #730
+#717 := [monotonicity #571 #573]: #716
+#719 := [trans #717 #712]: #713
+#714 := [monotonicity #719]: #720
+#550 := [trans #714 #408]: #721
+#595 := [monotonicity #550 #711]: #594
+#699 := [trans #595 #702]: #604
+#680 := [monotonicity #699 #694 #676]: #679
+#668 := [trans #680 #677]: #682
+#729 := (iff #463 true)
+#724 := [rewrite]: #729
+#672 := [monotonicity #724 #668]: #671
+#654 := [trans #672 #670]: #674
+#723 := (iff #740 false)
+#728 := [rewrite]: #723
+#657 := [monotonicity #728 #654]: #655
+#659 := [trans #657 #677]: #658
+#665 := [monotonicity #659]: #664
+#667 := [trans #665 #656]: #664
+#663 := [quant-inst #9 #11]: #662
+#645 := [mp #663 #667]: #661
+#648 := [unit-resolution #645 #803]: #462
+#649 := [monotonicity #648]: #15
+#16 := (not #15)
+#66 := [asserted]: #16
+[unit-resolution #66 #649]: false
+b6547dc3ec1930e52fec661a7dc0e7e45f2f11a0 337 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int S3)
-#10 := 0::Int
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 0::Int)
+#9 := 1::Int
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 1::Int)
 decl f5 :: (-> S4 Int Int)
-#12 := 3::Int
+#11 := 3::Int
 decl f6 :: (-> S5 Int S4)
 decl f7 :: S5
-#9 := f7
-#11 := (f6 f7 0::Int)
-#13 := (f5 #11 3::Int)
-#14 := (f3 f4 #13)
-#16 := (= #14 #15)
-#807 := (= #13 0::Int)
+#8 := f7
+#10 := (f6 f7 1::Int)
+#12 := (f5 #10 3::Int)
+#13 := (f3 f4 #12)
+#15 := (= #13 #14)
+#463 := (= #12 1::Int)
 #24 := (:var 0 Int)
 #36 := (:var 1 Int)
 #56 := (f6 f7 #36)
 #57 := (f5 #56 #24)
-#891 := (pattern #57)
-#187 := -1::Int
-#191 := (* -1::Int #24)
-#188 := (* -1::Int #36)
-#252 := (mod #188 #191)
-#382 := (+ #57 #252)
-#383 := (= #382 0::Int)
+#797 := (pattern #57)
+#23 := 0::Int
+#132 := -1::Int
+#136 := (* -1::Int #24)
+#133 := (* -1::Int #36)
+#155 := (mod #133 #136)
+#346 := (+ #57 #155)
+#347 := (= #346 0::Int)
 #58 := (mod #36 #24)
-#379 := (* -1::Int #58)
-#380 := (+ #57 #379)
-#381 := (= #380 0::Int)
-#226 := (>= #36 0::Int)
-#219 := (<= #24 0::Int)
-#326 := (or #219 #226)
-#327 := (not #326)
-#215 := (<= #36 0::Int)
-#324 := (or #215 #219)
-#325 := (not #324)
-#330 := (or #325 #327)
-#384 := (ite #330 #381 #383)
-#378 := (= #57 0::Int)
+#343 := (* -1::Int #58)
+#344 := (+ #57 #343)
+#345 := (= #344 0::Int)
+#110 := (<= #24 0::Int)
+#222 := (>= #36 0::Int)
+#290 := (or #222 #110)
+#291 := (not #290)
+#106 := (<= #36 0::Int)
+#286 := (or #106 #110)
+#287 := (not #286)
+#294 := (or #287 #291)
+#348 := (if #294 #345 #347)
+#342 := (= #57 0::Int)
 #39 := (= #36 0::Int)
-#385 := (ite #39 #378 #384)
-#377 := (= #36 #57)
+#349 := (if #39 #342 #348)
+#341 := (= #57 #36)
 #40 := (= #24 0::Int)
-#386 := (ite #40 #377 #385)
-#892 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #891) #386)
-#389 := (forall (vars (?v0 Int) (?v1 Int)) #386)
-#895 := (iff #389 #892)
-#893 := (iff #386 #386)
-#894 := [refl]: #893
-#896 := [quant-intro #894]: #895
-#258 := (* -1::Int #252)
-#346 := (ite #330 #58 #258)
-#349 := (ite #39 0::Int #346)
-#352 := (ite #40 #36 #349)
-#355 := (= #57 #352)
-#358 := (forall (vars (?v0 Int) (?v1 Int)) #355)
-#390 := (iff #358 #389)
-#387 := (iff #355 #386)
-#388 := [rewrite]: #387
-#391 := [quant-intro #388]: #390
-#227 := (not #226)
-#220 := (not #219)
-#230 := (and #220 #227)
-#216 := (not #215)
-#223 := (and #216 #220)
-#233 := (or #223 #230)
-#278 := (ite #233 #58 #258)
-#281 := (ite #39 0::Int #278)
-#284 := (ite #40 #36 #281)
-#287 := (= #57 #284)
-#290 := (forall (vars (?v0 Int) (?v1 Int)) #287)
-#359 := (iff #290 #358)
-#356 := (iff #287 #355)
-#353 := (= #284 #352)
-#350 := (= #281 #349)
-#347 := (= #278 #346)
-#331 := (iff #233 #330)
-#328 := (iff #230 #327)
-#329 := [rewrite]: #328
-#309 := (iff #223 #325)
-#310 := [rewrite]: #309
-#332 := [monotonicity #310 #329]: #331
-#348 := [monotonicity #332]: #347
-#351 := [monotonicity #348]: #350
-#354 := [monotonicity #351]: #353
-#357 := [monotonicity #354]: #356
-#360 := [quant-intro #357]: #359
-#307 := (~ #290 #290)
-#321 := (~ #287 #287)
-#322 := [refl]: #321
-#308 := [nnf-pos #322]: #307
-#50 := (- #24)
-#49 := (- #36)
-#59 := (mod #49 #50)
-#60 := (- #59)
-#43 := (< 0::Int #24)
-#45 := (< #36 0::Int)
-#46 := (and #45 #43)
-#42 := (< 0::Int #36)
-#44 := (and #42 #43)
-#47 := (or #44 #46)
-#61 := (ite #47 #58 #60)
-#62 := (ite #39 0::Int #61)
-#63 := (ite #40 #36 #62)
-#64 := (= #57 #63)
-#65 := (forall (vars (?v0 Int) (?v1 Int)) #64)
-#293 := (iff #65 #290)
-#181 := (and #43 #45)
-#184 := (or #44 #181)
-#263 := (ite #184 #58 #258)
-#172 := (= 0::Int #36)
-#266 := (ite #172 0::Int #263)
-#175 := (= 0::Int #24)
-#269 := (ite #175 #36 #266)
-#272 := (= #57 #269)
-#275 := (forall (vars (?v0 Int) (?v1 Int)) #272)
-#291 := (iff #275 #290)
-#288 := (iff #272 #287)
-#285 := (= #269 #284)
-#282 := (= #266 #281)
-#279 := (= #263 #278)
-#234 := (iff #184 #233)
-#231 := (iff #181 #230)
-#228 := (iff #45 #227)
-#229 := [rewrite]: #228
-#221 := (iff #43 #220)
-#222 := [rewrite]: #221
-#232 := [monotonicity #222 #229]: #231
-#224 := (iff #44 #223)
-#217 := (iff #42 #216)
-#218 := [rewrite]: #217
-#225 := [monotonicity #218 #222]: #224
-#235 := [monotonicity #225 #232]: #234
-#280 := [monotonicity #235]: #279
-#209 := (iff #172 #39)
-#210 := [rewrite]: #209
-#283 := [monotonicity #210 #280]: #282
-#211 := (iff #175 #40)
-#212 := [rewrite]: #211
-#286 := [monotonicity #212 #283]: #285
-#289 := [monotonicity #286]: #288
-#292 := [quant-intro #289]: #291
-#276 := (iff #65 #275)
-#273 := (iff #64 #272)
-#270 := (= #63 #269)
-#267 := (= #62 #266)
-#264 := (= #61 #263)
-#261 := (= #60 #258)
-#255 := (- #252)
-#259 := (= #255 #258)
-#260 := [rewrite]: #259
-#256 := (= #60 #255)
-#253 := (= #59 #252)
-#192 := (= #50 #191)
-#193 := [rewrite]: #192
-#189 := (= #49 #188)
-#190 := [rewrite]: #189
-#254 := [monotonicity #190 #193]: #253
-#257 := [monotonicity #254]: #256
-#262 := [trans #257 #260]: #261
-#185 := (iff #47 #184)
-#182 := (iff #46 #181)
-#183 := [rewrite]: #182
-#186 := [monotonicity #183]: #185
-#265 := [monotonicity #186 #262]: #264
-#173 := (iff #39 #172)
-#174 := [rewrite]: #173
-#268 := [monotonicity #174 #265]: #267
-#176 := (iff #40 #175)
-#177 := [rewrite]: #176
-#271 := [monotonicity #177 #268]: #270
-#274 := [monotonicity #271]: #273
-#277 := [quant-intro #274]: #276
-#294 := [trans #277 #292]: #293
-#251 := [asserted]: #65
-#295 := [mp #251 #294]: #290
-#323 := [mp~ #295 #308]: #290
-#361 := [mp #323 #360]: #358
-#392 := [mp #361 #391]: #389
-#897 := [mp #392 #896]: #892
-#736 := (not #892)
-#737 := (or #736 #807)
-#819 := (* -1::Int 3::Int)
-#820 := (* -1::Int 0::Int)
-#821 := (mod #820 #819)
-#816 := (+ #13 #821)
-#817 := (= #816 0::Int)
-#822 := (mod 0::Int 3::Int)
-#823 := (* -1::Int #822)
-#818 := (+ #13 #823)
-#824 := (= #818 0::Int)
-#841 := (>= 0::Int 0::Int)
-#665 := (<= 3::Int 0::Int)
-#666 := (or #665 #841)
-#667 := (not #666)
-#809 := (<= 0::Int 0::Int)
-#810 := (or #809 #665)
-#811 := (not #810)
-#812 := (or #811 #667)
-#806 := (ite #812 #824 #817)
-#813 := (= 0::Int 0::Int)
-#814 := (ite #813 #807 #806)
-#808 := (= 0::Int #13)
-#815 := (= 3::Int 0::Int)
-#644 := (ite #815 #808 #814)
-#732 := (or #736 #644)
-#711 := (iff #732 #737)
-#713 := (iff #737 #737)
-#606 := [rewrite]: #713
-#734 := (iff #644 #807)
-#760 := (ite false #807 #807)
-#739 := (iff #760 #807)
-#740 := [rewrite]: #739
-#730 := (iff #644 #760)
-#733 := (iff #814 #807)
-#1 := true
-#744 := (ite true #807 #807)
-#741 := (iff #744 #807)
-#747 := [rewrite]: #741
-#745 := (iff #814 #744)
-#742 := (iff #806 #807)
-#750 := (iff #806 #760)
-#758 := (iff #817 #807)
-#756 := (= #816 #13)
-#770 := (+ #13 0::Int)
-#774 := (= #770 #13)
-#775 := [rewrite]: #774
-#754 := (= #816 #770)
-#752 := (= #821 0::Int)
-#765 := -3::Int
-#764 := (mod 0::Int -3::Int)
-#749 := (= #764 0::Int)
-#751 := [rewrite]: #749
-#768 := (= #821 #764)
-#766 := (= #819 -3::Int)
-#767 := [rewrite]: #766
-#784 := (= #820 0::Int)
-#778 := [rewrite]: #784
-#748 := [monotonicity #778 #767]: #768
-#753 := [trans #748 #751]: #752
-#755 := [monotonicity #753]: #754
-#757 := [trans #755 #775]: #756
-#759 := [monotonicity #757]: #758
-#762 := (iff #824 #807)
-#771 := (= #818 #13)
-#772 := (= #818 #770)
-#785 := (= #823 0::Int)
-#782 := (= #823 #820)
-#792 := (= #822 0::Int)
-#781 := [rewrite]: #792
-#783 := [monotonicity #781]: #782
-#769 := [trans #783 #778]: #785
-#773 := [monotonicity #769]: #772
-#776 := [trans #773 #775]: #771
-#763 := [monotonicity #776]: #762
-#791 := (iff #812 false)
-#780 := (or false false)
-#789 := (iff #780 false)
-#790 := [rewrite]: #789
-#777 := (iff #812 #780)
-#786 := (iff #667 false)
-#489 := (not true)
-#848 := (iff #489 false)
-#851 := [rewrite]: #848
-#795 := (iff #667 #489)
-#705 := (iff #666 true)
-#693 := (or false true)
-#703 := (iff #693 true)
-#704 := [rewrite]: #703
-#701 := (iff #666 #693)
-#847 := (iff #841 true)
-#849 := [rewrite]: #847
-#687 := (iff #665 false)
-#688 := [rewrite]: #687
-#702 := [monotonicity #688 #849]: #701
-#798 := [trans #702 #704]: #705
-#799 := [monotonicity #798]: #795
-#788 := [trans #799 #851]: #786
-#699 := (iff #811 false)
-#682 := (iff #811 #489)
-#794 := (iff #810 true)
-#689 := (or true false)
-#698 := (iff #689 true)
-#793 := [rewrite]: #698
-#648 := (iff #810 #689)
-#802 := (iff #809 true)
-#805 := [rewrite]: #802
-#796 := [monotonicity #805 #688]: #648
-#797 := [trans #796 #793]: #794
-#697 := [monotonicity #797]: #682
-#700 := [trans #697 #851]: #699
-#779 := [monotonicity #700 #788]: #777
-#787 := [trans #779 #790]: #791
-#761 := [monotonicity #787 #763 #759]: #750
-#743 := [trans #761 #740]: #742
-#803 := (iff #813 true)
-#804 := [rewrite]: #803
-#746 := [monotonicity #804 #743]: #745
-#729 := [trans #746 #747]: #733
-#800 := (iff #808 #807)
-#801 := [rewrite]: #800
-#646 := (iff #815 false)
-#647 := [rewrite]: #646
-#731 := [monotonicity #647 #801 #729]: #730
-#735 := [trans #731 #740]: #734
-#712 := [monotonicity #735]: #711
-#717 := [trans #712 #606]: #711
-#738 := [quant-inst #10 #12]: #732
-#718 := [mp #738 #717]: #737
-#724 := [unit-resolution #718 #897]: #807
-#720 := [monotonicity #724]: #16
-#17 := (not #16)
-#85 := [asserted]: #17
-[unit-resolution #85 #720]: false
-unsat
-e14d183d09c6b042e6338ab8deb492b16b39b14c 343 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#10 := 1::Int
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 1::Int)
-decl f5 :: (-> S4 Int Int)
-#12 := 3::Int
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#9 := f7
-#11 := (f6 f7 1::Int)
-#13 := (f5 #11 3::Int)
-#14 := (f3 f4 #13)
-#16 := (= #14 #15)
-#804 := (= #13 1::Int)
-#25 := (:var 0 Int)
-#37 := (:var 1 Int)
-#57 := (f6 f7 #37)
-#58 := (f5 #57 #25)
-#891 := (pattern #58)
-#24 := 0::Int
-#188 := -1::Int
-#192 := (* -1::Int #25)
-#189 := (* -1::Int #37)
-#253 := (mod #189 #192)
-#383 := (+ #58 #253)
-#384 := (= #383 0::Int)
-#59 := (mod #37 #25)
-#380 := (* -1::Int #59)
-#381 := (+ #58 #380)
-#382 := (= #381 0::Int)
-#227 := (>= #37 0::Int)
-#220 := (<= #25 0::Int)
-#327 := (or #220 #227)
-#328 := (not #327)
-#216 := (<= #37 0::Int)
-#325 := (or #216 #220)
-#326 := (not #325)
-#331 := (or #326 #328)
-#385 := (ite #331 #382 #384)
-#379 := (= #58 0::Int)
-#40 := (= #37 0::Int)
-#386 := (ite #40 #379 #385)
-#378 := (= #37 #58)
-#41 := (= #25 0::Int)
-#387 := (ite #41 #378 #386)
-#892 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #891) #387)
-#390 := (forall (vars (?v0 Int) (?v1 Int)) #387)
-#895 := (iff #390 #892)
-#893 := (iff #387 #387)
-#894 := [refl]: #893
-#896 := [quant-intro #894]: #895
-#259 := (* -1::Int #253)
-#347 := (ite #331 #59 #259)
-#350 := (ite #40 0::Int #347)
-#353 := (ite #41 #37 #350)
-#356 := (= #58 #353)
-#359 := (forall (vars (?v0 Int) (?v1 Int)) #356)
-#391 := (iff #359 #390)
-#388 := (iff #356 #387)
-#389 := [rewrite]: #388
-#392 := [quant-intro #389]: #391
-#228 := (not #227)
-#221 := (not #220)
-#231 := (and #221 #228)
-#217 := (not #216)
-#224 := (and #217 #221)
-#234 := (or #224 #231)
-#279 := (ite #234 #59 #259)
-#282 := (ite #40 0::Int #279)
-#285 := (ite #41 #37 #282)
-#288 := (= #58 #285)
-#291 := (forall (vars (?v0 Int) (?v1 Int)) #288)
-#360 := (iff #291 #359)
-#357 := (iff #288 #356)
-#354 := (= #285 #353)
-#351 := (= #282 #350)
-#348 := (= #279 #347)
-#332 := (iff #234 #331)
-#329 := (iff #231 #328)
-#330 := [rewrite]: #329
-#310 := (iff #224 #326)
-#311 := [rewrite]: #310
-#333 := [monotonicity #311 #330]: #332
-#349 := [monotonicity #333]: #348
-#352 := [monotonicity #349]: #351
-#355 := [monotonicity #352]: #354
-#358 := [monotonicity #355]: #357
-#361 := [quant-intro #358]: #360
-#308 := (~ #291 #291)
-#322 := (~ #288 #288)
-#323 := [refl]: #322
-#309 := [nnf-pos #323]: #308
-#51 := (- #25)
-#50 := (- #37)
-#60 := (mod #50 #51)
-#61 := (- #60)
-#44 := (< 0::Int #25)
-#46 := (< #37 0::Int)
-#47 := (and #46 #44)
-#43 := (< 0::Int #37)
-#45 := (and #43 #44)
-#48 := (or #45 #47)
-#62 := (ite #48 #59 #61)
-#63 := (ite #40 0::Int #62)
-#64 := (ite #41 #37 #63)
-#65 := (= #58 #64)
-#66 := (forall (vars (?v0 Int) (?v1 Int)) #65)
-#294 := (iff #66 #291)
-#182 := (and #44 #46)
-#185 := (or #45 #182)
-#264 := (ite #185 #59 #259)
-#173 := (= 0::Int #37)
-#267 := (ite #173 0::Int #264)
-#176 := (= 0::Int #25)
-#270 := (ite #176 #37 #267)
-#273 := (= #58 #270)
-#276 := (forall (vars (?v0 Int) (?v1 Int)) #273)
-#292 := (iff #276 #291)
-#289 := (iff #273 #288)
-#286 := (= #270 #285)
-#283 := (= #267 #282)
-#280 := (= #264 #279)
-#235 := (iff #185 #234)
-#232 := (iff #182 #231)
-#229 := (iff #46 #228)
-#230 := [rewrite]: #229
-#222 := (iff #44 #221)
-#223 := [rewrite]: #222
-#233 := [monotonicity #223 #230]: #232
-#225 := (iff #45 #224)
-#218 := (iff #43 #217)
-#219 := [rewrite]: #218
-#226 := [monotonicity #219 #223]: #225
-#236 := [monotonicity #226 #233]: #235
-#281 := [monotonicity #236]: #280
-#210 := (iff #173 #40)
-#211 := [rewrite]: #210
-#284 := [monotonicity #211 #281]: #283
-#212 := (iff #176 #41)
-#213 := [rewrite]: #212
-#287 := [monotonicity #213 #284]: #286
-#290 := [monotonicity #287]: #289
-#293 := [quant-intro #290]: #292
-#277 := (iff #66 #276)
-#274 := (iff #65 #273)
-#271 := (= #64 #270)
-#268 := (= #63 #267)
-#265 := (= #62 #264)
-#262 := (= #61 #259)
-#256 := (- #253)
-#260 := (= #256 #259)
-#261 := [rewrite]: #260
-#257 := (= #61 #256)
-#254 := (= #60 #253)
-#193 := (= #51 #192)
-#194 := [rewrite]: #193
-#190 := (= #50 #189)
-#191 := [rewrite]: #190
-#255 := [monotonicity #191 #194]: #254
+#350 := (if #40 #341 #349)
+#798 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #797) #350)
+#353 := (forall (vars (?v0 Int) (?v1 Int)) #350)
+#801 := (iff #353 #798)
+#799 := (iff #350 #350)
+#800 := [refl]: #799
+#802 := [quant-intro #800]: #801
+#161 := (* -1::Int #155)
+#310 := (if #294 #58 #161)
+#313 := (if #39 0::Int #310)
+#316 := (if #40 #36 #313)
+#319 := (= #57 #316)
+#322 := (forall (vars (?v0 Int) (?v1 Int)) #319)
+#354 := (iff #322 #353)
+#351 := (iff #319 #350)
+#352 := [rewrite]: #351
+#355 := [quant-intro #352]: #354
+#111 := (not #110)
+#225 := (not #222)
+#228 := (and #225 #111)
+#107 := (not #106)
+#114 := (and #107 #111)
+#231 := (or #114 #228)
+#247 := (if #231 #58 #161)
+#250 := (if #39 0::Int #247)
+#253 := (if #40 #36 #250)
+#256 := (= #57 #253)
+#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
+#323 := (iff #259 #322)
+#320 := (iff #256 #319)
+#317 := (= #253 #316)
+#314 := (= #250 #313)
+#311 := (= #247 #310)
+#295 := (iff #231 #294)
+#292 := (iff #228 #291)
+#293 := [rewrite]: #292
+#288 := (iff #114 #287)
+#289 := [rewrite]: #288
+#296 := [monotonicity #289 #293]: #295
+#312 := [monotonicity #296]: #311
+#315 := [monotonicity #312]: #314
+#318 := [monotonicity #315]: #317
+#321 := [monotonicity #318]: #320
+#324 := [quant-intro #321]: #323
+#283 := (~ #259 #259)
+#281 := (~ #256 #256)
+#282 := [refl]: #281
+#284 := [nnf-pos #282]: #283
+#117 := (<= 0::Int #36)
+#118 := (not #117)
+#126 := (and #118 #111)
+#129 := (or #114 #126)
+#166 := (if #129 #58 #161)
+#169 := (if #39 0::Int #166)
+#172 := (if #40 #36 #169)
+#175 := (= #57 #172)
+#178 := (forall (vars (?v0 Int) (?v1 Int)) #175)
+#260 := (iff #178 #259)
+#257 := (iff #175 #256)
+#254 := (= #172 #253)
+#251 := (= #169 #250)
+#248 := (= #166 #247)
+#232 := (iff #129 #231)
+#229 := (iff #126 #228)
+#226 := (iff #118 #225)
+#223 := (iff #117 #222)
+#224 := [rewrite]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#249 := [monotonicity #233]: #248
+#252 := [monotonicity #249]: #251
+#255 := [monotonicity #252]: #254
 #258 := [monotonicity #255]: #257
-#263 := [trans #258 #261]: #262
-#186 := (iff #48 #185)
-#183 := (iff #47 #182)
-#184 := [rewrite]: #183
-#187 := [monotonicity #184]: #186
-#266 := [monotonicity #187 #263]: #265
-#174 := (iff #40 #173)
-#175 := [rewrite]: #174
-#269 := [monotonicity #175 #266]: #268
-#177 := (iff #41 #176)
-#178 := [rewrite]: #177
-#272 := [monotonicity #178 #269]: #271
-#275 := [monotonicity #272]: #274
-#278 := [quant-intro #275]: #277
-#295 := [trans #278 #293]: #294
-#252 := [asserted]: #66
-#296 := [mp #252 #295]: #291
-#324 := [mp~ #296 #309]: #291
-#362 := [mp #324 #361]: #359
-#393 := [mp #362 #392]: #390
-#897 := [mp #393 #896]: #892
-#716 := (not #892)
-#684 := (or #716 #804)
-#821 := (* -1::Int 3::Int)
-#816 := (* -1::Int 1::Int)
-#817 := (mod #816 #821)
-#822 := (+ #13 #817)
-#823 := (= #822 0::Int)
-#818 := (mod 1::Int 3::Int)
-#824 := (* -1::Int #818)
-#665 := (+ #13 #824)
-#666 := (= #665 0::Int)
-#842 := (>= 1::Int 0::Int)
-#667 := (<= 3::Int 0::Int)
-#809 := (or #667 #842)
-#810 := (not #809)
-#811 := (<= 1::Int 0::Int)
-#812 := (or #811 #667)
-#806 := (not #812)
-#807 := (or #806 #810)
-#813 := (ite #807 #666 #823)
-#814 := (= #13 0::Int)
-#808 := (= 1::Int 0::Int)
-#815 := (ite #808 #814 #813)
-#644 := (= 1::Int #13)
-#646 := (= 3::Int 0::Int)
-#647 := (ite #646 #644 #815)
-#691 := (or #716 #647)
-#681 := (iff #691 #684)
-#685 := (iff #684 #684)
-#692 := [rewrite]: #685
-#715 := (iff #647 #804)
-#708 := (ite false #804 #804)
-#690 := (iff #708 #804)
-#714 := [rewrite]: #690
-#654 := (iff #647 #708)
-#723 := (iff #815 #804)
-#721 := (ite false #814 #804)
-#726 := (iff #721 #804)
-#727 := [rewrite]: #726
-#722 := (iff #815 #721)
-#724 := (iff #813 #804)
-#736 := -2::Int
-#737 := (= #13 -2::Int)
-#1 := true
-#713 := (ite true #804 #737)
-#718 := (iff #713 #804)
-#719 := [rewrite]: #718
-#606 := (iff #813 #713)
-#711 := (iff #823 #737)
-#761 := 2::Int
-#741 := (+ 2::Int #13)
-#731 := (= #741 0::Int)
-#732 := (iff #731 #737)
-#738 := [rewrite]: #732
-#734 := (iff #823 #731)
-#729 := (= #822 #741)
-#744 := (+ #13 2::Int)
-#747 := (= #744 #741)
-#733 := [rewrite]: #747
-#745 := (= #822 #744)
-#742 := (= #817 2::Int)
-#756 := -3::Int
-#759 := (mod -1::Int -3::Int)
-#739 := (= #759 2::Int)
-#740 := [rewrite]: #739
-#760 := (= #817 #759)
-#757 := (= #821 -3::Int)
-#758 := [rewrite]: #757
-#773 := (= #816 -1::Int)
-#774 := [rewrite]: #773
-#750 := [monotonicity #774 #758]: #760
-#743 := [trans #750 #740]: #742
-#746 := [monotonicity #743]: #745
-#730 := [trans #746 #733]: #729
-#735 := [monotonicity #730]: #734
-#712 := [trans #735 #738]: #711
-#754 := (iff #666 #804)
-#765 := (+ -1::Int #13)
-#748 := (= #765 0::Int)
-#752 := (iff #748 #804)
-#753 := [rewrite]: #752
-#749 := (iff #666 #748)
-#764 := (= #665 #765)
-#776 := (+ #13 -1::Int)
-#766 := (= #776 #765)
-#767 := [rewrite]: #766
-#762 := (= #665 #776)
-#775 := (= #824 -1::Int)
-#770 := (= #824 #816)
-#785 := (= #818 1::Int)
-#769 := [rewrite]: #785
-#772 := [monotonicity #769]: #770
-#771 := [trans #772 #774]: #775
-#763 := [monotonicity #771]: #762
-#768 := [trans #763 #767]: #764
-#751 := [monotonicity #768]: #749
-#755 := [trans #751 #753]: #754
-#784 := (iff #807 true)
-#787 := (or true false)
-#782 := (iff #787 true)
-#783 := [rewrite]: #782
-#792 := (iff #807 #787)
-#790 := (iff #810 false)
-#490 := (not true)
-#851 := (iff #490 false)
-#837 := [rewrite]: #851
-#779 := (iff #810 #490)
-#780 := (iff #809 true)
-#798 := (or false true)
-#786 := (iff #798 true)
-#788 := [rewrite]: #786
-#795 := (iff #809 #798)
-#849 := (iff #842 true)
-#489 := [rewrite]: #849
-#648 := (iff #667 false)
-#796 := [rewrite]: #648
-#799 := [monotonicity #796 #489]: #795
-#777 := [trans #799 #788]: #780
-#789 := [monotonicity #777]: #779
-#791 := [trans #789 #837]: #790
-#704 := (iff #806 true)
-#700 := (not false)
-#702 := (iff #700 true)
-#703 := [rewrite]: #702
-#693 := (iff #806 #700)
-#697 := (iff #812 false)
-#698 := (or false false)
-#797 := (iff #698 false)
-#682 := [rewrite]: #797
-#793 := (iff #812 #698)
-#688 := (iff #811 false)
-#689 := [rewrite]: #688
-#794 := [monotonicity #689 #796]: #793
-#699 := [trans #794 #682]: #697
-#701 := [monotonicity #699]: #693
-#705 := [trans #701 #703]: #704
-#781 := [monotonicity #705 #791]: #792
-#778 := [trans #781 #783]: #784
-#717 := [monotonicity #778 #755 #712]: #606
-#720 := [trans #717 #719]: #724
-#805 := (iff #808 false)
-#687 := [rewrite]: #805
-#725 := [monotonicity #687 #720]: #722
-#728 := [trans #725 #727]: #723
-#803 := (iff #644 #804)
-#802 := [rewrite]: #803
-#800 := (iff #646 false)
-#801 := [rewrite]: #800
-#709 := [monotonicity #801 #802 #728]: #654
-#710 := [trans #709 #714]: #715
-#683 := [monotonicity #710]: #681
-#694 := [trans #683 #692]: #681
-#650 := [quant-inst #10 #12]: #691
-#695 := [mp #650 #694]: #684
-#686 := [unit-resolution #695 #897]: #804
-#707 := [monotonicity #686]: #16
-#17 := (not #16)
-#86 := [asserted]: #17
-[unit-resolution #86 #707]: false
-unsat
-958d3f7cb567adebadc6dbc4451d5cffa3fe139d 318 0
-#2 := false
-decl f3 :: (-> S2 Int S3)
-#14 := 0::Int
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 0::Int)
-decl f5 :: (-> S4 Int Int)
-#10 := 3::Int
-decl f6 :: (-> S5 Int S4)
-decl f7 :: S5
-#9 := f7
-#11 := (f6 f7 3::Int)
-#12 := (f5 #11 3::Int)
-#13 := (f3 f4 #12)
-#16 := (= #13 #15)
-#806 := (= #12 0::Int)
-#24 := (:var 0 Int)
-#36 := (:var 1 Int)
-#56 := (f6 f7 #36)
-#57 := (f5 #56 #24)
-#891 := (pattern #57)
-#187 := -1::Int
-#191 := (* -1::Int #24)
-#188 := (* -1::Int #36)
-#252 := (mod #188 #191)
-#382 := (+ #57 #252)
-#383 := (= #382 0::Int)
-#58 := (mod #36 #24)
-#379 := (* -1::Int #58)
-#380 := (+ #57 #379)
-#381 := (= #380 0::Int)
-#226 := (>= #36 0::Int)
-#219 := (<= #24 0::Int)
-#326 := (or #219 #226)
-#327 := (not #326)
-#215 := (<= #36 0::Int)
-#324 := (or #215 #219)
-#325 := (not #324)
-#330 := (or #325 #327)
-#384 := (ite #330 #381 #383)
-#378 := (= #57 0::Int)
-#39 := (= #36 0::Int)
-#385 := (ite #39 #378 #384)
-#377 := (= #36 #57)
-#40 := (= #24 0::Int)
-#386 := (ite #40 #377 #385)
-#892 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #891) #386)
-#389 := (forall (vars (?v0 Int) (?v1 Int)) #386)
-#895 := (iff #389 #892)
-#893 := (iff #386 #386)
-#894 := [refl]: #893
-#896 := [quant-intro #894]: #895
-#258 := (* -1::Int #252)
-#346 := (ite #330 #58 #258)
-#349 := (ite #39 0::Int #346)
-#352 := (ite #40 #36 #349)
-#355 := (= #57 #352)
-#358 := (forall (vars (?v0 Int) (?v1 Int)) #355)
-#390 := (iff #358 #389)
-#387 := (iff #355 #386)
-#388 := [rewrite]: #387
-#391 := [quant-intro #388]: #390
-#227 := (not #226)
-#220 := (not #219)
-#230 := (and #220 #227)
-#216 := (not #215)
-#223 := (and #216 #220)
-#233 := (or #223 #230)
-#278 := (ite #233 #58 #258)
-#281 := (ite #39 0::Int #278)
-#284 := (ite #40 #36 #281)
-#287 := (= #57 #284)
-#290 := (forall (vars (?v0 Int) (?v1 Int)) #287)
-#359 := (iff #290 #358)
-#356 := (iff #287 #355)
-#353 := (= #284 #352)
-#350 := (= #281 #349)
-#347 := (= #278 #346)
-#331 := (iff #233 #330)
-#328 := (iff #230 #327)
-#329 := [rewrite]: #328
-#309 := (iff #223 #325)
-#310 := [rewrite]: #309
-#332 := [monotonicity #310 #329]: #331
-#348 := [monotonicity #332]: #347
-#351 := [monotonicity #348]: #350
-#354 := [monotonicity #351]: #353
-#357 := [monotonicity #354]: #356
-#360 := [quant-intro #357]: #359
-#307 := (~ #290 #290)
-#321 := (~ #287 #287)
-#322 := [refl]: #321
-#308 := [nnf-pos #322]: #307
-#50 := (- #24)
-#49 := (- #36)
-#59 := (mod #49 #50)
-#60 := (- #59)
-#43 := (< 0::Int #24)
-#45 := (< #36 0::Int)
-#46 := (and #45 #43)
-#42 := (< 0::Int #36)
-#44 := (and #42 #43)
-#47 := (or #44 #46)
-#61 := (ite #47 #58 #60)
-#62 := (ite #39 0::Int #61)
-#63 := (ite #40 #36 #62)
-#64 := (= #57 #63)
-#65 := (forall (vars (?v0 Int) (?v1 Int)) #64)
-#293 := (iff #65 #290)
-#181 := (and #43 #45)
-#184 := (or #44 #181)
-#263 := (ite #184 #58 #258)
-#172 := (= 0::Int #36)
-#266 := (ite #172 0::Int #263)
-#175 := (= 0::Int #24)
-#269 := (ite #175 #36 #266)
-#272 := (= #57 #269)
-#275 := (forall (vars (?v0 Int) (?v1 Int)) #272)
-#291 := (iff #275 #290)
-#288 := (iff #272 #287)
-#285 := (= #269 #284)
-#282 := (= #266 #281)
-#279 := (= #263 #278)
-#234 := (iff #184 #233)
-#231 := (iff #181 #230)
-#228 := (iff #45 #227)
-#229 := [rewrite]: #228
-#221 := (iff #43 #220)
-#222 := [rewrite]: #221
-#232 := [monotonicity #222 #229]: #231
-#224 := (iff #44 #223)
-#217 := (iff #42 #216)
-#218 := [rewrite]: #217
-#225 := [monotonicity #218 #222]: #224
-#235 := [monotonicity #225 #232]: #234
-#280 := [monotonicity #235]: #279
-#209 := (iff #172 #39)
-#210 := [rewrite]: #209
-#283 := [monotonicity #210 #280]: #282
-#211 := (iff #175 #40)
-#212 := [rewrite]: #211
-#286 := [monotonicity #212 #283]: #285
-#289 := [monotonicity #286]: #288
-#292 := [quant-intro #289]: #291
-#276 := (iff #65 #275)
-#273 := (iff #64 #272)
-#270 := (= #63 #269)
-#267 := (= #62 #266)
-#264 := (= #61 #263)
-#261 := (= #60 #258)
-#255 := (- #252)
-#259 := (= #255 #258)
-#260 := [rewrite]: #259
-#256 := (= #60 #255)
-#253 := (= #59 #252)
-#192 := (= #50 #191)
-#193 := [rewrite]: #192
-#189 := (= #49 #188)
-#190 := [rewrite]: #189
-#254 := [monotonicity #190 #193]: #253
-#257 := [monotonicity #254]: #256
-#262 := [trans #257 #260]: #261
-#185 := (iff #47 #184)
-#182 := (iff #46 #181)
-#183 := [rewrite]: #182
-#186 := [monotonicity #183]: #185
-#265 := [monotonicity #186 #262]: #264
-#173 := (iff #39 #172)
-#174 := [rewrite]: #173
-#268 := [monotonicity #174 #265]: #267
-#176 := (iff #40 #175)
-#177 := [rewrite]: #176
-#271 := [monotonicity #177 #268]: #270
-#274 := [monotonicity #271]: #273
-#277 := [quant-intro #274]: #276
-#294 := [trans #277 #292]: #293
-#251 := [asserted]: #65
-#295 := [mp #251 #294]: #290
-#323 := [mp~ #295 #308]: #290
-#361 := [mp #323 #360]: #358
-#392 := [mp #361 #391]: #389
-#897 := [mp #392 #896]: #892
-#711 := (not #892)
-#712 := (or #711 #806)
-#819 := (* -1::Int 3::Int)
-#820 := (mod #819 #819)
-#821 := (+ #12 #820)
-#816 := (= #821 0::Int)
-#817 := (mod 3::Int 3::Int)
-#822 := (* -1::Int #817)
-#823 := (+ #12 #822)
-#818 := (= #823 0::Int)
-#824 := (>= 3::Int 0::Int)
-#665 := (<= 3::Int 0::Int)
-#666 := (or #665 #824)
-#667 := (not #666)
-#809 := (or #665 #665)
-#810 := (not #809)
-#811 := (or #810 #667)
-#812 := (ite #811 #818 #816)
-#807 := (= 3::Int 0::Int)
-#813 := (ite #807 #806 #812)
-#814 := (= 3::Int #12)
-#808 := (ite #807 #814 #813)
-#713 := (or #711 #808)
-#717 := (iff #713 #712)
-#719 := (iff #712 #712)
-#724 := [rewrite]: #719
-#732 := (iff #808 #806)
-#647 := (= #12 3::Int)
-#731 := (ite false #647 #806)
-#736 := (iff #731 #806)
-#737 := [rewrite]: #736
-#734 := (iff #808 #731)
-#729 := (iff #813 #806)
-#745 := (ite false #806 #806)
-#747 := (iff #745 #806)
-#733 := [rewrite]: #747
-#746 := (iff #813 #745)
-#743 := (iff #812 #806)
-#1 := true
-#750 := (ite true #806 #806)
-#740 := (iff #750 #806)
-#742 := [rewrite]: #740
-#761 := (iff #812 #750)
-#759 := (iff #816 #806)
-#757 := (= #821 #12)
-#772 := (+ #12 0::Int)
-#775 := (= #772 #12)
-#771 := [rewrite]: #775
-#755 := (= #821 #772)
-#753 := (= #820 0::Int)
-#766 := -3::Int
-#768 := (mod -3::Int -3::Int)
-#751 := (= #768 0::Int)
-#752 := [rewrite]: #751
-#748 := (= #820 #768)
-#767 := (= #819 -3::Int)
-#764 := [rewrite]: #767
-#749 := [monotonicity #764 #764]: #748
-#754 := [trans #749 #752]: #753
-#756 := [monotonicity #754]: #755
-#758 := [trans #756 #771]: #757
-#760 := [monotonicity #758]: #759
-#763 := (iff #818 #806)
-#776 := (= #823 #12)
-#773 := (= #823 #772)
-#769 := (= #822 0::Int)
-#782 := (* -1::Int 0::Int)
-#778 := (= #782 0::Int)
-#785 := [rewrite]: #778
-#783 := (= #822 #782)
-#792 := (= #817 0::Int)
-#781 := [rewrite]: #792
-#784 := [monotonicity #781]: #783
-#770 := [trans #784 #785]: #769
-#774 := [monotonicity #770]: #773
-#762 := [trans #774 #771]: #776
-#765 := [monotonicity #762]: #763
-#791 := (iff #811 true)
-#780 := (or true false)
-#789 := (iff #780 true)
-#790 := [rewrite]: #789
-#777 := (iff #811 #780)
-#786 := (iff #667 false)
-#489 := (not true)
-#848 := (iff #489 false)
-#851 := [rewrite]: #848
-#795 := (iff #667 #489)
-#705 := (iff #666 true)
-#693 := (or false true)
-#703 := (iff #693 true)
-#704 := [rewrite]: #703
-#701 := (iff #666 #693)
-#699 := (iff #824 true)
-#700 := [rewrite]: #699
-#801 := (iff #665 false)
-#803 := [rewrite]: #801
-#702 := [monotonicity #803 #700]: #701
-#798 := [trans #702 #704]: #705
-#799 := [monotonicity #798]: #795
-#788 := [trans #799 #851]: #786
-#682 := (iff #810 true)
-#796 := (not false)
-#794 := (iff #796 true)
-#797 := [rewrite]: #794
-#698 := (iff #810 #796)
-#689 := (iff #809 false)
-#804 := (or false false)
-#687 := (iff #804 false)
-#688 := [rewrite]: #687
-#802 := (iff #809 #804)
-#805 := [monotonicity #803 #803]: #802
-#648 := [trans #805 #688]: #689
-#793 := [monotonicity #648]: #698
-#697 := [trans #793 #797]: #682
-#779 := [monotonicity #697 #788]: #777
-#787 := [trans #779 #790]: #791
-#739 := [monotonicity #787 #765 #760]: #761
-#744 := [trans #739 #742]: #743
-#815 := (iff #807 false)
-#644 := [rewrite]: #815
-#741 := [monotonicity #644 #744]: #746
-#730 := [trans #741 #733]: #729
-#646 := (iff #814 #647)
-#800 := [rewrite]: #646
-#735 := [monotonicity #644 #800 #730]: #734
-#738 := [trans #735 #737]: #732
-#718 := [monotonicity #738]: #717
-#720 := [trans #718 #724]: #717
-#606 := [quant-inst #10 #10]: #713
-#721 := [mp #606 #720]: #712
-#725 := [unit-resolution #721 #897]: #806
-#726 := [monotonicity #725]: #16
-#17 := (not #16)
-#85 := [asserted]: #17
-[unit-resolution #85 #726]: false
-unsat
-8055ca42aa095bbb36b136f82a880cc3b8c48d4b 460 0
-#2 := false
-#13 := 3::Int
-decl f6 :: (-> S4 S5 Int)
-decl f8 :: S5
-#10 := f8
-decl f7 :: S4
-#9 := f7
-#11 := (f6 f7 f8)
-#554 := (mod #11 3::Int)
-#748 := (>= #554 3::Int)
-#749 := (not #748)
-#1 := true
-#83 := [true-axiom]: true
-#736 := (or false #749)
-#732 := [th-lemma arith]: #736
-#733 := [unit-resolution #732 #83]: #749
-#23 := 0::Int
-#199 := -1::Int
-#533 := (* -1::Int #554)
-decl f3 :: (-> S2 Int Int)
-decl f4 :: (-> S3 Int S2)
-decl f5 :: S3
-#8 := f5
-#12 := (f4 f5 #11)
-#14 := (f3 #12 3::Int)
-#868 := (+ #14 #533)
-#815 := (<= #868 0::Int)
-#870 := (= #868 0::Int)
-#568 := -3::Int
-#549 := (* -1::Int #11)
-#847 := (mod #549 -3::Int)
-#558 := (+ #14 #847)
-#561 := (= #558 0::Int)
-#539 := (<= #11 0::Int)
-#856 := (not #539)
-#527 := (>= #11 0::Int)
-#860 := (not #527)
-#574 := (or #860 #856)
-#555 := (ite #574 #870 #561)
-#869 := (= #14 0::Int)
-#875 := (= #11 0::Int)
-#838 := (ite #875 #869 #555)
-#24 := (:var 0 Int)
-#36 := (:var 1 Int)
-#56 := (f4 f5 #36)
-#57 := (f3 #56 #24)
-#903 := (pattern #57)
-#203 := (* -1::Int #24)
-#200 := (* -1::Int #36)
-#264 := (mod #200 #203)
-#394 := (+ #57 #264)
-#395 := (= #394 0::Int)
-#58 := (mod #36 #24)
-#391 := (* -1::Int #58)
-#392 := (+ #57 #391)
-#393 := (= #392 0::Int)
-#238 := (>= #36 0::Int)
-#231 := (<= #24 0::Int)
-#338 := (or #231 #238)
-#339 := (not #338)
-#227 := (<= #36 0::Int)
-#336 := (or #227 #231)
-#337 := (not #336)
-#342 := (or #337 #339)
-#396 := (ite #342 #393 #395)
-#390 := (= #57 0::Int)
-#39 := (= #36 0::Int)
-#397 := (ite #39 #390 #396)
-#389 := (= #36 #57)
-#40 := (= #24 0::Int)
-#398 := (ite #40 #389 #397)
-#904 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #903) #398)
-#401 := (forall (vars (?v0 Int) (?v1 Int)) #398)
-#907 := (iff #401 #904)
-#905 := (iff #398 #398)
-#906 := [refl]: #905
-#908 := [quant-intro #906]: #907
-#270 := (* -1::Int #264)
-#358 := (ite #342 #58 #270)
-#361 := (ite #39 0::Int #358)
-#364 := (ite #40 #36 #361)
-#367 := (= #57 #364)
-#370 := (forall (vars (?v0 Int) (?v1 Int)) #367)
-#402 := (iff #370 #401)
-#399 := (iff #367 #398)
-#400 := [rewrite]: #399
-#403 := [quant-intro #400]: #402
-#239 := (not #238)
-#232 := (not #231)
-#242 := (and #232 #239)
-#228 := (not #227)
-#235 := (and #228 #232)
-#245 := (or #235 #242)
-#290 := (ite #245 #58 #270)
-#293 := (ite #39 0::Int #290)
-#296 := (ite #40 #36 #293)
-#299 := (= #57 #296)
-#302 := (forall (vars (?v0 Int) (?v1 Int)) #299)
-#371 := (iff #302 #370)
-#368 := (iff #299 #367)
-#365 := (= #296 #364)
-#362 := (= #293 #361)
-#359 := (= #290 #358)
-#343 := (iff #245 #342)
-#340 := (iff #242 #339)
-#341 := [rewrite]: #340
-#321 := (iff #235 #337)
-#322 := [rewrite]: #321
-#344 := [monotonicity #322 #341]: #343
-#360 := [monotonicity #344]: #359
-#363 := [monotonicity #360]: #362
-#366 := [monotonicity #363]: #365
-#369 := [monotonicity #366]: #368
-#372 := [quant-intro #369]: #371
-#319 := (~ #302 #302)
-#333 := (~ #299 #299)
-#334 := [refl]: #333
-#320 := [nnf-pos #334]: #319
+#261 := [quant-intro #258]: #260
 #50 := (- #24)
 #49 := (- #36)
 #59 := (mod #49 #50)
@@ -20209,5920 +18724,6336 @@
 #42 := (< 0::Int #36)
 #44 := (and #42 #43)
 #47 := (or #44 #46)
-#61 := (ite #47 #58 #60)
-#62 := (ite #39 0::Int #61)
-#63 := (ite #40 #36 #62)
+#61 := (if #47 #58 #60)
+#62 := (if #39 0::Int #61)
+#63 := (if #40 #36 #62)
 #64 := (= #57 #63)
 #65 := (forall (vars (?v0 Int) (?v1 Int)) #64)
-#305 := (iff #65 #302)
-#193 := (and #43 #45)
-#196 := (or #44 #193)
-#275 := (ite #196 #58 #270)
-#184 := (= 0::Int #36)
-#278 := (ite #184 0::Int #275)
-#187 := (= 0::Int #24)
-#281 := (ite #187 #36 #278)
-#284 := (= #57 #281)
-#287 := (forall (vars (?v0 Int) (?v1 Int)) #284)
-#303 := (iff #287 #302)
-#300 := (iff #284 #299)
-#297 := (= #281 #296)
-#294 := (= #278 #293)
-#291 := (= #275 #290)
-#246 := (iff #196 #245)
-#243 := (iff #193 #242)
-#240 := (iff #45 #239)
-#241 := [rewrite]: #240
-#233 := (iff #43 #232)
-#234 := [rewrite]: #233
-#244 := [monotonicity #234 #241]: #243
-#236 := (iff #44 #235)
-#229 := (iff #42 #228)
-#230 := [rewrite]: #229
-#237 := [monotonicity #230 #234]: #236
-#247 := [monotonicity #237 #244]: #246
-#292 := [monotonicity #247]: #291
-#221 := (iff #184 #39)
-#222 := [rewrite]: #221
-#295 := [monotonicity #222 #292]: #294
-#223 := (iff #187 #40)
-#224 := [rewrite]: #223
-#298 := [monotonicity #224 #295]: #297
-#301 := [monotonicity #298]: #300
-#304 := [quant-intro #301]: #303
-#288 := (iff #65 #287)
-#285 := (iff #64 #284)
-#282 := (= #63 #281)
-#279 := (= #62 #278)
-#276 := (= #61 #275)
-#273 := (= #60 #270)
-#267 := (- #264)
-#271 := (= #267 #270)
-#272 := [rewrite]: #271
-#268 := (= #60 #267)
-#265 := (= #59 #264)
-#204 := (= #50 #203)
-#205 := [rewrite]: #204
-#201 := (= #49 #200)
-#202 := [rewrite]: #201
-#266 := [monotonicity #202 #205]: #265
-#269 := [monotonicity #266]: #268
-#274 := [trans #269 #272]: #273
-#197 := (iff #47 #196)
-#194 := (iff #46 #193)
-#195 := [rewrite]: #194
-#198 := [monotonicity #195]: #197
-#277 := [monotonicity #198 #274]: #276
-#185 := (iff #39 #184)
-#186 := [rewrite]: #185
-#280 := [monotonicity #186 #277]: #279
-#188 := (iff #40 #187)
-#189 := [rewrite]: #188
-#283 := [monotonicity #189 #280]: #282
-#286 := [monotonicity #283]: #285
-#289 := [quant-intro #286]: #288
-#306 := [trans #289 #304]: #305
-#263 := [asserted]: #65
-#307 := [mp #263 #306]: #302
-#335 := [mp~ #307 #320]: #302
-#373 := [mp #335 #372]: #370
-#404 := [mp #373 #403]: #401
-#909 := [mp #404 #908]: #904
-#836 := (not #904)
-#677 := (or #836 #838)
-#548 := (* -1::Int 3::Int)
-#480 := (mod #549 #548)
-#553 := (+ #14 #480)
-#550 := (= #553 0::Int)
-#657 := (<= 3::Int 0::Int)
-#864 := (or #657 #527)
-#538 := (not #864)
-#871 := (or #539 #657)
-#872 := (not #871)
-#873 := (or #872 #538)
-#874 := (ite #873 #870 #550)
-#865 := (ite #875 #869 #874)
-#525 := (= #11 #14)
-#530 := (= 3::Int 0::Int)
-#866 := (ite #530 #525 #865)
-#678 := (or #836 #866)
-#821 := (iff #678 #677)
-#823 := (iff #677 #677)
-#824 := [rewrite]: #823
-#835 := (iff #866 #838)
-#832 := (ite false #525 #838)
-#829 := (iff #832 #838)
-#834 := [rewrite]: #829
-#833 := (iff #866 #832)
-#842 := (iff #865 #838)
-#837 := (iff #874 #555)
-#839 := (iff #550 #561)
-#559 := (= #553 #558)
-#844 := (= #480 #847)
-#569 := (= #548 -3::Int)
-#843 := [rewrite]: #569
-#848 := [monotonicity #843]: #844
-#560 := [monotonicity #848]: #559
-#840 := [monotonicity #560]: #839
-#845 := (iff #873 #574)
-#850 := (or #856 #860)
-#575 := (iff #850 #574)
-#468 := [rewrite]: #575
-#572 := (iff #873 #850)
-#863 := (iff #538 #860)
-#502 := (iff #864 #527)
-#858 := (or false #527)
-#861 := (iff #858 #527)
-#501 := [rewrite]: #861
-#496 := (iff #864 #858)
-#510 := (iff #657 false)
-#851 := [rewrite]: #510
-#859 := [monotonicity #851]: #496
-#862 := [trans #859 #501]: #502
-#849 := [monotonicity #862]: #863
-#857 := (iff #872 #856)
-#854 := (iff #871 #539)
-#514 := (or #539 false)
-#517 := (iff #514 #539)
-#853 := [rewrite]: #517
-#515 := (iff #871 #514)
-#516 := [monotonicity #851]: #515
-#855 := [trans #516 #853]: #854
-#852 := [monotonicity #855]: #857
-#573 := [monotonicity #852 #849]: #572
-#846 := [trans #573 #468]: #845
-#841 := [monotonicity #846 #840]: #837
-#831 := [monotonicity #841]: #842
-#526 := (iff #530 false)
-#867 := [rewrite]: #526
-#828 := [monotonicity #867 #831]: #833
-#830 := [trans #828 #834]: #835
-#822 := [monotonicity #830]: #821
-#818 := [trans #822 #824]: #821
-#679 := [quant-inst #11 #13]: #678
-#819 := [mp #679 #818]: #677
-#734 := [unit-resolution #819 #909]: #838
-#712 := (not #875)
-#711 := (not #838)
-#721 := (or #711 #712)
-#716 := (not #869)
-#825 := (<= #14 0::Int)
-#737 := (not #825)
-#90 := (>= #14 3::Int)
-#15 := (< #14 3::Int)
+#179 := (iff #65 #178)
+#176 := (iff #64 #175)
+#173 := (= #63 #172)
+#170 := (= #62 #169)
+#167 := (= #61 #166)
+#164 := (= #60 #161)
+#158 := (- #155)
+#162 := (= #158 #161)
+#163 := [rewrite]: #162
+#159 := (= #60 #158)
+#156 := (= #59 #155)
+#137 := (= #50 #136)
+#138 := [rewrite]: #137
+#134 := (= #49 #133)
+#135 := [rewrite]: #134
+#157 := [monotonicity #135 #138]: #156
+#160 := [monotonicity #157]: #159
+#165 := [trans #160 #163]: #164
+#130 := (iff #47 #129)
+#127 := (iff #46 #126)
+#112 := (iff #43 #111)
+#113 := [rewrite]: #112
+#119 := (iff #45 #118)
+#123 := (iff #118 #118)
+#121 := (iff #117 #117)
+#122 := [rewrite]: #121
+#124 := [monotonicity #122]: #123
+#120 := [rewrite]: #119
+#125 := [trans #120 #124]: #119
+#128 := [monotonicity #125 #113]: #127
+#115 := (iff #44 #114)
+#108 := (iff #42 #107)
+#109 := [rewrite]: #108
+#116 := [monotonicity #109 #113]: #115
+#131 := [monotonicity #116 #128]: #130
+#168 := [monotonicity #131 #165]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#180 := [quant-intro #177]: #179
+#72 := [asserted]: #65
+#181 := [mp #72 #180]: #178
+#262 := [mp #181 #261]: #259
+#285 := [mp~ #262 #284]: #259
+#325 := [mp #285 #324]: #322
+#356 := [mp #325 #355]: #353
+#803 := [mp #356 #802]: #798
+#638 := (not #798)
+#644 := (or #638 #463)
+#736 := (* -1::Int 3::Int)
+#732 := (* -1::Int 1::Int)
+#725 := (mod #732 #736)
+#726 := (+ #12 #725)
+#727 := (= #726 0::Int)
+#734 := (mod 1::Int 3::Int)
+#449 := (* -1::Int #734)
+#731 := (+ #12 #449)
+#735 := (= #731 0::Int)
+#742 := (<= 3::Int 0::Int)
+#551 := (>= 1::Int 0::Int)
+#454 := (or #551 #742)
+#455 := (not #454)
+#738 := (<= 1::Int 0::Int)
+#452 := (or #738 #742)
+#453 := (not #452)
+#733 := (or #453 #455)
+#722 := (if #733 #735 #727)
+#741 := (= #12 0::Int)
+#737 := (= 1::Int 0::Int)
+#723 := (if #737 #741 #722)
+#462 := (= 3::Int 0::Int)
+#728 := (if #462 #463 #723)
+#617 := (or #638 #728)
+#619 := (iff #617 #644)
+#623 := (iff #644 #644)
+#624 := [rewrite]: #623
+#642 := (iff #728 #463)
+#635 := (if false #463 #463)
+#640 := (iff #635 #463)
+#641 := [rewrite]: #640
+#636 := (iff #728 #635)
+#653 := (iff #723 #463)
+#649 := (if false #741 #463)
+#652 := (iff #649 #463)
+#647 := [rewrite]: #652
+#650 := (iff #723 #649)
+#646 := (iff #722 #463)
+#659 := -2::Int
+#660 := (= #12 -2::Int)
+#1 := true
+#665 := (if true #463 #660)
+#667 := (iff #665 #463)
+#645 := [rewrite]: #667
+#666 := (iff #722 #665)
+#663 := (iff #727 #660)
+#679 := 2::Int
+#672 := (+ 2::Int #12)
+#655 := (= #672 0::Int)
+#661 := (iff #655 #660)
+#662 := [rewrite]: #661
+#657 := (iff #727 #655)
+#674 := (= #726 #672)
+#668 := (+ #12 2::Int)
+#673 := (= #668 #672)
+#670 := [rewrite]: #673
+#669 := (= #726 #668)
+#677 := (= #725 2::Int)
+#690 := -3::Int
+#675 := (mod -1::Int -3::Int)
+#680 := (= #675 2::Int)
+#681 := [rewrite]: #680
+#676 := (= #725 #675)
+#684 := (= #736 -3::Int)
+#691 := [rewrite]: #684
+#609 := (= #732 -1::Int)
+#610 := [rewrite]: #609
+#678 := [monotonicity #610 #691]: #676
+#682 := [trans #678 #681]: #677
+#671 := [monotonicity #682]: #669
+#654 := [trans #671 #670]: #674
+#658 := [monotonicity #654]: #657
+#664 := [trans #658 #662]: #663
+#688 := (iff #735 #463)
+#694 := (+ -1::Int #12)
+#696 := (= #694 0::Int)
+#698 := (iff #696 #463)
+#687 := [rewrite]: #698
+#697 := (iff #735 #696)
+#685 := (= #731 #694)
+#701 := (+ #12 -1::Int)
+#686 := (= #701 #694)
+#683 := [rewrite]: #686
+#705 := (= #731 #701)
+#611 := (= #449 -1::Int)
+#607 := (= #449 #732)
+#606 := (= #734 1::Int)
+#599 := [rewrite]: #606
+#608 := [monotonicity #599]: #607
+#704 := [trans #608 #610]: #611
+#692 := [monotonicity #704]: #705
+#695 := [trans #692 #683]: #685
+#693 := [monotonicity #695]: #697
+#689 := [trans #693 #687]: #688
+#603 := (iff #733 true)
+#710 := (or true false)
+#593 := (iff #710 true)
+#594 := [rewrite]: #593
+#703 := (iff #733 #710)
+#699 := (iff #455 false)
+#420 := (not true)
+#745 := (iff #420 false)
+#408 := [rewrite]: #745
+#702 := (iff #455 #420)
+#595 := (iff #454 true)
+#708 := (iff #454 #710)
+#715 := (iff #742 false)
+#716 := [rewrite]: #715
+#424 := (iff #551 true)
+#760 := [rewrite]: #424
+#711 := [monotonicity #760 #716]: #708
+#554 := [trans #711 #594]: #595
+#604 := [monotonicity #554]: #702
+#700 := [trans #604 #408]: #699
+#707 := (iff #453 true)
+#721 := (not false)
+#553 := (iff #721 true)
+#706 := [rewrite]: #553
+#550 := (iff #453 #721)
+#720 := (iff #452 false)
+#717 := (or false false)
+#713 := (iff #717 false)
+#719 := [rewrite]: #713
+#718 := (iff #452 #717)
+#572 := (iff #738 false)
+#573 := [rewrite]: #572
+#712 := [monotonicity #573 #716]: #718
+#714 := [trans #712 #719]: #720
+#552 := [monotonicity #714]: #550
+#709 := [trans #552 #706]: #707
+#588 := [monotonicity #709 #700]: #703
+#605 := [trans #588 #594]: #603
+#656 := [monotonicity #605 #689 #664]: #666
+#648 := [trans #656 #645]: #646
+#730 := (iff #737 false)
+#571 := [rewrite]: #730
+#651 := [monotonicity #571 #648]: #650
+#639 := [trans #651 #647]: #653
+#729 := (iff #462 false)
+#724 := [rewrite]: #729
+#637 := [monotonicity #724 #639]: #636
+#643 := [trans #637 #641]: #642
+#512 := [monotonicity #643]: #619
+#625 := [trans #512 #624]: #619
+#618 := [quant-inst #9 #11]: #617
+#630 := [mp #618 #625]: #644
+#628 := [unit-resolution #630 #803]: #463
+#631 := [monotonicity #628]: #15
 #16 := (not #15)
-#97 := (iff #16 #90)
-#88 := (not #90)
-#92 := (not #88)
-#95 := (iff #92 #90)
-#96 := [rewrite]: #95
-#93 := (iff #16 #92)
-#89 := (iff #15 #88)
-#91 := [rewrite]: #89
-#94 := [monotonicity #91]: #93
-#98 := [trans #94 #96]: #97
-#85 := [asserted]: #16
-#99 := [mp #85 #98]: #90
-#738 := (or #737 #88)
-#739 := [th-lemma arith farkas 1 1]: #738
-#735 := [unit-resolution #739 #99]: #737
-#740 := (or #716 #825)
-#720 := [th-lemma arith triangle-eq]: #740
-#666 := [unit-resolution #720 #735]: #716
-#705 := (or #711 #712 #869)
-#713 := [def-axiom]: #705
-#702 := [unit-resolution #713 #666]: #721
-#726 := [unit-resolution #702 #734]: #712
-#714 := (or #711 #875 #555)
-#715 := [def-axiom]: #714
-#727 := [unit-resolution #715 #726 #734]: #555
+#67 := [asserted]: #16
+[unit-resolution #67 #631]: false
+5598c417fdf3bd603925adc251a35a82567199b0 312 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int S3)
+#13 := 0::Int
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 0::Int)
+decl f5 :: (-> S4 Int Int)
+#9 := 3::Int
+decl f6 :: (-> S5 Int S4)
+decl f7 :: S5
+#8 := f7
+#10 := (f6 f7 3::Int)
+#11 := (f5 #10 3::Int)
+#12 := (f3 f4 #11)
+#15 := (= #12 #14)
+#463 := (= #11 0::Int)
+#23 := (:var 0 Int)
+#35 := (:var 1 Int)
+#55 := (f6 f7 #35)
+#56 := (f5 #55 #23)
+#797 := (pattern #56)
+#131 := -1::Int
+#135 := (* -1::Int #23)
+#132 := (* -1::Int #35)
+#154 := (mod #132 #135)
+#345 := (+ #56 #154)
+#346 := (= #345 0::Int)
+#57 := (mod #35 #23)
+#342 := (* -1::Int #57)
+#343 := (+ #56 #342)
+#344 := (= #343 0::Int)
+#109 := (<= #23 0::Int)
+#221 := (>= #35 0::Int)
+#289 := (or #221 #109)
+#290 := (not #289)
+#105 := (<= #35 0::Int)
+#285 := (or #105 #109)
+#286 := (not #285)
+#293 := (or #286 #290)
+#347 := (if #293 #344 #346)
+#341 := (= #56 0::Int)
+#38 := (= #35 0::Int)
+#348 := (if #38 #341 #347)
+#340 := (= #56 #35)
+#39 := (= #23 0::Int)
+#349 := (if #39 #340 #348)
+#798 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #797) #349)
+#352 := (forall (vars (?v0 Int) (?v1 Int)) #349)
+#801 := (iff #352 #798)
+#799 := (iff #349 #349)
+#800 := [refl]: #799
+#802 := [quant-intro #800]: #801
+#160 := (* -1::Int #154)
+#309 := (if #293 #57 #160)
+#312 := (if #38 0::Int #309)
+#315 := (if #39 #35 #312)
+#318 := (= #56 #315)
+#321 := (forall (vars (?v0 Int) (?v1 Int)) #318)
+#353 := (iff #321 #352)
+#350 := (iff #318 #349)
+#351 := [rewrite]: #350
+#354 := [quant-intro #351]: #353
+#110 := (not #109)
+#224 := (not #221)
+#227 := (and #224 #110)
+#106 := (not #105)
+#113 := (and #106 #110)
+#230 := (or #113 #227)
+#246 := (if #230 #57 #160)
+#249 := (if #38 0::Int #246)
+#252 := (if #39 #35 #249)
+#255 := (= #56 #252)
+#258 := (forall (vars (?v0 Int) (?v1 Int)) #255)
+#322 := (iff #258 #321)
+#319 := (iff #255 #318)
+#316 := (= #252 #315)
+#313 := (= #249 #312)
+#310 := (= #246 #309)
+#294 := (iff #230 #293)
+#291 := (iff #227 #290)
+#292 := [rewrite]: #291
+#287 := (iff #113 #286)
+#288 := [rewrite]: #287
+#295 := [monotonicity #288 #292]: #294
+#311 := [monotonicity #295]: #310
+#314 := [monotonicity #311]: #313
+#317 := [monotonicity #314]: #316
+#320 := [monotonicity #317]: #319
+#323 := [quant-intro #320]: #322
+#282 := (~ #258 #258)
+#280 := (~ #255 #255)
+#281 := [refl]: #280
+#283 := [nnf-pos #281]: #282
+#116 := (<= 0::Int #35)
+#117 := (not #116)
+#125 := (and #117 #110)
+#128 := (or #113 #125)
+#165 := (if #128 #57 #160)
+#168 := (if #38 0::Int #165)
+#171 := (if #39 #35 #168)
+#174 := (= #56 #171)
+#177 := (forall (vars (?v0 Int) (?v1 Int)) #174)
+#259 := (iff #177 #258)
+#256 := (iff #174 #255)
+#253 := (= #171 #252)
+#250 := (= #168 #249)
+#247 := (= #165 #246)
+#231 := (iff #128 #230)
+#228 := (iff #125 #227)
+#225 := (iff #117 #224)
+#222 := (iff #116 #221)
+#223 := [rewrite]: #222
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#248 := [monotonicity #232]: #247
+#251 := [monotonicity #248]: #250
+#254 := [monotonicity #251]: #253
+#257 := [monotonicity #254]: #256
+#260 := [quant-intro #257]: #259
+#49 := (- #23)
+#48 := (- #35)
+#58 := (mod #48 #49)
+#59 := (- #58)
+#42 := (< 0::Int #23)
+#44 := (< #35 0::Int)
+#45 := (and #44 #42)
+#41 := (< 0::Int #35)
+#43 := (and #41 #42)
+#46 := (or #43 #45)
+#60 := (if #46 #57 #59)
+#61 := (if #38 0::Int #60)
+#62 := (if #39 #35 #61)
+#63 := (= #56 #62)
+#64 := (forall (vars (?v0 Int) (?v1 Int)) #63)
+#178 := (iff #64 #177)
+#175 := (iff #63 #174)
+#172 := (= #62 #171)
+#169 := (= #61 #168)
+#166 := (= #60 #165)
+#163 := (= #59 #160)
+#157 := (- #154)
+#161 := (= #157 #160)
+#162 := [rewrite]: #161
+#158 := (= #59 #157)
+#155 := (= #58 #154)
+#136 := (= #49 #135)
+#137 := [rewrite]: #136
+#133 := (= #48 #132)
+#134 := [rewrite]: #133
+#156 := [monotonicity #134 #137]: #155
+#159 := [monotonicity #156]: #158
+#164 := [trans #159 #162]: #163
+#129 := (iff #46 #128)
+#126 := (iff #45 #125)
+#111 := (iff #42 #110)
+#112 := [rewrite]: #111
+#118 := (iff #44 #117)
+#122 := (iff #117 #117)
+#120 := (iff #116 #116)
+#121 := [rewrite]: #120
+#123 := [monotonicity #121]: #122
+#119 := [rewrite]: #118
+#124 := [trans #119 #123]: #118
+#127 := [monotonicity #124 #112]: #126
+#114 := (iff #43 #113)
+#107 := (iff #41 #106)
+#108 := [rewrite]: #107
+#115 := [monotonicity #108 #112]: #114
+#130 := [monotonicity #115 #127]: #129
+#167 := [monotonicity #130 #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [monotonicity #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [quant-intro #176]: #178
+#71 := [asserted]: #64
+#180 := [mp #71 #179]: #177
+#261 := [mp #180 #260]: #258
+#284 := [mp~ #261 #283]: #258
+#324 := [mp #284 #323]: #321
+#355 := [mp #324 #354]: #352
+#803 := [mp #355 #802]: #798
+#664 := (not #798)
+#665 := (or #664 #463)
+#731 := (* -1::Int 3::Int)
+#735 := (mod #731 #731)
+#732 := (+ #11 #735)
+#736 := (= #732 0::Int)
+#455 := (mod 3::Int 3::Int)
+#733 := (* -1::Int #455)
+#734 := (+ #11 #733)
+#449 := (= #734 0::Int)
+#737 := (<= 3::Int 0::Int)
+#742 := (>= 3::Int 0::Int)
+#452 := (or #742 #737)
+#453 := (not #452)
+#741 := (or #737 #737)
+#738 := (not #741)
+#454 := (or #738 #453)
+#725 := (if #454 #449 #736)
+#740 := (= 3::Int 0::Int)
+#726 := (if #740 #463 #725)
+#462 := (= #11 3::Int)
+#727 := (if #740 #462 #726)
+#666 := (or #664 #727)
+#667 := (iff #666 #665)
+#646 := (iff #665 #665)
+#648 := [rewrite]: #646
+#662 := (iff #727 #463)
+#657 := (if false #462 #463)
+#660 := (iff #657 #463)
+#661 := [rewrite]: #660
+#658 := (iff #727 #657)
+#654 := (iff #726 #463)
+#671 := (if false #463 #463)
+#670 := (iff #671 #463)
+#674 := [rewrite]: #670
+#672 := (iff #726 #671)
+#668 := (iff #725 #463)
+#1 := true
+#679 := (if true #463 #463)
+#677 := (iff #679 #463)
+#682 := [rewrite]: #677
+#680 := (iff #725 #679)
+#676 := (iff #736 #463)
+#691 := (= #732 #11)
+#609 := (+ #11 0::Int)
+#704 := (= #609 #11)
+#701 := [rewrite]: #704
+#690 := (= #732 #609)
+#688 := (= #735 0::Int)
+#683 := -3::Int
+#696 := (mod -3::Int -3::Int)
+#698 := (= #696 0::Int)
+#687 := [rewrite]: #698
+#697 := (= #735 #696)
+#685 := (= #731 -3::Int)
+#695 := [rewrite]: #685
+#693 := [monotonicity #695 #695]: #697
+#689 := [trans #693 #687]: #688
+#684 := [monotonicity #689]: #690
+#675 := [trans #684 #701]: #691
+#678 := [monotonicity #675]: #676
+#694 := (iff #449 #463)
+#705 := (= #734 #11)
+#610 := (= #734 #609)
+#607 := (= #733 0::Int)
+#588 := (* -1::Int 0::Int)
+#606 := (= #588 0::Int)
+#599 := [rewrite]: #606
+#603 := (= #733 #588)
+#700 := (= #455 0::Int)
+#703 := [rewrite]: #700
+#605 := [monotonicity #703]: #603
+#608 := [trans #605 #599]: #607
+#611 := [monotonicity #608]: #610
+#692 := [trans #611 #701]: #705
+#686 := [monotonicity #692]: #694
+#604 := (iff #454 true)
+#552 := (or true false)
+#707 := (iff #552 true)
+#709 := [rewrite]: #707
+#554 := (iff #454 #552)
+#594 := (iff #453 false)
+#420 := (not true)
+#745 := (iff #420 false)
+#408 := [rewrite]: #745
+#711 := (iff #453 #420)
+#710 := (iff #452 true)
+#553 := (iff #452 #552)
+#728 := (iff #737 false)
+#729 := [rewrite]: #728
+#721 := (iff #742 true)
+#550 := [rewrite]: #721
+#706 := [monotonicity #550 #729]: #553
+#708 := [trans #706 #709]: #710
+#593 := [monotonicity #708]: #711
+#595 := [trans #593 #408]: #594
+#720 := (iff #738 true)
+#717 := (not false)
+#713 := (iff #717 true)
+#719 := [rewrite]: #713
+#718 := (iff #738 #717)
+#715 := (iff #741 false)
+#724 := (or false false)
+#572 := (iff #724 false)
+#573 := [rewrite]: #572
+#730 := (iff #741 #724)
+#571 := [monotonicity #729 #729]: #730
+#716 := [trans #571 #573]: #715
+#712 := [monotonicity #716]: #718
+#714 := [trans #712 #719]: #720
+#702 := [monotonicity #714 #595]: #554
+#699 := [trans #702 #709]: #604
+#681 := [monotonicity #699 #686 #678]: #680
+#669 := [trans #681 #682]: #668
+#722 := (iff #740 false)
+#723 := [rewrite]: #722
+#673 := [monotonicity #723 #669]: #672
+#655 := [trans #673 #674]: #654
+#659 := [monotonicity #723 #655]: #658
+#663 := [trans #659 #661]: #662
+#645 := [monotonicity #663]: #667
+#649 := [trans #645 #648]: #667
+#656 := [quant-inst #9 #9]: #666
+#650 := [mp #656 #649]: #665
+#652 := [unit-resolution #650 #803]: #463
+#647 := [monotonicity #652]: #15
+#16 := (not #15)
+#66 := [asserted]: #16
+[unit-resolution #66 #647]: false
+27ee577964e39eea43c2a96bf389faf26aa731a2 437 0
+unsat
+#2 := false
+#12 := 3::Int
+decl f6 :: (-> S4 S5 Int)
+decl f8 :: S5
+#9 := f8
+decl f7 :: S4
+#8 := f7
+#10 := (f6 f7 f8)
+#454 := (mod #10 3::Int)
+#669 := (>= #454 3::Int)
+#670 := (not #669)
+#1 := true
+#215 := [true-axiom]: true
+#661 := (or false #670)
+#662 := [th-lemma arith]: #661
+#663 := [unit-resolution #662 #215]: #670
+#22 := 0::Int
+#148 := -1::Int
+#786 := (* -1::Int #454)
+decl f3 :: (-> S2 Int Int)
+decl f4 :: (-> S3 Int S2)
+decl f5 :: S3
+#7 := f5
+#11 := (f4 f5 #10)
+#13 := (f3 #11 3::Int)
+#787 := (+ #13 #786)
+#573 := (<= #787 0::Int)
+#788 := (= #787 0::Int)
+#490 := -3::Int
+#789 := (* -1::Int #10)
+#761 := (mod #789 -3::Int)
+#758 := (+ #13 #761)
+#763 := (= #758 0::Int)
+#442 := (>= #10 0::Int)
+#778 := (not #442)
+#469 := (<= #10 0::Int)
+#772 := (not #469)
+#487 := (or #772 #778)
+#475 := (if #487 #788 #763)
+#465 := (= #13 0::Int)
+#468 := (= #10 0::Int)
+#755 := (if #468 #465 #475)
+#23 := (:var 0 Int)
+#35 := (:var 1 Int)
+#55 := (f4 f5 #35)
+#56 := (f3 #55 #23)
+#818 := (pattern #56)
+#152 := (* -1::Int #23)
+#149 := (* -1::Int #35)
+#171 := (mod #149 #152)
+#366 := (+ #56 #171)
+#367 := (= #366 0::Int)
+#57 := (mod #35 #23)
+#363 := (* -1::Int #57)
+#364 := (+ #56 #363)
+#365 := (= #364 0::Int)
+#126 := (<= #23 0::Int)
+#242 := (>= #35 0::Int)
+#310 := (or #242 #126)
+#311 := (not #310)
+#122 := (<= #35 0::Int)
+#306 := (or #122 #126)
+#307 := (not #306)
+#314 := (or #307 #311)
+#368 := (if #314 #365 #367)
+#362 := (= #56 0::Int)
+#38 := (= #35 0::Int)
+#369 := (if #38 #362 #368)
+#361 := (= #56 #35)
+#39 := (= #23 0::Int)
+#370 := (if #39 #361 #369)
+#819 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #818) #370)
+#373 := (forall (vars (?v0 Int) (?v1 Int)) #370)
+#822 := (iff #373 #819)
+#820 := (iff #370 #370)
+#821 := [refl]: #820
+#823 := [quant-intro #821]: #822
+#177 := (* -1::Int #171)
+#330 := (if #314 #57 #177)
+#333 := (if #38 0::Int #330)
+#336 := (if #39 #35 #333)
+#339 := (= #56 #336)
+#342 := (forall (vars (?v0 Int) (?v1 Int)) #339)
+#374 := (iff #342 #373)
+#371 := (iff #339 #370)
+#372 := [rewrite]: #371
+#375 := [quant-intro #372]: #374
+#127 := (not #126)
+#245 := (not #242)
+#248 := (and #245 #127)
+#123 := (not #122)
+#130 := (and #123 #127)
+#251 := (or #130 #248)
+#267 := (if #251 #57 #177)
+#270 := (if #38 0::Int #267)
+#273 := (if #39 #35 #270)
+#276 := (= #56 #273)
+#279 := (forall (vars (?v0 Int) (?v1 Int)) #276)
+#343 := (iff #279 #342)
+#340 := (iff #276 #339)
+#337 := (= #273 #336)
+#334 := (= #270 #333)
+#331 := (= #267 #330)
+#315 := (iff #251 #314)
+#312 := (iff #248 #311)
+#313 := [rewrite]: #312
+#308 := (iff #130 #307)
+#309 := [rewrite]: #308
+#316 := [monotonicity #309 #313]: #315
+#332 := [monotonicity #316]: #331
+#335 := [monotonicity #332]: #334
+#338 := [monotonicity #335]: #337
+#341 := [monotonicity #338]: #340
+#344 := [quant-intro #341]: #343
+#303 := (~ #279 #279)
+#301 := (~ #276 #276)
+#302 := [refl]: #301
+#304 := [nnf-pos #302]: #303
+#133 := (<= 0::Int #35)
+#134 := (not #133)
+#142 := (and #134 #127)
+#145 := (or #130 #142)
+#182 := (if #145 #57 #177)
+#185 := (if #38 0::Int #182)
+#188 := (if #39 #35 #185)
+#191 := (= #56 #188)
+#194 := (forall (vars (?v0 Int) (?v1 Int)) #191)
+#280 := (iff #194 #279)
+#277 := (iff #191 #276)
+#274 := (= #188 #273)
+#271 := (= #185 #270)
+#268 := (= #182 #267)
+#252 := (iff #145 #251)
+#249 := (iff #142 #248)
+#246 := (iff #134 #245)
+#243 := (iff #133 #242)
+#244 := [rewrite]: #243
+#247 := [monotonicity #244]: #246
+#250 := [monotonicity #247]: #249
+#253 := [monotonicity #250]: #252
+#269 := [monotonicity #253]: #268
+#272 := [monotonicity #269]: #271
+#275 := [monotonicity #272]: #274
+#278 := [monotonicity #275]: #277
+#281 := [quant-intro #278]: #280
+#49 := (- #23)
+#48 := (- #35)
+#58 := (mod #48 #49)
+#59 := (- #58)
+#42 := (< 0::Int #23)
+#44 := (< #35 0::Int)
+#45 := (and #44 #42)
+#41 := (< 0::Int #35)
+#43 := (and #41 #42)
+#46 := (or #43 #45)
+#60 := (if #46 #57 #59)
+#61 := (if #38 0::Int #60)
+#62 := (if #39 #35 #61)
+#63 := (= #56 #62)
+#64 := (forall (vars (?v0 Int) (?v1 Int)) #63)
+#195 := (iff #64 #194)
+#192 := (iff #63 #191)
+#189 := (= #62 #188)
+#186 := (= #61 #185)
+#183 := (= #60 #182)
+#180 := (= #59 #177)
+#174 := (- #171)
+#178 := (= #174 #177)
+#179 := [rewrite]: #178
+#175 := (= #59 #174)
+#172 := (= #58 #171)
+#153 := (= #49 #152)
+#154 := [rewrite]: #153
+#150 := (= #48 #149)
+#151 := [rewrite]: #150
+#173 := [monotonicity #151 #154]: #172
+#176 := [monotonicity #173]: #175
+#181 := [trans #176 #179]: #180
+#146 := (iff #46 #145)
+#143 := (iff #45 #142)
+#128 := (iff #42 #127)
+#129 := [rewrite]: #128
+#135 := (iff #44 #134)
+#139 := (iff #134 #134)
+#137 := (iff #133 #133)
+#138 := [rewrite]: #137
+#140 := [monotonicity #138]: #139
+#136 := [rewrite]: #135
+#141 := [trans #136 #140]: #135
+#144 := [monotonicity #141 #129]: #143
+#131 := (iff #43 #130)
+#124 := (iff #41 #123)
+#125 := [rewrite]: #124
+#132 := [monotonicity #125 #129]: #131
+#147 := [monotonicity #132 #144]: #146
+#184 := [monotonicity #147 #181]: #183
+#187 := [monotonicity #184]: #186
+#190 := [monotonicity #187]: #189
+#193 := [monotonicity #190]: #192
+#196 := [quant-intro #193]: #195
+#71 := [asserted]: #64
+#197 := [mp #71 #196]: #194
+#282 := [mp #197 #281]: #279
+#305 := [mp~ #282 #304]: #279
+#345 := [mp #305 #344]: #342
+#376 := [mp #345 #375]: #373
+#824 := [mp #376 #823]: #819
+#744 := (not #819)
+#749 := (or #744 #755)
+#784 := (* -1::Int 3::Int)
+#790 := (mod #789 #784)
+#780 := (+ #13 #790)
+#440 := (= #780 0::Int)
+#448 := (<= 3::Int 0::Int)
+#572 := (or #442 #448)
+#779 := (not #572)
+#783 := (or #469 #448)
+#785 := (not #783)
+#453 := (or #785 #779)
+#445 := (if #453 #788 #440)
+#781 := (if #468 #465 #445)
+#464 := (= #13 #10)
+#463 := (= 3::Int 0::Int)
+#441 := (if #463 #464 #781)
+#750 := (or #744 #441)
+#751 := (iff #750 #749)
+#593 := (iff #749 #749)
+#594 := [rewrite]: #593
+#748 := (iff #441 #755)
+#756 := (if false #464 #755)
+#746 := (iff #756 #755)
+#747 := [rewrite]: #746
+#753 := (iff #441 #756)
+#470 := (iff #781 #755)
+#476 := (iff #445 #475)
+#473 := (iff #440 #763)
+#762 := (= #780 #758)
+#483 := (= #790 #761)
+#383 := (= #784 -3::Int)
+#760 := [rewrite]: #383
+#484 := [monotonicity #760]: #483
+#759 := [monotonicity #484]: #762
+#474 := [monotonicity #759]: #473
+#488 := (iff #453 #487)
+#764 := (iff #779 #778)
+#777 := (iff #572 #442)
+#411 := (or #442 false)
+#416 := (iff #411 #442)
+#417 := [rewrite]: #416
+#774 := (iff #572 #411)
+#766 := (iff #448 false)
+#429 := [rewrite]: #766
+#776 := [monotonicity #429]: #774
+#775 := [trans #776 #417]: #777
+#765 := [monotonicity #775]: #764
+#767 := (iff #785 #772)
+#770 := (iff #783 #469)
+#430 := (or #469 false)
+#768 := (iff #430 #469)
+#769 := [rewrite]: #768
+#431 := (iff #783 #430)
+#432 := [monotonicity #429]: #431
+#771 := [trans #432 #769]: #770
+#773 := [monotonicity #771]: #767
+#489 := [monotonicity #773 #765]: #488
+#754 := [monotonicity #489 #474]: #476
+#752 := [monotonicity #754]: #470
+#782 := (iff #463 false)
+#425 := [rewrite]: #782
+#757 := [monotonicity #425 #752]: #753
+#743 := [trans #757 #747]: #748
+#592 := [monotonicity #743]: #751
+#736 := [trans #592 #594]: #751
+#745 := [quant-inst #10 #12]: #750
+#737 := [mp #745 #736]: #749
+#664 := [unit-resolution #737 #824]: #755
+#724 := (not #468)
+#721 := (not #755)
+#646 := (or #721 #724)
+#620 := (not #465)
+#738 := (<= #13 0::Int)
+#659 := (not #738)
+#218 := (>= #13 3::Int)
+#75 := (<= 3::Int #13)
+#217 := (iff #75 #218)
+#219 := [rewrite]: #217
+#14 := (< #13 3::Int)
+#15 := (not #14)
+#89 := (iff #15 #75)
+#76 := (not #75)
+#84 := (not #76)
+#87 := (iff #84 #75)
+#88 := [rewrite]: #87
+#85 := (iff #15 #84)
+#77 := (iff #14 #76)
+#81 := (iff #76 #76)
+#79 := (iff #75 #75)
+#80 := [rewrite]: #79
+#82 := [monotonicity #80]: #81
+#78 := [rewrite]: #77
+#83 := [trans #78 #82]: #77
+#86 := [monotonicity #83]: #85
+#90 := [trans #86 #88]: #89
+#66 := [asserted]: #15
+#91 := [mp #66 #90]: #75
+#220 := [mp #91 #219]: #218
+#665 := (not #218)
+#638 := (or #659 #665)
+#639 := [th-lemma arith farkas 1 1]: #638
+#640 := [unit-resolution #639 #220]: #659
+#533 := (or #620 #738)
+#644 := [th-lemma arith triangle-eq]: #533
+#645 := [unit-resolution #644 #640]: #620
+#609 := (or #721 #724 #465)
+#624 := [def-axiom]: #609
+#651 := [unit-resolution #624 #645]: #646
+#647 := [unit-resolution #651 #664]: #724
+#626 := (or #721 #468 #475)
+#627 := [def-axiom]: #626
+#648 := [unit-resolution #627 #647 #664]: #475
 decl f9 :: (-> S6 Int S5)
 decl f10 :: S6
-#17 := f10
-#462 := (f9 f10 #11)
-#798 := (f6 f7 #462)
-#800 := (= #798 0::Int)
-#706 := (not #800)
-#707 := (iff #712 #706)
-#697 := (iff #875 #800)
-#693 := (iff #800 #875)
-#703 := (= #798 #11)
-#728 := (= #462 f8)
-#547 := (= f8 #462)
-#18 := (:var 0 S5)
-#19 := (f6 f7 #18)
-#876 := (pattern #19)
-#20 := (f9 f10 #19)
-#87 := (= #18 #20)
-#877 := (forall (vars (?v0 S5)) (:pat #876) #87)
-#102 := (forall (vars (?v0 S5)) #87)
-#880 := (iff #102 #877)
-#878 := (iff #87 #87)
-#879 := [refl]: #878
-#881 := [quant-intro #879]: #880
-#325 := (~ #102 #102)
-#323 := (~ #87 #87)
-#324 := [refl]: #323
-#326 := [nnf-pos #324]: #325
-#21 := (= #20 #18)
-#22 := (forall (vars (?v0 S5)) #21)
-#103 := (iff #22 #102)
-#100 := (iff #21 #87)
-#101 := [rewrite]: #100
-#104 := [quant-intro #101]: #103
-#86 := [asserted]: #22
-#107 := [mp #86 #104]: #102
-#311 := [mp~ #107 #326]: #102
-#882 := [mp #311 #881]: #877
-#540 := (not #877)
-#551 := (or #540 #547)
-#552 := [quant-inst #10]: #551
-#722 := [unit-resolution #552 #882]: #547
-#696 := [symm #722]: #728
-#662 := [monotonicity #696]: #703
-#695 := [monotonicity #662]: #693
-#704 := [symm #695]: #697
-#708 := [monotonicity #704]: #707
-#718 := [mp #726 #708]: #706
-#789 := (or #527 #800)
-#26 := (f9 f10 #24)
-#883 := (pattern #26)
-#124 := (>= #24 0::Int)
-#27 := (f6 f7 #26)
-#32 := (= #27 0::Int)
-#172 := (or #32 #124)
-#890 := (forall (vars (?v0 Int)) (:pat #883) #172)
-#177 := (forall (vars (?v0 Int)) #172)
-#893 := (iff #177 #890)
-#891 := (iff #172 #172)
-#892 := [refl]: #891
-#894 := [quant-intro #892]: #893
-#315 := (~ #177 #177)
-#327 := (~ #172 #172)
-#328 := [refl]: #327
-#316 := [nnf-pos #328]: #315
-#31 := (< #24 0::Int)
-#33 := (implies #31 #32)
-#34 := (forall (vars (?v0 Int)) #33)
-#180 := (iff #34 #177)
-#143 := (= 0::Int #27)
-#149 := (not #31)
-#150 := (or #149 #143)
-#155 := (forall (vars (?v0 Int)) #150)
-#178 := (iff #155 #177)
-#175 := (iff #150 #172)
-#169 := (or #124 #32)
-#173 := (iff #169 #172)
-#174 := [rewrite]: #173
-#170 := (iff #150 #169)
-#167 := (iff #143 #32)
-#168 := [rewrite]: #167
-#165 := (iff #149 #124)
-#125 := (not #124)
-#160 := (not #125)
-#163 := (iff #160 #124)
-#164 := [rewrite]: #163
-#161 := (iff #149 #160)
-#158 := (iff #31 #125)
-#159 := [rewrite]: #158
-#162 := [monotonicity #159]: #161
-#166 := [trans #162 #164]: #165
-#171 := [monotonicity #166 #168]: #170
-#176 := [trans #171 #174]: #175
-#179 := [quant-intro #176]: #178
-#156 := (iff #34 #155)
-#153 := (iff #33 #150)
-#146 := (implies #31 #143)
-#151 := (iff #146 #150)
-#152 := [rewrite]: #151
-#147 := (iff #33 #146)
-#144 := (iff #32 #143)
-#145 := [rewrite]: #144
-#148 := [monotonicity #145]: #147
-#154 := [trans #148 #152]: #153
-#157 := [quant-intro #154]: #156
-#181 := [trans #157 #179]: #180
-#142 := [asserted]: #34
-#182 := [mp #142 #181]: #177
-#329 := [mp~ #182 #316]: #177
-#895 := [mp #329 #894]: #890
-#802 := (not #890)
-#803 := (or #802 #527 #800)
-#792 := (or #800 #527)
-#799 := (or #802 #792)
-#797 := (iff #799 #803)
-#793 := (or #802 #789)
-#796 := (iff #793 #803)
-#790 := [rewrite]: #796
-#794 := (iff #799 #793)
-#791 := (iff #792 #789)
-#801 := [rewrite]: #791
-#795 := [monotonicity #801]: #794
-#781 := [trans #795 #790]: #797
-#804 := [quant-inst #11]: #799
-#782 := [mp #804 #781]: #803
-#698 := [unit-resolution #782 #895]: #789
-#719 := [unit-resolution #698 #718]: #527
-#674 := (or #875 #856 #860)
-#675 := [th-lemma arith triangle-eq]: #674
-#680 := [unit-resolution #675 #726]: #850
-#681 := [unit-resolution #680 #719]: #856
-#656 := (or #574 #539)
-#658 := [def-axiom]: #656
-#682 := [unit-resolution #658 #681]: #574
-#659 := (not #574)
-#699 := (not #555)
-#700 := (or #699 #659 #870)
-#701 := [def-axiom]: #700
-#683 := [unit-resolution #701 #682 #727]: #870
-#710 := (not #870)
-#684 := (or #710 #815)
-#685 := [th-lemma arith triangle-eq]: #684
-#686 := [unit-resolution #685 #683]: #815
-[th-lemma arith farkas -1 1 1 #99 #686 #733]: false
-unsat
-0c32a24472b6c1312e94e12aa85113077d009d0a 670 0
-#2 := false
-#14 := 3::Int
+#16 := f10
+#377 := (f9 f10 #10)
+#632 := (f6 f7 #377)
+#725 := (= #632 0::Int)
+#581 := (not #725)
+#636 := (iff #724 #581)
+#655 := (iff #468 #725)
+#654 := (iff #725 #468)
+#652 := (= #632 #10)
+#462 := (= #377 f8)
+#17 := (:var 0 S5)
+#18 := (f6 f7 #17)
+#791 := (pattern #18)
+#19 := (f9 f10 #18)
+#20 := (= #19 #17)
+#792 := (forall (vars (?v0 S5)) (:pat #791) #20)
+#21 := (forall (vars (?v0 S5)) #20)
+#795 := (iff #21 #792)
+#793 := (iff #20 #20)
+#794 := [refl]: #793
+#796 := [quant-intro #794]: #795
+#283 := (~ #21 #21)
+#291 := (~ #20 #20)
+#292 := [refl]: #291
+#284 := [nnf-pos #292]: #283
+#67 := [asserted]: #21
+#293 := [mp~ #67 #284]: #21
+#797 := [mp #293 #796]: #792
+#455 := (not #792)
+#466 := (or #455 #462)
+#467 := [quant-inst #9]: #466
+#649 := [unit-resolution #467 #797]: #462
+#653 := [monotonicity #649]: #652
+#650 := [monotonicity #653]: #654
+#635 := [symm #650]: #655
+#617 := [monotonicity #635]: #636
+#641 := [mp #647 #617]: #581
+#722 := (or #442 #725)
+#25 := (f9 f10 #23)
+#798 := (pattern #25)
+#26 := (f6 f7 #25)
+#31 := (= #26 0::Int)
+#222 := (>= #23 0::Int)
+#235 := (or #222 #31)
+#805 := (forall (vars (?v0 Int)) (:pat #798) #235)
+#238 := (forall (vars (?v0 Int)) #235)
+#808 := (iff #238 #805)
+#806 := (iff #235 #235)
+#807 := [refl]: #806
+#809 := [quant-intro #807]: #808
+#287 := (~ #238 #238)
+#216 := (~ #235 #235)
+#221 := [refl]: #216
+#288 := [nnf-pos #221]: #287
+#24 := (<= 0::Int #23)
+#113 := (or #24 #31)
+#118 := (forall (vars (?v0 Int)) #113)
+#239 := (iff #118 #238)
+#236 := (iff #113 #235)
+#223 := (iff #24 #222)
+#224 := [rewrite]: #223
+#237 := [monotonicity #224]: #236
+#240 := [quant-intro #237]: #239
+#30 := (< #23 0::Int)
+#32 := (implies #30 #31)
+#33 := (forall (vars (?v0 Int)) #32)
+#119 := (iff #33 #118)
+#116 := (iff #32 #113)
+#96 := (not #24)
+#110 := (implies #96 #31)
+#114 := (iff #110 #113)
+#115 := [rewrite]: #114
+#111 := (iff #32 #110)
+#105 := (iff #30 #96)
+#107 := (iff #96 #96)
+#92 := (iff #24 #24)
+#93 := [rewrite]: #92
+#108 := [monotonicity #93]: #107
+#106 := [rewrite]: #105
+#109 := [trans #106 #108]: #105
+#112 := [monotonicity #109]: #111
+#117 := [trans #112 #115]: #116
+#120 := [quant-intro #117]: #119
+#69 := [asserted]: #33
+#121 := [mp #69 #120]: #118
+#241 := [mp #121 #240]: #238
+#295 := [mp~ #241 #288]: #238
+#810 := [mp #295 #809]: #805
+#715 := (not #805)
+#707 := (or #715 #442 #725)
+#704 := (or #715 #722)
+#716 := (iff #704 #707)
+#717 := [rewrite]: #716
+#706 := [quant-inst #10]: #704
+#718 := [mp #706 #717]: #707
+#642 := [unit-resolution #718 #810]: #722
+#637 := [unit-resolution #642 #641]: #442
+#643 := (or #468 #772 #778)
+#611 := [th-lemma arith triangle-eq]: #643
+#618 := [unit-resolution #611 #647]: #487
+#577 := [unit-resolution #618 #637]: #772
+#733 := (or #487 #469)
+#734 := [def-axiom]: #733
+#608 := [unit-resolution #734 #577]: #487
+#735 := (not #487)
+#730 := (not #475)
+#731 := (or #730 #735 #788)
+#729 := [def-axiom]: #731
+#610 := [unit-resolution #729 #608 #648]: #788
+#615 := (not #788)
+#612 := (or #615 #573)
+#619 := [th-lemma arith triangle-eq]: #612
+#621 := [unit-resolution #619 #610]: #573
+[th-lemma arith farkas -1 1 1 #220 #621 #663]: false
+6084ebd236b571d1d73842a11d064afa9bdf415b 618 0
+unsat
+#2 := false
+#13 := 3::Int
 decl f8 :: (-> S6 S3 Int)
 decl f10 :: S3
-#11 := f10
+#10 := f10
 decl f9 :: S6
-#10 := f9
-#12 := (f8 f9 f10)
-#890 := (mod #12 3::Int)
-#713 := (>= #890 3::Int)
-#714 := (not #713)
-#1 := true
-#86 := [true-axiom]: true
-#673 := (or false #714)
-#674 := [th-lemma arith]: #673
-#676 := [unit-resolution #674 #86]: #714
-#111 := (>= #12 3::Int)
-#109 := (not #111)
-#626 := [hypothesis]: #109
-#26 := 0::Int
-#227 := -1::Int
-#888 := (* -1::Int #890)
+#9 := f9
+#11 := (f8 f9 f10)
+#785 := (mod #11 3::Int)
+#643 := (>= #785 3::Int)
+#623 := (not #643)
+#1 := true
+#222 := [true-axiom]: true
+#660 := (or false #623)
+#646 := [th-lemma arith]: #660
+#627 := [unit-resolution #646 #222]: #623
+#226 := (>= #11 3::Int)
+#387 := (not #226)
+#546 := [hypothesis]: #387
+#25 := 0::Int
+#155 := -1::Int
+#788 := (* -1::Int #785)
 decl f5 :: (-> S4 Int Int)
 decl f6 :: (-> S5 Int S4)
 decl f7 :: S5
-#9 := f7
-#13 := (f6 f7 #12)
-#15 := (f5 #13 3::Int)
-#891 := (+ #15 #888)
-#831 := (<= #891 0::Int)
-#877 := (= #891 0::Int)
-#871 := (= #12 0::Int)
-#816 := (not #871)
+#8 := f7
+#12 := (f6 f7 #11)
+#14 := (f5 #12 3::Int)
+#774 := (+ #14 #788)
+#725 := (<= #774 0::Int)
+#775 := (= #774 0::Int)
+#781 := (= #11 0::Int)
+#707 := (not #781)
 decl f3 :: (-> S2 Int S3)
 decl f4 :: S2
-#8 := f4
-#16 := (f3 f4 #15)
-#89 := (= f10 #16)
-#579 := (not #89)
-#581 := (or #579 #111)
-#120 := (iff #89 #111)
-#18 := (< #12 3::Int)
-#17 := (= #16 f10)
-#19 := (iff #17 #18)
-#20 := (not #19)
-#123 := (iff #20 #120)
-#103 := (not #18)
-#104 := (iff #89 #103)
-#121 := (iff #104 #120)
-#118 := (iff #103 #111)
-#113 := (not #109)
-#116 := (iff #113 #111)
-#117 := [rewrite]: #116
-#114 := (iff #103 #113)
-#110 := (iff #18 #109)
-#112 := [rewrite]: #110
-#115 := [monotonicity #112]: #114
-#119 := [trans #115 #117]: #118
-#122 := [monotonicity #119]: #121
-#107 := (iff #20 #104)
-#95 := (iff #18 #89)
-#100 := (not #95)
-#105 := (iff #100 #104)
+#7 := f4
+#15 := (f3 f4 #14)
+#16 := (= #15 f10)
+#477 := (not #16)
+#479 := (or #477 #226)
+#228 := (iff #16 #226)
+#78 := (<= 3::Int #11)
+#94 := (iff #16 #78)
+#229 := (iff #94 #228)
+#225 := (iff #78 #226)
+#227 := [rewrite]: #225
+#230 := [monotonicity #227]: #229
+#17 := (< #11 3::Int)
+#18 := (iff #16 #17)
+#19 := (not #18)
+#96 := (iff #19 #94)
+#79 := (not #78)
+#87 := (iff #16 #79)
+#90 := (not #87)
+#93 := (iff #90 #94)
+#95 := [rewrite]: #93
+#91 := (iff #19 #90)
+#88 := (iff #18 #87)
+#80 := (iff #17 #79)
+#84 := (iff #79 #79)
+#82 := (iff #78 #78)
+#83 := [rewrite]: #82
+#85 := [monotonicity #83]: #84
+#81 := [rewrite]: #80
+#86 := [trans #81 #85]: #80
+#89 := [monotonicity #86]: #88
+#92 := [monotonicity #89]: #91
+#97 := [trans #92 #95]: #96
+#69 := [asserted]: #19
+#98 := [mp #69 #97]: #94
+#231 := [mp #98 #230]: #228
+#472 := (not #228)
+#478 := (or #477 #226 #472)
+#475 := [def-axiom]: #478
+#458 := [unit-resolution #475 #231]: #479
+#554 := [unit-resolution #458 #546]: #477
+#675 := (or #707 #16)
+#793 := (f3 f4 #11)
+#795 := (= #793 f10)
+#20 := (:var 0 S3)
+#21 := (f8 f9 #20)
+#801 := (pattern #21)
+#22 := (f3 f4 #21)
+#23 := (= #22 #20)
+#802 := (forall (vars (?v0 S3)) (:pat #801) #23)
+#24 := (forall (vars (?v0 S3)) #23)
+#805 := (iff #24 #802)
+#803 := (iff #23 #23)
+#804 := [refl]: #803
+#806 := [quant-intro #804]: #805
+#295 := (~ #24 #24)
+#293 := (~ #23 #23)
+#294 := [refl]: #293
+#296 := [nnf-pos #294]: #295
+#70 := [asserted]: #24
+#299 := [mp~ #70 #296]: #24
+#807 := [mp #299 #806]: #802
+#789 := (not #802)
+#463 := (or #789 #795)
+#464 := [quant-inst #10]: #463
+#683 := [unit-resolution #464 #807]: #795
+#672 := (= #15 #793)
+#776 := (= #14 #11)
+#667 := (= 0::Int #11)
+#678 := [hypothesis]: #781
+#668 := [symm #678]: #667
+#782 := (= #14 0::Int)
+#684 := (or #707 #782)
+#604 := -3::Int
+#497 := (* -1::Int #11)
+#748 := (mod #497 -3::Int)
+#744 := (+ #14 #748)
+#745 := (= #744 0::Int)
+#786 := (>= #11 0::Int)
+#759 := (not #786)
+#777 := (<= #11 0::Int)
+#480 := (not #777)
+#761 := (or #480 #759)
+#583 := (if #761 #775 #745)
+#738 := (if #781 #782 #583)
+#26 := (:var 0 Int)
+#38 := (:var 1 Int)
+#58 := (f6 f7 #38)
+#59 := (f5 #58 #26)
+#828 := (pattern #59)
+#159 := (* -1::Int #26)
+#156 := (* -1::Int #38)
+#178 := (mod #156 #159)
+#376 := (+ #59 #178)
+#377 := (= #376 0::Int)
+#60 := (mod #38 #26)
+#373 := (* -1::Int #60)
+#374 := (+ #59 #373)
+#375 := (= #374 0::Int)
+#133 := (<= #26 0::Int)
+#252 := (>= #38 0::Int)
+#320 := (or #252 #133)
+#321 := (not #320)
+#129 := (<= #38 0::Int)
+#316 := (or #129 #133)
+#317 := (not #316)
+#324 := (or #317 #321)
+#378 := (if #324 #375 #377)
+#372 := (= #59 0::Int)
+#41 := (= #38 0::Int)
+#379 := (if #41 #372 #378)
+#371 := (= #59 #38)
+#42 := (= #26 0::Int)
+#380 := (if #42 #371 #379)
+#829 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #828) #380)
+#383 := (forall (vars (?v0 Int) (?v1 Int)) #380)
+#832 := (iff #383 #829)
+#830 := (iff #380 #380)
+#831 := [refl]: #830
+#833 := [quant-intro #831]: #832
+#184 := (* -1::Int #178)
+#340 := (if #324 #60 #184)
+#343 := (if #41 0::Int #340)
+#346 := (if #42 #38 #343)
+#349 := (= #59 #346)
+#352 := (forall (vars (?v0 Int) (?v1 Int)) #349)
+#384 := (iff #352 #383)
+#381 := (iff #349 #380)
+#382 := [rewrite]: #381
+#385 := [quant-intro #382]: #384
+#134 := (not #133)
+#255 := (not #252)
+#258 := (and #255 #134)
+#130 := (not #129)
+#137 := (and #130 #134)
+#261 := (or #137 #258)
+#277 := (if #261 #60 #184)
+#280 := (if #41 0::Int #277)
+#283 := (if #42 #38 #280)
+#286 := (= #59 #283)
+#289 := (forall (vars (?v0 Int) (?v1 Int)) #286)
+#353 := (iff #289 #352)
+#350 := (iff #286 #349)
+#347 := (= #283 #346)
+#344 := (= #280 #343)
+#341 := (= #277 #340)
+#325 := (iff #261 #324)
+#322 := (iff #258 #321)
+#323 := [rewrite]: #322
+#318 := (iff #137 #317)
+#319 := [rewrite]: #318
+#326 := [monotonicity #319 #323]: #325
+#342 := [monotonicity #326]: #341
+#345 := [monotonicity #342]: #344
+#348 := [monotonicity #345]: #347
+#351 := [monotonicity #348]: #350
+#354 := [quant-intro #351]: #353
+#313 := (~ #289 #289)
+#311 := (~ #286 #286)
+#312 := [refl]: #311
+#314 := [nnf-pos #312]: #313
+#140 := (<= 0::Int #38)
+#141 := (not #140)
+#149 := (and #141 #134)
+#152 := (or #137 #149)
+#189 := (if #152 #60 #184)
+#192 := (if #41 0::Int #189)
+#195 := (if #42 #38 #192)
+#198 := (= #59 #195)
+#201 := (forall (vars (?v0 Int) (?v1 Int)) #198)
+#290 := (iff #201 #289)
+#287 := (iff #198 #286)
+#284 := (= #195 #283)
+#281 := (= #192 #280)
+#278 := (= #189 #277)
+#262 := (iff #152 #261)
+#259 := (iff #149 #258)
+#256 := (iff #141 #255)
+#253 := (iff #140 #252)
+#254 := [rewrite]: #253
+#257 := [monotonicity #254]: #256
+#260 := [monotonicity #257]: #259
+#263 := [monotonicity #260]: #262
+#279 := [monotonicity #263]: #278
+#282 := [monotonicity #279]: #281
+#285 := [monotonicity #282]: #284
+#288 := [monotonicity #285]: #287
+#291 := [quant-intro #288]: #290
+#52 := (- #26)
+#51 := (- #38)
+#61 := (mod #51 #52)
+#62 := (- #61)
+#45 := (< 0::Int #26)
+#47 := (< #38 0::Int)
+#48 := (and #47 #45)
+#44 := (< 0::Int #38)
+#46 := (and #44 #45)
+#49 := (or #46 #48)
+#63 := (if #49 #60 #62)
+#64 := (if #41 0::Int #63)
+#65 := (if #42 #38 #64)
+#66 := (= #59 #65)
+#67 := (forall (vars (?v0 Int) (?v1 Int)) #66)
+#202 := (iff #67 #201)
+#199 := (iff #66 #198)
+#196 := (= #65 #195)
+#193 := (= #64 #192)
+#190 := (= #63 #189)
+#187 := (= #62 #184)
+#181 := (- #178)
+#185 := (= #181 #184)
+#186 := [rewrite]: #185
+#182 := (= #62 #181)
+#179 := (= #61 #178)
+#160 := (= #52 #159)
+#161 := [rewrite]: #160
+#157 := (= #51 #156)
+#158 := [rewrite]: #157
+#180 := [monotonicity #158 #161]: #179
+#183 := [monotonicity #180]: #182
+#188 := [trans #183 #186]: #187
+#153 := (iff #49 #152)
+#150 := (iff #48 #149)
+#135 := (iff #45 #134)
+#136 := [rewrite]: #135
+#142 := (iff #47 #141)
+#146 := (iff #141 #141)
+#144 := (iff #140 #140)
+#145 := [rewrite]: #144
+#147 := [monotonicity #145]: #146
+#143 := [rewrite]: #142
+#148 := [trans #143 #147]: #142
+#151 := [monotonicity #148 #136]: #150
+#138 := (iff #46 #137)
+#131 := (iff #44 #130)
+#132 := [rewrite]: #131
+#139 := [monotonicity #132 #136]: #138
+#154 := [monotonicity #139 #151]: #153
+#191 := [monotonicity #154 #188]: #190
+#194 := [monotonicity #191]: #193
+#197 := [monotonicity #194]: #196
+#200 := [monotonicity #197]: #199
+#203 := [quant-intro #200]: #202
+#74 := [asserted]: #67
+#204 := [mp #74 #203]: #201
+#292 := [mp #204 #291]: #289
+#315 := [mp~ #292 #314]: #289
+#355 := [mp #315 #354]: #352
+#386 := [mp #355 #385]: #383
+#834 := [mp #386 #833]: #829
+#635 := (not #829)
+#730 := (or #635 #738)
+#498 := (* -1::Int 3::Int)
+#499 := (mod #497 #498)
+#500 := (+ #14 #499)
+#393 := (= #500 0::Int)
+#783 := (<= 3::Int 0::Int)
+#426 := (or #786 #783)
+#427 := (not #426)
+#421 := (or #777 #783)
+#784 := (not #421)
+#787 := (or #784 #427)
+#770 := (if #787 #775 #393)
+#771 := (if #781 #782 #770)
+#435 := (= 3::Int 0::Int)
+#493 := (if #435 #776 #771)
+#731 := (or #635 #493)
+#619 := (iff #731 #730)
+#636 := (iff #730 #730)
+#637 := [rewrite]: #636
+#585 := (iff #493 #738)
+#739 := (if false #776 #738)
+#625 := (iff #739 #738)
+#626 := [rewrite]: #625
+#742 := (iff #493 #739)
+#740 := (iff #771 #738)
+#584 := (iff #770 #583)
+#752 := (iff #393 #745)
+#750 := (= #500 #744)
+#749 := (= #499 #748)
+#746 := (= #498 -3::Int)
+#747 := [rewrite]: #746
+#743 := [monotonicity #747]: #749
+#751 := [monotonicity #743]: #750
+#581 := [monotonicity #751]: #752
+#602 := (iff #787 #761)
+#760 := (iff #427 #759)
+#753 := (iff #426 #786)
+#763 := (or #786 false)
+#757 := (iff #763 #786)
+#758 := [rewrite]: #757
+#767 := (iff #426 #763)
+#772 := (iff #783 false)
+#769 := [rewrite]: #772
+#756 := [monotonicity #769]: #767
+#754 := [trans #756 #758]: #753
+#755 := [monotonicity #754]: #760
+#762 := (iff #784 #480)
+#764 := (iff #421 #777)
+#773 := (or #777 false)
+#485 := (iff #773 #777)
+#486 := [rewrite]: #485
+#483 := (iff #421 #773)
+#484 := [monotonicity #769]: #483
+#765 := [trans #484 #486]: #764
+#766 := [monotonicity #765]: #762
+#603 := [monotonicity #766 #755]: #602
+#737 := [monotonicity #603 #581]: #584
+#741 := [monotonicity #737]: #740
+#494 := (iff #435 false)
+#768 := [rewrite]: #494
+#624 := [monotonicity #768 #741]: #742
+#733 := [trans #624 #626]: #585
+#634 := [monotonicity #733]: #619
+#630 := [trans #634 #637]: #619
+#734 := [quant-inst #11 #13]: #731
+#638 := [mp #734 #630]: #730
+#693 := [unit-resolution #638 #834]: #738
+#706 := (not #738)
+#709 := (or #706 #707 #782)
+#710 := [def-axiom]: #709
+#670 := [unit-resolution #710 #693]: #684
+#666 := [unit-resolution #670 #678]: #782
+#671 := [trans #666 #668]: #776
+#673 := [monotonicity #671]: #672
+#674 := [trans #673 #683]: #16
+#682 := [hypothesis]: #477
+#669 := [unit-resolution #682 #674]: false
+#648 := [lemma #669]: #675
+#547 := [unit-resolution #648 #554]: #707
+#680 := (or #781 #775)
+#705 := [hypothesis]: #707
+#732 := (not #761)
+#718 := (not #775)
+#685 := [hypothesis]: #718
+#694 := (or #781 #583)
+#711 := (or #706 #781 #583)
+#712 := [def-axiom]: #711
+#695 := [unit-resolution #712 #693]: #694
+#696 := [unit-resolution #695 #705]: #583
+#726 := (not #583)
+#727 := (or #726 #732 #775)
+#728 := [def-axiom]: #727
+#697 := [unit-resolution #728 #696 #685]: #732
+#640 := (or #761 #777)
+#641 := [def-axiom]: #640
+#687 := [unit-resolution #641 #697]: #777
+#642 := (or #761 #786)
+#735 := [def-axiom]: #642
+#698 := [unit-resolution #735 #697]: #786
+#676 := (or #781 #480 #759)
+#677 := [th-lemma arith triangle-eq]: #676
+#679 := [unit-resolution #677 #698 #687 #705]: false
+#681 := [lemma #679]: #680
+#550 := [unit-resolution #681 #547]: #775
+#551 := (or #718 #725)
+#537 := [th-lemma arith triangle-eq]: #551
+#539 := [unit-resolution #537 #550]: #725
+#649 := (div #11 3::Int)
+#662 := (* -3::Int #649)
+#663 := (+ #11 #662 #788)
+#665 := (<= #663 0::Int)
+#659 := (= #663 0::Int)
+#612 := (or false #659)
+#613 := [th-lemma arith]: #612
+#614 := [unit-resolution #613 #222]: #659
+#615 := (not #659)
+#590 := (or #615 #665)
+#592 := [th-lemma arith triangle-eq]: #590
+#593 := [unit-resolution #592 #614]: #665
+#405 := 1::Int
+#573 := -2::Int
+#557 := (* -2::Int #649)
+#562 := (+ #11 #557 #788)
+#552 := (>= #562 1::Int)
+#655 := (* -1::Int #14)
+#656 := (+ #11 #655)
+#661 := (<= #656 0::Int)
+#527 := (not #661)
+#611 := (= #11 #14)
+#586 := (not #611)
+#588 := (or #586 #16)
+#616 := [hypothesis]: #611
+#601 := [symm #616]: #776
+#617 := [monotonicity #601]: #672
+#578 := [trans #617 #683]: #16
+#579 := [unit-resolution #682 #578]: false
+#589 := [lemma #579]: #588
+#534 := [unit-resolution #589 #554]: #586
+#657 := (>= #656 0::Int)
+#664 := (>= #649 0::Int)
+#703 := (f8 f9 #793)
+#704 := (= #703 0::Int)
+#517 := (not #704)
+#518 := (iff #707 #517)
+#515 := (iff #781 #704)
+#536 := (iff #704 #781)
+#535 := (= #703 #11)
+#524 := [monotonicity #683]: #535
+#513 := [monotonicity #524]: #536
+#516 := [symm #513]: #515
+#519 := [monotonicity #516]: #518
+#520 := [mp #547 #519]: #517
+#701 := (or #786 #704)
+#28 := (f3 f4 #26)
+#808 := (pattern #28)
+#29 := (f8 f9 #28)
+#34 := (= #29 0::Int)
+#232 := (>= #26 0::Int)
+#245 := (or #232 #34)
+#815 := (forall (vars (?v0 Int)) (:pat #808) #245)
+#248 := (forall (vars (?v0 Int)) #245)
+#818 := (iff #248 #815)
+#816 := (iff #245 #245)
+#817 := [refl]: #816
+#819 := [quant-intro #817]: #818
+#297 := (~ #248 #248)
+#223 := (~ #245 #245)
+#224 := [refl]: #223
+#298 := [nnf-pos #224]: #297
+#27 := (<= 0::Int #26)
+#120 := (or #27 #34)
+#125 := (forall (vars (?v0 Int)) #120)
+#249 := (iff #125 #248)
+#246 := (iff #120 #245)
+#233 := (iff #27 #232)
+#234 := [rewrite]: #233
+#247 := [monotonicity #234]: #246
+#250 := [quant-intro #247]: #249
+#33 := (< #26 0::Int)
+#35 := (implies #33 #34)
+#36 := (forall (vars (?v0 Int)) #35)
+#126 := (iff #36 #125)
+#123 := (iff #35 #120)
+#103 := (not #27)
+#117 := (implies #103 #34)
+#121 := (iff #117 #120)
+#122 := [rewrite]: #121
+#118 := (iff #35 #117)
+#112 := (iff #33 #103)
+#114 := (iff #103 #103)
+#99 := (iff #27 #27)
+#100 := [rewrite]: #99
+#115 := [monotonicity #100]: #114
+#113 := [rewrite]: #112
+#116 := [trans #113 #115]: #112
+#119 := [monotonicity #116]: #118
+#124 := [trans #119 #122]: #123
+#127 := [quant-intro #124]: #126
+#72 := [asserted]: #36
+#128 := [mp #72 #127]: #125
+#251 := [mp #128 #250]: #248
+#305 := [mp~ #251 #298]: #248
+#820 := [mp #305 #819]: #815
+#439 := (not #815)
+#686 := (or #439 #786 #704)
+#688 := (or #439 #701)
+#690 := (iff #688 #686)
+#691 := [rewrite]: #690
+#689 := [quant-inst #11]: #688
+#692 := [mp #689 #691]: #686
+#521 := [unit-resolution #692 #820]: #701
+#514 := [unit-resolution #521 #520]: #786
+#580 := (or #664 #759)
+#594 := (not #664)
+#595 := [hypothesis]: #594
+#596 := [hypothesis]: #786
+#597 := [th-lemma arith farkas 1 3 1 1 #596 #595 #593 #627]: false
+#598 := [lemma #597]: #580
+#522 := [unit-resolution #598 #514]: #664
+#605 := (not #725)
+#563 := (or #657 #605 #594)
+#631 := (not #657)
+#632 := [hypothesis]: #631
+#645 := (>= #663 0::Int)
+#576 := (or #615 #645)
+#572 := [th-lemma arith triangle-eq]: #576
+#577 := [unit-resolution #572 #614]: #645
+#556 := [hypothesis]: #664
+#644 := [hypothesis]: #725
+#559 := [th-lemma arith farkas 1 -3 -1 1 #644 #556 #577 #632]: false
+#565 := [lemma #559]: #563
+#507 := [unit-resolution #565 #539 #522]: #657
+#508 := (or #611 #527 #631)
+#509 := [th-lemma arith triangle-eq]: #508
+#511 := [unit-resolution #509 #507 #534]: #527
+#717 := (>= #774 0::Int)
+#510 := (or #718 #717)
+#512 := [th-lemma arith triangle-eq]: #510
+#501 := [unit-resolution #512 #550]: #717
+#531 := (not #717)
+#532 := (or #552 #531 #661)
+#541 := (not #552)
+#526 := [hypothesis]: #541
+#528 := [hypothesis]: #527
+#529 := [hypothesis]: #717
+#530 := [th-lemma arith farkas -2/3 -1/3 -1/3 1 #577 #529 #528 #526]: false
+#533 := [lemma #530]: #532
+#502 := [unit-resolution #533 #501 #511]: #552
+#452 := (>= #14 0::Int)
+#591 := (>= #785 0::Int)
+#503 := (or false #591)
+#495 := [th-lemma arith]: #503
+#504 := [unit-resolution #495 #222]: #591
+#505 := (not #591)
+#496 := (or #452 #505 #531)
+#506 := [th-lemma arith assign-bounds 1 1]: #496
+#487 := [unit-resolution #506 #501 #504]: #452
+#488 := [th-lemma arith farkas -1 -3 2 1 1 #487 #502 #593 #539 #546]: false
+#489 := [lemma #488]: #226
+#796 := (f8 f9 #15)
+#797 := (= #796 #14)
+#456 := (iff #797 #611)
+#471 := (= #796 #11)
+#465 := (or #16 #387)
+#473 := (or #16 #387 #472)
+#474 := [def-axiom]: #473
+#476 := [unit-resolution #474 #231]: #465
+#460 := [unit-resolution #476 #489]: #16
+#454 := [monotonicity #460]: #471
+#457 := [monotonicity #454]: #456
+#482 := (or #480 #387)
+#492 := [th-lemma arith farkas 1 1]: #482
+#459 := [unit-resolution #492 #489]: #480
+#461 := (or #707 #777)
+#462 := [th-lemma arith triangle-eq]: #461
+#453 := [unit-resolution #462 #459]: #707
+#466 := [unit-resolution #681 #453]: #775
+#467 := [unit-resolution #512 #466]: #717
+#468 := [unit-resolution #506 #467 #504]: #452
+#582 := (not #452)
+#798 := (or #582 #797)
+#30 := (= #29 #26)
+#235 := (not #232)
+#238 := (or #235 #30)
+#809 := (forall (vars (?v0 Int)) (:pat #808) #238)
+#241 := (forall (vars (?v0 Int)) #238)
+#812 := (iff #241 #809)
+#810 := (iff #238 #238)
+#811 := [refl]: #810
+#813 := [quant-intro #811]: #812
+#302 := (~ #241 #241)
+#300 := (~ #238 #238)
+#301 := [refl]: #300
+#303 := [nnf-pos #301]: #302
+#104 := (or #103 #30)
+#108 := (forall (vars (?v0 Int)) #104)
+#242 := (iff #108 #241)
+#239 := (iff #104 #238)
+#236 := (iff #103 #235)
+#237 := [monotonicity #234]: #236
+#240 := [monotonicity #237]: #239
+#243 := [quant-intro #240]: #242
+#31 := (implies #27 #30)
+#32 := (forall (vars (?v0 Int)) #31)
+#109 := (iff #32 #108)
+#105 := (iff #31 #104)
 #106 := [rewrite]: #105
-#101 := (iff #20 #100)
-#98 := (iff #19 #95)
-#92 := (iff #89 #18)
-#96 := (iff #92 #95)
-#97 := [rewrite]: #96
-#93 := (iff #19 #92)
-#90 := (iff #17 #89)
-#91 := [rewrite]: #90
-#94 := [monotonicity #91]: #93
-#99 := [trans #94 #97]: #98
-#102 := [monotonicity #99]: #101
-#108 := [trans #102 #106]: #107
-#124 := [trans #108 #122]: #123
-#88 := [asserted]: #20
-#125 := [mp #88 #124]: #120
-#490 := (not #120)
-#580 := (or #579 #111 #490)
-#508 := [def-axiom]: #580
-#578 := [unit-resolution #508 #125]: #581
-#643 := [unit-resolution #578 #626]: #579
-#760 := (or #816 #89)
-#582 := (f3 f4 #12)
-#757 := (= #582 #16)
-#753 := (= #16 #582)
-#778 := (= #15 #12)
-#777 := (= 0::Int #12)
-#771 := [hypothesis]: #871
-#772 := [symm #771]: #777
-#597 := (= #15 0::Int)
-#774 := (or #816 #597)
-#847 := -3::Int
-#887 := (* -1::Int #12)
-#848 := (mod #887 -3::Int)
-#686 := (+ #15 #848)
-#841 := (= #686 0::Int)
-#878 := (>= #12 0::Int)
-#707 := (not #878)
-#603 := (<= #12 0::Int)
-#860 := (not #603)
-#851 := (or #860 #707)
-#842 := (ite #851 #877 #841)
-#728 := (ite #871 #597 #842)
-#27 := (:var 0 Int)
-#39 := (:var 1 Int)
-#59 := (f6 f7 #39)
-#60 := (f5 #59 #27)
-#931 := (pattern #60)
-#231 := (* -1::Int #27)
-#228 := (* -1::Int #39)
-#292 := (mod #228 #231)
-#422 := (+ #60 #292)
-#423 := (= #422 0::Int)
-#61 := (mod #39 #27)
-#419 := (* -1::Int #61)
-#420 := (+ #60 #419)
-#421 := (= #420 0::Int)
-#266 := (>= #39 0::Int)
-#259 := (<= #27 0::Int)
-#366 := (or #259 #266)
-#367 := (not #366)
-#255 := (<= #39 0::Int)
-#364 := (or #255 #259)
-#365 := (not #364)
-#370 := (or #365 #367)
-#424 := (ite #370 #421 #423)
-#418 := (= #60 0::Int)
-#42 := (= #39 0::Int)
-#425 := (ite #42 #418 #424)
-#417 := (= #39 #60)
-#43 := (= #27 0::Int)
-#426 := (ite #43 #417 #425)
-#932 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #931) #426)
-#429 := (forall (vars (?v0 Int) (?v1 Int)) #426)
-#935 := (iff #429 #932)
-#933 := (iff #426 #426)
-#934 := [refl]: #933
-#936 := [quant-intro #934]: #935
-#298 := (* -1::Int #292)
-#386 := (ite #370 #61 #298)
-#389 := (ite #42 0::Int #386)
-#392 := (ite #43 #39 #389)
-#395 := (= #60 #392)
-#398 := (forall (vars (?v0 Int) (?v1 Int)) #395)
-#430 := (iff #398 #429)
-#427 := (iff #395 #426)
-#428 := [rewrite]: #427
-#431 := [quant-intro #428]: #430
-#267 := (not #266)
-#260 := (not #259)
-#270 := (and #260 #267)
-#256 := (not #255)
-#263 := (and #256 #260)
-#273 := (or #263 #270)
-#318 := (ite #273 #61 #298)
-#321 := (ite #42 0::Int #318)
-#324 := (ite #43 #39 #321)
-#327 := (= #60 #324)
-#330 := (forall (vars (?v0 Int) (?v1 Int)) #327)
-#399 := (iff #330 #398)
-#396 := (iff #327 #395)
-#393 := (= #324 #392)
-#390 := (= #321 #389)
-#387 := (= #318 #386)
-#371 := (iff #273 #370)
-#368 := (iff #270 #367)
-#369 := [rewrite]: #368
-#349 := (iff #263 #365)
-#350 := [rewrite]: #349
-#372 := [monotonicity #350 #369]: #371
-#388 := [monotonicity #372]: #387
-#391 := [monotonicity #388]: #390
-#394 := [monotonicity #391]: #393
-#397 := [monotonicity #394]: #396
-#400 := [quant-intro #397]: #399
-#347 := (~ #330 #330)
-#361 := (~ #327 #327)
-#362 := [refl]: #361
-#348 := [nnf-pos #362]: #347
-#53 := (- #27)
-#52 := (- #39)
-#62 := (mod #52 #53)
-#63 := (- #62)
-#46 := (< 0::Int #27)
-#48 := (< #39 0::Int)
-#49 := (and #48 #46)
-#45 := (< 0::Int #39)
-#47 := (and #45 #46)
-#50 := (or #47 #49)
-#64 := (ite #50 #61 #63)
-#65 := (ite #42 0::Int #64)
-#66 := (ite #43 #39 #65)
-#67 := (= #60 #66)
-#68 := (forall (vars (?v0 Int) (?v1 Int)) #67)
-#333 := (iff #68 #330)
-#221 := (and #46 #48)
-#224 := (or #47 #221)
-#303 := (ite #224 #61 #298)
-#212 := (= 0::Int #39)
-#306 := (ite #212 0::Int #303)
-#215 := (= 0::Int #27)
-#309 := (ite #215 #39 #306)
-#312 := (= #60 #309)
-#315 := (forall (vars (?v0 Int) (?v1 Int)) #312)
-#331 := (iff #315 #330)
-#328 := (iff #312 #327)
-#325 := (= #309 #324)
-#322 := (= #306 #321)
-#319 := (= #303 #318)
-#274 := (iff #224 #273)
-#271 := (iff #221 #270)
-#268 := (iff #48 #267)
-#269 := [rewrite]: #268
-#261 := (iff #46 #260)
-#262 := [rewrite]: #261
-#272 := [monotonicity #262 #269]: #271
-#264 := (iff #47 #263)
-#257 := (iff #45 #256)
-#258 := [rewrite]: #257
-#265 := [monotonicity #258 #262]: #264
-#275 := [monotonicity #265 #272]: #274
-#320 := [monotonicity #275]: #319
-#249 := (iff #212 #42)
-#250 := [rewrite]: #249
-#323 := [monotonicity #250 #320]: #322
-#251 := (iff #215 #43)
-#252 := [rewrite]: #251
-#326 := [monotonicity #252 #323]: #325
-#329 := [monotonicity #326]: #328
-#332 := [quant-intro #329]: #331
-#316 := (iff #68 #315)
-#313 := (iff #67 #312)
-#310 := (= #66 #309)
-#307 := (= #65 #306)
-#304 := (= #64 #303)
-#301 := (= #63 #298)
-#295 := (- #292)
-#299 := (= #295 #298)
-#300 := [rewrite]: #299
-#296 := (= #63 #295)
-#293 := (= #62 #292)
-#232 := (= #53 #231)
-#233 := [rewrite]: #232
-#229 := (= #52 #228)
-#230 := [rewrite]: #229
-#294 := [monotonicity #230 #233]: #293
-#297 := [monotonicity #294]: #296
-#302 := [trans #297 #300]: #301
-#225 := (iff #50 #224)
-#222 := (iff #49 #221)
-#223 := [rewrite]: #222
-#226 := [monotonicity #223]: #225
-#305 := [monotonicity #226 #302]: #304
-#213 := (iff #42 #212)
-#214 := [rewrite]: #213
-#308 := [monotonicity #214 #305]: #307
-#216 := (iff #43 #215)
-#217 := [rewrite]: #216
-#311 := [monotonicity #217 #308]: #310
-#314 := [monotonicity #311]: #313
-#317 := [quant-intro #314]: #316
-#334 := [trans #317 #332]: #333
-#291 := [asserted]: #68
-#335 := [mp #291 #334]: #330
-#363 := [mp~ #335 #348]: #330
-#401 := [mp #363 #400]: #398
-#432 := [mp #401 #431]: #429
-#937 := [mp #432 #936]: #932
-#739 := (not #932)
-#740 := (or #739 #728)
-#524 := (* -1::Int 3::Int)
-#889 := (mod #887 #524)
-#529 := (+ #15 #889)
-#530 := (= #529 0::Int)
-#600 := (<= 3::Int 0::Int)
-#601 := (or #600 #878)
-#602 := (not #601)
-#496 := (or #603 #600)
-#873 := (not #496)
-#874 := (or #873 #602)
-#596 := (ite #874 #877 #530)
-#875 := (ite #871 #597 #596)
-#872 := (= #12 #15)
-#876 := (= 3::Int 0::Int)
-#586 := (ite #876 #872 #875)
-#733 := (or #739 #586)
-#742 := (iff #733 #740)
-#744 := (iff #740 #740)
-#745 := [rewrite]: #744
-#722 := (iff #586 #728)
-#836 := (ite false #872 #728)
-#834 := (iff #836 #728)
-#837 := [rewrite]: #834
-#738 := (iff #586 #836)
-#729 := (iff #875 #728)
-#845 := (iff #596 #842)
-#843 := (iff #530 #841)
-#687 := (= #529 #686)
-#855 := (= #889 #848)
-#853 := (= #524 -3::Int)
-#854 := [rewrite]: #853
-#684 := [monotonicity #854]: #855
-#840 := [monotonicity #684]: #687
-#844 := [monotonicity #840]: #843
-#852 := (iff #874 #851)
-#849 := (iff #602 #707)
-#705 := (iff #601 #878)
-#857 := (or false #878)
-#858 := (iff #857 #878)
-#864 := [rewrite]: #858
-#862 := (iff #601 #857)
-#589 := (iff #600 false)
-#867 := [rewrite]: #589
-#863 := [monotonicity #867]: #862
-#706 := [trans #863 #864]: #705
-#850 := [monotonicity #706]: #849
-#861 := (iff #873 #860)
-#870 := (iff #496 #603)
-#868 := (or #603 false)
-#869 := (iff #868 #603)
-#866 := [rewrite]: #869
-#583 := (iff #496 #868)
-#865 := [monotonicity #867]: #583
-#859 := [trans #865 #866]: #870
-#856 := [monotonicity #859]: #861
-#846 := [monotonicity #856 #850]: #852
-#727 := [monotonicity #846 #844]: #845
-#688 := [monotonicity #727]: #729
-#587 := (iff #876 false)
-#588 := [rewrite]: #587
-#833 := [monotonicity #588 #688]: #738
-#737 := [trans #833 #837]: #722
-#743 := [monotonicity #737]: #742
-#838 := [trans #743 #745]: #742
-#741 := [quant-inst #12 #14]: #733
-#835 := [mp #741 #838]: #740
-#801 := [unit-resolution #835 #937]: #728
-#811 := (not #728)
-#802 := (or #811 #816 #597)
-#803 := [def-axiom]: #802
-#775 := [unit-resolution #803 #801]: #774
-#776 := [unit-resolution #775 #771]: #597
-#751 := [trans #776 #772]: #778
-#646 := [monotonicity #751]: #753
-#758 := [symm #646]: #757
-#561 := (= f10 #582)
-#21 := (:var 0 S3)
-#22 := (f8 f9 #21)
-#904 := (pattern #22)
-#23 := (f3 f4 #22)
-#127 := (= #21 #23)
-#905 := (forall (vars (?v0 S3)) (:pat #904) #127)
-#130 := (forall (vars (?v0 S3)) #127)
-#908 := (iff #130 #905)
-#906 := (iff #127 #127)
-#907 := [refl]: #906
-#909 := [quant-intro #907]: #908
-#353 := (~ #130 #130)
-#351 := (~ #127 #127)
-#352 := [refl]: #351
-#354 := [nnf-pos #352]: #353
-#24 := (= #23 #21)
-#25 := (forall (vars (?v0 S3)) #24)
-#131 := (iff #25 #130)
-#128 := (iff #24 #127)
-#129 := [rewrite]: #128
-#132 := [quant-intro #129]: #131
-#126 := [asserted]: #25
-#135 := [mp #126 #132]: #130
-#339 := [mp~ #135 #354]: #130
-#910 := [mp #339 #909]: #905
-#555 := (not #905)
-#685 := (or #555 #561)
-#892 := [quant-inst #11]: #685
-#752 := [unit-resolution #892 #910]: #561
-#759 := [trans #752 #758]: #89
-#770 := [hypothesis]: #579
-#764 := [unit-resolution #770 #759]: false
-#761 := [lemma #764]: #760
-#641 := [unit-resolution #761 #643]: #816
-#773 := (or #871 #877)
-#794 := [hypothesis]: #816
-#819 := (not #851)
-#809 := (not #877)
-#795 := [hypothesis]: #809
-#779 := (or #871 #842)
-#805 := (or #811 #871 #842)
-#806 := [def-axiom]: #805
-#780 := [unit-resolution #806 #801]: #779
-#782 := [unit-resolution #780 #794]: #842
-#822 := (not #842)
-#823 := (or #822 #819 #877)
-#824 := [def-axiom]: #823
-#783 := [unit-resolution #824 #782 #795]: #819
-#826 := (or #851 #603)
-#828 := [def-axiom]: #826
-#784 := [unit-resolution #828 #783]: #603
-#820 := (or #851 #878)
-#817 := [def-axiom]: #820
-#785 := [unit-resolution #817 #783]: #878
-#786 := (or #871 #860 #707)
-#781 := [th-lemma arith triangle-eq]: #786
-#787 := [unit-resolution #781 #785 #784 #794]: false
-#769 := [lemma #787]: #773
-#630 := [unit-resolution #769 #641]: #877
-#631 := (or #809 #831)
-#632 := [th-lemma arith triangle-eq]: #631
-#633 := [unit-resolution #632 #630]: #831
-#762 := (div #12 3::Int)
-#754 := (* -3::Int #762)
-#755 := (+ #754 #888)
-#750 := (+ #12 #755)
-#731 := (<= #750 0::Int)
-#730 := (= #750 0::Int)
-#677 := (or false #730)
-#678 := [th-lemma arith]: #677
-#521 := [unit-resolution #678 #86]: #730
-#679 := (not #730)
-#675 := (or #679 #731)
-#680 := [th-lemma arith triangle-eq]: #675
-#659 := [unit-resolution #680 #521]: #731
-#637 := 1::Int
-#628 := -2::Int
-#634 := (* -2::Int #762)
-#635 := (+ #634 #888)
-#636 := (+ #12 #635)
-#638 := (>= #636 1::Int)
-#689 := (* -1::Int #15)
-#691 := (+ #12 #689)
-#692 := (<= #691 0::Int)
-#621 := (not #692)
-#683 := (not #872)
-#701 := (or #683 #89)
-#695 := [hypothesis]: #872
-#696 := [symm #695]: #778
-#697 := [monotonicity #696]: #753
-#698 := [symm #697]: #757
-#699 := [trans #752 #698]: #89
-#700 := [unit-resolution #770 #699]: false
-#671 := [lemma #700]: #701
-#615 := [unit-resolution #671 #643]: #683
-#693 := (>= #691 0::Int)
-#672 := (>= #762 0::Int)
-#791 := (f8 f9 #582)
-#792 := (= #791 0::Int)
-#607 := (not #792)
-#608 := (iff #816 #607)
-#606 := (iff #871 #792)
-#604 := (iff #792 #871)
-#611 := (= #791 #12)
-#614 := (= #582 f10)
-#613 := [symm #752]: #614
-#612 := [monotonicity #613]: #611
-#605 := [monotonicity #612]: #604
-#598 := [symm #605]: #606
-#599 := [monotonicity #598]: #608
-#609 := [mp #641 #599]: #607
-#793 := (or #792 #878)
-#29 := (f3 f4 #27)
-#911 := (pattern #29)
-#152 := (>= #27 0::Int)
-#30 := (f8 f9 #29)
-#35 := (= #30 0::Int)
-#200 := (or #35 #152)
-#918 := (forall (vars (?v0 Int)) (:pat #911) #200)
-#205 := (forall (vars (?v0 Int)) #200)
-#921 := (iff #205 #918)
-#919 := (iff #200 #200)
-#920 := [refl]: #919
-#922 := [quant-intro #920]: #921
-#343 := (~ #205 #205)
-#355 := (~ #200 #200)
-#356 := [refl]: #355
-#344 := [nnf-pos #356]: #343
-#34 := (< #27 0::Int)
-#36 := (implies #34 #35)
-#37 := (forall (vars (?v0 Int)) #36)
-#208 := (iff #37 #205)
-#171 := (= 0::Int #30)
-#177 := (not #34)
-#178 := (or #177 #171)
-#183 := (forall (vars (?v0 Int)) #178)
-#206 := (iff #183 #205)
-#203 := (iff #178 #200)
-#197 := (or #152 #35)
-#201 := (iff #197 #200)
-#202 := [rewrite]: #201
-#198 := (iff #178 #197)
-#195 := (iff #171 #35)
-#196 := [rewrite]: #195
-#193 := (iff #177 #152)
-#153 := (not #152)
-#188 := (not #153)
-#191 := (iff #188 #152)
-#192 := [rewrite]: #191
-#189 := (iff #177 #188)
-#186 := (iff #34 #153)
-#187 := [rewrite]: #186
-#190 := [monotonicity #187]: #189
-#194 := [trans #190 #192]: #193
-#199 := [monotonicity #194 #196]: #198
-#204 := [trans #199 #202]: #203
-#207 := [quant-intro #204]: #206
-#184 := (iff #37 #183)
-#181 := (iff #36 #178)
-#174 := (implies #34 #171)
-#179 := (iff #174 #178)
-#180 := [rewrite]: #179
-#175 := (iff #36 #174)
-#172 := (iff #35 #171)
-#173 := [rewrite]: #172
-#176 := [monotonicity #173]: #175
-#182 := [trans #176 #180]: #181
-#185 := [quant-intro #182]: #184
-#209 := [trans #185 #207]: #208
-#170 := [asserted]: #37
-#210 := [mp #170 #209]: #205
-#357 := [mp~ #210 #344]: #205
-#923 := [mp #357 #922]: #918
-#879 := (not #918)
-#796 := (or #879 #792 #878)
-#797 := (or #879 #793)
-#799 := (iff #797 #796)
-#800 := [rewrite]: #799
-#798 := [quant-inst #12]: #797
-#790 := [mp #798 #800]: #796
-#590 := [unit-resolution #790 #923]: #793
-#591 := [unit-resolution #590 #609]: #878
-#667 := (or #672 #707)
-#662 := (not #672)
-#666 := [hypothesis]: #662
-#668 := [hypothesis]: #878
-#669 := [th-lemma arith farkas 1 3 1 1 #668 #666 #659 #676]: false
-#670 := [lemma #669]: #667
-#592 := [unit-resolution #670 #591]: #672
-#655 := (not #831)
-#640 := (or #693 #655 #662)
-#663 := (not #693)
-#664 := [hypothesis]: #663
-#690 := (>= #750 0::Int)
-#649 := (or #679 #690)
-#657 := [th-lemma arith triangle-eq]: #649
-#650 := [unit-resolution #657 #521]: #690
-#653 := [hypothesis]: #672
-#661 := [hypothesis]: #831
-#654 := [th-lemma arith farkas 1 -3 -1 1 #661 #653 #650 #664]: false
-#642 := [lemma #654]: #640
-#584 := [unit-resolution #642 #633 #592]: #693
-#593 := (or #872 #621 #663)
-#594 := [th-lemma arith triangle-eq]: #593
-#585 := [unit-resolution #594 #584 #615]: #621
-#827 := (>= #891 0::Int)
-#595 := (or #809 #827)
-#562 := [th-lemma arith triangle-eq]: #595
-#564 := [unit-resolution #562 #630]: #827
-#617 := (not #827)
-#625 := (or #638 #617 #692)
-#616 := (not #638)
-#620 := [hypothesis]: #616
-#622 := [hypothesis]: #621
-#623 := [hypothesis]: #827
-#624 := [th-lemma arith farkas -2/3 -1/3 -1/3 1 #650 #623 #622 #620]: false
-#610 := [lemma #624]: #625
-#565 := [unit-resolution #610 #564 #585]: #638
-#896 := (>= #15 0::Int)
-#721 := (>= #890 0::Int)
-#556 := (or false #721)
-#569 := [th-lemma arith]: #556
-#570 := [unit-resolution #569 #86]: #721
-#571 := (not #721)
-#572 := (or #896 #571 #617)
-#573 := [th-lemma arith assign-bounds 1 1]: #572
-#563 := [unit-resolution #573 #564 #570]: #896
-#574 := [th-lemma arith farkas -1 -3 2 1 1 #563 #565 #659 #633 #626]: false
-#557 := [lemma #574]: #111
-#566 := (f8 f9 #16)
-#567 := (= #15 #566)
-#528 := (iff #567 #872)
-#525 := (iff #778 #872)
-#527 := [commutativity]: #525
-#534 := (iff #567 #778)
-#535 := (= #566 #12)
-#577 := (or #89 #109)
-#575 := (or #89 #109 #490)
-#576 := [def-axiom]: #575
-#568 := [unit-resolution #576 #125]: #577
-#552 := [unit-resolution #568 #557]: #89
-#533 := [symm #552]: #17
-#536 := [monotonicity #533]: #535
-#537 := [monotonicity #536]: #534
-#531 := [trans #537 #527]: #528
-#559 := (or #860 #109)
-#560 := [th-lemma arith farkas 1 1]: #559
-#539 := [unit-resolution #560 #557]: #860
-#541 := (or #816 #603)
-#546 := [th-lemma arith triangle-eq]: #541
-#547 := [unit-resolution #546 #539]: #816
-#548 := [unit-resolution #769 #547]: #877
-#549 := [unit-resolution #562 #548]: #827
-#550 := [unit-resolution #573 #549 #570]: #896
-#898 := (not #896)
-#899 := (or #567 #898)
-#134 := (= #27 #30)
-#159 := (or #134 #153)
-#912 := (forall (vars (?v0 Int)) (:pat #911) #159)
-#164 := (forall (vars (?v0 Int)) #159)
-#915 := (iff #164 #912)
-#913 := (iff #159 #159)
-#914 := [refl]: #913
-#916 := [quant-intro #914]: #915
-#341 := (~ #164 #164)
-#340 := (~ #159 #159)
-#337 := [refl]: #340
-#342 := [nnf-pos #337]: #341
-#31 := (= #30 #27)
-#28 := (<= 0::Int #27)
-#32 := (implies #28 #31)
-#33 := (forall (vars (?v0 Int)) #32)
-#167 := (iff #33 #164)
-#141 := (not #28)
-#142 := (or #141 #134)
-#147 := (forall (vars (?v0 Int)) #142)
-#165 := (iff #147 #164)
-#162 := (iff #142 #159)
-#156 := (or #153 #134)
-#160 := (iff #156 #159)
-#161 := [rewrite]: #160
-#157 := (iff #142 #156)
-#154 := (iff #141 #153)
-#150 := (iff #28 #152)
-#151 := [rewrite]: #150
-#155 := [monotonicity #151]: #154
-#158 := [monotonicity #155]: #157
-#163 := [trans #158 #161]: #162
-#166 := [quant-intro #163]: #165
-#148 := (iff #33 #147)
-#145 := (iff #32 #142)
-#138 := (implies #28 #134)
-#143 := (iff #138 #142)
-#144 := [rewrite]: #143
-#139 := (iff #32 #138)
-#136 := (iff #31 #134)
-#137 := [rewrite]: #136
-#140 := [monotonicity #137]: #139
-#146 := [trans #140 #144]: #145
-#149 := [quant-intro #146]: #148
-#168 := [trans #149 #166]: #167
-#133 := [asserted]: #33
-#169 := [mp #133 #168]: #164
-#338 := [mp~ #169 #342]: #164
-#917 := [mp #338 #916]: #912
-#902 := (not #912)
-#897 := (or #902 #567 #898)
-#903 := (or #902 #899)
-#553 := (iff #903 #897)
-#558 := [rewrite]: #553
-#893 := [quant-inst #15]: #903
-#894 := [mp #893 #558]: #897
-#551 := [unit-resolution #894 #917]: #899
-#540 := [unit-resolution #551 #550]: #567
-#526 := [mp #540 #531]: #872
-#532 := (or #683 #692)
-#506 := [th-lemma arith triangle-eq]: #532
-#511 := [unit-resolution #506 #526]: #692
-#512 := [unit-resolution #632 #548]: #831
-[th-lemma arith farkas 1 1 -1 1 #512 #511 #557 #676]: false
-unsat
-64e52f0d144c27e355fe51228451050fa17f1e44 838 0
-#2 := false
-decl f4 :: (-> S3 Int S2)
-decl f6 :: (-> S4 Int Int)
-#14 := 1::Int
-decl f7 :: (-> S5 Int S4)
+#101 := (iff #31 #31)
+#102 := [monotonicity #100]: #101
+#107 := [trans #102 #106]: #105
+#110 := [quant-intro #107]: #109
+#71 := [asserted]: #32
+#111 := [mp #71 #110]: #108
+#244 := [mp #111 #243]: #241
+#304 := [mp~ #244 #303]: #241
+#814 := [mp #304 #813]: #809
+#800 := (not #809)
+#790 := (or #800 #582 #797)
+#450 := (or #800 #798)
+#791 := (iff #450 #790)
+#451 := [rewrite]: #791
+#455 := [quant-inst #14]: #450
+#792 := [mp #455 #451]: #790
+#469 := [unit-resolution #792 #814]: #798
+#470 := [unit-resolution #469 #468]: #797
+#436 := [mp #470 #457]: #611
+#438 := (or #586 #661)
+#443 := [th-lemma arith triangle-eq]: #438
+#444 := [unit-resolution #443 #436]: #661
+#445 := [unit-resolution #537 #466]: #725
+[th-lemma arith farkas 1 1 -1 1 #445 #444 #489 #627]: false
+39e38a4cd6cf46af7d8d64c6a30d6324a7b844a7 778 0
+unsat
+#2 := false
+#28 := 0::Int
 decl f9 :: (-> S6 S2 Int)
 decl f3 :: S2
-#8 := f3
+#7 := f3
 decl f10 :: S6
-#11 := f10
-#12 := (f9 f10 f3)
-decl f11 :: S5
-#17 := f11
-#18 := (f7 f11 #12)
-#19 := (f6 #18 1::Int)
-decl f8 :: S5
-#10 := f8
-#13 := (f7 f8 #12)
-#15 := (f6 #13 1::Int)
-#93 := (+ #15 #19)
-decl f5 :: S3
-#9 := f5
-#96 := (f4 f5 #93)
-#99 := (= f3 #96)
-#560 := (f9 f10 #96)
-#478 := (f4 f5 #560)
-#990 := (= #478 #96)
-#481 := (= #96 #478)
-#24 := (:var 0 S2)
-#25 := (f9 f10 #24)
-#883 := (pattern #25)
-#26 := (f4 f5 #25)
-#106 := (= #24 #26)
-#884 := (forall (vars (?v0 S2)) (:pat #883) #106)
-#110 := (forall (vars (?v0 S2)) #106)
-#887 := (iff #110 #884)
-#885 := (iff #106 #106)
-#886 := [refl]: #885
-#888 := [quant-intro #886]: #887
-#333 := (~ #110 #110)
-#331 := (~ #106 #106)
-#332 := [refl]: #331
-#334 := [nnf-pos #332]: #333
-#27 := (= #26 #24)
-#28 := (forall (vars (?v0 S2)) #27)
-#111 := (iff #28 #110)
-#108 := (iff #27 #106)
-#109 := [rewrite]: #108
-#112 := [quant-intro #109]: #111
-#105 := [asserted]: #28
-#115 := [mp #105 #112]: #110
-#319 := [mp~ #115 #334]: #110
-#889 := [mp #319 #888]: #884
-#547 := (not #884)
-#938 := (or #547 #481)
-#939 := [quant-inst #96]: #938
-#985 := [unit-resolution #939 #889]: #481
-#991 := [symm #985]: #990
-#992 := (= f3 #478)
-#470 := (f4 f5 #12)
-#988 := (= #470 #478)
-#986 := (= #478 #470)
-#983 := (= #560 #12)
-#29 := 0::Int
-#981 := (= 0::Int #12)
-#855 := (= #12 0::Int)
-#942 := (= #470 #96)
-#940 := (= #12 #93)
-#923 := (= #15 #93)
-#678 := (<= #19 0::Int)
-#765 := (= #19 0::Int)
-#852 := (<= #12 0::Int)
-#684 := (not #852)
-#580 := (>= #12 0::Int)
-#833 := (not #580)
-#726 := (or #833 #684 #855)
-#502 := [hypothesis]: #833
-#638 := (f9 f10 #470)
-#641 := (= #638 0::Int)
-#518 := (iff #641 #855)
-#538 := (= #638 #12)
-#488 := (= #12 #638)
-#554 := (= f3 #470)
-#558 := (or #547 #554)
-#559 := [quant-inst #8]: #558
-#542 := [unit-resolution #559 #889]: #554
-#489 := [monotonicity #542]: #488
-#492 := [symm #489]: #538
-#493 := [monotonicity #492]: #518
-#647 := (or #580 #641)
-#30 := (:var 0 Int)
-#32 := (f4 f5 #30)
-#890 := (pattern #32)
-#132 := (>= #30 0::Int)
-#33 := (f9 f10 #32)
-#38 := (= #33 0::Int)
-#180 := (or #38 #132)
-#897 := (forall (vars (?v0 Int)) (:pat #890) #180)
-#185 := (forall (vars (?v0 Int)) #180)
-#900 := (iff #185 #897)
-#898 := (iff #180 #180)
-#899 := [refl]: #898
-#901 := [quant-intro #899]: #900
-#323 := (~ #185 #185)
-#335 := (~ #180 #180)
-#336 := [refl]: #335
-#324 := [nnf-pos #336]: #323
-#37 := (< #30 0::Int)
-#39 := (implies #37 #38)
-#40 := (forall (vars (?v0 Int)) #39)
-#188 := (iff #40 #185)
-#151 := (= 0::Int #33)
-#157 := (not #37)
-#158 := (or #157 #151)
-#163 := (forall (vars (?v0 Int)) #158)
-#186 := (iff #163 #185)
-#183 := (iff #158 #180)
-#177 := (or #132 #38)
-#181 := (iff #177 #180)
-#182 := [rewrite]: #181
-#178 := (iff #158 #177)
-#175 := (iff #151 #38)
-#176 := [rewrite]: #175
-#173 := (iff #157 #132)
-#133 := (not #132)
-#168 := (not #133)
-#171 := (iff #168 #132)
-#172 := [rewrite]: #171
-#169 := (iff #157 #168)
-#166 := (iff #37 #133)
-#167 := [rewrite]: #166
-#170 := [monotonicity #167]: #169
-#174 := [trans #170 #172]: #173
-#179 := [monotonicity #174 #176]: #178
-#184 := [trans #179 #182]: #183
-#187 := [quant-intro #184]: #186
-#164 := (iff #40 #163)
-#161 := (iff #39 #158)
-#154 := (implies #37 #151)
-#159 := (iff #154 #158)
-#160 := [rewrite]: #159
-#155 := (iff #39 #154)
-#152 := (iff #38 #151)
-#153 := [rewrite]: #152
-#156 := [monotonicity #153]: #155
-#162 := [trans #156 #160]: #161
-#165 := [quant-intro #162]: #164
-#189 := [trans #165 #187]: #188
-#150 := [asserted]: #40
-#190 := [mp #150 #189]: #185
-#337 := [mp~ #190 #324]: #185
-#902 := [mp #337 #901]: #897
-#861 := (not #897)
-#649 := (or #861 #580 #641)
-#645 := (or #641 #580)
-#637 := (or #861 #645)
-#624 := (iff #637 #649)
-#642 := (or #861 #647)
-#644 := (iff #642 #649)
-#634 := [rewrite]: #644
-#643 := (iff #637 #642)
-#648 := (iff #645 #647)
-#646 := [rewrite]: #648
-#639 := [monotonicity #646]: #643
-#626 := [trans #639 #634]: #624
-#640 := [quant-inst #12]: #637
-#627 := [mp #640 #626]: #649
-#519 := [unit-resolution #627 #902]: #647
-#485 := [unit-resolution #519 #502]: #641
-#494 := [mp #485 #493]: #855
-#771 := (not #855)
-#487 := (or #771 #580)
-#495 := [th-lemma arith triangle-eq]: #487
-#480 := [unit-resolution #495 #494 #502]: false
-#477 := [lemma #480]: #580
-#482 := [hypothesis]: #771
-#512 := (or #855 #684 #833)
-#514 := [th-lemma arith triangle-eq]: #512
-#483 := [unit-resolution #514 #482 #477]: #684
-#670 := (or #726 #852)
-#671 := [def-axiom]: #670
-#471 := [unit-resolution #671 #483]: #726
-#675 := (not #726)
-#474 := (or #675 #765)
-#207 := -1::Int
-#860 := (* -1::Int #12)
-#792 := (mod #860 -1::Int)
-#744 := (+ #19 #792)
-#742 := (= #744 0::Int)
-#687 := (ite #726 #765 #742)
-#41 := (:var 1 Int)
-#61 := (f7 f11 #41)
-#62 := (f6 #61 #30)
-#910 := (pattern #62)
-#211 := (* -1::Int #30)
-#208 := (* -1::Int #41)
-#272 := (mod #208 #211)
-#402 := (+ #62 #272)
-#403 := (= #402 0::Int)
-#63 := (mod #41 #30)
-#399 := (* -1::Int #63)
-#400 := (+ #62 #399)
-#401 := (= #400 0::Int)
-#246 := (>= #41 0::Int)
-#239 := (<= #30 0::Int)
-#346 := (or #239 #246)
-#347 := (not #346)
-#235 := (<= #41 0::Int)
-#344 := (or #235 #239)
-#345 := (not #344)
-#350 := (or #345 #347)
-#404 := (ite #350 #401 #403)
-#398 := (= #62 0::Int)
-#44 := (= #41 0::Int)
-#405 := (ite #44 #398 #404)
-#397 := (= #41 #62)
-#45 := (= #30 0::Int)
-#406 := (ite #45 #397 #405)
-#911 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #910) #406)
-#409 := (forall (vars (?v0 Int) (?v1 Int)) #406)
-#914 := (iff #409 #911)
-#912 := (iff #406 #406)
-#913 := [refl]: #912
-#915 := [quant-intro #913]: #914
-#278 := (* -1::Int #272)
-#366 := (ite #350 #63 #278)
-#369 := (ite #44 0::Int #366)
-#372 := (ite #45 #41 #369)
-#375 := (= #62 #372)
-#378 := (forall (vars (?v0 Int) (?v1 Int)) #375)
-#410 := (iff #378 #409)
-#407 := (iff #375 #406)
-#408 := [rewrite]: #407
-#411 := [quant-intro #408]: #410
-#247 := (not #246)
-#240 := (not #239)
-#250 := (and #240 #247)
-#236 := (not #235)
-#243 := (and #236 #240)
-#253 := (or #243 #250)
-#298 := (ite #253 #63 #278)
-#301 := (ite #44 0::Int #298)
-#304 := (ite #45 #41 #301)
-#307 := (= #62 #304)
-#310 := (forall (vars (?v0 Int) (?v1 Int)) #307)
-#379 := (iff #310 #378)
-#376 := (iff #307 #375)
-#373 := (= #304 #372)
-#370 := (= #301 #369)
-#367 := (= #298 #366)
-#351 := (iff #253 #350)
-#348 := (iff #250 #347)
-#349 := [rewrite]: #348
-#329 := (iff #243 #345)
-#330 := [rewrite]: #329
-#352 := [monotonicity #330 #349]: #351
-#368 := [monotonicity #352]: #367
-#371 := [monotonicity #368]: #370
-#374 := [monotonicity #371]: #373
-#377 := [monotonicity #374]: #376
-#380 := [quant-intro #377]: #379
-#327 := (~ #310 #310)
-#341 := (~ #307 #307)
-#342 := [refl]: #341
-#328 := [nnf-pos #342]: #327
-#55 := (- #30)
-#54 := (- #41)
-#64 := (mod #54 #55)
-#65 := (- #64)
-#48 := (< 0::Int #30)
-#50 := (< #41 0::Int)
-#51 := (and #50 #48)
-#47 := (< 0::Int #41)
-#49 := (and #47 #48)
-#52 := (or #49 #51)
-#66 := (ite #52 #63 #65)
-#67 := (ite #44 0::Int #66)
-#68 := (ite #45 #41 #67)
-#69 := (= #62 #68)
-#70 := (forall (vars (?v0 Int) (?v1 Int)) #69)
-#313 := (iff #70 #310)
-#201 := (and #48 #50)
-#204 := (or #49 #201)
-#283 := (ite #204 #63 #278)
-#192 := (= 0::Int #41)
-#286 := (ite #192 0::Int #283)
-#195 := (= 0::Int #30)
-#289 := (ite #195 #41 #286)
-#292 := (= #62 #289)
-#295 := (forall (vars (?v0 Int) (?v1 Int)) #292)
-#311 := (iff #295 #310)
-#308 := (iff #292 #307)
-#305 := (= #289 #304)
-#302 := (= #286 #301)
-#299 := (= #283 #298)
-#254 := (iff #204 #253)
-#251 := (iff #201 #250)
-#248 := (iff #50 #247)
-#249 := [rewrite]: #248
-#241 := (iff #48 #240)
-#242 := [rewrite]: #241
-#252 := [monotonicity #242 #249]: #251
-#244 := (iff #49 #243)
-#237 := (iff #47 #236)
-#238 := [rewrite]: #237
-#245 := [monotonicity #238 #242]: #244
-#255 := [monotonicity #245 #252]: #254
-#300 := [monotonicity #255]: #299
-#229 := (iff #192 #44)
-#230 := [rewrite]: #229
-#303 := [monotonicity #230 #300]: #302
-#231 := (iff #195 #45)
-#232 := [rewrite]: #231
-#306 := [monotonicity #232 #303]: #305
-#309 := [monotonicity #306]: #308
-#312 := [quant-intro #309]: #311
-#296 := (iff #70 #295)
-#293 := (iff #69 #292)
-#290 := (= #68 #289)
-#287 := (= #67 #286)
-#284 := (= #66 #283)
-#281 := (= #65 #278)
-#275 := (- #272)
-#279 := (= #275 #278)
-#280 := [rewrite]: #279
-#276 := (= #65 #275)
-#273 := (= #64 #272)
-#212 := (= #55 #211)
-#213 := [rewrite]: #212
-#209 := (= #54 #208)
-#210 := [rewrite]: #209
-#274 := [monotonicity #210 #213]: #273
-#277 := [monotonicity #274]: #276
-#282 := [trans #277 #280]: #281
-#205 := (iff #52 #204)
-#202 := (iff #51 #201)
-#203 := [rewrite]: #202
-#206 := [monotonicity #203]: #205
-#285 := [monotonicity #206 #282]: #284
-#193 := (iff #44 #192)
-#194 := [rewrite]: #193
-#288 := [monotonicity #194 #285]: #287
-#196 := (iff #45 #195)
-#197 := [rewrite]: #196
-#291 := [monotonicity #197 #288]: #290
-#294 := [monotonicity #291]: #293
-#297 := [quant-intro #294]: #296
-#314 := [trans #297 #312]: #313
-#271 := [asserted]: #70
-#315 := [mp #271 #314]: #310
-#343 := [mp~ #315 #328]: #310
-#381 := [mp #343 #380]: #378
-#412 := [mp #381 #411]: #409
-#916 := [mp #412 #915]: #911
-#692 := (not #911)
-#693 := (or #692 #687)
-#524 := (* -1::Int 1::Int)
-#780 := (mod #860 #524)
-#758 := (+ #19 #780)
-#759 := (= #758 0::Int)
-#788 := (mod #12 1::Int)
-#761 := (* -1::Int #788)
-#762 := (+ #19 #761)
-#763 := (= #762 0::Int)
-#581 := (<= 1::Int 0::Int)
-#582 := (or #581 #580)
-#476 := (not #582)
-#853 := (or #852 #581)
-#575 := (not #853)
-#576 := (or #575 #476)
-#764 := (ite #576 #763 #759)
-#760 := (ite #855 #765 #764)
-#766 := (= #12 #19)
-#851 := (= 1::Int 0::Int)
-#752 := (ite #851 #766 #760)
-#694 := (or #692 #752)
-#696 := (iff #694 #693)
-#698 := (iff #693 #693)
-#683 := [rewrite]: #698
-#690 := (iff #752 #687)
-#819 := (or #833 #684)
-#735 := (or #819 #855)
-#703 := (ite #735 #765 #742)
-#688 := (iff #703 #687)
-#681 := (iff #735 #726)
-#682 := [rewrite]: #681
-#689 := [monotonicity #682]: #688
-#725 := (iff #752 #703)
-#704 := (ite false #766 #703)
-#714 := (iff #704 #703)
-#715 := [rewrite]: #714
-#711 := (iff #752 #704)
-#700 := (iff #760 #703)
-#673 := (ite #819 #765 #742)
-#733 := (ite #855 #765 #673)
-#710 := (iff #733 #703)
-#669 := [rewrite]: #710
-#734 := (iff #760 #733)
-#728 := (iff #764 #673)
-#747 := (iff #759 #742)
-#745 := (= #758 #744)
-#740 := (= #780 #792)
-#824 := (= #524 -1::Int)
-#706 := [rewrite]: #824
-#741 := [monotonicity #706]: #740
-#746 := [monotonicity #741]: #745
-#727 := [monotonicity #746]: #747
-#743 := (iff #763 #765)
-#737 := (= #762 #19)
-#730 := (+ #19 0::Int)
-#625 := (= #730 #19)
-#736 := [rewrite]: #625
-#731 := (= #762 #730)
-#751 := (= #761 0::Int)
-#750 := (* -1::Int 0::Int)
-#755 := (= #750 0::Int)
-#756 := [rewrite]: #755
-#753 := (= #761 #750)
-#748 := (= #788 0::Int)
-#749 := [rewrite]: #748
-#754 := [monotonicity #749]: #753
-#757 := [trans #754 #756]: #751
-#732 := [monotonicity #757]: #731
-#738 := [trans #732 #736]: #737
-#739 := [monotonicity #738]: #743
-#823 := (iff #576 #819)
-#663 := (or #684 #833)
-#820 := (iff #663 #819)
-#822 := [rewrite]: #820
-#665 := (iff #576 #663)
-#827 := (iff #476 #833)
-#826 := (iff #582 #580)
-#828 := (or false #580)
-#831 := (iff #828 #580)
-#825 := [rewrite]: #831
-#829 := (iff #582 #828)
-#838 := (iff #581 false)
-#839 := [rewrite]: #838
-#830 := [monotonicity #839]: #829
-#832 := [trans #830 #825]: #826
-#834 := [monotonicity #832]: #827
-#685 := (iff #575 #684)
-#837 := (iff #853 #852)
-#840 := (or #852 false)
-#841 := (iff #840 #852)
-#842 := [rewrite]: #841
-#835 := (iff #853 #840)
-#836 := [monotonicity #839]: #835
-#843 := [trans #836 #842]: #837
-#686 := [monotonicity #843]: #685
-#666 := [monotonicity #686 #834]: #665
-#821 := [trans #666 #822]: #823
-#709 := [monotonicity #821 #739 #727]: #728
-#729 := [monotonicity #709]: #734
-#702 := [trans #729 #669]: #700
-#567 := (iff #851 false)
-#568 := [rewrite]: #567
-#713 := [monotonicity #568 #702]: #711
-#705 := [trans #713 #715]: #725
-#691 := [trans #705 #689]: #690
-#697 := [monotonicity #691]: #696
-#699 := [trans #697 #683]: #696
-#695 := [quant-inst #12 #14]: #694
-#660 := [mp #695 #699]: #693
-#473 := [unit-resolution #660 #916]: #687
-#650 := (not #687)
-#651 := (or #650 #675 #765)
-#652 := [def-axiom]: #651
-#472 := [unit-resolution #652 #473]: #474
-#475 := [unit-resolution #472 #471]: #765
-#656 := (not #765)
-#917 := (or #656 #678)
-#918 := [th-lemma arith triangle-eq]: #917
-#919 := [unit-resolution #918 #475]: #678
-#679 := (>= #19 0::Int)
-#920 := (or #656 #679)
-#921 := [th-lemma arith triangle-eq]: #920
-#922 := [unit-resolution #921 #475]: #679
-#924 := [th-lemma arith eq-propagate -1 -1 #922 #919]: #923
-#936 := (= #12 #15)
-#870 := (div #12 1::Int)
-#856 := (* -1::Int #870)
-#857 := (+ #15 #856)
-#789 := (<= #857 0::Int)
-#579 := (= #857 0::Int)
-#801 := (or #819 #852)
-#802 := [def-axiom]: #801
-#925 := [unit-resolution #802 #483]: #819
-#707 := (div #860 -1::Int)
-#815 := (* -1::Int #707)
-#813 := (+ #15 #815)
-#716 := (= #813 0::Int)
-#712 := (ite #819 #579 #716)
-#550 := (or #855 #712)
-#854 := (= #15 0::Int)
-#722 := (ite #855 #854 #712)
-#42 := (f7 f8 #41)
-#43 := (f6 #42 #30)
-#903 := (pattern #43)
-#214 := (div #208 #211)
-#386 := (* -1::Int #214)
-#387 := (+ #43 #386)
-#388 := (= #387 0::Int)
-#53 := (div #41 #30)
-#383 := (* -1::Int #53)
-#384 := (+ #43 #383)
-#385 := (= #384 0::Int)
-#389 := (ite #350 #385 #388)
-#382 := (= #43 0::Int)
-#46 := (or #44 #45)
-#390 := (ite #46 #382 #389)
-#904 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #903) #390)
-#393 := (forall (vars (?v0 Int) (?v1 Int)) #390)
-#907 := (iff #393 #904)
-#905 := (iff #390 #390)
-#906 := [refl]: #905
-#908 := [quant-intro #906]: #907
-#353 := (ite #350 #53 #214)
-#356 := (ite #46 0::Int #353)
-#359 := (= #43 #356)
-#362 := (forall (vars (?v0 Int) (?v1 Int)) #359)
-#394 := (iff #362 #393)
-#391 := (iff #359 #390)
-#392 := [rewrite]: #391
-#395 := [quant-intro #392]: #394
-#256 := (ite #253 #53 #214)
-#259 := (ite #46 0::Int #256)
-#262 := (= #43 #259)
-#265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
-#363 := (iff #265 #362)
-#360 := (iff #262 #359)
-#357 := (= #259 #356)
-#354 := (= #256 #353)
-#355 := [monotonicity #352]: #354
-#358 := [monotonicity #355]: #357
-#361 := [monotonicity #358]: #360
-#364 := [quant-intro #361]: #363
-#325 := (~ #265 #265)
-#338 := (~ #262 #262)
-#339 := [refl]: #338
-#326 := [nnf-pos #339]: #325
-#56 := (div #54 #55)
-#57 := (ite #52 #53 #56)
-#58 := (ite #46 0::Int #57)
-#59 := (= #43 #58)
-#60 := (forall (vars (?v0 Int) (?v1 Int)) #59)
-#268 := (iff #60 #265)
-#217 := (ite #204 #53 #214)
-#198 := (or #192 #195)
-#220 := (ite #198 0::Int #217)
-#223 := (= #43 #220)
-#226 := (forall (vars (?v0 Int) (?v1 Int)) #223)
-#266 := (iff #226 #265)
-#263 := (iff #223 #262)
-#260 := (= #220 #259)
-#257 := (= #217 #256)
-#258 := [monotonicity #255]: #257
-#233 := (iff #198 #46)
-#234 := [monotonicity #230 #232]: #233
-#261 := [monotonicity #234 #258]: #260
-#264 := [monotonicity #261]: #263
-#267 := [quant-intro #264]: #266
-#227 := (iff #60 #226)
-#224 := (iff #59 #223)
-#221 := (= #58 #220)
-#218 := (= #57 #217)
-#215 := (= #56 #214)
-#216 := [monotonicity #210 #213]: #215
-#219 := [monotonicity #206 #216]: #218
-#199 := (iff #46 #198)
-#200 := [monotonicity #194 #197]: #199
-#222 := [monotonicity #200 #219]: #221
-#225 := [monotonicity #222]: #224
-#228 := [quant-intro #225]: #227
-#269 := [trans #228 #267]: #268
-#191 := [asserted]: #60
-#270 := [mp #191 #269]: #265
-#340 := [mp~ #270 #326]: #265
-#365 := [mp #340 #364]: #362
-#396 := [mp #365 #395]: #393
-#909 := [mp #396 #908]: #904
-#817 := (not #904)
-#814 := (or #817 #722)
-#508 := (div #860 #524)
-#509 := (* -1::Int #508)
-#869 := (+ #15 #509)
-#867 := (= #869 0::Int)
-#850 := (ite #576 #579 #867)
-#565 := (or #855 #851)
-#566 := (ite #565 #854 #850)
-#818 := (or #817 #566)
-#807 := (iff #818 #814)
-#796 := (iff #814 #814)
-#798 := [rewrite]: #796
-#723 := (iff #566 #722)
-#720 := (iff #850 #712)
-#718 := (iff #867 #716)
-#816 := (= #869 #813)
-#717 := (= #509 #815)
-#708 := (= #508 #707)
-#667 := [monotonicity #706]: #708
-#812 := [monotonicity #667]: #717
-#701 := [monotonicity #812]: #816
-#719 := [monotonicity #701]: #718
-#721 := [monotonicity #821 #719]: #720
-#845 := (iff #565 #855)
-#846 := (or #855 false)
-#844 := (iff #846 #855)
-#848 := [rewrite]: #844
-#847 := (iff #565 #846)
-#562 := [monotonicity #568]: #847
-#849 := [trans #562 #848]: #845
-#724 := [monotonicity #849 #721]: #723
-#799 := [monotonicity #724]: #807
-#808 := [trans #799 #798]: #807
-#805 := [quant-inst #12 #14]: #818
-#809 := [mp #805 #808]: #814
-#544 := [unit-resolution #809 #909]: #722
-#770 := (not #722)
-#774 := (or #770 #855 #712)
-#775 := [def-axiom]: #774
-#551 := [unit-resolution #775 #544]: #550
-#926 := [unit-resolution #551 #482]: #712
-#803 := (not #819)
-#790 := (not #712)
-#795 := (or #790 #803 #579)
-#781 := [def-axiom]: #795
-#927 := [unit-resolution #781 #926 #925]: #579
-#785 := (not #579)
-#928 := (or #785 #789)
-#929 := [th-lemma arith triangle-eq]: #928
-#930 := [unit-resolution #929 #927]: #789
-#791 := (>= #857 0::Int)
-#506 := (or #785 #791)
-#507 := [th-lemma arith triangle-eq]: #506
-#931 := [unit-resolution #507 #927]: #791
-#614 := (+ #12 #856)
-#618 := (<= #614 0::Int)
-#613 := (= #614 0::Int)
-#1 := true
-#88 := [true-axiom]: true
-#571 := (or false #613)
-#563 := [th-lemma arith]: #571
-#572 := [unit-resolution #563 #88]: #613
-#496 := (not #613)
-#498 := (or #496 #618)
-#499 := [th-lemma arith triangle-eq]: #498
-#932 := [unit-resolution #499 #572]: #618
-#595 := (>= #614 0::Int)
-#933 := (or #496 #595)
-#934 := [th-lemma arith triangle-eq]: #933
-#935 := [unit-resolution #934 #572]: #595
-#937 := [th-lemma arith eq-propagate 1 1 -1 -1 #935 #932 #931 #930]: #936
-#941 := [trans #937 #924]: #940
-#943 := [monotonicity #941]: #942
-#944 := [trans #542 #943]: #99
-#102 := (not #99)
-#16 := (* #15 1::Int)
-#20 := (+ #16 #19)
-#21 := (f4 f5 #20)
-#22 := (= f3 #21)
-#23 := (not #22)
-#103 := (iff #23 #102)
-#100 := (iff #22 #99)
-#97 := (= #21 #96)
-#94 := (= #20 #93)
-#91 := (= #16 #15)
-#92 := [rewrite]: #91
-#95 := [monotonicity #92]: #94
-#98 := [monotonicity #95]: #97
-#101 := [monotonicity #98]: #100
-#104 := [monotonicity #101]: #103
-#90 := [asserted]: #23
-#107 := [mp #90 #104]: #102
-#945 := [unit-resolution #107 #944]: false
-#946 := [lemma #945]: #855
-#982 := [symm #946]: #981
-#522 := (= #560 0::Int)
-#868 := (>= #560 0::Int)
-#672 := (or #726 #771)
-#674 := [def-axiom]: #672
-#479 := [unit-resolution #674 #946]: #726
-#484 := [unit-resolution #472 #479]: #765
-#947 := [unit-resolution #921 #484]: #679
-#806 := (>= #15 0::Int)
-#505 := (not #618)
-#573 := (not #806)
-#564 := [hypothesis]: #573
-#776 := (not #854)
-#574 := (or #776 #806)
-#541 := [th-lemma arith triangle-eq]: #574
-#543 := [unit-resolution #541 #564]: #776
-#535 := (or #771 #854)
-#772 := (or #770 #771 #854)
-#773 := [def-axiom]: #772
-#548 := [unit-resolution #773 #544]: #535
-#549 := [unit-resolution #548 #543]: #771
-#552 := [unit-resolution #551 #549]: #712
-#527 := (not #641)
-#528 := (iff #771 #527)
-#525 := (iff #855 #641)
-#553 := (= #470 f3)
-#536 := [symm #542]: #553
-#539 := [monotonicity #536]: #538
-#520 := [monotonicity #539]: #518
-#526 := [symm #520]: #525
-#529 := [monotonicity #526]: #528
-#530 := [mp #549 #529]: #527
-#531 := [unit-resolution #519 #530]: #580
-#515 := [unit-resolution #514 #549]: #663
-#513 := [unit-resolution #515 #531]: #684
-#516 := [unit-resolution #802 #513]: #819
-#504 := [unit-resolution #781 #516 #552]: #579
-#510 := [unit-resolution #507 #504]: #791
-#511 := (not #791)
-#486 := (or #505 #833 #806 #511)
-#490 := [th-lemma arith assign-bounds 1 1 -1]: #486
-#491 := [unit-resolution #490 #531 #510 #564]: #505
-#501 := [unit-resolution #499 #491 #572]: false
-#497 := [lemma #501]: #806
-#540 := (* -1::Int #560)
-#875 := (+ #19 #540)
-#877 := (+ #15 #875)
-#858 := (<= #877 0::Int)
-#534 := (= #877 0::Int)
-#555 := (>= #93 0::Int)
-#948 := (not #679)
-#949 := (or #555 #573 #948)
-#950 := [th-lemma arith assign-bounds -1 -1]: #949
-#951 := [unit-resolution #950 #947 #497]: #555
-#556 := (not #555)
-#545 := (or #534 #556)
-#114 := (= #30 #33)
-#139 := (or #114 #133)
-#891 := (forall (vars (?v0 Int)) (:pat #890) #139)
-#144 := (forall (vars (?v0 Int)) #139)
-#894 := (iff #144 #891)
-#892 := (iff #139 #139)
-#893 := [refl]: #892
-#895 := [quant-intro #893]: #894
-#321 := (~ #144 #144)
-#320 := (~ #139 #139)
-#317 := [refl]: #320
-#322 := [nnf-pos #317]: #321
-#34 := (= #33 #30)
-#31 := (<= 0::Int #30)
-#35 := (implies #31 #34)
-#36 := (forall (vars (?v0 Int)) #35)
-#147 := (iff #36 #144)
-#121 := (not #31)
-#122 := (or #121 #114)
-#127 := (forall (vars (?v0 Int)) #122)
-#145 := (iff #127 #144)
-#142 := (iff #122 #139)
-#136 := (or #133 #114)
-#140 := (iff #136 #139)
-#141 := [rewrite]: #140
-#137 := (iff #122 #136)
-#134 := (iff #121 #133)
-#130 := (iff #31 #132)
-#131 := [rewrite]: #130
-#135 := [monotonicity #131]: #134
-#138 := [monotonicity #135]: #137
-#143 := [trans #138 #141]: #142
-#146 := [quant-intro #143]: #145
-#128 := (iff #36 #127)
-#125 := (iff #35 #122)
-#118 := (implies #31 #114)
-#123 := (iff #118 #122)
-#124 := [rewrite]: #123
-#119 := (iff #35 #118)
-#116 := (iff #34 #114)
-#117 := [rewrite]: #116
-#120 := [monotonicity #117]: #119
-#126 := [trans #120 #124]: #125
-#129 := [quant-intro #126]: #128
-#148 := [trans #129 #146]: #147
-#113 := [asserted]: #36
-#149 := [mp #113 #148]: #144
-#318 := [mp~ #149 #322]: #144
-#896 := [mp #318 #895]: #891
-#879 := (not #891)
-#880 := (or #879 #534 #556)
-#557 := (= #93 #560)
-#561 := (or #557 #556)
-#881 := (or #879 #561)
-#533 := (iff #881 #880)
-#882 := (or #879 #545)
-#537 := (iff #882 #880)
-#873 := [rewrite]: #537
-#872 := (iff #881 #882)
-#546 := (iff #561 #545)
-#664 := (iff #557 #534)
-#871 := [rewrite]: #664
-#878 := [monotonicity #871]: #546
-#532 := [monotonicity #878]: #872
-#874 := [trans #532 #873]: #533
-#876 := [quant-inst #93]: #881
-#517 := [mp #876 #874]: #880
-#952 := [unit-resolution #517 #896]: #545
-#953 := [unit-resolution #952 #951]: #534
-#954 := (not #534)
-#955 := (or #954 #858)
-#956 := [th-lemma arith triangle-eq]: #955
-#957 := [unit-resolution #956 #953]: #858
-#958 := (not #858)
-#959 := (or #868 #948 #958 #573)
-#960 := [th-lemma arith assign-bounds -1 1 -1]: #959
-#961 := [unit-resolution #960 #957 #497 #947]: #868
-#866 := (<= #560 0::Int)
-#962 := [unit-resolution #918 #484]: #678
-#810 := (<= #15 0::Int)
-#963 := [unit-resolution #548 #946]: #854
-#964 := (or #776 #810)
-#965 := [th-lemma arith triangle-eq]: #964
-#966 := [unit-resolution #965 #963]: #810
-#521 := (>= #877 0::Int)
-#967 := (or #954 #521)
-#968 := [th-lemma arith triangle-eq]: #967
-#969 := [unit-resolution #968 #953]: #521
-#972 := (not #810)
-#971 := (not #521)
-#970 := (not #678)
-#973 := (or #866 #970 #971 #972)
-#974 := [th-lemma arith assign-bounds -1 1 -1]: #973
-#975 := [unit-resolution #974 #969 #966 #962]: #866
-#977 := (not #868)
-#976 := (not #866)
-#978 := (or #522 #976 #977)
-#979 := [th-lemma arith triangle-eq]: #978
-#980 := [unit-resolution #979 #975 #961]: #522
-#984 := [trans #980 #982]: #983
-#987 := [monotonicity #984]: #986
-#989 := [symm #987]: #988
-#993 := [trans #542 #989]: #992
-#994 := [trans #993 #991]: #99
-[unit-resolution #107 #994]: false
-unsat
-7bbfb44660d3b5877236ebec13ff8c94702addce 884 0
-#2 := false
+#10 := f10
+#11 := (f9 f10 f3)
+#762 := (>= #11 0::Int)
+#738 := (not #762)
+#415 := (<= #11 0::Int)
+#749 := (not #415)
+#740 := (or #749 #738)
+#716 := (not #740)
+#429 := (= #11 0::Int)
+#692 := (not #429)
 decl f4 :: (-> S3 Int S2)
 decl f6 :: (-> S4 Int Int)
-#14 := 3::Int
+#13 := 1::Int
 decl f7 :: (-> S5 Int S4)
+decl f11 :: S5
+#16 := f11
+#17 := (f7 f11 #11)
+#18 := (f6 #17 1::Int)
+decl f8 :: S5
+#9 := f8
+#12 := (f7 f8 #11)
+#14 := (f6 #12 1::Int)
+#82 := (+ #14 #18)
+decl f5 :: S3
+#8 := f5
+#85 := (f4 f5 #82)
+#88 := (= f3 #85)
+#466 := (f9 f10 #85)
+#445 := (f4 f5 #466)
+#424 := (= #445 #85)
+#23 := (:var 0 S2)
+#24 := (f9 f10 #23)
+#789 := (pattern #24)
+#25 := (f4 f5 #24)
+#26 := (= #25 #23)
+#790 := (forall (vars (?v0 S2)) (:pat #789) #26)
+#27 := (forall (vars (?v0 S2)) #26)
+#793 := (iff #27 #790)
+#791 := (iff #26 #26)
+#792 := [refl]: #791
+#794 := [quant-intro #792]: #793
+#219 := (~ #27 #27)
+#282 := (~ #26 #26)
+#283 := [refl]: #282
+#220 := [nnf-pos #283]: #219
+#72 := [asserted]: #27
+#284 := [mp~ #72 #220]: #27
+#795 := [mp #284 #794]: #790
+#453 := (not #790)
+#555 := (or #453 #424)
+#562 := [quant-inst #85]: #555
+#535 := [unit-resolution #562 #795]: #424
+#541 := (= f3 #445)
+#376 := (f4 f5 #11)
+#379 := (= #376 #445)
+#390 := (= #445 #376)
+#536 := (= #466 #11)
+#551 := (= 0::Int #11)
+#539 := [hypothesis]: #429
+#553 := [symm #539]: #551
+#427 := (= #466 0::Int)
+#772 := (>= #466 0::Int)
+#611 := (>= #18 0::Int)
+#682 := (= #18 0::Int)
+#538 := (or #692 #682)
+#151 := -1::Int
+#759 := (* -1::Int #11)
+#709 := (mod #759 -1::Int)
+#643 := (+ #18 #709)
+#645 := (= #643 0::Int)
+#650 := (if #740 #682 #645)
+#648 := (if #429 #682 #650)
+#29 := (:var 0 Int)
+#40 := (:var 1 Int)
+#60 := (f7 f11 #40)
+#61 := (f6 #60 #29)
+#816 := (pattern #61)
+#155 := (* -1::Int #29)
+#152 := (* -1::Int #40)
+#174 := (mod #152 #155)
+#365 := (+ #61 #174)
+#366 := (= #365 0::Int)
+#62 := (mod #40 #29)
+#362 := (* -1::Int #62)
+#363 := (+ #61 #362)
+#364 := (= #363 0::Int)
+#129 := (<= #29 0::Int)
+#241 := (>= #40 0::Int)
+#309 := (or #241 #129)
+#310 := (not #309)
+#125 := (<= #40 0::Int)
+#305 := (or #125 #129)
+#306 := (not #305)
+#313 := (or #306 #310)
+#367 := (if #313 #364 #366)
+#361 := (= #61 0::Int)
+#43 := (= #40 0::Int)
+#368 := (if #43 #361 #367)
+#360 := (= #61 #40)
+#44 := (= #29 0::Int)
+#369 := (if #44 #360 #368)
+#817 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #816) #369)
+#372 := (forall (vars (?v0 Int) (?v1 Int)) #369)
+#820 := (iff #372 #817)
+#818 := (iff #369 #369)
+#819 := [refl]: #818
+#821 := [quant-intro #819]: #820
+#180 := (* -1::Int #174)
+#329 := (if #313 #62 #180)
+#332 := (if #43 0::Int #329)
+#335 := (if #44 #40 #332)
+#338 := (= #61 #335)
+#341 := (forall (vars (?v0 Int) (?v1 Int)) #338)
+#373 := (iff #341 #372)
+#370 := (iff #338 #369)
+#371 := [rewrite]: #370
+#374 := [quant-intro #371]: #373
+#130 := (not #129)
+#244 := (not #241)
+#247 := (and #244 #130)
+#126 := (not #125)
+#133 := (and #126 #130)
+#250 := (or #133 #247)
+#266 := (if #250 #62 #180)
+#269 := (if #43 0::Int #266)
+#272 := (if #44 #40 #269)
+#275 := (= #61 #272)
+#278 := (forall (vars (?v0 Int) (?v1 Int)) #275)
+#342 := (iff #278 #341)
+#339 := (iff #275 #338)
+#336 := (= #272 #335)
+#333 := (= #269 #332)
+#330 := (= #266 #329)
+#314 := (iff #250 #313)
+#311 := (iff #247 #310)
+#312 := [rewrite]: #311
+#307 := (iff #133 #306)
+#308 := [rewrite]: #307
+#315 := [monotonicity #308 #312]: #314
+#331 := [monotonicity #315]: #330
+#334 := [monotonicity #331]: #333
+#337 := [monotonicity #334]: #336
+#340 := [monotonicity #337]: #339
+#343 := [quant-intro #340]: #342
+#302 := (~ #278 #278)
+#300 := (~ #275 #275)
+#301 := [refl]: #300
+#303 := [nnf-pos #301]: #302
+#136 := (<= 0::Int #40)
+#137 := (not #136)
+#145 := (and #137 #130)
+#148 := (or #133 #145)
+#185 := (if #148 #62 #180)
+#188 := (if #43 0::Int #185)
+#191 := (if #44 #40 #188)
+#194 := (= #61 #191)
+#197 := (forall (vars (?v0 Int) (?v1 Int)) #194)
+#279 := (iff #197 #278)
+#276 := (iff #194 #275)
+#273 := (= #191 #272)
+#270 := (= #188 #269)
+#267 := (= #185 #266)
+#251 := (iff #148 #250)
+#248 := (iff #145 #247)
+#245 := (iff #137 #244)
+#242 := (iff #136 #241)
+#243 := [rewrite]: #242
+#246 := [monotonicity #243]: #245
+#249 := [monotonicity #246]: #248
+#252 := [monotonicity #249]: #251
+#268 := [monotonicity #252]: #267
+#271 := [monotonicity #268]: #270
+#274 := [monotonicity #271]: #273
+#277 := [monotonicity #274]: #276
+#280 := [quant-intro #277]: #279
+#54 := (- #29)
+#53 := (- #40)
+#63 := (mod #53 #54)
+#64 := (- #63)
+#47 := (< 0::Int #29)
+#49 := (< #40 0::Int)
+#50 := (and #49 #47)
+#46 := (< 0::Int #40)
+#48 := (and #46 #47)
+#51 := (or #48 #50)
+#65 := (if #51 #62 #64)
+#66 := (if #43 0::Int #65)
+#67 := (if #44 #40 #66)
+#68 := (= #61 #67)
+#69 := (forall (vars (?v0 Int) (?v1 Int)) #68)
+#198 := (iff #69 #197)
+#195 := (iff #68 #194)
+#192 := (= #67 #191)
+#189 := (= #66 #188)
+#186 := (= #65 #185)
+#183 := (= #64 #180)
+#177 := (- #174)
+#181 := (= #177 #180)
+#182 := [rewrite]: #181
+#178 := (= #64 #177)
+#175 := (= #63 #174)
+#156 := (= #54 #155)
+#157 := [rewrite]: #156
+#153 := (= #53 #152)
+#154 := [rewrite]: #153
+#176 := [monotonicity #154 #157]: #175
+#179 := [monotonicity #176]: #178
+#184 := [trans #179 #182]: #183
+#149 := (iff #51 #148)
+#146 := (iff #50 #145)
+#131 := (iff #47 #130)
+#132 := [rewrite]: #131
+#138 := (iff #49 #137)
+#142 := (iff #137 #137)
+#140 := (iff #136 #136)
+#141 := [rewrite]: #140
+#143 := [monotonicity #141]: #142
+#139 := [rewrite]: #138
+#144 := [trans #139 #143]: #138
+#147 := [monotonicity #144 #132]: #146
+#134 := (iff #48 #133)
+#127 := (iff #46 #126)
+#128 := [rewrite]: #127
+#135 := [monotonicity #128 #132]: #134
+#150 := [monotonicity #135 #147]: #149
+#187 := [monotonicity #150 #184]: #186
+#190 := [monotonicity #187]: #189
+#193 := [monotonicity #190]: #192
+#196 := [monotonicity #193]: #195
+#199 := [quant-intro #196]: #198
+#76 := [asserted]: #69
+#200 := [mp #76 #199]: #197
+#281 := [mp #200 #280]: #278
+#304 := [mp~ #281 #303]: #278
+#344 := [mp #304 #343]: #341
+#375 := [mp #344 #374]: #372
+#822 := [mp #375 #821]: #817
+#609 := (not #817)
+#616 := (or #609 #648)
+#481 := (* -1::Int 1::Int)
+#675 := (mod #759 #481)
+#686 := (+ #18 #675)
+#664 := (= #686 0::Int)
+#706 := (mod #11 1::Int)
+#683 := (* -1::Int #706)
+#684 := (+ #18 #683)
+#685 := (= #684 0::Int)
+#775 := (<= 1::Int 0::Int)
+#763 := (or #762 #775)
+#485 := (not #763)
+#773 := (or #415 #775)
+#776 := (not #773)
+#486 := (or #776 #485)
+#665 := (if #486 #685 #664)
+#667 := (if #429 #682 #665)
+#681 := (= #18 #11)
+#430 := (= 1::Int 0::Int)
+#668 := (if #430 #681 #667)
+#575 := (or #609 #668)
+#608 := (iff #575 #616)
+#617 := (iff #616 #616)
+#619 := [rewrite]: #617
+#635 := (iff #668 #648)
+#579 := (if false #681 #648)
+#639 := (iff #579 #648)
+#640 := [rewrite]: #639
+#634 := (iff #668 #579)
+#653 := (iff #667 #648)
+#651 := (iff #665 #650)
+#646 := (iff #664 #645)
+#644 := (= #686 #643)
+#531 := (= #675 #709)
+#572 := (= #481 -1::Int)
+#725 := [rewrite]: #572
+#642 := [monotonicity #725]: #531
+#649 := [monotonicity #642]: #644
+#647 := [monotonicity #649]: #646
+#637 := (iff #685 #682)
+#663 := (= #684 #18)
+#659 := (+ #18 0::Int)
+#662 := (= #659 #18)
+#657 := [rewrite]: #662
+#660 := (= #684 #659)
+#655 := (= #683 0::Int)
+#671 := (* -1::Int 0::Int)
+#658 := (= #671 0::Int)
+#654 := [rewrite]: #658
+#666 := (= #683 #671)
+#669 := (= #706 0::Int)
+#670 := [rewrite]: #669
+#672 := [monotonicity #670]: #666
+#656 := [trans #672 #654]: #655
+#661 := [monotonicity #656]: #660
+#636 := [trans #661 #657]: #663
+#638 := [monotonicity #636]: #637
+#569 := (iff #486 #740)
+#739 := (iff #485 #738)
+#731 := (iff #763 #762)
+#592 := (or #762 false)
+#736 := (iff #592 #762)
+#737 := [rewrite]: #736
+#734 := (iff #763 #592)
+#755 := (iff #775 false)
+#744 := [rewrite]: #755
+#735 := [monotonicity #744]: #734
+#732 := [trans #735 #737]: #731
+#733 := [monotonicity #732]: #739
+#590 := (iff #776 #749)
+#748 := (iff #773 #415)
+#745 := (or #415 false)
+#742 := (iff #745 #415)
+#747 := [rewrite]: #742
+#746 := (iff #773 #745)
+#741 := [monotonicity #744]: #746
+#743 := [trans #741 #747]: #748
+#591 := [monotonicity #743]: #590
+#571 := [monotonicity #591 #733]: #569
+#652 := [monotonicity #571 #638 #647]: #651
+#633 := [monotonicity #652]: #653
+#472 := (iff #430 false)
+#473 := [rewrite]: #472
+#615 := [monotonicity #473 #633]: #634
+#641 := [trans #615 #640]: #635
+#610 := [monotonicity #641]: #608
+#620 := [trans #610 #619]: #608
+#606 := [quant-inst #11 #13]: #575
+#621 := [mp #606 #620]: #616
+#434 := [unit-resolution #621 #822]: #648
+#603 := (not #648)
+#604 := (or #603 #692 #682)
+#589 := [def-axiom]: #604
+#543 := [unit-resolution #589 #434]: #538
+#546 := [unit-resolution #543 #539]: #682
+#597 := (not #682)
+#419 := (or #597 #611)
+#422 := [th-lemma arith triangle-eq]: #419
+#525 := [unit-resolution #422 #546]: #611
+#705 := (>= #14 0::Int)
+#487 := (div #11 1::Int)
+#488 := (* -1::Int #487)
+#549 := (+ #11 #488)
+#548 := (= #549 0::Int)
+#1 := true
+#218 := [true-axiom]: true
+#512 := (or false #548)
+#524 := [th-lemma arith]: #512
+#501 := [unit-resolution #524 #218]: #548
+#532 := (<= #549 0::Int)
+#441 := (not #532)
+#503 := (not #705)
+#504 := [hypothesis]: #503
+#382 := (+ #14 #488)
+#708 := (>= #382 0::Int)
+#758 := (= #382 0::Int)
+#726 := (div #759 -1::Int)
+#727 := (* -1::Int #726)
+#613 := (+ #14 #727)
+#721 := (= #613 0::Int)
+#719 := (if #740 #758 #721)
+#414 := (= #14 0::Int)
+#676 := (not #414)
+#505 := (or #676 #705)
+#506 := [th-lemma arith triangle-eq]: #505
+#507 := [unit-resolution #506 #504]: #676
+#509 := (or #692 #414)
+#622 := (if #429 #414 #719)
+#41 := (f7 f8 #40)
+#42 := (f6 #41 #29)
+#809 := (pattern #42)
+#158 := (div #152 #155)
+#349 := (* -1::Int #158)
+#350 := (+ #42 #349)
+#351 := (= #350 0::Int)
+#52 := (div #40 #29)
+#346 := (* -1::Int #52)
+#347 := (+ #42 #346)
+#348 := (= #347 0::Int)
+#352 := (if #313 #348 #351)
+#345 := (= #42 0::Int)
+#45 := (or #43 #44)
+#353 := (if #45 #345 #352)
+#810 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #809) #353)
+#356 := (forall (vars (?v0 Int) (?v1 Int)) #353)
+#813 := (iff #356 #810)
+#811 := (iff #353 #353)
+#812 := [refl]: #811
+#814 := [quant-intro #812]: #813
+#316 := (if #313 #52 #158)
+#319 := (if #45 0::Int #316)
+#322 := (= #42 #319)
+#325 := (forall (vars (?v0 Int) (?v1 Int)) #322)
+#357 := (iff #325 #356)
+#354 := (iff #322 #353)
+#355 := [rewrite]: #354
+#358 := [quant-intro #355]: #357
+#253 := (if #250 #52 #158)
+#256 := (if #45 0::Int #253)
+#259 := (= #42 #256)
+#262 := (forall (vars (?v0 Int) (?v1 Int)) #259)
+#326 := (iff #262 #325)
+#323 := (iff #259 #322)
+#320 := (= #256 #319)
+#317 := (= #253 #316)
+#318 := [monotonicity #315]: #317
+#321 := [monotonicity #318]: #320
+#324 := [monotonicity #321]: #323
+#327 := [quant-intro #324]: #326
+#297 := (~ #262 #262)
+#295 := (~ #259 #259)
+#296 := [refl]: #295
+#298 := [nnf-pos #296]: #297
+#161 := (if #148 #52 #158)
+#164 := (if #45 0::Int #161)
+#167 := (= #42 #164)
+#170 := (forall (vars (?v0 Int) (?v1 Int)) #167)
+#263 := (iff #170 #262)
+#260 := (iff #167 #259)
+#257 := (= #164 #256)
+#254 := (= #161 #253)
+#255 := [monotonicity #252]: #254
+#258 := [monotonicity #255]: #257
+#261 := [monotonicity #258]: #260
+#264 := [quant-intro #261]: #263
+#55 := (div #53 #54)
+#56 := (if #51 #52 #55)
+#57 := (if #45 0::Int #56)
+#58 := (= #42 #57)
+#59 := (forall (vars (?v0 Int) (?v1 Int)) #58)
+#171 := (iff #59 #170)
+#168 := (iff #58 #167)
+#165 := (= #57 #164)
+#162 := (= #56 #161)
+#159 := (= #55 #158)
+#160 := [monotonicity #154 #157]: #159
+#163 := [monotonicity #150 #160]: #162
+#166 := [monotonicity #163]: #165
+#169 := [monotonicity #166]: #168
+#172 := [quant-intro #169]: #171
+#75 := [asserted]: #59
+#173 := [mp #75 #172]: #170
+#265 := [mp #173 #264]: #262
+#299 := [mp~ #265 #298]: #262
+#328 := [mp #299 #327]: #325
+#359 := [mp #328 #358]: #356
+#815 := [mp #359 #814]: #810
+#618 := (not #810)
+#626 := (or #618 #622)
+#482 := (div #759 #481)
+#756 := (* -1::Int #482)
+#760 := (+ #14 #756)
+#757 := (= #760 0::Int)
+#761 := (if #486 #758 #757)
+#774 := (or #429 #430)
+#471 := (if #774 #414 #761)
+#627 := (or #618 #471)
+#629 := (iff #627 #626)
+#723 := (iff #626 #626)
+#720 := [rewrite]: #723
+#624 := (iff #471 #622)
+#722 := (iff #761 #719)
+#623 := (iff #757 #721)
+#614 := (= #760 #613)
+#730 := (= #756 #727)
+#728 := (= #482 #726)
+#729 := [monotonicity #725]: #728
+#612 := [monotonicity #729]: #730
+#573 := [monotonicity #612]: #614
+#718 := [monotonicity #573]: #623
+#607 := [monotonicity #571 #718]: #722
+#754 := (iff #774 #429)
+#474 := (or #429 false)
+#468 := (iff #474 #429)
+#750 := [rewrite]: #468
+#752 := (iff #774 #474)
+#753 := [monotonicity #473]: #752
+#751 := [trans #753 #750]: #754
+#625 := [monotonicity #751 #607]: #624
+#630 := [monotonicity #625]: #629
+#724 := [trans #630 #720]: #629
+#628 := [quant-inst #11 #13]: #627
+#711 := [mp #628 #724]: #626
+#508 := [unit-resolution #711 #815]: #622
+#691 := (not #622)
+#689 := (or #691 #692 #414)
+#693 := [def-axiom]: #689
+#502 := [unit-resolution #693 #508]: #509
+#510 := [unit-resolution #502 #507]: #692
+#495 := (or #429 #719)
+#673 := (or #691 #429 #719)
+#674 := [def-axiom]: #673
+#496 := [unit-resolution #674 #508]: #495
+#497 := [unit-resolution #496 #510]: #719
+#578 := (f9 f10 #376)
+#580 := (= #578 0::Int)
+#492 := (not #580)
+#493 := (iff #692 #492)
+#491 := (iff #429 #580)
+#489 := (iff #580 #429)
+#498 := (= #578 #11)
+#460 := (= #376 f3)
+#464 := (or #453 #460)
+#465 := [quant-inst #7]: #464
+#499 := [unit-resolution #465 #795]: #460
+#500 := [monotonicity #499]: #498
+#490 := [monotonicity #500]: #489
+#483 := [symm #490]: #491
+#484 := [monotonicity #483]: #493
+#494 := [mp #510 #484]: #492
+#581 := (or #762 #580)
+#31 := (f4 f5 #29)
+#796 := (pattern #31)
+#32 := (f9 f10 #31)
+#37 := (= #32 0::Int)
+#221 := (>= #29 0::Int)
+#234 := (or #221 #37)
+#803 := (forall (vars (?v0 Int)) (:pat #796) #234)
+#237 := (forall (vars (?v0 Int)) #234)
+#806 := (iff #237 #803)
+#804 := (iff #234 #234)
+#805 := [refl]: #804
+#807 := [quant-intro #805]: #806
+#288 := (~ #237 #237)
+#286 := (~ #234 #234)
+#287 := [refl]: #286
+#289 := [nnf-pos #287]: #288
+#30 := (<= 0::Int #29)
+#116 := (or #30 #37)
+#121 := (forall (vars (?v0 Int)) #116)
+#238 := (iff #121 #237)
+#235 := (iff #116 #234)
+#222 := (iff #30 #221)
+#223 := [rewrite]: #222
+#236 := [monotonicity #223]: #235
+#239 := [quant-intro #236]: #238
+#36 := (< #29 0::Int)
+#38 := (implies #36 #37)
+#39 := (forall (vars (?v0 Int)) #38)
+#122 := (iff #39 #121)
+#119 := (iff #38 #116)
+#99 := (not #30)
+#113 := (implies #99 #37)
+#117 := (iff #113 #116)
+#118 := [rewrite]: #117
+#114 := (iff #38 #113)
+#108 := (iff #36 #99)
+#110 := (iff #99 #99)
+#95 := (iff #30 #30)
+#96 := [rewrite]: #95
+#111 := [monotonicity #96]: #110
+#109 := [rewrite]: #108
+#112 := [trans #109 #111]: #108
+#115 := [monotonicity #112]: #114
+#120 := [trans #115 #118]: #119
+#123 := [quant-intro #120]: #122
+#74 := [asserted]: #39
+#124 := [mp #74 #123]: #121
+#240 := [mp #124 #239]: #237
+#294 := [mp~ #240 #289]: #237
+#808 := [mp #294 #807]: #803
+#766 := (not #803)
+#584 := (or #766 #762 #580)
+#585 := (or #766 #581)
+#586 := (iff #585 #584)
+#556 := [rewrite]: #586
+#568 := [quant-inst #11]: #585
+#557 := [mp #568 #556]: #584
+#475 := [unit-resolution #557 #808]: #581
+#476 := [unit-resolution #475 #494]: #762
+#477 := (or #429 #749 #738)
+#469 := [th-lemma arith triangle-eq]: #477
+#478 := [unit-resolution #469 #510]: #740
+#479 := [unit-resolution #478 #476]: #749
+#702 := (or #740 #415)
+#704 := [def-axiom]: #702
+#470 := [unit-resolution #704 #479]: #740
+#694 := (not #719)
+#695 := (or #694 #716 #758)
+#697 := [def-axiom]: #695
+#480 := [unit-resolution #697 #470 #497]: #758
+#700 := (not #758)
+#447 := (or #700 #708)
+#449 := [th-lemma arith triangle-eq]: #447
+#450 := [unit-resolution #449 #480]: #708
+#454 := (not #708)
+#455 := (or #441 #738 #705 #454)
+#456 := [th-lemma arith assign-bounds 1 1 -1]: #455
+#457 := [unit-resolution #456 #476 #450 #504]: #441
+#458 := (not #548)
+#448 := (or #458 #532)
+#459 := [th-lemma arith triangle-eq]: #448
+#442 := [unit-resolution #459 #457 #501]: false
+#444 := [lemma #442]: #705
+#440 := (* -1::Int #466)
+#570 := (+ #14 #18 #440)
+#423 := (<= #570 0::Int)
+#783 := (= #570 0::Int)
+#461 := (>= #82 0::Int)
+#545 := (not #611)
+#550 := (or #461 #503 #545)
+#540 := [th-lemma arith assign-bounds 1 -1]: #550
+#530 := [unit-resolution #540 #525 #444]: #461
+#462 := (not #461)
+#777 := (or #462 #783)
+#33 := (= #32 #29)
+#224 := (not #221)
+#227 := (or #224 #33)
+#797 := (forall (vars (?v0 Int)) (:pat #796) #227)
+#230 := (forall (vars (?v0 Int)) #227)
+#800 := (iff #230 #797)
+#798 := (iff #227 #227)
+#799 := [refl]: #798
+#801 := [quant-intro #799]: #800
+#291 := (~ #230 #230)
+#285 := (~ #227 #227)
+#290 := [refl]: #285
+#292 := [nnf-pos #290]: #291
+#100 := (or #99 #33)
+#104 := (forall (vars (?v0 Int)) #100)
+#231 := (iff #104 #230)
+#228 := (iff #100 #227)
+#225 := (iff #99 #224)
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [quant-intro #229]: #231
+#34 := (implies #30 #33)
+#35 := (forall (vars (?v0 Int)) #34)
+#105 := (iff #35 #104)
+#101 := (iff #34 #100)
+#102 := [rewrite]: #101
+#97 := (iff #34 #34)
+#98 := [monotonicity #96]: #97
+#103 := [trans #98 #102]: #101
+#106 := [quant-intro #103]: #105
+#73 := [asserted]: #35
+#107 := [mp #73 #106]: #104
+#233 := [mp #107 #232]: #230
+#293 := [mp~ #233 #292]: #230
+#802 := [mp #293 #801]: #797
+#784 := (not #797)
+#785 := (or #784 #462 #783)
+#463 := (= #466 #82)
+#467 := (or #462 #463)
+#786 := (or #784 #467)
+#779 := (iff #786 #785)
+#782 := (or #784 #777)
+#438 := (iff #782 #785)
+#443 := [rewrite]: #438
+#788 := (iff #786 #782)
+#451 := (iff #467 #777)
+#781 := (iff #463 #783)
+#446 := [rewrite]: #781
+#452 := [monotonicity #446]: #451
+#778 := [monotonicity #452]: #788
+#439 := [trans #778 #443]: #779
+#787 := [quant-inst #82]: #786
+#780 := [mp #787 #439]: #785
+#522 := [unit-resolution #780 #802]: #777
+#523 := [unit-resolution #522 #530]: #783
+#564 := (not #783)
+#511 := (or #564 #423)
+#560 := [th-lemma arith triangle-eq]: #511
+#565 := [unit-resolution #560 #523]: #423
+#544 := (not #423)
+#432 := (or #772 #503 #545 #544)
+#547 := [th-lemma arith assign-bounds 1 -1 1]: #432
+#433 := [unit-resolution #547 #565 #444 #525]: #772
+#409 := (<= #466 0::Int)
+#631 := (<= #18 0::Int)
+#418 := (or #597 #631)
+#420 := [th-lemma arith triangle-eq]: #418
+#391 := [unit-resolution #420 #546]: #631
+#713 := (<= #14 0::Int)
+#394 := [unit-resolution #502 #539]: #414
+#388 := (or #676 #713)
+#542 := [th-lemma arith triangle-eq]: #388
+#527 := [unit-resolution #542 #394]: #713
+#764 := (>= #570 0::Int)
+#521 := (or #564 #764)
+#515 := [th-lemma arith triangle-eq]: #521
+#528 := [unit-resolution #515 #523]: #764
+#529 := (not #764)
+#526 := (not #631)
+#554 := (not #713)
+#513 := (or #409 #554 #526 #529)
+#514 := [th-lemma arith assign-bounds -1 -1 1]: #513
+#516 := [unit-resolution #514 #528 #527 #391]: #409
+#518 := (not #772)
+#517 := (not #409)
+#519 := (or #427 #517 #518)
+#520 := [th-lemma arith triangle-eq]: #519
+#552 := [unit-resolution #520 #516 #433]: #427
+#534 := [trans #552 #553]: #536
+#377 := [monotonicity #534]: #390
+#537 := [symm #377]: #379
+#399 := (= f3 #376)
+#400 := [symm #499]: #399
+#824 := [trans #400 #537]: #541
+#825 := [trans #824 #535]: #88
+#91 := (not #88)
+#15 := (* #14 1::Int)
+#19 := (+ #15 #18)
+#20 := (f4 f5 #19)
+#21 := (= f3 #20)
+#22 := (not #21)
+#92 := (iff #22 #91)
+#89 := (iff #21 #88)
+#86 := (= #20 #85)
+#83 := (= #19 #82)
+#80 := (= #15 #14)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#87 := [monotonicity #84]: #86
+#90 := [monotonicity #87]: #89
+#93 := [monotonicity #90]: #92
+#71 := [asserted]: #22
+#94 := [mp #71 #93]: #91
+#826 := [unit-resolution #94 #825]: false
+#827 := [lemma #826]: #692
+#384 := (or #429 #716)
+#393 := (= #376 #85)
+#395 := (= #11 #82)
+#412 := (= #14 #82)
+#426 := [hypothesis]: #740
+#431 := [hypothesis]: #692
+#435 := (or #429 #650)
+#605 := (or #603 #429 #650)
+#566 := [def-axiom]: #605
+#436 := [unit-resolution #566 #434]: #435
+#425 := [unit-resolution #436 #431]: #650
+#588 := (not #650)
+#593 := (or #588 #716 #682)
+#594 := [def-axiom]: #593
+#437 := [unit-resolution #594 #425 #426]: #682
+#421 := [unit-resolution #420 #437]: #631
+#410 := [unit-resolution #422 #437]: #611
+#413 := [th-lemma arith eq-propagate -1 -1 #410 #421]: #412
+#403 := (= #11 #14)
+#707 := (<= #382 0::Int)
+#416 := [unit-resolution #496 #431]: #719
+#411 := [unit-resolution #697 #416 #426]: #758
+#417 := (or #700 #707)
+#392 := [th-lemma arith triangle-eq]: #417
+#396 := [unit-resolution #392 #411]: #707
+#397 := [unit-resolution #449 #411]: #708
+#402 := [unit-resolution #459 #501]: #532
+#533 := (>= #549 0::Int)
+#404 := (or #458 #533)
+#405 := [th-lemma arith triangle-eq]: #404
+#407 := [unit-resolution #405 #501]: #533
+#408 := [th-lemma arith eq-propagate 1 1 -1 -1 #407 #402 #397 #396]: #403
+#398 := [trans #408 #413]: #395
+#401 := [monotonicity #398]: #393
+#386 := [trans #400 #401]: #88
+#383 := [unit-resolution #94 #386]: false
+#387 := [lemma #383]: #384
+#389 := [unit-resolution #387 #827]: #716
+#381 := (or #429 #738)
+#380 := [hypothesis]: #762
+#559 := [hypothesis]: #749
+#561 := [unit-resolution #704 #559]: #740
+#563 := [unit-resolution #387 #561]: #429
+#582 := (or #692 #415)
+#583 := [th-lemma arith triangle-eq]: #582
+#558 := [unit-resolution #583 #563 #559]: false
+#406 := [lemma #558]: #415
+#378 := [unit-resolution #469 #431 #406 #380]: false
+#823 := [lemma #378]: #381
+#385 := [unit-resolution #823 #827]: #738
+#714 := (or #740 #762)
+#715 := [def-axiom]: #714
+[unit-resolution #715 #385 #389]: false
+727c827bb11139e8216aa2242907ab223b6a5c32 832 0
+unsat
+#2 := false
+#28 := 0::Int
 decl f9 :: (-> S6 S2 Int)
 decl f3 :: S2
-#8 := f3
+#7 := f3
 decl f10 :: S6
-#11 := f10
-#12 := (f9 f10 f3)
+#10 := f10
+#11 := (f9 f10 f3)
+#764 := (>= #11 0::Int)
+#740 := (not #764)
+#417 := (<= #11 0::Int)
+#751 := (not #417)
+#742 := (or #751 #740)
+#714 := (not #742)
+#431 := (= #11 0::Int)
+#691 := (not #431)
+decl f4 :: (-> S3 Int S2)
+decl f6 :: (-> S4 Int Int)
+#13 := 3::Int
+decl f7 :: (-> S5 Int S4)
 decl f11 :: S5
-#17 := f11
-#18 := (f7 f11 #12)
-#19 := (f6 #18 3::Int)
+#16 := f11
+#17 := (f7 f11 #11)
+#18 := (f6 #17 3::Int)
 decl f8 :: S5
-#10 := f8
-#13 := (f7 f8 #12)
-#15 := (f6 #13 3::Int)
-#91 := (* 3::Int #15)
-#94 := (+ #91 #19)
-decl f5 :: S3
-#9 := f5
-#97 := (f4 f5 #94)
-#100 := (= f3 #97)
-#471 := (f4 f5 #12)
-#1038 := (= #471 #97)
-#1036 := (= #97 #471)
-#1034 := (= #94 #12)
-#29 := 0::Int
-#1030 := (= 0::Int #12)
-#840 := (= #12 0::Int)
-#489 := (f9 f10 #97)
-#562 := (= #94 #489)
-#950 := (not #562)
-#852 := (div #12 3::Int)
-#208 := -1::Int
-#856 := (* -1::Int #852)
-#853 := (+ #15 #856)
-#789 := (<= #853 0::Int)
-#857 := (= #853 0::Int)
-#848 := (<= #12 0::Int)
-#836 := (not #848)
-#567 := (>= #12 0::Int)
-#708 := (not #567)
-#814 := (or #708 #836)
-#602 := [hypothesis]: #708
-#679 := (f9 f10 #471)
-#680 := (= #679 0::Int)
-#543 := (iff #680 #840)
-#566 := (= #679 #12)
-#604 := (= #12 #679)
-#556 := (= f3 #471)
-#24 := (:var 0 S2)
-#25 := (f9 f10 #24)
-#885 := (pattern #25)
-#26 := (f4 f5 #25)
-#107 := (= #24 #26)
-#886 := (forall (vars (?v0 S2)) (:pat #885) #107)
-#111 := (forall (vars (?v0 S2)) #107)
-#889 := (iff #111 #886)
-#887 := (iff #107 #107)
-#888 := [refl]: #887
-#890 := [quant-intro #888]: #889
-#334 := (~ #111 #111)
-#332 := (~ #107 #107)
-#333 := [refl]: #332
-#335 := [nnf-pos #333]: #334
-#27 := (= #26 #24)
-#28 := (forall (vars (?v0 S2)) #27)
-#112 := (iff #28 #111)
-#109 := (iff #27 #107)
-#110 := [rewrite]: #109
-#113 := [quant-intro #110]: #112
-#106 := [asserted]: #28
-#116 := [mp #106 #113]: #111
-#320 := [mp~ #116 #335]: #111
-#891 := [mp #320 #890]: #886
-#549 := (not #886)
-#560 := (or #549 #556)
-#561 := [quant-inst #8]: #560
-#565 := [unit-resolution #561 #891]: #556
-#605 := [monotonicity #565]: #604
-#598 := [symm #605]: #566
-#506 := [monotonicity #598]: #543
-#664 := (or #567 #680)
-#30 := (:var 0 Int)
-#32 := (f4 f5 #30)
-#892 := (pattern #32)
-#133 := (>= #30 0::Int)
-#33 := (f9 f10 #32)
-#38 := (= #33 0::Int)
-#181 := (or #38 #133)
-#899 := (forall (vars (?v0 Int)) (:pat #892) #181)
-#186 := (forall (vars (?v0 Int)) #181)
-#902 := (iff #186 #899)
-#900 := (iff #181 #181)
-#901 := [refl]: #900
-#903 := [quant-intro #901]: #902
-#324 := (~ #186 #186)
-#336 := (~ #181 #181)
-#337 := [refl]: #336
-#325 := [nnf-pos #337]: #324
-#37 := (< #30 0::Int)
-#39 := (implies #37 #38)
-#40 := (forall (vars (?v0 Int)) #39)
-#189 := (iff #40 #186)
-#152 := (= 0::Int #33)
-#158 := (not #37)
-#159 := (or #158 #152)
-#164 := (forall (vars (?v0 Int)) #159)
-#187 := (iff #164 #186)
-#184 := (iff #159 #181)
-#178 := (or #133 #38)
-#182 := (iff #178 #181)
+#9 := f8
+#12 := (f7 f8 #11)
+#14 := (f6 #12 3::Int)
+#80 := (* 3::Int #14)
+#83 := (+ #80 #18)
+decl f5 :: S3
+#8 := f5
+#86 := (f4 f5 #83)
+#89 := (= f3 #86)
+#377 := (f4 f5 #11)
+#903 := (= #377 #86)
+#901 := (= #86 #377)
+#899 := (= #83 #11)
+#895 := (= 0::Int #11)
+#859 := [hypothesis]: #431
+#896 := [symm #859]: #895
+#897 := (= #83 0::Int)
+#468 := (f9 f10 #86)
+#429 := (= #468 0::Int)
+#774 := (>= #468 0::Int)
+#636 := (>= #18 0::Int)
+#685 := (= #18 0::Int)
+#840 := (or #691 #685)
+#574 := -3::Int
+#152 := -1::Int
+#761 := (* -1::Int #11)
+#705 := (mod #761 -3::Int)
+#668 := (+ #18 #705)
+#656 := (= #668 0::Int)
+#709 := (mod #11 3::Int)
+#686 := (* -1::Int #709)
+#687 := (+ #18 #686)
+#677 := (= #687 0::Int)
+#661 := (if #742 #677 #656)
+#664 := (if #431 #685 #661)
+#29 := (:var 0 Int)
+#40 := (:var 1 Int)
+#60 := (f7 f11 #40)
+#61 := (f6 #60 #29)
+#818 := (pattern #61)
+#156 := (* -1::Int #29)
+#153 := (* -1::Int #40)
+#175 := (mod #153 #156)
+#366 := (+ #61 #175)
+#367 := (= #366 0::Int)
+#62 := (mod #40 #29)
+#363 := (* -1::Int #62)
+#364 := (+ #61 #363)
+#365 := (= #364 0::Int)
+#130 := (<= #29 0::Int)
+#242 := (>= #40 0::Int)
+#310 := (or #242 #130)
+#311 := (not #310)
+#126 := (<= #40 0::Int)
+#306 := (or #126 #130)
+#307 := (not #306)
+#314 := (or #307 #311)
+#368 := (if #314 #365 #367)
+#362 := (= #61 0::Int)
+#43 := (= #40 0::Int)
+#369 := (if #43 #362 #368)
+#361 := (= #61 #40)
+#44 := (= #29 0::Int)
+#370 := (if #44 #361 #369)
+#819 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #818) #370)
+#373 := (forall (vars (?v0 Int) (?v1 Int)) #370)
+#822 := (iff #373 #819)
+#820 := (iff #370 #370)
+#821 := [refl]: #820
+#823 := [quant-intro #821]: #822
+#181 := (* -1::Int #175)
+#330 := (if #314 #62 #181)
+#333 := (if #43 0::Int #330)
+#336 := (if #44 #40 #333)
+#339 := (= #61 #336)
+#342 := (forall (vars (?v0 Int) (?v1 Int)) #339)
+#374 := (iff #342 #373)
+#371 := (iff #339 #370)
+#372 := [rewrite]: #371
+#375 := [quant-intro #372]: #374
+#131 := (not #130)
+#245 := (not #242)
+#248 := (and #245 #131)
+#127 := (not #126)
+#134 := (and #127 #131)
+#251 := (or #134 #248)
+#267 := (if #251 #62 #181)
+#270 := (if #43 0::Int #267)
+#273 := (if #44 #40 #270)
+#276 := (= #61 #273)
+#279 := (forall (vars (?v0 Int) (?v1 Int)) #276)
+#343 := (iff #279 #342)
+#340 := (iff #276 #339)
+#337 := (= #273 #336)
+#334 := (= #270 #333)
+#331 := (= #267 #330)
+#315 := (iff #251 #314)
+#312 := (iff #248 #311)
+#313 := [rewrite]: #312
+#308 := (iff #134 #307)
+#309 := [rewrite]: #308
+#316 := [monotonicity #309 #313]: #315
+#332 := [monotonicity #316]: #331
+#335 := [monotonicity #332]: #334
+#338 := [monotonicity #335]: #337
+#341 := [monotonicity #338]: #340
+#344 := [quant-intro #341]: #343
+#303 := (~ #279 #279)
+#301 := (~ #276 #276)
+#302 := [refl]: #301
+#304 := [nnf-pos #302]: #303
+#137 := (<= 0::Int #40)
+#138 := (not #137)
+#146 := (and #138 #131)
+#149 := (or #134 #146)
+#186 := (if #149 #62 #181)
+#189 := (if #43 0::Int #186)
+#192 := (if #44 #40 #189)
+#195 := (= #61 #192)
+#198 := (forall (vars (?v0 Int) (?v1 Int)) #195)
+#280 := (iff #198 #279)
+#277 := (iff #195 #276)
+#274 := (= #192 #273)
+#271 := (= #189 #270)
+#268 := (= #186 #267)
+#252 := (iff #149 #251)
+#249 := (iff #146 #248)
+#246 := (iff #138 #245)
+#243 := (iff #137 #242)
+#244 := [rewrite]: #243
+#247 := [monotonicity #244]: #246
+#250 := [monotonicity #247]: #249
+#253 := [monotonicity #250]: #252
+#269 := [monotonicity #253]: #268
+#272 := [monotonicity #269]: #271
+#275 := [monotonicity #272]: #274
+#278 := [monotonicity #275]: #277
+#281 := [quant-intro #278]: #280
+#54 := (- #29)
+#53 := (- #40)
+#63 := (mod #53 #54)
+#64 := (- #63)
+#47 := (< 0::Int #29)
+#49 := (< #40 0::Int)
+#50 := (and #49 #47)
+#46 := (< 0::Int #40)
+#48 := (and #46 #47)
+#51 := (or #48 #50)
+#65 := (if #51 #62 #64)
+#66 := (if #43 0::Int #65)
+#67 := (if #44 #40 #66)
+#68 := (= #61 #67)
+#69 := (forall (vars (?v0 Int) (?v1 Int)) #68)
+#199 := (iff #69 #198)
+#196 := (iff #68 #195)
+#193 := (= #67 #192)
+#190 := (= #66 #189)
+#187 := (= #65 #186)
+#184 := (= #64 #181)
+#178 := (- #175)
+#182 := (= #178 #181)
 #183 := [rewrite]: #182
-#179 := (iff #159 #178)
-#176 := (iff #152 #38)
-#177 := [rewrite]: #176
-#174 := (iff #158 #133)
-#134 := (not #133)
-#169 := (not #134)
-#172 := (iff #169 #133)
-#173 := [rewrite]: #172
-#170 := (iff #158 #169)
-#167 := (iff #37 #134)
-#168 := [rewrite]: #167
-#171 := [monotonicity #168]: #170
-#175 := [trans #171 #173]: #174
-#180 := [monotonicity #175 #177]: #179
+#179 := (= #64 #178)
+#176 := (= #63 #175)
+#157 := (= #54 #156)
+#158 := [rewrite]: #157
+#154 := (= #53 #153)
+#155 := [rewrite]: #154
+#177 := [monotonicity #155 #158]: #176
+#180 := [monotonicity #177]: #179
 #185 := [trans #180 #183]: #184
-#188 := [quant-intro #185]: #187
-#165 := (iff #40 #164)
-#162 := (iff #39 #159)
-#155 := (implies #37 #152)
-#160 := (iff #155 #159)
-#161 := [rewrite]: #160
-#156 := (iff #39 #155)
-#153 := (iff #38 #152)
-#154 := [rewrite]: #153
-#157 := [monotonicity #154]: #156
-#163 := [trans #157 #161]: #162
-#166 := [quant-intro #163]: #165
-#190 := [trans #166 #188]: #189
-#151 := [asserted]: #40
-#191 := [mp #151 #190]: #186
-#338 := [mp~ #191 #325]: #186
-#904 := [mp #338 #903]: #899
-#867 := (not #899)
-#653 := (or #867 #567 #680)
-#681 := (or #680 #567)
-#654 := (or #867 #681)
-#656 := (iff #654 #653)
-#657 := (or #867 #664)
-#502 := (iff #657 #653)
-#660 := [rewrite]: #502
-#658 := (iff #654 #657)
-#682 := (iff #681 #664)
-#652 := [rewrite]: #682
-#659 := [monotonicity #652]: #658
-#661 := [trans #659 #660]: #656
-#655 := [quant-inst #12]: #654
-#640 := [mp #655 #661]: #653
-#554 := [unit-resolution #640 #904]: #664
-#603 := [unit-resolution #554 #602]: #680
-#508 := [mp #603 #506]: #840
-#763 := (not #840)
-#509 := (or #763 #567)
-#512 := [th-lemma arith triangle-eq]: #509
-#507 := [unit-resolution #512 #508 #602]: false
-#513 := [lemma #507]: #567
-#488 := [hypothesis]: #763
-#555 := (or #840 #836 #708)
-#538 := [th-lemma arith triangle-eq]: #555
-#497 := [unit-resolution #538 #488 #513]: #836
-#783 := (or #814 #848)
-#784 := [def-axiom]: #783
-#496 := [unit-resolution #784 #497]: #814
-#720 := -3::Int
-#477 := (* -1::Int #12)
-#722 := (div #477 -3::Int)
-#725 := (* -1::Int #722)
-#816 := (+ #15 #725)
-#809 := (= #816 0::Int)
-#800 := (ite #814 #857 #809)
-#571 := (or #840 #800)
-#847 := (= #15 0::Int)
-#812 := (ite #840 #847 #800)
-#41 := (:var 1 Int)
-#42 := (f7 f8 #41)
-#43 := (f6 #42 #30)
-#905 := (pattern #43)
-#212 := (* -1::Int #30)
-#209 := (* -1::Int #41)
-#215 := (div #209 #212)
-#387 := (* -1::Int #215)
-#388 := (+ #43 #387)
-#389 := (= #388 0::Int)
-#53 := (div #41 #30)
-#384 := (* -1::Int #53)
-#385 := (+ #43 #384)
-#386 := (= #385 0::Int)
-#247 := (>= #41 0::Int)
-#240 := (<= #30 0::Int)
-#347 := (or #240 #247)
-#348 := (not #347)
-#236 := (<= #41 0::Int)
-#345 := (or #236 #240)
-#346 := (not #345)
-#351 := (or #346 #348)
-#390 := (ite #351 #386 #389)
-#383 := (= #43 0::Int)
-#45 := (= #30 0::Int)
-#44 := (= #41 0::Int)
-#46 := (or #44 #45)
-#391 := (ite #46 #383 #390)
-#906 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #905) #391)
-#394 := (forall (vars (?v0 Int) (?v1 Int)) #391)
-#909 := (iff #394 #906)
-#907 := (iff #391 #391)
-#908 := [refl]: #907
-#910 := [quant-intro #908]: #909
-#354 := (ite #351 #53 #215)
-#357 := (ite #46 0::Int #354)
-#360 := (= #43 #357)
-#363 := (forall (vars (?v0 Int) (?v1 Int)) #360)
-#395 := (iff #363 #394)
-#392 := (iff #360 #391)
-#393 := [rewrite]: #392
-#396 := [quant-intro #393]: #395
-#248 := (not #247)
-#241 := (not #240)
-#251 := (and #241 #248)
-#237 := (not #236)
-#244 := (and #237 #241)
-#254 := (or #244 #251)
-#257 := (ite #254 #53 #215)
-#260 := (ite #46 0::Int #257)
-#263 := (= #43 #260)
-#266 := (forall (vars (?v0 Int) (?v1 Int)) #263)
-#364 := (iff #266 #363)
-#361 := (iff #263 #360)
-#358 := (= #260 #357)
-#355 := (= #257 #354)
-#352 := (iff #254 #351)
-#349 := (iff #251 #348)
-#350 := [rewrite]: #349
-#330 := (iff #244 #346)
-#331 := [rewrite]: #330
-#353 := [monotonicity #331 #350]: #352
-#356 := [monotonicity #353]: #355
-#359 := [monotonicity #356]: #358
-#362 := [monotonicity #359]: #361
-#365 := [quant-intro #362]: #364
-#326 := (~ #266 #266)
-#339 := (~ #263 #263)
-#340 := [refl]: #339
-#327 := [nnf-pos #340]: #326
-#55 := (- #30)
-#54 := (- #41)
-#56 := (div #54 #55)
-#48 := (< 0::Int #30)
-#50 := (< #41 0::Int)
-#51 := (and #50 #48)
-#47 := (< 0::Int #41)
-#49 := (and #47 #48)
-#52 := (or #49 #51)
-#57 := (ite #52 #53 #56)
-#58 := (ite #46 0::Int #57)
-#59 := (= #43 #58)
-#60 := (forall (vars (?v0 Int) (?v1 Int)) #59)
-#269 := (iff #60 #266)
-#202 := (and #48 #50)
-#205 := (or #49 #202)
-#218 := (ite #205 #53 #215)
-#196 := (= 0::Int #30)
-#193 := (= 0::Int #41)
-#199 := (or #193 #196)
-#221 := (ite #199 0::Int #218)
-#224 := (= #43 #221)
-#227 := (forall (vars (?v0 Int) (?v1 Int)) #224)
-#267 := (iff #227 #266)
-#264 := (iff #224 #263)
-#261 := (= #221 #260)
-#258 := (= #218 #257)
-#255 := (iff #205 #254)
-#252 := (iff #202 #251)
-#249 := (iff #50 #248)
-#250 := [rewrite]: #249
-#242 := (iff #48 #241)
-#243 := [rewrite]: #242
-#253 := [monotonicity #243 #250]: #252
-#245 := (iff #49 #244)
-#238 := (iff #47 #237)
-#239 := [rewrite]: #238
-#246 := [monotonicity #239 #243]: #245
-#256 := [monotonicity #246 #253]: #255
+#150 := (iff #51 #149)
+#147 := (iff #50 #146)
+#132 := (iff #47 #131)
+#133 := [rewrite]: #132
+#139 := (iff #49 #138)
+#143 := (iff #138 #138)
+#141 := (iff #137 #137)
+#142 := [rewrite]: #141
+#144 := [monotonicity #142]: #143
+#140 := [rewrite]: #139
+#145 := [trans #140 #144]: #139
+#148 := [monotonicity #145 #133]: #147
+#135 := (iff #48 #134)
+#128 := (iff #46 #127)
+#129 := [rewrite]: #128
+#136 := [monotonicity #129 #133]: #135
+#151 := [monotonicity #136 #148]: #150
+#188 := [monotonicity #151 #185]: #187
+#191 := [monotonicity #188]: #190
+#194 := [monotonicity #191]: #193
+#197 := [monotonicity #194]: #196
+#200 := [quant-intro #197]: #199
+#76 := [asserted]: #69
+#201 := [mp #76 #200]: #198
+#282 := [mp #201 #281]: #279
+#305 := [mp~ #282 #304]: #279
+#345 := [mp #305 #344]: #342
+#376 := [mp #345 #375]: #373
+#824 := [mp #376 #823]: #819
+#651 := (not #819)
+#647 := (or #651 #664)
+#483 := (* -1::Int 3::Int)
+#688 := (mod #761 #483)
+#666 := (+ #18 #688)
+#667 := (= #666 0::Int)
+#777 := (<= 3::Int 0::Int)
+#765 := (or #764 #777)
+#487 := (not #765)
+#775 := (or #417 #777)
+#778 := (not #775)
+#488 := (or #778 #487)
+#669 := (if #488 #677 #667)
+#670 := (if #431 #685 #669)
+#684 := (= #18 #11)
+#432 := (= 3::Int 0::Int)
+#671 := (if #432 #684 #670)
+#648 := (or #651 #671)
+#652 := (iff #648 #647)
+#654 := (iff #647 #647)
+#650 := [rewrite]: #654
+#645 := (iff #671 #664)
+#638 := (if false #684 #664)
+#533 := (iff #638 #664)
+#644 := [rewrite]: #533
+#639 := (iff #671 #638)
+#659 := (iff #670 #664)
+#662 := (iff #669 #661)
+#657 := (iff #667 #656)
+#674 := (= #666 #668)
+#672 := (= #688 #705)
+#727 := (= #483 -3::Int)
+#728 := [rewrite]: #727
+#673 := [monotonicity #728]: #672
+#660 := [monotonicity #673]: #674
+#658 := [monotonicity #660]: #657
+#571 := (iff #488 #742)
+#741 := (iff #487 #740)
+#733 := (iff #765 #764)
+#594 := (or #764 false)
+#738 := (iff #594 #764)
+#739 := [rewrite]: #738
+#736 := (iff #765 #594)
+#757 := (iff #777 false)
+#746 := [rewrite]: #757
+#737 := [monotonicity #746]: #736
+#734 := [trans #737 #739]: #733
+#735 := [monotonicity #734]: #741
+#592 := (iff #778 #751)
+#750 := (iff #775 #417)
+#747 := (or #417 false)
+#744 := (iff #747 #417)
+#749 := [rewrite]: #744
+#748 := (iff #775 #747)
+#743 := [monotonicity #746]: #748
+#745 := [trans #743 #749]: #750
+#593 := [monotonicity #745]: #592
+#573 := [monotonicity #593 #735]: #571
+#663 := [monotonicity #573 #658]: #662
+#665 := [monotonicity #663]: #659
+#474 := (iff #432 false)
+#475 := [rewrite]: #474
+#640 := [monotonicity #475 #665]: #639
+#646 := [trans #640 #644]: #645
+#653 := [monotonicity #646]: #652
+#655 := [trans #653 #650]: #652
+#649 := [quant-inst #11 #13]: #648
+#635 := [mp #649 #655]: #647
+#580 := [unit-resolution #635 #824]: #664
+#633 := (not #664)
+#613 := (or #633 #691 #685)
+#634 := [def-axiom]: #613
+#837 := [unit-resolution #634 #580]: #840
+#850 := [unit-resolution #837 #859]: #685
+#595 := (not #685)
+#851 := (or #595 #636)
+#838 := [th-lemma arith triangle-eq]: #851
+#839 := [unit-resolution #838 #850]: #636
+#704 := (>= #14 0::Int)
+#489 := (div #11 3::Int)
+#585 := (* -3::Int #489)
+#586 := (+ #11 #585 #686)
+#584 := (= #586 0::Int)
+#1 := true
+#219 := [true-axiom]: true
+#539 := (or false #584)
+#543 := [th-lemma arith]: #539
+#536 := [unit-resolution #543 #219]: #584
+#588 := (<= #586 0::Int)
+#500 := (not #588)
+#545 := (>= #709 3::Int)
+#548 := (not #545)
+#544 := (or false #548)
+#537 := [th-lemma arith]: #544
+#540 := [unit-resolution #537 #219]: #548
+#541 := (not #704)
+#527 := [hypothesis]: #541
+#490 := (* -1::Int #489)
+#383 := (+ #14 #490)
+#711 := (>= #383 0::Int)
+#760 := (= #383 0::Int)
+#730 := (div #761 -3::Int)
+#732 := (* -1::Int #730)
+#616 := (+ #14 #732)
+#625 := (= #616 0::Int)
+#724 := (if #742 #760 #625)
+#416 := (= #14 0::Int)
+#679 := (not #416)
+#529 := (or #679 #704)
+#530 := [th-lemma arith triangle-eq]: #529
+#528 := [unit-resolution #530 #527]: #679
+#513 := (or #691 #416)
+#626 := (if #431 #416 #724)
+#41 := (f7 f8 #40)
+#42 := (f6 #41 #29)
+#811 := (pattern #42)
+#159 := (div #153 #156)
+#350 := (* -1::Int #159)
+#351 := (+ #42 #350)
+#352 := (= #351 0::Int)
+#52 := (div #40 #29)
+#347 := (* -1::Int #52)
+#348 := (+ #42 #347)
+#349 := (= #348 0::Int)
+#353 := (if #314 #349 #352)
+#346 := (= #42 0::Int)
+#45 := (or #43 #44)
+#354 := (if #45 #346 #353)
+#812 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #811) #354)
+#357 := (forall (vars (?v0 Int) (?v1 Int)) #354)
+#815 := (iff #357 #812)
+#813 := (iff #354 #354)
+#814 := [refl]: #813
+#816 := [quant-intro #814]: #815
+#317 := (if #314 #52 #159)
+#320 := (if #45 0::Int #317)
+#323 := (= #42 #320)
+#326 := (forall (vars (?v0 Int) (?v1 Int)) #323)
+#358 := (iff #326 #357)
+#355 := (iff #323 #354)
+#356 := [rewrite]: #355
+#359 := [quant-intro #356]: #358
+#254 := (if #251 #52 #159)
+#257 := (if #45 0::Int #254)
+#260 := (= #42 #257)
+#263 := (forall (vars (?v0 Int) (?v1 Int)) #260)
+#327 := (iff #263 #326)
+#324 := (iff #260 #323)
+#321 := (= #257 #320)
+#318 := (= #254 #317)
+#319 := [monotonicity #316]: #318
+#322 := [monotonicity #319]: #321
+#325 := [monotonicity #322]: #324
+#328 := [quant-intro #325]: #327
+#298 := (~ #263 #263)
+#296 := (~ #260 #260)
+#297 := [refl]: #296
+#299 := [nnf-pos #297]: #298
+#162 := (if #149 #52 #159)
+#165 := (if #45 0::Int #162)
+#168 := (= #42 #165)
+#171 := (forall (vars (?v0 Int) (?v1 Int)) #168)
+#264 := (iff #171 #263)
+#261 := (iff #168 #260)
+#258 := (= #165 #257)
+#255 := (= #162 #254)
+#256 := [monotonicity #253]: #255
 #259 := [monotonicity #256]: #258
-#234 := (iff #199 #46)
-#232 := (iff #196 #45)
-#233 := [rewrite]: #232
-#230 := (iff #193 #44)
-#231 := [rewrite]: #230
-#235 := [monotonicity #231 #233]: #234
-#262 := [monotonicity #235 #259]: #261
-#265 := [monotonicity #262]: #264
-#268 := [quant-intro #265]: #267
-#228 := (iff #60 #227)
-#225 := (iff #59 #224)
-#222 := (= #58 #221)
-#219 := (= #57 #218)
-#216 := (= #56 #215)
-#213 := (= #55 #212)
-#214 := [rewrite]: #213
-#210 := (= #54 #209)
-#211 := [rewrite]: #210
-#217 := [monotonicity #211 #214]: #216
-#206 := (iff #52 #205)
-#203 := (iff #51 #202)
-#204 := [rewrite]: #203
-#207 := [monotonicity #204]: #206
-#220 := [monotonicity #207 #217]: #219
-#200 := (iff #46 #199)
-#197 := (iff #45 #196)
-#198 := [rewrite]: #197
-#194 := (iff #44 #193)
-#195 := [rewrite]: #194
-#201 := [monotonicity #195 #198]: #200
-#223 := [monotonicity #201 #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [quant-intro #226]: #228
-#270 := [trans #229 #268]: #269
-#192 := [asserted]: #60
-#271 := [mp #192 #270]: #266
-#341 := [mp~ #271 #327]: #266
-#366 := [mp #341 #365]: #363
-#397 := [mp #366 #396]: #394
-#911 := [mp #397 #910]: #906
-#802 := (not #906)
-#803 := (or #802 #812)
-#584 := (* -1::Int 3::Int)
-#854 := (div #477 #584)
-#855 := (* -1::Int #854)
-#577 := (+ #15 #855)
-#578 := (= #577 0::Int)
-#568 := (<= 3::Int 0::Int)
-#569 := (or #568 #567)
-#570 := (not #569)
-#849 := (or #848 #568)
-#564 := (not #849)
-#846 := (or #564 #570)
-#850 := (ite #846 #857 #578)
-#851 := (= 3::Int 0::Int)
-#841 := (or #840 #851)
-#842 := (ite #841 #847 #850)
-#804 := (or #802 #842)
-#799 := (iff #804 #803)
-#790 := (iff #803 #803)
-#791 := [rewrite]: #790
-#808 := (iff #842 #812)
-#810 := (iff #850 #800)
-#801 := (iff #578 #809)
-#820 := (= #577 #816)
-#726 := (= #855 #725)
-#723 := (= #854 #722)
-#721 := (= #584 -3::Int)
-#714 := [rewrite]: #721
-#724 := [monotonicity #714]: #723
-#819 := [monotonicity #724]: #726
-#807 := [monotonicity #819]: #820
-#798 := [monotonicity #807]: #801
-#703 := (iff #846 #814)
-#669 := (or #836 #708)
-#815 := (iff #669 #814)
-#818 := [rewrite]: #815
-#817 := (iff #846 #669)
-#709 := (iff #570 #708)
-#823 := (iff #569 #567)
-#668 := (or false #567)
-#824 := (iff #668 #567)
-#825 := [rewrite]: #824
-#821 := (iff #569 #668)
-#830 := (iff #568 false)
-#831 := [rewrite]: #830
-#822 := [monotonicity #831]: #821
-#826 := [trans #822 #825]: #823
-#710 := [monotonicity #826]: #709
-#665 := (iff #564 #836)
-#835 := (iff #849 #848)
-#832 := (or #848 false)
-#828 := (iff #832 #848)
-#834 := [rewrite]: #828
-#833 := (iff #849 #832)
-#827 := [monotonicity #831]: #833
-#829 := [trans #827 #834]: #835
-#667 := [monotonicity #829]: #665
-#719 := [monotonicity #667 #710]: #817
-#718 := [trans #719 #818]: #703
-#811 := [monotonicity #718 #798]: #810
-#687 := (iff #841 #840)
-#843 := (or #840 false)
-#845 := (iff #843 #840)
-#686 := [rewrite]: #845
-#844 := (iff #841 #843)
-#837 := (iff #851 false)
-#838 := [rewrite]: #837
-#839 := [monotonicity #838]: #844
-#688 := [trans #839 #686]: #687
-#813 := [monotonicity #688 #811]: #808
-#806 := [monotonicity #813]: #799
-#793 := [trans #806 #791]: #799
-#805 := [quant-inst #12 #14]: #804
-#794 := [mp #805 #793]: #803
-#588 := [unit-resolution #794 #911]: #812
-#761 := (not #812)
-#766 := (or #761 #840 #800)
-#767 := [def-axiom]: #766
-#572 := [unit-resolution #767 #588]: #571
-#481 := [unit-resolution #572 #488]: #800
-#786 := (not #814)
-#774 := (not #800)
-#775 := (or #774 #786 #857)
-#776 := [def-axiom]: #775
-#478 := [unit-resolution #776 #481 #496]: #857
-#779 := (not #857)
-#479 := (or #779 #789)
-#953 := [th-lemma arith triangle-eq]: #479
-#954 := [unit-resolution #953 #478]: #789
-#785 := (mod #12 3::Int)
-#757 := (* -1::Int #785)
-#758 := (+ #19 #757)
-#683 := (<= #758 0::Int)
-#753 := (= #758 0::Int)
-#770 := (mod #477 -3::Int)
-#740 := (+ #19 #770)
-#742 := (= #740 0::Int)
-#747 := (ite #814 #753 #742)
-#956 := (or #840 #747)
-#732 := (= #19 0::Int)
-#749 := (ite #840 #732 #747)
-#61 := (f7 f11 #41)
-#62 := (f6 #61 #30)
-#912 := (pattern #62)
-#273 := (mod #209 #212)
-#403 := (+ #62 #273)
-#404 := (= #403 0::Int)
-#63 := (mod #41 #30)
-#400 := (* -1::Int #63)
-#401 := (+ #62 #400)
-#402 := (= #401 0::Int)
-#405 := (ite #351 #402 #404)
-#399 := (= #62 0::Int)
-#406 := (ite #44 #399 #405)
-#398 := (= #41 #62)
-#407 := (ite #45 #398 #406)
-#913 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #912) #407)
-#410 := (forall (vars (?v0 Int) (?v1 Int)) #407)
-#916 := (iff #410 #913)
-#914 := (iff #407 #407)
-#915 := [refl]: #914
-#917 := [quant-intro #915]: #916
-#279 := (* -1::Int #273)
-#367 := (ite #351 #63 #279)
-#370 := (ite #44 0::Int #367)
-#373 := (ite #45 #41 #370)
-#376 := (= #62 #373)
-#379 := (forall (vars (?v0 Int) (?v1 Int)) #376)
-#411 := (iff #379 #410)
-#408 := (iff #376 #407)
-#409 := [rewrite]: #408
-#412 := [quant-intro #409]: #411
-#299 := (ite #254 #63 #279)
-#302 := (ite #44 0::Int #299)
-#305 := (ite #45 #41 #302)
-#308 := (= #62 #305)
-#311 := (forall (vars (?v0 Int) (?v1 Int)) #308)
-#380 := (iff #311 #379)
-#377 := (iff #308 #376)
-#374 := (= #305 #373)
-#371 := (= #302 #370)
-#368 := (= #299 #367)
-#369 := [monotonicity #353]: #368
-#372 := [monotonicity #369]: #371
-#375 := [monotonicity #372]: #374
-#378 := [monotonicity #375]: #377
-#381 := [quant-intro #378]: #380
-#328 := (~ #311 #311)
-#342 := (~ #308 #308)
-#343 := [refl]: #342
-#329 := [nnf-pos #343]: #328
-#64 := (mod #54 #55)
-#65 := (- #64)
-#66 := (ite #52 #63 #65)
-#67 := (ite #44 0::Int #66)
-#68 := (ite #45 #41 #67)
-#69 := (= #62 #68)
-#70 := (forall (vars (?v0 Int) (?v1 Int)) #69)
-#314 := (iff #70 #311)
-#284 := (ite #205 #63 #279)
-#287 := (ite #193 0::Int #284)
-#290 := (ite #196 #41 #287)
-#293 := (= #62 #290)
-#296 := (forall (vars (?v0 Int) (?v1 Int)) #293)
-#312 := (iff #296 #311)
-#309 := (iff #293 #308)
-#306 := (= #290 #305)
-#303 := (= #287 #302)
-#300 := (= #284 #299)
-#301 := [monotonicity #256]: #300
-#304 := [monotonicity #231 #301]: #303
-#307 := [monotonicity #233 #304]: #306
-#310 := [monotonicity #307]: #309
-#313 := [quant-intro #310]: #312
-#297 := (iff #70 #296)
-#294 := (iff #69 #293)
-#291 := (= #68 #290)
-#288 := (= #67 #287)
-#285 := (= #66 #284)
-#282 := (= #65 #279)
-#276 := (- #273)
-#280 := (= #276 #279)
-#281 := [rewrite]: #280
-#277 := (= #65 #276)
-#274 := (= #64 #273)
-#275 := [monotonicity #211 #214]: #274
-#278 := [monotonicity #275]: #277
-#283 := [trans #278 #281]: #282
-#286 := [monotonicity #207 #283]: #285
-#289 := [monotonicity #195 #286]: #288
-#292 := [monotonicity #198 #289]: #291
-#295 := [monotonicity #292]: #294
-#298 := [quant-intro #295]: #297
-#315 := [trans #298 #313]: #314
-#272 := [asserted]: #70
-#316 := [mp #272 #315]: #311
-#344 := [mp~ #316 #329]: #311
-#382 := [mp #344 #381]: #379
-#413 := [mp #382 #412]: #410
-#918 := [mp #413 #917]: #913
-#712 := (not #913)
-#671 := (or #712 #749)
-#752 := (mod #477 #584)
-#755 := (+ #19 #752)
-#756 := (= #755 0::Int)
-#759 := (ite #846 #753 #756)
-#733 := (ite #840 #732 #759)
-#734 := (= #12 #19)
-#627 := (ite #851 #734 #733)
-#702 := (or #712 #627)
-#706 := (iff #702 #671)
-#715 := (iff #671 #671)
-#716 := [rewrite]: #715
-#737 := (iff #627 #749)
-#730 := (ite false #734 #749)
-#736 := (iff #730 #749)
-#731 := [rewrite]: #736
-#711 := (iff #627 #730)
-#729 := (iff #733 #749)
-#748 := (iff #759 #747)
-#743 := (iff #756 #742)
-#745 := (= #755 #740)
-#738 := (= #752 #770)
-#739 := [monotonicity #714]: #738
-#741 := [monotonicity #739]: #745
-#746 := [monotonicity #741]: #743
-#744 := [monotonicity #718 #746]: #748
-#675 := [monotonicity #744]: #729
-#735 := [monotonicity #838 #675]: #711
-#705 := [trans #735 #731]: #737
-#713 := [monotonicity #705]: #706
-#717 := [trans #713 #716]: #706
-#704 := [quant-inst #12 #14]: #702
-#727 := [mp #704 #717]: #671
-#955 := [unit-resolution #727 #918]: #749
-#701 := (not #749)
-#670 := (or #701 #840 #747)
-#672 := [def-axiom]: #670
-#957 := [unit-resolution #672 #955]: #956
-#958 := [unit-resolution #957 #488]: #747
-#691 := (not #747)
-#692 := (or #691 #786 #753)
-#693 := [def-axiom]: #692
-#959 := [unit-resolution #693 #958 #496]: #753
-#696 := (not #753)
-#960 := (or #696 #683)
-#961 := [th-lemma arith triangle-eq]: #960
-#962 := [unit-resolution #961 #959]: #683
-#769 := (>= #853 0::Int)
-#527 := (or #779 #769)
-#528 := [th-lemma arith triangle-eq]: #527
-#963 := [unit-resolution #528 #478]: #769
-#684 := (>= #758 0::Int)
-#964 := (or #696 #684)
-#965 := [th-lemma arith triangle-eq]: #964
-#966 := [unit-resolution #965 #959]: #684
-#923 := (not #789)
-#924 := (not #683)
-#531 := (not #769)
-#931 := (not #684)
-#951 := (or #950 #931 #531 #924 #923)
-#501 := (f4 f5 #489)
-#944 := (= #501 #97)
-#503 := (= #97 #501)
-#486 := (or #549 #503)
-#490 := [quant-inst #97]: #486
-#474 := [unit-resolution #490 #891]: #503
-#945 := [symm #474]: #944
-#946 := (= f3 #501)
-#942 := (= #471 #501)
-#940 := (= #12 #489)
-#475 := [hypothesis]: #562
-#483 := (= #12 #94)
-#484 := (* -1::Int #94)
-#480 := (+ #12 #484)
-#472 := (>= #480 0::Int)
-#473 := [hypothesis]: #789
-#629 := (* -3::Int #852)
-#632 := (+ #757 #629)
-#633 := (+ #12 #632)
-#635 := (>= #633 0::Int)
-#628 := (= #633 0::Int)
-#1 := true
-#88 := [true-axiom]: true
-#606 := (or false #628)
-#591 := [th-lemma arith]: #606
-#592 := [unit-resolution #591 #88]: #628
-#514 := (not #628)
-#476 := (or #514 #635)
-#919 := [th-lemma arith triangle-eq]: #476
-#920 := [unit-resolution #919 #592]: #635
-#921 := [hypothesis]: #683
-#922 := (not #635)
-#925 := (or #472 #922 #923 #924)
-#926 := [th-lemma arith assign-bounds -1 3 1]: #925
-#927 := [unit-resolution #926 #921 #920 #473]: #472
-#485 := (<= #480 0::Int)
-#928 := [hypothesis]: #769
-#634 := (<= #633 0::Int)
-#516 := (or #514 #634)
-#517 := [th-lemma arith triangle-eq]: #516
-#929 := [unit-resolution #517 #592]: #634
-#930 := [hypothesis]: #684
-#530 := (not #634)
-#932 := (or #485 #530 #531 #931)
-#933 := [th-lemma arith assign-bounds -1 3 1]: #932
-#934 := [unit-resolution #933 #930 #929 #928]: #485
-#936 := (not #472)
-#935 := (not #485)
-#937 := (or #483 #935 #936)
-#938 := [th-lemma arith triangle-eq]: #937
-#939 := [unit-resolution #938 #934 #927]: #483
-#941 := [trans #939 #475]: #940
-#943 := [monotonicity #941]: #942
-#947 := [trans #565 #943]: #946
-#948 := [trans #947 #945]: #100
-#103 := (not #100)
-#16 := (* #15 3::Int)
-#20 := (+ #16 #19)
-#21 := (f4 f5 #20)
-#22 := (= f3 #21)
-#23 := (not #22)
-#104 := (iff #23 #103)
-#101 := (iff #22 #100)
-#98 := (= #21 #97)
-#95 := (= #20 #94)
-#92 := (= #16 #91)
-#93 := [rewrite]: #92
-#96 := [monotonicity #93]: #95
-#99 := [monotonicity #96]: #98
-#102 := [monotonicity #99]: #101
-#105 := [monotonicity #102]: #104
-#90 := [asserted]: #23
-#108 := [mp #90 #105]: #103
-#949 := [unit-resolution #108 #948]: false
-#952 := [lemma #949]: #951
-#967 := [unit-resolution #952 #966 #963 #962 #954]: #950
-#563 := (* -1::Int #489)
-#494 := (+ #94 #563)
-#495 := (<= #494 0::Int)
-#542 := (+ #19 #563)
-#877 := (+ #91 #542)
-#526 := (<= #877 0::Int)
-#879 := (= #877 0::Int)
-#557 := (>= #94 0::Int)
-#796 := (>= #15 0::Int)
-#608 := (>= #785 3::Int)
-#620 := (not #608)
-#593 := (or false #620)
-#595 := [th-lemma arith]: #593
-#594 := [unit-resolution #595 #88]: #620
-#596 := (not #796)
-#585 := [hypothesis]: #596
-#762 := (not #847)
-#586 := (or #762 #796)
-#587 := [th-lemma arith triangle-eq]: #586
-#579 := [unit-resolution #587 #585]: #762
-#589 := (or #763 #847)
-#764 := (or #761 #763 #847)
-#765 := [def-axiom]: #764
-#580 := [unit-resolution #765 #588]: #589
-#590 := [unit-resolution #580 #579]: #763
-#573 := [unit-resolution #572 #590]: #800
-#550 := (not #680)
-#551 := (iff #763 #550)
-#546 := (iff #840 #680)
-#574 := (= #471 f3)
-#575 := [symm #565]: #574
-#576 := [monotonicity #575]: #566
-#545 := [monotonicity #576]: #543
-#537 := [symm #545]: #546
-#552 := [monotonicity #537]: #551
-#553 := [mp #590 #552]: #550
-#544 := [unit-resolution #554 #553]: #567
-#540 := [unit-resolution #538 #590]: #669
-#541 := [unit-resolution #540 #544]: #836
-#520 := [unit-resolution #784 #541]: #814
-#522 := [unit-resolution #776 #520 #573]: #857
-#529 := [unit-resolution #528 #522]: #769
-#532 := (or #530 #708 #608 #796 #531)
-#521 := [th-lemma arith assign-bounds 1 1 3 -3]: #532
-#533 := [unit-resolution #521 #544 #529 #585 #594]: #530
-#515 := [unit-resolution #517 #533 #592]: false
-#518 := [lemma #515]: #796
-#728 := (>= #19 0::Int)
-#621 := (>= #785 0::Int)
-#968 := (or false #621)
-#969 := [th-lemma arith]: #968
-#970 := [unit-resolution #969 #88]: #621
-#971 := (not #621)
-#972 := (or #728 #971 #931)
-#973 := [th-lemma arith assign-bounds 1 1]: #972
-#974 := [unit-resolution #973 #966 #970]: #728
-#975 := (not #728)
-#976 := (or #557 #975 #596)
-#977 := [th-lemma arith assign-bounds 1 3]: #976
-#978 := [unit-resolution #977 #974 #518]: #557
-#558 := (not #557)
-#880 := (or #558 #879)
-#115 := (= #30 #33)
-#140 := (or #115 #134)
-#893 := (forall (vars (?v0 Int)) (:pat #892) #140)
-#145 := (forall (vars (?v0 Int)) #140)
-#896 := (iff #145 #893)
-#894 := (iff #140 #140)
-#895 := [refl]: #894
-#897 := [quant-intro #895]: #896
-#322 := (~ #145 #145)
-#321 := (~ #140 #140)
-#318 := [refl]: #321
-#323 := [nnf-pos #318]: #322
-#34 := (= #33 #30)
-#31 := (<= 0::Int #30)
-#35 := (implies #31 #34)
-#36 := (forall (vars (?v0 Int)) #35)
-#148 := (iff #36 #145)
-#122 := (not #31)
-#123 := (or #122 #115)
-#128 := (forall (vars (?v0 Int)) #123)
-#146 := (iff #128 #145)
-#143 := (iff #123 #140)
-#137 := (or #134 #115)
-#141 := (iff #137 #140)
-#142 := [rewrite]: #141
-#138 := (iff #123 #137)
-#135 := (iff #122 #134)
-#131 := (iff #31 #133)
-#132 := [rewrite]: #131
-#136 := [monotonicity #132]: #135
-#139 := [monotonicity #136]: #138
-#144 := [trans #139 #142]: #143
-#147 := [quant-intro #144]: #146
-#129 := (iff #36 #128)
-#126 := (iff #35 #123)
-#119 := (implies #31 #115)
-#124 := (iff #119 #123)
-#125 := [rewrite]: #124
-#120 := (iff #35 #119)
-#117 := (iff #34 #115)
-#118 := [rewrite]: #117
-#121 := [monotonicity #118]: #120
-#127 := [trans #121 #125]: #126
-#130 := [quant-intro #127]: #129
-#149 := [trans #130 #147]: #148
-#114 := [asserted]: #36
-#150 := [mp #114 #149]: #145
-#319 := [mp~ #150 #323]: #145
-#898 := [mp #319 #897]: #893
-#884 := (not #893)
-#874 := (or #884 #558 #879)
-#559 := (or #562 #558)
-#534 := (or #884 #559)
-#523 := (iff #534 #874)
-#875 := (or #884 #880)
-#519 := (iff #875 #874)
-#860 := [rewrite]: #519
-#535 := (iff #534 #875)
-#883 := (iff #559 #880)
-#873 := (or #879 #558)
-#881 := (iff #873 #880)
-#882 := [rewrite]: #881
-#547 := (iff #559 #873)
-#536 := (iff #562 #879)
-#666 := [rewrite]: #536
-#548 := [monotonicity #666]: #547
-#878 := [trans #548 #882]: #883
-#876 := [monotonicity #878]: #535
-#524 := [trans #876 #860]: #523
-#539 := [quant-inst #94]: #534
-#525 := [mp #539 #524]: #874
-#979 := [unit-resolution #525 #898]: #880
-#980 := [unit-resolution #979 #978]: #879
-#981 := (not #879)
-#982 := (or #981 #526)
-#983 := [th-lemma arith triangle-eq]: #982
-#984 := [unit-resolution #983 #980]: #526
-#985 := (not #526)
-#986 := (or #495 #985)
-#987 := [th-lemma arith assign-bounds -1]: #986
-#988 := [unit-resolution #987 #984]: #495
-#482 := (>= #494 0::Int)
-#862 := (>= #877 0::Int)
-#989 := (or #981 #862)
-#990 := [th-lemma arith triangle-eq]: #989
-#991 := [unit-resolution #990 #980]: #862
-#992 := (not #862)
-#993 := (or #482 #992)
-#994 := [th-lemma arith assign-bounds -1]: #993
-#995 := [unit-resolution #994 #991]: #482
-#997 := (not #482)
-#996 := (not #495)
-#998 := (or #562 #996 #997)
-#999 := [th-lemma arith triangle-eq]: #998
-#1000 := [unit-resolution #999 #995 #988 #967]: false
-#1001 := [lemma #1000]: #840
-#1031 := [symm #1001]: #1030
-#1032 := (= #94 0::Int)
-#863 := (= #489 0::Int)
-#583 := (>= #489 0::Int)
-#487 := (or #763 #732)
-#662 := (or #701 #763 #732)
-#663 := [def-axiom]: #662
-#492 := [unit-resolution #663 #955]: #487
-#493 := [unit-resolution #492 #1001]: #732
-#673 := (not #732)
-#498 := (or #673 #728)
-#500 := [th-lemma arith triangle-eq]: #498
-#1002 := [unit-resolution #500 #493]: #728
-#1003 := [unit-resolution #977 #1002 #518]: #557
-#1004 := [unit-resolution #979 #1003]: #879
-#1005 := [unit-resolution #983 #1004]: #526
-#1006 := (or #583 #975 #985 #596)
-#1007 := [th-lemma arith assign-bounds 1 1 3]: #1006
-#1008 := [unit-resolution #1007 #1005 #518 #1002]: #583
-#582 := (<= #489 0::Int)
-#707 := (<= #19 0::Int)
-#1009 := (or #673 #707)
-#1010 := [th-lemma arith triangle-eq]: #1009
-#1011 := [unit-resolution #1010 #493]: #707
-#795 := (<= #15 0::Int)
-#1012 := [unit-resolution #580 #1001]: #847
-#1013 := (or #762 #795)
-#1014 := [th-lemma arith triangle-eq]: #1013
-#1015 := [unit-resolution #1014 #1012]: #795
-#1016 := [unit-resolution #990 #1004]: #862
-#1018 := (not #795)
-#1017 := (not #707)
-#1019 := (or #582 #1017 #992 #1018)
-#1020 := [th-lemma arith assign-bounds -1 1 -3]: #1019
-#1021 := [unit-resolution #1020 #1016 #1015 #1011]: #582
-#1023 := (not #583)
-#1022 := (not #582)
-#1024 := (or #863 #1022 #1023)
-#1025 := [th-lemma arith triangle-eq]: #1024
-#1026 := [unit-resolution #1025 #1021 #1008]: #863
-#1027 := [unit-resolution #987 #1005]: #495
-#1028 := [unit-resolution #994 #1016]: #482
-#1029 := [unit-resolution #999 #1028 #1027]: #562
-#1033 := [trans #1029 #1026]: #1032
-#1035 := [trans #1033 #1031]: #1034
-#1037 := [monotonicity #1035]: #1036
-#1039 := [symm #1037]: #1038
-#1040 := [trans #565 #1039]: #100
-[unit-resolution #108 #1040]: false
-unsat
-9fcb3a18989ceb011583d7488b7d67a1464c8b3d 76 0
+#262 := [monotonicity #259]: #261
+#265 := [quant-intro #262]: #264
+#55 := (div #53 #54)
+#56 := (if #51 #52 #55)
+#57 := (if #45 0::Int #56)
+#58 := (= #42 #57)
+#59 := (forall (vars (?v0 Int) (?v1 Int)) #58)
+#172 := (iff #59 #171)
+#169 := (iff #58 #168)
+#166 := (= #57 #165)
+#163 := (= #56 #162)
+#160 := (= #55 #159)
+#161 := [monotonicity #155 #158]: #160
+#164 := [monotonicity #151 #161]: #163
+#167 := [monotonicity #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [quant-intro #170]: #172
+#75 := [asserted]: #59
+#174 := [mp #75 #173]: #171
+#266 := [mp #174 #265]: #263
+#300 := [mp~ #266 #299]: #263
+#329 := [mp #300 #328]: #326
+#360 := [mp #329 #359]: #357
+#817 := [mp #360 #816]: #812
+#628 := (not #812)
+#629 := (or #628 #626)
+#484 := (div #761 #483)
+#758 := (* -1::Int #484)
+#762 := (+ #14 #758)
+#759 := (= #762 0::Int)
+#763 := (if #488 #760 #759)
+#776 := (or #431 #432)
+#473 := (if #776 #416 #763)
+#630 := (or #628 #473)
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+#726 := [rewrite]: #722
+#627 := (iff #473 #626)
+#609 := (iff #763 #724)
+#720 := (iff #759 #625)
+#575 := (= #762 #616)
+#614 := (= #758 #732)
+#731 := (= #484 #730)
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+#615 := [monotonicity #729]: #614
+#723 := [monotonicity #615]: #575
+#721 := [monotonicity #723]: #720
+#624 := [monotonicity #573 #721]: #609
+#756 := (iff #776 #431)
+#476 := (or #431 false)
+#470 := (iff #476 #431)
+#752 := [rewrite]: #470
+#754 := (iff #776 #476)
+#755 := [monotonicity #475]: #754
+#753 := [trans #755 #752]: #756
+#620 := [monotonicity #753 #624]: #627
+#725 := [monotonicity #620]: #632
+#713 := [trans #725 #726]: #632
+#631 := [quant-inst #11 #13]: #630
+#715 := [mp #631 #713]: #629
+#531 := [unit-resolution #715 #817]: #626
+#694 := (not #626)
+#695 := (or #694 #691 #416)
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+#515 := [unit-resolution #675 #531]: #513
+#516 := [unit-resolution #515 #528]: #691
+#517 := (or #431 #724)
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+#519 := [unit-resolution #518 #516]: #724
+#600 := (f9 f10 #377)
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+#503 := (iff #691 #526)
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+#521 := (= #600 #11)
+#462 := (= #377 f3)
+#23 := (:var 0 S2)
+#24 := (f9 f10 #23)
+#791 := (pattern #24)
+#25 := (f4 f5 #24)
+#26 := (= #25 #23)
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+#27 := (forall (vars (?v0 S2)) #26)
+#795 := (iff #27 #792)
+#793 := (iff #26 #26)
+#794 := [refl]: #793
+#796 := [quant-intro #794]: #795
+#291 := (~ #27 #27)
+#289 := (~ #26 #26)
+#290 := [refl]: #289
+#292 := [nnf-pos #290]: #291
+#72 := [asserted]: #27
+#283 := [mp~ #72 #292]: #27
+#797 := [mp #283 #796]: #792
+#455 := (not #792)
+#466 := (or #455 #462)
+#467 := [quant-inst #7]: #466
+#520 := [unit-resolution #467 #797]: #462
+#522 := [monotonicity #520]: #521
+#524 := [monotonicity #522]: #523
+#514 := [symm #524]: #525
+#505 := [monotonicity #514]: #503
+#506 := [mp #516 #505]: #526
+#602 := (or #764 #601)
+#31 := (f4 f5 #29)
+#798 := (pattern #31)
+#32 := (f9 f10 #31)
+#37 := (= #32 0::Int)
+#222 := (>= #29 0::Int)
+#235 := (or #222 #37)
+#805 := (forall (vars (?v0 Int)) (:pat #798) #235)
+#238 := (forall (vars (?v0 Int)) #235)
+#808 := (iff #238 #805)
+#806 := (iff #235 #235)
+#807 := [refl]: #806
+#809 := [quant-intro #807]: #808
+#293 := (~ #238 #238)
+#220 := (~ #235 #235)
+#221 := [refl]: #220
+#294 := [nnf-pos #221]: #293
+#30 := (<= 0::Int #29)
+#117 := (or #30 #37)
+#122 := (forall (vars (?v0 Int)) #117)
+#239 := (iff #122 #238)
+#236 := (iff #117 #235)
+#223 := (iff #30 #222)
+#224 := [rewrite]: #223
+#237 := [monotonicity #224]: #236
+#240 := [quant-intro #237]: #239
+#36 := (< #29 0::Int)
+#38 := (implies #36 #37)
+#39 := (forall (vars (?v0 Int)) #38)
+#123 := (iff #39 #122)
+#120 := (iff #38 #117)
+#100 := (not #30)
+#114 := (implies #100 #37)
+#118 := (iff #114 #117)
+#119 := [rewrite]: #118
+#115 := (iff #38 #114)
+#109 := (iff #36 #100)
+#111 := (iff #100 #100)
+#96 := (iff #30 #30)
+#97 := [rewrite]: #96
+#112 := [monotonicity #97]: #111
+#110 := [rewrite]: #109
+#113 := [trans #110 #112]: #109
+#116 := [monotonicity #113]: #115
+#121 := [trans #116 #119]: #120
+#124 := [quant-intro #121]: #123
+#74 := [asserted]: #39
+#125 := [mp #74 #124]: #122
+#241 := [mp #125 #240]: #238
+#295 := [mp~ #241 #294]: #238
+#810 := [mp #295 #809]: #805
+#768 := (not #805)
+#605 := (or #768 #764 #601)
+#606 := (or #768 #602)
+#607 := (iff #606 #605)
+#568 := [rewrite]: #607
+#591 := [quant-inst #11]: #606
+#569 := [mp #591 #568]: #605
+#507 := [unit-resolution #569 #810]: #602
+#508 := [unit-resolution #507 #506]: #764
+#509 := (or #431 #751 #740)
+#510 := [th-lemma arith triangle-eq]: #509
+#511 := [unit-resolution #510 #516]: #742
+#504 := [unit-resolution #511 #508]: #751
+#706 := (or #742 #417)
+#716 := [def-axiom]: #706
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+#697 := (not #724)
+#699 := (or #697 #714 #760)
+#700 := [def-axiom]: #699
+#497 := [unit-resolution #700 #512 #519]: #760
+#698 := (not #760)
+#498 := (or #698 #711)
+#499 := [th-lemma arith triangle-eq]: #498
+#501 := [unit-resolution #499 #497]: #711
+#502 := (not #711)
+#491 := (or #500 #740 #545 #704 #502)
+#492 := [th-lemma arith assign-bounds 1 1 3 -3]: #491
+#493 := [unit-resolution #492 #508 #501 #527 #540]: #500
+#485 := (not #584)
+#494 := (or #485 #588)
+#495 := [th-lemma arith triangle-eq]: #494
+#486 := [unit-resolution #495 #493 #536]: false
+#496 := [lemma #486]: #704
+#572 := (* -1::Int #468)
+#779 := (+ #80 #18 #572)
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+#442 := (= #779 0::Int)
+#463 := (>= #83 0::Int)
+#565 := (not #636)
+#408 := (or #463 #541 #565)
+#563 := [th-lemma arith assign-bounds 3 -1]: #408
+#458 := [unit-resolution #563 #839 #496]: #463
+#464 := (not #463)
+#783 := (or #464 #442)
+#33 := (= #32 #29)
+#225 := (not #222)
+#228 := (or #225 #33)
+#799 := (forall (vars (?v0 Int)) (:pat #798) #228)
+#231 := (forall (vars (?v0 Int)) #228)
+#802 := (iff #231 #799)
+#800 := (iff #228 #228)
+#801 := [refl]: #800
+#803 := [quant-intro #801]: #802
+#288 := (~ #231 #231)
+#284 := (~ #228 #228)
+#287 := [refl]: #284
+#285 := [nnf-pos #287]: #288
+#101 := (or #100 #33)
+#105 := (forall (vars (?v0 Int)) #101)
+#232 := (iff #105 #231)
+#229 := (iff #101 #228)
+#226 := (iff #100 #225)
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [quant-intro #230]: #232
+#34 := (implies #30 #33)
+#35 := (forall (vars (?v0 Int)) #34)
+#106 := (iff #35 #105)
+#102 := (iff #34 #101)
+#103 := [rewrite]: #102
+#98 := (iff #34 #34)
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+#104 := [trans #99 #103]: #102
+#107 := [quant-intro #104]: #106
+#73 := [asserted]: #35
+#108 := [mp #73 #107]: #105
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+#804 := [mp #286 #803]: #799
+#786 := (not #799)
+#787 := (or #786 #464 #442)
+#465 := (= #468 #83)
+#469 := (or #464 #465)
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+#781 := (iff #788 #787)
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+#440 := (iff #784 #787)
+#445 := [rewrite]: #440
+#790 := (iff #788 #784)
+#453 := (iff #469 #783)
+#785 := (iff #465 #442)
+#448 := [rewrite]: #785
+#454 := [monotonicity #448]: #453
+#780 := [monotonicity #454]: #790
+#441 := [trans #780 #445]: #781
+#789 := [quant-inst #83]: #788
+#782 := [mp #789 #441]: #787
+#387 := [unit-resolution #782 #804]: #783
+#844 := [unit-resolution #387 #458]: #442
+#385 := (not #442)
+#388 := (or #385 #425)
+#389 := [th-lemma arith triangle-eq]: #388
+#858 := [unit-resolution #389 #844]: #425
+#386 := (not #425)
+#860 := (or #774 #541 #565 #386)
+#845 := [th-lemma arith assign-bounds 3 -1 1]: #860
+#846 := [unit-resolution #845 #858 #496 #839]: #774
+#411 := (<= #468 0::Int)
+#581 := (<= #18 0::Int)
+#847 := (or #595 #581)
+#848 := [th-lemma arith triangle-eq]: #847
+#849 := [unit-resolution #848 #850]: #581
+#707 := (<= #14 0::Int)
+#852 := [unit-resolution #515 #859]: #416
+#853 := (or #679 #707)
+#854 := [th-lemma arith triangle-eq]: #853
+#855 := [unit-resolution #854 #852]: #707
+#766 := (>= #779 0::Int)
+#381 := (or #385 #766)
+#379 := [th-lemma arith triangle-eq]: #381
+#842 := [unit-resolution #379 #844]: #766
+#825 := (not #766)
+#881 := (not #581)
+#843 := (not #707)
+#882 := (or #411 #843 #881 #825)
+#883 := [th-lemma arith assign-bounds -3 -1 1]: #882
+#884 := [unit-resolution #883 #842 #855 #849]: #411
+#856 := (not #774)
+#885 := (not #411)
+#857 := (or #429 #885 #856)
+#890 := [th-lemma arith triangle-eq]: #857
+#891 := [unit-resolution #890 #884 #846]: #429
+#482 := (= #83 #468)
+#449 := (+ #83 #572)
+#459 := (<= #449 0::Int)
+#391 := (or #459 #386)
+#378 := [th-lemma arith assign-bounds -1]: #391
+#892 := [unit-resolution #378 #858]: #459
+#460 := (>= #449 0::Int)
+#826 := (or #460 #825)
+#827 := [th-lemma arith assign-bounds -1]: #826
+#893 := [unit-resolution #827 #842]: #460
+#830 := (not #460)
+#829 := (not #459)
+#831 := (or #482 #829 #830)
+#832 := [th-lemma arith triangle-eq]: #831
+#894 := [unit-resolution #832 #893 #892]: #482
+#898 := [trans #894 #891]: #897
+#900 := [trans #898 #896]: #899
+#902 := [monotonicity #900]: #901
+#904 := [symm #902]: #903
+#409 := (= f3 #377)
+#405 := [symm #520]: #409
+#905 := [trans #405 #904]: #89
+#92 := (not #89)
+#15 := (* #14 3::Int)
+#19 := (+ #15 #18)
+#20 := (f4 f5 #19)
+#21 := (= f3 #20)
+#22 := (not #21)
+#93 := (iff #22 #92)
+#90 := (iff #21 #89)
+#87 := (= #20 #86)
+#84 := (= #19 #83)
+#81 := (= #15 #80)
+#82 := [rewrite]: #81
+#85 := [monotonicity #82]: #84
+#88 := [monotonicity #85]: #87
+#91 := [monotonicity #88]: #90
+#94 := [monotonicity #91]: #93
+#71 := [asserted]: #22
+#95 := [mp #71 #94]: #92
+#906 := [unit-resolution #95 #905]: false
+#907 := [lemma #906]: #691
+#835 := (or #431 #714)
+#710 := (<= #383 0::Int)
+#603 := [hypothesis]: #742
+#604 := [hypothesis]: #691
+#576 := [unit-resolution #518 #604]: #724
+#583 := [unit-resolution #700 #576 #603]: #760
+#582 := (or #698 #710)
+#578 := [th-lemma arith triangle-eq]: #582
+#579 := [unit-resolution #578 #583]: #710
+#617 := (<= #687 0::Int)
+#567 := (or #431 #661)
+#589 := (or #633 #431 #661)
+#590 := [def-axiom]: #589
+#546 := [unit-resolution #590 #580]: #567
+#566 := [unit-resolution #546 #604]: #661
+#643 := (not #661)
+#611 := (or #643 #714 #677)
+#618 := [def-axiom]: #611
+#562 := [unit-resolution #618 #566 #603]: #677
+#610 := (not #677)
+#549 := (or #610 #617)
+#553 := [th-lemma arith triangle-eq]: #549
+#555 := [unit-resolution #553 #562]: #617
+#556 := [unit-resolution #499 #583]: #711
+#641 := (>= #687 0::Int)
+#554 := (or #610 #641)
+#557 := [th-lemma arith triangle-eq]: #554
+#550 := [unit-resolution #557 #562]: #641
+#559 := (>= #709 0::Int)
+#551 := (or false #559)
+#547 := [th-lemma arith]: #551
+#552 := [unit-resolution #547 #219]: #559
+#414 := (not #641)
+#587 := (not #559)
+#570 := (or #636 #587 #414)
+#560 := [th-lemma arith assign-bounds 1 1]: #570
+#561 := [unit-resolution #560 #550 #552]: #636
+#564 := [unit-resolution #563 #561 #496]: #463
+#384 := [unit-resolution #387 #564]: #442
+#390 := [unit-resolution #389 #384]: #425
+#380 := [unit-resolution #378 #390]: #459
+#382 := [unit-resolution #379 #384]: #766
+#828 := [unit-resolution #827 #382]: #460
+#833 := [unit-resolution #832 #828 #380]: #482
+#427 := (not #710)
+#439 := (not #617)
+#402 := (not #482)
+#394 := (or #402 #414 #502 #439 #427)
+#477 := (f4 f5 #468)
+#478 := (= #477 #86)
+#480 := (or #455 #478)
+#481 := [quant-inst #86]: #480
+#426 := [unit-resolution #481 #797]: #478
+#396 := (= f3 #477)
+#410 := (= #377 #477)
+#406 := (= #11 #468)
+#428 := [hypothesis]: #482
+#450 := (= #11 #83)
+#461 := (* -1::Int #83)
+#444 := (+ #11 #461)
+#447 := (>= #444 0::Int)
+#433 := [hypothesis]: #710
+#558 := (>= #586 0::Int)
+#434 := (or #485 #558)
+#435 := [th-lemma arith triangle-eq]: #434
+#436 := [unit-resolution #435 #536]: #558
+#437 := [hypothesis]: #617
+#438 := (not #558)
+#420 := (or #447 #438 #427 #439)
+#422 := [th-lemma arith assign-bounds -1 3 1]: #420
+#423 := [unit-resolution #422 #437 #436 #433]: #447
+#446 := (<= #444 0::Int)
+#421 := [hypothesis]: #711
+#424 := [unit-resolution #495 #536]: #588
+#412 := [hypothesis]: #641
+#415 := (or #446 #500 #502 #414)
+#418 := [th-lemma arith assign-bounds -1 3 1]: #415
+#413 := [unit-resolution #418 #412 #424 #421]: #446
+#393 := (not #447)
+#419 := (not #446)
+#398 := (or #450 #419 #393)
+#399 := [th-lemma arith triangle-eq]: #398
+#404 := [unit-resolution #399 #413 #423]: #450
+#407 := [trans #404 #428]: #406
+#392 := [monotonicity #407]: #410
+#397 := [trans #405 #392]: #396
+#400 := [trans #397 #426]: #89
+#401 := [unit-resolution #95 #400]: false
+#403 := [lemma #401]: #394
+#834 := [unit-resolution #403 #833 #550 #556 #555 #579]: false
+#836 := [lemma #834]: #835
+#908 := [unit-resolution #836 #907]: #714
+#888 := (or #431 #740)
+#886 := [hypothesis]: #764
+#542 := [hypothesis]: #751
+#532 := [unit-resolution #716 #542]: #742
+#534 := [unit-resolution #836 #532]: #431
+#535 := (or #691 #417)
+#538 := [th-lemma arith triangle-eq]: #535
+#452 := [unit-resolution #538 #534 #542]: false
+#443 := [lemma #452]: #417
+#887 := [unit-resolution #510 #604 #443 #886]: false
+#889 := [lemma #887]: #888
+#909 := [unit-resolution #889 #907]: #740
+#717 := (or #742 #764)
+#718 := [def-axiom]: #717
+[unit-resolution #718 #909 #908]: false
+810a5a888a26e956d3d96c0f529162bda0f4210f 76 0
+unsat
+#2 := false
+#23 := 0::Int
+decl f3 :: (-> S2 S3 Int)
+decl f6 :: S3
+#10 := f6
+decl f5 :: S3
+#8 := f5
+decl f4 :: S2
+#7 := f4
+#11 := (f3 f4 f6)
+#93 := -1::Int
+#94 := (* -1::Int #11)
+#9 := (f3 f4 f5)
+#95 := (+ #9 #94)
+#96 := (<= #95 0::Int)
+#99 := (if #96 f5 f6)
+#102 := (f3 f4 #99)
+#110 := (* -1::Int #102)
+#539 := (+ #11 #110)
+#250 := (>= #539 0::Int)
+#535 := (= #11 #102)
+#238 := (= f6 #99)
+#153 := (not #96)
+#152 := (= f5 #99)
+#534 := (not #152)
+#550 := (= #9 #102)
+#537 := [hypothesis]: #152
+#259 := [monotonicity #537]: #550
+#263 := (not #550)
+#111 := (+ #9 #110)
+#109 := (>= #111 0::Int)
+#115 := (not #109)
+#12 := (<= #9 #11)
+#13 := (if #12 f5 f6)
+#14 := (f3 f4 #13)
+#15 := (<= #14 #9)
+#16 := (not #15)
+#116 := (iff #16 #115)
+#113 := (iff #15 #109)
+#105 := (<= #102 #9)
+#108 := (iff #105 #109)
+#112 := [rewrite]: #108
+#106 := (iff #15 #105)
+#103 := (= #14 #102)
+#100 := (= #13 #99)
+#97 := (iff #12 #96)
+#98 := [rewrite]: #97
+#101 := [monotonicity #98]: #100
+#104 := [monotonicity #101]: #103
+#107 := [monotonicity #104]: #106
+#114 := [trans #107 #112]: #113
+#117 := [monotonicity #114]: #116
+#36 := [asserted]: #16
+#118 := [mp #36 #117]: #115
+#264 := (or #263 #109)
+#265 := [th-lemma arith triangle-eq]: #264
+#536 := [unit-resolution #265 #118]: #263
+#260 := [unit-resolution #536 #259]: false
+#538 := [lemma #260]: #534
+#239 := (or #153 #152)
+#240 := [def-axiom]: #239
+#251 := [unit-resolution #240 #538]: #153
+#231 := (or #96 #238)
+#242 := [def-axiom]: #231
+#252 := [unit-resolution #242 #251]: #238
+#530 := [monotonicity #252]: #535
+#531 := (not #535)
+#246 := (or #531 #250)
+#528 := [th-lemma arith triangle-eq]: #246
+#532 := [unit-resolution #528 #530]: #250
+#552 := (<= #111 0::Int)
+#529 := (or #552 #109)
+#533 := [th-lemma arith farkas 1 1]: #529
+#522 := [unit-resolution #533 #118]: #552
+[th-lemma arith farkas 1 1 1 #522 #251 #532]: false
+c764f14739302794beeeecf4b3e02d727d24560d 70 0
+unsat
+#2 := false
+decl f3 :: (-> S2 S3 Int)
+decl f6 :: S3
+#10 := f6
+decl f5 :: S3
+#8 := f5
+#23 := 0::Int
+decl f4 :: S2
+#7 := f4
+#11 := (f3 f4 f6)
+#93 := -1::Int
+#94 := (* -1::Int #11)
+#9 := (f3 f4 f5)
+#95 := (+ #9 #94)
+#96 := (<= #95 0::Int)
+#99 := (if #96 f5 f6)
+#102 := (f3 f4 #99)
+#541 := (= #11 #102)
+#238 := (= f6 #99)
+#153 := (not #96)
+#264 := [hypothesis]: #96
+#109 := (* -1::Int #102)
+#110 := (+ #11 #109)
+#108 := (>= #110 0::Int)
+#115 := (not #108)
+#12 := (<= #9 #11)
+#13 := (if #12 f5 f6)
+#14 := (f3 f4 #13)
+#15 := (<= #14 #11)
+#16 := (not #15)
+#116 := (iff #16 #115)
+#113 := (iff #15 #108)
+#105 := (<= #102 #11)
+#111 := (iff #105 #108)
+#112 := [rewrite]: #111
+#106 := (iff #15 #105)
+#103 := (= #14 #102)
+#100 := (= #13 #99)
+#97 := (iff #12 #96)
+#98 := [rewrite]: #97
+#101 := [monotonicity #98]: #100
+#104 := [monotonicity #101]: #103
+#107 := [monotonicity #104]: #106
+#114 := [trans #107 #112]: #113
+#117 := [monotonicity #114]: #116
+#36 := [asserted]: #16
+#118 := [mp #36 #117]: #115
+#552 := (+ #9 #109)
+#263 := (>= #552 0::Int)
+#550 := (= #9 #102)
+#152 := (= f5 #99)
+#239 := (or #153 #152)
+#240 := [def-axiom]: #239
+#265 := [unit-resolution #240 #264]: #152
+#266 := [monotonicity #265]: #550
+#159 := (not #550)
+#536 := (or #159 #263)
+#537 := [th-lemma arith triangle-eq]: #536
+#259 := [unit-resolution #537 #266]: #263
+#260 := [th-lemma arith farkas -1 1 1 #259 #118 #264]: false
+#534 := [lemma #260]: #153
+#231 := (or #96 #238)
+#242 := [def-axiom]: #231
+#535 := [unit-resolution #242 #534]: #238
+#539 := [monotonicity #535]: #541
+#249 := (not #541)
+#250 := (or #249 #108)
+#251 := [th-lemma arith triangle-eq]: #250
+[unit-resolution #251 #118 #539]: false
+70478f198d5c721b2266791e6619f9347bb3a4b8 247 0
+unsat
 #2 := false
 #24 := 0::Int
 decl f3 :: (-> S2 S3 Int)
+decl f5 :: S3
+#8 := f5
+decl f4 :: S2
+#7 := f4
+#9 := (f3 f4 f5)
+#505 := (= #9 0::Int)
+decl f7 :: (-> S4 Int S3)
+decl f8 :: S4
+#18 := f8
+#244 := (f7 f8 #9)
+#563 := (f3 f4 #244)
+#566 := (= #563 0::Int)
+#231 := (>= #9 0::Int)
+#405 := (not #231)
 decl f6 :: S3
-#11 := f6
-decl f5 :: S3
-#9 := f5
-decl f4 :: S2
-#8 := f4
-#12 := (f3 f4 f6)
-#58 := -1::Int
-#59 := (* -1::Int #12)
-#10 := (f3 f4 f5)
-#60 := (+ #10 #59)
-#61 := (<= #60 0::Int)
-#64 := (ite #61 f5 f6)
-#67 := (f3 f4 #64)
-#75 := (* -1::Int #67)
-#607 := (+ #12 #75)
-#613 := (>= #607 0::Int)
-#612 := (= #12 #67)
-#326 := (= f6 #64)
-#241 := (not #61)
-#240 := (= f5 #64)
-#610 := (not #240)
-#625 := (= #10 #67)
-#620 := [hypothesis]: #240
-#617 := [monotonicity #620]: #625
-#339 := (not #625)
-#76 := (+ #10 #75)
-#74 := (>= #76 0::Int)
-#80 := (not #74)
-#13 := (<= #10 #12)
-#14 := (ite #13 f5 f6)
-#15 := (f3 f4 #14)
-#16 := (<= #15 #10)
+#10 := f6
+#11 := (f3 f4 f6)
+#94 := -1::Int
+#95 := (* -1::Int #11)
+#96 := (+ #9 #95)
+#97 := (<= #96 0::Int)
+#100 := (if #97 f5 f6)
+#103 := (f3 f4 #100)
+#111 := (* -1::Int #103)
+#112 := (+ #9 #11 #111)
+#110 := (>= #112 0::Int)
+#116 := (not #110)
+#15 := (+ #9 #11)
+#12 := (<= #9 #11)
+#13 := (if #12 f5 f6)
+#14 := (f3 f4 #13)
+#16 := (<= #14 #15)
 #17 := (not #16)
-#81 := (iff #17 #80)
-#78 := (iff #16 #74)
-#70 := (<= #67 #10)
-#73 := (iff #70 #74)
-#77 := [rewrite]: #73
-#71 := (iff #16 #70)
-#68 := (= #15 #67)
-#65 := (= #14 #64)
-#62 := (iff #13 #61)
+#117 := (iff #17 #116)
+#114 := (iff #16 #110)
+#106 := (<= #103 #15)
+#109 := (iff #106 #110)
+#113 := [rewrite]: #109
+#107 := (iff #16 #106)
+#104 := (= #14 #103)
+#101 := (= #13 #100)
+#98 := (iff #12 #97)
+#99 := [rewrite]: #98
+#102 := [monotonicity #99]: #101
+#105 := [monotonicity #102]: #104
+#108 := [monotonicity #105]: #107
+#115 := [trans #108 #113]: #114
+#118 := [monotonicity #115]: #117
+#37 := [asserted]: #17
+#119 := [mp #37 #118]: #116
+#542 := (+ #11 #111)
+#507 := (>= #542 0::Int)
+#511 := (= #11 #103)
+#239 := (= f6 #100)
+#219 := (f7 f8 #103)
+#349 := (= #219 #100)
+#19 := (:var 0 S3)
+#20 := (f3 f4 #19)
+#568 := (pattern #20)
+#21 := (f7 f8 #20)
+#22 := (= #21 #19)
+#569 := (forall (vars (?v0 S3)) (:pat #568) #22)
+#23 := (forall (vars (?v0 S3)) #22)
+#572 := (iff #23 #569)
+#570 := (iff #22 #22)
+#571 := [refl]: #570
+#573 := [quant-intro #571]: #572
+#92 := (~ #23 #23)
+#142 := (~ #22 #22)
+#143 := [refl]: #142
+#93 := [nnf-pos #143]: #92
+#38 := [asserted]: #23
+#146 := [mp~ #38 #93]: #23
+#574 := [mp #146 #573]: #569
+#225 := (not #569)
+#564 := (or #225 #349)
+#565 := [quant-inst #100]: #564
+#267 := [unit-resolution #565 #574]: #349
+#519 := (= f6 #219)
+#242 := (f7 f8 #11)
+#518 := (= #242 #219)
+#209 := (f3 f4 #219)
+#371 := (= #209 #103)
+#522 := (= #103 #209)
+#532 := (= #100 #219)
+#247 := [symm #267]: #532
+#528 := [monotonicity #247]: #522
+#513 := [symm #528]: #371
+#516 := (= #11 #209)
+#369 := (= 0::Int #209)
+#550 := (= #209 0::Int)
+#208 := (>= #103 0::Int)
+#536 := (not #208)
+#553 := (+ #9 #111)
+#264 := (>= #553 0::Int)
+#551 := (= #9 #103)
+#153 := (= f5 #100)
+#265 := (not #239)
+#266 := [hypothesis]: #265
+#232 := (or #97 #239)
+#243 := [def-axiom]: #232
+#160 := [unit-resolution #243 #266]: #97
+#154 := (not #97)
+#240 := (or #154 #153)
+#241 := [def-axiom]: #240
+#537 := [unit-resolution #241 #160]: #153
+#538 := [monotonicity #537]: #551
+#260 := (not #551)
+#261 := (or #260 #264)
+#535 := [th-lemma arith triangle-eq]: #261
+#539 := [unit-resolution #535 #538]: #264
+#540 := (not #264)
+#250 := (or #536 #540 #154 #110)
+#251 := [th-lemma arith assign-bounds 2 -1 -1]: #250
+#252 := [unit-resolution #251 #160 #119 #539]: #536
+#188 := (or #208 #550)
+#25 := (:var 0 Int)
+#27 := (f7 f8 #25)
+#575 := (pattern #27)
+#28 := (f3 f4 #27)
+#33 := (= #28 0::Int)
+#121 := (>= #25 0::Int)
+#133 := (or #121 #33)
+#582 := (forall (vars (?v0 Int)) (:pat #575) #133)
+#136 := (forall (vars (?v0 Int)) #133)
+#585 := (iff #136 #582)
+#583 := (iff #133 #133)
+#584 := [refl]: #583
+#586 := [quant-intro #584]: #585
+#150 := (~ #136 #136)
+#148 := (~ #133 #133)
+#149 := [refl]: #148
+#151 := [nnf-pos #149]: #150
+#26 := (<= 0::Int #25)
+#65 := (or #26 #33)
+#70 := (forall (vars (?v0 Int)) #65)
+#137 := (iff #70 #136)
+#134 := (iff #65 #133)
+#120 := (iff #26 #121)
+#122 := [rewrite]: #120
+#135 := [monotonicity #122]: #134
+#138 := [quant-intro #135]: #137
+#32 := (< #25 0::Int)
+#34 := (implies #32 #33)
+#35 := (forall (vars (?v0 Int)) #34)
+#71 := (iff #35 #70)
+#68 := (iff #34 #65)
+#48 := (not #26)
+#62 := (implies #48 #33)
+#66 := (iff #62 #65)
+#67 := [rewrite]: #66
+#63 := (iff #34 #62)
+#57 := (iff #32 #48)
+#59 := (iff #48 #48)
+#44 := (iff #26 #26)
+#45 := [rewrite]: #44
+#60 := [monotonicity #45]: #59
+#58 := [rewrite]: #57
+#61 := [trans #58 #60]: #57
+#64 := [monotonicity #61]: #63
+#69 := [trans #64 #67]: #68
+#72 := [quant-intro #69]: #71
+#40 := [asserted]: #35
+#73 := [mp #40 #72]: #70
+#139 := [mp #73 #138]: #136
+#152 := [mp~ #139 #151]: #136
+#587 := [mp #152 #586]: #582
+#217 := (not #582)
+#193 := (or #217 #208 #550)
+#194 := (or #217 #188)
+#552 := (iff #194 #193)
+#555 := [rewrite]: #552
+#554 := [quant-inst #103]: #194
+#541 := [mp #554 #555]: #193
+#253 := [unit-resolution #541 #587]: #188
+#531 := [unit-resolution #253 #252]: #550
+#370 := [symm #531]: #369
+#514 := (= #11 0::Int)
+#557 := (f3 f4 #242)
+#206 := (= #557 0::Int)
+#567 := (>= #11 0::Int)
+#529 := (not #567)
+#533 := (or #529 #540 #110)
+#530 := [th-lemma arith assign-bounds 1 -1]: #533
+#534 := [unit-resolution #530 #539 #119]: #529
+#207 := (or #567 #206)
+#545 := (or #217 #567 #206)
+#546 := (or #217 #207)
+#548 := (iff #546 #545)
+#549 := [rewrite]: #548
+#547 := [quant-inst #11]: #546
+#544 := [mp #547 #549]: #545
+#523 := [unit-resolution #544 #587]: #207
+#524 := [unit-resolution #523 #534]: #206
+#526 := (= #11 #557)
+#520 := (= f6 #242)
+#246 := (= #242 f6)
+#556 := (or #225 #246)
+#230 := [quant-inst #10]: #556
+#525 := [unit-resolution #230 #574]: #246
+#521 := [symm #525]: #520
+#527 := [monotonicity #521]: #526
+#515 := [trans #527 #524]: #514
+#510 := [trans #515 #370]: #516
+#517 := [trans #510 #513]: #511
+#512 := [monotonicity #517]: #518
+#348 := [trans #521 #512]: #519
+#350 := [trans #348 #267]: #239
+#351 := [unit-resolution #266 #350]: false
+#504 := [lemma #351]: #239
+#508 := [monotonicity #504]: #511
+#497 := (not #507)
+#498 := [hypothesis]: #497
+#501 := (not #511)
+#386 := (or #501 #507)
+#401 := [th-lemma arith triangle-eq]: #386
+#403 := [unit-resolution #401 #498 #508]: false
+#404 := [lemma #403]: #507
+#406 := (or #405 #497 #110)
+#407 := [th-lemma arith assign-bounds 1 -1]: #406
+#408 := [unit-resolution #407 #404 #119]: #405
+#561 := (or #231 #566)
+#222 := (or #217 #231 #566)
+#558 := (or #217 #561)
+#559 := (iff #558 #222)
+#202 := [rewrite]: #559
+#218 := [quant-inst #9]: #558
+#543 := [mp #218 #202]: #222
+#409 := [unit-resolution #543 #587]: #561
+#502 := [unit-resolution #409 #408]: #566
+#492 := (= #9 #563)
+#503 := (= f5 #244)
+#245 := (= #244 f5)
+#560 := (or #225 #245)
+#562 := [quant-inst #8]: #560
+#499 := [unit-resolution #562 #574]: #245
+#490 := [symm #499]: #503
+#484 := [monotonicity #490]: #492
+#481 := [trans #484 #502]: #505
+#483 := (not #505)
+#493 := (or #483 #231)
+#494 := [th-lemma arith triangle-eq]: #493
+[unit-resolution #494 #408 #481]: false
+989cfc1345d635e466325cf81719187753d0ea0c 134 0
+unsat
+#2 := false
+decl f3 :: (-> S2 S3 Int)
+decl f7 :: S3
+#13 := f7
+decl f6 :: S3
+#10 := f6
+#29 := 0::Int
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 f7)
+#131 := -1::Int
+#163 := (* -1::Int #14)
+#11 := (f3 f4 f6)
+#170 := (+ #11 #163)
+#171 := (<= #170 0::Int)
+#174 := (if #171 f6 f7)
+#177 := (f3 f4 #174)
+#565 := (= #14 #177)
+#290 := (= f7 #174)
+#205 := (not #171)
+#204 := (= f6 #174)
+#422 := (not #204)
+#588 := (= #11 #177)
+#579 := [hypothesis]: #204
+#420 := [monotonicity #579]: #588
+#576 := (not #588)
+#185 := (* -1::Int #177)
+#589 := (+ #11 #185)
+#301 := (<= #589 0::Int)
+#582 := (not #301)
+decl f5 :: S3
+#8 := f5
+#9 := (f3 f4 f5)
+#186 := (+ #9 #185)
+#184 := (>= #186 0::Int)
+#17 := (<= #11 #14)
+#18 := (if #17 f6 f7)
+#19 := (f3 f4 #18)
+#60 := (<= #19 #9)
+#188 := (iff #60 #184)
+#180 := (<= #177 #9)
+#183 := (iff #180 #184)
+#187 := [rewrite]: #183
+#181 := (iff #60 #180)
+#178 := (= #19 #177)
+#175 := (= #18 #174)
+#172 := (iff #17 #171)
+#173 := [rewrite]: #172
+#176 := [monotonicity #173]: #175
+#179 := [monotonicity #176]: #178
+#182 := [monotonicity #179]: #181
+#189 := [trans #182 #187]: #188
+#61 := (not #60)
+#53 := (<= #14 #9)
+#54 := (not #53)
+#49 := (<= #11 #9)
+#50 := (not #49)
+#57 := (and #50 #54)
+#67 := (not #57)
+#68 := (or #67 #61)
+#73 := (not #68)
+#20 := (< #9 #19)
+#15 := (< #9 #14)
+#12 := (< #9 #11)
+#16 := (and #12 #15)
+#21 := (implies #16 #20)
+#22 := (not #21)
+#74 := (iff #22 #73)
+#71 := (iff #21 #68)
+#64 := (implies #57 #61)
+#69 := (iff #64 #68)
+#70 := [rewrite]: #69
+#65 := (iff #21 #64)
+#62 := (iff #20 #61)
 #63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#79 := [trans #72 #77]: #78
-#82 := [monotonicity #79]: #81
-#55 := [asserted]: #17
-#83 := [mp #55 #82]: #80
-#340 := (or #339 #74)
-#618 := [th-lemma arith triangle-eq]: #340
-#616 := [unit-resolution #618 #83]: #339
-#621 := [unit-resolution #616 #617]: false
-#611 := [lemma #621]: #610
-#327 := (or #241 #240)
-#328 := [def-axiom]: #327
-#614 := [unit-resolution #328 #611]: #241
-#319 := (or #61 #326)
-#330 := [def-axiom]: #319
-#609 := [unit-resolution #330 #614]: #326
-#615 := [monotonicity #609]: #612
-#456 := (not #612)
-#457 := (or #456 #613)
-#458 := [th-lemma arith triangle-eq]: #457
-#600 := [unit-resolution #458 #615]: #613
-#347 := (<= #76 0::Int)
-#601 := (or #347 #74)
-#602 := [th-lemma arith farkas 1 1]: #601
-#603 := [unit-resolution #602 #83]: #347
-[th-lemma arith farkas 1 1 1 #603 #614 #600]: false
-unsat
-a449127c090f0317dd4d9ec8e341e46a848862fd 70 0
+#58 := (iff #16 #57)
+#55 := (iff #15 #54)
+#56 := [rewrite]: #55
+#51 := (iff #12 #50)
+#52 := [rewrite]: #51
+#59 := [monotonicity #52 #56]: #58
+#66 := [monotonicity #59 #63]: #65
+#72 := [trans #66 #70]: #71
+#75 := [monotonicity #72]: #74
+#42 := [asserted]: #22
+#76 := [mp #42 #75]: #73
+#80 := [not-or-elim #76]: #60
+#190 := [mp #80 #189]: #184
+#134 := (* -1::Int #11)
+#135 := (+ #9 #134)
+#133 := (>= #135 0::Int)
+#137 := (not #133)
+#138 := (iff #50 #137)
+#132 := (iff #49 #133)
+#136 := [rewrite]: #132
+#139 := [monotonicity #136]: #138
+#77 := [not-or-elim #76]: #57
+#78 := [and-elim #77]: #50
+#140 := [mp #78 #139]: #137
+#303 := [hypothesis]: #301
+#304 := [th-lemma arith farkas -1 -1 1 #303 #140 #190]: false
+#583 := [lemma #304]: #582
+#571 := (or #576 #301)
+#572 := [th-lemma arith triangle-eq]: #571
+#573 := [unit-resolution #572 #583]: #576
+#421 := [unit-resolution #573 #420]: false
+#564 := [lemma #421]: #422
+#291 := (or #205 #204)
+#292 := [def-axiom]: #291
+#567 := [unit-resolution #292 #564]: #205
+#283 := (or #171 #290)
+#294 := [def-axiom]: #283
+#561 := [unit-resolution #294 #567]: #290
+#562 := [monotonicity #561]: #565
+#302 := (+ #14 #185)
+#298 := (<= #302 0::Int)
+#585 := (not #298)
+#164 := (+ #9 #163)
+#162 := (>= #164 0::Int)
+#166 := (not #162)
+#167 := (iff #54 #166)
+#161 := (iff #53 #162)
+#165 := [rewrite]: #161
+#168 := [monotonicity #165]: #167
+#79 := [and-elim #77]: #54
+#169 := [mp #79 #168]: #166
+#584 := [hypothesis]: #298
+#581 := [th-lemma arith farkas -1 -1 1 #584 #169 #190]: false
+#574 := [lemma #581]: #585
+#568 := (not #565)
+#569 := (or #568 #298)
+#563 := [th-lemma arith triangle-eq]: #569
+[unit-resolution #563 #574 #562]: false
+369b4cfbe0601f80981c4727d0056934614954c0 151 0
+unsat
+#2 := false
+decl f5 :: S3
+#8 := f5
+decl f6 :: S3
+#10 := f6
+#24 := 0::Int
+decl f3 :: (-> S2 S3 Int)
+decl f4 :: S2
+#7 := f4
+#11 := (f3 f4 f6)
+#94 := -1::Int
+#95 := (* -1::Int #11)
+#9 := (f3 f4 f5)
+#96 := (+ #9 #95)
+#104 := (>= #96 0::Int)
+#106 := (if #104 f6 f5)
+#97 := (<= #96 0::Int)
+#100 := (if #97 f5 f6)
+#109 := (= #100 #106)
+#240 := (= f6 #106)
+#504 := (iff #240 #109)
+#501 := (iff #109 #240)
+#551 := (= #100 f6)
+#235 := (= f6 #100)
+#150 := (not #97)
+#149 := (= f5 #100)
+#507 := (not #149)
+#510 := (iff #149 #109)
+#367 := (iff #109 #149)
+#523 := (= #100 f5)
+#365 := (iff #523 #149)
+#366 := [commutativity]: #365
+#518 := (iff #109 #523)
+#248 := (= #106 f5)
+#241 := (= f5 #106)
+#542 := (not #241)
+#543 := [hypothesis]: #542
+#556 := (or #104 #241)
+#558 := [def-axiom]: #556
+#189 := [unit-resolution #558 #543]: #104
+#238 := (not #104)
+#242 := (or #238 #240)
+#221 := [def-axiom]: #242
+#190 := [unit-resolution #221 #189]: #240
+#519 := (= f5 f6)
+decl f7 :: (-> S4 Int S3)
+decl f8 :: S4
+#18 := f8
+#552 := (f7 f8 #11)
+#226 := (= #552 f6)
+#19 := (:var 0 S3)
+#20 := (f3 f4 #19)
+#564 := (pattern #20)
+#21 := (f7 f8 #20)
+#22 := (= #21 #19)
+#565 := (forall (vars (?v0 S3)) (:pat #564) #22)
+#23 := (forall (vars (?v0 S3)) #22)
+#568 := (iff #23 #565)
+#566 := (iff #22 #22)
+#567 := [refl]: #566
+#569 := [quant-intro #567]: #568
+#138 := (~ #23 #23)
+#140 := (~ #22 #22)
+#141 := [refl]: #140
+#139 := [nnf-pos #141]: #138
+#38 := [asserted]: #23
+#136 := [mp~ #38 #139]: #23
+#570 := [mp #136 #569]: #565
+#227 := (not #565)
+#557 := (or #227 #226)
+#563 := [quant-inst #10]: #557
+#246 := [unit-resolution #563 #570]: #226
+#526 := (= f5 #552)
+#215 := (f7 f8 #9)
+#525 := (= #215 #552)
+#249 := (= #552 #215)
+#532 := (= #11 #9)
+#531 := (= #9 #11)
+#156 := (not #235)
+#112 := (not #109)
+#533 := (iff #112 #156)
+#262 := (iff #109 #235)
+#260 := (iff #551 #235)
+#261 := [commutativity]: #260
+#537 := (iff #109 #551)
+#550 := (= #106 f6)
+#548 := [symm #190]: #550
+#538 := [monotonicity #548]: #537
+#263 := [trans #538 #261]: #262
+#534 := [monotonicity #263]: #533
+#14 := (<= #11 #9)
+#15 := (if #14 f6 f5)
+#12 := (<= #9 #11)
+#13 := (if #12 f5 f6)
+#16 := (= #13 #15)
+#17 := (not #16)
+#113 := (iff #17 #112)
+#110 := (iff #16 #109)
+#107 := (= #15 #106)
+#103 := (iff #14 #104)
+#105 := [rewrite]: #103
+#108 := [monotonicity #105]: #107
+#101 := (= #13 #100)
+#98 := (iff #12 #97)
+#99 := [rewrite]: #98
+#102 := [monotonicity #99]: #101
+#111 := [monotonicity #102 #108]: #110
+#114 := [monotonicity #111]: #113
+#37 := [asserted]: #17
+#115 := [mp #37 #114]: #112
+#256 := [mp #115 #534]: #156
+#228 := (or #97 #235)
+#239 := [def-axiom]: #228
+#257 := [unit-resolution #239 #256]: #97
+#535 := [th-lemma arith eq-propagate 1 1 #189 #257]: #531
+#536 := [symm #535]: #532
+#527 := [monotonicity #536]: #249
+#529 := [symm #527]: #525
+#528 := (= f5 #215)
+#345 := (= #215 f5)
+#559 := (or #227 #345)
+#560 := [quant-inst #8]: #559
+#549 := [unit-resolution #560 #570]: #345
+#243 := [symm #549]: #528
+#530 := [trans #243 #529]: #526
+#520 := [trans #530 #246]: #519
+#521 := [trans #520 #190]: #241
+#516 := [unit-resolution #543 #521]: false
+#517 := [lemma #516]: #241
+#522 := [symm #517]: #248
+#524 := [monotonicity #522]: #518
+#509 := [trans #524 #366]: #367
+#511 := [symm #509]: #510
+#247 := [hypothesis]: #149
+#512 := [mp #247 #511]: #109
+#506 := [unit-resolution #115 #512]: false
+#513 := [lemma #506]: #507
+#236 := (or #150 #149)
+#237 := [def-axiom]: #236
+#514 := [unit-resolution #237 #513]: #150
+#347 := [unit-resolution #239 #514]: #235
+#500 := [symm #347]: #551
+#503 := [monotonicity #500]: #501
+#502 := [symm #503]: #504
+#508 := (or #104 #97)
+#515 := [th-lemma arith farkas 1 1]: #508
+#344 := [unit-resolution #515 #514]: #104
+#346 := [unit-resolution #221 #344]: #240
+#505 := [mp #346 #502]: #109
+[unit-resolution #115 #505]: false
+07eaca6d75830c4f4db4caa421c6648570513c0f 242 0
+unsat
+#2 := false
+decl f6 :: (-> S4 Int S3)
+#11 := 0::Int
+decl f7 :: S4
+#10 := f7
+#12 := (f6 f7 0::Int)
+decl f5 :: S3
+#8 := f5
+decl f3 :: (-> S2 S3 Int)
+decl f4 :: S2
+#7 := f4
+#13 := (f3 f4 #12)
+#92 := -1::Int
+#93 := (* -1::Int #13)
+#9 := (f3 f4 f5)
+#94 := (+ #9 #93)
+#95 := (<= #94 0::Int)
+#98 := (if #95 f5 #12)
+#227 := (= #12 #98)
+#141 := (= f5 #98)
+#519 := (not #227)
+#101 := (= #98 #12)
+#104 := (not #101)
+#520 := (iff #104 #519)
+#240 := (iff #101 #227)
+#241 := [commutativity]: #240
+#235 := [monotonicity #241]: #520
+#14 := (<= #9 #13)
+#15 := (if #14 f5 #12)
+#16 := (= #15 #12)
+#17 := (not #16)
+#105 := (iff #17 #104)
+#102 := (iff #16 #101)
+#99 := (= #15 #98)
+#96 := (iff #14 #95)
+#97 := [rewrite]: #96
+#100 := [monotonicity #97]: #99
+#103 := [monotonicity #100]: #102
+#106 := [monotonicity #103]: #105
+#35 := [asserted]: #17
+#107 := [mp #35 #106]: #104
+#517 := [mp #107 #235]: #519
+#220 := (or #95 #227)
+#231 := [def-axiom]: #220
+#521 := [unit-resolution #231 #517]: #95
+#142 := (not #95)
+#228 := (or #142 #141)
+#229 := [def-axiom]: #228
+#503 := [unit-resolution #229 #521]: #141
+#496 := (= #12 f5)
+#232 := (f6 f7 #9)
+#233 := (= #232 f5)
+#18 := (:var 0 S3)
+#19 := (f3 f4 #18)
+#556 := (pattern #19)
+#20 := (f6 f7 #19)
+#21 := (= #20 #18)
+#557 := (forall (vars (?v0 S3)) (:pat #556) #21)
+#22 := (forall (vars (?v0 S3)) #21)
+#560 := (iff #22 #557)
+#558 := (iff #21 #21)
+#559 := [refl]: #558
+#561 := [quant-intro #559]: #560
+#130 := (~ #22 #22)
+#128 := (~ #21 #21)
+#129 := [refl]: #128
+#131 := [nnf-pos #129]: #130
+#36 := [asserted]: #22
+#134 := [mp~ #36 #131]: #22
+#562 := [mp #134 #561]: #557
+#213 := (not #557)
+#548 := (or #213 #233)
+#550 := [quant-inst #8]: #548
+#516 := [unit-resolution #550 #562]: #233
+#339 := (= #12 #232)
+#336 := (= 0::Int #9)
+#255 := (f3 f4 #232)
+#357 := (= #255 #9)
+#499 := (= #9 #255)
+#504 := (= f5 #232)
+#498 := [symm #516]: #504
+#505 := [monotonicity #498]: #499
+#507 := [symm #505]: #357
+#506 := (= 0::Int #255)
+#148 := (= #255 0::Int)
+#542 := (= #9 0::Int)
+#248 := (<= #9 0::Int)
+#541 := (<= #13 0::Int)
+#219 := (= #13 0::Int)
+#23 := (:var 0 Int)
+#25 := (f6 f7 #23)
+#563 := (pattern #25)
+#26 := (f3 f4 #25)
+#27 := (= #26 #23)
+#109 := (>= #23 0::Int)
+#111 := (not #109)
+#114 := (or #111 #27)
+#564 := (forall (vars (?v0 Int)) (:pat #563) #114)
+#117 := (forall (vars (?v0 Int)) #114)
+#567 := (iff #117 #564)
+#565 := (iff #114 #114)
+#566 := [refl]: #565
+#568 := [quant-intro #566]: #567
+#133 := (~ #117 #117)
+#135 := (~ #114 #114)
+#132 := [refl]: #135
+#90 := [nnf-pos #132]: #133
+#24 := (<= 0::Int #23)
+#46 := (not #24)
+#47 := (or #46 #27)
+#51 := (forall (vars (?v0 Int)) #47)
+#118 := (iff #51 #117)
+#115 := (iff #47 #114)
+#112 := (iff #46 #111)
+#108 := (iff #24 #109)
+#110 := [rewrite]: #108
+#113 := [monotonicity #110]: #112
+#116 := [monotonicity #113]: #115
+#119 := [quant-intro #116]: #118
+#28 := (implies #24 #27)
+#29 := (forall (vars (?v0 Int)) #28)
+#52 := (iff #29 #51)
+#48 := (iff #28 #47)
+#49 := [rewrite]: #48
+#44 := (iff #28 #28)
+#42 := (iff #24 #24)
+#43 := [rewrite]: #42
+#45 := [monotonicity #43]: #44
+#50 := [trans #45 #49]: #48
+#53 := [quant-intro #50]: #52
+#37 := [asserted]: #29
+#54 := [mp #37 #53]: #51
+#120 := [mp #54 #119]: #117
+#91 := [mp~ #120 #90]: #117
+#569 := [mp #91 #568]: #564
+#197 := (not #564)
+#533 := (or #197 #219)
+#207 := (>= 0::Int 0::Int)
+#337 := (not #207)
+#551 := (or #337 #219)
+#534 := (or #197 #551)
+#536 := (iff #534 #533)
+#532 := (iff #533 #533)
+#538 := [rewrite]: #532
+#195 := (iff #551 #219)
+#206 := (or false #219)
+#531 := (iff #206 #219)
+#194 := [rewrite]: #531
+#547 := (iff #551 #206)
+#210 := (iff #337 false)
+#1 := true
+#554 := (not true)
+#545 := (iff #554 false)
+#205 := [rewrite]: #545
+#549 := (iff #337 #554)
+#552 := (iff #207 true)
+#553 := [rewrite]: #552
+#555 := [monotonicity #553]: #549
+#546 := [trans #555 #205]: #210
+#190 := [monotonicity #546]: #547
+#196 := [trans #190 #194]: #195
+#537 := [monotonicity #196]: #536
+#176 := [trans #537 #538]: #536
+#535 := [quant-inst #11]: #534
+#539 := [mp #535 #176]: #533
+#518 := [unit-resolution #539 #569]: #219
+#522 := (not #219)
+#511 := (or #522 #541)
+#512 := [th-lemma arith triangle-eq]: #511
+#513 := [unit-resolution #512 #518]: #541
+#508 := (not #248)
+#509 := [hypothesis]: #508
+#514 := [th-lemma arith farkas -1 1 1 #509 #513 #521]: false
+#515 := [lemma #514]: #248
+#254 := (>= #9 0::Int)
+#540 := (not #148)
+#543 := [hypothesis]: #540
+#525 := (or #254 #148)
+#31 := (= #26 0::Int)
+#121 := (or #109 #31)
+#570 := (forall (vars (?v0 Int)) (:pat #563) #121)
+#124 := (forall (vars (?v0 Int)) #121)
+#573 := (iff #124 #570)
+#571 := (iff #121 #121)
+#572 := [refl]: #571
+#574 := [quant-intro #572]: #573
+#138 := (~ #124 #124)
+#136 := (~ #121 #121)
+#137 := [refl]: #136
+#139 := [nnf-pos #137]: #138
+#63 := (or #24 #31)
+#68 := (forall (vars (?v0 Int)) #63)
+#125 := (iff #68 #124)
+#122 := (iff #63 #121)
+#123 := [monotonicity #110]: #122
+#126 := [quant-intro #123]: #125
+#30 := (< #23 0::Int)
+#32 := (implies #30 #31)
+#33 := (forall (vars (?v0 Int)) #32)
+#69 := (iff #33 #68)
+#66 := (iff #32 #63)
+#60 := (implies #46 #31)
+#64 := (iff #60 #63)
+#65 := [rewrite]: #64
+#61 := (iff #32 #60)
+#55 := (iff #30 #46)
+#57 := (iff #46 #46)
+#58 := [monotonicity #43]: #57
+#56 := [rewrite]: #55
+#59 := [trans #56 #58]: #55
+#62 := [monotonicity #59]: #61
+#67 := [trans #62 #65]: #66
+#70 := [quant-intro #67]: #69
+#38 := [asserted]: #33
+#71 := [mp #38 #70]: #68
+#127 := [mp #71 #126]: #124
+#140 := [mp~ #127 #139]: #124
+#575 := [mp #140 #574]: #570
+#249 := (not #570)
+#523 := (or #249 #254 #148)
+#527 := (or #249 #525)
+#528 := (iff #527 #523)
+#238 := [rewrite]: #528
+#524 := [quant-inst #9]: #527
+#239 := [mp #524 #238]: #523
+#529 := [unit-resolution #239 #575]: #525
+#530 := [unit-resolution #529 #543]: #254
+#252 := (not #254)
+#253 := (or #542 #508 #252)
+#526 := [th-lemma arith triangle-eq]: #253
+#510 := [unit-resolution #526 #530 #515]: #542
+#358 := [monotonicity #516]: #357
+#359 := [trans #358 #510]: #148
+#501 := [unit-resolution #543 #359]: false
+#502 := [lemma #501]: #148
+#500 := [symm #502]: #506
+#338 := [trans #500 #507]: #336
+#492 := [monotonicity #338]: #339
+#494 := [trans #492 #516]: #496
+#497 := [trans #494 #503]: #227
+[unit-resolution #517 #497]: false
+023391835b440558305b8b251ef349da3d22790f 70 0
+unsat
 #2 := false
 decl f3 :: (-> S2 S3 Int)
+decl f5 :: S3
+#8 := f5
 decl f6 :: S3
-#11 := f6
-decl f5 :: S3
-#9 := f5
+#10 := f6
+#23 := 0::Int
+decl f4 :: S2
+#7 := f4
+#11 := (f3 f4 f6)
+#93 := -1::Int
+#94 := (* -1::Int #11)
+#9 := (f3 f4 f5)
+#95 := (+ #9 #94)
+#96 := (<= #95 0::Int)
+#99 := (if #96 f6 f5)
+#102 := (f3 f4 #99)
+#263 := (= #9 #102)
+#238 := (= f5 #99)
+#153 := (not #96)
+#264 := [hypothesis]: #96
+#108 := (* -1::Int #102)
+#109 := (+ #9 #108)
+#110 := (<= #109 0::Int)
+#115 := (not #110)
+#12 := (<= #9 #11)
+#13 := (if #12 f6 f5)
+#14 := (f3 f4 #13)
+#15 := (<= #9 #14)
+#16 := (not #15)
+#116 := (iff #16 #115)
+#113 := (iff #15 #110)
+#105 := (<= #9 #102)
+#111 := (iff #105 #110)
+#112 := [rewrite]: #111
+#106 := (iff #15 #105)
+#103 := (= #14 #102)
+#100 := (= #13 #99)
+#97 := (iff #12 #96)
+#98 := [rewrite]: #97
+#101 := [monotonicity #98]: #100
+#104 := [monotonicity #101]: #103
+#107 := [monotonicity #104]: #106
+#114 := [trans #107 #112]: #113
+#117 := [monotonicity #114]: #116
+#36 := [asserted]: #16
+#118 := [mp #36 #117]: #115
+#552 := (+ #11 #108)
+#541 := (<= #552 0::Int)
+#550 := (= #11 #102)
+#152 := (= f6 #99)
+#239 := (or #153 #152)
+#240 := [def-axiom]: #239
+#265 := [unit-resolution #240 #264]: #152
+#266 := [monotonicity #265]: #550
+#159 := (not #550)
+#536 := (or #159 #541)
+#537 := [th-lemma arith triangle-eq]: #536
+#259 := [unit-resolution #537 #266]: #541
+#260 := [th-lemma arith farkas 1 -1 1 #259 #118 #264]: false
+#534 := [lemma #260]: #153
+#231 := (or #96 #238)
+#242 := [def-axiom]: #231
+#535 := [unit-resolution #242 #534]: #238
+#539 := [monotonicity #535]: #263
+#249 := (not #263)
+#250 := (or #249 #110)
+#251 := [th-lemma arith triangle-eq]: #250
+[unit-resolution #251 #118 #539]: false
+de9a0b9ce99106c695a3982a129801da9aa3b403 76 0
+unsat
+#2 := false
+#23 := 0::Int
+decl f3 :: (-> S2 S3 Int)
+decl f6 :: S3
+#10 := f6
+decl f5 :: S3
+#8 := f5
+decl f4 :: S2
+#7 := f4
+#11 := (f3 f4 f6)
+#93 := -1::Int
+#96 := (* -1::Int #11)
+#9 := (f3 f4 f5)
+#97 := (+ #9 #96)
+#95 := (>= #97 0::Int)
+#99 := (if #95 f5 f6)
+#102 := (f3 f4 #99)
+#108 := (* -1::Int #102)
+#539 := (+ #11 #108)
+#249 := (<= #539 0::Int)
+#535 := (= #11 #102)
+#238 := (= f6 #99)
+#153 := (not #95)
+#152 := (= f5 #99)
+#534 := (not #152)
+#550 := (= #9 #102)
+#537 := [hypothesis]: #152
+#259 := [monotonicity #537]: #550
+#263 := (not #550)
+#109 := (+ #9 #108)
+#110 := (<= #109 0::Int)
+#115 := (not #110)
+#12 := (<= #11 #9)
+#13 := (if #12 f5 f6)
+#14 := (f3 f4 #13)
+#15 := (<= #9 #14)
+#16 := (not #15)
+#116 := (iff #16 #115)
+#113 := (iff #15 #110)
+#105 := (<= #9 #102)
+#111 := (iff #105 #110)
+#112 := [rewrite]: #111
+#106 := (iff #15 #105)
+#103 := (= #14 #102)
+#100 := (= #13 #99)
+#94 := (iff #12 #95)
+#98 := [rewrite]: #94
+#101 := [monotonicity #98]: #100
+#104 := [monotonicity #101]: #103
+#107 := [monotonicity #104]: #106
+#114 := [trans #107 #112]: #113
+#117 := [monotonicity #114]: #116
+#36 := [asserted]: #16
+#118 := [mp #36 #117]: #115
+#264 := (or #263 #110)
+#265 := [th-lemma arith triangle-eq]: #264
+#536 := [unit-resolution #265 #118]: #263
+#260 := [unit-resolution #536 #259]: false
+#538 := [lemma #260]: #534
+#239 := (or #153 #152)
+#240 := [def-axiom]: #239
+#251 := [unit-resolution #240 #538]: #153
+#231 := (or #95 #238)
+#242 := [def-axiom]: #231
+#252 := [unit-resolution #242 #251]: #238
+#530 := [monotonicity #252]: #535
+#531 := (not #535)
+#246 := (or #531 #249)
+#528 := [th-lemma arith triangle-eq]: #246
+#532 := [unit-resolution #528 #530]: #249
+#552 := (>= #109 0::Int)
+#529 := (or #552 #110)
+#533 := [th-lemma arith farkas 1 1]: #529
+#522 := [unit-resolution #533 #118]: #552
+[th-lemma arith farkas 1 1 1 #522 #251 #532]: false
+e2d5671413f0e92bd5580899b040818b49d8e5b4 479 0
+unsat
+#2 := false
+#30 := 0::Int
+decl f3 :: (-> S2 S3 Int)
+decl f7 :: S3
+#9 := f7
+decl f4 :: S2
+#7 := f4
+#10 := (f3 f4 f7)
+#387 := (= #10 0::Int)
+decl f5 :: (-> S4 Int S3)
+decl f6 :: S4
+#8 := f6
+#298 := (f5 f6 #10)
+#406 := (f3 f4 #298)
+#554 := (= #406 0::Int)
+#447 := (>= #10 0::Int)
+#384 := (not #447)
+decl f8 :: S3
+#11 := f8
+#12 := (f3 f4 f8)
+#50 := -1::Int
+#51 := (* -1::Int #12)
+#52 := (+ #10 #51)
+#147 := (<= #52 0::Int)
+#150 := (if #147 f8 f7)
+#153 := (f3 f4 #150)
+#159 := (* -1::Int #153)
+#400 := (+ #12 #159)
+#407 := (<= #400 0::Int)
+#506 := (= #12 #153)
+#207 := (= f8 #150)
+#61 := (* -1::Int #10)
+#129 := (+ #61 #12)
+#132 := (f5 f6 #129)
+#135 := (f3 f4 #132)
+#570 := (= #135 0::Int)
+#435 := (not #570)
+#445 := (<= #135 0::Int)
+#414 := (not #445)
+#541 := (>= #153 0::Int)
+#505 := (= #153 0::Int)
+#620 := (f5 f6 #153)
+#542 := (f3 f4 #620)
+#532 := (= #542 0::Int)
+#487 := (not #541)
+#488 := [hypothesis]: #487
+#533 := (or #541 #532)
+#31 := (:var 0 Int)
+#33 := (f5 f6 #31)
+#629 := (pattern #33)
+#34 := (f3 f4 #33)
+#39 := (= #34 0::Int)
+#175 := (>= #31 0::Int)
+#187 := (or #175 #39)
+#636 := (forall (vars (?v0 Int)) (:pat #629) #187)
+#190 := (forall (vars (?v0 Int)) #187)
+#639 := (iff #190 #636)
+#637 := (iff #187 #187)
+#638 := [refl]: #637
+#640 := [quant-intro #638]: #639
+#204 := (~ #190 #190)
+#202 := (~ #187 #187)
+#203 := [refl]: #202
+#205 := [nnf-pos #203]: #204
+#32 := (<= 0::Int #31)
+#102 := (or #32 #39)
+#107 := (forall (vars (?v0 Int)) #102)
+#191 := (iff #107 #190)
+#188 := (iff #102 #187)
+#174 := (iff #32 #175)
+#176 := [rewrite]: #174
+#189 := [monotonicity #176]: #188
+#192 := [quant-intro #189]: #191
+#38 := (< #31 0::Int)
+#40 := (implies #38 #39)
+#41 := (forall (vars (?v0 Int)) #40)
+#108 := (iff #41 #107)
+#105 := (iff #40 #102)
+#85 := (not #32)
+#99 := (implies #85 #39)
+#103 := (iff #99 #102)
+#104 := [rewrite]: #103
+#100 := (iff #40 #99)
+#94 := (iff #38 #85)
+#96 := (iff #85 #85)
+#81 := (iff #32 #32)
+#82 := [rewrite]: #81
+#97 := [monotonicity #82]: #96
+#95 := [rewrite]: #94
+#98 := [trans #95 #97]: #94
+#101 := [monotonicity #98]: #100
+#106 := [trans #101 #104]: #105
+#109 := [quant-intro #106]: #108
+#46 := [asserted]: #41
+#110 := [mp #46 #109]: #107
+#193 := [mp #110 #192]: #190
+#206 := [mp~ #193 #205]: #190
+#641 := [mp #206 #640]: #636
+#214 := (not #636)
+#520 := (or #214 #541 #532)
+#521 := (or #214 #533)
+#524 := (iff #521 #520)
+#525 := [rewrite]: #524
+#523 := [quant-inst #153]: #521
+#522 := [mp #523 #525]: #520
+#489 := [unit-resolution #522 #641]: #533
+#492 := [unit-resolution #489 #488]: #532
+#490 := (= #153 #542)
+#494 := (= #150 #620)
+#615 := (= #620 #150)
+#25 := (:var 0 S3)
+#26 := (f3 f4 #25)
+#622 := (pattern #26)
+#27 := (f5 f6 #26)
+#28 := (= #27 #25)
+#623 := (forall (vars (?v0 S3)) (:pat #622) #28)
+#29 := (forall (vars (?v0 S3)) #28)
+#626 := (iff #29 #623)
+#624 := (iff #28 #28)
+#625 := [refl]: #624
+#627 := [quant-intro #625]: #626
+#198 := (~ #29 #29)
+#200 := (~ #28 #28)
+#201 := [refl]: #200
+#199 := [nnf-pos #201]: #198
+#44 := [asserted]: #29
+#196 := [mp~ #44 #199]: #29
+#628 := [mp #196 #627]: #623
+#279 := (not #623)
+#612 := (or #279 #615)
+#272 := [quant-inst #150]: #612
+#493 := [unit-resolution #272 #628]: #615
+#495 := [symm #493]: #494
+#496 := [monotonicity #495]: #490
+#469 := [trans #496 #492]: #505
+#470 := (not #505)
+#471 := (or #470 #541)
+#364 := [th-lemma arith triangle-eq]: #471
+#475 := [unit-resolution #364 #488 #469]: false
+#476 := [lemma #475]: #541
+#55 := (f5 f6 #52)
+#58 := (f3 f4 #55)
+#160 := (+ #58 #135 #159)
+#161 := (<= #160 0::Int)
+#166 := (not #161)
+#20 := (<= #10 #12)
+#21 := (if #20 f8 f7)
+#22 := (f3 f4 #21)
+#62 := (+ #12 #61)
+#65 := (f5 f6 #62)
+#68 := (f3 f4 #65)
+#71 := (+ #58 #68)
+#74 := (<= #71 #22)
+#77 := (not #74)
+#169 := (iff #77 #166)
+#138 := (+ #58 #135)
+#141 := (<= #138 #22)
+#144 := (not #141)
+#167 := (iff #144 #166)
+#164 := (iff #141 #161)
+#156 := (<= #138 #153)
+#162 := (iff #156 #161)
+#163 := [rewrite]: #162
+#157 := (iff #141 #156)
+#154 := (= #22 #153)
+#151 := (= #21 #150)
+#148 := (iff #20 #147)
+#149 := [rewrite]: #148
+#152 := [monotonicity #149]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#165 := [trans #158 #163]: #164
+#168 := [monotonicity #165]: #167
+#145 := (iff #77 #144)
+#142 := (iff #74 #141)
+#139 := (= #71 #138)
+#136 := (= #68 #135)
+#133 := (= #65 #132)
+#130 := (= #62 #129)
+#131 := [rewrite]: #130
+#134 := [monotonicity #131]: #133
+#137 := [monotonicity #134]: #136
+#140 := [monotonicity #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [monotonicity #143]: #145
+#170 := [trans #146 #168]: #169
+#16 := (- #12 #10)
+#17 := (f5 f6 #16)
+#18 := (f3 f4 #17)
+#13 := (- #10 #12)
+#14 := (f5 f6 #13)
+#15 := (f3 f4 #14)
+#19 := (+ #15 #18)
+#23 := (<= #19 #22)
+#24 := (not #23)
+#78 := (iff #24 #77)
+#75 := (iff #23 #74)
+#72 := (= #19 #71)
+#69 := (= #18 #68)
+#66 := (= #17 #65)
+#63 := (= #16 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#70 := [monotonicity #67]: #69
+#59 := (= #15 #58)
+#56 := (= #14 #55)
+#53 := (= #13 #52)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#60 := [monotonicity #57]: #59
+#73 := [monotonicity #60 #70]: #72
+#76 := [monotonicity #73]: #75
+#79 := [monotonicity #76]: #78
+#43 := [asserted]: #24
+#80 := [mp #43 #79]: #77
+#171 := [mp #80 #170]: #166
+#590 := (<= #58 0::Int)
+#318 := (= #58 0::Int)
+#534 := (+ #10 #159)
+#526 := (<= #534 0::Int)
+#529 := (= #10 #153)
+#293 := (= f7 #150)
+#208 := (not #147)
+#468 := (not #590)
+#512 := (not #318)
+#477 := [hypothesis]: #512
+#449 := (or #318 #468)
+#594 := (>= #58 0::Int)
+#273 := (f5 f6 #58)
+#461 := (f3 f4 #273)
+#462 := (= #461 0::Int)
+#500 := (not #462)
+#501 := (iff #512 #500)
+#497 := (iff #318 #462)
+#508 := (iff #462 #318)
+#517 := (= #461 #58)
+#403 := (= #273 #55)
+#618 := (or #279 #403)
+#619 := [quant-inst #55]: #618
+#516 := [unit-resolution #619 #628]: #403
+#518 := [monotonicity #516]: #517
+#519 := [monotonicity #518]: #508
+#498 := [symm #519]: #497
+#502 := [monotonicity #498]: #501
+#507 := (not #594)
+#509 := [hypothesis]: #507
+#513 := (or #512 #594)
+#514 := [th-lemma arith triangle-eq]: #513
+#515 := [unit-resolution #514 #509]: #512
+#503 := [mp #515 #502]: #500
+#538 := (or #594 #462)
+#547 := (or #214 #594 #462)
+#548 := (or #214 #538)
+#545 := (iff #548 #547)
+#550 := [rewrite]: #545
+#549 := [quant-inst #58]: #548
+#539 := [mp #549 #550]: #547
+#510 := [unit-resolution #539 #641]: #538
+#511 := [unit-resolution #510 #509]: #462
+#504 := [unit-resolution #511 #503]: false
+#499 := [lemma #504]: #594
+#474 := (or #318 #468 #507)
+#442 := [th-lemma arith triangle-eq]: #474
+#408 := [unit-resolution #442 #499]: #449
+#439 := [unit-resolution #408 #477]: #468
+#260 := (* -1::Int #58)
+#261 := (+ #10 #51 #260)
+#596 := (>= #261 0::Int)
+#597 := (= #261 0::Int)
+#271 := (>= #52 0::Int)
+#319 := (or #271 #318)
+#591 := (or #214 #271 #318)
+#592 := (or #214 #319)
+#315 := (iff #592 #591)
+#589 := [rewrite]: #315
+#314 := [quant-inst #52]: #592
+#593 := [mp #314 #589]: #591
+#441 := [unit-resolution #593 #641]: #319
+#443 := [unit-resolution #441 #477]: #271
+#276 := (not #271)
+#599 := (or #276 #597)
+#35 := (= #34 #31)
+#177 := (not #175)
+#180 := (or #177 #35)
+#630 := (forall (vars (?v0 Int)) (:pat #629) #180)
+#183 := (forall (vars (?v0 Int)) #180)
+#633 := (iff #183 #630)
+#631 := (iff #180 #180)
+#632 := [refl]: #631
+#634 := [quant-intro #632]: #633
+#195 := (~ #183 #183)
+#197 := (~ #180 #180)
+#194 := [refl]: #197
+#172 := [nnf-pos #194]: #195
+#86 := (or #85 #35)
+#90 := (forall (vars (?v0 Int)) #86)
+#184 := (iff #90 #183)
+#181 := (iff #86 #180)
+#178 := (iff #85 #177)
+#179 := [monotonicity #176]: #178
+#182 := [monotonicity #179]: #181
+#185 := [quant-intro #182]: #184
+#36 := (implies #32 #35)
+#37 := (forall (vars (?v0 Int)) #36)
+#91 := (iff #37 #90)
+#87 := (iff #36 #86)
+#88 := [rewrite]: #87
+#83 := (iff #36 #36)
+#84 := [monotonicity #82]: #83
+#89 := [trans #84 #88]: #87
+#92 := [quant-intro #89]: #91
+#45 := [asserted]: #37
+#93 := [mp #45 #92]: #90
+#186 := [mp #93 #185]: #183
+#173 := [mp~ #186 #172]: #183
+#635 := [mp #173 #634]: #630
+#602 := (not #630)
+#603 := (or #602 #276 #597)
+#613 := (= #58 #52)
+#256 := (or #276 #613)
+#598 := (or #602 #256)
+#608 := (iff #598 #603)
+#242 := (or #602 #599)
+#247 := (iff #242 #603)
+#248 := [rewrite]: #247
+#605 := (iff #598 #242)
+#600 := (iff #256 #599)
+#262 := (iff #613 #597)
+#263 := [rewrite]: #262
+#601 := [monotonicity #263]: #600
+#607 := [monotonicity #601]: #605
+#606 := [trans #607 #248]: #608
+#604 := [quant-inst #52]: #598
+#609 := [mp #604 #606]: #603
+#450 := [unit-resolution #609 #635]: #599
+#452 := [unit-resolution #450 #443]: #597
+#453 := (not #597)
+#454 := (or #453 #596)
+#464 := [th-lemma arith triangle-eq]: #454
+#444 := [unit-resolution #464 #452]: #596
+#465 := (not #596)
+#420 := (or #208 #590 #465)
+#421 := [th-lemma arith assign-bounds -1 -1]: #420
+#426 := [unit-resolution #421 #444 #439]: #208
+#286 := (or #147 #293)
+#297 := [def-axiom]: #286
+#427 := [unit-resolution #297 #426]: #293
+#428 := [monotonicity #427]: #529
+#429 := (not #529)
+#430 := (or #429 #526)
+#431 := [th-lemma arith triangle-eq]: #430
+#432 := [unit-resolution #431 #428]: #526
+#565 := (or #147 #570)
+#566 := (or #214 #147 #570)
+#320 := (>= #129 0::Int)
+#564 := (or #320 #570)
+#573 := (or #214 #564)
+#562 := (iff #573 #566)
+#404 := (or #214 #565)
+#559 := (iff #404 #566)
+#561 := [rewrite]: #559
+#405 := (iff #573 #404)
+#571 := (iff #564 #565)
+#306 := (iff #320 #147)
+#307 := [rewrite]: #306
+#572 := [monotonicity #307]: #571
+#558 := [monotonicity #572]: #405
+#560 := [trans #558 #561]: #562
+#402 := [quant-inst #129]: #573
+#563 := [mp #402 #560]: #566
+#433 := [unit-resolution #563 #641]: #565
+#434 := [unit-resolution #433 #426]: #570
+#436 := (or #435 #445)
+#437 := [th-lemma arith triangle-eq]: #436
+#422 := [unit-resolution #437 #434]: #445
+#551 := (>= #12 0::Int)
+#491 := (= #12 0::Int)
+#296 := (f5 f6 #12)
+#552 := (f3 f4 #296)
+#459 := (= #552 0::Int)
+#482 := (not #551)
+#478 := [hypothesis]: #482
+#460 := (or #551 #459)
+#463 := (or #214 #551 #459)
+#556 := (or #214 #460)
+#557 := (iff #556 #463)
+#544 := [rewrite]: #557
+#553 := [quant-inst #12]: #556
+#546 := [mp #553 #544]: #463
+#479 := [unit-resolution #546 #641]: #460
+#480 := [unit-resolution #479 #478]: #459
+#481 := (= #12 #552)
+#484 := (= f8 #296)
+#300 := (= #296 f8)
+#610 := (or #279 #300)
+#284 := [quant-inst #11]: #610
+#483 := [unit-resolution #284 #628]: #300
+#485 := [symm #483]: #484
+#486 := [monotonicity #485]: #481
+#466 := [trans #486 #480]: #491
+#412 := (not #491)
+#467 := (or #412 #551)
+#448 := [th-lemma arith triangle-eq]: #467
+#472 := [unit-resolution #448 #478 #466]: false
+#473 := [lemma #472]: #551
+#438 := [th-lemma arith farkas -1 -1 1 -1 1 #473 #444 #422 #171 #432]: false
+#399 := [lemma #438]: #318
+#410 := (or #512 #590)
+#411 := [th-lemma arith triangle-eq]: #410
+#413 := [unit-resolution #411 #399]: #590
+#415 := (or #414 #487 #161 #468)
+#416 := [th-lemma arith assign-bounds -1 -1 1]: #415
+#417 := [unit-resolution #416 #413 #171 #476]: #414
+#418 := [unit-resolution #437 #417]: #435
+#401 := [unit-resolution #433 #418]: #147
+#294 := (or #208 #207)
+#295 := [def-axiom]: #294
+#419 := [unit-resolution #295 #401]: #207
+#389 := [monotonicity #419]: #506
+#390 := (not #506)
+#391 := (or #390 #407)
+#392 := [th-lemma arith triangle-eq]: #391
+#394 := [unit-resolution #392 #389]: #407
+#301 := (+ #10 #51 #135)
+#568 := (<= #301 0::Int)
+#583 := (= #301 0::Int)
+#588 := (or #208 #583)
+#579 := (or #602 #208 #583)
+#304 := (= #135 #129)
+#321 := (not #320)
+#305 := (or #321 #304)
+#574 := (or #602 #305)
+#424 := (iff #574 #579)
+#580 := (or #602 #588)
+#582 := (iff #580 #579)
+#423 := [rewrite]: #582
+#581 := (iff #574 #580)
+#577 := (iff #305 #588)
+#587 := (iff #304 #583)
+#584 := [rewrite]: #587
+#585 := (iff #321 #208)
+#586 := [monotonicity #307]: #585
+#578 := [monotonicity #586 #584]: #577
+#576 := [monotonicity #578]: #581
+#425 := [trans #576 #423]: #424
+#575 := [quant-inst #129]: #574
+#567 := [mp #575 #425]: #579
+#395 := [unit-resolution #567 #635]: #588
+#396 := [unit-resolution #395 #401]: #583
+#239 := (not #583)
+#397 := (or #239 #568)
+#393 := [th-lemma arith triangle-eq]: #397
+#398 := [unit-resolution #393 #396]: #568
+#377 := [hypothesis]: #447
+#380 := [th-lemma arith farkas 1 -1 1 -1 1 #413 #377 #398 #171 #394]: false
+#386 := [lemma #380]: #384
+#456 := (or #447 #554)
+#555 := (or #214 #447 #554)
+#440 := (or #214 #456)
+#457 := (iff #440 #555)
+#458 := [rewrite]: #457
+#455 := [quant-inst #10]: #440
+#451 := [mp #455 #458]: #555
+#388 := [unit-resolution #451 #641]: #456
+#376 := [unit-resolution #388 #386]: #554
+#378 := (= #10 #406)
+#381 := (= f7 #298)
+#299 := (= #298 f7)
+#614 := (or #279 #299)
+#616 := [quant-inst #9]: #614
+#379 := [unit-resolution #616 #628]: #299
+#382 := [symm #379]: #381
+#383 := [monotonicity #382]: #378
+#373 := [trans #383 #376]: #387
+#363 := (not #387)
+#365 := (or #363 #447)
+#366 := [th-lemma arith triangle-eq]: #365
+[unit-resolution #366 #386 #373]: false
+160657a6999b6fa22bbfbba0cea75e9e766dc484 131 0
+unsat
+#2 := false
+#29 := 0::Int
+decl f3 :: (-> S2 S3 Int)
+decl f5 :: S3
+#8 := f5
+decl f7 :: S3
+#13 := f7
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 f7)
+#131 := -1::Int
+#161 := (* -1::Int #14)
+#9 := (f3 f4 f5)
+#170 := (+ #9 #161)
+#171 := (<= #170 0::Int)
+#174 := (if #171 f7 f5)
+#177 := (f3 f4 #174)
+#183 := (* -1::Int #177)
+decl f6 :: S3
+#10 := f6
+#11 := (f3 f4 f6)
+#184 := (+ #11 #183)
+#185 := (<= #184 0::Int)
+#17 := (<= #9 #14)
+#18 := (if #17 f7 f5)
+#19 := (f3 f4 #18)
+#60 := (<= #11 #19)
+#188 := (iff #60 #185)
+#180 := (<= #11 #177)
+#186 := (iff #180 #185)
+#187 := [rewrite]: #186
+#181 := (iff #60 #180)
+#178 := (= #19 #177)
+#175 := (= #18 #174)
+#172 := (iff #17 #171)
+#173 := [rewrite]: #172
+#176 := [monotonicity #173]: #175
+#179 := [monotonicity #176]: #178
+#182 := [monotonicity #179]: #181
+#189 := [trans #182 #187]: #188
+#61 := (not #60)
+#53 := (<= #11 #14)
+#54 := (not #53)
+#49 := (<= #11 #9)
+#50 := (not #49)
+#57 := (and #50 #54)
+#67 := (not #57)
+#68 := (or #67 #61)
+#73 := (not #68)
+#20 := (< #19 #11)
+#15 := (< #14 #11)
+#12 := (< #9 #11)
+#16 := (and #12 #15)
+#21 := (implies #16 #20)
+#22 := (not #21)
+#74 := (iff #22 #73)
+#71 := (iff #21 #68)
+#64 := (implies #57 #61)
+#69 := (iff #64 #68)
+#70 := [rewrite]: #69
+#65 := (iff #21 #64)
+#62 := (iff #20 #61)
+#63 := [rewrite]: #62
+#58 := (iff #16 #57)
+#55 := (iff #15 #54)
+#56 := [rewrite]: #55
+#51 := (iff #12 #50)
+#52 := [rewrite]: #51
+#59 := [monotonicity #52 #56]: #58
+#66 := [monotonicity #59 #63]: #65
+#72 := [trans #66 #70]: #71
+#75 := [monotonicity #72]: #74
+#42 := [asserted]: #22
+#76 := [mp #42 #75]: #73
+#80 := [not-or-elim #76]: #60
+#190 := [mp #80 #189]: #185
+#134 := (* -1::Int #11)
+#135 := (+ #9 #134)
+#133 := (>= #135 0::Int)
+#137 := (not #133)
+#138 := (iff #50 #137)
+#132 := (iff #49 #133)
+#136 := [rewrite]: #132
+#139 := [monotonicity #136]: #138
+#77 := [not-or-elim #76]: #57
+#78 := [and-elim #77]: #50
+#140 := [mp #78 #139]: #137
+#579 := (+ #9 #183)
+#421 := (>= #579 0::Int)
+#573 := (= #9 #177)
+#290 := (= f5 #174)
+#205 := (not #171)
+#204 := (= f7 #174)
+#577 := (not #204)
+#588 := (= #14 #177)
+#576 := [hypothesis]: #204
+#571 := [monotonicity #576]: #588
+#580 := (not #588)
+#589 := (+ #14 #183)
+#302 := (>= #589 0::Int)
+#582 := (not #302)
+#162 := (+ #11 #161)
+#163 := (<= #162 0::Int)
+#166 := (not #163)
+#167 := (iff #54 #166)
+#164 := (iff #53 #163)
+#165 := [rewrite]: #164
+#168 := [monotonicity #165]: #167
+#79 := [and-elim #77]: #54
+#169 := [mp #79 #168]: #166
+#303 := [hypothesis]: #302
+#304 := [th-lemma arith farkas -1 -1 1 #303 #169 #190]: false
+#583 := [lemma #304]: #582
+#584 := (or #580 #302)
+#581 := [th-lemma arith triangle-eq]: #584
+#575 := [unit-resolution #581 #583]: #580
+#572 := [unit-resolution #575 #571]: false
+#578 := [lemma #572]: #577
+#291 := (or #205 #204)
+#292 := [def-axiom]: #291
+#422 := [unit-resolution #292 #578]: #205
+#283 := (or #171 #290)
+#294 := [def-axiom]: #283
+#564 := [unit-resolution #294 #422]: #290
+#565 := [monotonicity #564]: #573
+#566 := (not #573)
+#567 := (or #566 #421)
+#561 := [th-lemma arith triangle-eq]: #567
+#562 := [unit-resolution #561 #565]: #421
+[th-lemma arith farkas -1 1 1 #562 #140 #190]: false
+fb8c3e38f29442a2c97cb122a92a02cfe400dc8f 149 0
+unsat
+#2 := false
+decl f6 :: S3
+#10 := f6
+decl f5 :: S3
+#8 := f5
 #24 := 0::Int
-decl f4 :: S2
-#8 := f4
-#12 := (f3 f4 f6)
-#58 := -1::Int
-#59 := (* -1::Int #12)
-#10 := (f3 f4 f5)
-#60 := (+ #10 #59)
-#61 := (<= #60 0::Int)
-#64 := (ite #61 f5 f6)
-#67 := (f3 f4 #64)
-#338 := (= #12 #67)
-#326 := (= f6 #64)
-#241 := (not #61)
-#340 := [hypothesis]: #61
-#74 := (* -1::Int #67)
-#75 := (+ #12 #74)
-#73 := (>= #75 0::Int)
-#80 := (not #73)
-#13 := (<= #10 #12)
-#14 := (ite #13 f5 f6)
-#15 := (f3 f4 #14)
-#16 := (<= #15 #12)
+decl f3 :: (-> S2 S3 Int)
+decl f4 :: S2
+#7 := f4
+#11 := (f3 f4 f6)
+#94 := -1::Int
+#95 := (* -1::Int #11)
+#9 := (f3 f4 f5)
+#96 := (+ #9 #95)
+#104 := (>= #96 0::Int)
+#106 := (if #104 f5 f6)
+#97 := (<= #96 0::Int)
+#100 := (if #97 f6 f5)
+#109 := (= #100 #106)
+#240 := (= f5 #106)
+#501 := (iff #240 #109)
+#347 := (iff #109 #240)
+#551 := (= #100 f5)
+#235 := (= f5 #100)
+#150 := (not #97)
+#149 := (= f6 #100)
+#512 := (not #149)
+#367 := (iff #149 #109)
+#365 := (iff #109 #149)
+#517 := (= #100 f6)
+#518 := (iff #517 #149)
+#524 := [commutativity]: #518
+#522 := (iff #109 #517)
+#521 := (= #106 f6)
+#241 := (= f6 #106)
+#542 := (not #241)
+#543 := [hypothesis]: #542
+#556 := (or #104 #241)
+#558 := [def-axiom]: #556
+#549 := [unit-resolution #558 #543]: #104
+#238 := (not #104)
+#242 := (or #238 #240)
+#221 := [def-axiom]: #242
+#189 := [unit-resolution #221 #549]: #240
+#525 := (= f6 f5)
+decl f7 :: (-> S4 Int S3)
+decl f8 :: S4
+#18 := f8
+#215 := (f7 f8 #9)
+#345 := (= #215 f5)
+#19 := (:var 0 S3)
+#20 := (f3 f4 #19)
+#564 := (pattern #20)
+#21 := (f7 f8 #20)
+#22 := (= #21 #19)
+#565 := (forall (vars (?v0 S3)) (:pat #564) #22)
+#23 := (forall (vars (?v0 S3)) #22)
+#568 := (iff #23 #565)
+#566 := (iff #22 #22)
+#567 := [refl]: #566
+#569 := [quant-intro #567]: #568
+#138 := (~ #23 #23)
+#140 := (~ #22 #22)
+#141 := [refl]: #140
+#139 := [nnf-pos #141]: #138
+#38 := [asserted]: #23
+#136 := [mp~ #38 #139]: #23
+#570 := [mp #136 #569]: #565
+#227 := (not #565)
+#559 := (or #227 #345)
+#560 := [quant-inst #8]: #559
+#190 := [unit-resolution #560 #570]: #345
+#528 := (= f6 #215)
+#552 := (f7 f8 #11)
+#249 := (= #552 #215)
+#532 := (= #11 #9)
+#531 := (= #9 #11)
+#156 := (not #235)
+#112 := (not #109)
+#533 := (iff #112 #156)
+#262 := (iff #109 #235)
+#260 := (iff #551 #235)
+#261 := [commutativity]: #260
+#537 := (iff #109 #551)
+#550 := (= #106 f5)
+#548 := [symm #189]: #550
+#538 := [monotonicity #548]: #537
+#263 := [trans #538 #261]: #262
+#534 := [monotonicity #263]: #533
+#14 := (<= #11 #9)
+#15 := (if #14 f5 f6)
+#12 := (<= #9 #11)
+#13 := (if #12 f6 f5)
+#16 := (= #13 #15)
 #17 := (not #16)
-#81 := (iff #17 #80)
-#78 := (iff #16 #73)
-#70 := (<= #67 #12)
-#76 := (iff #70 #73)
-#77 := [rewrite]: #76
-#71 := (iff #16 #70)
-#68 := (= #15 #67)
-#65 := (= #14 #64)
-#62 := (iff #13 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#79 := [trans #72 #77]: #78
-#82 := [monotonicity #79]: #81
-#55 := [asserted]: #17
-#83 := [mp #55 #82]: #80
-#347 := (+ #10 #74)
-#339 := (>= #347 0::Int)
-#625 := (= #10 #67)
-#240 := (= f5 #64)
-#327 := (or #241 #240)
-#328 := [def-axiom]: #327
-#618 := [unit-resolution #328 #340]: #240
-#619 := [monotonicity #618]: #625
-#334 := (not #625)
-#616 := (or #334 #339)
-#620 := [th-lemma arith triangle-eq]: #616
-#617 := [unit-resolution #620 #619]: #339
-#621 := [th-lemma arith farkas -1 1 1 #617 #83 #340]: false
-#610 := [lemma #621]: #241
-#319 := (or #61 #326)
-#330 := [def-axiom]: #319
-#612 := [unit-resolution #330 #610]: #326
-#607 := [monotonicity #612]: #338
-#608 := (not #338)
-#613 := (or #608 #73)
-#614 := [th-lemma arith triangle-eq]: #613
-[unit-resolution #614 #83 #607]: false
-unsat
-2f52c0eb5cf7f99a57b987b4ca5bf5d9d94c7e8e 277 0
-#2 := false
-#25 := 0::Int
+#113 := (iff #17 #112)
+#110 := (iff #16 #109)
+#107 := (= #15 #106)
+#103 := (iff #14 #104)
+#105 := [rewrite]: #103
+#108 := [monotonicity #105]: #107
+#101 := (= #13 #100)
+#98 := (iff #12 #97)
+#99 := [rewrite]: #98
+#102 := [monotonicity #99]: #101
+#111 := [monotonicity #102 #108]: #110
+#114 := [monotonicity #111]: #113
+#37 := [asserted]: #17
+#115 := [mp #37 #114]: #112
+#256 := [mp #115 #534]: #156
+#228 := (or #97 #235)
+#239 := [def-axiom]: #228
+#257 := [unit-resolution #239 #256]: #97
+#535 := [th-lemma arith eq-propagate 1 1 #549 #257]: #531
+#536 := [symm #535]: #532
+#527 := [monotonicity #536]: #249
+#247 := (= f6 #552)
+#226 := (= #552 f6)
+#557 := (or #227 #226)
+#563 := [quant-inst #10]: #557
+#246 := [unit-resolution #563 #570]: #226
+#248 := [symm #246]: #247
+#243 := [trans #248 #527]: #528
+#529 := [trans #243 #190]: #525
+#526 := [trans #529 #189]: #241
+#530 := [unit-resolution #543 #526]: false
+#519 := [lemma #530]: #241
+#516 := [symm #519]: #521
+#523 := [monotonicity #516]: #522
+#366 := [trans #523 #524]: #365
+#509 := [symm #366]: #367
+#520 := [hypothesis]: #149
+#510 := [mp #520 #509]: #109
+#511 := [unit-resolution #115 #510]: false
+#506 := [lemma #511]: #512
+#236 := (or #150 #149)
+#237 := [def-axiom]: #236
+#507 := [unit-resolution #237 #506]: #150
+#344 := [unit-resolution #239 #507]: #235
+#346 := [symm #344]: #551
+#500 := [monotonicity #346]: #347
+#503 := [symm #500]: #501
+#513 := (or #104 #97)
+#514 := [th-lemma arith farkas 1 1]: #513
+#508 := [unit-resolution #514 #507]: #104
+#515 := [unit-resolution #221 #508]: #240
+#504 := [mp #515 #503]: #109
+[unit-resolution #115 #504]: false
+e64a5f6562eb36da4004d28b7f33df8ec768098a 238 0
+unsat
+#2 := false
+decl f5 :: S3
+#8 := f5
+decl f6 :: (-> S4 Int S3)
+#11 := 0::Int
+decl f7 :: S4
+#10 := f7
+#12 := (f6 f7 0::Int)
+decl f3 :: (-> S2 S3 Int)
+decl f4 :: S2
+#7 := f4
+#13 := (f3 f4 #12)
+#92 := -1::Int
+#93 := (* -1::Int #13)
+#9 := (f3 f4 f5)
+#94 := (+ #9 #93)
+#95 := (<= #94 0::Int)
+#98 := (if #95 #12 f5)
+#227 := (= f5 #98)
+#141 := (= #12 #98)
+#519 := (not #227)
+#101 := (= #98 f5)
+#104 := (not #101)
+#520 := (iff #104 #519)
+#240 := (iff #101 #227)
+#241 := [commutativity]: #240
+#235 := [monotonicity #241]: #520
+#14 := (<= #9 #13)
+#15 := (if #14 #12 f5)
+#16 := (= #15 f5)
+#17 := (not #16)
+#105 := (iff #17 #104)
+#102 := (iff #16 #101)
+#99 := (= #15 #98)
+#96 := (iff #14 #95)
+#97 := [rewrite]: #96
+#100 := [monotonicity #97]: #99
+#103 := [monotonicity #100]: #102
+#106 := [monotonicity #103]: #105
+#35 := [asserted]: #17
+#107 := [mp #35 #106]: #104
+#517 := [mp #107 #235]: #519
+#220 := (or #95 #227)
+#231 := [def-axiom]: #220
+#521 := [unit-resolution #231 #517]: #95
+#142 := (not #95)
+#228 := (or #142 #141)
+#229 := [def-axiom]: #228
+#503 := [unit-resolution #229 #521]: #141
+#339 := (= f5 #12)
+#232 := (f6 f7 #9)
+#500 := (= #232 #12)
+#542 := (= #9 0::Int)
+#255 := (f3 f4 #232)
+#148 := (= #255 0::Int)
+#248 := (<= #9 0::Int)
+#541 := (<= #13 0::Int)
+#219 := (= #13 0::Int)
+#23 := (:var 0 Int)
+#25 := (f6 f7 #23)
+#563 := (pattern #25)
+#26 := (f3 f4 #25)
+#27 := (= #26 #23)
+#109 := (>= #23 0::Int)
+#111 := (not #109)
+#114 := (or #111 #27)
+#564 := (forall (vars (?v0 Int)) (:pat #563) #114)
+#117 := (forall (vars (?v0 Int)) #114)
+#567 := (iff #117 #564)
+#565 := (iff #114 #114)
+#566 := [refl]: #565
+#568 := [quant-intro #566]: #567
+#135 := (~ #117 #117)
+#133 := (~ #114 #114)
+#134 := [refl]: #133
+#130 := [nnf-pos #134]: #135
+#24 := (<= 0::Int #23)
+#46 := (not #24)
+#47 := (or #46 #27)
+#51 := (forall (vars (?v0 Int)) #47)
+#118 := (iff #51 #117)
+#115 := (iff #47 #114)
+#112 := (iff #46 #111)
+#108 := (iff #24 #109)
+#110 := [rewrite]: #108
+#113 := [monotonicity #110]: #112
+#116 := [monotonicity #113]: #115
+#119 := [quant-intro #116]: #118
+#28 := (implies #24 #27)
+#29 := (forall (vars (?v0 Int)) #28)
+#52 := (iff #29 #51)
+#48 := (iff #28 #47)
+#49 := [rewrite]: #48
+#44 := (iff #28 #28)
+#42 := (iff #24 #24)
+#43 := [rewrite]: #42
+#45 := [monotonicity #43]: #44
+#50 := [trans #45 #49]: #48
+#53 := [quant-intro #50]: #52
+#37 := [asserted]: #29
+#54 := [mp #37 #53]: #51
+#120 := [mp #54 #119]: #117
+#131 := [mp~ #120 #130]: #117
+#569 := [mp #131 #568]: #564
+#197 := (not #564)
+#533 := (or #197 #219)
+#207 := (>= 0::Int 0::Int)
+#337 := (not #207)
+#551 := (or #337 #219)
+#534 := (or #197 #551)
+#536 := (iff #534 #533)
+#532 := (iff #533 #533)
+#538 := [rewrite]: #532
+#195 := (iff #551 #219)
+#206 := (or false #219)
+#531 := (iff #206 #219)
+#194 := [rewrite]: #531
+#547 := (iff #551 #206)
+#210 := (iff #337 false)
+#1 := true
+#554 := (not true)
+#545 := (iff #554 false)
+#205 := [rewrite]: #545
+#549 := (iff #337 #554)
+#552 := (iff #207 true)
+#553 := [rewrite]: #552
+#555 := [monotonicity #553]: #549
+#546 := [trans #555 #205]: #210
+#190 := [monotonicity #546]: #547
+#196 := [trans #190 #194]: #195
+#537 := [monotonicity #196]: #536
+#176 := [trans #537 #538]: #536
+#535 := [quant-inst #11]: #534
+#539 := [mp #535 #176]: #533
+#518 := [unit-resolution #539 #569]: #219
+#522 := (not #219)
+#511 := (or #522 #541)
+#512 := [th-lemma arith triangle-eq]: #511
+#513 := [unit-resolution #512 #518]: #541
+#508 := (not #248)
+#509 := [hypothesis]: #508
+#514 := [th-lemma arith farkas -1 1 1 #509 #513 #521]: false
+#515 := [lemma #514]: #248
+#254 := (>= #9 0::Int)
+#540 := (not #148)
+#543 := [hypothesis]: #540
+#525 := (or #254 #148)
+#31 := (= #26 0::Int)
+#121 := (or #109 #31)
+#570 := (forall (vars (?v0 Int)) (:pat #563) #121)
+#124 := (forall (vars (?v0 Int)) #121)
+#573 := (iff #124 #570)
+#571 := (iff #121 #121)
+#572 := [refl]: #571
+#574 := [quant-intro #572]: #573
+#138 := (~ #124 #124)
+#136 := (~ #121 #121)
+#137 := [refl]: #136
+#139 := [nnf-pos #137]: #138
+#63 := (or #24 #31)
+#68 := (forall (vars (?v0 Int)) #63)
+#125 := (iff #68 #124)
+#122 := (iff #63 #121)
+#123 := [monotonicity #110]: #122
+#126 := [quant-intro #123]: #125
+#30 := (< #23 0::Int)
+#32 := (implies #30 #31)
+#33 := (forall (vars (?v0 Int)) #32)
+#69 := (iff #33 #68)
+#66 := (iff #32 #63)
+#60 := (implies #46 #31)
+#64 := (iff #60 #63)
+#65 := [rewrite]: #64
+#61 := (iff #32 #60)
+#55 := (iff #30 #46)
+#57 := (iff #46 #46)
+#58 := [monotonicity #43]: #57
+#56 := [rewrite]: #55
+#59 := [trans #56 #58]: #55
+#62 := [monotonicity #59]: #61
+#67 := [trans #62 #65]: #66
+#70 := [quant-intro #67]: #69
+#38 := [asserted]: #33
+#71 := [mp #38 #70]: #68
+#127 := [mp #71 #126]: #124
+#140 := [mp~ #127 #139]: #124
+#575 := [mp #140 #574]: #570
+#249 := (not #570)
+#523 := (or #249 #254 #148)
+#527 := (or #249 #525)
+#528 := (iff #527 #523)
+#238 := [rewrite]: #528
+#524 := [quant-inst #9]: #527
+#239 := [mp #524 #238]: #523
+#529 := [unit-resolution #239 #575]: #525
+#530 := [unit-resolution #529 #543]: #254
+#252 := (not #254)
+#253 := (or #542 #508 #252)
+#526 := [th-lemma arith triangle-eq]: #253
+#510 := [unit-resolution #526 #530 #515]: #542
+#357 := (= #255 #9)
+#233 := (= #232 f5)
+#18 := (:var 0 S3)
+#19 := (f3 f4 #18)
+#556 := (pattern #19)
+#20 := (f6 f7 #19)
+#21 := (= #20 #18)
+#557 := (forall (vars (?v0 S3)) (:pat #556) #21)
+#22 := (forall (vars (?v0 S3)) #21)
+#560 := (iff #22 #557)
+#558 := (iff #21 #21)
+#559 := [refl]: #558
+#561 := [quant-intro #559]: #560
+#128 := (~ #22 #22)
+#90 := (~ #21 #21)
+#91 := [refl]: #90
+#129 := [nnf-pos #91]: #128
+#36 := [asserted]: #22
+#132 := [mp~ #36 #129]: #22
+#562 := [mp #132 #561]: #557
+#213 := (not #557)
+#548 := (or #213 #233)
+#550 := [quant-inst #8]: #548
+#516 := [unit-resolution #550 #562]: #233
+#358 := [monotonicity #516]: #357
+#359 := [trans #358 #510]: #148
+#501 := [unit-resolution #543 #359]: false
+#502 := [lemma #501]: #148
+#499 := (= #9 #255)
+#504 := (= f5 #232)
+#498 := [symm #516]: #504
+#505 := [monotonicity #498]: #499
+#506 := [trans #505 #502]: #542
+#507 := [monotonicity #506]: #500
+#492 := [trans #498 #507]: #339
+#493 := [trans #492 #503]: #227
+[unit-resolution #517 #493]: false
+296289ecaade249ef4b64fabef5f8f640a51e417 123 0
+unsat
+#2 := false
+#7 := 0::Int
 decl f3 :: (-> S2 S3 Int)
 decl f5 :: S3
 #9 := f5
 decl f4 :: S2
 #8 := f4
 #10 := (f3 f4 f5)
-#340 := (= #10 0::Int)
-decl f7 :: (-> S4 Int S3)
-decl f8 :: S4
-#19 := f8
-#333 := (f7 f8 #10)
-#320 := (f3 f4 #333)
-#654 := (= #320 0::Int)
-#319 := (>= #10 0::Int)
-#572 := (not #319)
-decl f6 :: S3
-#11 := f6
-#12 := (f3 f4 f6)
-#59 := -1::Int
-#60 := (* -1::Int #12)
-#61 := (+ #10 #60)
-#62 := (<= #61 0::Int)
-#65 := (ite #62 f5 f6)
-#68 := (f3 f4 #65)
-#77 := (* -1::Int #68)
-#78 := (+ #12 #77)
-#79 := (+ #10 #78)
-#75 := (>= #79 0::Int)
-#82 := (not #75)
-#16 := (+ #10 #12)
-#13 := (<= #10 #12)
-#14 := (ite #13 f5 f6)
+#222 := (= #10 0::Int)
+decl f6 :: (-> S4 Int S3)
+decl f7 :: S4
+#13 := f7
+#219 := (f6 f7 #10)
+#220 := (f3 f4 #219)
+#221 := (= #220 0::Int)
+#19 := (:var 0 Int)
+#21 := (f6 f7 #19)
+#556 := (pattern #21)
+#22 := (f3 f4 #21)
+#27 := (= #22 0::Int)
+#102 := (>= #19 0::Int)
+#113 := (or #102 #27)
+#563 := (forall (vars (?v0 Int)) (:pat #556) #113)
+#116 := (forall (vars (?v0 Int)) #113)
+#566 := (iff #116 #563)
+#564 := (iff #113 #113)
+#565 := [refl]: #564
+#567 := [quant-intro #565]: #566
+#130 := (~ #116 #116)
+#128 := (~ #113 #113)
+#129 := [refl]: #128
+#131 := [nnf-pos #129]: #130
+#20 := (<= 0::Int #19)
+#64 := (or #20 #27)
+#69 := (forall (vars (?v0 Int)) #64)
+#117 := (iff #69 #116)
+#114 := (iff #64 #113)
+#100 := (iff #20 #102)
+#101 := [rewrite]: #100
+#115 := [monotonicity #101]: #114
+#118 := [quant-intro #115]: #117
+#26 := (< #19 0::Int)
+#28 := (implies #26 #27)
+#29 := (forall (vars (?v0 Int)) #28)
+#70 := (iff #29 #69)
+#67 := (iff #28 #64)
+#47 := (not #20)
+#61 := (implies #47 #27)
+#65 := (iff #61 #64)
+#66 := [rewrite]: #65
+#62 := (iff #28 #61)
+#56 := (iff #26 #47)
+#58 := (iff #47 #47)
+#43 := (iff #20 #20)
+#44 := [rewrite]: #43
+#59 := [monotonicity #44]: #58
+#57 := [rewrite]: #56
+#60 := [trans #57 #59]: #56
+#63 := [monotonicity #60]: #62
+#68 := [trans #63 #66]: #67
+#71 := [quant-intro #68]: #70
+#34 := [asserted]: #29
+#72 := [mp #34 #71]: #69
+#119 := [mp #72 #118]: #116
+#132 := [mp~ #119 #131]: #116
+#568 := [mp #132 #567]: #563
+#94 := (>= #10 0::Int)
+#95 := (not #94)
+#11 := (<= 0::Int #10)
+#12 := (not #11)
+#96 := (iff #12 #95)
+#92 := (iff #11 #94)
+#93 := [rewrite]: #92
+#97 := [monotonicity #93]: #96
+#40 := (iff #12 #12)
+#38 := (iff #11 #11)
+#39 := [rewrite]: #38
+#41 := [monotonicity #39]: #40
+#31 := [asserted]: #12
+#42 := [mp #31 #41]: #12
+#98 := [mp #42 #97]: #95
+#205 := (not #563)
+#541 := (or #205 #94 #221)
+#225 := (or #94 #221)
+#543 := (or #205 #225)
+#330 := (iff #543 #541)
+#537 := [rewrite]: #330
+#199 := [quant-inst #10]: #543
+#210 := [mp #199 #537]: #541
+#211 := [unit-resolution #210 #98 #568]: #221
+#547 := (= #10 #220)
+#545 := (= f5 #219)
+#134 := (= #219 f5)
+#14 := (:var 0 S3)
 #15 := (f3 f4 #14)
-#17 := (<= #15 #16)
-#18 := (not #17)
-#83 := (iff #18 #82)
-#80 := (iff #17 #75)
-#71 := (<= #68 #16)
-#74 := (iff #71 #75)
-#76 := [rewrite]: #74
-#72 := (iff #17 #71)
-#69 := (= #15 #68)
-#66 := (= #14 #65)
-#63 := (iff #13 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#70 := [monotonicity #67]: #69
-#73 := [monotonicity #70]: #72
-#81 := [trans #73 #76]: #80
-#84 := [monotonicity #81]: #83
-#56 := [asserted]: #18
-#85 := [mp #56 #84]: #82
-#590 := (>= #78 0::Int)
-#597 := (= #12 #68)
-#328 := (= f6 #65)
-#651 := (f7 f8 #68)
-#481 := (= #651 #65)
-#308 := (= #65 #651)
-#20 := (:var 0 S3)
-#21 := (f3 f4 #20)
-#657 := (pattern #21)
-#22 := (f7 f8 #21)
-#58 := (= #20 #22)
-#658 := (forall (vars (?v0 S3)) (:pat #657) #58)
-#88 := (forall (vars (?v0 S3)) #58)
-#661 := (iff #88 #658)
-#659 := (iff #58 #58)
-#660 := [refl]: #659
-#662 := [quant-intro #660]: #661
-#182 := (~ #88 #88)
-#180 := (~ #58 #58)
-#181 := [refl]: #180
-#183 := [nnf-pos #181]: #182
-#23 := (= #22 #20)
-#24 := (forall (vars (?v0 S3)) #23)
-#89 := (iff #24 #88)
-#86 := (iff #23 #58)
-#87 := [rewrite]: #86
-#90 := [quant-intro #87]: #89
-#57 := [asserted]: #24
-#93 := [mp #57 #90]: #88
-#172 := [mp~ #93 #183]: #88
-#663 := [mp #172 #662]: #658
-#335 := (not #658)
-#652 := (or #335 #308)
-#653 := [quant-inst #65]: #652
-#621 := [unit-resolution #653 #663]: #308
-#482 := [symm #621]: #481
-#441 := (= f6 #651)
-#334 := (f7 f8 #12)
-#598 := (= #334 #651)
-#356 := (f3 f4 #651)
-#437 := (= #356 #68)
-#606 := (= #68 #356)
-#607 := [monotonicity #621]: #606
-#439 := [symm #607]: #437
-#594 := (= #12 #356)
-#601 := (= 0::Int #356)
-#249 := (= #356 0::Int)
-#355 := (>= #68 0::Int)
-#614 := (not #355)
-#349 := (+ #10 #77)
-#341 := (>= #349 0::Int)
-#627 := (= #10 #68)
-#242 := (= f5 #65)
-#342 := (not #328)
-#620 := [hypothesis]: #342
-#321 := (or #62 #328)
-#332 := [def-axiom]: #321
-#336 := [unit-resolution #332 #620]: #62
-#243 := (not #62)
-#329 := (or #243 #242)
-#330 := [def-axiom]: #329
-#618 := [unit-resolution #330 #336]: #242
-#622 := [monotonicity #618]: #627
-#619 := (not #627)
-#623 := (or #619 #341)
-#612 := [th-lemma arith triangle-eq]: #623
-#613 := [unit-resolution #612 #622]: #341
-#609 := (not #341)
-#610 := (or #614 #609 #243 #75)
-#615 := [th-lemma arith assign-bounds 2 -1 -1]: #610
-#616 := [unit-resolution #615 #336 #85 #613]: #614
-#626 := (or #249 #355)
-#26 := (:var 0 Int)
-#28 := (f7 f8 #26)
-#664 := (pattern #28)
-#109 := (>= #26 0::Int)
-#29 := (f3 f4 #28)
-#34 := (= #29 0::Int)
-#158 := (or #34 #109)
-#671 := (forall (vars (?v0 Int)) (:pat #664) #158)
-#163 := (forall (vars (?v0 Int)) #158)
-#674 := (iff #163 #671)
-#672 := (iff #158 #158)
-#673 := [refl]: #672
-#675 := [quant-intro #673]: #674
-#176 := (~ #163 #163)
-#184 := (~ #158 #158)
-#185 := [refl]: #184
-#177 := [nnf-pos #185]: #176
-#33 := (< #26 0::Int)
-#35 := (implies #33 #34)
-#36 := (forall (vars (?v0 Int)) #35)
-#166 := (iff #36 #163)
-#129 := (= 0::Int #29)
-#135 := (not #33)
-#136 := (or #135 #129)
-#141 := (forall (vars (?v0 Int)) #136)
-#164 := (iff #141 #163)
-#161 := (iff #136 #158)
-#155 := (or #109 #34)
-#159 := (iff #155 #158)
-#160 := [rewrite]: #159
-#156 := (iff #136 #155)
-#153 := (iff #129 #34)
-#154 := [rewrite]: #153
-#151 := (iff #135 #109)
-#111 := (not #109)
-#146 := (not #111)
-#149 := (iff #146 #109)
-#150 := [rewrite]: #149
-#147 := (iff #135 #146)
-#144 := (iff #33 #111)
-#145 := [rewrite]: #144
-#148 := [monotonicity #145]: #147
-#152 := [trans #148 #150]: #151
-#157 := [monotonicity #152 #154]: #156
-#162 := [trans #157 #160]: #161
-#165 := [quant-intro #162]: #164
-#142 := (iff #36 #141)
-#139 := (iff #35 #136)
-#132 := (implies #33 #129)
-#137 := (iff #132 #136)
-#138 := [rewrite]: #137
-#133 := (iff #35 #132)
-#130 := (iff #34 #129)
-#131 := [rewrite]: #130
-#134 := [monotonicity #131]: #133
-#140 := [trans #134 #138]: #139
-#143 := [quant-intro #140]: #142
-#167 := [trans #143 #165]: #166
-#128 := [asserted]: #36
-#168 := [mp #128 #167]: #163
-#186 := [mp~ #168 #177]: #163
-#676 := [mp #186 #675]: #671
-#306 := (not #671)
-#350 := (or #306 #249 #355)
-#624 := (or #306 #626)
-#625 := (iff #624 #350)
-#629 := [rewrite]: #625
-#628 := [quant-inst #68]: #624
-#339 := [mp #628 #629]: #350
-#611 := [unit-resolution #339 #676]: #626
-#617 := [unit-resolution #611 #616]: #249
-#608 := [symm #617]: #601
-#440 := (= #12 0::Int)
-#636 := (f3 f4 #334)
-#637 := (= #636 0::Int)
-#635 := (>= #12 0::Int)
-#458 := (not #635)
-#459 := (or #458 #609 #75)
-#460 := [th-lemma arith assign-bounds 1 -1]: #459
-#602 := [unit-resolution #460 #613 #85]: #458
-#633 := (or #635 #637)
-#640 := (or #306 #635 #637)
-#638 := (or #637 #635)
-#642 := (or #306 #638)
-#631 := (iff #642 #640)
-#283 := (or #306 #633)
-#644 := (iff #283 #640)
-#630 := [rewrite]: #644
-#643 := (iff #642 #283)
-#639 := (iff #638 #633)
-#277 := [rewrite]: #639
-#641 := [monotonicity #277]: #643
-#353 := [trans #641 #630]: #631
-#282 := [quant-inst #12]: #642
-#354 := [mp #282 #353]: #640
-#603 := [unit-resolution #354 #676]: #633
-#604 := [unit-resolution #603 #602]: #637
-#599 := (= #12 #636)
-#331 := (= f6 #334)
-#438 := (or #335 #331)
-#645 := [quant-inst #11]: #438
-#605 := [unit-resolution #645 #663]: #331
-#600 := [monotonicity #605]: #599
-#593 := [trans #600 #604]: #440
-#596 := [trans #593 #608]: #594
-#595 := [trans #596 #439]: #597
-#480 := [monotonicity #595]: #598
-#589 := [trans #605 #480]: #441
-#491 := [trans #589 #482]: #328
-#586 := [unit-resolution #620 #491]: false
-#587 := [lemma #586]: #328
-#475 := [monotonicity #587]: #597
-#493 := (not #590)
-#486 := [hypothesis]: #493
-#588 := (not #597)
-#592 := (or #588 #590)
-#579 := [th-lemma arith triangle-eq]: #592
-#581 := [unit-resolution #579 #486 #475]: false
-#573 := [lemma #581]: #590
-#582 := (or #572 #493 #75)
-#583 := [th-lemma arith assign-bounds 1 -1]: #582
-#584 := [unit-resolution #583 #573 #85]: #572
-#650 := (or #319 #654)
-#311 := (or #306 #319 #654)
-#655 := (or #654 #319)
-#647 := (or #306 #655)
-#297 := (iff #647 #311)
-#648 := (or #306 #650)
-#295 := (iff #648 #311)
-#296 := [rewrite]: #295
-#291 := (iff #647 #648)
-#656 := (iff #655 #650)
-#646 := [rewrite]: #656
-#632 := [monotonicity #646]: #291
-#298 := [trans #632 #296]: #297
-#307 := [quant-inst #10]: #647
-#634 := [mp #307 #298]: #311
-#580 := [unit-resolution #634 #676]: #650
-#585 := [unit-resolution #580 #584]: #654
-#577 := (= #10 #320)
-#261 := (= f5 #333)
-#314 := (or #335 #261)
-#649 := [quant-inst #9]: #314
-#574 := [unit-resolution #649 #663]: #261
-#571 := [monotonicity #574]: #577
-#578 := [trans #571 #585]: #340
-#562 := (not #340)
-#563 := (or #562 #319)
-#565 := [th-lemma arith triangle-eq]: #563
-[unit-resolution #565 #584 #578]: false
-unsat
-4e6556ab36648cdf433cba24ee625ef22ea51c56 123 0
-#2 := false
-decl f3 :: (-> S2 S3 Int)
-decl f7 :: S3
-#14 := f7
-decl f6 :: S3
-#11 := f6
-#30 := 0::Int
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 f7)
-#69 := -1::Int
-#78 := (* -1::Int #15)
-#12 := (f3 f4 f6)
-#88 := (+ #12 #78)
-#89 := (<= #88 0::Int)
-#92 := (ite #89 f6 f7)
-#95 := (f3 f4 #92)
-#652 := (= #12 #95)
-#280 := (= f6 #92)
-#366 := (= f7 #92)
-#479 := (not #366)
-#637 := (= #15 #95)
-#518 := [hypothesis]: #366
-#519 := [monotonicity #518]: #637
-#631 := (not #637)
-#103 := (* -1::Int #95)
-#638 := (+ #15 #103)
-#644 := (<= #638 0::Int)
-#475 := (not #644)
-decl f5 :: S3
-#9 := f5
-#10 := (f3 f4 f5)
-#104 := (+ #10 #103)
-#102 := (>= #104 0::Int)
-#101 := (not #102)
-#79 := (+ #10 #78)
-#77 := (>= #79 0::Int)
-#76 := (not #77)
-#72 := (* -1::Int #12)
-#73 := (+ #10 #72)
-#71 := (>= #73 0::Int)
-#70 := (not #71)
-#82 := (and #70 #76)
-#85 := (not #82)
-#109 := (or #85 #101)
-#112 := (not #109)
-#18 := (<= #12 #15)
-#19 := (ite #18 f6 f7)
-#20 := (f3 f4 #19)
-#21 := (< #10 #20)
-#16 := (< #10 #15)
-#13 := (< #10 #12)
-#17 := (and #13 #16)
-#22 := (implies #17 #21)
-#23 := (not #22)
-#115 := (iff #23 #112)
-#62 := (not #17)
-#63 := (or #62 #21)
-#66 := (not #63)
-#113 := (iff #66 #112)
-#110 := (iff #63 #109)
-#107 := (iff #21 #101)
-#98 := (< #10 #95)
-#105 := (iff #98 #101)
-#106 := [rewrite]: #105
-#99 := (iff #21 #98)
-#96 := (= #20 #95)
-#93 := (= #19 #92)
-#90 := (iff #18 #89)
-#91 := [rewrite]: #90
-#94 := [monotonicity #91]: #93
-#97 := [monotonicity #94]: #96
-#100 := [monotonicity #97]: #99
-#108 := [trans #100 #106]: #107
-#86 := (iff #62 #85)
-#83 := (iff #17 #82)
-#80 := (iff #16 #76)
-#81 := [rewrite]: #80
-#74 := (iff #13 #70)
-#75 := [rewrite]: #74
-#84 := [monotonicity #75 #81]: #83
-#87 := [monotonicity #84]: #86
-#111 := [monotonicity #87 #108]: #110
-#114 := [monotonicity #111]: #113
-#67 := (iff #23 #66)
-#64 := (iff #22 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#116 := [trans #68 #114]: #115
-#61 := [asserted]: #23
-#117 := [mp #61 #116]: #112
-#121 := [not-or-elim #117]: #102
-#118 := [not-or-elim #117]: #82
-#120 := [and-elim #118]: #76
-#639 := [hypothesis]: #644
-#646 := [th-lemma arith farkas -1 -1 1 #639 #120 #121]: false
-#477 := [lemma #646]: #475
-#632 := (or #631 #644)
-#634 := [th-lemma arith triangle-eq]: #632
-#636 := [unit-resolution #634 #477]: #631
-#520 := [unit-resolution #636 #519]: false
-#627 := [lemma #520]: #479
-#359 := (or #89 #366)
-#370 := [def-axiom]: #359
-#624 := [unit-resolution #370 #627]: #89
-#281 := (not #89)
-#367 := (or #281 #280)
-#368 := [def-axiom]: #367
-#625 := [unit-resolution #368 #624]: #280
-#628 := [monotonicity #625]: #652
-#498 := (not #652)
-#647 := (+ #12 #103)
-#648 := (<= #647 0::Int)
-#655 := (not #648)
-#119 := [and-elim #118]: #70
-#654 := [hypothesis]: #648
-#649 := [th-lemma arith farkas -1 -1 1 #654 #119 #121]: false
-#496 := [lemma #649]: #655
-#640 := (or #498 #648)
-#641 := [th-lemma arith triangle-eq]: #640
-#529 := [unit-resolution #641 #496]: #498
-[unit-resolution #529 #628]: false
-unsat
-01147de59b42ac4a29c41704be4c71d5a4b3cce2 158 0
-#2 := false
-decl f5 :: S3
-#9 := f5
-decl f6 :: S3
-#11 := f6
-#25 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f4 :: S2
-#8 := f4
-#12 := (f3 f4 f6)
-#59 := -1::Int
-#60 := (* -1::Int #12)
-#10 := (f3 f4 f5)
-#61 := (+ #10 #60)
-#69 := (>= #61 0::Int)
-#71 := (ite #69 f6 f5)
-#62 := (<= #61 0::Int)
-#65 := (ite #62 f5 f6)
-#74 := (= #65 #71)
-#328 := (= f6 #71)
-#488 := (iff #328 #74)
-#485 := (iff #74 #328)
-#620 := (= #65 f6)
-#323 := (= f6 #65)
-#238 := (not #62)
-#237 := (= f5 #65)
-#476 := (not #237)
-#592 := (iff #237 #74)
-#589 := (iff #74 #237)
-#603 := (= #65 f5)
-#435 := (iff #603 #237)
-#588 := [commutativity]: #435
-#432 := (iff #74 #603)
-#602 := (= #71 f5)
-#256 := (= f5 #71)
-#621 := (not #256)
-#622 := [hypothesis]: #621
-#309 := (or #69 #256)
-#644 := [def-axiom]: #309
-#344 := [unit-resolution #644 #622]: #69
-#329 := (not #69)
-#326 := (or #329 #328)
-#330 := [def-axiom]: #326
-#345 := [unit-resolution #330 #344]: #328
-#598 := (= f5 f6)
-decl f7 :: (-> S4 Int S3)
-decl f8 :: S4
-#19 := f8
-#433 := (f7 f8 #12)
-#453 := (= #433 f6)
-#640 := (= f6 #433)
-#20 := (:var 0 S3)
-#21 := (f3 f4 #20)
-#652 := (pattern #21)
-#22 := (f7 f8 #21)
-#58 := (= #20 #22)
-#653 := (forall (vars (?v0 S3)) (:pat #652) #58)
-#83 := (forall (vars (?v0 S3)) #58)
-#656 := (iff #83 #653)
-#654 := (iff #58 #58)
-#655 := [refl]: #654
-#657 := [quant-intro #655]: #656
-#177 := (~ #83 #83)
-#175 := (~ #58 #58)
-#176 := [refl]: #175
-#178 := [nnf-pos #176]: #177
-#23 := (= #22 #20)
-#24 := (forall (vars (?v0 S3)) #23)
-#84 := (iff #24 #83)
-#81 := (iff #23 #58)
-#82 := [rewrite]: #81
-#85 := [quant-intro #82]: #84
-#57 := [asserted]: #24
-#88 := [mp #57 #85]: #83
-#167 := [mp~ #88 #178]: #83
-#658 := [mp #167 #657]: #653
-#314 := (not #653)
-#650 := (or #314 #640)
-#645 := [quant-inst #11]: #650
-#604 := [unit-resolution #645 #658]: #640
-#454 := [symm #604]: #453
-#455 := (= f5 #433)
-#646 := (f7 f8 #10)
-#606 := (= #646 #433)
-#610 := (= #433 #646)
-#608 := (= #12 #10)
-#618 := (= #10 #12)
-#616 := (not #323)
-#77 := (not #74)
-#331 := (iff #77 #616)
-#337 := (iff #74 #323)
-#335 := (iff #620 #323)
-#336 := [commutativity]: #335
-#624 := (iff #74 #620)
-#619 := (= #71 f6)
-#623 := [symm #345]: #619
-#334 := [monotonicity #623]: #624
-#615 := [trans #334 #336]: #337
-#613 := [monotonicity #615]: #331
-#15 := (<= #12 #10)
-#16 := (ite #15 f6 f5)
-#13 := (<= #10 #12)
-#14 := (ite #13 f5 f6)
-#17 := (= #14 #16)
-#18 := (not #17)
-#78 := (iff #18 #77)
-#75 := (iff #17 #74)
-#72 := (= #16 #71)
-#68 := (iff #15 #69)
-#70 := [rewrite]: #68
-#73 := [monotonicity #70]: #72
-#66 := (= #14 #65)
-#63 := (iff #13 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#76 := [monotonicity #67 #73]: #75
-#79 := [monotonicity #76]: #78
-#56 := [asserted]: #18
-#80 := [mp #56 #79]: #77
-#617 := [mp #80 #613]: #616
-#316 := (or #62 #323)
-#327 := [def-axiom]: #316
-#614 := [unit-resolution #327 #617]: #62
-#607 := [th-lemma arith eq-propagate 1 1 #344 #614]: #618
-#609 := [symm #607]: #608
-#611 := [monotonicity #609]: #610
-#612 := [symm #611]: #606
-#303 := (= f5 #646)
-#315 := (or #314 #303)
-#647 := [quant-inst #9]: #315
-#605 := [unit-resolution #647 #658]: #303
-#597 := [trans #605 #612]: #455
-#599 := [trans #597 #454]: #598
-#600 := [trans #599 #345]: #256
-#594 := [unit-resolution #622 #600]: false
-#595 := [lemma #594]: #256
-#596 := [symm #595]: #602
-#434 := [monotonicity #596]: #432
-#591 := [trans #434 #588]: #589
-#590 := [symm #591]: #592
-#601 := [hypothesis]: #237
-#593 := [mp #601 #590]: #74
-#475 := [unit-resolution #80 #593]: false
-#477 := [lemma #475]: #476
-#324 := (or #238 #237)
-#325 := [def-axiom]: #324
-#436 := [unit-resolution #325 #477]: #238
-#585 := [unit-resolution #327 #436]: #323
-#470 := [symm #585]: #620
-#487 := [monotonicity #470]: #485
-#481 := [symm #487]: #488
-#584 := (or #69 #62)
-#486 := [th-lemma arith farkas 1 1]: #584
-#581 := [unit-resolution #486 #436]: #69
-#582 := [unit-resolution #330 #581]: #328
-#489 := [mp #582 #481]: #74
-[unit-resolution #80 #489]: false
-unsat
-fbf994cf5d4385a5ee6e3cff92f24bb0bf6bf2e2 306 0
+#549 := (pattern #15)
+#16 := (f6 f7 #15)
+#17 := (= #16 #14)
+#550 := (forall (vars (?v0 S3)) (:pat #549) #17)
+#18 := (forall (vars (?v0 S3)) #17)
+#553 := (iff #18 #550)
+#551 := (iff #17 #17)
+#552 := [refl]: #551
+#554 := [quant-intro #552]: #553
+#122 := (~ #18 #18)
+#91 := (~ #17 #17)
+#99 := [refl]: #91
+#123 := [nnf-pos #99]: #122
+#32 := [asserted]: #18
+#126 := [mp~ #32 #123]: #18
+#555 := [mp #126 #554]: #550
+#212 := (not #550)
+#223 := (or #212 #134)
+#224 := [quant-inst #9]: #223
+#544 := [unit-resolution #224 #555]: #134
+#546 := [symm #544]: #545
+#542 := [monotonicity #546]: #547
+#548 := [trans #542 #211]: #222
+#538 := (not #222)
+#197 := (or #538 #94)
+#202 := [th-lemma arith triangle-eq]: #197
+[unit-resolution #202 #98 #548]: false
+5c14f8fdcb62dad5c500fbe42194f9994e95aaad 82 0
+unsat
 #2 := false
 decl f6 :: (-> S4 Int S3)
-#12 := 0::Int
+#12 := 1::Int
 decl f7 :: S4
-#11 := f7
-#13 := (f6 f7 0::Int)
-decl f5 :: S3
-#9 := f5
-decl f3 :: (-> S2 S3 Int)
-decl f4 :: S2
-#8 := f4
-#14 := (f3 f4 #13)
-#61 := -1::Int
-#62 := (* -1::Int #14)
-#10 := (f3 f4 f5)
-#63 := (+ #10 #62)
-#64 := (<= #63 0::Int)
-#67 := (ite #64 f5 #13)
-#70 := (= #13 #67)
-#327 := (f3 f4 #67)
-#328 := (f6 f7 #327)
-#593 := (= #328 #67)
-#256 := (= #67 #328)
-#19 := (:var 0 S3)
-#20 := (f3 f4 #19)
-#652 := (pattern #20)
-#21 := (f6 f7 #20)
-#80 := (= #19 #21)
-#653 := (forall (vars (?v0 S3)) (:pat #652) #80)
-#83 := (forall (vars (?v0 S3)) #80)
-#656 := (iff #83 #653)
-#654 := (iff #80 #80)
-#655 := [refl]: #654
-#657 := [quant-intro #655]: #656
-#177 := (~ #83 #83)
-#175 := (~ #80 #80)
-#176 := [refl]: #175
-#178 := [nnf-pos #176]: #177
-#22 := (= #21 #19)
-#23 := (forall (vars (?v0 S3)) #22)
-#84 := (iff #23 #83)
-#81 := (iff #22 #80)
-#82 := [rewrite]: #81
-#85 := [quant-intro #82]: #84
-#79 := [asserted]: #23
-#88 := [mp #79 #85]: #83
-#167 := [mp~ #88 #178]: #83
-#658 := [mp #167 #657]: #653
-#330 := (not #653)
-#309 := (or #330 #256)
-#644 := [quant-inst #67]: #309
-#603 := [unit-resolution #644 #658]: #256
-#475 := [symm #603]: #593
-#565 := (= #13 #328)
-#576 := (= 0::Int #327)
-#589 := (= #10 #327)
-#435 := (= #327 #10)
-#432 := (= #67 f5)
-#237 := (= f5 #67)
-#73 := (not #70)
-#15 := (<= #10 #14)
-#16 := (ite #15 f5 #13)
-#17 := (= #16 #13)
-#18 := (not #17)
-#76 := (iff #18 #73)
-#55 := (= #13 #16)
-#58 := (not #55)
-#74 := (iff #58 #73)
-#71 := (iff #55 #70)
-#68 := (= #16 #67)
-#65 := (iff #15 #64)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#59 := (iff #18 #58)
-#56 := (iff #17 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#77 := [trans #60 #75]: #76
-#54 := [asserted]: #18
-#78 := [mp #54 #77]: #73
-#325 := (or #64 #70)
-#316 := [def-axiom]: #325
-#609 := [unit-resolution #316 #78]: #64
-#323 := (not #64)
-#238 := (or #323 #237)
-#324 := [def-axiom]: #238
-#596 := [unit-resolution #324 #609]: #237
-#434 := [symm #596]: #432
-#588 := [monotonicity #434]: #435
-#591 := [symm #588]: #589
-#587 := (= 0::Int #10)
-#621 := (f6 f7 #10)
-#622 := (f3 f4 #621)
-#486 := (= #622 #10)
-#491 := (= #10 #622)
-#489 := (= f5 #621)
-#485 := (= #328 #621)
-#592 := (= #621 #328)
-#590 := [monotonicity #591]: #592
-#487 := [symm #590]: #485
-#488 := (= f5 #328)
-#481 := [trans #596 #603]: #488
-#490 := [trans #481 #487]: #489
-#492 := [monotonicity #490]: #491
-#583 := [symm #492]: #486
-#493 := (= 0::Int #622)
-#344 := (= #622 0::Int)
-#607 := (= #10 0::Int)
-#608 := (<= #10 0::Int)
-#278 := (<= #14 0::Int)
-#647 := (= #14 0::Int)
-#24 := (:var 0 Int)
-#26 := (f6 f7 #24)
-#659 := (pattern #26)
-#104 := (>= #24 0::Int)
-#106 := (not #104)
-#27 := (f3 f4 #26)
-#87 := (= #24 #27)
-#112 := (or #87 #106)
-#660 := (forall (vars (?v0 Int)) (:pat #659) #112)
-#117 := (forall (vars (?v0 Int)) #112)
-#663 := (iff #117 #660)
-#661 := (iff #112 #112)
-#662 := [refl]: #661
-#664 := [quant-intro #662]: #663
-#169 := (~ #117 #117)
-#168 := (~ #112 #112)
-#165 := [refl]: #168
-#170 := [nnf-pos #165]: #169
-#28 := (= #27 #24)
-#25 := (<= 0::Int #24)
-#29 := (implies #25 #28)
-#30 := (forall (vars (?v0 Int)) #29)
-#120 := (iff #30 #117)
-#94 := (not #25)
-#95 := (or #94 #87)
-#100 := (forall (vars (?v0 Int)) #95)
-#118 := (iff #100 #117)
-#115 := (iff #95 #112)
-#109 := (or #106 #87)
-#113 := (iff #109 #112)
-#114 := [rewrite]: #113
-#110 := (iff #95 #109)
-#107 := (iff #94 #106)
-#103 := (iff #25 #104)
-#105 := [rewrite]: #103
-#108 := [monotonicity #105]: #107
-#111 := [monotonicity #108]: #110
-#116 := [trans #111 #114]: #115
-#119 := [quant-intro #116]: #118
-#101 := (iff #30 #100)
-#98 := (iff #29 #95)
-#91 := (implies #25 #87)
-#96 := (iff #91 #95)
-#97 := [rewrite]: #96
-#92 := (iff #29 #91)
-#89 := (iff #28 #87)
-#90 := [rewrite]: #89
-#93 := [monotonicity #90]: #92
-#99 := [trans #93 #97]: #98
-#102 := [quant-intro #99]: #101
-#121 := [trans #102 #119]: #120
-#86 := [asserted]: #30
-#122 := [mp #86 #121]: #117
-#166 := [mp~ #122 #170]: #117
-#665 := [mp #166 #664]: #660
-#630 := (not #660)
-#631 := (or #630 #647)
-#646 := (>= 0::Int 0::Int)
-#303 := (not #646)
-#314 := (= 0::Int #14)
-#315 := (or #314 #303)
-#632 := (or #630 #315)
-#628 := (iff #632 #631)
-#272 := (iff #631 #631)
-#635 := [rewrite]: #272
-#293 := (iff #315 #647)
-#286 := (or #647 false)
-#291 := (iff #286 #647)
-#292 := [rewrite]: #291
-#627 := (iff #315 #286)
-#302 := (iff #303 false)
-#1 := true
-#651 := (not true)
-#306 := (iff #651 false)
-#642 := [rewrite]: #306
-#641 := (iff #303 #651)
-#650 := (iff #646 true)
-#645 := [rewrite]: #650
-#301 := [monotonicity #645]: #641
-#643 := [trans #301 #642]: #302
-#648 := (iff #314 #647)
-#649 := [rewrite]: #648
-#290 := [monotonicity #649 #643]: #627
-#629 := [trans #290 #292]: #293
-#634 := [monotonicity #629]: #628
-#637 := [trans #634 #635]: #628
-#633 := [quant-inst #12]: #632
-#277 := [mp #633 #637]: #631
-#604 := [unit-resolution #277 #665]: #647
-#605 := (not #647)
-#610 := (or #605 #278)
-#611 := [th-lemma arith triangle-eq]: #610
-#606 := [unit-resolution #611 #604]: #278
-#612 := (not #608)
-#453 := [hypothesis]: #612
-#454 := [th-lemma arith farkas -1 1 1 #453 #606 #609]: false
-#455 := [lemma #454]: #608
-#244 := (>= #10 0::Int)
-#597 := (not #344)
-#598 := [hypothesis]: #597
-#619 := (or #244 #344)
-#32 := (= #27 0::Int)
-#153 := (or #32 #104)
-#666 := (forall (vars (?v0 Int)) (:pat #659) #153)
-#158 := (forall (vars (?v0 Int)) #153)
-#669 := (iff #158 #666)
-#667 := (iff #153 #153)
-#668 := [refl]: #667
-#670 := [quant-intro #668]: #669
-#171 := (~ #158 #158)
-#179 := (~ #153 #153)
-#180 := [refl]: #179
-#172 := [nnf-pos #180]: #171
-#31 := (< #24 0::Int)
-#33 := (implies #31 #32)
-#34 := (forall (vars (?v0 Int)) #33)
-#161 := (iff #34 #158)
-#124 := (= 0::Int #27)
-#130 := (not #31)
-#131 := (or #130 #124)
-#136 := (forall (vars (?v0 Int)) #131)
-#159 := (iff #136 #158)
-#156 := (iff #131 #153)
-#150 := (or #104 #32)
-#154 := (iff #150 #153)
-#155 := [rewrite]: #154
-#151 := (iff #131 #150)
-#148 := (iff #124 #32)
-#149 := [rewrite]: #148
-#146 := (iff #130 #104)
-#141 := (not #106)
-#144 := (iff #141 #104)
-#145 := [rewrite]: #144
-#142 := (iff #130 #141)
-#139 := (iff #31 #106)
-#140 := [rewrite]: #139
-#143 := [monotonicity #140]: #142
-#147 := [trans #143 #145]: #146
-#152 := [monotonicity #147 #149]: #151
-#157 := [trans #152 #155]: #156
-#160 := [quant-intro #157]: #159
-#137 := (iff #34 #136)
-#134 := (iff #33 #131)
-#127 := (implies #31 #124)
-#132 := (iff #127 #131)
-#133 := [rewrite]: #132
-#128 := (iff #33 #127)
-#125 := (iff #32 #124)
-#126 := [rewrite]: #125
-#129 := [monotonicity #126]: #128
-#135 := [trans #129 #133]: #134
-#138 := [quant-intro #135]: #137
-#162 := [trans #138 #160]: #161
-#123 := [asserted]: #34
-#163 := [mp #123 #162]: #158
-#181 := [mp~ #163 #172]: #158
-#671 := [mp #181 #670]: #666
-#624 := (not #666)
-#334 := (or #624 #244 #344)
-#345 := (or #344 #244)
-#335 := (or #624 #345)
-#617 := (iff #335 #334)
-#337 := (or #624 #619)
-#331 := (iff #337 #334)
-#613 := [rewrite]: #331
-#615 := (iff #335 #337)
-#623 := (iff #345 #619)
-#620 := [rewrite]: #623
-#616 := [monotonicity #620]: #615
-#614 := [trans #616 #613]: #617
-#336 := [quant-inst #10]: #335
-#618 := [mp #336 #614]: #334
-#599 := [unit-resolution #618 #671]: #619
-#600 := [unit-resolution #599 #598]: #244
-#594 := (not #244)
-#595 := (or #607 #612 #594)
-#601 := [th-lemma arith triangle-eq]: #595
-#602 := [unit-resolution #601 #600 #455]: #607
-#436 := (= #621 f5)
-#476 := (= #621 #67)
-#477 := [trans #590 #475]: #476
-#584 := [trans #477 #434]: #436
-#581 := [monotonicity #584]: #486
-#582 := [trans #581 #602]: #344
-#585 := [unit-resolution #598 #582]: false
-#470 := [lemma #585]: #344
-#586 := [symm #470]: #493
-#574 := [trans #586 #583]: #587
-#568 := [trans #574 #591]: #576
-#567 := [monotonicity #568]: #565
-#577 := [trans #567 #475]: #70
-[unit-resolution #78 #577]: false
-unsat
-85603e9b42628a46d445e616c7b00cbba3c82418 70 0
-#2 := false
-decl f3 :: (-> S2 S3 Int)
-decl f5 :: S3
-#9 := f5
-decl f6 :: S3
-#11 := f6
-#24 := 0::Int
-decl f4 :: S2
-#8 := f4
-#12 := (f3 f4 f6)
-#58 := -1::Int
-#59 := (* -1::Int #12)
-#10 := (f3 f4 f5)
-#60 := (+ #10 #59)
-#61 := (<= #60 0::Int)
-#64 := (ite #61 f6 f5)
-#67 := (f3 f4 #64)
-#339 := (= #10 #67)
-#326 := (= f5 #64)
-#241 := (not #61)
-#340 := [hypothesis]: #61
-#73 := (* -1::Int #67)
-#74 := (+ #10 #73)
-#75 := (<= #74 0::Int)
-#80 := (not #75)
-#13 := (<= #10 #12)
-#14 := (ite #13 f6 f5)
-#15 := (f3 f4 #14)
-#16 := (<= #10 #15)
-#17 := (not #16)
-#81 := (iff #17 #80)
-#78 := (iff #16 #75)
-#70 := (<= #10 #67)
-#76 := (iff #70 #75)
-#77 := [rewrite]: #76
-#71 := (iff #16 #70)
-#68 := (= #15 #67)
-#65 := (= #14 #64)
-#62 := (iff #13 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#79 := [trans #72 #77]: #78
-#82 := [monotonicity #79]: #81
-#55 := [asserted]: #17
-#83 := [mp #55 #82]: #80
-#347 := (+ #12 #73)
-#338 := (<= #347 0::Int)
-#625 := (= #12 #67)
-#240 := (= f6 #64)
-#327 := (or #241 #240)
-#328 := [def-axiom]: #327
-#618 := [unit-resolution #328 #340]: #240
-#619 := [monotonicity #618]: #625
-#334 := (not #625)
-#616 := (or #334 #338)
-#620 := [th-lemma arith triangle-eq]: #616
-#617 := [unit-resolution #620 #619]: #338
-#621 := [th-lemma arith farkas 1 -1 1 #617 #83 #340]: false
-#610 := [lemma #621]: #241
-#319 := (or #61 #326)
-#330 := [def-axiom]: #319
-#612 := [unit-resolution #330 #610]: #326
-#607 := [monotonicity #612]: #339
-#608 := (not #339)
-#613 := (or #608 #75)
-#614 := [th-lemma arith triangle-eq]: #613
-[unit-resolution #614 #83 #607]: false
-unsat
-526d46cdfc0d87a1360427bc329d54e3e7b2ca5a 76 0
-#2 := false
-#24 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#11 := f6
+#15 := f7
+#16 := (f6 f7 1::Int)
 decl f5 :: S3
 #9 := f5
-decl f4 :: S2
-#8 := f4
-#12 := (f3 f4 f6)
-#58 := -1::Int
-#61 := (* -1::Int #12)
-#10 := (f3 f4 f5)
-#62 := (+ #10 #61)
-#60 := (>= #62 0::Int)
-#64 := (ite #60 f5 f6)
-#67 := (f3 f4 #64)
-#73 := (* -1::Int #67)
-#607 := (+ #12 #73)
-#608 := (<= #607 0::Int)
-#612 := (= #12 #67)
-#326 := (= f6 #64)
-#241 := (not #60)
-#240 := (= f5 #64)
-#610 := (not #240)
-#625 := (= #10 #67)
-#620 := [hypothesis]: #240
-#617 := [monotonicity #620]: #625
-#339 := (not #625)
-#74 := (+ #10 #73)
-#75 := (<= #74 0::Int)
-#80 := (not #75)
-#13 := (<= #12 #10)
-#14 := (ite #13 f5 f6)
-#15 := (f3 f4 #14)
-#16 := (<= #10 #15)
-#17 := (not #16)
-#81 := (iff #17 #80)
-#78 := (iff #16 #75)
-#70 := (<= #10 #67)
-#76 := (iff #70 #75)
-#77 := [rewrite]: #76
-#71 := (iff #16 #70)
-#68 := (= #15 #67)
-#65 := (= #14 #64)
-#59 := (iff #13 #60)
-#63 := [rewrite]: #59
-#66 := [monotonicity #63]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#79 := [trans #72 #77]: #78
-#82 := [monotonicity #79]: #81
-#55 := [asserted]: #17
-#83 := [mp #55 #82]: #80
-#340 := (or #339 #75)
-#618 := [th-lemma arith triangle-eq]: #340
-#616 := [unit-resolution #618 #83]: #339
-#621 := [unit-resolution #616 #617]: false
-#611 := [lemma #621]: #610
-#327 := (or #241 #240)
-#328 := [def-axiom]: #327
-#614 := [unit-resolution #328 #611]: #241
-#319 := (or #60 #326)
-#330 := [def-axiom]: #319
-#609 := [unit-resolution #330 #614]: #326
-#615 := [monotonicity #609]: #612
-#456 := (not #612)
-#457 := (or #456 #608)
-#458 := [th-lemma arith triangle-eq]: #457
-#600 := [unit-resolution #458 #615]: #608
-#347 := (>= #74 0::Int)
-#601 := (or #347 #75)
-#602 := [th-lemma arith farkas 1 1]: #601
-#603 := [unit-resolution #602 #83]: #347
-[th-lemma arith farkas 1 1 1 #603 #614 #600]: false
-unsat
-dada420705bc38de0c45602e9e3a17776a13efd2 465 0
-#2 := false
-decl f3 :: (-> S2 S3 Int)
-decl f7 :: S3
-#10 := f7
-decl f8 :: S3
-#12 := f8
-#31 := 0::Int
-decl f4 :: S2
-#8 := f4
-#13 := (f3 f4 f8)
-#63 := -1::Int
-#64 := (* -1::Int #13)
-#11 := (f3 f4 f7)
-#65 := (+ #11 #64)
-#93 := (<= #65 0::Int)
-#96 := (ite #93 f8 f7)
-#99 := (f3 f4 #96)
-#471 := (= #11 #99)
-#363 := (= f7 #96)
-#278 := (not #93)
-#566 := (= #13 #99)
-#277 := (= f8 #96)
-#420 := [hypothesis]: #93
-#364 := (or #278 #277)
-#365 := [def-axiom]: #364
-#421 := [unit-resolution #365 #420]: #277
-#422 := [monotonicity #421]: #566
-#105 := (* -1::Int #99)
-#541 := (+ #13 #105)
-#508 := (<= #541 0::Int)
-#466 := (not #508)
-decl f5 :: (-> S4 Int S3)
-decl f6 :: S4
-#9 := f6
-#68 := (f5 f6 #65)
-#71 := (f3 f4 #68)
-#660 := (<= #71 0::Int)
-#326 := (* -1::Int #71)
-#667 := (+ #64 #326)
-#330 := (+ #11 #667)
-#666 := (>= #330 0::Int)
-#331 := (= #330 0::Int)
-#681 := (>= #65 0::Int)
-#341 := (not #681)
-#447 := [hypothesis]: #341
-#443 := (or #681 #93)
-#433 := [th-lemma arith farkas 1 1]: #443
-#435 := [unit-resolution #433 #447]: #93
-#436 := [unit-resolution #365 #435]: #277
-#439 := [monotonicity #436]: #566
-#388 := (= #71 0::Int)
-#389 := (or #388 #681)
-#32 := (:var 0 Int)
-#34 := (f5 f6 #32)
-#699 := (pattern #34)
-#144 := (>= #32 0::Int)
-#35 := (f3 f4 #34)
-#40 := (= #35 0::Int)
-#193 := (or #40 #144)
-#706 := (forall (vars (?v0 Int)) (:pat #699) #193)
-#198 := (forall (vars (?v0 Int)) #193)
-#709 := (iff #198 #706)
-#707 := (iff #193 #193)
-#708 := [refl]: #707
-#710 := [quant-intro #708]: #709
-#211 := (~ #198 #198)
-#219 := (~ #193 #193)
-#220 := [refl]: #219
-#212 := [nnf-pos #220]: #211
-#39 := (< #32 0::Int)
-#41 := (implies #39 #40)
-#42 := (forall (vars (?v0 Int)) #41)
-#201 := (iff #42 #198)
-#164 := (= 0::Int #35)
-#170 := (not #39)
-#171 := (or #170 #164)
-#176 := (forall (vars (?v0 Int)) #171)
-#199 := (iff #176 #198)
-#196 := (iff #171 #193)
-#190 := (or #144 #40)
-#194 := (iff #190 #193)
-#195 := [rewrite]: #194
-#191 := (iff #171 #190)
-#188 := (iff #164 #40)
-#189 := [rewrite]: #188
-#186 := (iff #170 #144)
-#146 := (not #144)
-#181 := (not #146)
-#184 := (iff #181 #144)
-#185 := [rewrite]: #184
-#182 := (iff #170 #181)
-#179 := (iff #39 #146)
-#180 := [rewrite]: #179
-#183 := [monotonicity #180]: #182
-#187 := [trans #183 #185]: #186
-#192 := [monotonicity #187 #189]: #191
-#197 := [trans #192 #195]: #196
-#200 := [quant-intro #197]: #199
-#177 := (iff #42 #176)
-#174 := (iff #41 #171)
-#167 := (implies #39 #164)
-#172 := (iff #167 #171)
-#173 := [rewrite]: #172
-#168 := (iff #41 #167)
-#165 := (iff #40 #164)
-#166 := [rewrite]: #165
-#169 := [monotonicity #166]: #168
-#175 := [trans #169 #173]: #174
-#178 := [quant-intro #175]: #177
-#202 := [trans #178 #200]: #201
-#163 := [asserted]: #42
-#203 := [mp #163 #202]: #198
-#221 := [mp~ #203 #212]: #198
-#711 := [mp #221 #710]: #706
-#284 := (not #706)
-#661 := (or #284 #388 #681)
-#662 := (or #284 #389)
-#385 := (iff #662 #661)
-#659 := [rewrite]: #385
-#384 := [quant-inst #65]: #662
-#663 := [mp #384 #659]: #661
-#440 := [unit-resolution #663 #711]: #389
-#444 := [unit-resolution #440 #447]: #388
-#552 := (not #388)
-#437 := (or #552 #660)
-#445 := [th-lemma arith triangle-eq]: #437
-#438 := [unit-resolution #445 #444]: #660
-#521 := (>= #11 0::Int)
-#468 := (= #11 0::Int)
-#368 := (f5 f6 #11)
-#529 := (f3 f4 #368)
-#530 := (= #529 0::Int)
-#464 := (not #521)
-#450 := [hypothesis]: #464
-#532 := (or #521 #530)
-#623 := (or #284 #521 #530)
-#531 := (or #530 #521)
-#627 := (or #284 #531)
-#618 := (iff #627 #623)
-#616 := (or #284 #532)
-#607 := (iff #616 #623)
-#617 := [rewrite]: #607
-#608 := (iff #627 #616)
-#533 := (iff #531 #532)
-#626 := [rewrite]: #533
-#605 := [monotonicity #626]: #608
-#619 := [trans #605 #617]: #618
-#614 := [quant-inst #11]: #627
-#615 := [mp #614 #619]: #623
-#454 := [unit-resolution #615 #711]: #532
-#456 := [unit-resolution #454 #450]: #530
-#455 := (= #11 #529)
-#296 := (= f7 #368)
-#26 := (:var 0 S3)
-#27 := (f3 f4 #26)
-#692 := (pattern #27)
-#28 := (f5 f6 #27)
-#120 := (= #26 #28)
-#693 := (forall (vars (?v0 S3)) (:pat #692) #120)
-#123 := (forall (vars (?v0 S3)) #120)
-#696 := (iff #123 #693)
-#694 := (iff #120 #120)
-#695 := [refl]: #694
-#697 := [quant-intro #695]: #696
-#217 := (~ #123 #123)
-#215 := (~ #120 #120)
-#216 := [refl]: #215
-#218 := [nnf-pos #216]: #217
-#29 := (= #28 #26)
-#30 := (forall (vars (?v0 S3)) #29)
-#124 := (iff #30 #123)
-#121 := (iff #29 #120)
-#122 := [rewrite]: #121
-#125 := [quant-intro #122]: #124
-#119 := [asserted]: #30
-#128 := [mp #119 #125]: #123
-#207 := [mp~ #128 #218]: #123
-#698 := [mp #207 #697]: #693
-#370 := (not #693)
-#349 := (or #370 #296)
-#684 := [quant-inst #10]: #349
-#457 := [unit-resolution #684 #698]: #296
-#458 := [monotonicity #457]: #455
-#446 := [trans #458 #456]: #468
-#449 := (not #468)
-#451 := (or #449 #521)
-#452 := [th-lemma arith triangle-eq]: #451
-#448 := [unit-resolution #452 #450 #446]: false
-#453 := [lemma #448]: #521
-#74 := (* -1::Int #11)
-#75 := (+ #74 #13)
-#78 := (f5 f6 #75)
-#81 := (f3 f4 #78)
-#656 := (+ #64 #81)
-#371 := (+ #11 #656)
-#642 := (<= #371 0::Int)
-#377 := (= #371 0::Int)
-#644 := (or #278 #377)
-#127 := (= #32 #35)
-#152 := (or #127 #146)
-#700 := (forall (vars (?v0 Int)) (:pat #699) #152)
-#157 := (forall (vars (?v0 Int)) #152)
-#703 := (iff #157 #700)
-#701 := (iff #152 #152)
-#702 := [refl]: #701
-#704 := [quant-intro #702]: #703
-#209 := (~ #157 #157)
-#208 := (~ #152 #152)
-#205 := [refl]: #208
-#210 := [nnf-pos #205]: #209
-#36 := (= #35 #32)
-#33 := (<= 0::Int #32)
-#37 := (implies #33 #36)
-#38 := (forall (vars (?v0 Int)) #37)
-#160 := (iff #38 #157)
-#134 := (not #33)
-#135 := (or #134 #127)
-#140 := (forall (vars (?v0 Int)) #135)
-#158 := (iff #140 #157)
-#155 := (iff #135 #152)
-#149 := (or #146 #127)
-#153 := (iff #149 #152)
-#154 := [rewrite]: #153
-#150 := (iff #135 #149)
-#147 := (iff #134 #146)
-#143 := (iff #33 #144)
-#145 := [rewrite]: #143
-#148 := [monotonicity #145]: #147
-#151 := [monotonicity #148]: #150
-#156 := [trans #151 #154]: #155
-#159 := [quant-intro #156]: #158
-#141 := (iff #38 #140)
-#138 := (iff #37 #135)
-#131 := (implies #33 #127)
-#136 := (iff #131 #135)
-#137 := [rewrite]: #136
-#132 := (iff #37 #131)
-#129 := (iff #36 #127)
-#130 := [rewrite]: #129
-#133 := [monotonicity #130]: #132
-#139 := [trans #133 #137]: #138
-#142 := [quant-intro #139]: #141
-#161 := [trans #142 #159]: #160
-#126 := [asserted]: #38
-#162 := [mp #126 #161]: #157
-#206 := [mp~ #162 #210]: #157
-#705 := [mp #206 #704]: #700
-#672 := (not #700)
-#652 := (or #672 #278 #377)
-#390 := (>= #75 0::Int)
-#391 := (not #390)
-#374 := (= #75 #81)
-#375 := (or #374 #391)
-#493 := (or #672 #375)
-#634 := (iff #493 #652)
-#495 := (or #672 #644)
-#639 := (iff #495 #652)
-#640 := [rewrite]: #639
-#637 := (iff #493 #495)
-#651 := (iff #375 #644)
-#647 := (or #377 #278)
-#645 := (iff #647 #644)
-#650 := [rewrite]: #645
-#648 := (iff #375 #647)
-#654 := (iff #391 #278)
-#653 := (iff #390 #93)
-#657 := [rewrite]: #653
-#658 := [monotonicity #657]: #654
-#376 := (iff #374 #377)
-#655 := [rewrite]: #376
-#649 := [monotonicity #655 #658]: #648
-#646 := [trans #649 #650]: #651
-#638 := [monotonicity #646]: #637
-#635 := [trans #638 #640]: #634
-#494 := [quant-inst #75]: #493
-#641 := [mp #494 #635]: #652
-#441 := [unit-resolution #641 #705]: #644
-#442 := [unit-resolution #441 #435]: #377
-#428 := (not #377)
-#430 := (or #428 #642)
-#431 := [th-lemma arith triangle-eq]: #430
-#429 := [unit-resolution #431 #442]: #642
-#309 := (not #642)
-#465 := (not #660)
-#467 := (or #464 #465 #466 #309)
-#489 := [hypothesis]: #642
-#459 := [hypothesis]: #521
-#460 := [hypothesis]: #508
-#461 := [hypothesis]: #660
-#106 := (+ #81 #105)
-#107 := (+ #71 #106)
-#108 := (<= #107 0::Int)
-#113 := (not #108)
-#21 := (<= #11 #13)
-#22 := (ite #21 f8 f7)
-#23 := (f3 f4 #22)
-#17 := (- #13 #11)
-#18 := (f5 f6 #17)
-#19 := (f3 f4 #18)
-#14 := (- #11 #13)
-#15 := (f5 f6 #14)
-#16 := (f3 f4 #15)
-#20 := (+ #16 #19)
-#24 := (<= #20 #23)
-#25 := (not #24)
-#116 := (iff #25 #113)
-#84 := (+ #71 #81)
-#87 := (<= #84 #23)
-#90 := (not #87)
-#114 := (iff #90 #113)
-#111 := (iff #87 #108)
-#102 := (<= #84 #99)
-#109 := (iff #102 #108)
-#110 := [rewrite]: #109
-#103 := (iff #87 #102)
-#100 := (= #23 #99)
-#97 := (= #22 #96)
-#94 := (iff #21 #93)
-#95 := [rewrite]: #94
-#98 := [monotonicity #95]: #97
-#101 := [monotonicity #98]: #100
-#104 := [monotonicity #101]: #103
-#112 := [trans #104 #110]: #111
-#115 := [monotonicity #112]: #114
-#91 := (iff #25 #90)
-#88 := (iff #24 #87)
-#85 := (= #20 #84)
-#82 := (= #19 #81)
-#79 := (= #18 #78)
-#76 := (= #17 #75)
-#77 := [rewrite]: #76
-#80 := [monotonicity #77]: #79
-#83 := [monotonicity #80]: #82
-#72 := (= #16 #71)
-#69 := (= #15 #68)
-#66 := (= #14 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#73 := [monotonicity #70]: #72
-#86 := [monotonicity #73 #83]: #85
-#89 := [monotonicity #86]: #88
-#92 := [monotonicity #89]: #91
-#117 := [trans #92 #115]: #116
-#62 := [asserted]: #25
-#118 := [mp #62 #117]: #113
-#462 := [th-lemma arith farkas -1 1 1 -1 1 #118 #461 #460 #459 #489]: false
-#463 := [lemma #462]: #467
-#432 := [unit-resolution #463 #429 #453 #438]: #466
-#414 := (not #566)
-#416 := (or #414 #508)
-#417 := [th-lemma arith triangle-eq]: #416
-#418 := [unit-resolution #417 #432 #439]: false
-#419 := [lemma #418]: #681
-#669 := (or #331 #341)
-#673 := (or #672 #331 #341)
-#342 := (= #65 #71)
-#683 := (or #342 #341)
-#668 := (or #672 #683)
-#678 := (iff #668 #673)
-#312 := (or #672 #669)
-#317 := (iff #312 #673)
-#318 := [rewrite]: #317
-#675 := (iff #668 #312)
-#670 := (iff #683 #669)
-#332 := (iff #342 #331)
-#333 := [rewrite]: #332
-#671 := [monotonicity #333]: #670
-#677 := [monotonicity #671]: #675
-#676 := [trans #677 #318]: #678
-#674 := [quant-inst #65]: #668
-#679 := [mp #674 #676]: #673
-#423 := [unit-resolution #679 #705]: #669
-#424 := [unit-resolution #423 #419]: #331
-#425 := (not #331)
-#426 := (or #425 #666)
-#415 := [th-lemma arith triangle-eq]: #426
-#427 := [unit-resolution #415 #424]: #666
-#504 := (not #666)
-#404 := (or #278 #660 #504)
-#406 := [th-lemma arith assign-bounds -1 -1]: #404
-#407 := [unit-resolution #406 #420 #427]: #660
-#408 := [unit-resolution #441 #420]: #377
-#409 := [unit-resolution #431 #408]: #642
-#410 := [unit-resolution #463 #409 #453 #407]: #466
-#411 := [unit-resolution #417 #410 #422]: false
-#412 := [lemma #411]: #278
-#356 := (or #93 #363)
-#367 := [def-axiom]: #356
-#413 := [unit-resolution #367 #412]: #363
-#398 := [monotonicity #413]: #471
-#539 := (+ #11 #105)
-#540 := (<= #539 0::Int)
-#505 := (not #540)
-#527 := (<= #81 0::Int)
-#643 := (= #81 0::Int)
-#629 := (or #93 #643)
-#515 := (or #284 #93 #643)
-#472 := (or #643 #390)
-#516 := (or #284 #472)
-#625 := (iff #516 #515)
-#476 := (or #284 #629)
-#621 := (iff #476 #515)
-#622 := [rewrite]: #621
-#624 := (iff #516 #476)
-#630 := (iff #472 #629)
-#474 := (or #643 #93)
-#631 := (iff #474 #629)
-#632 := [rewrite]: #631
-#475 := (iff #472 #474)
-#628 := [monotonicity #657]: #475
-#633 := [trans #628 #632]: #630
-#526 := [monotonicity #633]: #624
-#510 := [trans #526 #622]: #625
-#517 := [quant-inst #75]: #516
-#525 := [mp #517 #510]: #515
-#399 := [unit-resolution #525 #711]: #629
-#400 := [unit-resolution #399 #412]: #643
-#402 := (not #643)
-#401 := (or #402 #527)
-#403 := [th-lemma arith triangle-eq]: #401
-#392 := [unit-resolution #403 #400]: #527
-#503 := (not #527)
-#393 := (or #503 #504 #505)
-#620 := (>= #13 0::Int)
-#492 := (= #13 0::Int)
-#369 := (f5 f6 #13)
-#609 := (f3 f4 #369)
-#610 := (= #609 0::Int)
-#502 := (not #620)
-#469 := [hypothesis]: #502
-#611 := (or #610 #620)
-#613 := (or #284 #610 #620)
-#597 := (or #284 #611)
-#600 := (iff #597 #613)
-#601 := [rewrite]: #600
-#598 := [quant-inst #13]: #597
-#602 := [mp #598 #601]: #613
-#470 := [unit-resolution #602 #711]: #611
-#477 := [unit-resolution #470 #469]: #610
-#480 := (= #13 #609)
-#366 := (= f8 #369)
-#473 := (or #370 #366)
-#680 := [quant-inst #12]: #473
-#479 := [unit-resolution #680 #698]: #366
-#481 := [monotonicity #479]: #480
-#483 := [trans #481 #477]: #492
-#484 := (not #492)
-#485 := (or #484 #620)
-#486 := [th-lemma arith triangle-eq]: #485
-#487 := [unit-resolution #486 #469 #483]: false
-#488 := [lemma #487]: #620
-#506 := (or #502 #503 #504 #505)
-#509 := [hypothesis]: #540
-#498 := [hypothesis]: #666
-#499 := [hypothesis]: #620
-#500 := [hypothesis]: #527
-#501 := [th-lemma arith farkas 1 -1 -1 -1 1 #500 #118 #499 #498 #509]: false
-#507 := [lemma #501]: #506
-#394 := [unit-resolution #507 #488]: #393
-#386 := [unit-resolution #394 #392 #427]: #505
-#395 := (not #471)
-#396 := (or #395 #540)
-#387 := [th-lemma arith triangle-eq]: #396
-[unit-resolution #387 #386 #398]: false
-unsat
-6b12b12d963545c3e361f7fde145e90f2cb84243 123 0
-#2 := false
-decl f3 :: (-> S2 S3 Int)
-decl f5 :: S3
-#9 := f5
-decl f7 :: S3
-#14 := f7
-#30 := 0::Int
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 f7)
-#69 := -1::Int
-#76 := (* -1::Int #15)
-#10 := (f3 f4 f5)
-#88 := (+ #10 #76)
-#89 := (<= #88 0::Int)
-#92 := (ite #89 f7 f5)
-#95 := (f3 f4 #92)
-#637 := (= #10 #95)
-#366 := (= f5 #92)
-#281 := (not #89)
-#280 := (= f7 #92)
-#479 := (not #280)
-#652 := (= #15 #95)
-#518 := [hypothesis]: #280
-#519 := [monotonicity #518]: #652
-#498 := (not #652)
-#101 := (* -1::Int #95)
-#647 := (+ #15 #101)
-#653 := (>= #647 0::Int)
-#655 := (not #653)
-decl f6 :: S3
-#11 := f6
-#12 := (f3 f4 f6)
-#102 := (+ #12 #101)
-#103 := (<= #102 0::Int)
-#104 := (not #103)
-#77 := (+ #12 #76)
-#78 := (<= #77 0::Int)
-#79 := (not #78)
-#72 := (* -1::Int #12)
-#73 := (+ #10 #72)
-#71 := (>= #73 0::Int)
-#70 := (not #71)
-#82 := (and #70 #79)
-#85 := (not #82)
-#109 := (or #85 #104)
-#112 := (not #109)
-#18 := (<= #10 #15)
-#19 := (ite #18 f7 f5)
-#20 := (f3 f4 #19)
-#21 := (< #20 #12)
-#16 := (< #15 #12)
-#13 := (< #10 #12)
-#17 := (and #13 #16)
-#22 := (implies #17 #21)
-#23 := (not #22)
-#115 := (iff #23 #112)
-#62 := (not #17)
-#63 := (or #62 #21)
-#66 := (not #63)
-#113 := (iff #66 #112)
-#110 := (iff #63 #109)
-#107 := (iff #21 #104)
-#98 := (< #95 #12)
-#105 := (iff #98 #104)
-#106 := [rewrite]: #105
-#99 := (iff #21 #98)
-#96 := (= #20 #95)
-#93 := (= #19 #92)
-#90 := (iff #18 #89)
-#91 := [rewrite]: #90
-#94 := [monotonicity #91]: #93
-#97 := [monotonicity #94]: #96
-#100 := [monotonicity #97]: #99
-#108 := [trans #100 #106]: #107
-#86 := (iff #62 #85)
-#83 := (iff #17 #82)
-#80 := (iff #16 #79)
-#81 := [rewrite]: #80
-#74 := (iff #13 #70)
-#75 := [rewrite]: #74
-#84 := [monotonicity #75 #81]: #83
-#87 := [monotonicity #84]: #86
-#111 := [monotonicity #87 #108]: #110
-#114 := [monotonicity #111]: #113
-#67 := (iff #23 #66)
-#64 := (iff #22 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#116 := [trans #68 #114]: #115
-#61 := [asserted]: #23
-#117 := [mp #61 #116]: #112
-#121 := [not-or-elim #117]: #103
-#118 := [not-or-elim #117]: #82
-#120 := [and-elim #118]: #79
-#654 := [hypothesis]: #653
-#649 := [th-lemma arith farkas -1 -1 1 #654 #120 #121]: false
-#496 := [lemma #649]: #655
-#640 := (or #498 #653)
-#641 := [th-lemma arith triangle-eq]: #640
-#636 := [unit-resolution #641 #496]: #498
-#520 := [unit-resolution #636 #519]: false
-#627 := [lemma #520]: #479
-#367 := (or #281 #280)
-#368 := [def-axiom]: #367
-#624 := [unit-resolution #368 #627]: #281
-#359 := (or #89 #366)
-#370 := [def-axiom]: #359
-#625 := [unit-resolution #370 #624]: #366
-#628 := [monotonicity #625]: #637
-#631 := (not #637)
-#638 := (+ #10 #101)
-#645 := (>= #638 0::Int)
-#475 := (not #645)
-#119 := [and-elim #118]: #70
-#639 := [hypothesis]: #645
-#646 := [th-lemma arith farkas -1 1 1 #639 #119 #121]: false
-#477 := [lemma #646]: #475
-#632 := (or #631 #645)
-#634 := [th-lemma arith triangle-eq]: #632
-#529 := [unit-resolution #634 #477]: #631
-[unit-resolution #529 #628]: false
-unsat
-0359c130ac749e033da47f8655a4eeb481185054 156 0
-#2 := false
-decl f6 :: S3
-#11 := f6
-decl f5 :: S3
-#9 := f5
-#25 := 0::Int
+#17 := (= f5 #16)
 decl f3 :: (-> S2 S3 Int)
 decl f4 :: S2
 #8 := f4
-#12 := (f3 f4 f6)
-#59 := -1::Int
-#60 := (* -1::Int #12)
-#10 := (f3 f4 f5)
-#61 := (+ #10 #60)
-#69 := (>= #61 0::Int)
-#71 := (ite #69 f5 f6)
-#62 := (<= #61 0::Int)
-#65 := (ite #62 f6 f5)
-#74 := (= #65 #71)
-#328 := (= f5 #71)
-#485 := (iff #328 #74)
-#585 := (iff #74 #328)
-#624 := (= #65 f5)
-#323 := (= f5 #65)
-#238 := (not #62)
-#237 := (= f6 #65)
-#593 := (not #237)
-#589 := (iff #237 #74)
-#435 := (iff #74 #237)
-#602 := (= #65 f6)
-#432 := (iff #602 #237)
-#434 := [commutativity]: #432
-#596 := (iff #74 #602)
-#595 := (= #71 f6)
-#256 := (= f6 #71)
-#621 := (not #256)
-#622 := [hypothesis]: #621
-#309 := (or #69 #256)
-#644 := [def-axiom]: #309
-#345 := [unit-resolution #644 #622]: #69
-#329 := (not #69)
-#326 := (or #329 #328)
-#330 := [def-axiom]: #326
-#619 := [unit-resolution #330 #345]: #328
-#455 := (= f6 f5)
-decl f7 :: (-> S4 Int S3)
-decl f8 :: S4
-#19 := f8
-#646 := (f7 f8 #10)
-#606 := (= #646 f5)
-#303 := (= f5 #646)
-#20 := (:var 0 S3)
-#21 := (f3 f4 #20)
-#652 := (pattern #21)
-#22 := (f7 f8 #21)
-#58 := (= #20 #22)
-#653 := (forall (vars (?v0 S3)) (:pat #652) #58)
-#83 := (forall (vars (?v0 S3)) #58)
-#656 := (iff #83 #653)
-#654 := (iff #58 #58)
-#655 := [refl]: #654
-#657 := [quant-intro #655]: #656
-#177 := (~ #83 #83)
-#175 := (~ #58 #58)
-#176 := [refl]: #175
-#178 := [nnf-pos #176]: #177
-#23 := (= #22 #20)
-#24 := (forall (vars (?v0 S3)) #23)
-#84 := (iff #24 #83)
-#81 := (iff #23 #58)
-#82 := [rewrite]: #81
-#85 := [quant-intro #82]: #84
-#57 := [asserted]: #24
-#88 := [mp #57 #85]: #83
-#167 := [mp~ #88 #178]: #83
-#658 := [mp #167 #657]: #653
-#314 := (not #653)
-#315 := (or #314 #303)
-#647 := [quant-inst #9]: #315
-#344 := [unit-resolution #647 #658]: #303
-#612 := [symm #344]: #606
-#453 := (= f6 #646)
-#433 := (f7 f8 #12)
-#610 := (= #433 #646)
-#609 := (= #12 #10)
-#607 := (= #10 #12)
-#331 := (not #323)
-#77 := (not #74)
-#613 := (iff #77 #331)
-#615 := (iff #74 #323)
-#336 := (iff #624 #323)
-#337 := [commutativity]: #336
-#334 := (iff #74 #624)
-#623 := (= #71 f5)
-#620 := [symm #619]: #623
-#335 := [monotonicity #620]: #334
-#616 := [trans #335 #337]: #615
-#617 := [monotonicity #616]: #613
-#15 := (<= #12 #10)
-#16 := (ite #15 f5 f6)
-#13 := (<= #10 #12)
-#14 := (ite #13 f6 f5)
-#17 := (= #14 #16)
-#18 := (not #17)
-#78 := (iff #18 #77)
-#75 := (iff #17 #74)
-#72 := (= #16 #71)
-#68 := (iff #15 #69)
-#70 := [rewrite]: #68
-#73 := [monotonicity #70]: #72
-#66 := (= #14 #65)
-#63 := (iff #13 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#76 := [monotonicity #67 #73]: #75
-#79 := [monotonicity #76]: #78
-#56 := [asserted]: #18
-#80 := [mp #56 #79]: #77
-#614 := [mp #80 #617]: #331
-#316 := (or #62 #323)
-#327 := [def-axiom]: #316
-#618 := [unit-resolution #327 #614]: #62
-#608 := [th-lemma arith eq-propagate 1 1 #345 #618]: #607
-#604 := [symm #608]: #609
-#611 := [monotonicity #604]: #610
-#640 := (= f6 #433)
-#650 := (or #314 #640)
-#645 := [quant-inst #11]: #650
-#605 := [unit-resolution #645 #658]: #640
-#454 := [trans #605 #611]: #453
-#597 := [trans #454 #612]: #455
-#598 := [trans #597 #619]: #256
-#599 := [unit-resolution #622 #598]: false
-#600 := [lemma #599]: #256
-#601 := [symm #600]: #595
-#603 := [monotonicity #601]: #596
-#588 := [trans #603 #434]: #435
-#591 := [symm #588]: #589
-#594 := [hypothesis]: #237
-#592 := [mp #594 #591]: #74
-#590 := [unit-resolution #80 #592]: false
-#475 := [lemma #590]: #593
-#324 := (or #238 #237)
-#325 := [def-axiom]: #324
-#476 := [unit-resolution #325 #475]: #238
-#581 := [unit-resolution #327 #476]: #323
-#582 := [symm #581]: #624
-#470 := [monotonicity #582]: #585
-#487 := [symm #470]: #485
-#477 := (or #69 #62)
-#436 := [th-lemma arith farkas 1 1]: #477
-#584 := [unit-resolution #436 #476]: #69
-#486 := [unit-resolution #330 #584]: #328
-#488 := [mp #486 #487]: #74
-[unit-resolution #80 #488]: false
-unsat
-84ed7acbaf0767eafcf3a11dec0969faefcbf9ae 282 0
-#2 := false
-decl f5 :: S3
-#9 := f5
-decl f6 :: (-> S4 Int S3)
-#12 := 0::Int
-decl f7 :: S4
-#11 := f7
-#13 := (f6 f7 0::Int)
-decl f3 :: (-> S2 S3 Int)
-decl f4 :: S2
-#8 := f4
-#14 := (f3 f4 #13)
-#61 := -1::Int
-#62 := (* -1::Int #14)
-#10 := (f3 f4 f5)
-#63 := (+ #10 #62)
-#64 := (<= #63 0::Int)
-#67 := (ite #64 #13 f5)
-#70 := (= f5 #67)
-#237 := (= #13 #67)
-#73 := (not #70)
-#15 := (<= #10 #14)
-#16 := (ite #15 #13 f5)
-#17 := (= #16 f5)
-#18 := (not #17)
-#76 := (iff #18 #73)
-#55 := (= f5 #16)
-#58 := (not #55)
-#74 := (iff #58 #73)
-#71 := (iff #55 #70)
-#68 := (= #16 #67)
-#65 := (iff #15 #64)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#59 := (iff #18 #58)
-#56 := (iff #17 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#77 := [trans #60 #75]: #76
-#54 := [asserted]: #18
-#78 := [mp #54 #77]: #73
-#325 := (or #64 #70)
-#316 := [def-axiom]: #325
-#608 := [unit-resolution #316 #78]: #64
-#323 := (not #64)
-#238 := (or #323 #237)
-#324 := [def-axiom]: #238
-#591 := [unit-resolution #324 #608]: #237
-#477 := (= f5 #13)
-#327 := (f6 f7 #10)
-#475 := (= #327 #13)
-#618 := (= #10 0::Int)
-#621 := (f3 f4 #327)
-#622 := (= #621 0::Int)
-#607 := (<= #10 0::Int)
-#278 := (<= #14 0::Int)
-#647 := (= #14 0::Int)
-#24 := (:var 0 Int)
-#26 := (f6 f7 #24)
-#659 := (pattern #26)
-#104 := (>= #24 0::Int)
-#106 := (not #104)
-#27 := (f3 f4 #26)
-#87 := (= #24 #27)
-#112 := (or #87 #106)
-#660 := (forall (vars (?v0 Int)) (:pat #659) #112)
-#117 := (forall (vars (?v0 Int)) #112)
-#663 := (iff #117 #660)
-#661 := (iff #112 #112)
-#662 := [refl]: #661
-#664 := [quant-intro #662]: #663
-#169 := (~ #117 #117)
-#168 := (~ #112 #112)
-#165 := [refl]: #168
-#170 := [nnf-pos #165]: #169
-#28 := (= #27 #24)
-#25 := (<= 0::Int #24)
-#29 := (implies #25 #28)
-#30 := (forall (vars (?v0 Int)) #29)
-#120 := (iff #30 #117)
-#94 := (not #25)
-#95 := (or #94 #87)
-#100 := (forall (vars (?v0 Int)) #95)
-#118 := (iff #100 #117)
-#115 := (iff #95 #112)
-#109 := (or #106 #87)
-#113 := (iff #109 #112)
-#114 := [rewrite]: #113
-#110 := (iff #95 #109)
-#107 := (iff #94 #106)
-#103 := (iff #25 #104)
-#105 := [rewrite]: #103
-#108 := [monotonicity #105]: #107
-#111 := [monotonicity #108]: #110
-#116 := [trans #111 #114]: #115
-#119 := [quant-intro #116]: #118
-#101 := (iff #30 #100)
-#98 := (iff #29 #95)
-#91 := (implies #25 #87)
-#96 := (iff #91 #95)
-#97 := [rewrite]: #96
-#92 := (iff #29 #91)
-#89 := (iff #28 #87)
-#90 := [rewrite]: #89
-#93 := [monotonicity #90]: #92
-#99 := [trans #93 #97]: #98
-#102 := [quant-intro #99]: #101
-#121 := [trans #102 #119]: #120
-#86 := [asserted]: #30
-#122 := [mp #86 #121]: #117
-#166 := [mp~ #122 #170]: #117
-#665 := [mp #166 #664]: #660
-#630 := (not #660)
-#631 := (or #630 #647)
-#646 := (>= 0::Int 0::Int)
-#303 := (not #646)
-#314 := (= 0::Int #14)
-#315 := (or #314 #303)
-#632 := (or #630 #315)
-#628 := (iff #632 #631)
-#272 := (iff #631 #631)
-#635 := [rewrite]: #272
-#293 := (iff #315 #647)
-#286 := (or #647 false)
-#291 := (iff #286 #647)
-#292 := [rewrite]: #291
-#627 := (iff #315 #286)
-#302 := (iff #303 false)
-#1 := true
-#651 := (not true)
-#306 := (iff #651 false)
-#642 := [rewrite]: #306
-#641 := (iff #303 #651)
-#650 := (iff #646 true)
-#645 := [rewrite]: #650
-#301 := [monotonicity #645]: #641
-#643 := [trans #301 #642]: #302
-#648 := (iff #314 #647)
-#649 := [rewrite]: #648
-#290 := [monotonicity #649 #643]: #627
-#629 := [trans #290 #292]: #293
-#634 := [monotonicity #629]: #628
-#637 := [trans #634 #635]: #628
-#633 := [quant-inst #12]: #632
-#277 := [mp #633 #637]: #631
-#609 := [unit-resolution #277 #665]: #647
-#604 := (not #647)
-#605 := (or #604 #278)
-#610 := [th-lemma arith triangle-eq]: #605
-#611 := [unit-resolution #610 #609]: #278
-#606 := (not #607)
-#612 := [hypothesis]: #606
-#453 := [th-lemma arith farkas -1 1 1 #612 #611 #608]: false
-#454 := [lemma #453]: #607
-#244 := (>= #10 0::Int)
-#455 := (not #622)
-#597 := [hypothesis]: #455
-#345 := (or #244 #622)
-#32 := (= #27 0::Int)
-#153 := (or #32 #104)
-#666 := (forall (vars (?v0 Int)) (:pat #659) #153)
-#158 := (forall (vars (?v0 Int)) #153)
-#669 := (iff #158 #666)
-#667 := (iff #153 #153)
-#668 := [refl]: #667
-#670 := [quant-intro #668]: #669
-#171 := (~ #158 #158)
-#179 := (~ #153 #153)
-#180 := [refl]: #179
-#172 := [nnf-pos #180]: #171
-#31 := (< #24 0::Int)
-#33 := (implies #31 #32)
-#34 := (forall (vars (?v0 Int)) #33)
-#161 := (iff #34 #158)
-#124 := (= 0::Int #27)
-#130 := (not #31)
-#131 := (or #130 #124)
-#136 := (forall (vars (?v0 Int)) #131)
-#159 := (iff #136 #158)
-#156 := (iff #131 #153)
-#150 := (or #104 #32)
-#154 := (iff #150 #153)
-#155 := [rewrite]: #154
-#151 := (iff #131 #150)
-#148 := (iff #124 #32)
-#149 := [rewrite]: #148
-#146 := (iff #130 #104)
-#141 := (not #106)
-#144 := (iff #141 #104)
-#145 := [rewrite]: #144
-#142 := (iff #130 #141)
-#139 := (iff #31 #106)
-#140 := [rewrite]: #139
-#143 := [monotonicity #140]: #142
-#147 := [trans #143 #145]: #146
-#152 := [monotonicity #147 #149]: #151
-#157 := [trans #152 #155]: #156
-#160 := [quant-intro #157]: #159
-#137 := (iff #34 #136)
-#134 := (iff #33 #131)
-#127 := (implies #31 #124)
-#132 := (iff #127 #131)
-#133 := [rewrite]: #132
-#128 := (iff #33 #127)
-#125 := (iff #32 #124)
-#126 := [rewrite]: #125
-#129 := [monotonicity #126]: #128
-#135 := [trans #129 #133]: #134
-#138 := [quant-intro #135]: #137
-#162 := [trans #138 #160]: #161
-#123 := [asserted]: #34
-#163 := [mp #123 #162]: #158
-#181 := [mp~ #163 #172]: #158
-#671 := [mp #181 #670]: #666
-#620 := (not #666)
-#624 := (or #620 #244 #622)
-#344 := (or #622 #244)
-#334 := (or #620 #344)
-#613 := (iff #334 #624)
-#336 := (or #620 #345)
-#616 := (iff #336 #624)
-#331 := [rewrite]: #616
-#337 := (iff #334 #336)
-#619 := (iff #344 #345)
-#623 := [rewrite]: #619
-#615 := [monotonicity #623]: #337
-#617 := [trans #615 #331]: #613
-#335 := [quant-inst #10]: #334
-#614 := [mp #335 #617]: #624
-#598 := [unit-resolution #614 #671]: #345
-#599 := [unit-resolution #598 #597]: #244
-#600 := (not #244)
-#594 := (or #618 #606 #600)
-#595 := [th-lemma arith triangle-eq]: #594
-#601 := [unit-resolution #595 #599 #454]: #618
-#432 := (= #621 #10)
-#596 := (= #327 f5)
-#328 := (= f5 #327)
-#19 := (:var 0 S3)
-#20 := (f3 f4 #19)
-#652 := (pattern #20)
-#21 := (f6 f7 #20)
-#80 := (= #19 #21)
-#653 := (forall (vars (?v0 S3)) (:pat #652) #80)
-#83 := (forall (vars (?v0 S3)) #80)
-#656 := (iff #83 #653)
-#654 := (iff #80 #80)
-#655 := [refl]: #654
-#657 := [quant-intro #655]: #656
-#177 := (~ #83 #83)
-#175 := (~ #80 #80)
-#176 := [refl]: #175
-#178 := [nnf-pos #176]: #177
-#22 := (= #21 #19)
-#23 := (forall (vars (?v0 S3)) #22)
-#84 := (iff #23 #83)
-#81 := (iff #22 #80)
-#82 := [rewrite]: #81
-#85 := [quant-intro #82]: #84
-#79 := [asserted]: #23
-#88 := [mp #79 #85]: #83
-#167 := [mp~ #88 #178]: #83
-#658 := [mp #167 #657]: #653
-#326 := (not #653)
-#330 := (or #326 #328)
-#309 := [quant-inst #9]: #330
-#602 := [unit-resolution #309 #658]: #328
-#603 := [symm #602]: #596
-#434 := [monotonicity #603]: #432
-#435 := [trans #434 #601]: #622
-#588 := [unit-resolution #597 #435]: false
-#589 := [lemma #588]: #622
-#592 := (= #10 #621)
-#590 := [monotonicity #602]: #592
-#593 := [trans #590 #589]: #618
-#476 := [monotonicity #593]: #475
-#436 := [trans #602 #476]: #477
-#584 := [trans #436 #591]: #70
-[unit-resolution #78 #584]: false
-unsat
-068d7b92a99be7dc4cc7b601acb4e869b185110c 142 0
-#2 := false
-#8 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f5 :: S3
-#10 := f5
-decl f4 :: S2
-#9 := f4
-#11 := (f3 f4 f5)
-#630 := (= #11 0::Int)
-decl f6 :: (-> S4 Int S3)
-decl f7 :: S4
-#14 := f7
-#216 := (f6 f7 #11)
-#217 := (f3 f4 #216)
-#303 := (= #217 0::Int)
-#20 := (:var 0 Int)
-#22 := (f6 f7 #20)
-#639 := (pattern #22)
-#84 := (>= #20 0::Int)
-#23 := (f3 f4 #22)
-#28 := (= #23 0::Int)
-#132 := (or #28 #84)
-#646 := (forall (vars (?v0 Int)) (:pat #639) #132)
-#137 := (forall (vars (?v0 Int)) #132)
-#649 := (iff #137 #646)
-#647 := (iff #132 #132)
-#648 := [refl]: #647
-#650 := [quant-intro #648]: #649
-#150 := (~ #137 #137)
-#158 := (~ #132 #132)
-#159 := [refl]: #158
-#151 := [nnf-pos #159]: #150
-#27 := (< #20 0::Int)
-#29 := (implies #27 #28)
-#30 := (forall (vars (?v0 Int)) #29)
-#140 := (iff #30 #137)
-#103 := (= 0::Int #23)
-#109 := (not #27)
-#110 := (or #109 #103)
-#115 := (forall (vars (?v0 Int)) #110)
-#138 := (iff #115 #137)
-#135 := (iff #110 #132)
-#129 := (or #84 #28)
-#133 := (iff #129 #132)
-#134 := [rewrite]: #133
-#130 := (iff #110 #129)
-#127 := (iff #103 #28)
-#128 := [rewrite]: #127
-#125 := (iff #109 #84)
-#85 := (not #84)
-#120 := (not #85)
-#123 := (iff #120 #84)
-#124 := [rewrite]: #123
-#121 := (iff #109 #120)
-#118 := (iff #27 #85)
-#119 := [rewrite]: #118
-#122 := [monotonicity #119]: #121
-#126 := [trans #122 #124]: #125
-#131 := [monotonicity #126 #128]: #130
-#136 := [trans #131 #134]: #135
-#139 := [quant-intro #136]: #138
-#116 := (iff #30 #115)
-#113 := (iff #29 #110)
-#106 := (implies #27 #103)
-#111 := (iff #106 #110)
-#112 := [rewrite]: #111
-#107 := (iff #29 #106)
-#104 := (iff #28 #103)
-#105 := [rewrite]: #104
-#108 := [monotonicity #105]: #107
-#114 := [trans #108 #112]: #113
-#117 := [quant-intro #114]: #116
-#141 := [trans #117 #139]: #140
-#102 := [asserted]: #30
-#142 := [mp #102 #141]: #137
-#160 := [mp~ #142 #151]: #137
-#651 := [mp #160 #650]: #646
-#55 := (>= #11 0::Int)
-#56 := (not #55)
-#12 := (<= 0::Int #11)
-#13 := (not #12)
-#57 := (iff #13 #56)
-#53 := (iff #12 #55)
-#54 := [rewrite]: #53
-#58 := [monotonicity #54]: #57
-#50 := [asserted]: #13
-#59 := [mp #50 #58]: #56
-#309 := (not #646)
-#288 := (or #309 #55 #303)
-#307 := (or #303 #55)
-#624 := (or #309 #307)
-#627 := (iff #624 #288)
-#235 := (or #55 #303)
-#282 := (or #309 #235)
-#293 := (iff #282 #288)
-#294 := [rewrite]: #293
-#413 := (iff #624 #282)
-#308 := (iff #307 #235)
-#305 := [rewrite]: #308
-#620 := [monotonicity #305]: #413
-#628 := [trans #620 #294]: #627
-#626 := [quant-inst #11]: #624
-#629 := [mp #626 #628]: #288
-#631 := [unit-resolution #629 #59 #651]: #303
-#280 := (= #11 #217)
-#302 := (= f5 #216)
-#15 := (:var 0 S3)
-#16 := (f3 f4 #15)
-#632 := (pattern #16)
-#17 := (f6 f7 #16)
-#52 := (= #15 #17)
-#633 := (forall (vars (?v0 S3)) (:pat #632) #52)
-#62 := (forall (vars (?v0 S3)) #52)
-#636 := (iff #62 #633)
-#634 := (iff #52 #52)
-#635 := [refl]: #634
-#637 := [quant-intro #635]: #636
-#156 := (~ #62 #62)
-#154 := (~ #52 #52)
-#155 := [refl]: #154
-#157 := [nnf-pos #155]: #156
-#18 := (= #17 #15)
-#19 := (forall (vars (?v0 S3)) #18)
-#63 := (iff #19 #62)
-#60 := (iff #18 #52)
-#61 := [rewrite]: #60
-#64 := [quant-intro #61]: #63
-#51 := [asserted]: #19
-#67 := [mp #51 #64]: #62
-#146 := [mp~ #67 #157]: #62
-#638 := [mp #146 #637]: #633
-#304 := (not #633)
-#295 := (or #304 #302)
-#306 := [quant-inst #10]: #295
-#621 := [unit-resolution #306 #638]: #302
-#285 := [monotonicity #621]: #280
-#622 := [trans #285 #631]: #630
-#281 := (not #630)
-#623 := (or #281 #55)
-#265 := [th-lemma arith triangle-eq]: #623
-[unit-resolution #265 #59 #622]: false
-unsat
-5c3635bde03236679c5aa59e91b8371f17c3315c 103 0
-#2 := false
-decl f6 :: (-> S4 Int S3)
-#13 := 1::Int
-decl f7 :: S4
-#16 := f7
-#17 := (f6 f7 1::Int)
-decl f5 :: S3
-#10 := f5
-#18 := (= f5 #17)
-decl f3 :: (-> S2 S3 Int)
-decl f4 :: S2
-#9 := f4
-#11 := (f3 f4 f5)
-#256 := (f6 f7 #11)
-#367 := (= #256 #17)
-#645 := (= #17 #256)
-#655 := (= 1::Int #11)
-#296 := (= #11 1::Int)
-#14 := (<= #11 1::Int)
-#8 := 0::Int
-#64 := (<= #11 0::Int)
-#65 := (not #64)
-#71 := (and #14 #65)
-#76 := (not #71)
-#82 := (or #18 #76)
-#87 := (not #82)
-#12 := (< 0::Int #11)
-#15 := (and #12 #14)
-#19 := (implies #15 #18)
-#20 := (not #19)
-#90 := (iff #20 #87)
-#57 := (not #15)
-#58 := (or #57 #18)
-#61 := (not #58)
-#88 := (iff #61 #87)
-#85 := (iff #58 #82)
-#79 := (or #76 #18)
-#83 := (iff #79 #82)
-#84 := [rewrite]: #83
-#80 := (iff #58 #79)
-#77 := (iff #57 #76)
-#74 := (iff #15 #71)
-#68 := (and #65 #14)
-#72 := (iff #68 #71)
-#73 := [rewrite]: #72
-#69 := (iff #15 #68)
-#66 := (iff #12 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#75 := [trans #70 #73]: #74
-#78 := [monotonicity #75]: #77
-#81 := [monotonicity #78]: #80
-#86 := [trans #81 #84]: #85
-#89 := [monotonicity #86]: #88
-#62 := (iff #20 #61)
-#59 := (iff #19 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#91 := [trans #63 #89]: #90
-#56 := [asserted]: #20
-#92 := [mp #56 #91]: #87
-#95 := [not-or-elim #92]: #71
-#96 := [and-elim #95]: #14
-#97 := [and-elim #95]: #65
-#657 := [th-lemma arith eq-propagate 0 0 #97 #96]: #296
-#658 := [symm #657]: #655
-#352 := [monotonicity #658]: #645
-#368 := [symm #352]: #367
-#341 := (= f5 #256)
-#21 := (:var 0 S3)
-#22 := (f3 f4 #21)
-#671 := (pattern #22)
-#23 := (f6 f7 #22)
-#99 := (= #21 #23)
-#672 := (forall (vars (?v0 S3)) (:pat #671) #99)
-#102 := (forall (vars (?v0 S3)) #99)
-#675 := (iff #102 #672)
-#673 := (iff #99 #99)
-#674 := [refl]: #673
-#676 := [quant-intro #674]: #675
-#200 := (~ #102 #102)
-#198 := (~ #99 #99)
-#199 := [refl]: #198
-#201 := [nnf-pos #199]: #200
-#24 := (= #23 #21)
-#25 := (forall (vars (?v0 S3)) #24)
-#103 := (iff #25 #102)
-#100 := (iff #24 #99)
-#101 := [rewrite]: #100
-#104 := [quant-intro #101]: #103
-#98 := [asserted]: #25
-#107 := [mp #98 #104]: #102
-#190 := [mp~ #107 #201]: #102
-#677 := [mp #190 #676]: #672
-#343 := (not #672)
-#334 := (or #343 #341)
-#345 := [quant-inst #10]: #334
-#644 := [unit-resolution #345 #677]: #341
-#369 := [trans #644 #368]: #18
-#93 := (not #18)
-#94 := [not-or-elim #92]: #93
-[unit-resolution #94 #369]: false
-unsat
-90ecf2a0f6182d20e85e5caa15ec520fe6639d37 22 0
-#2 := false
-decl f3 :: (-> S2 S3 Int)
-decl f5 :: S3
-#9 := f5
-decl f4 :: S2
-#8 := f4
 #10 := (f3 f4 f5)
-#11 := (<= #10 #10)
-#12 := (not #11)
-#60 := (iff #12 false)
-#1 := true
-#55 := (not true)
-#58 := (iff #55 false)
-#59 := [rewrite]: #58
-#56 := (iff #12 #55)
-#53 := (iff #11 true)
-#54 := [rewrite]: #53
-#57 := [monotonicity #54]: #56
-#61 := [trans #57 #59]: #60
-#50 := [asserted]: #12
-[mp #50 #61]: false
-unsat
-a9de0c4310af4f5739de23ef772c907d133787bf 56 0
+#237 := (f6 f7 #10)
+#263 := (= #237 #16)
+#554 := (= #16 #237)
+#553 := (= 1::Int #10)
+#191 := (= #10 1::Int)
+#13 := (<= #10 1::Int)
+#7 := 0::Int
+#44 := (<= #10 0::Int)
+#45 := (not #44)
+#48 := (and #45 #13)
+#54 := (not #48)
+#55 := (or #54 #17)
+#60 := (not #55)
+#11 := (< 0::Int #10)
+#14 := (and #11 #13)
+#18 := (implies #14 #17)
+#19 := (not #18)
+#61 := (iff #19 #60)
+#58 := (iff #18 #55)
+#51 := (implies #48 #17)
+#56 := (iff #51 #55)
+#57 := [rewrite]: #56
+#52 := (iff #18 #51)
+#49 := (iff #14 #48)
+#46 := (iff #11 #45)
+#47 := [rewrite]: #46
+#50 := [monotonicity #47]: #49
+#53 := [monotonicity #50]: #52
+#59 := [trans #53 #57]: #58
+#62 := [monotonicity #59]: #61
+#37 := [asserted]: #19
+#63 := [mp #37 #62]: #60
+#64 := [not-or-elim #63]: #48
+#66 := [and-elim #64]: #13
+#65 := [and-elim #64]: #45
+#192 := [th-lemma arith eq-propagate 0 0 #65 #66]: #191
+#551 := [symm #192]: #553
+#540 := [monotonicity #551]: #554
+#264 := [symm #540]: #263
+#541 := (= f5 #237)
+#153 := (= #237 f5)
+#20 := (:var 0 S3)
+#21 := (f3 f4 #20)
+#567 := (pattern #21)
+#22 := (f6 f7 #21)
+#23 := (= #22 #20)
+#568 := (forall (vars (?v0 S3)) (:pat #567) #23)
+#24 := (forall (vars (?v0 S3)) #23)
+#571 := (iff #24 #568)
+#569 := (iff #23 #23)
+#570 := [refl]: #569
+#572 := [quant-intro #570]: #571
+#141 := (~ #24 #24)
+#139 := (~ #23 #23)
+#140 := [refl]: #139
+#142 := [nnf-pos #140]: #141
+#38 := [asserted]: #24
+#149 := [mp~ #38 #142]: #24
+#573 := [mp #149 #572]: #568
+#230 := (not #568)
+#241 := (or #230 #153)
+#242 := [quant-inst #9]: #241
+#552 := [unit-resolution #242 #573]: #153
+#248 := [symm #552]: #541
+#265 := [trans #248 #264]: #17
+#67 := (not #17)
+#68 := [not-or-elim #63]: #67
+[unit-resolution #68 #265]: false
+ca3f6f470a64812f20f034a206f85f1299e90bba 22 0
+unsat
 #2 := false
 decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#11 := f6
-decl f4 :: S2
-#8 := f4
-#12 := (f3 f4 f6)
-#14 := 3::Int
-#16 := (* 3::Int #12)
-decl f5 :: S3
-#9 := f5
-#10 := (f3 f4 f5)
-#15 := (* 3::Int #10)
-#17 := (<= #15 #16)
-#13 := (<= #10 #12)
-#18 := (implies #13 #17)
-#19 := (not #18)
-#90 := (iff #19 false)
-#58 := (not #13)
-#59 := (or #58 #17)
-#62 := (not #59)
-#88 := (iff #62 false)
-#1 := true
-#83 := (not true)
-#86 := (iff #83 false)
-#87 := [rewrite]: #86
-#84 := (iff #62 #83)
-#81 := (iff #59 true)
-#26 := 0::Int
-#65 := -1::Int
-#66 := (* -1::Int #12)
-#67 := (+ #10 #66)
-#68 := (<= #67 0::Int)
-#71 := (not #68)
-#76 := (or #71 #68)
-#79 := (iff #76 true)
-#80 := [rewrite]: #79
-#77 := (iff #59 #76)
-#74 := (iff #17 #68)
-#75 := [rewrite]: #74
-#72 := (iff #58 #71)
-#69 := (iff #13 #68)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#78 := [monotonicity #73 #75]: #77
-#82 := [trans #78 #80]: #81
-#85 := [monotonicity #82]: #84
-#89 := [trans #85 #87]: #88
-#63 := (iff #19 #62)
-#60 := (iff #18 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#91 := [trans #64 #89]: #90
-#57 := [asserted]: #19
-[mp #57 #91]: false
-unsat
-d762995aadd1557f770900e730ed2ac53179faf4 61 0
-#2 := false
+decl f5 :: S3
+#8 := f5
+decl f4 :: S2
+#7 := f4
+#9 := (f3 f4 f5)
+#10 := (<= #9 #9)
+#11 := (not #10)
+#45 := (iff #11 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #11 #40)
+#38 := (iff #10 true)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#31 := [asserted]: #11
+[mp #31 #46]: false
+bb3772327fe7ed3d47e357b17ea25e71f87441c8 55 0
+unsat
+#2 := false
+#25 := 0::Int
 decl f3 :: (-> S2 S3 Int)
 decl f6 :: S3
-#11 := f6
-decl f4 :: S2
-#8 := f4
-#12 := (f3 f4 f6)
-#14 := 3::Int
-#16 := (* 3::Int #12)
-decl f5 :: S3
-#9 := f5
-#10 := (f3 f4 f5)
-#15 := (* 3::Int #10)
-#17 := (< #15 #16)
-#13 := (< #10 #12)
-#18 := (implies #13 #17)
-#19 := (not #18)
-#95 := (iff #19 false)
-#58 := (not #13)
-#59 := (or #58 #17)
-#62 := (not #59)
-#93 := (iff #62 false)
-#1 := true
-#88 := (not true)
-#91 := (iff #88 false)
-#92 := [rewrite]: #91
-#89 := (iff #62 #88)
-#86 := (iff #59 true)
-#26 := 0::Int
-#65 := -1::Int
-#68 := (* -1::Int #12)
-#69 := (+ #10 #68)
-#67 := (>= #69 0::Int)
-#66 := (not #67)
-#80 := (or #67 #66)
-#84 := (iff #80 true)
-#85 := [rewrite]: #84
-#82 := (iff #59 #80)
-#81 := (iff #17 #66)
-#79 := [rewrite]: #81
-#77 := (iff #58 #67)
-#72 := (not #66)
-#75 := (iff #72 #67)
-#76 := [rewrite]: #75
-#73 := (iff #58 #72)
-#70 := (iff #13 #66)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#78 := [trans #74 #76]: #77
-#83 := [monotonicity #78 #79]: #82
-#87 := [trans #83 #85]: #86
-#90 := [monotonicity #87]: #89
-#94 := [trans #90 #92]: #93
-#63 := (iff #19 #62)
-#60 := (iff #18 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#96 := [trans #64 #94]: #95
-#57 := [asserted]: #19
-[mp #57 #96]: false
-unsat
-a713cfdad41abece70ff154554a3a68431ecc97d 57 0
-#2 := false
-#23 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#11 := f6
-decl f4 :: S2
-#8 := f4
-#12 := (f3 f4 f6)
-#62 := -1::Int
-#65 := (* -1::Int #12)
-decl f5 :: S3
-#9 := f5
-#10 := (f3 f4 f5)
-#66 := (+ #10 #65)
-#76 := (<= #66 0::Int)
-#89 := (not #76)
-#64 := (>= #66 0::Int)
-#79 := (or #64 #76)
-#82 := (not #79)
-#14 := (<= #10 #12)
-#13 := (< #10 #12)
-#15 := (implies #13 #14)
-#16 := (not #15)
-#85 := (iff #16 #82)
-#55 := (not #13)
-#56 := (or #55 #14)
-#59 := (not #56)
-#83 := (iff #59 #82)
-#80 := (iff #56 #79)
-#77 := (iff #14 #76)
-#78 := [rewrite]: #77
-#74 := (iff #55 #64)
-#63 := (not #64)
-#69 := (not #63)
-#72 := (iff #69 #64)
-#73 := [rewrite]: #72
-#70 := (iff #55 #69)
-#67 := (iff #13 #63)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#75 := [trans #71 #73]: #74
-#81 := [monotonicity #75 #78]: #80
-#84 := [monotonicity #81]: #83
-#60 := (iff #16 #59)
-#57 := (iff #15 #56)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#86 := [trans #61 #84]: #85
-#54 := [asserted]: #16
-#87 := [mp #54 #86]: #82
-#90 := [not-or-elim #87]: #89
-#88 := [not-or-elim #87]: #63
-#249 := (or #76 #64)
-#335 := [th-lemma arith farkas 1 1]: #249
-#250 := [unit-resolution #335 #88]: #76
-[unit-resolution #250 #90]: false
-unsat
-7f843b4a4724aa1a653b0a828c65e6e29162883a 78 0
+#10 := f6
+decl f4 :: S2
+#7 := f4
+#11 := (f3 f4 f6)
+#106 := -1::Int
+#107 := (* -1::Int #11)
+decl f5 :: S3
+#8 := f5
+#9 := (f3 f4 f5)
+#108 := (+ #9 #107)
+#109 := (<= #108 0::Int)
+#135 := (not #109)
+#152 := (iff #135 false)
+#1 := true
+#147 := (not true)
+#150 := (iff #147 false)
+#151 := [rewrite]: #150
+#148 := (iff #135 #147)
+#139 := (iff #109 true)
+#12 := (<= #9 #11)
+#110 := (iff #12 #109)
+#111 := [rewrite]: #110
+#13 := 3::Int
+#15 := (* 3::Int #11)
+#14 := (* 3::Int #9)
+#16 := (<= #14 #15)
+#45 := (not #12)
+#46 := (or #45 #16)
+#49 := (not #46)
+#17 := (implies #12 #16)
+#18 := (not #17)
+#50 := (iff #18 #49)
+#47 := (iff #17 #46)
+#48 := [rewrite]: #47
+#51 := [monotonicity #48]: #50
+#38 := [asserted]: #18
+#52 := [mp #38 #51]: #49
+#53 := [not-or-elim #52]: #12
+#112 := [mp #53 #111]: #109
+#140 := [iff-true #112]: #139
+#149 := [monotonicity #140]: #148
+#153 := [trans #149 #151]: #152
+#54 := (not #16)
+#136 := (iff #54 #135)
+#133 := (iff #16 #109)
+#134 := [rewrite]: #133
+#137 := [monotonicity #134]: #136
+#55 := [not-or-elim #52]: #54
+#138 := [mp #55 #137]: #135
+[mp #138 #153]: false
+a8aaa55cc1afac102005fa52e6f6290192b8b656 58 0
+unsat
 #2 := false
 #25 := 0::Int
 decl f3 :: (-> S2 S3 Int)
 decl f6 :: S3
-#11 := f6
-decl f4 :: S2
-#8 := f4
-#12 := (f3 f4 f6)
-#75 := -1::Int
-#76 := (* -1::Int #12)
-decl f5 :: S3
-#9 := f5
-#10 := (f3 f4 f5)
-#77 := (+ #10 #76)
-#82 := (>= #77 0::Int)
-#78 := (<= #77 -1::Int)
-#334 := (not #78)
-#81 := (not #82)
-#368 := [hypothesis]: #81
-#347 := (or #334 #82)
-#92 := (iff #78 #82)
-#14 := 1::Int
-#15 := (+ #10 1::Int)
-#16 := (<= #15 #12)
-#13 := (< #10 #12)
-#17 := (iff #13 #16)
+#10 := f6
+decl f4 :: S2
+#7 := f4
+#11 := (f3 f4 f6)
+#117 := -1::Int
+#120 := (* -1::Int #11)
+decl f5 :: S3
+#8 := f5
+#9 := (f3 f4 f5)
+#121 := (+ #9 #120)
+#119 := (>= #121 0::Int)
+#150 := (iff #119 false)
+#123 := (not #119)
+#45 := (<= #11 #9)
+#46 := (not #45)
+#124 := (iff #46 #123)
+#118 := (iff #45 #119)
+#122 := [rewrite]: #118
+#125 := [monotonicity #122]: #124
+#13 := 3::Int
+#14 := (* 3::Int #9)
+#15 := (* 3::Int #11)
+#49 := (<= #15 #14)
+#50 := (not #49)
+#56 := (or #45 #50)
+#61 := (not #56)
+#16 := (< #14 #15)
+#12 := (< #9 #11)
+#17 := (implies #12 #16)
 #18 := (not #17)
-#95 := (iff #18 #92)
-#69 := (not #13)
-#57 := (+ 1::Int #10)
-#60 := (<= #57 #12)
-#70 := (iff #60 #69)
-#93 := (iff #70 #92)
-#90 := (iff #69 #82)
-#85 := (not #81)
-#88 := (iff #85 #82)
-#89 := [rewrite]: #88
-#86 := (iff #69 #85)
-#83 := (iff #13 #81)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#91 := [trans #87 #89]: #90
-#79 := (iff #60 #78)
-#80 := [rewrite]: #79
-#94 := [monotonicity #80 #91]: #93
-#73 := (iff #18 #70)
-#63 := (iff #13 #60)
-#66 := (not #63)
-#71 := (iff #66 #70)
-#72 := [rewrite]: #71
-#67 := (iff #18 #66)
-#64 := (iff #17 #63)
-#61 := (iff #16 #60)
-#58 := (= #15 #57)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#65 := [monotonicity #62]: #64
-#68 := [monotonicity #65]: #67
-#74 := [trans #68 #72]: #73
-#96 := [trans #74 #94]: #95
-#56 := [asserted]: #18
-#97 := [mp #56 #96]: #92
-#256 := (not #92)
-#345 := (or #334 #82 #256)
-#346 := [def-axiom]: #345
-#344 := [unit-resolution #346 #97]: #347
-#369 := [unit-resolution #344 #368]: #334
-#263 := [th-lemma arith farkas 1 1 #368 #369]: false
-#639 := [lemma #263]: #82
-#640 := (or #81 #334)
-#362 := [th-lemma arith farkas 1 1]: #640
-#363 := [unit-resolution #362 #639]: #334
-#342 := (or #78 #81)
-#341 := (or #78 #81 #256)
-#257 := [def-axiom]: #341
-#343 := [unit-resolution #257 #97]: #342
-[unit-resolution #343 #363 #639]: false
-unsat
-8b705266e9e4f0706f9d3c335e68f3d792ff2c66 19 0
+#62 := (iff #18 #61)
+#59 := (iff #17 #56)
+#53 := (implies #46 #50)
+#57 := (iff #53 #56)
+#58 := [rewrite]: #57
+#54 := (iff #17 #53)
+#51 := (iff #16 #50)
+#52 := [rewrite]: #51
+#47 := (iff #12 #46)
+#48 := [rewrite]: #47
+#55 := [monotonicity #48 #52]: #54
+#60 := [trans #55 #58]: #59
+#63 := [monotonicity #60]: #62
+#38 := [asserted]: #18
+#64 := [mp #38 #63]: #61
+#65 := [not-or-elim #64]: #46
+#126 := [mp #65 #125]: #123
+#151 := [iff-false #126]: #150
+#149 := (iff #49 #119)
+#147 := [rewrite]: #149
+#66 := [not-or-elim #64]: #49
+#148 := [mp #66 #147]: #119
+[mp #148 #151]: false
+bc68f2688dca4da409b0f564f117c7120d85d804 57 0
+unsat
+#2 := false
+#22 := 0::Int
+decl f3 :: (-> S2 S3 Int)
+decl f6 :: S3
+#10 := f6
+decl f4 :: S2
+#7 := f4
+#11 := (f3 f4 f6)
+#111 := -1::Int
+#114 := (* -1::Int #11)
+decl f5 :: S3
+#8 := f5
+#9 := (f3 f4 f5)
+#115 := (+ #9 #114)
+#141 := (<= #115 0::Int)
+#144 := (not #141)
+#13 := (<= #9 #11)
+#59 := (not #13)
+#145 := (iff #59 #144)
+#142 := (iff #13 #141)
+#143 := [rewrite]: #142
+#146 := [monotonicity #143]: #145
+#42 := (<= #11 #9)
+#49 := (or #42 #13)
+#54 := (not #49)
+#12 := (< #9 #11)
+#14 := (implies #12 #13)
+#15 := (not #14)
+#55 := (iff #15 #54)
+#52 := (iff #14 #49)
+#43 := (not #42)
+#46 := (implies #43 #13)
+#50 := (iff #46 #49)
+#51 := [rewrite]: #50
+#47 := (iff #14 #46)
+#44 := (iff #12 #43)
+#45 := [rewrite]: #44
+#48 := [monotonicity #45]: #47
+#53 := [trans #48 #51]: #52
+#56 := [monotonicity #53]: #55
+#35 := [asserted]: #15
+#57 := [mp #35 #56]: #54
+#60 := [not-or-elim #57]: #59
+#147 := [mp #60 #146]: #144
+#113 := (>= #115 0::Int)
+#117 := (not #113)
+#118 := (iff #43 #117)
+#112 := (iff #42 #113)
+#116 := [rewrite]: #112
+#119 := [monotonicity #116]: #118
+#58 := [not-or-elim #57]: #43
+#120 := [mp #58 #119]: #117
+#163 := (or #141 #113)
+#247 := [th-lemma arith farkas 1 1]: #163
+#164 := [unit-resolution #247 #120]: #141
+[unit-resolution #164 #147]: false
+2313b6a33df28a371c3d91af7ee3267d8ec1adcb 79 0
+unsat
+#2 := false
+#54 := -1::Int
+decl f3 :: (-> S2 S3 Int)
+decl f6 :: S3
+#10 := f6
+decl f4 :: S2
+#7 := f4
+#11 := (f3 f4 f6)
+#125 := (* -1::Int #11)
+decl f5 :: S3
+#8 := f5
+#9 := (f3 f4 f5)
+#126 := (+ #9 #125)
+#128 := (<= #126 -1::Int)
+#24 := 0::Int
+#124 := (>= #126 0::Int)
+#257 := (not #124)
+#168 := (not #128)
+#222 := [hypothesis]: #168
+#256 := (or #257 #128)
+#131 := (iff #124 #128)
+#55 := (+ -1::Int #11)
+#56 := (<= #9 #55)
+#44 := (<= #11 #9)
+#67 := (iff #44 #56)
+#132 := (iff #67 #131)
+#129 := (iff #56 #128)
+#130 := [rewrite]: #129
+#123 := (iff #44 #124)
+#127 := [rewrite]: #123
+#133 := [monotonicity #127 #130]: #132
+#13 := 1::Int
+#14 := (+ #9 1::Int)
+#15 := (<= #14 #11)
+#12 := (< #9 #11)
+#16 := (iff #12 #15)
+#17 := (not #16)
+#70 := (iff #17 #67)
+#45 := (not #44)
+#61 := (iff #45 #56)
+#64 := (not #61)
+#68 := (iff #64 #67)
+#69 := [rewrite]: #68
+#65 := (iff #17 #64)
+#62 := (iff #16 #61)
+#59 := (iff #15 #56)
+#48 := (+ 1::Int #9)
+#51 := (<= #48 #11)
+#57 := (iff #51 #56)
+#58 := [rewrite]: #57
+#52 := (iff #15 #51)
+#49 := (= #14 #48)
+#50 := [rewrite]: #49
+#53 := [monotonicity #50]: #52
+#60 := [trans #53 #58]: #59
+#46 := (iff #12 #45)
+#47 := [rewrite]: #46
+#63 := [monotonicity #47 #60]: #62
+#66 := [monotonicity #63]: #65
+#71 := [trans #66 #69]: #70
+#37 := [asserted]: #17
+#72 := [mp #37 #71]: #67
+#134 := [mp #72 #133]: #131
+#253 := (not #131)
+#258 := (or #257 #128 #253)
+#259 := [def-axiom]: #258
+#260 := [unit-resolution #259 #134]: #256
+#223 := [unit-resolution #260 #222]: #257
+#564 := [th-lemma arith farkas 1 1 #222 #223]: false
+#202 := [lemma #564]: #128
+#565 := (or #168 #257)
+#567 := [th-lemma arith farkas 1 1]: #565
+#207 := [unit-resolution #567 #202]: #257
+#255 := (or #124 #168)
+#169 := (or #124 #168 #253)
+#254 := [def-axiom]: #169
+#246 := [unit-resolution #254 #134]: #255
+[unit-resolution #246 #207 #202]: false
+6fee3152946968f658ff9cf86ca496852eca7ae9 40 0
+unsat
 #2 := false
 decl f3 :: (-> S2 S3 Int)
 decl f5 :: S3
-#9 := f5
-decl f4 :: S2
-#8 := f4
-#10 := (f3 f4 f5)
-#11 := (< #10 #10)
+#8 := f5
+decl f4 :: S2
+#7 := f4
+#9 := (f3 f4 f5)
+#10 := (< #9 #9)
+#11 := (not #10)
 #12 := (not #11)
-#13 := (not #12)
-#56 := (iff #13 false)
-#54 := (iff #11 false)
-#55 := [rewrite]: #54
-#52 := (iff #13 #11)
-#53 := [rewrite]: #52
-#57 := [trans #53 #55]: #56
-#51 := [asserted]: #13
-[mp #51 #57]: false
-unsat
-a47f8885da8e6a2dd769c0d058b020acc80a3413 81 0
-#2 := false
-#27 := 0::Int
+#63 := (iff #12 false)
+#1 := true
+#45 := (not true)
+#48 := (iff #45 false)
+#49 := [rewrite]: #48
+#61 := (iff #12 #45)
+#59 := (iff #11 true)
+#54 := (not false)
+#57 := (iff #54 true)
+#58 := [rewrite]: #57
+#55 := (iff #11 #54)
+#52 := (iff #10 false)
+#39 := (<= #9 #9)
+#40 := (not #39)
+#50 := (iff #40 false)
+#46 := (iff #40 #45)
+#43 := (iff #39 true)
+#44 := [rewrite]: #43
+#47 := [monotonicity #44]: #46
+#51 := [trans #47 #49]: #50
+#41 := (iff #10 #40)
+#42 := [rewrite]: #41
+#53 := [trans #42 #51]: #52
+#56 := [monotonicity #53]: #55
+#60 := [trans #56 #58]: #59
+#62 := [monotonicity #60]: #61
+#64 := [trans #62 #49]: #63
+#32 := [asserted]: #12
+[mp #32 #64]: false
+fcb70069c91934ffce190a7f4790ad5fefc7b891 65 0
+unsat
+#2 := false
+#26 := 0::Int
+decl f3 :: (-> S2 S3 Int)
+decl f7 :: S3
+#13 := f7
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 f7)
+#117 := -1::Int
+#144 := (* -1::Int #14)
+decl f6 :: S3
+#10 := f6
+#11 := (f3 f4 f6)
+#145 := (+ #11 #144)
+#146 := (<= #145 0::Int)
+#15 := (<= #11 #14)
+#147 := (iff #15 #146)
+#148 := [rewrite]: #147
+decl f5 :: S3
+#8 := f5
+#9 := (f3 f4 f5)
+#16 := (<= #9 #14)
+#46 := (not #15)
+#12 := (<= #9 #11)
+#53 := (not #12)
+#54 := (or #53 #46 #16)
+#59 := (not #54)
+#17 := (implies #15 #16)
+#18 := (implies #12 #17)
+#19 := (not #18)
+#60 := (iff #19 #59)
+#57 := (iff #18 #54)
+#47 := (or #46 #16)
+#50 := (implies #12 #47)
+#55 := (iff #50 #54)
+#56 := [rewrite]: #55
+#51 := (iff #18 #50)
+#48 := (iff #17 #47)
+#49 := [rewrite]: #48
+#52 := [monotonicity #49]: #51
+#58 := [trans #52 #56]: #57
+#61 := [monotonicity #58]: #60
+#39 := [asserted]: #19
+#62 := [mp #39 #61]: #59
+#64 := [not-or-elim #62]: #15
+#149 := [mp #64 #148]: #146
+#150 := (+ #9 #144)
+#151 := (<= #150 0::Int)
+#154 := (not #151)
+#65 := (not #16)
+#155 := (iff #65 #154)
+#152 := (iff #16 #151)
+#153 := [rewrite]: #152
+#156 := [monotonicity #153]: #155
+#66 := [not-or-elim #62]: #65
+#157 := [mp #66 #156]: #154
+#118 := (* -1::Int #11)
+#119 := (+ #9 #118)
+#120 := (<= #119 0::Int)
+#121 := (iff #12 #120)
+#122 := [rewrite]: #121
+#63 := [not-or-elim #62]: #12
+#123 := [mp #63 #122]: #120
+[th-lemma arith farkas 1 -1 1 #123 #157 #149]: false
+314578dd8533fcbb8964e37afa9ad18771a56310 71 0
+unsat
+#2 := false
+#26 := 0::Int
 decl f3 :: (-> S2 S3 Int)
 decl f7 :: S3
-#14 := f7
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 f7)
-#75 := -1::Int
-#76 := (* -1::Int #15)
+#13 := f7
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 f7)
+#120 := -1::Int
+#150 := (* -1::Int #14)
+decl f6 :: S3
+#10 := f6
+#11 := (f3 f4 f6)
+#151 := (+ #11 #150)
+#152 := (<= #151 0::Int)
+#15 := (<= #11 #14)
+#153 := (iff #15 #152)
+#154 := [rewrite]: #153
+decl f5 :: S3
+#8 := f5
+#9 := (f3 f4 f5)
+#16 := (<= #9 #14)
+#50 := (not #15)
+#46 := (<= #11 #9)
+#57 := (or #46 #50 #16)
+#62 := (not #57)
+#17 := (implies #15 #16)
+#12 := (< #9 #11)
+#18 := (implies #12 #17)
+#19 := (not #18)
+#63 := (iff #19 #62)
+#60 := (iff #18 #57)
+#51 := (or #50 #16)
+#47 := (not #46)
+#54 := (implies #47 #51)
+#58 := (iff #54 #57)
+#59 := [rewrite]: #58
+#55 := (iff #18 #54)
+#52 := (iff #17 #51)
+#53 := [rewrite]: #52
+#48 := (iff #12 #47)
+#49 := [rewrite]: #48
+#56 := [monotonicity #49 #53]: #55
+#61 := [trans #56 #59]: #60
+#64 := [monotonicity #61]: #63
+#39 := [asserted]: #19
+#65 := [mp #39 #64]: #62
+#67 := [not-or-elim #65]: #15
+#155 := [mp #67 #154]: #152
+#123 := (* -1::Int #11)
+#124 := (+ #9 #123)
+#122 := (>= #124 0::Int)
+#126 := (not #122)
+#127 := (iff #47 #126)
+#121 := (iff #46 #122)
+#125 := [rewrite]: #121
+#128 := [monotonicity #125]: #127
+#66 := [not-or-elim #65]: #47
+#129 := [mp #66 #128]: #126
+#156 := (+ #9 #150)
+#157 := (<= #156 0::Int)
+#160 := (not #157)
+#68 := (not #16)
+#161 := (iff #68 #160)
+#158 := (iff #16 #157)
+#159 := [rewrite]: #158
+#162 := [monotonicity #159]: #161
+#69 := [not-or-elim #65]: #68
+#163 := [mp #69 #162]: #160
+[th-lemma arith farkas 1 1 1 #163 #129 #155]: false
+171ded070b8a8323b4f2cd46ab63f8d215cdbc40 76 0
+unsat
+#2 := false
+#26 := 0::Int
+decl f3 :: (-> S2 S3 Int)
+decl f7 :: S3
+#13 := f7
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 f7)
+#125 := -1::Int
+#153 := (* -1::Int #14)
+decl f5 :: S3
+#8 := f5
+#9 := (f3 f4 f5)
+#161 := (+ #9 #153)
+#162 := (<= #161 0::Int)
+#165 := (not #162)
+#16 := (<= #9 #14)
+#73 := (not #16)
+#166 := (iff #73 #165)
+#163 := (iff #16 #162)
+#164 := [rewrite]: #163
+#167 := [monotonicity #164]: #166
 decl f6 :: S3
-#11 := f6
-#12 := (f3 f4 f6)
-#77 := (+ #12 #76)
-#78 := (<= #77 0::Int)
-#88 := (* -1::Int #12)
-decl f5 :: S3
-#9 := f5
-#10 := (f3 f4 f5)
-#89 := (+ #10 #88)
-#90 := (<= #89 0::Int)
-#93 := (not #90)
-#84 := (+ #10 #76)
-#85 := (<= #84 0::Int)
-#81 := (not #78)
-#102 := (or #81 #85 #93)
-#107 := (not #102)
-#17 := (<= #10 #15)
-#16 := (<= #12 #15)
-#18 := (implies #16 #17)
-#13 := (<= #10 #12)
-#19 := (implies #13 #18)
-#20 := (not #19)
-#110 := (iff #20 #107)
-#59 := (not #16)
-#60 := (or #59 #17)
-#66 := (not #13)
-#67 := (or #66 #60)
-#72 := (not #67)
-#108 := (iff #72 #107)
-#105 := (iff #67 #102)
-#96 := (or #81 #85)
-#99 := (or #93 #96)
-#103 := (iff #99 #102)
-#104 := [rewrite]: #103
-#100 := (iff #67 #99)
-#97 := (iff #60 #96)
-#86 := (iff #17 #85)
-#87 := [rewrite]: #86
-#82 := (iff #59 #81)
-#79 := (iff #16 #78)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#98 := [monotonicity #83 #87]: #97
-#94 := (iff #66 #93)
-#91 := (iff #13 #90)
-#92 := [rewrite]: #91
-#95 := [monotonicity #92]: #94
-#101 := [monotonicity #95 #98]: #100
-#106 := [trans #101 #104]: #105
-#109 := [monotonicity #106]: #108
-#73 := (iff #20 #72)
-#70 := (iff #19 #67)
-#63 := (implies #13 #60)
-#68 := (iff #63 #67)
-#69 := [rewrite]: #68
-#64 := (iff #19 #63)
-#61 := (iff #18 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#71 := [trans #65 #69]: #70
-#74 := [monotonicity #71]: #73
-#111 := [trans #74 #109]: #110
-#58 := [asserted]: #20
-#112 := [mp #58 #111]: #107
-#113 := [not-or-elim #112]: #78
-#114 := (not #85)
-#115 := [not-or-elim #112]: #114
-#116 := [not-or-elim #112]: #90
-[th-lemma arith farkas 1 -1 1 #116 #115 #113]: false
-unsat
-855f8ec444546329497deff0085d8e9571a25bb7 86 0
+#10 := f6
+#11 := (f3 f4 f6)
+#46 := (<= #14 #11)
+#12 := (<= #9 #11)
+#61 := (not #12)
+#62 := (or #61 #46 #16)
+#67 := (not #62)
+#15 := (< #11 #14)
+#17 := (implies #15 #16)
+#18 := (implies #12 #17)
+#19 := (not #18)
+#68 := (iff #19 #67)
+#65 := (iff #18 #62)
+#53 := (or #46 #16)
+#58 := (implies #12 #53)
+#63 := (iff #58 #62)
+#64 := [rewrite]: #63
+#59 := (iff #18 #58)
+#56 := (iff #17 #53)
+#47 := (not #46)
+#50 := (implies #47 #16)
+#54 := (iff #50 #53)
+#55 := [rewrite]: #54
+#51 := (iff #17 #50)
+#48 := (iff #15 #47)
+#49 := [rewrite]: #48
+#52 := [monotonicity #49]: #51
+#57 := [trans #52 #55]: #56
+#60 := [monotonicity #57]: #59
+#66 := [trans #60 #64]: #65
+#69 := [monotonicity #66]: #68
+#39 := [asserted]: #19
+#70 := [mp #39 #69]: #67
+#74 := [not-or-elim #70]: #73
+#168 := [mp #74 #167]: #165
+#154 := (+ #11 #153)
+#152 := (>= #154 0::Int)
+#157 := (not #152)
+#158 := (iff #47 #157)
+#155 := (iff #46 #152)
+#156 := [rewrite]: #155
+#159 := [monotonicity #156]: #158
+#72 := [not-or-elim #70]: #47
+#160 := [mp #72 #159]: #157
+#126 := (* -1::Int #11)
+#127 := (+ #9 #126)
+#128 := (<= #127 0::Int)
+#129 := (iff #12 #128)
+#130 := [rewrite]: #129
+#71 := [not-or-elim #70]: #12
+#131 := [mp #71 #130]: #128
+[th-lemma arith farkas 1 1 1 #131 #160 #168]: false
+3442e0ff683ec86dfe8263beead19ae007eb6c5a 82 0
+unsat
+#2 := false
+#26 := 0::Int
+decl f3 :: (-> S2 S3 Int)
+decl f7 :: S3
+#13 := f7
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 f7)
+#131 := -1::Int
+#162 := (* -1::Int #14)
+decl f5 :: S3
+#8 := f5
+#9 := (f3 f4 f5)
+#172 := (+ #9 #162)
+#171 := (>= #172 0::Int)
+#54 := (<= #14 #9)
+#170 := (iff #54 #171)
+#173 := [rewrite]: #170
+#55 := (not #54)
+decl f6 :: S3
+#10 := f6
+#11 := (f3 f4 f6)
+#50 := (<= #14 #11)
+#46 := (<= #11 #9)
+#69 := (or #46 #50 #55)
+#74 := (not #69)
+#16 := (< #9 #14)
+#15 := (< #11 #14)
+#17 := (implies #15 #16)
+#12 := (< #9 #11)
+#18 := (implies #12 #17)
+#19 := (not #18)
+#75 := (iff #19 #74)
+#72 := (iff #18 #69)
+#61 := (or #50 #55)
+#47 := (not #46)
+#66 := (implies #47 #61)
+#70 := (iff #66 #69)
+#71 := [rewrite]: #70
+#67 := (iff #18 #66)
+#64 := (iff #17 #61)
+#51 := (not #50)
+#58 := (implies #51 #55)
+#62 := (iff #58 #61)
+#63 := [rewrite]: #62
+#59 := (iff #17 #58)
+#56 := (iff #16 #55)
+#57 := [rewrite]: #56
+#52 := (iff #15 #51)
+#53 := [rewrite]: #52
+#60 := [monotonicity #53 #57]: #59
+#65 := [trans #60 #63]: #64
+#48 := (iff #12 #47)
+#49 := [rewrite]: #48
+#68 := [monotonicity #49 #65]: #67
+#73 := [trans #68 #71]: #72
+#76 := [monotonicity #73]: #75
+#39 := [asserted]: #19
+#77 := [mp #39 #76]: #74
+#80 := [not-or-elim #77]: #54
+#174 := [mp #80 #173]: #171
+#163 := (+ #11 #162)
+#161 := (>= #163 0::Int)
+#166 := (not #161)
+#167 := (iff #51 #166)
+#164 := (iff #50 #161)
+#165 := [rewrite]: #164
+#168 := [monotonicity #165]: #167
+#79 := [not-or-elim #77]: #51
+#169 := [mp #79 #168]: #166
+#134 := (* -1::Int #11)
+#135 := (+ #9 #134)
+#133 := (>= #135 0::Int)
+#137 := (not #133)
+#138 := (iff #47 #137)
+#132 := (iff #46 #133)
+#136 := [rewrite]: #132
+#139 := [monotonicity #136]: #138
+#78 := [not-or-elim #77]: #47
+#140 := [mp #78 #139]: #137
+[th-lemma arith farkas 1 1 1 #140 #169 #174]: false
+29a6322268f6966071dac48d687e18d152c2d9a2 90 0
+unsat
 #2 := false
 #27 := 0::Int
 decl f3 :: (-> S2 S3 Int)
 decl f7 :: S3
-#14 := f7
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 f7)
-#75 := -1::Int
-#76 := (* -1::Int #15)
+#13 := f7
+decl f4 :: S2
+#7 := f4
+#14 := (f3 f4 f7)
+#136 := -1::Int
+#167 := (* -1::Int #14)
+decl f5 :: S3
+#8 := f5
+#9 := (f3 f4 f5)
+#175 := (+ #9 #167)
+#176 := (<= #175 0::Int)
+#179 := (not #176)
+#58 := (<= #9 #14)
+#59 := (not #58)
+#180 := (iff #59 #179)
+#177 := (iff #58 #176)
+#178 := [rewrite]: #177
+#181 := [monotonicity #178]: #180
 decl f6 :: S3
-#11 := f6
-#12 := (f3 f4 f6)
-#77 := (+ #12 #76)
-#78 := (<= #77 0::Int)
-#90 := (* -1::Int #12)
-decl f5 :: S3
-#9 := f5
-#10 := (f3 f4 f5)
-#91 := (+ #10 #90)
-#89 := (>= #91 0::Int)
-#84 := (+ #10 #76)
-#85 := (<= #84 0::Int)
-#81 := (not #78)
-#107 := (or #81 #85 #89)
-#112 := (not #107)
-#17 := (<= #10 #15)
-#16 := (<= #12 #15)
-#18 := (implies #16 #17)
-#13 := (< #10 #12)
-#19 := (implies #13 #18)
-#20 := (not #19)
-#115 := (iff #20 #112)
-#59 := (not #16)
-#60 := (or #59 #17)
-#66 := (not #13)
-#67 := (or #66 #60)
-#72 := (not #67)
-#113 := (iff #72 #112)
-#110 := (iff #67 #107)
-#101 := (or #81 #85)
-#104 := (or #89 #101)
-#108 := (iff #104 #107)
-#109 := [rewrite]: #108
-#105 := (iff #67 #104)
-#102 := (iff #60 #101)
-#86 := (iff #17 #85)
-#87 := [rewrite]: #86
-#82 := (iff #59 #81)
-#79 := (iff #16 #78)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#103 := [monotonicity #83 #87]: #102
-#99 := (iff #66 #89)
-#88 := (not #89)
-#94 := (not #88)
-#97 := (iff #94 #89)
-#98 := [rewrite]: #97
-#95 := (iff #66 #94)
-#92 := (iff #13 #88)
-#93 := [rewrite]: #92
-#96 := [monotonicity #93]: #95
-#100 := [trans #96 #98]: #99
-#106 := [monotonicity #100 #103]: #105
-#111 := [trans #106 #109]: #110
-#114 := [monotonicity #111]: #113
-#73 := (iff #20 #72)
-#70 := (iff #19 #67)
-#63 := (implies #13 #60)
-#68 := (iff #63 #67)
-#69 := [rewrite]: #68
-#64 := (iff #19 #63)
-#61 := (iff #18 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#71 := [trans #65 #69]: #70
-#74 := [monotonicity #71]: #73
-#116 := [trans #74 #114]: #115
-#58 := [asserted]: #20
-#117 := [mp #58 #116]: #112
-#118 := [not-or-elim #117]: #78
-#119 := (not #85)
-#120 := [not-or-elim #117]: #119
-#121 := [not-or-elim #117]: #88
-[th-lemma arith farkas 1 1 1 #121 #120 #118]: false
-unsat
-5b8b51f4b0b17c7b86316066d52d623031015f7f 86 0
-#2 := false
-#27 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f6 :: S3
-#11 := f6
-decl f4 :: S2
-#8 := f4
-#12 := (f3 f4 f6)
-#75 := -1::Int
-#93 := (* -1::Int #12)
-decl f5 :: S3
-#9 := f5
-#10 := (f3 f4 f5)
-#94 := (+ #10 #93)
-#95 := (<= #94 0::Int)
-#98 := (not #95)
-decl f7 :: S3
-#14 := f7
-#15 := (f3 f4 f7)
-#78 := (* -1::Int #15)
-#89 := (+ #10 #78)
-#90 := (<= #89 0::Int)
-#79 := (+ #12 #78)
-#77 := (>= #79 0::Int)
-#107 := (or #77 #90 #98)
-#112 := (not #107)
-#17 := (<= #10 #15)
-#16 := (< #12 #15)
-#18 := (implies #16 #17)
-#13 := (<= #10 #12)
-#19 := (implies #13 #18)
+#10 := f6
+#11 := (f3 f4 f6)
+#51 := (<= #14 #11)
+#52 := (not #51)
+#47 := (<= #11 #9)
+#48 := (not #47)
+#55 := (and #48 #52)
+#72 := (not #55)
+#73 := (or #72 #58)
+#78 := (not #73)
+#17 := (< #14 #9)
+#18 := (not #17)
+#15 := (< #11 #14)
+#12 := (< #9 #11)
+#16 := (and #12 #15)
+#19 := (implies #16 #18)
 #20 := (not #19)
-#115 := (iff #20 #112)
-#59 := (not #16)
-#60 := (or #59 #17)
-#66 := (not #13)
-#67 := (or #66 #60)
-#72 := (not #67)
-#113 := (iff #72 #112)
-#110 := (iff #67 #107)
-#101 := (or #77 #90)
-#104 := (or #98 #101)
-#108 := (iff #104 #107)
-#109 := [rewrite]: #108
-#105 := (iff #67 #104)
-#102 := (iff #60 #101)
-#91 := (iff #17 #90)
-#92 := [rewrite]: #91
-#87 := (iff #59 #77)
-#76 := (not #77)
-#82 := (not #76)
-#85 := (iff #82 #77)
-#86 := [rewrite]: #85
-#83 := (iff #59 #82)
-#80 := (iff #16 #76)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#88 := [trans #84 #86]: #87
-#103 := [monotonicity #88 #92]: #102
-#99 := (iff #66 #98)
-#96 := (iff #13 #95)
-#97 := [rewrite]: #96
-#100 := [monotonicity #97]: #99
-#106 := [monotonicity #100 #103]: #105
-#111 := [trans #106 #109]: #110
-#114 := [monotonicity #111]: #113
-#73 := (iff #20 #72)
-#70 := (iff #19 #67)
-#63 := (implies #13 #60)
-#68 := (iff #63 #67)
-#69 := [rewrite]: #68
-#64 := (iff #19 #63)
-#61 := (iff #18 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#71 := [trans #65 #69]: #70
-#74 := [monotonicity #71]: #73
-#116 := [trans #74 #114]: #115
-#58 := [asserted]: #20
-#117 := [mp #58 #116]: #112
-#121 := [not-or-elim #117]: #95
-#119 := (not #90)
-#120 := [not-or-elim #117]: #119
-#118 := [not-or-elim #117]: #76
-[th-lemma arith farkas 1 1 1 #118 #120 #121]: false
-unsat
-1dc9e0401f3e6d68ca3f3c4cf618ee7dc6f0ce31 91 0
-#2 := false
-#27 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f7 :: S3
-#14 := f7
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 f7)
-#75 := -1::Int
-#78 := (* -1::Int #15)
-decl f5 :: S3
-#9 := f5
-#10 := (f3 f4 f5)
-#91 := (+ #10 #78)
-#90 := (>= #91 0::Int)
-decl f6 :: S3
-#11 := f6
-#12 := (f3 f4 f6)
-#96 := (* -1::Int #12)
-#97 := (+ #10 #96)
-#95 := (>= #97 0::Int)
-#89 := (not #90)
-#79 := (+ #12 #78)
-#77 := (>= #79 0::Int)
-#113 := (or #77 #89 #95)
-#118 := (not #113)
-#17 := (< #10 #15)
-#16 := (< #12 #15)
-#18 := (implies #16 #17)
-#13 := (< #10 #12)
-#19 := (implies #13 #18)
-#20 := (not #19)
-#121 := (iff #20 #118)
-#59 := (not #16)
-#60 := (or #59 #17)
-#66 := (not #13)
-#67 := (or #66 #60)
-#72 := (not #67)
-#119 := (iff #72 #118)
-#116 := (iff #67 #113)
-#107 := (or #77 #89)
-#110 := (or #95 #107)
-#114 := (iff #110 #113)
-#115 := [rewrite]: #114
-#111 := (iff #67 #110)
-#108 := (iff #60 #107)
-#92 := (iff #17 #89)
-#93 := [rewrite]: #92
-#87 := (iff #59 #77)
-#76 := (not #77)
-#82 := (not #76)
-#85 := (iff #82 #77)
-#86 := [rewrite]: #85
-#83 := (iff #59 #82)
-#80 := (iff #16 #76)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#88 := [trans #84 #86]: #87
-#109 := [monotonicity #88 #93]: #108
-#105 := (iff #66 #95)
-#94 := (not #95)
-#100 := (not #94)
-#103 := (iff #100 #95)
-#104 := [rewrite]: #103
-#101 := (iff #66 #100)
-#98 := (iff #13 #94)
-#99 := [rewrite]: #98
-#102 := [monotonicity #99]: #101
-#106 := [trans #102 #104]: #105
-#112 := [monotonicity #106 #109]: #111
-#117 := [trans #112 #115]: #116
-#120 := [monotonicity #117]: #119
-#73 := (iff #20 #72)
-#70 := (iff #19 #67)
-#63 := (implies #13 #60)
-#68 := (iff #63 #67)
-#69 := [rewrite]: #68
-#64 := (iff #19 #63)
-#61 := (iff #18 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#71 := [trans #65 #69]: #70
-#74 := [monotonicity #71]: #73
-#122 := [trans #74 #120]: #121
-#58 := [asserted]: #20
-#123 := [mp #58 #122]: #118
-#125 := [not-or-elim #123]: #90
-#124 := [not-or-elim #123]: #76
-#126 := [not-or-elim #123]: #94
-[th-lemma arith farkas 1 1 1 #126 #124 #125]: false
-unsat
-16e044a831706a18531bf6261ba78fef95060579 75 0
-#2 := false
-#28 := 0::Int
-decl f3 :: (-> S2 S3 Int)
-decl f7 :: S3
-#14 := f7
-decl f4 :: S2
-#8 := f4
-#15 := (f3 f4 f7)
-#67 := -1::Int
-#75 := (* -1::Int #15)
-decl f5 :: S3
-#9 := f5
-#10 := (f3 f4 f5)
-#86 := (+ #10 #75)
-#87 := (<= #86 0::Int)
-#88 := (not #87)
-decl f6 :: S3
-#11 := f6
-#12 := (f3 f4 f6)
-#76 := (+ #12 #75)
-#74 := (>= #76 0::Int)
-#77 := (not #74)
-#70 := (* -1::Int #12)
-#71 := (+ #10 #70)
-#69 := (>= #71 0::Int)
-#68 := (not #69)
-#80 := (and #68 #77)
-#83 := (not #80)
-#98 := (or #83 #87)
-#101 := (not #98)
-#18 := (< #15 #10)
-#19 := (not #18)
-#16 := (< #12 #15)
-#13 := (< #10 #12)
-#17 := (and #13 #16)
-#20 := (implies #17 #19)
-#21 := (not #20)
-#104 := (iff #21 #101)
-#60 := (not #17)
-#61 := (or #60 #19)
-#64 := (not #61)
-#102 := (iff #64 #101)
-#99 := (iff #61 #98)
-#96 := (iff #19 #87)
-#91 := (not #88)
-#94 := (iff #91 #87)
-#95 := [rewrite]: #94
-#92 := (iff #19 #91)
-#89 := (iff #18 #88)
-#90 := [rewrite]: #89
-#93 := [monotonicity #90]: #92
-#97 := [trans #93 #95]: #96
-#84 := (iff #60 #83)
-#81 := (iff #17 #80)
-#78 := (iff #16 #77)
-#79 := [rewrite]: #78
-#72 := (iff #13 #68)
-#73 := [rewrite]: #72
-#82 := [monotonicity #73 #79]: #81
-#85 := [monotonicity #82]: #84
-#100 := [monotonicity #85 #97]: #99
-#103 := [monotonicity #100]: #102
-#65 := (iff #21 #64)
-#62 := (iff #20 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#105 := [trans #66 #103]: #104
-#59 := [asserted]: #21
-#106 := [mp #59 #105]: #101
-#110 := [not-or-elim #106]: #88
-#107 := [not-or-elim #106]: #80
-#109 := [and-elim #107]: #77
-#108 := [and-elim #107]: #68
-[th-lemma arith farkas 1 1 1 #108 #109 #110]: false
-unsat
-13113e7e58018c6880ea2f28cb5993925582157c 17 0
-#2 := false
-#8 := 0::Int
-#9 := (= 0::Int 0::Int)
+#79 := (iff #20 #78)
+#76 := (iff #19 #73)
+#69 := (implies #55 #58)
+#74 := (iff #69 #73)
+#75 := [rewrite]: #74
+#70 := (iff #19 #69)
+#67 := (iff #18 #58)
+#62 := (not #59)
+#65 := (iff #62 #58)
+#66 := [rewrite]: #65
+#63 := (iff #18 #62)
+#60 := (iff #17 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#68 := [trans #64 #66]: #67
+#56 := (iff #16 #55)
+#53 := (iff #15 #52)
+#54 := [rewrite]: #53
+#49 := (iff #12 #48)
+#50 := [rewrite]: #49
+#57 := [monotonicity #50 #54]: #56
+#71 := [monotonicity #57 #68]: #70
+#77 := [trans #71 #75]: #76
+#80 := [monotonicity #77]: #79
+#40 := [asserted]: #20
+#81 := [mp #40 #80]: #78
+#85 := [not-or-elim #81]: #59
+#182 := [mp #85 #181]: #179
+#168 := (+ #11 #167)
+#166 := (>= #168 0::Int)
+#171 := (not #166)
+#172 := (iff #52 #171)
+#169 := (iff #51 #166)
+#170 := [rewrite]: #169
+#173 := [monotonicity #170]: #172
+#82 := [not-or-elim #81]: #55
+#84 := [and-elim #82]: #52
+#174 := [mp #84 #173]: #171
+#139 := (* -1::Int #11)
+#140 := (+ #9 #139)
+#138 := (>= #140 0::Int)
+#142 := (not #138)
+#143 := (iff #48 #142)
+#137 := (iff #47 #138)
+#141 := [rewrite]: #137
+#144 := [monotonicity #141]: #143
+#83 := [and-elim #82]: #48
+#145 := [mp #83 #144]: #142
+[th-lemma arith farkas 1 1 1 #145 #174 #182]: false
+6d0934f7a1554664ef5aab68f018c40077851491 17 0
+unsat
+#2 := false
+#7 := 0::Int
+#8 := (= 0::Int 0::Int)
+#9 := (not #8)
+#22 := (iff #9 false)
+#1 := true
+#17 := (not true)
+#20 := (iff #17 false)
+#21 := [rewrite]: #20
+#18 := (iff #9 #17)
+#15 := (iff #8 true)
+#16 := [rewrite]: #15
+#19 := [monotonicity #16]: #18
+#23 := [trans #19 #21]: #22
+#11 := [asserted]: #9
+[mp #11 #23]: false
+d7b98ca131502dcbf6e72e7a62827571cacaa1f4 25 0
+unsat
+#2 := false
+#7 := 0::Int
+#8 := (- 0::Int)
+#9 := (= 0::Int #8)
 #10 := (not #9)
-#38 := (iff #10 false)
-#1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#31 := (iff #9 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#30 := [asserted]: #10
-[mp #30 #39]: false
-unsat
-1056717a1a09b6c4176c8b78807918dcff0f057a 25 0
-#2 := false
-#8 := 0::Int
-#9 := (- 0::Int)
-#10 := (= 0::Int #9)
+#30 := (iff #10 false)
+#1 := true
+#25 := (not true)
+#28 := (iff #25 false)
+#29 := [rewrite]: #28
+#26 := (iff #10 #25)
+#23 := (iff #9 true)
+#18 := (= 0::Int 0::Int)
+#21 := (iff #18 true)
+#22 := [rewrite]: #21
+#19 := (iff #9 #18)
+#16 := (= #8 0::Int)
+#17 := [rewrite]: #16
+#20 := [monotonicity #17]: #19
+#24 := [trans #20 #22]: #23
+#27 := [monotonicity #24]: #26
+#31 := [trans #27 #29]: #30
+#12 := [asserted]: #10
+[mp #12 #31]: false
+7b0ec950272ab38d7bef78f0f0033a39806c5288 17 0
+unsat
+#2 := false
+#7 := 1::Int
+#8 := (= 1::Int 1::Int)
+#9 := (not #8)
+#23 := (iff #9 false)
+#1 := true
+#18 := (not true)
+#21 := (iff #18 false)
+#22 := [rewrite]: #21
+#19 := (iff #9 #18)
+#16 := (iff #8 true)
+#17 := [rewrite]: #16
+#20 := [monotonicity #17]: #19
+#24 := [trans #20 #22]: #23
+#11 := [asserted]: #9
+[mp #11 #24]: false
+5bacae6f5a25de48b565a5f4f260454983cf0324 34 0
+unsat
+#2 := false
+#7 := 1::Int
+#8 := (- 1::Int)
+#9 := (= #8 1::Int)
+#10 := (not #9)
+#11 := (not #10)
+#41 := (iff #11 false)
+#1 := true
+#36 := (not true)
+#39 := (iff #36 false)
+#40 := [rewrite]: #39
+#37 := (iff #11 #36)
+#34 := (iff #10 true)
+#29 := (not false)
+#32 := (iff #29 true)
+#33 := [rewrite]: #32
+#30 := (iff #10 #29)
+#27 := (iff #9 false)
+#17 := -1::Int
+#20 := (= -1::Int 1::Int)
+#25 := (iff #20 false)
+#26 := [rewrite]: #25
+#21 := (iff #9 #20)
+#18 := (= #8 -1::Int)
+#19 := [rewrite]: #18
+#22 := [monotonicity #19]: #21
+#28 := [trans #22 #26]: #27
+#31 := [monotonicity #28]: #30
+#35 := [trans #31 #33]: #34
+#38 := [monotonicity #35]: #37
+#42 := [trans #38 #40]: #41
+#13 := [asserted]: #11
+[mp #13 #42]: false
+51cefbb0434bd040121aa77cae27123fd91052b1 50 0
+unsat
+#2 := false
+#11 := 567::Int
+#9 := 345::Int
+#7 := 123::Int
+#8 := (- 123::Int)
+#10 := (+ #8 345::Int)
+#12 := (< #10 567::Int)
+#13 := (not #12)
+#56 := (iff #13 false)
+#1 := true
+#51 := (not true)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #13 #51)
+#49 := (iff #12 true)
+#25 := 222::Int
+#33 := (<= 567::Int 222::Int)
+#34 := (not #33)
+#47 := (iff #34 true)
+#42 := (not false)
+#45 := (iff #42 true)
+#46 := [rewrite]: #45
+#43 := (iff #34 #42)
+#39 := (iff #33 false)
+#41 := [rewrite]: #39
+#44 := [monotonicity #41]: #43
+#48 := [trans #44 #46]: #47
+#37 := (iff #12 #34)
+#30 := (< 222::Int 567::Int)
+#35 := (iff #30 #34)
+#36 := [rewrite]: #35
+#31 := (iff #12 #30)
+#28 := (= #10 222::Int)
+#19 := -123::Int
+#22 := (+ -123::Int 345::Int)
+#26 := (= #22 222::Int)
+#27 := [rewrite]: #26
+#23 := (= #10 #22)
+#20 := (= #8 -123::Int)
+#21 := [rewrite]: #20
+#24 := [monotonicity #21]: #23
+#29 := [trans #24 #27]: #28
+#32 := [monotonicity #29]: #31
+#38 := [trans #32 #36]: #37
+#50 := [trans #38 #48]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#15 := [asserted]: #13
+[mp #15 #57]: false
+7a443dccb932d2e9c10f10108463fa3fd7f3208f 40 0
+unsat
+#2 := false
+#9 := 2345678901::Int
+#7 := 123456789::Int
+#8 := (- 123456789::Int)
+#10 := (< #8 2345678901::Int)
 #11 := (not #10)
 #46 := (iff #11 false)
 #1 := true
@@ -26131,1100 +25062,1288 @@
 #45 := [rewrite]: #44
 #42 := (iff #11 #41)
 #39 := (iff #10 true)
-#34 := (= 0::Int 0::Int)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #10 #34)
-#32 := (= #9 0::Int)
-#33 := [rewrite]: #32
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
+#17 := -123456789::Int
+#23 := (<= 2345678901::Int -123456789::Int)
+#24 := (not #23)
+#37 := (iff #24 true)
+#32 := (not false)
+#35 := (iff #32 true)
+#36 := [rewrite]: #35
+#33 := (iff #24 #32)
+#29 := (iff #23 false)
+#31 := [rewrite]: #29
+#34 := [monotonicity #31]: #33
+#38 := [trans #34 #36]: #37
+#27 := (iff #10 #24)
+#20 := (< -123456789::Int 2345678901::Int)
+#25 := (iff #20 #24)
+#26 := [rewrite]: #25
+#21 := (iff #10 #20)
+#18 := (= #8 -123456789::Int)
+#19 := [rewrite]: #18
+#22 := [monotonicity #19]: #21
+#28 := [trans #22 #26]: #27
+#40 := [trans #28 #38]: #39
 #43 := [monotonicity #40]: #42
 #47 := [trans #43 #45]: #46
-#31 := [asserted]: #11
-[mp #31 #47]: false
-unsat
-52057012d500bf36246da2f6fe0e5f4fead2daa8 17 0
-#2 := false
-#8 := 1::Int
-#9 := (= 1::Int 1::Int)
-#10 := (not #9)
-#38 := (iff #10 false)
-#1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#31 := (iff #9 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#30 := [asserted]: #10
-[mp #30 #39]: false
-unsat
-3896508560f827467603181397afe4ea7af60b1b 34 0
-#2 := false
-#8 := 1::Int
-#9 := (- 1::Int)
-#10 := (= #9 1::Int)
+#13 := [asserted]: #11
+[mp #13 #47]: false
+50989c5e2e539fd2d1d21182edd10ff7b62c09eb 26 0
+unsat
+#2 := false
+decl f3 :: Int
+#7 := f3
+#8 := 0::Int
+#9 := (+ f3 0::Int)
+#10 := (= #9 f3)
 #11 := (not #10)
-#12 := (not #11)
-#55 := (iff #12 false)
-#1 := true
-#50 := (not true)
-#53 := (iff #50 false)
-#54 := [rewrite]: #53
-#51 := (iff #12 #50)
-#48 := (iff #11 true)
-#43 := (not false)
-#46 := (iff #43 true)
-#47 := [rewrite]: #46
-#44 := (iff #11 #43)
-#41 := (iff #10 false)
-#33 := -1::Int
-#36 := (= -1::Int 1::Int)
-#39 := (iff #36 false)
-#40 := [rewrite]: #39
-#37 := (iff #10 #36)
-#34 := (= #9 -1::Int)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#32 := [asserted]: #12
-[mp #32 #56]: false
-unsat
-abda142ed88ecbb996b79ee8162fe49b344031b3 40 0
-#2 := false
-#12 := 567::Int
-#10 := 345::Int
-#8 := 123::Int
-#9 := (- 123::Int)
-#11 := (+ #9 345::Int)
-#13 := (< #11 567::Int)
-#14 := (not #13)
-#61 := (iff #14 false)
-#41 := 222::Int
-#46 := (< 222::Int 567::Int)
-#49 := (not #46)
-#59 := (iff #49 false)
-#1 := true
-#54 := (not true)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #49 #54)
-#52 := (iff #46 true)
-#53 := [rewrite]: #52
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#50 := (iff #14 #49)
-#47 := (iff #13 #46)
-#44 := (= #11 222::Int)
-#35 := -123::Int
-#38 := (+ -123::Int 345::Int)
-#42 := (= #38 222::Int)
-#43 := [rewrite]: #42
-#39 := (= #11 #38)
-#36 := (= #9 -123::Int)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#45 := [trans #40 #43]: #44
-#48 := [monotonicity #45]: #47
-#51 := [monotonicity #48]: #50
-#62 := [trans #51 #60]: #61
-#34 := [asserted]: #14
-[mp #34 #62]: false
-unsat
-52ee66296beec0b85b106a54f57287052dcd7f89 30 0
-#2 := false
-#10 := 2345678901::Int
-#8 := 123456789::Int
-#9 := (- 123456789::Int)
-#11 := (< #9 2345678901::Int)
-#12 := (not #11)
-#51 := (iff #12 false)
-#33 := -123456789::Int
-#36 := (< -123456789::Int 2345678901::Int)
-#39 := (not #36)
-#49 := (iff #39 false)
-#1 := true
-#44 := (not true)
-#47 := (iff #44 false)
-#48 := [rewrite]: #47
-#45 := (iff #39 #44)
-#42 := (iff #36 true)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#40 := (iff #12 #39)
-#37 := (iff #11 #36)
-#34 := (= #9 -123456789::Int)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#41 := [monotonicity #38]: #40
-#52 := [trans #41 #50]: #51
-#32 := [asserted]: #12
-[mp #32 #52]: false
-unsat
-cc3c0a2b103dc2bb6601e0a4c48514f8376c297a 26 0
+#30 := (iff #11 false)
+#1 := true
+#25 := (not true)
+#28 := (iff #25 false)
+#29 := [rewrite]: #28
+#26 := (iff #11 #25)
+#23 := (iff #10 true)
+#18 := (= f3 f3)
+#21 := (iff #18 true)
+#22 := [rewrite]: #21
+#19 := (iff #10 #18)
+#17 := [rewrite]: #10
+#20 := [monotonicity #17]: #19
+#24 := [trans #20 #22]: #23
+#27 := [monotonicity #24]: #26
+#31 := [trans #27 #29]: #30
+#13 := [asserted]: #11
+[mp #13 #31]: false
+46aef7ce6988ff7631483393ec6098c7fafc37bd 26 0
+unsat
 #2 := false
 decl f3 :: Int
 #8 := f3
-#9 := 0::Int
-#10 := (+ f3 0::Int)
-#11 := (= #10 f3)
+#7 := 0::Int
+#9 := (+ 0::Int f3)
+#10 := (= #9 f3)
+#11 := (not #10)
+#30 := (iff #11 false)
+#1 := true
+#25 := (not true)
+#28 := (iff #25 false)
+#29 := [rewrite]: #28
+#26 := (iff #11 #25)
+#23 := (iff #10 true)
+#18 := (= f3 f3)
+#21 := (iff #18 true)
+#22 := [rewrite]: #21
+#19 := (iff #10 #18)
+#17 := [rewrite]: #10
+#20 := [monotonicity #17]: #19
+#24 := [trans #20 #22]: #23
+#27 := [monotonicity #24]: #26
+#31 := [trans #27 #29]: #30
+#13 := [asserted]: #11
+[mp #13 #31]: false
+9152c9719df8a2e68b390a97f0a98cb0b7ca2d0c 22 0
+unsat
+#2 := false
+decl f3 :: Int
+#7 := f3
+decl f4 :: Int
+#8 := f4
+#10 := (+ f4 f3)
+#9 := (+ f3 f4)
+#11 := (= #9 #10)
 #12 := (not #11)
-#46 := (iff #12 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
+#26 := (iff #12 false)
+#1 := true
+#21 := (not true)
+#24 := (iff #21 false)
+#25 := [rewrite]: #24
+#22 := (iff #12 #21)
+#19 := (iff #11 true)
+#20 := [rewrite]: #19
+#23 := [monotonicity #20]: #22
+#27 := [trans #23 #25]: #26
+#14 := [asserted]: #12
+[mp #14 #27]: false
+95e4d4805727a56da5d566d8d814d0ecdf083226 36 0
+unsat
+#2 := false
+decl f5 :: Int
+#9 := f5
+decl f4 :: Int
+#8 := f4
+decl f3 :: Int
+#7 := f3
+#12 := (+ f3 f4)
+#13 := (+ #12 f5)
+#10 := (+ f4 f5)
+#11 := (+ f3 #10)
+#14 := (= #11 #13)
+#15 := (not #14)
+#39 := (iff #15 false)
+#1 := true
+#34 := (not true)
+#37 := (iff #34 false)
 #38 := [rewrite]: #37
-#35 := (iff #11 #34)
-#33 := [rewrite]: #11
+#35 := (iff #15 #34)
+#32 := (iff #14 true)
+#21 := (+ f3 f4 f5)
+#26 := (= #21 #21)
+#30 := (iff #26 true)
+#31 := [rewrite]: #30
+#27 := (iff #14 #26)
+#24 := (= #13 #21)
+#25 := [rewrite]: #24
+#22 := (= #11 #21)
+#23 := [rewrite]: #22
+#28 := [monotonicity #23 #25]: #27
+#33 := [trans #28 #31]: #32
 #36 := [monotonicity #33]: #35
 #40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #12
-[mp #32 #47]: false
-unsat
-fd47edbfbac88ee3d94d488f80d6a8ea5bf561a8 26 0
+#17 := [asserted]: #15
+[mp #17 #40]: false
+1425e9f9c7d957418c96ef3737bc95f0ad15e232 44 0
+unsat
+#2 := false
+decl f4 :: Int
+#8 := f4
+#21 := -1::Int
+#22 := (* -1::Int f4)
+decl f3 :: Int
+#7 := f3
+#25 := (= f3 #22)
+#10 := 0::Int
+#9 := (+ f3 f4)
+#11 := (= #9 0::Int)
+#34 := (not #11)
+#35 := (iff #34 #25)
+#68 := (iff #35 false)
+#63 := (iff #34 #11)
+#66 := (iff #63 false)
+#67 := [rewrite]: #66
+#64 := (iff #35 #63)
+#61 := (iff #25 #11)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#69 := [trans #65 #67]: #68
+#12 := (- f4)
+#13 := (= f3 #12)
+#14 := (iff #11 #13)
+#15 := (not #14)
+#38 := (iff #15 #35)
+#28 := (iff #11 #25)
+#31 := (not #28)
+#36 := (iff #31 #35)
+#37 := [rewrite]: #36
+#32 := (iff #15 #31)
+#29 := (iff #14 #28)
+#26 := (iff #13 #25)
+#23 := (= #12 #22)
+#24 := [rewrite]: #23
+#27 := [monotonicity #24]: #26
+#30 := [monotonicity #27]: #29
+#33 := [monotonicity #30]: #32
+#39 := [trans #33 #37]: #38
+#17 := [asserted]: #15
+#40 := [mp #17 #39]: #35
+[mp #40 #69]: false
+3d809dbe33000063b4a57a66bb51f680bedfd6e0 26 0
+unsat
+#2 := false
+#7 := 1::Int
+#8 := (- 1::Int)
+#9 := (= #8 #8)
+#10 := (not #9)
+#32 := (iff #10 false)
+#1 := true
+#27 := (not true)
+#30 := (iff #27 false)
+#31 := [rewrite]: #30
+#28 := (iff #10 #27)
+#25 := (iff #9 true)
+#16 := -1::Int
+#19 := (= -1::Int -1::Int)
+#23 := (iff #19 true)
+#24 := [rewrite]: #23
+#20 := (iff #9 #19)
+#17 := (= #8 -1::Int)
+#18 := [rewrite]: #17
+#21 := [monotonicity #18 #18]: #20
+#26 := [trans #21 #24]: #25
+#29 := [monotonicity #26]: #28
+#33 := [trans #29 #31]: #32
+#12 := [asserted]: #10
+[mp #12 #33]: false
+feed10a69235d8fa170bcc786549b25dc16a103c 26 0
+unsat
+#2 := false
+#7 := 3::Int
+#8 := (- 3::Int)
+#9 := (= #8 #8)
+#10 := (not #9)
+#32 := (iff #10 false)
+#1 := true
+#27 := (not true)
+#30 := (iff #27 false)
+#31 := [rewrite]: #30
+#28 := (iff #10 #27)
+#25 := (iff #9 true)
+#16 := -3::Int
+#19 := (= -3::Int -3::Int)
+#23 := (iff #19 true)
+#24 := [rewrite]: #23
+#20 := (iff #9 #19)
+#17 := (= #8 -3::Int)
+#18 := [rewrite]: #17
+#21 := [monotonicity #18 #18]: #20
+#26 := [trans #21 #24]: #25
+#29 := [monotonicity #26]: #28
+#33 := [trans #29 #31]: #32
+#12 := [asserted]: #10
+[mp #12 #33]: false
+e72ea83a2103fac5da57de85cef39aa4509d9d7f 50 0
+unsat
 #2 := false
 decl f3 :: Int
-#9 := f3
+#7 := f3
+#9 := 0::Int
+#11 := (< 0::Int f3)
+#8 := (- f3)
+#10 := (< #8 0::Int)
+#12 := (iff #10 #11)
+#13 := (not #12)
+#54 := (iff #13 false)
+#1 := true
+#49 := (not true)
+#52 := (iff #49 false)
+#53 := [rewrite]: #52
+#50 := (iff #13 #49)
+#47 := (iff #12 true)
+#32 := (<= f3 0::Int)
+#35 := (not #32)
+#42 := (iff #35 #35)
+#45 := (iff #42 true)
+#46 := [rewrite]: #45
+#43 := (iff #12 #42)
+#40 := (iff #11 #35)
+#41 := [rewrite]: #40
+#38 := (iff #10 #35)
+#19 := -1::Int
+#20 := (* -1::Int f3)
+#26 := (<= 0::Int #20)
+#27 := (not #26)
+#36 := (iff #27 #35)
+#33 := (iff #26 #32)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#30 := (iff #10 #27)
+#23 := (< #20 0::Int)
+#28 := (iff #23 #27)
+#29 := [rewrite]: #28
+#24 := (iff #10 #23)
+#21 := (= #8 #20)
+#22 := [rewrite]: #21
+#25 := [monotonicity #22]: #24
+#31 := [trans #25 #29]: #30
+#39 := [trans #31 #37]: #38
+#44 := [monotonicity #39 #41]: #43
+#48 := [trans #44 #46]: #47
+#51 := [monotonicity #48]: #50
+#55 := [trans #51 #53]: #54
+#15 := [asserted]: #13
+[mp #15 #55]: false
+6091664b0a1373cda23f55c1b3120db85d0b3b95 50 0
+unsat
+#2 := false
+#7 := 0::Int
+decl f3 :: Int
+#8 := f3
+#10 := (- f3)
+#11 := (< #10 0::Int)
+#9 := (< 0::Int f3)
+#12 := (implies #9 #11)
+#13 := (not #12)
+#54 := (iff #13 false)
+#1 := true
+#49 := (not true)
+#52 := (iff #49 false)
+#53 := [rewrite]: #52
+#50 := (iff #13 #49)
+#47 := (iff #12 true)
+#19 := (<= f3 0::Int)
+#20 := (not #19)
+#42 := (implies #20 #20)
+#45 := (iff #42 true)
+#46 := [rewrite]: #45
+#43 := (iff #12 #42)
+#40 := (iff #11 #20)
+#23 := -1::Int
+#24 := (* -1::Int f3)
+#30 := (<= 0::Int #24)
+#31 := (not #30)
+#38 := (iff #31 #20)
+#36 := (iff #30 #19)
+#37 := [rewrite]: #36
+#39 := [monotonicity #37]: #38
+#34 := (iff #11 #31)
+#27 := (< #24 0::Int)
+#32 := (iff #27 #31)
+#33 := [rewrite]: #32
+#28 := (iff #11 #27)
+#25 := (= #10 #24)
+#26 := [rewrite]: #25
+#29 := [monotonicity #26]: #28
+#35 := [trans #29 #33]: #34
+#41 := [trans #35 #39]: #40
+#21 := (iff #9 #20)
+#22 := [rewrite]: #21
+#44 := [monotonicity #22 #41]: #43
+#48 := [trans #44 #46]: #47
+#51 := [monotonicity #48]: #50
+#55 := [trans #51 #53]: #54
+#15 := [asserted]: #13
+[mp #15 #55]: false
+3e653d037824a2320dc7a17d2f1470042381c4df 61 0
+unsat
+#2 := false
 #8 := 0::Int
-#10 := (+ 0::Int f3)
-#11 := (= #10 f3)
-#12 := (not #11)
-#46 := (iff #12 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
+decl f3 :: Int
+#7 := f3
+#41 := (>= f3 0::Int)
+#44 := (not #41)
+#19 := (<= 0::Int f3)
+#52 := (or #19 #44)
+#57 := (not #52)
+#10 := (- f3)
+#11 := (< 0::Int #10)
+#9 := (< f3 0::Int)
+#12 := (implies #9 #11)
+#13 := (not #12)
+#58 := (iff #13 #57)
+#55 := (iff #12 #52)
+#20 := (not #19)
+#49 := (implies #20 #44)
+#53 := (iff #49 #52)
+#54 := [rewrite]: #53
+#50 := (iff #12 #49)
+#47 := (iff #11 #44)
+#28 := -1::Int
+#29 := (* -1::Int f3)
+#35 := (<= #29 0::Int)
+#36 := (not #35)
+#45 := (iff #36 #44)
+#42 := (iff #35 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#39 := (iff #11 #36)
+#32 := (< 0::Int #29)
+#37 := (iff #32 #36)
 #38 := [rewrite]: #37
-#35 := (iff #11 #34)
-#33 := [rewrite]: #11
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #12
-[mp #32 #47]: false
-unsat
-567ac5e5181b99e579edcd5a30f3a17097bdc207 29 0
+#33 := (iff #11 #32)
+#30 := (= #10 #29)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31]: #33
+#40 := [trans #34 #38]: #39
+#48 := [trans #40 #46]: #47
+#21 := (iff #9 #20)
+#25 := (iff #20 #20)
+#23 := (iff #19 #19)
+#24 := [rewrite]: #23
+#26 := [monotonicity #24]: #25
+#22 := [rewrite]: #21
+#27 := [trans #22 #26]: #21
+#51 := [monotonicity #27 #48]: #50
+#56 := [trans #51 #54]: #55
+#59 := [monotonicity #56]: #58
+#15 := [asserted]: #13
+#60 := [mp #15 #59]: #57
+#62 := [not-or-elim #60]: #41
+#84 := (iff #20 #44)
+#82 := (iff #19 #41)
+#83 := [rewrite]: #82
+#85 := [monotonicity #83]: #84
+#61 := [not-or-elim #60]: #20
+#86 := [mp #61 #85]: #44
+[unit-resolution #86 #62]: false
+2b8f6d15a2659a02e850b9785f0f1bc3c34740a1 40 0
+unsat
+#2 := false
+decl f3 :: Int
+#7 := f3
+#8 := 0::Int
+#9 := (- f3 0::Int)
+#10 := (= #9 f3)
+#11 := (not #10)
+#44 := (iff #11 false)
+#1 := true
+#39 := (not true)
+#42 := (iff #39 false)
+#43 := [rewrite]: #42
+#40 := (iff #11 #39)
+#37 := (iff #10 true)
+#32 := (= f3 f3)
+#35 := (iff #32 true)
+#36 := [rewrite]: #35
+#33 := (iff #10 #32)
+#17 := -1::Int
+#18 := (* -1::Int 0::Int)
+#19 := (+ f3 #18)
+#29 := (= #19 f3)
+#24 := (+ f3 0::Int)
+#27 := (= #24 f3)
+#28 := [rewrite]: #27
+#25 := (= #19 #24)
+#22 := (= #18 0::Int)
+#23 := [rewrite]: #22
+#26 := [monotonicity #23]: #25
+#30 := [trans #26 #28]: #29
+#20 := (= #9 #19)
+#21 := [rewrite]: #20
+#31 := [trans #21 #30]: #10
+#34 := [monotonicity #31]: #33
+#38 := [trans #34 #36]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#13 := [asserted]: #11
+[mp #13 #45]: false
+769c85c7c62c5c6e67155574fc1ee91975c07c09 37 0
+unsat
 #2 := false
 decl f3 :: Int
 #8 := f3
-decl f4 :: Int
-#9 := f4
-#11 := (+ f4 f3)
-#10 := (+ f3 f4)
-#12 := (= #10 #11)
-#13 := (not #12)
-#48 := (iff #13 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #13 #43)
-#41 := (iff #12 true)
-#36 := (= #10 #10)
-#39 := (iff #36 true)
+#10 := (- f3)
+#7 := 0::Int
+#9 := (- 0::Int f3)
+#11 := (= #9 #10)
+#12 := (not #11)
+#41 := (iff #12 false)
+#1 := true
+#36 := (not true)
+#39 := (iff #36 false)
 #40 := [rewrite]: #39
 #37 := (iff #12 #36)
-#34 := (= #11 #10)
-#35 := [rewrite]: #34
+#34 := (iff #11 true)
+#18 := -1::Int
+#19 := (* -1::Int f3)
+#29 := (= #19 #19)
+#32 := (iff #29 true)
+#33 := [rewrite]: #32
+#30 := (iff #11 #29)
+#27 := (= #10 #19)
+#28 := [rewrite]: #27
+#25 := (= #9 #19)
+#20 := (+ 0::Int #19)
+#23 := (= #20 #19)
+#24 := [rewrite]: #23
+#21 := (= #9 #20)
+#22 := [rewrite]: #21
+#26 := [trans #22 #24]: #25
+#31 := [monotonicity #26 #28]: #30
+#35 := [trans #31 #33]: #34
 #38 := [monotonicity #35]: #37
 #42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#33 := [asserted]: #13
-[mp #33 #49]: false
-unsat
-2fe26988f5a773923b0b53e62aca5ed502114903 33 0
+#14 := [asserted]: #12
+[mp #14 #42]: false
+179a1947e4f03fe1aa70eea2951bab256e0fd919 61 0
+unsat
+#2 := false
+#11 := 0::Int
+decl f4 :: Int
+#8 := f4
+#24 := -1::Int
+#25 := (* -1::Int f4)
+decl f3 :: Int
+#7 := f3
+#26 := (+ f3 #25)
+#78 := (>= #26 0::Int)
+#32 := (<= 0::Int #26)
+#76 := (iff #32 #78)
+#84 := [rewrite]: #76
+#33 := (not #32)
+#20 := (<= f4 f3)
+#46 := (or #20 #33)
+#51 := (not #46)
+#10 := (- f3 f4)
+#12 := (< #10 0::Int)
+#9 := (< f3 f4)
+#13 := (implies #9 #12)
+#14 := (not #13)
+#52 := (iff #14 #51)
+#49 := (iff #13 #46)
+#21 := (not #20)
+#43 := (implies #21 #33)
+#47 := (iff #43 #46)
+#48 := [rewrite]: #47
+#44 := (iff #13 #43)
+#36 := (iff #12 #33)
+#40 := (iff #33 #33)
+#38 := (iff #32 #32)
+#39 := [rewrite]: #38
+#41 := [monotonicity #39]: #40
+#29 := (< #26 0::Int)
+#34 := (iff #29 #33)
+#35 := [rewrite]: #34
+#30 := (iff #12 #29)
+#27 := (= #10 #26)
+#28 := [rewrite]: #27
+#31 := [monotonicity #28]: #30
+#37 := [trans #31 #35]: #36
+#42 := [trans #37 #41]: #36
+#22 := (iff #9 #21)
+#23 := [rewrite]: #22
+#45 := [monotonicity #23 #42]: #44
+#50 := [trans #45 #48]: #49
+#53 := [monotonicity #50]: #52
+#16 := [asserted]: #14
+#54 := [mp #16 #53]: #51
+#56 := [not-or-elim #54]: #32
+#85 := [mp #56 #84]: #78
+#80 := (not #78)
+#81 := (iff #21 #80)
+#77 := (iff #20 #78)
+#79 := [rewrite]: #77
+#82 := [monotonicity #79]: #81
+#55 := [not-or-elim #54]: #21
+#83 := [mp #55 #82]: #80
+[unit-resolution #83 #85]: false
+e163b714ba9729323f06150e30f725561ec36e35 58 0
+unsat
+#2 := false
+decl f3 :: Int
+#7 := f3
+decl f4 :: Int
+#8 := f4
+#10 := (- f4 f3)
+#11 := (- #10)
+#9 := (- f3 f4)
+#12 := (= #9 #11)
+#13 := (not #12)
+#62 := (iff #13 false)
+#1 := true
+#57 := (not true)
+#60 := (iff #57 false)
+#61 := [rewrite]: #60
+#58 := (iff #13 #57)
+#55 := (iff #12 true)
+#19 := -1::Int
+#20 := (* -1::Int f4)
+#42 := (+ #20 f3)
+#21 := (+ f3 #20)
+#49 := (= #21 #42)
+#53 := (iff #49 true)
+#54 := [rewrite]: #53
+#50 := (iff #12 #49)
+#47 := (= #11 #42)
+#24 := (* -1::Int f3)
+#25 := (+ f4 #24)
+#31 := (* -1::Int #25)
+#45 := (= #31 #42)
+#36 := (* -1::Int #24)
+#37 := (+ #20 #36)
+#43 := (= #37 #42)
+#40 := (= #36 f3)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#38 := (= #31 #37)
+#39 := [rewrite]: #38
+#46 := [trans #39 #44]: #45
+#34 := (= #11 #31)
+#28 := (- #25)
+#32 := (= #28 #31)
+#33 := [rewrite]: #32
+#29 := (= #11 #28)
+#26 := (= #10 #25)
+#27 := [rewrite]: #26
+#30 := [monotonicity #27]: #29
+#35 := [trans #30 #33]: #34
+#48 := [trans #35 #46]: #47
+#22 := (= #9 #21)
+#23 := [rewrite]: #22
+#51 := [monotonicity #23 #48]: #50
+#56 := [trans #51 #54]: #55
+#59 := [monotonicity #56]: #58
+#63 := [trans #59 #61]: #62
+#15 := [asserted]: #13
+[mp #15 #63]: false
+76ebef49c2c39345953ea02ba782064201efe7f8 38 0
+unsat
+#2 := false
+decl f3 :: Int
+#7 := f3
+decl f4 :: Int
+#8 := f4
+#10 := (- f4)
+#11 := (+ #10 f3)
+#9 := (- f3 f4)
+#12 := (= #9 #11)
+#13 := (not #12)
+#42 := (iff #13 false)
+#1 := true
+#37 := (not true)
+#40 := (iff #37 false)
+#41 := [rewrite]: #40
+#38 := (iff #13 #37)
+#35 := (iff #12 true)
+#19 := -1::Int
+#20 := (* -1::Int f4)
+#26 := (+ #20 f3)
+#21 := (+ f3 #20)
+#29 := (= #21 #26)
+#33 := (iff #29 true)
+#34 := [rewrite]: #33
+#30 := (iff #12 #29)
+#27 := (= #11 #26)
+#24 := (= #10 #20)
+#25 := [rewrite]: #24
+#28 := [monotonicity #25]: #27
+#22 := (= #9 #21)
+#23 := [rewrite]: #22
+#31 := [monotonicity #23 #28]: #30
+#36 := [trans #31 #34]: #35
+#39 := [monotonicity #36]: #38
+#43 := [trans #39 #41]: #42
+#15 := [asserted]: #13
+[mp #15 #43]: false
+5d73f38cd523b8ddc4eb2499e422417f533163f7 66 0
+unsat
 #2 := false
 decl f5 :: Int
 #10 := f5
 decl f4 :: Int
-#9 := f4
+#8 := f4
+#12 := (+ f4 f5)
 decl f3 :: Int
-#8 := f3
-#13 := (+ f3 f4)
-#14 := (+ #13 f5)
-#11 := (+ f4 f5)
-#12 := (+ f3 #11)
-#15 := (= #12 #14)
-#16 := (not #15)
-#51 := (iff #16 false)
-#1 := true
-#46 := (not true)
-#49 := (iff #46 false)
-#50 := [rewrite]: #49
-#47 := (iff #16 #46)
-#44 := (iff #15 true)
-#39 := (= #12 #12)
-#42 := (iff #39 true)
+#7 := f3
+#13 := (- f3 #12)
+#9 := (- f3 f4)
+#11 := (- #9 f5)
+#14 := (= #11 #13)
+#15 := (not #14)
+#69 := (iff #15 false)
+#1 := true
+#64 := (not true)
+#67 := (iff #64 false)
+#68 := [rewrite]: #67
+#65 := (iff #15 #64)
+#62 := (iff #14 true)
+#21 := -1::Int
+#29 := (* -1::Int f5)
+#22 := (* -1::Int f4)
+#35 := (+ f3 #22 #29)
+#56 := (= #35 #35)
+#60 := (iff #56 true)
+#61 := [rewrite]: #60
+#57 := (iff #14 #56)
+#54 := (= #13 #35)
+#40 := (* -1::Int #12)
+#41 := (+ f3 #40)
+#52 := (= #41 #35)
+#44 := (+ #22 #29)
+#47 := (+ f3 #44)
+#50 := (= #47 #35)
+#51 := [rewrite]: #50
+#48 := (= #41 #47)
+#45 := (= #40 #44)
+#46 := [rewrite]: #45
+#49 := [monotonicity #46]: #48
+#53 := [trans #49 #51]: #52
+#42 := (= #13 #41)
 #43 := [rewrite]: #42
-#40 := (iff #15 #39)
-#37 := (= #14 #12)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#45 := [trans #41 #43]: #44
-#48 := [monotonicity #45]: #47
-#52 := [trans #48 #50]: #51
-#36 := [asserted]: #16
-[mp #36 #52]: false
-unsat
-aa9232285ab331eb0061966d9cc17b455a15a8b2 45 0
-#2 := false
-decl f4 :: Int
-#9 := f4
-#13 := (- f4)
+#55 := [trans #43 #53]: #54
+#38 := (= #11 #35)
+#23 := (+ f3 #22)
+#30 := (+ #23 #29)
+#36 := (= #30 #35)
+#37 := [rewrite]: #36
+#33 := (= #11 #30)
+#26 := (- #23 f5)
+#31 := (= #26 #30)
+#32 := [rewrite]: #31
+#27 := (= #11 #26)
+#24 := (= #9 #23)
+#25 := [rewrite]: #24
+#28 := [monotonicity #25]: #27
+#34 := [trans #28 #32]: #33
+#39 := [trans #34 #37]: #38
+#58 := [monotonicity #39 #55]: #57
+#63 := [trans #58 #61]: #62
+#66 := [monotonicity #63]: #65
+#70 := [trans #66 #68]: #69
+#17 := [asserted]: #15
+[mp #17 #70]: false
+5f00c1479a6cf5f46157c2337e3fcd3ab961af7a 26 0
+unsat
+#2 := false
+#8 := 0::Int
+decl f3 :: Int
+#7 := f3
+#9 := (* f3 0::Int)
+#10 := (= #9 0::Int)
+#11 := (not #10)
+#30 := (iff #11 false)
+#1 := true
+#25 := (not true)
+#28 := (iff #25 false)
+#29 := [rewrite]: #28
+#26 := (iff #11 #25)
+#23 := (iff #10 true)
+#18 := (= 0::Int 0::Int)
+#21 := (iff #18 true)
+#22 := [rewrite]: #21
+#19 := (iff #10 #18)
+#17 := [rewrite]: #10
+#20 := [monotonicity #17]: #19
+#24 := [trans #20 #22]: #23
+#27 := [monotonicity #24]: #26
+#31 := [trans #27 #29]: #30
+#13 := [asserted]: #11
+[mp #13 #31]: false
+99923a7a287bb7b5f864ee54973e794a9b3c80b0 26 0
+unsat
+#2 := false
+#7 := 0::Int
 decl f3 :: Int
 #8 := f3
-#14 := (= f3 #13)
-#11 := 0::Int
-#10 := (+ f3 f4)
-#12 := (= #10 0::Int)
-#15 := (iff #12 #14)
-#16 := (not #15)
-#65 := (iff #16 false)
-#50 := (not #12)
-#37 := -1::Int
-#38 := (* -1::Int f4)
-#41 := (= f3 #38)
-#51 := (iff #41 #50)
-#63 := (iff #51 false)
-#58 := (iff #12 #50)
-#61 := (iff #58 false)
-#62 := [rewrite]: #61
-#59 := (iff #51 #58)
-#56 := (iff #41 #12)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#54 := (iff #16 #51)
-#44 := (iff #12 #41)
-#47 := (not #44)
-#52 := (iff #47 #51)
-#53 := [rewrite]: #52
-#48 := (iff #16 #47)
-#45 := (iff #15 #44)
-#42 := (iff #14 #41)
-#39 := (= #13 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#49 := [monotonicity #46]: #48
-#55 := [trans #49 #53]: #54
-#66 := [trans #55 #64]: #65
-#36 := [asserted]: #16
-[mp #36 #66]: false
-unsat
-3f272fd1319f78b4692aa5dda96df513e4645a9a 26 0
-#2 := false
-#8 := 1::Int
-#9 := (- 1::Int)
-#10 := (= #9 #9)
+#9 := (* 0::Int f3)
+#10 := (= #9 0::Int)
 #11 := (not #10)
-#47 := (iff #11 false)
-#1 := true
-#42 := (not true)
-#45 := (iff #42 false)
-#46 := [rewrite]: #45
-#43 := (iff #11 #42)
-#40 := (iff #10 true)
-#32 := -1::Int
-#35 := (= -1::Int -1::Int)
-#38 := (iff #35 true)
-#39 := [rewrite]: #38
-#36 := (iff #10 #35)
-#33 := (= #9 -1::Int)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34 #34]: #36
-#41 := [trans #37 #39]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#31 := [asserted]: #11
-[mp #31 #48]: false
-unsat
-e2a7b8949fe3993d5fd2b8dd48b8d65ca6a5debe 26 0
-#2 := false
-#8 := 3::Int
-#9 := (- 3::Int)
-#10 := (= #9 #9)
+#30 := (iff #11 false)
+#1 := true
+#25 := (not true)
+#28 := (iff #25 false)
+#29 := [rewrite]: #28
+#26 := (iff #11 #25)
+#23 := (iff #10 true)
+#18 := (= 0::Int 0::Int)
+#21 := (iff #18 true)
+#22 := [rewrite]: #21
+#19 := (iff #10 #18)
+#17 := [rewrite]: #10
+#20 := [monotonicity #17]: #19
+#24 := [trans #20 #22]: #23
+#27 := [monotonicity #24]: #26
+#31 := [trans #27 #29]: #30
+#13 := [asserted]: #11
+[mp #13 #31]: false
+85a0977cd430199dfbbef0919269ea745bb45aab 26 0
+unsat
+#2 := false
+decl f3 :: Int
+#7 := f3
+#8 := 1::Int
+#9 := (* f3 1::Int)
+#10 := (= #9 f3)
 #11 := (not #10)
-#47 := (iff #11 false)
-#1 := true
-#42 := (not true)
-#45 := (iff #42 false)
-#46 := [rewrite]: #45
-#43 := (iff #11 #42)
-#40 := (iff #10 true)
-#32 := -3::Int
-#35 := (= -3::Int -3::Int)
-#38 := (iff #35 true)
-#39 := [rewrite]: #38
-#36 := (iff #10 #35)
-#33 := (= #9 -3::Int)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34 #34]: #36
-#41 := [trans #37 #39]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#31 := [asserted]: #11
-[mp #31 #48]: false
-unsat
-6f4d8de64d01428967bef903e3d6b1e134e99c36 58 0
+#31 := (iff #11 false)
+#1 := true
+#26 := (not true)
+#29 := (iff #26 false)
+#30 := [rewrite]: #29
+#27 := (iff #11 #26)
+#24 := (iff #10 true)
+#18 := (= f3 f3)
+#22 := (iff #18 true)
+#23 := [rewrite]: #22
+#19 := (iff #10 #18)
+#17 := [rewrite]: #10
+#20 := [monotonicity #17]: #19
+#25 := [trans #20 #23]: #24
+#28 := [monotonicity #25]: #27
+#32 := [trans #28 #30]: #31
+#13 := [asserted]: #11
+[mp #13 #32]: false
+eabe283eca86a8acdb0440d8b7874ab4e2e55097 26 0
+unsat
 #2 := false
 decl f3 :: Int
 #8 := f3
-#10 := 0::Int
-#12 := (< 0::Int f3)
-#9 := (- f3)
-#11 := (< #9 0::Int)
-#13 := (iff #11 #12)
-#14 := (not #13)
-#79 := (iff #14 false)
-#53 := (not #12)
-#35 := -1::Int
-#36 := (* -1::Int f3)
-#39 := (< #36 0::Int)
-#54 := (iff #39 #53)
-#77 := (iff #54 false)
-#59 := (<= f3 0::Int)
-#60 := (not #59)
-#72 := (iff #60 #59)
-#75 := (iff #72 false)
-#76 := [rewrite]: #75
-#73 := (iff #54 #72)
-#70 := (iff #53 #59)
-#65 := (not #60)
-#68 := (iff #65 #59)
-#69 := [rewrite]: #68
-#66 := (iff #53 #65)
-#63 := (iff #12 #60)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#71 := [trans #67 #69]: #70
-#61 := (iff #39 #60)
-#62 := [rewrite]: #61
-#74 := [monotonicity #62 #71]: #73
-#78 := [trans #74 #76]: #77
-#57 := (iff #14 #54)
-#45 := (iff #12 #39)
-#50 := (not #45)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #14 #50)
-#48 := (iff #13 #45)
-#42 := (iff #39 #12)
-#46 := (iff #42 #45)
-#47 := [rewrite]: #46
-#43 := (iff #13 #42)
-#40 := (iff #11 #39)
-#37 := (= #9 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#44 := [monotonicity #41]: #43
-#49 := [trans #44 #47]: #48
-#52 := [monotonicity #49]: #51
-#58 := [trans #52 #56]: #57
-#80 := [trans #58 #78]: #79
-#34 := [asserted]: #14
-[mp #34 #80]: false
-unsat
-564c0a73934063d90154f68605ccc2409e9fa075 61 0
-#2 := false
-#8 := 0::Int
-decl f3 :: Int
-#9 := f3
-#11 := (- f3)
-#12 := (< #11 0::Int)
-#10 := (< 0::Int f3)
-#13 := (implies #10 #12)
-#14 := (not #13)
-#81 := (iff #14 false)
-#35 := -1::Int
-#36 := (* -1::Int f3)
-#39 := (< #36 0::Int)
-#45 := (not #10)
-#46 := (or #45 #39)
-#51 := (not #46)
-#79 := (iff #51 false)
-#1 := true
-#74 := (not true)
-#77 := (iff #74 false)
-#78 := [rewrite]: #77
-#75 := (iff #51 #74)
-#72 := (iff #46 true)
-#54 := (<= f3 0::Int)
-#55 := (not #54)
-#67 := (or #54 #55)
-#70 := (iff #67 true)
-#71 := [rewrite]: #70
-#68 := (iff #46 #67)
-#65 := (iff #39 #55)
-#66 := [rewrite]: #65
-#63 := (iff #45 #54)
-#58 := (not #55)
-#61 := (iff #58 #54)
-#62 := [rewrite]: #61
-#59 := (iff #45 #58)
-#56 := (iff #10 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#69 := [monotonicity #64 #66]: #68
-#73 := [trans #69 #71]: #72
-#76 := [monotonicity #73]: #75
-#80 := [trans #76 #78]: #79
-#52 := (iff #14 #51)
-#49 := (iff #13 #46)
-#42 := (implies #10 #39)
-#47 := (iff #42 #46)
-#48 := [rewrite]: #47
-#43 := (iff #13 #42)
-#40 := (iff #12 #39)
-#37 := (= #11 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#44 := [monotonicity #41]: #43
-#50 := [trans #44 #48]: #49
-#53 := [monotonicity #50]: #52
-#82 := [trans #53 #80]: #81
-#34 := [asserted]: #14
-[mp #34 #82]: false
-unsat
-62e66d279aac101c29ec561e3c1aa729670803a3 61 0
+#7 := 1::Int
+#9 := (* 1::Int f3)
+#10 := (= #9 f3)
+#11 := (not #10)
+#31 := (iff #11 false)
+#1 := true
+#26 := (not true)
+#29 := (iff #26 false)
+#30 := [rewrite]: #29
+#27 := (iff #11 #26)
+#24 := (iff #10 true)
+#18 := (= f3 f3)
+#22 := (iff #18 true)
+#23 := [rewrite]: #22
+#19 := (iff #10 #18)
+#17 := [rewrite]: #10
+#20 := [monotonicity #17]: #19
+#25 := [trans #20 #23]: #24
+#28 := [monotonicity #25]: #27
+#32 := [trans #28 #30]: #31
+#13 := [asserted]: #11
+[mp #13 #32]: false
+524caed43f932116157b3dcc870eedde37cec3e7 40 0
+unsat
 #2 := false
 decl f3 :: Int
-#8 := f3
+#7 := f3
 #11 := (- f3)
-#9 := 0::Int
-#12 := (< 0::Int #11)
-#10 := (< f3 0::Int)
-#13 := (implies #10 #12)
-#14 := (not #13)
-#81 := (iff #14 false)
-#35 := -1::Int
-#36 := (* -1::Int f3)
-#39 := (< 0::Int #36)
-#45 := (not #10)
-#46 := (or #45 #39)
-#51 := (not #46)
-#79 := (iff #51 false)
-#1 := true
-#74 := (not true)
-#77 := (iff #74 false)
-#78 := [rewrite]: #77
-#75 := (iff #51 #74)
-#72 := (iff #46 true)
-#54 := (>= f3 0::Int)
-#55 := (not #54)
-#67 := (or #54 #55)
-#70 := (iff #67 true)
-#71 := [rewrite]: #70
-#68 := (iff #46 #67)
-#65 := (iff #39 #55)
-#66 := [rewrite]: #65
-#63 := (iff #45 #54)
-#58 := (not #55)
-#61 := (iff #58 #54)
-#62 := [rewrite]: #61
-#59 := (iff #45 #58)
-#56 := (iff #10 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#69 := [monotonicity #64 #66]: #68
-#73 := [trans #69 #71]: #72
-#76 := [monotonicity #73]: #75
-#80 := [trans #76 #78]: #79
-#52 := (iff #14 #51)
-#49 := (iff #13 #46)
-#42 := (implies #10 #39)
-#47 := (iff #42 #46)
-#48 := [rewrite]: #47
-#43 := (iff #13 #42)
-#40 := (iff #12 #39)
-#37 := (= #11 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#44 := [monotonicity #41]: #43
-#50 := [trans #44 #48]: #49
-#53 := [monotonicity #50]: #52
-#82 := [trans #53 #80]: #81
-#34 := [asserted]: #14
-[mp #34 #82]: false
-unsat
-36e3e0be50e13bfd349cb4dd2f24507689560060 26 0
-#2 := false
-decl f3 :: Int
-#8 := f3
-#9 := 0::Int
-#10 := (- f3 0::Int)
-#11 := (= #10 f3)
-#12 := (not #11)
-#46 := (iff #12 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #11 #34)
-#33 := [rewrite]: #11
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #12
-[mp #32 #47]: false
-unsat
-967752e39c59bb7230849d17d3298eda01ba97f0 32 0
+#8 := 1::Int
+#9 := (- 1::Int)
+#10 := (* f3 #9)
+#12 := (= #10 #11)
+#13 := (not #12)
+#45 := (iff #13 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #13 #40)
+#38 := (iff #12 true)
+#19 := -1::Int
+#25 := (* -1::Int f3)
+#32 := (= #25 #25)
+#36 := (iff #32 true)
+#37 := [rewrite]: #36
+#33 := (iff #12 #32)
+#30 := (= #11 #25)
+#31 := [rewrite]: #30
+#28 := (= #10 #25)
+#22 := (* f3 -1::Int)
+#26 := (= #22 #25)
+#27 := [rewrite]: #26
+#23 := (= #10 #22)
+#20 := (= #9 -1::Int)
+#21 := [rewrite]: #20
+#24 := [monotonicity #21]: #23
+#29 := [trans #24 #27]: #28
+#34 := [monotonicity #29 #31]: #33
+#39 := [trans #34 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#15 := [asserted]: #13
+[mp #15 #46]: false
+0a10cdb7548396fe24d3599f572cec679b5a5887 35 0
+unsat
 #2 := false
 decl f3 :: Int
 #9 := f3
 #11 := (- f3)
-#8 := 0::Int
-#10 := (- 0::Int f3)
+#7 := 1::Int
+#8 := (- 1::Int)
+#10 := (* #8 f3)
 #12 := (= #10 #11)
 #13 := (not #12)
-#52 := (iff #13 false)
-#1 := true
-#47 := (not true)
-#50 := (iff #47 false)
-#51 := [rewrite]: #50
-#48 := (iff #13 #47)
-#45 := (iff #12 true)
-#34 := -1::Int
-#35 := (* -1::Int f3)
-#40 := (= #35 #35)
-#43 := (iff #40 true)
-#44 := [rewrite]: #43
-#41 := (iff #12 #40)
-#38 := (= #11 #35)
+#40 := (iff #13 false)
+#1 := true
+#35 := (not true)
+#38 := (iff #35 false)
 #39 := [rewrite]: #38
-#36 := (= #10 #35)
-#37 := [rewrite]: #36
-#42 := [monotonicity #37 #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#33 := [asserted]: #13
-[mp #33 #53]: false
-unsat
-d66c19efaea02c4da5b9f725e7d8d3733e147b06 64 0
-#2 := false
-#12 := 0::Int
-decl f4 :: Int
-#9 := f4
-decl f3 :: Int
-#8 := f3
-#11 := (- f3 f4)
-#13 := (< #11 0::Int)
-#10 := (< f3 f4)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#83 := (iff #15 false)
-#36 := -1::Int
-#37 := (* -1::Int f4)
-#38 := (+ f3 #37)
-#41 := (< #38 0::Int)
-#47 := (not #10)
-#48 := (or #47 #41)
-#53 := (not #48)
-#81 := (iff #53 false)
-#1 := true
-#76 := (not true)
-#79 := (iff #76 false)
-#80 := [rewrite]: #79
-#77 := (iff #53 #76)
-#74 := (iff #48 true)
-#57 := (>= #38 0::Int)
-#56 := (not #57)
-#69 := (or #57 #56)
-#72 := (iff #69 true)
-#73 := [rewrite]: #72
-#70 := (iff #48 #69)
-#67 := (iff #41 #56)
-#68 := [rewrite]: #67
-#65 := (iff #47 #57)
-#60 := (not #56)
-#63 := (iff #60 #57)
-#64 := [rewrite]: #63
-#61 := (iff #47 #60)
-#58 := (iff #10 #56)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#66 := [trans #62 #64]: #65
-#71 := [monotonicity #66 #68]: #70
-#75 := [trans #71 #73]: #74
-#78 := [monotonicity #75]: #77
-#82 := [trans #78 #80]: #81
-#54 := (iff #15 #53)
-#51 := (iff #14 #48)
-#44 := (implies #10 #41)
-#49 := (iff #44 #48)
-#50 := [rewrite]: #49
-#45 := (iff #14 #44)
-#42 := (iff #13 #41)
-#39 := (= #11 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#52 := [trans #46 #50]: #51
-#55 := [monotonicity #52]: #54
-#84 := [trans #55 #82]: #83
-#35 := [asserted]: #15
-[mp #35 #84]: false
-unsat
-b4a0e97ac26aaa849b0de7e06daad43acc3105c3 44 0
-#2 := false
-decl f3 :: Int
-#8 := f3
-decl f4 :: Int
-#9 := f4
-#11 := (- f4 f3)
-#12 := (- #11)
-#10 := (- f3 f4)
-#13 := (= #10 #12)
-#14 := (not #13)
-#63 := (iff #14 false)
-#1 := true
-#58 := (not true)
-#61 := (iff #58 false)
-#62 := [rewrite]: #61
-#59 := (iff #14 #58)
-#56 := (iff #13 true)
-#35 := -1::Int
-#36 := (* -1::Int f4)
-#37 := (+ f3 #36)
-#51 := (= #37 #37)
-#54 := (iff #51 true)
-#55 := [rewrite]: #54
-#52 := (iff #13 #51)
-#49 := (= #12 #37)
-#40 := (* -1::Int f3)
-#41 := (+ #40 f4)
-#44 := (- #41)
-#47 := (= #44 #37)
-#48 := [rewrite]: #47
-#45 := (= #12 #44)
-#42 := (= #11 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#38 := (= #10 #37)
-#39 := [rewrite]: #38
-#53 := [monotonicity #39 #50]: #52
-#57 := [trans #53 #55]: #56
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#34 := [asserted]: #14
-[mp #34 #64]: false
-unsat
-f0c92a75694daf72953722c261a7985603bb0bf1 42 0
-#2 := false
-decl f3 :: Int
-#8 := f3
-decl f4 :: Int
-#9 := f4
-#11 := (- f4)
-#12 := (+ #11 f3)
-#10 := (- f3 f4)
-#13 := (= #10 #12)
-#14 := (not #13)
-#61 := (iff #14 false)
-#1 := true
-#56 := (not true)
-#59 := (iff #56 false)
-#60 := [rewrite]: #59
-#57 := (iff #14 #56)
-#54 := (iff #13 true)
-#35 := -1::Int
-#36 := (* -1::Int f4)
-#37 := (+ f3 #36)
-#49 := (= #37 #37)
-#52 := (iff #49 true)
-#53 := [rewrite]: #52
-#50 := (iff #13 #49)
-#47 := (= #12 #37)
-#42 := (+ #36 f3)
-#45 := (= #42 #37)
-#46 := [rewrite]: #45
-#43 := (= #12 #42)
-#40 := (= #11 #36)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#38 := (= #10 #37)
-#39 := [rewrite]: #38
-#51 := [monotonicity #39 #48]: #50
-#55 := [trans #51 #53]: #54
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#34 := [asserted]: #14
-[mp #34 #62]: false
-unsat
-8923322f057ed7cee840582974da3314f48d3c1d 48 0
-#2 := false
-decl f5 :: Int
-#11 := f5
-decl f4 :: Int
-#9 := f4
-#13 := (+ f4 f5)
+#36 := (iff #13 #35)
+#33 := (iff #12 true)
+#19 := -1::Int
+#22 := (* -1::Int f3)
+#27 := (= #22 #22)
+#31 := (iff #27 true)
+#32 := [rewrite]: #31
+#28 := (iff #12 #27)
+#25 := (= #11 #22)
+#26 := [rewrite]: #25
+#23 := (= #10 #22)
+#20 := (= #8 -1::Int)
+#21 := [rewrite]: #20
+#24 := [monotonicity #21]: #23
+#29 := [monotonicity #24 #26]: #28
+#34 := [trans #29 #32]: #33
+#37 := [monotonicity #34]: #36
+#41 := [trans #37 #39]: #40
+#15 := [asserted]: #13
+[mp #15 #41]: false
+d71969b90f628712f4f547371d51686666dd58b0 28 0
+unsat
+#2 := false
+#7 := 3::Int
 decl f3 :: Int
 #8 := f3
-#14 := (- f3 #13)
-#10 := (- f3 f4)
-#12 := (- #10 f5)
-#15 := (= #12 #14)
-#16 := (not #15)
-#66 := (iff #16 false)
-#1 := true
-#61 := (not true)
-#64 := (iff #61 false)
-#65 := [rewrite]: #64
-#62 := (iff #16 #61)
-#59 := (iff #15 true)
-#37 := -1::Int
-#45 := (* -1::Int f5)
-#38 := (* -1::Int f4)
-#46 := (+ #38 #45)
-#47 := (+ f3 #46)
-#54 := (= #47 #47)
-#57 := (iff #54 true)
-#58 := [rewrite]: #57
-#55 := (iff #15 #54)
-#52 := (= #14 #47)
-#53 := [rewrite]: #52
-#50 := (= #12 #47)
-#39 := (+ f3 #38)
-#42 := (- #39 f5)
-#48 := (= #42 #47)
-#49 := [rewrite]: #48
-#43 := (= #12 #42)
-#40 := (= #10 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#51 := [trans #44 #49]: #50
-#56 := [monotonicity #51 #53]: #55
-#60 := [trans #56 #58]: #59
-#63 := [monotonicity #60]: #62
-#67 := [trans #63 #65]: #66
-#36 := [asserted]: #16
-[mp #36 #67]: false
-unsat
-1d827628bfc865305d062976dd88c9223e790cae 26 0
-#2 := false
-#9 := 0::Int
-decl f3 :: Int
-#8 := f3
-#10 := (* f3 0::Int)
-#11 := (= #10 0::Int)
+#10 := (* f3 3::Int)
+#9 := (* 3::Int f3)
+#11 := (= #9 #10)
 #12 := (not #11)
-#46 := (iff #12 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 true)
-#34 := (= 0::Int 0::Int)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #11 #34)
-#33 := [rewrite]: #11
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #12
-[mp #32 #47]: false
-unsat
-268dc80516cad8e0537058bf237f1fac47b44dd9 26 0
-#2 := false
+#33 := (iff #12 false)
+#1 := true
+#28 := (not true)
+#31 := (iff #28 false)
+#32 := [rewrite]: #31
+#29 := (iff #12 #28)
+#26 := (iff #11 true)
+#20 := (= #9 #9)
+#24 := (iff #20 true)
+#25 := [rewrite]: #24
+#21 := (iff #11 #20)
+#18 := (= #10 #9)
+#19 := [rewrite]: #18
+#22 := [monotonicity #19]: #21
+#27 := [trans #22 #25]: #26
+#30 := [monotonicity #27]: #29
+#34 := [trans #30 #32]: #33
+#14 := [asserted]: #12
+[mp #14 #34]: false
+bf2fd8bbd9bf762047f17f623f8a7b706117dda0 254 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#15 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#13 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#14 := (f4 f5 #13)
+#16 := (f3 #14 #15)
+#682 := (pattern #16)
 #8 := 0::Int
-decl f3 :: Int
-#9 := f3
-#10 := (* 0::Int f3)
+#78 := -1::Int
+#82 := (* -1::Int #15)
+#79 := (* -1::Int #13)
+#85 := (div #79 #82)
+#241 := (* -1::Int #85)
+#242 := (+ #16 #241)
+#243 := (= #242 0::Int)
+#26 := (div #13 #15)
+#238 := (* -1::Int #26)
+#239 := (+ #16 #238)
+#240 := (= #239 0::Int)
+#56 := (<= #15 0::Int)
+#148 := (>= #13 0::Int)
+#201 := (or #148 #56)
+#202 := (not #201)
+#52 := (<= #13 0::Int)
+#197 := (or #52 #56)
+#198 := (not #197)
+#205 := (or #198 #202)
+#244 := (if #205 #240 #243)
+#237 := (= #16 0::Int)
+#18 := (= #15 0::Int)
+#17 := (= #13 0::Int)
+#19 := (or #17 #18)
+#245 := (if #19 #237 #244)
+#683 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #682) #245)
+#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
+#686 := (iff #248 #683)
+#684 := (iff #245 #245)
+#685 := [refl]: #684
+#687 := [quant-intro #685]: #686
+#208 := (if #205 #26 #85)
+#211 := (if #19 0::Int #208)
+#214 := (= #16 #211)
+#217 := (forall (vars (?v0 Int) (?v1 Int)) #214)
+#249 := (iff #217 #248)
+#246 := (iff #214 #245)
+#247 := [rewrite]: #246
+#250 := [quant-intro #247]: #249
+#57 := (not #56)
+#151 := (not #148)
+#154 := (and #151 #57)
+#53 := (not #52)
+#60 := (and #53 #57)
+#157 := (or #60 #154)
+#160 := (if #157 #26 #85)
+#163 := (if #19 0::Int #160)
+#166 := (= #16 #163)
+#169 := (forall (vars (?v0 Int) (?v1 Int)) #166)
+#218 := (iff #169 #217)
+#215 := (iff #166 #214)
+#212 := (= #163 #211)
+#209 := (= #160 #208)
+#206 := (iff #157 #205)
+#203 := (iff #154 #202)
+#204 := [rewrite]: #203
+#199 := (iff #60 #198)
+#200 := [rewrite]: #199
+#207 := [monotonicity #200 #204]: #206
+#210 := [monotonicity #207]: #209
+#213 := [monotonicity #210]: #212
+#216 := [monotonicity #213]: #215
+#219 := [quant-intro #216]: #218
+#191 := (~ #169 #169)
+#193 := (~ #166 #166)
+#194 := [refl]: #193
+#192 := [nnf-pos #194]: #191
+#63 := (<= 0::Int #13)
+#64 := (not #63)
+#72 := (and #64 #57)
+#75 := (or #60 #72)
+#88 := (if #75 #26 #85)
+#91 := (if #19 0::Int #88)
+#94 := (= #16 #91)
+#97 := (forall (vars (?v0 Int) (?v1 Int)) #94)
+#170 := (iff #97 #169)
+#167 := (iff #94 #166)
+#164 := (= #91 #163)
+#161 := (= #88 #160)
+#158 := (iff #75 #157)
+#155 := (iff #72 #154)
+#152 := (iff #64 #151)
+#149 := (iff #63 #148)
+#150 := [rewrite]: #149
+#153 := [monotonicity #150]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [monotonicity #162]: #164
+#168 := [monotonicity #165]: #167
+#171 := [quant-intro #168]: #170
+#28 := (- #15)
+#27 := (- #13)
+#29 := (div #27 #28)
+#21 := (< 0::Int #15)
+#23 := (< #13 0::Int)
+#24 := (and #23 #21)
+#20 := (< 0::Int #13)
+#22 := (and #20 #21)
+#25 := (or #22 #24)
+#30 := (if #25 #26 #29)
+#31 := (if #19 0::Int #30)
+#32 := (= #16 #31)
+#33 := (forall (vars (?v0 Int) (?v1 Int)) #32)
+#98 := (iff #33 #97)
+#95 := (iff #32 #94)
+#92 := (= #31 #91)
+#89 := (= #30 #88)
+#86 := (= #29 #85)
+#83 := (= #28 #82)
+#84 := [rewrite]: #83
+#80 := (= #27 #79)
+#81 := [rewrite]: #80
+#87 := [monotonicity #81 #84]: #86
+#76 := (iff #25 #75)
+#73 := (iff #24 #72)
+#58 := (iff #21 #57)
+#59 := [rewrite]: #58
+#65 := (iff #23 #64)
+#69 := (iff #64 #64)
+#67 := (iff #63 #63)
+#68 := [rewrite]: #67
+#70 := [monotonicity #68]: #69
+#66 := [rewrite]: #65
+#71 := [trans #66 #70]: #65
+#74 := [monotonicity #71 #59]: #73
+#61 := (iff #22 #60)
+#54 := (iff #20 #53)
+#55 := [rewrite]: #54
+#62 := [monotonicity #55 #59]: #61
+#77 := [monotonicity #62 #74]: #76
+#90 := [monotonicity #77 #87]: #89
+#93 := [monotonicity #90]: #92
+#96 := [monotonicity #93]: #95
+#99 := [quant-intro #96]: #98
+#47 := [asserted]: #33
+#100 := [mp #47 #99]: #97
+#172 := [mp #100 #171]: #169
+#189 := [mp~ #172 #192]: #169
+#220 := [mp #189 #219]: #217
+#251 := [mp #220 #250]: #248
+#688 := [mp #251 #687]: #683
+#9 := (f4 f5 0::Int)
+#10 := (f3 #9 0::Int)
 #11 := (= #10 0::Int)
 #12 := (not #11)
-#46 := (iff #12 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 true)
-#34 := (= 0::Int 0::Int)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #11 #34)
-#33 := [rewrite]: #11
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #12
-[mp #32 #47]: false
-unsat
-d2498e6f1e4e863ac89298e0d00130df98aa8bf9 26 0
-#2 := false
-decl f3 :: Int
-#8 := f3
-#9 := 1::Int
-#10 := (* f3 1::Int)
-#11 := (= #10 f3)
-#12 := (not #11)
-#46 := (iff #12 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #11 #34)
-#33 := [rewrite]: #11
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #12
-[mp #32 #47]: false
-unsat
-d26161837b1f05cfdb35001c90ead1460ca18bec 26 0
-#2 := false
-decl f3 :: Int
-#9 := f3
-#8 := 1::Int
-#10 := (* 1::Int f3)
-#11 := (= #10 f3)
-#12 := (not #11)
-#46 := (iff #12 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #11 #34)
-#33 := [rewrite]: #11
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #12
-[mp #32 #47]: false
-unsat
-855f0121ef7db6c69742bc5a6c6901549956abdf 40 0
-#2 := false
-decl f3 :: Int
-#8 := f3
-#12 := (- f3)
-#9 := 1::Int
-#10 := (- 1::Int)
-#11 := (* f3 #10)
-#13 := (= #11 #12)
-#14 := (not #13)
-#60 := (iff #14 false)
-#1 := true
-#55 := (not true)
-#58 := (iff #55 false)
-#59 := [rewrite]: #58
-#56 := (iff #14 #55)
-#53 := (iff #13 true)
-#35 := -1::Int
-#41 := (* -1::Int f3)
-#48 := (= #41 #41)
-#51 := (iff #48 true)
-#52 := [rewrite]: #51
-#49 := (iff #13 #48)
-#46 := (= #12 #41)
-#47 := [rewrite]: #46
-#44 := (= #11 #41)
-#38 := (* f3 -1::Int)
-#42 := (= #38 #41)
-#43 := [rewrite]: #42
-#39 := (= #11 #38)
-#36 := (= #10 -1::Int)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#45 := [trans #40 #43]: #44
-#50 := [monotonicity #45 #47]: #49
-#54 := [trans #50 #52]: #53
-#57 := [monotonicity #54]: #56
-#61 := [trans #57 #59]: #60
-#34 := [asserted]: #14
-[mp #34 #61]: false
-unsat
-5d21e0de4aaaaeca789bd4695bdd117eea163e38 35 0
-#2 := false
-decl f3 :: Int
-#10 := f3
-#12 := (- f3)
-#8 := 1::Int
-#9 := (- 1::Int)
-#11 := (* #9 f3)
-#13 := (= #11 #12)
-#14 := (not #13)
-#55 := (iff #14 false)
-#1 := true
-#50 := (not true)
-#53 := (iff #50 false)
-#54 := [rewrite]: #53
-#51 := (iff #14 #50)
-#48 := (iff #13 true)
-#35 := -1::Int
-#38 := (* -1::Int f3)
-#43 := (= #38 #38)
-#46 := (iff #43 true)
-#47 := [rewrite]: #46
-#44 := (iff #13 #43)
-#41 := (= #12 #38)
-#42 := [rewrite]: #41
-#39 := (= #11 #38)
-#36 := (= #9 -1::Int)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#45 := [monotonicity #40 #42]: #44
-#49 := [trans #45 #47]: #48
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#34 := [asserted]: #14
-[mp #34 #56]: false
-unsat
-9d12a5c7c6846be4a5b4be5e467c3f4cb34e4d39 28 0
-#2 := false
-#8 := 3::Int
-decl f3 :: Int
-#9 := f3
-#11 := (* f3 3::Int)
-#10 := (* 3::Int f3)
-#12 := (= #10 #11)
-#13 := (not #12)
-#48 := (iff #13 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #13 #43)
-#41 := (iff #12 true)
-#36 := (= #10 #10)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #12 #36)
-#34 := (= #11 #10)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#33 := [asserted]: #13
-[mp #33 #49]: false
-unsat
-84f32aa4eeda327e1332824fe194fc79ffa88b5a 259 0
+#46 := [asserted]: #12
+#641 := (not #683)
+#636 := (or #641 #11)
+#333 := (* -1::Int 0::Int)
+#463 := (div #333 #333)
+#670 := (* -1::Int #463)
+#344 := (+ #10 #670)
+#345 := (= #344 0::Int)
+#360 := (div 0::Int 0::Int)
+#339 := (* -1::Int #360)
+#674 := (+ #10 #339)
+#676 := (= #674 0::Int)
+#354 := (<= 0::Int 0::Int)
+#357 := (>= 0::Int 0::Int)
+#358 := (or #357 #354)
+#359 := (not #358)
+#355 := (or #354 #354)
+#346 := (not #355)
+#356 := (or #346 #359)
+#677 := (if #356 #676 #345)
+#268 := (= 0::Int 0::Int)
+#353 := (or #268 #268)
+#678 := (if #353 #11 #677)
+#642 := (or #641 #678)
+#484 := (iff #642 #636)
+#627 := (iff #636 #636)
+#628 := [rewrite]: #627
+#635 := (iff #678 #11)
+#1 := true
+#648 := (if true #11 #676)
+#639 := (iff #648 #11)
+#634 := [rewrite]: #639
+#637 := (iff #678 #648)
+#647 := (iff #677 #676)
+#367 := (if false #676 #676)
+#361 := (iff #367 #676)
+#643 := [rewrite]: #361
+#645 := (iff #677 #367)
+#365 := (iff #345 #676)
+#654 := (= #344 #674)
+#653 := (= #670 #339)
+#375 := (= #463 #360)
+#652 := (= #333 0::Int)
+#374 := [rewrite]: #652
+#649 := [monotonicity #374 #374]: #375
+#650 := [monotonicity #649]: #653
+#364 := [monotonicity #650]: #654
+#366 := [monotonicity #364]: #365
+#274 := (iff #356 false)
+#656 := (or false false)
+#380 := (iff #656 false)
+#381 := [rewrite]: #380
+#378 := (iff #356 #656)
+#669 := (iff #359 false)
+#323 := (not true)
+#661 := (iff #323 false)
+#662 := [rewrite]: #661
+#668 := (iff #359 #323)
+#307 := (iff #358 true)
+#675 := (or true true)
+#331 := (iff #675 true)
+#336 := [rewrite]: #331
+#665 := (iff #358 #675)
+#673 := (iff #354 true)
+#316 := [rewrite]: #673
+#664 := (iff #357 true)
+#302 := [rewrite]: #664
+#667 := [monotonicity #302 #316]: #665
+#308 := [trans #667 #336]: #307
+#666 := [monotonicity #308]: #668
+#655 := [trans #666 #662]: #669
+#663 := (iff #346 false)
+#659 := (iff #346 #323)
+#321 := (iff #355 true)
+#657 := (iff #355 #675)
+#320 := [monotonicity #316 #316]: #657
+#322 := [trans #320 #336]: #321
+#660 := [monotonicity #322]: #659
+#658 := [trans #660 #662]: #663
+#379 := [monotonicity #658 #655]: #378
+#651 := [trans #379 #381]: #274
+#646 := [monotonicity #651 #366]: #645
+#644 := [trans #646 #643]: #647
+#672 := (iff #353 true)
+#681 := (iff #353 #675)
+#679 := (iff #268 true)
+#680 := [rewrite]: #679
+#671 := [monotonicity #680 #680]: #681
+#332 := [trans #671 #336]: #672
+#638 := [monotonicity #332 #644]: #637
+#640 := [trans #638 #634]: #635
+#485 := [monotonicity #640]: #484
+#629 := [trans #485 #628]: #484
+#483 := [quant-inst #8 #8]: #642
+#630 := [mp #483 #629]: #636
+[unit-resolution #630 #46 #688]: false
+d3465e8250b8cbddcfc31648b91d12f4e7d1b403 267 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #16 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #14 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #15 := (f4 f5 #14)
 #17 := (f3 #15 #16)
-#754 := (pattern #17)
-#9 := 0::Int
-#92 := -1::Int
-#96 := (* -1::Int #16)
-#93 := (* -1::Int #14)
-#99 := (div #93 #96)
-#256 := (* -1::Int #99)
-#257 := (+ #17 #256)
-#258 := (= #257 0::Int)
+#683 := (pattern #17)
+#10 := 0::Int
+#79 := -1::Int
+#83 := (* -1::Int #16)
+#80 := (* -1::Int #14)
+#86 := (div #80 #83)
+#242 := (* -1::Int #86)
+#243 := (+ #17 #242)
+#244 := (= #243 0::Int)
 #27 := (div #14 #16)
-#253 := (* -1::Int #27)
-#254 := (+ #17 #253)
-#255 := (= #254 0::Int)
-#131 := (>= #14 0::Int)
-#124 := (<= #16 0::Int)
-#216 := (or #124 #131)
-#217 := (not #216)
-#120 := (<= #14 0::Int)
-#214 := (or #120 #124)
-#215 := (not #214)
-#220 := (or #215 #217)
-#259 := (ite #220 #255 #258)
-#252 := (= #17 0::Int)
+#239 := (* -1::Int #27)
+#240 := (+ #17 #239)
+#241 := (= #240 0::Int)
+#57 := (<= #16 0::Int)
+#149 := (>= #14 0::Int)
+#202 := (or #149 #57)
+#203 := (not #202)
+#53 := (<= #14 0::Int)
+#198 := (or #53 #57)
+#199 := (not #198)
+#206 := (or #199 #203)
+#245 := (if #206 #241 #244)
+#238 := (= #17 0::Int)
 #19 := (= #16 0::Int)
 #18 := (= #14 0::Int)
 #20 := (or #18 #19)
-#260 := (ite #20 #252 #259)
-#755 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #754) #260)
-#263 := (forall (vars (?v0 Int) (?v1 Int)) #260)
-#758 := (iff #263 #755)
-#756 := (iff #260 #260)
-#757 := [refl]: #756
-#759 := [quant-intro #757]: #758
-#223 := (ite #220 #27 #99)
-#226 := (ite #20 0::Int #223)
-#229 := (= #17 #226)
-#232 := (forall (vars (?v0 Int) (?v1 Int)) #229)
-#264 := (iff #232 #263)
-#261 := (iff #229 #260)
-#262 := [rewrite]: #261
-#265 := [quant-intro #262]: #264
-#132 := (not #131)
-#125 := (not #124)
-#135 := (and #125 #132)
-#121 := (not #120)
-#128 := (and #121 #125)
-#138 := (or #128 #135)
-#141 := (ite #138 #27 #99)
-#144 := (ite #20 0::Int #141)
-#147 := (= #17 #144)
-#150 := (forall (vars (?v0 Int) (?v1 Int)) #147)
-#233 := (iff #150 #232)
-#230 := (iff #147 #229)
-#227 := (= #144 #226)
-#224 := (= #141 #223)
-#221 := (iff #138 #220)
-#218 := (iff #135 #217)
-#219 := [rewrite]: #218
-#208 := (iff #128 #215)
-#209 := [rewrite]: #208
-#222 := [monotonicity #209 #219]: #221
-#225 := [monotonicity #222]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [quant-intro #231]: #233
-#212 := (~ #150 #150)
-#210 := (~ #147 #147)
-#211 := [refl]: #210
-#213 := [nnf-pos #211]: #212
+#246 := (if #20 #238 #245)
+#684 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #683) #246)
+#249 := (forall (vars (?v0 Int) (?v1 Int)) #246)
+#687 := (iff #249 #684)
+#685 := (iff #246 #246)
+#686 := [refl]: #685
+#688 := [quant-intro #686]: #687
+#209 := (if #206 #27 #86)
+#212 := (if #20 0::Int #209)
+#215 := (= #17 #212)
+#218 := (forall (vars (?v0 Int) (?v1 Int)) #215)
+#250 := (iff #218 #249)
+#247 := (iff #215 #246)
+#248 := [rewrite]: #247
+#251 := [quant-intro #248]: #250
+#58 := (not #57)
+#152 := (not #149)
+#155 := (and #152 #58)
+#54 := (not #53)
+#61 := (and #54 #58)
+#158 := (or #61 #155)
+#161 := (if #158 #27 #86)
+#164 := (if #20 0::Int #161)
+#167 := (= #17 #164)
+#170 := (forall (vars (?v0 Int) (?v1 Int)) #167)
+#219 := (iff #170 #218)
+#216 := (iff #167 #215)
+#213 := (= #164 #212)
+#210 := (= #161 #209)
+#207 := (iff #158 #206)
+#204 := (iff #155 #203)
+#205 := [rewrite]: #204
+#200 := (iff #61 #199)
+#201 := [rewrite]: #200
+#208 := [monotonicity #201 #205]: #207
+#211 := [monotonicity #208]: #210
+#214 := [monotonicity #211]: #213
+#217 := [monotonicity #214]: #216
+#220 := [quant-intro #217]: #219
+#192 := (~ #170 #170)
+#194 := (~ #167 #167)
+#195 := [refl]: #194
+#193 := [nnf-pos #195]: #192
+#64 := (<= 0::Int #14)
+#65 := (not #64)
+#73 := (and #65 #58)
+#76 := (or #61 #73)
+#89 := (if #76 #27 #86)
+#92 := (if #20 0::Int #89)
+#95 := (= #17 #92)
+#98 := (forall (vars (?v0 Int) (?v1 Int)) #95)
+#171 := (iff #98 #170)
+#168 := (iff #95 #167)
+#165 := (= #92 #164)
+#162 := (= #89 #161)
+#159 := (iff #76 #158)
+#156 := (iff #73 #155)
+#153 := (iff #65 #152)
+#150 := (iff #64 #149)
+#151 := [rewrite]: #150
+#154 := [monotonicity #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [monotonicity #163]: #165
+#169 := [monotonicity #166]: #168
+#172 := [quant-intro #169]: #171
 #29 := (- #16)
 #28 := (- #14)
 #30 := (div #28 #29)
@@ -27234,827 +26353,1218 @@
 #21 := (< 0::Int #14)
 #23 := (and #21 #22)
 #26 := (or #23 #25)
-#31 := (ite #26 #27 #30)
-#32 := (ite #20 0::Int #31)
+#31 := (if #26 #27 #30)
+#32 := (if #20 0::Int #31)
 #33 := (= #17 #32)
 #34 := (forall (vars (?v0 Int) (?v1 Int)) #33)
-#153 := (iff #34 #150)
-#86 := (and #22 #24)
-#89 := (or #23 #86)
-#102 := (ite #89 #27 #99)
-#80 := (= 0::Int #16)
-#77 := (= 0::Int #14)
-#83 := (or #77 #80)
-#105 := (ite #83 0::Int #102)
-#108 := (= #17 #105)
-#111 := (forall (vars (?v0 Int) (?v1 Int)) #108)
-#151 := (iff #111 #150)
-#148 := (iff #108 #147)
-#145 := (= #105 #144)
-#142 := (= #102 #141)
-#139 := (iff #89 #138)
-#136 := (iff #86 #135)
-#133 := (iff #24 #132)
-#134 := [rewrite]: #133
-#126 := (iff #22 #125)
-#127 := [rewrite]: #126
-#137 := [monotonicity #127 #134]: #136
-#129 := (iff #23 #128)
-#122 := (iff #21 #121)
-#123 := [rewrite]: #122
-#130 := [monotonicity #123 #127]: #129
-#140 := [monotonicity #130 #137]: #139
-#143 := [monotonicity #140]: #142
-#118 := (iff #83 #20)
-#116 := (iff #80 #19)
-#117 := [rewrite]: #116
-#114 := (iff #77 #18)
-#115 := [rewrite]: #114
-#119 := [monotonicity #115 #117]: #118
-#146 := [monotonicity #119 #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [quant-intro #149]: #151
-#112 := (iff #34 #111)
-#109 := (iff #33 #108)
-#106 := (= #32 #105)
-#103 := (= #31 #102)
-#100 := (= #30 #99)
-#97 := (= #29 #96)
-#98 := [rewrite]: #97
-#94 := (= #28 #93)
-#95 := [rewrite]: #94
-#101 := [monotonicity #95 #98]: #100
-#90 := (iff #26 #89)
-#87 := (iff #25 #86)
-#88 := [rewrite]: #87
-#91 := [monotonicity #88]: #90
-#104 := [monotonicity #91 #101]: #103
-#84 := (iff #20 #83)
-#81 := (iff #19 #80)
+#99 := (iff #34 #98)
+#96 := (iff #33 #95)
+#93 := (= #32 #92)
+#90 := (= #31 #89)
+#87 := (= #30 #86)
+#84 := (= #29 #83)
+#85 := [rewrite]: #84
+#81 := (= #28 #80)
 #82 := [rewrite]: #81
-#78 := (iff #18 #77)
-#79 := [rewrite]: #78
-#85 := [monotonicity #79 #82]: #84
-#107 := [monotonicity #85 #104]: #106
-#110 := [monotonicity #107]: #109
-#113 := [quant-intro #110]: #112
-#154 := [trans #113 #152]: #153
-#76 := [asserted]: #34
-#155 := [mp #76 #154]: #150
-#204 := [mp~ #155 #213]: #150
-#235 := [mp #204 #234]: #232
-#266 := [mp #235 #265]: #263
-#760 := [mp #266 #759]: #755
-#10 := (f4 f5 0::Int)
-#11 := (f3 #10 0::Int)
+#88 := [monotonicity #82 #85]: #87
+#77 := (iff #26 #76)
+#74 := (iff #25 #73)
+#59 := (iff #22 #58)
+#60 := [rewrite]: #59
+#66 := (iff #24 #65)
+#70 := (iff #65 #65)
+#68 := (iff #64 #64)
+#69 := [rewrite]: #68
+#71 := [monotonicity #69]: #70
+#67 := [rewrite]: #66
+#72 := [trans #67 #71]: #66
+#75 := [monotonicity #72 #60]: #74
+#62 := (iff #23 #61)
+#55 := (iff #21 #54)
+#56 := [rewrite]: #55
+#63 := [monotonicity #56 #60]: #62
+#78 := [monotonicity #63 #75]: #77
+#91 := [monotonicity #78 #88]: #90
+#94 := [monotonicity #91]: #93
+#97 := [monotonicity #94]: #96
+#100 := [quant-intro #97]: #99
+#48 := [asserted]: #34
+#101 := [mp #48 #100]: #98
+#173 := [mp #101 #172]: #170
+#190 := [mp~ #173 #193]: #170
+#221 := [mp #190 #220]: #218
+#252 := [mp #221 #251]: #249
+#689 := [mp #252 #688]: #684
+decl f6 :: Int
+#8 := f6
+#9 := (f4 f5 f6)
+#11 := (f3 #9 0::Int)
 #12 := (= #11 0::Int)
 #13 := (not #12)
-#65 := [asserted]: #13
-#712 := (not #755)
-#713 := (or #712 #12)
-#340 := (* -1::Int 0::Int)
-#425 := (div #340 #340)
-#426 := (* -1::Int #425)
-#427 := (+ #11 #426)
-#418 := (= #427 0::Int)
-#429 := (div 0::Int 0::Int)
-#430 := (* -1::Int #429)
-#358 := (+ #11 #430)
-#431 := (= #358 0::Int)
-#428 := (>= 0::Int 0::Int)
-#432 := (<= 0::Int 0::Int)
-#411 := (or #432 #428)
-#746 := (not #411)
-#748 := (or #432 #432)
-#405 := (not #748)
-#535 := (or #405 #746)
-#742 := (ite #535 #431 #418)
-#416 := (= 0::Int 0::Int)
-#417 := (or #416 #416)
-#749 := (ite #417 #12 #742)
-#708 := (or #712 #749)
-#555 := (iff #708 #713)
-#557 := (iff #713 #713)
-#699 := [rewrite]: #557
-#706 := (iff #749 #12)
-#1 := true
-#716 := (ite true #12 #431)
-#710 := (iff #716 #12)
-#711 := [rewrite]: #710
-#720 := (iff #749 #716)
-#715 := (iff #742 #431)
-#438 := (ite false #431 #431)
-#718 := (iff #438 #431)
-#433 := [rewrite]: #718
-#439 := (iff #742 #438)
-#436 := (iff #418 #431)
-#722 := (= #427 #358)
-#721 := (= #426 #430)
-#446 := (= #425 #429)
-#723 := (= #340 0::Int)
-#724 := [rewrite]: #723
-#447 := [monotonicity #724 #724]: #446
-#725 := [monotonicity #447]: #721
-#726 := [monotonicity #725]: #722
-#437 := [monotonicity #726]: #436
-#453 := (iff #535 false)
-#727 := (or false false)
-#451 := (iff #727 false)
-#452 := [rewrite]: #451
-#728 := (iff #535 #727)
-#738 := (iff #746 false)
-#394 := (not true)
-#732 := (iff #394 false)
-#733 := [rewrite]: #732
-#380 := (iff #746 #394)
-#739 := (iff #411 true)
-#752 := (or true true)
-#743 := (iff #752 true)
-#403 := [rewrite]: #743
-#374 := (iff #411 #752)
-#730 := (iff #428 true)
-#736 := [rewrite]: #730
-#404 := (iff #432 true)
-#745 := [rewrite]: #404
-#737 := [monotonicity #745 #736]: #374
-#379 := [trans #737 #403]: #739
-#740 := [monotonicity #379]: #380
-#741 := [trans #740 #733]: #738
-#734 := (iff #405 false)
-#395 := (iff #405 #394)
-#392 := (iff #748 true)
-#388 := (iff #748 #752)
-#729 := [monotonicity #745 #745]: #388
-#393 := [trans #729 #403]: #392
-#731 := [monotonicity #393]: #395
-#735 := [trans #731 #733]: #734
-#450 := [monotonicity #735 #741]: #728
-#346 := [trans #450 #452]: #453
-#717 := [monotonicity #346 #437]: #439
-#719 := [trans #717 #433]: #715
-#408 := (iff #417 true)
-#747 := (iff #417 #752)
-#750 := (iff #416 true)
-#751 := [rewrite]: #750
-#753 := [monotonicity #751 #751]: #747
-#744 := [trans #753 #403]: #408
-#709 := [monotonicity #744 #719]: #720
-#707 := [trans #709 #711]: #706
-#556 := [monotonicity #707]: #555
-#700 := [trans #556 #699]: #555
-#714 := [quant-inst #9 #9]: #708
-#701 := [mp #714 #700]: #713
-[unit-resolution #701 #65 #760]: false
-unsat
-9fbbb1a5156a787e9413d37350d9f3d76a725d67 272 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#16 := (f4 f5 #15)
-#18 := (f3 #16 #17)
-#755 := (pattern #18)
-#11 := 0::Int
-#93 := -1::Int
-#97 := (* -1::Int #17)
-#94 := (* -1::Int #15)
-#100 := (div #94 #97)
-#257 := (* -1::Int #100)
-#258 := (+ #18 #257)
-#259 := (= #258 0::Int)
-#28 := (div #15 #17)
-#254 := (* -1::Int #28)
-#255 := (+ #18 #254)
-#256 := (= #255 0::Int)
-#132 := (>= #15 0::Int)
-#125 := (<= #17 0::Int)
-#217 := (or #125 #132)
-#218 := (not #217)
-#121 := (<= #15 0::Int)
-#215 := (or #121 #125)
-#216 := (not #215)
-#221 := (or #216 #218)
-#260 := (ite #221 #256 #259)
-#253 := (= #18 0::Int)
-#20 := (= #17 0::Int)
-#19 := (= #15 0::Int)
-#21 := (or #19 #20)
-#261 := (ite #21 #253 #260)
-#756 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #755) #261)
-#264 := (forall (vars (?v0 Int) (?v1 Int)) #261)
-#759 := (iff #264 #756)
-#757 := (iff #261 #261)
-#758 := [refl]: #757
-#760 := [quant-intro #758]: #759
-#224 := (ite #221 #28 #100)
-#227 := (ite #21 0::Int #224)
-#230 := (= #18 #227)
-#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
-#265 := (iff #233 #264)
-#262 := (iff #230 #261)
-#263 := [rewrite]: #262
-#266 := [quant-intro #263]: #265
-#133 := (not #132)
-#126 := (not #125)
-#136 := (and #126 #133)
-#122 := (not #121)
-#129 := (and #122 #126)
-#139 := (or #129 #136)
-#142 := (ite #139 #28 #100)
-#145 := (ite #21 0::Int #142)
-#148 := (= #18 #145)
-#151 := (forall (vars (?v0 Int) (?v1 Int)) #148)
-#234 := (iff #151 #233)
-#231 := (iff #148 #230)
-#228 := (= #145 #227)
-#225 := (= #142 #224)
-#222 := (iff #139 #221)
-#219 := (iff #136 #218)
-#220 := [rewrite]: #219
-#209 := (iff #129 #216)
-#210 := [rewrite]: #209
-#223 := [monotonicity #210 #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [monotonicity #229]: #231
-#235 := [quant-intro #232]: #234
-#213 := (~ #151 #151)
-#211 := (~ #148 #148)
-#212 := [refl]: #211
-#214 := [nnf-pos #212]: #213
-#30 := (- #17)
-#29 := (- #15)
-#31 := (div #29 #30)
-#23 := (< 0::Int #17)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#32 := (ite #27 #28 #31)
-#33 := (ite #21 0::Int #32)
-#34 := (= #18 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#154 := (iff #35 #151)
-#87 := (and #23 #25)
-#90 := (or #24 #87)
-#103 := (ite #90 #28 #100)
-#81 := (= 0::Int #17)
-#78 := (= 0::Int #15)
-#84 := (or #78 #81)
-#106 := (ite #84 0::Int #103)
-#109 := (= #18 #106)
-#112 := (forall (vars (?v0 Int) (?v1 Int)) #109)
-#152 := (iff #112 #151)
-#149 := (iff #109 #148)
-#146 := (= #106 #145)
-#143 := (= #103 #142)
-#140 := (iff #90 #139)
-#137 := (iff #87 #136)
-#134 := (iff #25 #133)
-#135 := [rewrite]: #134
-#127 := (iff #23 #126)
-#128 := [rewrite]: #127
-#138 := [monotonicity #128 #135]: #137
-#130 := (iff #24 #129)
-#123 := (iff #22 #122)
-#124 := [rewrite]: #123
-#131 := [monotonicity #124 #128]: #130
-#141 := [monotonicity #131 #138]: #140
-#144 := [monotonicity #141]: #143
-#119 := (iff #84 #21)
-#117 := (iff #81 #20)
-#118 := [rewrite]: #117
-#115 := (iff #78 #19)
-#116 := [rewrite]: #115
-#120 := [monotonicity #116 #118]: #119
-#147 := [monotonicity #120 #144]: #146
-#150 := [monotonicity #147]: #149
-#153 := [quant-intro #150]: #152
-#113 := (iff #35 #112)
-#110 := (iff #34 #109)
-#107 := (= #33 #106)
-#104 := (= #32 #103)
-#101 := (= #31 #100)
-#98 := (= #30 #97)
-#99 := [rewrite]: #98
-#95 := (= #29 #94)
-#96 := [rewrite]: #95
-#102 := [monotonicity #96 #99]: #101
-#91 := (iff #27 #90)
-#88 := (iff #26 #87)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#105 := [monotonicity #92 #102]: #104
-#85 := (iff #21 #84)
-#82 := (iff #20 #81)
-#83 := [rewrite]: #82
-#79 := (iff #19 #78)
-#80 := [rewrite]: #79
-#86 := [monotonicity #80 #83]: #85
-#108 := [monotonicity #86 #105]: #107
-#111 := [monotonicity #108]: #110
-#114 := [quant-intro #111]: #113
-#155 := [trans #114 #153]: #154
-#77 := [asserted]: #35
-#156 := [mp #77 #155]: #151
-#205 := [mp~ #156 #214]: #151
-#236 := [mp #205 #235]: #233
-#267 := [mp #236 #266]: #264
-#761 := [mp #267 #760]: #756
-decl f6 :: Int
-#9 := f6
-#10 := (f4 f5 f6)
-#12 := (f3 #10 0::Int)
-#13 := (= #12 0::Int)
-#14 := (not #13)
-#66 := [asserted]: #14
-#697 := (not #756)
-#698 := (or #697 #13)
-#341 := (* -1::Int 0::Int)
-#426 := (* -1::Int f6)
-#427 := (div #426 #341)
-#428 := (* -1::Int #427)
-#419 := (+ #12 #428)
-#430 := (= #419 0::Int)
-#431 := (div f6 0::Int)
-#359 := (* -1::Int #431)
-#432 := (+ #12 #359)
-#429 := (= #432 0::Int)
-#433 := (>= f6 0::Int)
-#412 := (<= 0::Int 0::Int)
-#747 := (or #412 #433)
-#749 := (not #747)
-#406 := (<= f6 0::Int)
-#536 := (or #406 #412)
-#743 := (not #536)
-#417 := (or #743 #749)
-#418 := (ite #417 #429 #430)
-#750 := (= 0::Int 0::Int)
-#751 := (= f6 0::Int)
-#752 := (or #751 #750)
-#753 := (ite #752 #13 #418)
-#704 := (or #697 #753)
-#699 := (iff #704 #698)
-#535 := (iff #698 #698)
-#537 := [rewrite]: #535
-#702 := (iff #753 #13)
-#438 := (div #426 0::Int)
-#718 := (* -1::Int #438)
-#716 := (+ #12 #718)
-#721 := (= #716 0::Int)
-#1 := true
-#556 := (ite true #13 #721)
-#700 := (iff #556 #13)
-#701 := [rewrite]: #700
-#557 := (iff #753 #556)
-#709 := (iff #418 #721)
-#712 := (ite false #429 #721)
-#713 := (iff #712 #721)
-#714 := [rewrite]: #713
-#707 := (iff #418 #712)
-#710 := (iff #430 #721)
-#720 := (= #419 #716)
-#719 := (= #428 #718)
-#439 := (= #427 #438)
-#727 := (= #341 0::Int)
-#437 := [rewrite]: #727
-#440 := [monotonicity #437]: #439
-#434 := [monotonicity #440]: #719
-#717 := [monotonicity #434]: #720
-#711 := [monotonicity #717]: #710
-#726 := (iff #417 false)
-#724 := (or false false)
-#448 := (iff #724 false)
-#722 := [rewrite]: #448
-#725 := (iff #417 #724)
-#454 := (iff #749 false)
-#736 := (not true)
-#375 := (iff #736 false)
-#738 := [rewrite]: #375
-#452 := (iff #749 #736)
-#729 := (iff #747 true)
-#381 := (or true #433)
-#742 := (iff #381 true)
-#728 := [rewrite]: #742
-#741 := (iff #747 #381)
-#730 := (iff #412 true)
-#393 := [rewrite]: #730
-#739 := [monotonicity #393]: #741
-#451 := [trans #739 #728]: #729
-#453 := [monotonicity #451]: #452
-#347 := [trans #453 #738]: #454
-#740 := (iff #743 false)
-#731 := (iff #743 #736)
-#734 := (iff #536 true)
-#394 := (or #406 true)
-#732 := (iff #394 true)
-#733 := [rewrite]: #732
-#395 := (iff #536 #394)
-#396 := [monotonicity #393]: #395
-#735 := [trans #396 #733]: #734
-#737 := [monotonicity #735]: #731
-#380 := [trans #737 #738]: #740
-#447 := [monotonicity #380 #347]: #725
-#723 := [trans #447 #722]: #726
-#708 := [monotonicity #723 #711]: #707
-#715 := [trans #708 #714]: #709
-#746 := (iff #752 true)
-#744 := (or #751 true)
-#745 := (iff #744 true)
-#405 := [rewrite]: #745
-#404 := (iff #752 #744)
-#748 := (iff #750 true)
-#754 := [rewrite]: #748
-#409 := [monotonicity #754]: #404
-#389 := [trans #409 #405]: #746
-#558 := [monotonicity #389 #715]: #557
-#703 := [trans #558 #701]: #702
-#706 := [monotonicity #703]: #699
-#538 := [trans #706 #537]: #699
-#705 := [quant-inst #9 #11]: #704
-#691 := [mp #705 #538]: #698
-[unit-resolution #691 #66 #761]: false
-unsat
-aac15ec211f322a6810a9bf44dec67adf9e8201f 296 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#16 := (f4 f5 #15)
-#18 := (f3 #16 #17)
-#754 := (pattern #18)
-#9 := 0::Int
-#93 := -1::Int
-#97 := (* -1::Int #17)
-#94 := (* -1::Int #15)
-#100 := (div #94 #97)
-#257 := (* -1::Int #100)
-#258 := (+ #18 #257)
-#259 := (= #258 0::Int)
-#28 := (div #15 #17)
-#254 := (* -1::Int #28)
-#255 := (+ #18 #254)
-#256 := (= #255 0::Int)
-#132 := (>= #15 0::Int)
-#125 := (<= #17 0::Int)
-#217 := (or #125 #132)
-#218 := (not #217)
-#121 := (<= #15 0::Int)
-#215 := (or #121 #125)
-#216 := (not #215)
-#221 := (or #216 #218)
-#260 := (ite #221 #256 #259)
-#253 := (= #18 0::Int)
-#20 := (= #17 0::Int)
-#19 := (= #15 0::Int)
-#21 := (or #19 #20)
-#261 := (ite #21 #253 #260)
-#755 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #754) #261)
-#264 := (forall (vars (?v0 Int) (?v1 Int)) #261)
-#758 := (iff #264 #755)
-#756 := (iff #261 #261)
-#757 := [refl]: #756
-#759 := [quant-intro #757]: #758
-#224 := (ite #221 #28 #100)
-#227 := (ite #21 0::Int #224)
-#230 := (= #18 #227)
-#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
-#265 := (iff #233 #264)
-#262 := (iff #230 #261)
-#263 := [rewrite]: #262
-#266 := [quant-intro #263]: #265
-#133 := (not #132)
-#126 := (not #125)
-#136 := (and #126 #133)
-#122 := (not #121)
-#129 := (and #122 #126)
-#139 := (or #129 #136)
-#142 := (ite #139 #28 #100)
-#145 := (ite #21 0::Int #142)
-#148 := (= #18 #145)
-#151 := (forall (vars (?v0 Int) (?v1 Int)) #148)
-#234 := (iff #151 #233)
-#231 := (iff #148 #230)
-#228 := (= #145 #227)
-#225 := (= #142 #224)
-#222 := (iff #139 #221)
-#219 := (iff #136 #218)
-#220 := [rewrite]: #219
-#209 := (iff #129 #216)
-#210 := [rewrite]: #209
-#223 := [monotonicity #210 #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [monotonicity #229]: #231
-#235 := [quant-intro #232]: #234
-#213 := (~ #151 #151)
-#211 := (~ #148 #148)
-#212 := [refl]: #211
-#214 := [nnf-pos #212]: #213
-#30 := (- #17)
-#29 := (- #15)
-#31 := (div #29 #30)
-#23 := (< 0::Int #17)
-#25 := (< #15 0::Int)
-#26 := (and #25 #23)
-#22 := (< 0::Int #15)
-#24 := (and #22 #23)
-#27 := (or #24 #26)
-#32 := (ite #27 #28 #31)
-#33 := (ite #21 0::Int #32)
-#34 := (= #18 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#154 := (iff #35 #151)
-#87 := (and #23 #25)
-#90 := (or #24 #87)
-#103 := (ite #90 #28 #100)
-#81 := (= 0::Int #17)
-#78 := (= 0::Int #15)
-#84 := (or #78 #81)
-#106 := (ite #84 0::Int #103)
-#109 := (= #18 #106)
-#112 := (forall (vars (?v0 Int) (?v1 Int)) #109)
-#152 := (iff #112 #151)
-#149 := (iff #109 #148)
-#146 := (= #106 #145)
-#143 := (= #103 #142)
-#140 := (iff #90 #139)
-#137 := (iff #87 #136)
-#134 := (iff #25 #133)
-#135 := [rewrite]: #134
-#127 := (iff #23 #126)
-#128 := [rewrite]: #127
-#138 := [monotonicity #128 #135]: #137
-#130 := (iff #24 #129)
-#123 := (iff #22 #122)
-#124 := [rewrite]: #123
-#131 := [monotonicity #124 #128]: #130
-#141 := [monotonicity #131 #138]: #140
-#144 := [monotonicity #141]: #143
-#119 := (iff #84 #21)
-#117 := (iff #81 #20)
-#118 := [rewrite]: #117
-#115 := (iff #78 #19)
-#116 := [rewrite]: #115
-#120 := [monotonicity #116 #118]: #119
-#147 := [monotonicity #120 #144]: #146
-#150 := [monotonicity #147]: #149
-#153 := [quant-intro #150]: #152
-#113 := (iff #35 #112)
-#110 := (iff #34 #109)
-#107 := (= #33 #106)
-#104 := (= #32 #103)
-#101 := (= #31 #100)
-#98 := (= #30 #97)
-#99 := [rewrite]: #98
-#95 := (= #29 #94)
-#96 := [rewrite]: #95
-#102 := [monotonicity #96 #99]: #101
-#91 := (iff #27 #90)
-#88 := (iff #26 #87)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#105 := [monotonicity #92 #102]: #104
-#85 := (iff #21 #84)
-#82 := (iff #20 #81)
-#83 := [rewrite]: #82
-#79 := (iff #19 #78)
-#80 := [rewrite]: #79
-#86 := [monotonicity #80 #83]: #85
-#108 := [monotonicity #86 #105]: #107
-#111 := [monotonicity #108]: #110
-#114 := [quant-intro #111]: #113
-#155 := [trans #114 #153]: #154
-#77 := [asserted]: #35
-#156 := [mp #77 #155]: #151
-#205 := [mp~ #156 #214]: #151
-#236 := [mp #205 #235]: #233
-#267 := [mp #236 #266]: #264
-#760 := [mp #267 #759]: #755
-#11 := 1::Int
-#10 := (f4 f5 0::Int)
-#12 := (f3 #10 1::Int)
-#13 := (= #12 0::Int)
-#14 := (not #13)
-#66 := [asserted]: #14
-#589 := (not #755)
-#590 := (or #589 #13)
-#341 := (* -1::Int 1::Int)
-#425 := (* -1::Int 0::Int)
-#426 := (div #425 #341)
-#427 := (* -1::Int #426)
-#418 := (+ #12 #427)
-#429 := (= #418 0::Int)
-#430 := (div 0::Int 1::Int)
-#431 := (* -1::Int #430)
-#428 := (+ #12 #431)
-#432 := (= #428 0::Int)
-#411 := (>= 0::Int 0::Int)
-#746 := (<= 1::Int 0::Int)
-#748 := (or #746 #411)
-#405 := (not #748)
-#535 := (<= 0::Int 0::Int)
-#742 := (or #535 #746)
-#416 := (not #742)
-#417 := (or #416 #405)
-#749 := (ite #417 #432 #429)
-#750 := (= 1::Int 0::Int)
-#751 := (= 0::Int 0::Int)
-#752 := (or #751 #750)
-#747 := (ite #752 #13 #749)
-#583 := (or #589 #747)
-#592 := (iff #583 #590)
-#594 := (iff #590 #590)
-#595 := [rewrite]: #594
-#572 := (iff #747 #13)
-#1 := true
-#686 := (ite true #13 #13)
-#684 := (iff #686 #13)
-#687 := [rewrite]: #684
-#588 := (iff #747 #686)
-#579 := (iff #749 #13)
-#694 := (ite false #13 #13)
-#577 := (iff #694 #13)
-#578 := [rewrite]: #577
-#692 := (iff #749 #694)
-#691 := (iff #429 #13)
-#537 := (= #418 #12)
-#709 := (+ #12 0::Int)
-#706 := (= #709 #12)
-#707 := [rewrite]: #706
-#534 := (= #418 #709)
-#698 := (= #427 0::Int)
-#715 := (= #425 0::Int)
-#719 := [rewrite]: #715
-#703 := (= #427 #425)
-#696 := (= #426 0::Int)
-#557 := (div 0::Int -1::Int)
-#701 := (= #557 0::Int)
-#702 := [rewrite]: #701
-#699 := (= #426 #557)
-#555 := (= #341 -1::Int)
-#556 := [rewrite]: #555
-#700 := [monotonicity #719 #556]: #699
-#697 := [trans #700 #702]: #696
-#704 := [monotonicity #697]: #703
-#705 := [trans #704 #719]: #698
-#536 := [monotonicity #705]: #534
-#690 := [trans #536 #707]: #537
-#693 := [monotonicity #690]: #691
-#708 := (iff #432 #13)
-#712 := (= #428 #12)
-#710 := (= #428 #709)
-#716 := (= #431 0::Int)
-#718 := (= #431 #425)
-#439 := (= #430 0::Int)
-#717 := [rewrite]: #439
-#433 := [monotonicity #717]: #718
-#720 := [trans #433 #719]: #716
-#711 := [monotonicity #720]: #710
-#713 := [trans #711 #707]: #712
-#714 := [monotonicity #713]: #708
-#437 := (iff #417 false)
-#721 := (or false false)
-#726 := (iff #721 false)
-#436 := [rewrite]: #726
-#725 := (iff #417 #721)
-#446 := (iff #405 false)
-#736 := (not true)
-#739 := (iff #736 false)
-#379 := [rewrite]: #739
-#723 := (iff #405 #736)
-#453 := (iff #748 true)
-#727 := (or false true)
-#451 := (iff #727 true)
-#452 := [rewrite]: #451
-#728 := (iff #748 #727)
-#738 := (iff #411 true)
-#741 := [rewrite]: #738
-#731 := (iff #746 false)
-#732 := [rewrite]: #731
-#450 := [monotonicity #732 #741]: #728
-#347 := [trans #450 #452]: #453
-#724 := [monotonicity #347]: #723
-#447 := [trans #724 #379]: #446
-#380 := (iff #416 false)
-#374 := (iff #416 #736)
-#735 := (iff #742 true)
-#744 := (or true false)
-#388 := (iff #744 true)
-#729 := [rewrite]: #388
-#733 := (iff #742 #744)
-#394 := (iff #535 true)
-#395 := [rewrite]: #394
-#734 := [monotonicity #395 #732]: #733
-#730 := [trans #734 #729]: #735
-#737 := [monotonicity #730]: #374
-#740 := [trans #737 #379]: #380
-#722 := [monotonicity #740 #447]: #725
-#438 := [trans #722 #436]: #437
-#695 := [monotonicity #438 #714 #693]: #692
-#538 := [trans #695 #578]: #579
-#392 := (iff #752 true)
-#404 := (iff #752 #744)
-#403 := (iff #750 false)
-#408 := [rewrite]: #403
-#753 := (iff #751 true)
-#743 := [rewrite]: #753
-#745 := [monotonicity #743 #408]: #404
-#393 := [trans #745 #729]: #392
-#683 := [monotonicity #393 #538]: #588
-#587 := [trans #683 #687]: #572
-#593 := [monotonicity #587]: #592
-#688 := [trans #593 #595]: #592
-#591 := [quant-inst #9 #11]: #583
-#685 := [mp #591 #688]: #590
-[unit-resolution #685 #66 #760]: false
-unsat
-575117f1eb706f5a1dbf04aa3800a1f178601599 284 0
+#47 := [asserted]: #13
+#626 := (not #684)
+#632 := (or #626 #12)
+#345 := (* -1::Int 0::Int)
+#671 := (* -1::Int f6)
+#346 := (div #671 #345)
+#678 := (* -1::Int #346)
+#679 := (+ #11 #678)
+#680 := (= #679 0::Int)
+#675 := (div f6 0::Int)
+#677 := (* -1::Int #675)
+#334 := (+ #11 #677)
+#464 := (= #334 0::Int)
+#347 := (<= 0::Int 0::Int)
+#360 := (>= f6 0::Int)
+#357 := (or #360 #347)
+#361 := (not #357)
+#356 := (<= f6 0::Int)
+#358 := (or #356 #347)
+#359 := (not #358)
+#340 := (or #359 #361)
+#681 := (if #340 #464 #680)
+#354 := (= 0::Int 0::Int)
+#269 := (= f6 0::Int)
+#355 := (or #269 #354)
+#676 := (if #355 #12 #681)
+#633 := (or #626 #676)
+#634 := (iff #633 #632)
+#465 := (iff #632 #632)
+#466 := [rewrite]: #465
+#631 := (iff #676 #12)
+#367 := (div #671 0::Int)
+#647 := (* -1::Int #367)
+#648 := (+ #11 #647)
+#638 := (= #648 0::Int)
+#1 := true
+#485 := (if true #12 #638)
+#629 := (iff #485 #12)
+#630 := [rewrite]: #629
+#486 := (iff #676 #485)
+#643 := (iff #681 #638)
+#635 := (if false #464 #638)
+#642 := (iff #635 #638)
+#637 := [rewrite]: #642
+#636 := (iff #681 #635)
+#639 := (iff #680 #638)
+#645 := (= #679 #648)
+#362 := (= #678 #647)
+#368 := (= #346 #367)
+#365 := (= #345 0::Int)
+#366 := [rewrite]: #365
+#646 := [monotonicity #366]: #368
+#644 := [monotonicity #646]: #362
+#649 := [monotonicity #644]: #645
+#640 := [monotonicity #649]: #639
+#651 := (iff #340 false)
+#653 := (or false false)
+#650 := (iff #653 false)
+#654 := [rewrite]: #650
+#375 := (iff #340 #653)
+#275 := (iff #361 false)
+#659 := (not true)
+#666 := (iff #659 false)
+#668 := [rewrite]: #666
+#381 := (iff #361 #659)
+#379 := (iff #357 true)
+#669 := (or #360 true)
+#656 := (iff #669 true)
+#657 := [rewrite]: #656
+#667 := (iff #357 #669)
+#321 := (iff #347 true)
+#322 := [rewrite]: #321
+#670 := [monotonicity #322]: #667
+#380 := [trans #670 #657]: #379
+#382 := [monotonicity #380]: #381
+#652 := [trans #382 #668]: #275
+#308 := (iff #359 false)
+#665 := (iff #359 #659)
+#663 := (iff #358 true)
+#323 := (or #356 true)
+#661 := (iff #323 true)
+#662 := [rewrite]: #661
+#324 := (iff #358 #323)
+#660 := [monotonicity #322]: #324
+#664 := [trans #660 #662]: #663
+#303 := [monotonicity #664]: #665
+#309 := [trans #303 #668]: #308
+#376 := [monotonicity #309 #652]: #375
+#655 := [trans #376 #654]: #651
+#641 := [monotonicity #655 #640]: #636
+#484 := [trans #641 #637]: #643
+#317 := (iff #355 true)
+#332 := (or #269 true)
+#333 := (iff #332 true)
+#674 := [rewrite]: #333
+#337 := (iff #355 #332)
+#682 := (iff #354 true)
+#672 := [rewrite]: #682
+#673 := [monotonicity #672]: #337
+#658 := [trans #673 #674]: #317
+#628 := [monotonicity #658 #484]: #486
+#625 := [trans #628 #630]: #631
+#463 := [monotonicity #625]: #634
+#619 := [trans #463 #466]: #634
+#627 := [quant-inst #8 #10]: #633
+#620 := [mp #627 #619]: #632
+[unit-resolution #620 #47 #689]: false
+4a9ad09bb6074d903a151e76b4a561a7a6bdd95b 288 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #16 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #14 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #15 := (f4 f5 #14)
 #17 := (f3 #15 #16)
-#739 := (pattern #17)
-#18 := 0::Int
-#84 := -1::Int
-#88 := (* -1::Int #16)
-#85 := (* -1::Int #14)
-#91 := (div #85 #88)
-#242 := (* -1::Int #91)
+#682 := (pattern #17)
+#8 := 0::Int
+#79 := -1::Int
+#83 := (* -1::Int #16)
+#80 := (* -1::Int #14)
+#86 := (div #80 #83)
+#242 := (* -1::Int #86)
 #243 := (+ #17 #242)
 #244 := (= #243 0::Int)
-#28 := (div #14 #16)
-#239 := (* -1::Int #28)
+#27 := (div #14 #16)
+#239 := (* -1::Int #27)
 #240 := (+ #17 #239)
 #241 := (= #240 0::Int)
-#117 := (>= #14 0::Int)
-#110 := (<= #16 0::Int)
-#202 := (or #110 #117)
+#57 := (<= #16 0::Int)
+#149 := (>= #14 0::Int)
+#202 := (or #149 #57)
 #203 := (not #202)
-#106 := (<= #14 0::Int)
-#200 := (or #106 #110)
-#201 := (not #200)
-#206 := (or #201 #203)
-#245 := (ite #206 #241 #244)
+#53 := (<= #14 0::Int)
+#198 := (or #53 #57)
+#199 := (not #198)
+#206 := (or #199 #203)
+#245 := (if #206 #241 #244)
 #238 := (= #17 0::Int)
-#20 := (= #16 0::Int)
-#19 := (= #14 0::Int)
-#21 := (or #19 #20)
-#246 := (ite #21 #238 #245)
-#740 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #739) #246)
+#19 := (= #16 0::Int)
+#18 := (= #14 0::Int)
+#20 := (or #18 #19)
+#246 := (if #20 #238 #245)
+#683 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #682) #246)
 #249 := (forall (vars (?v0 Int) (?v1 Int)) #246)
-#743 := (iff #249 #740)
-#741 := (iff #246 #246)
-#742 := [refl]: #741
-#744 := [quant-intro #742]: #743
-#209 := (ite #206 #28 #91)
-#212 := (ite #21 0::Int #209)
+#686 := (iff #249 #683)
+#684 := (iff #246 #246)
+#685 := [refl]: #684
+#687 := [quant-intro #685]: #686
+#209 := (if #206 #27 #86)
+#212 := (if #20 0::Int #209)
 #215 := (= #17 #212)
 #218 := (forall (vars (?v0 Int) (?v1 Int)) #215)
 #250 := (iff #218 #249)
 #247 := (iff #215 #246)
 #248 := [rewrite]: #247
 #251 := [quant-intro #248]: #250
-#118 := (not #117)
-#111 := (not #110)
-#121 := (and #111 #118)
-#107 := (not #106)
-#114 := (and #107 #111)
-#124 := (or #114 #121)
-#127 := (ite #124 #28 #91)
-#130 := (ite #21 0::Int #127)
-#133 := (= #17 #130)
-#136 := (forall (vars (?v0 Int) (?v1 Int)) #133)
-#219 := (iff #136 #218)
-#216 := (iff #133 #215)
-#213 := (= #130 #212)
-#210 := (= #127 #209)
-#207 := (iff #124 #206)
-#204 := (iff #121 #203)
+#58 := (not #57)
+#152 := (not #149)
+#155 := (and #152 #58)
+#54 := (not #53)
+#61 := (and #54 #58)
+#158 := (or #61 #155)
+#161 := (if #158 #27 #86)
+#164 := (if #20 0::Int #161)
+#167 := (= #17 #164)
+#170 := (forall (vars (?v0 Int) (?v1 Int)) #167)
+#219 := (iff #170 #218)
+#216 := (iff #167 #215)
+#213 := (= #164 #212)
+#210 := (= #161 #209)
+#207 := (iff #158 #206)
+#204 := (iff #155 #203)
 #205 := [rewrite]: #204
-#194 := (iff #114 #201)
-#195 := [rewrite]: #194
-#208 := [monotonicity #195 #205]: #207
+#200 := (iff #61 #199)
+#201 := [rewrite]: #200
+#208 := [monotonicity #201 #205]: #207
+#211 := [monotonicity #208]: #210
+#214 := [monotonicity #211]: #213
+#217 := [monotonicity #214]: #216
+#220 := [quant-intro #217]: #219
+#192 := (~ #170 #170)
+#194 := (~ #167 #167)
+#195 := [refl]: #194
+#193 := [nnf-pos #195]: #192
+#64 := (<= 0::Int #14)
+#65 := (not #64)
+#73 := (and #65 #58)
+#76 := (or #61 #73)
+#89 := (if #76 #27 #86)
+#92 := (if #20 0::Int #89)
+#95 := (= #17 #92)
+#98 := (forall (vars (?v0 Int) (?v1 Int)) #95)
+#171 := (iff #98 #170)
+#168 := (iff #95 #167)
+#165 := (= #92 #164)
+#162 := (= #89 #161)
+#159 := (iff #76 #158)
+#156 := (iff #73 #155)
+#153 := (iff #65 #152)
+#150 := (iff #64 #149)
+#151 := [rewrite]: #150
+#154 := [monotonicity #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [monotonicity #163]: #165
+#169 := [monotonicity #166]: #168
+#172 := [quant-intro #169]: #171
+#29 := (- #16)
+#28 := (- #14)
+#30 := (div #28 #29)
+#22 := (< 0::Int #16)
+#24 := (< #14 0::Int)
+#25 := (and #24 #22)
+#21 := (< 0::Int #14)
+#23 := (and #21 #22)
+#26 := (or #23 #25)
+#31 := (if #26 #27 #30)
+#32 := (if #20 0::Int #31)
+#33 := (= #17 #32)
+#34 := (forall (vars (?v0 Int) (?v1 Int)) #33)
+#99 := (iff #34 #98)
+#96 := (iff #33 #95)
+#93 := (= #32 #92)
+#90 := (= #31 #89)
+#87 := (= #30 #86)
+#84 := (= #29 #83)
+#85 := [rewrite]: #84
+#81 := (= #28 #80)
+#82 := [rewrite]: #81
+#88 := [monotonicity #82 #85]: #87
+#77 := (iff #26 #76)
+#74 := (iff #25 #73)
+#59 := (iff #22 #58)
+#60 := [rewrite]: #59
+#66 := (iff #24 #65)
+#70 := (iff #65 #65)
+#68 := (iff #64 #64)
+#69 := [rewrite]: #68
+#71 := [monotonicity #69]: #70
+#67 := [rewrite]: #66
+#72 := [trans #67 #71]: #66
+#75 := [monotonicity #72 #60]: #74
+#62 := (iff #23 #61)
+#55 := (iff #21 #54)
+#56 := [rewrite]: #55
+#63 := [monotonicity #56 #60]: #62
+#78 := [monotonicity #63 #75]: #77
+#91 := [monotonicity #78 #88]: #90
+#94 := [monotonicity #91]: #93
+#97 := [monotonicity #94]: #96
+#100 := [quant-intro #97]: #99
+#48 := [asserted]: #34
+#101 := [mp #48 #100]: #98
+#173 := [mp #101 #172]: #170
+#190 := [mp~ #173 #193]: #170
+#221 := [mp #190 #220]: #218
+#252 := [mp #221 #251]: #249
+#688 := [mp #252 #687]: #683
+#10 := 1::Int
+#9 := (f4 f5 0::Int)
+#11 := (f3 #9 1::Int)
+#12 := (= #11 0::Int)
+#13 := (not #12)
+#47 := [asserted]: #13
+#615 := (not #683)
+#500 := (or #615 #12)
+#344 := (* -1::Int 1::Int)
+#670 := (* -1::Int 0::Int)
+#345 := (div #670 #344)
+#677 := (* -1::Int #345)
+#678 := (+ #11 #677)
+#679 := (= #678 0::Int)
+#674 := (div 0::Int 1::Int)
+#676 := (* -1::Int #674)
+#333 := (+ #11 #676)
+#463 := (= #333 0::Int)
+#346 := (<= 1::Int 0::Int)
+#359 := (>= 0::Int 0::Int)
+#356 := (or #359 #346)
+#360 := (not #356)
+#355 := (<= 0::Int 0::Int)
+#357 := (or #355 #346)
+#358 := (not #357)
+#339 := (or #358 #360)
+#680 := (if #339 #463 #679)
+#353 := (= 1::Int 0::Int)
+#269 := (= 0::Int 0::Int)
+#354 := (or #269 #353)
+#675 := (if #354 #12 #680)
+#515 := (or #615 #675)
+#518 := (iff #515 #500)
+#519 := (iff #500 #500)
+#520 := [rewrite]: #519
+#611 := (iff #675 #12)
+#1 := true
+#506 := (if true #12 #12)
+#614 := (iff #506 #12)
+#516 := [rewrite]: #614
+#507 := (iff #675 #506)
+#623 := (iff #680 #12)
+#618 := (if false #12 #12)
+#622 := (iff #618 #12)
+#620 := [rewrite]: #622
+#619 := (iff #680 #618)
+#464 := (iff #679 #12)
+#633 := (= #678 #11)
+#647 := (+ #11 0::Int)
+#637 := (= #647 #11)
+#638 := [rewrite]: #637
+#632 := (= #678 #647)
+#625 := (= #677 0::Int)
+#645 := (= #670 0::Int)
+#646 := [rewrite]: #645
+#630 := (= #677 #670)
+#628 := (= #345 0::Int)
+#642 := (div 0::Int -1::Int)
+#485 := (= #642 0::Int)
+#627 := [rewrite]: #485
+#483 := (= #345 #642)
+#641 := (= #344 -1::Int)
+#636 := [rewrite]: #641
+#484 := [monotonicity #646 #636]: #483
+#629 := [trans #484 #627]: #628
+#624 := [monotonicity #629]: #630
+#631 := [trans #624 #646]: #625
+#626 := [monotonicity #631]: #632
+#462 := [trans #626 #638]: #633
+#465 := [monotonicity #462]: #464
+#635 := (iff #463 #12)
+#639 := (= #333 #11)
+#644 := (= #333 #647)
+#361 := (= #676 0::Int)
+#366 := (= #676 #670)
+#364 := (= #674 0::Int)
+#365 := [rewrite]: #364
+#367 := [monotonicity #365]: #366
+#643 := [trans #367 #646]: #361
+#648 := [monotonicity #643]: #644
+#634 := [trans #648 #638]: #639
+#640 := [monotonicity #634]: #635
+#650 := (iff #339 false)
+#652 := (or false false)
+#649 := (iff #652 false)
+#653 := [rewrite]: #649
+#374 := (iff #339 #652)
+#275 := (iff #360 false)
+#664 := (not true)
+#667 := (iff #664 false)
+#307 := [rewrite]: #667
+#380 := (iff #360 #664)
+#378 := (iff #356 true)
+#672 := (or true false)
+#316 := (iff #672 true)
+#657 := [rewrite]: #316
+#655 := (iff #356 #672)
+#659 := (iff #346 false)
+#660 := [rewrite]: #659
+#666 := (iff #359 true)
+#669 := [rewrite]: #666
+#656 := [monotonicity #669 #660]: #655
+#379 := [trans #656 #657]: #378
+#381 := [monotonicity #379]: #380
+#651 := [trans #381 #307]: #275
+#308 := (iff #358 false)
+#302 := (iff #358 #664)
+#663 := (iff #357 true)
+#661 := (iff #357 #672)
+#322 := (iff #355 true)
+#323 := [rewrite]: #322
+#662 := [monotonicity #323 #660]: #661
+#658 := [trans #662 #657]: #663
+#665 := [monotonicity #658]: #302
+#668 := [trans #665 #307]: #308
+#375 := [monotonicity #668 #651]: #374
+#654 := [trans #375 #653]: #650
+#621 := [monotonicity #654 #640 #465]: #619
+#505 := [trans #621 #620]: #623
+#320 := (iff #354 true)
+#332 := (iff #354 #672)
+#331 := (iff #353 false)
+#336 := [rewrite]: #331
+#681 := (iff #269 true)
+#671 := [rewrite]: #681
+#673 := [monotonicity #671 #336]: #332
+#321 := [trans #673 #657]: #320
+#466 := [monotonicity #321 #505]: #507
+#612 := [trans #466 #516]: #611
+#511 := [monotonicity #612]: #518
+#521 := [trans #511 #520]: #518
+#517 := [quant-inst #8 #10]: #515
+#522 := [mp #517 #521]: #500
+[unit-resolution #522 #47 #688]: false
+08b9dc0e318003c903e382519352a2ba5a18727d 291 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#15 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#13 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#14 := (f4 f5 #13)
+#16 := (f3 #14 #15)
+#682 := (pattern #16)
+#17 := 0::Int
+#79 := -1::Int
+#83 := (* -1::Int #15)
+#80 := (* -1::Int #13)
+#86 := (div #80 #83)
+#242 := (* -1::Int #86)
+#243 := (+ #16 #242)
+#244 := (= #243 0::Int)
+#27 := (div #13 #15)
+#239 := (* -1::Int #27)
+#240 := (+ #16 #239)
+#241 := (= #240 0::Int)
+#57 := (<= #15 0::Int)
+#149 := (>= #13 0::Int)
+#202 := (or #149 #57)
+#203 := (not #202)
+#53 := (<= #13 0::Int)
+#198 := (or #53 #57)
+#199 := (not #198)
+#206 := (or #199 #203)
+#245 := (if #206 #241 #244)
+#238 := (= #16 0::Int)
+#19 := (= #15 0::Int)
+#18 := (= #13 0::Int)
+#20 := (or #18 #19)
+#246 := (if #20 #238 #245)
+#683 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #682) #246)
+#249 := (forall (vars (?v0 Int) (?v1 Int)) #246)
+#686 := (iff #249 #683)
+#684 := (iff #246 #246)
+#685 := [refl]: #684
+#687 := [quant-intro #685]: #686
+#209 := (if #206 #27 #86)
+#212 := (if #20 0::Int #209)
+#215 := (= #16 #212)
+#218 := (forall (vars (?v0 Int) (?v1 Int)) #215)
+#250 := (iff #218 #249)
+#247 := (iff #215 #246)
+#248 := [rewrite]: #247
+#251 := [quant-intro #248]: #250
+#58 := (not #57)
+#152 := (not #149)
+#155 := (and #152 #58)
+#54 := (not #53)
+#61 := (and #54 #58)
+#158 := (or #61 #155)
+#161 := (if #158 #27 #86)
+#164 := (if #20 0::Int #161)
+#167 := (= #16 #164)
+#170 := (forall (vars (?v0 Int) (?v1 Int)) #167)
+#219 := (iff #170 #218)
+#216 := (iff #167 #215)
+#213 := (= #164 #212)
+#210 := (= #161 #209)
+#207 := (iff #158 #206)
+#204 := (iff #155 #203)
+#205 := [rewrite]: #204
+#200 := (iff #61 #199)
+#201 := [rewrite]: #200
+#208 := [monotonicity #201 #205]: #207
 #211 := [monotonicity #208]: #210
 #214 := [monotonicity #211]: #213
 #217 := [monotonicity #214]: #216
 #220 := [quant-intro #217]: #219
-#198 := (~ #136 #136)
-#196 := (~ #133 #133)
-#197 := [refl]: #196
-#199 := [nnf-pos #197]: #198
+#192 := (~ #170 #170)
+#194 := (~ #167 #167)
+#195 := [refl]: #194
+#193 := [nnf-pos #195]: #192
+#64 := (<= 0::Int #13)
+#65 := (not #64)
+#73 := (and #65 #58)
+#76 := (or #61 #73)
+#89 := (if #76 #27 #86)
+#92 := (if #20 0::Int #89)
+#95 := (= #16 #92)
+#98 := (forall (vars (?v0 Int) (?v1 Int)) #95)
+#171 := (iff #98 #170)
+#168 := (iff #95 #167)
+#165 := (= #92 #164)
+#162 := (= #89 #161)
+#159 := (iff #76 #158)
+#156 := (iff #73 #155)
+#153 := (iff #65 #152)
+#150 := (iff #64 #149)
+#151 := [rewrite]: #150
+#154 := [monotonicity #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [monotonicity #163]: #165
+#169 := [monotonicity #166]: #168
+#172 := [quant-intro #169]: #171
+#29 := (- #15)
+#28 := (- #13)
+#30 := (div #28 #29)
+#22 := (< 0::Int #15)
+#24 := (< #13 0::Int)
+#25 := (and #24 #22)
+#21 := (< 0::Int #13)
+#23 := (and #21 #22)
+#26 := (or #23 #25)
+#31 := (if #26 #27 #30)
+#32 := (if #20 0::Int #31)
+#33 := (= #16 #32)
+#34 := (forall (vars (?v0 Int) (?v1 Int)) #33)
+#99 := (iff #34 #98)
+#96 := (iff #33 #95)
+#93 := (= #32 #92)
+#90 := (= #31 #89)
+#87 := (= #30 #86)
+#84 := (= #29 #83)
+#85 := [rewrite]: #84
+#81 := (= #28 #80)
+#82 := [rewrite]: #81
+#88 := [monotonicity #82 #85]: #87
+#77 := (iff #26 #76)
+#74 := (iff #25 #73)
+#59 := (iff #22 #58)
+#60 := [rewrite]: #59
+#66 := (iff #24 #65)
+#70 := (iff #65 #65)
+#68 := (iff #64 #64)
+#69 := [rewrite]: #68
+#71 := [monotonicity #69]: #70
+#67 := [rewrite]: #66
+#72 := [trans #67 #71]: #66
+#75 := [monotonicity #72 #60]: #74
+#62 := (iff #23 #61)
+#55 := (iff #21 #54)
+#56 := [rewrite]: #55
+#63 := [monotonicity #56 #60]: #62
+#78 := [monotonicity #63 #75]: #77
+#91 := [monotonicity #78 #88]: #90
+#94 := [monotonicity #91]: #93
+#97 := [monotonicity #94]: #96
+#100 := [quant-intro #97]: #99
+#48 := [asserted]: #34
+#101 := [mp #48 #100]: #98
+#173 := [mp #101 #172]: #170
+#190 := [mp~ #173 #193]: #170
+#221 := [mp #190 #220]: #218
+#252 := [mp #221 #251]: #249
+#688 := [mp #252 #687]: #683
+#8 := 1::Int
+#9 := (f4 f5 1::Int)
+#10 := (f3 #9 1::Int)
+#11 := (= #10 1::Int)
+#12 := (not #11)
+#47 := [asserted]: #12
+#517 := (not #683)
+#518 := (or #517 #11)
+#463 := (* -1::Int 1::Int)
+#670 := (div #463 #463)
+#344 := (* -1::Int #670)
+#345 := (+ #10 #344)
+#677 := (= #345 0::Int)
+#339 := (div 1::Int 1::Int)
+#674 := (* -1::Int #339)
+#676 := (+ #10 #674)
+#333 := (= #676 0::Int)
+#355 := (<= 1::Int 0::Int)
+#358 := (>= 1::Int 0::Int)
+#359 := (or #358 #355)
+#356 := (not #359)
+#346 := (or #355 #355)
+#357 := (not #346)
+#360 := (or #357 #356)
+#678 := (if #360 #333 #677)
+#354 := (= #10 0::Int)
+#269 := (= 1::Int 0::Int)
+#353 := (or #269 #269)
+#679 := (if #353 #354 #678)
+#511 := (or #517 #679)
+#520 := (iff #511 #518)
+#522 := (iff #518 #518)
+#523 := [rewrite]: #522
+#500 := (iff #679 #11)
+#614 := (if false #354 #11)
+#612 := (iff #614 #11)
+#615 := [rewrite]: #612
+#516 := (iff #679 #614)
+#507 := (iff #678 #11)
+#1 := true
+#622 := (if true #11 #11)
+#505 := (iff #622 #11)
+#506 := [rewrite]: #505
+#620 := (iff #678 #622)
+#619 := (iff #677 #11)
+#647 := (+ -1::Int #10)
+#639 := (= #647 0::Int)
+#640 := (iff #639 #11)
+#641 := [rewrite]: #640
+#465 := (iff #677 #639)
+#462 := (= #345 #647)
+#646 := (+ #10 -1::Int)
+#644 := (= #646 #647)
+#648 := [rewrite]: #644
+#626 := (= #345 #646)
+#631 := (= #344 -1::Int)
+#365 := (= #463 -1::Int)
+#366 := [rewrite]: #365
+#624 := (= #344 #463)
+#629 := (= #670 1::Int)
+#483 := (div -1::Int -1::Int)
+#627 := (= #483 1::Int)
+#628 := [rewrite]: #627
+#484 := (= #670 #483)
+#485 := [monotonicity #366 #366]: #484
+#630 := [trans #485 #628]: #629
+#625 := [monotonicity #630]: #624
+#632 := [trans #625 #366]: #631
+#633 := [monotonicity #632]: #626
+#464 := [trans #633 #648]: #462
+#618 := [monotonicity #464]: #465
+#621 := [trans #618 #641]: #619
+#636 := (iff #333 #11)
+#634 := (iff #333 #639)
+#637 := (= #676 #647)
+#361 := (= #676 #646)
+#367 := (= #674 -1::Int)
+#654 := (= #674 #463)
+#653 := (= #339 1::Int)
+#650 := [rewrite]: #653
+#364 := [monotonicity #650]: #654
+#645 := [trans #364 #366]: #367
+#643 := [monotonicity #645]: #361
+#638 := [trans #643 #648]: #637
+#635 := [monotonicity #638]: #634
+#642 := [trans #635 #641]: #636
+#375 := (iff #360 true)
+#667 := (or true false)
+#668 := (iff #667 true)
+#666 := [rewrite]: #668
+#652 := (iff #360 #667)
+#275 := (iff #356 false)
+#656 := (not true)
+#380 := (iff #656 false)
+#381 := [rewrite]: #380
+#378 := (iff #356 #656)
+#669 := (iff #359 true)
+#307 := (iff #359 #667)
+#316 := (iff #355 false)
+#657 := [rewrite]: #316
+#302 := (iff #358 true)
+#665 := [rewrite]: #302
+#308 := [monotonicity #665 #657]: #307
+#655 := [trans #308 #666]: #669
+#379 := [monotonicity #655]: #378
+#651 := [trans #379 #381]: #275
+#658 := (iff #357 true)
+#659 := (not false)
+#662 := (iff #659 true)
+#663 := [rewrite]: #662
+#660 := (iff #357 #659)
+#322 := (iff #346 false)
+#681 := (or false false)
+#336 := (iff #681 false)
+#672 := [rewrite]: #336
+#320 := (iff #346 #681)
+#321 := [monotonicity #657 #657]: #320
+#323 := [trans #321 #672]: #322
+#661 := [monotonicity #323]: #660
+#664 := [trans #661 #663]: #658
+#374 := [monotonicity #664 #651]: #652
+#649 := [trans #374 #666]: #375
+#623 := [monotonicity #649 #642 #621]: #620
+#466 := [trans #623 #506]: #507
+#332 := (iff #353 false)
+#671 := (iff #353 #681)
+#680 := (iff #269 false)
+#675 := [rewrite]: #680
+#331 := [monotonicity #675 #675]: #671
+#673 := [trans #331 #672]: #332
+#611 := [monotonicity #673 #466]: #516
+#515 := [trans #611 #615]: #500
+#521 := [monotonicity #515]: #520
+#616 := [trans #521 #523]: #520
+#519 := [quant-inst #8 #8]: #511
+#613 := [mp #519 #616]: #518
+[unit-resolution #613 #47 #688]: false
+ad4c91889628d5e832117b163debdedc3d43ede3 302 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#16 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#14 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#15 := (f4 f5 #14)
+#17 := (f3 #15 #16)
+#683 := (pattern #17)
+#18 := 0::Int
+#80 := -1::Int
+#84 := (* -1::Int #16)
+#81 := (* -1::Int #14)
+#87 := (div #81 #84)
+#243 := (* -1::Int #87)
+#244 := (+ #17 #243)
+#245 := (= #244 0::Int)
+#28 := (div #14 #16)
+#240 := (* -1::Int #28)
+#241 := (+ #17 #240)
+#242 := (= #241 0::Int)
+#58 := (<= #16 0::Int)
+#150 := (>= #14 0::Int)
+#203 := (or #150 #58)
+#204 := (not #203)
+#54 := (<= #14 0::Int)
+#199 := (or #54 #58)
+#200 := (not #199)
+#207 := (or #200 #204)
+#246 := (if #207 #242 #245)
+#239 := (= #17 0::Int)
+#20 := (= #16 0::Int)
+#19 := (= #14 0::Int)
+#21 := (or #19 #20)
+#247 := (if #21 #239 #246)
+#684 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #683) #247)
+#250 := (forall (vars (?v0 Int) (?v1 Int)) #247)
+#687 := (iff #250 #684)
+#685 := (iff #247 #247)
+#686 := [refl]: #685
+#688 := [quant-intro #686]: #687
+#210 := (if #207 #28 #87)
+#213 := (if #21 0::Int #210)
+#216 := (= #17 #213)
+#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
+#251 := (iff #219 #250)
+#248 := (iff #216 #247)
+#249 := [rewrite]: #248
+#252 := [quant-intro #249]: #251
+#59 := (not #58)
+#153 := (not #150)
+#156 := (and #153 #59)
+#55 := (not #54)
+#62 := (and #55 #59)
+#159 := (or #62 #156)
+#162 := (if #159 #28 #87)
+#165 := (if #21 0::Int #162)
+#168 := (= #17 #165)
+#171 := (forall (vars (?v0 Int) (?v1 Int)) #168)
+#220 := (iff #171 #219)
+#217 := (iff #168 #216)
+#214 := (= #165 #213)
+#211 := (= #162 #210)
+#208 := (iff #159 #207)
+#205 := (iff #156 #204)
+#206 := [rewrite]: #205
+#201 := (iff #62 #200)
+#202 := [rewrite]: #201
+#209 := [monotonicity #202 #206]: #208
+#212 := [monotonicity #209]: #211
+#215 := [monotonicity #212]: #214
+#218 := [monotonicity #215]: #217
+#221 := [quant-intro #218]: #220
+#148 := (~ #171 #171)
+#193 := (~ #168 #168)
+#194 := [refl]: #193
+#149 := [nnf-pos #194]: #148
+#65 := (<= 0::Int #14)
+#66 := (not #65)
+#74 := (and #66 #59)
+#77 := (or #62 #74)
+#90 := (if #77 #28 #87)
+#93 := (if #21 0::Int #90)
+#96 := (= #17 #93)
+#99 := (forall (vars (?v0 Int) (?v1 Int)) #96)
+#172 := (iff #99 #171)
+#169 := (iff #96 #168)
+#166 := (= #93 #165)
+#163 := (= #90 #162)
+#160 := (iff #77 #159)
+#157 := (iff #74 #156)
+#154 := (iff #66 #153)
+#151 := (iff #65 #150)
+#152 := [rewrite]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [monotonicity #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [quant-intro #170]: #172
+#30 := (- #16)
+#29 := (- #14)
+#31 := (div #29 #30)
+#23 := (< 0::Int #16)
+#25 := (< #14 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #14)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#32 := (if #27 #28 #31)
+#33 := (if #21 0::Int #32)
+#34 := (= #17 #33)
+#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
+#100 := (iff #35 #99)
+#97 := (iff #34 #96)
+#94 := (= #33 #93)
+#91 := (= #32 #90)
+#88 := (= #31 #87)
+#85 := (= #30 #84)
+#86 := [rewrite]: #85
+#82 := (= #29 #81)
+#83 := [rewrite]: #82
+#89 := [monotonicity #83 #86]: #88
+#78 := (iff #27 #77)
+#75 := (iff #26 #74)
+#60 := (iff #23 #59)
+#61 := [rewrite]: #60
+#67 := (iff #25 #66)
+#71 := (iff #66 #66)
+#69 := (iff #65 #65)
+#70 := [rewrite]: #69
+#72 := [monotonicity #70]: #71
+#68 := [rewrite]: #67
+#73 := [trans #68 #72]: #67
+#76 := [monotonicity #73 #61]: #75
+#63 := (iff #24 #62)
+#56 := (iff #22 #55)
+#57 := [rewrite]: #56
+#64 := [monotonicity #57 #61]: #63
+#79 := [monotonicity #64 #76]: #78
+#92 := [monotonicity #79 #89]: #91
+#95 := [monotonicity #92]: #94
+#98 := [monotonicity #95]: #97
+#101 := [quant-intro #98]: #100
+#49 := [asserted]: #35
+#102 := [mp #49 #101]: #99
+#174 := [mp #102 #173]: #171
+#191 := [mp~ #174 #149]: #171
+#222 := [mp #191 #221]: #219
+#253 := [mp #222 #252]: #250
+#689 := [mp #253 #688]: #684
+#8 := 3::Int
+#10 := 1::Int
+#9 := (f4 f5 3::Int)
+#11 := (f3 #9 1::Int)
+#12 := (= #11 3::Int)
+#13 := (not #12)
+#48 := [asserted]: #13
+#618 := (not #684)
+#605 := (or #618 #12)
+#346 := (* -1::Int 1::Int)
+#345 := (* -1::Int 3::Int)
+#678 := (div #345 #346)
+#679 := (* -1::Int #678)
+#680 := (+ #11 #679)
+#681 := (= #680 0::Int)
+#677 := (div 3::Int 1::Int)
+#334 := (* -1::Int #677)
+#464 := (+ #11 #334)
+#671 := (= #464 0::Int)
+#358 := (<= 1::Int 0::Int)
+#357 := (>= 3::Int 0::Int)
+#361 := (or #357 #358)
+#340 := (not #361)
+#347 := (<= 3::Int 0::Int)
+#359 := (or #347 #358)
+#360 := (not #359)
+#675 := (or #360 #340)
+#676 := (if #675 #671 #681)
+#356 := (= #11 0::Int)
+#354 := (= 1::Int 0::Int)
+#270 := (= 3::Int 0::Int)
+#355 := (or #270 #354)
+#682 := (if #355 #356 #676)
+#607 := (or #618 #682)
+#596 := (iff #607 #605)
+#608 := (iff #605 #605)
+#609 := [rewrite]: #608
+#617 := (iff #682 #12)
+#520 := (if false #356 #12)
+#523 := (iff #520 #12)
+#524 := [rewrite]: #523
+#521 := (iff #682 #520)
+#519 := (iff #676 #12)
+#1 := true
+#613 := (if true #12 #12)
+#516 := (iff #613 #12)
+#518 := [rewrite]: #516
+#616 := (iff #676 #613)
+#517 := (iff #681 #12)
+#648 := -3::Int
+#641 := (+ -3::Int #11)
+#485 := (= #641 0::Int)
+#629 := (iff #485 #12)
+#630 := [rewrite]: #629
+#467 := (iff #681 #485)
+#507 := (= #680 #641)
+#640 := (+ #11 -3::Int)
+#642 := (= #640 #641)
+#637 := [rewrite]: #642
+#624 := (= #680 #640)
+#623 := (= #679 -3::Int)
+#645 := (= #345 -3::Int)
+#649 := [rewrite]: #645
+#620 := (= #679 #345)
+#466 := (= #678 3::Int)
+#633 := (div -3::Int -1::Int)
+#463 := (= #633 3::Int)
+#465 := [rewrite]: #463
+#627 := (= #678 #633)
+#626 := (= #346 -1::Int)
+#632 := [rewrite]: #626
+#634 := [monotonicity #649 #632]: #627
+#619 := [trans #634 #465]: #466
+#622 := [monotonicity #619]: #620
+#621 := [trans #622 #649]: #623
+#506 := [monotonicity #621]: #624
+#508 := [trans #506 #637]: #507
+#615 := [monotonicity #508]: #467
+#612 := [trans #615 #630]: #517
+#631 := (iff #671 #12)
+#486 := (iff #671 #485)
+#643 := (= #464 #641)
+#635 := (= #464 #640)
+#638 := (= #334 -3::Int)
+#362 := (= #334 #345)
+#646 := (= #677 3::Int)
+#647 := [rewrite]: #646
+#644 := [monotonicity #647]: #362
+#639 := [trans #644 #649]: #638
+#636 := [monotonicity #639]: #635
+#484 := [trans #636 #637]: #643
+#628 := [monotonicity #484]: #486
+#625 := [trans #628 #630]: #631
+#367 := (iff #675 true)
+#657 := (or true false)
+#381 := (iff #657 true)
+#382 := [rewrite]: #381
+#365 := (iff #675 #657)
+#651 := (iff #340 false)
+#653 := (not true)
+#650 := (iff #653 false)
+#654 := [rewrite]: #650
+#375 := (iff #340 #653)
+#276 := (iff #361 true)
+#379 := (iff #361 #657)
+#661 := (iff #358 false)
+#662 := [rewrite]: #661
+#670 := (iff #357 true)
+#656 := [rewrite]: #670
+#380 := [monotonicity #656 #662]: #379
+#652 := [trans #380 #382]: #276
+#376 := [monotonicity #652]: #375
+#655 := [trans #376 #654]: #651
+#669 := (iff #360 true)
+#303 := (not false)
+#308 := (iff #303 true)
+#309 := [rewrite]: #308
+#666 := (iff #360 #303)
+#659 := (iff #359 false)
+#333 := (or false false)
+#658 := (iff #333 false)
+#321 := [rewrite]: #658
+#663 := (iff #359 #333)
+#324 := (iff #347 false)
+#660 := [rewrite]: #324
+#664 := [monotonicity #660 #662]: #663
+#665 := [trans #664 #321]: #659
+#668 := [monotonicity #665]: #666
+#667 := [trans #668 #309]: #669
+#366 := [monotonicity #667 #655]: #365
+#368 := [trans #366 #382]: #367
+#501 := [monotonicity #368 #625 #612]: #616
+#512 := [trans #501 #518]: #519
+#322 := (iff #355 false)
+#674 := (iff #355 #333)
+#337 := (iff #354 false)
+#673 := [rewrite]: #337
+#672 := (iff #270 false)
+#332 := [rewrite]: #672
+#317 := [monotonicity #332 #673]: #674
+#323 := [trans #317 #321]: #322
+#522 := [monotonicity #323 #512]: #521
+#614 := [trans #522 #524]: #617
+#598 := [monotonicity #614]: #596
+#610 := [trans #598 #609]: #596
+#599 := [quant-inst #8 #10]: #607
+#606 := [mp #599 #610]: #605
+[unit-resolution #606 #48 #689]: false
+66efac954bb1bd3de1e46f930d0903efeef6fa16 330 0
+unsat
+#2 := false
+#18 := 0::Int
+decl f3 :: (-> S2 Int Int)
+#10 := 1::Int
+decl f4 :: (-> S3 Int S2)
+decl f6 :: Int
+#8 := f6
+decl f5 :: S3
+#7 := f5
+#9 := (f4 f5 f6)
+#11 := (f3 #9 1::Int)
+#356 := (= #11 0::Int)
+#516 := (not #356)
+#12 := (= #11 f6)
+#13 := (not #12)
+#595 := (iff #13 #516)
+#594 := (iff #12 #356)
+#589 := (iff #356 #12)
+#580 := (= 0::Int f6)
+#270 := (= f6 0::Int)
+#677 := (div f6 1::Int)
+#80 := -1::Int
+#334 := (* -1::Int #677)
+#464 := (+ #11 #334)
+#671 := (= #464 0::Int)
+#621 := (not #671)
+#585 := (= #677 f6)
+#528 := (= f6 #677)
+#567 := (+ f6 #334)
+#573 := (<= #567 0::Int)
+#587 := (= #567 0::Int)
+#1 := true
+#147 := [true-axiom]: true
+#539 := (or false #587)
+#540 := [th-lemma arith]: #539
+#541 := [unit-resolution #540 #147]: #587
+#544 := (not #587)
+#545 := (or #544 #573)
+#546 := [th-lemma arith triangle-eq]: #545
+#542 := [unit-resolution #546 #541]: #573
+#574 := (>= #567 0::Int)
+#547 := (or #544 #574)
+#527 := [th-lemma arith triangle-eq]: #547
+#473 := [unit-resolution #527 #541]: #574
+#509 := [th-lemma arith eq-propagate 1 1 #473 #542]: #528
+#529 := [symm #509]: #585
+#538 := (= #11 #677)
+#633 := (<= #464 0::Int)
+#557 := [hypothesis]: #671
+#530 := (or #621 #633)
+#531 := [th-lemma arith triangle-eq]: #530
+#532 := [unit-resolution #531 #557]: #633
+#627 := (>= #464 0::Int)
+#425 := (or #621 #627)
+#536 := [th-lemma arith triangle-eq]: #425
+#537 := [unit-resolution #536 #557]: #627
+#543 := [th-lemma arith eq-propagate 1 1 #537 #532]: #538
+#535 := [trans #543 #529]: #12
+#48 := [asserted]: #13
+#503 := [unit-resolution #48 #535]: false
+#510 := [lemma #503]: #621
+#345 := (* -1::Int f6)
+#375 := (div #345 -1::Int)
+#654 := (* -1::Int #375)
+#365 := (+ #11 #654)
+#368 := (= #365 0::Int)
+#357 := (>= f6 0::Int)
+#657 := (not #357)
+#347 := (<= f6 0::Int)
+#665 := (not #347)
+#381 := (or #665 #657)
+#362 := (if #381 #671 #368)
+#517 := (not #270)
+#607 := [hypothesis]: #517
+#601 := (or #270 #362)
+#645 := (if #270 #356 #362)
+#16 := (:var 0 Int)
+#14 := (:var 1 Int)
+#15 := (f4 f5 #14)
+#17 := (f3 #15 #16)
+#683 := (pattern #17)
+#84 := (* -1::Int #16)
+#81 := (* -1::Int #14)
+#87 := (div #81 #84)
+#243 := (* -1::Int #87)
+#244 := (+ #17 #243)
+#245 := (= #244 0::Int)
+#28 := (div #14 #16)
+#240 := (* -1::Int #28)
+#241 := (+ #17 #240)
+#242 := (= #241 0::Int)
+#58 := (<= #16 0::Int)
+#150 := (>= #14 0::Int)
+#203 := (or #150 #58)
+#204 := (not #203)
+#54 := (<= #14 0::Int)
+#199 := (or #54 #58)
+#200 := (not #199)
+#207 := (or #200 #204)
+#246 := (if #207 #242 #245)
+#239 := (= #17 0::Int)
+#20 := (= #16 0::Int)
+#19 := (= #14 0::Int)
+#21 := (or #19 #20)
+#247 := (if #21 #239 #246)
+#684 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #683) #247)
+#250 := (forall (vars (?v0 Int) (?v1 Int)) #247)
+#687 := (iff #250 #684)
+#685 := (iff #247 #247)
+#686 := [refl]: #685
+#688 := [quant-intro #686]: #687
+#210 := (if #207 #28 #87)
+#213 := (if #21 0::Int #210)
+#216 := (= #17 #213)
+#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
+#251 := (iff #219 #250)
+#248 := (iff #216 #247)
+#249 := [rewrite]: #248
+#252 := [quant-intro #249]: #251
+#59 := (not #58)
+#153 := (not #150)
+#156 := (and #153 #59)
+#55 := (not #54)
+#62 := (and #55 #59)
+#159 := (or #62 #156)
+#162 := (if #159 #28 #87)
+#165 := (if #21 0::Int #162)
+#168 := (= #17 #165)
+#171 := (forall (vars (?v0 Int) (?v1 Int)) #168)
+#220 := (iff #171 #219)
+#217 := (iff #168 #216)
+#214 := (= #165 #213)
+#211 := (= #162 #210)
+#208 := (iff #159 #207)
+#205 := (iff #156 #204)
+#206 := [rewrite]: #205
+#201 := (iff #62 #200)
+#202 := [rewrite]: #201
+#209 := [monotonicity #202 #206]: #208
+#212 := [monotonicity #209]: #211
+#215 := [monotonicity #212]: #214
+#218 := [monotonicity #215]: #217
+#221 := [quant-intro #218]: #220
+#193 := (~ #171 #171)
+#195 := (~ #168 #168)
+#196 := [refl]: #195
+#194 := [nnf-pos #196]: #193
+#65 := (<= 0::Int #14)
+#66 := (not #65)
+#74 := (and #66 #59)
+#77 := (or #62 #74)
+#90 := (if #77 #28 #87)
+#93 := (if #21 0::Int #90)
+#96 := (= #17 #93)
+#99 := (forall (vars (?v0 Int) (?v1 Int)) #96)
+#172 := (iff #99 #171)
+#169 := (iff #96 #168)
+#166 := (= #93 #165)
+#163 := (= #90 #162)
+#160 := (iff #77 #159)
+#157 := (iff #74 #156)
+#154 := (iff #66 #153)
+#151 := (iff #65 #150)
+#152 := [rewrite]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [monotonicity #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [quant-intro #170]: #172
 #30 := (- #16)
 #29 := (- #14)
 #31 := (div #29 #30)
@@ -28064,2217 +27574,259 @@
 #22 := (< 0::Int #14)
 #24 := (and #22 #23)
 #27 := (or #24 #26)
-#32 := (ite #27 #28 #31)
-#33 := (ite #21 0::Int #32)
+#32 := (if #27 #28 #31)
+#33 := (if #21 0::Int #32)
 #34 := (= #17 #33)
 #35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#139 := (iff #35 #136)
-#78 := (and #23 #25)
-#81 := (or #24 #78)
-#94 := (ite #81 #28 #91)
-#97 := (ite #21 0::Int #94)
-#100 := (= #17 #97)
-#103 := (forall (vars (?v0 Int) (?v1 Int)) #100)
-#137 := (iff #103 #136)
-#134 := (iff #100 #133)
-#131 := (= #97 #130)
-#128 := (= #94 #127)
-#125 := (iff #81 #124)
-#122 := (iff #78 #121)
-#119 := (iff #25 #118)
-#120 := [rewrite]: #119
-#112 := (iff #23 #111)
-#113 := [rewrite]: #112
-#123 := [monotonicity #113 #120]: #122
-#115 := (iff #24 #114)
-#108 := (iff #22 #107)
-#109 := [rewrite]: #108
-#116 := [monotonicity #109 #113]: #115
-#126 := [monotonicity #116 #123]: #125
-#129 := [monotonicity #126]: #128
-#132 := [monotonicity #129]: #131
-#135 := [monotonicity #132]: #134
-#138 := [quant-intro #135]: #137
-#104 := (iff #35 #103)
-#101 := (iff #34 #100)
-#98 := (= #33 #97)
-#95 := (= #32 #94)
-#92 := (= #31 #91)
-#89 := (= #30 #88)
-#90 := [rewrite]: #89
-#86 := (= #29 #85)
-#87 := [rewrite]: #86
-#93 := [monotonicity #87 #90]: #92
-#82 := (iff #27 #81)
-#79 := (iff #26 #78)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#96 := [monotonicity #83 #93]: #95
-#99 := [monotonicity #96]: #98
-#102 := [monotonicity #99]: #101
-#105 := [quant-intro #102]: #104
-#140 := [trans #105 #138]: #139
-#77 := [asserted]: #35
-#141 := [mp #77 #140]: #136
-#190 := [mp~ #141 #199]: #136
-#221 := [mp #190 #220]: #218
-#252 := [mp #221 #251]: #249
-#745 := [mp #252 #744]: #740
-#9 := 1::Int
-#10 := (f4 f5 1::Int)
-#11 := (f3 #10 1::Int)
-#12 := (= #11 1::Int)
-#13 := (not #12)
-#66 := [asserted]: #13
-#576 := (not #740)
-#577 := (or #576 #12)
-#326 := (* -1::Int 1::Int)
-#410 := (div #326 #326)
-#411 := (* -1::Int #410)
-#412 := (+ #11 #411)
-#403 := (= #412 0::Int)
-#414 := (div 1::Int 1::Int)
-#415 := (* -1::Int #414)
-#416 := (+ #11 #415)
-#413 := (= #416 0::Int)
-#417 := (>= 1::Int 0::Int)
-#396 := (<= 1::Int 0::Int)
-#731 := (or #396 #417)
-#733 := (not #731)
-#390 := (or #396 #396)
-#520 := (not #390)
-#727 := (or #520 #733)
-#401 := (ite #727 #413 #403)
-#402 := (= #11 0::Int)
-#734 := (= 1::Int 0::Int)
-#735 := (or #734 #734)
-#736 := (ite #735 #402 #401)
-#578 := (or #576 #736)
-#580 := (iff #578 #577)
-#670 := (iff #577 #577)
-#674 := [rewrite]: #670
-#575 := (iff #736 #12)
-#669 := (ite false #402 #12)
-#572 := (iff #669 #12)
-#574 := [rewrite]: #572
-#672 := (iff #736 #669)
-#573 := (iff #401 #12)
-#1 := true
-#562 := (ite true #12 #12)
-#523 := (iff #562 #12)
-#671 := [rewrite]: #523
-#563 := (iff #401 #562)
-#677 := (iff #403 #12)
-#694 := (+ -1::Int #11)
-#697 := (= #694 0::Int)
-#699 := (iff #697 #12)
-#540 := [rewrite]: #699
-#678 := (iff #403 #697)
-#675 := (= #412 #694)
-#704 := (+ #11 -1::Int)
-#695 := (= #704 #694)
-#696 := [rewrite]: #695
-#521 := (= #412 #704)
-#690 := (= #411 -1::Int)
-#702 := (= #326 -1::Int)
-#703 := [rewrite]: #702
-#689 := (= #411 #326)
-#682 := (= #410 1::Int)
-#684 := (div -1::Int -1::Int)
-#687 := (= #684 1::Int)
-#681 := [rewrite]: #687
-#685 := (= #410 #684)
-#686 := [monotonicity #703 #703]: #685
-#688 := [trans #686 #681]: #682
-#683 := [monotonicity #688]: #689
-#519 := [trans #683 #703]: #690
-#522 := [monotonicity #519]: #521
-#676 := [trans #522 #696]: #675
-#679 := [monotonicity #676]: #678
-#680 := [trans #679 #540]: #677
-#541 := (iff #413 #12)
-#698 := (iff #413 #697)
-#691 := (= #416 #694)
-#701 := (= #416 #704)
-#418 := (= #415 -1::Int)
-#423 := (= #415 #326)
-#421 := (= #414 1::Int)
-#422 := [rewrite]: #421
-#424 := [monotonicity #422]: #423
-#700 := [trans #424 #703]: #418
-#705 := [monotonicity #700]: #701
-#692 := [trans #705 #696]: #691
-#693 := [monotonicity #692]: #698
-#542 := [trans #693 #540]: #541
-#707 := (iff #727 true)
-#709 := (or true false)
-#706 := (iff #709 true)
-#710 := [rewrite]: #706
-#431 := (iff #727 #709)
-#332 := (iff #733 false)
-#713 := (not true)
-#437 := (iff #713 false)
-#438 := [rewrite]: #437
-#435 := (iff #733 #713)
-#726 := (iff #731 true)
-#724 := (or false true)
-#725 := (iff #724 true)
-#723 := [rewrite]: #725
-#364 := (iff #731 #724)
-#359 := (iff #417 true)
-#722 := [rewrite]: #359
-#373 := (iff #396 false)
-#714 := [rewrite]: #373
-#365 := [monotonicity #714 #722]: #364
-#712 := [trans #365 #723]: #726
-#436 := [monotonicity #712]: #435
-#708 := [trans #436 #438]: #332
-#715 := (iff #520 true)
-#716 := (not false)
-#719 := (iff #716 true)
-#720 := [rewrite]: #719
-#717 := (iff #520 #716)
-#379 := (iff #390 false)
-#738 := (or false false)
-#393 := (iff #738 false)
-#729 := [rewrite]: #393
-#377 := (iff #390 #738)
-#378 := [monotonicity #714 #714]: #377
-#380 := [trans #378 #729]: #379
-#718 := [monotonicity #380]: #717
-#721 := [trans #718 #720]: #715
-#432 := [monotonicity #721 #708]: #431
-#711 := [trans #432 #710]: #707
-#564 := [monotonicity #711 #542 #680]: #563
-#668 := [trans #564 #671]: #573
-#389 := (iff #735 false)
-#728 := (iff #735 #738)
-#737 := (iff #734 false)
-#732 := [rewrite]: #737
-#388 := [monotonicity #732 #732]: #728
-#730 := [trans #388 #729]: #389
-#557 := [monotonicity #730 #668]: #672
-#568 := [trans #557 #574]: #575
-#673 := [monotonicity #568]: #580
-#661 := [trans #673 #674]: #580
-#579 := [quant-inst #9 #9]: #578
-#663 := [mp #579 #661]: #577
-[unit-resolution #663 #66 #745]: false
-unsat
-9e2cb4354c0a45ed596c8dff93f29dc26a938b99 295 0
+#100 := (iff #35 #99)
+#97 := (iff #34 #96)
+#94 := (= #33 #93)
+#91 := (= #32 #90)
+#88 := (= #31 #87)
+#85 := (= #30 #84)
+#86 := [rewrite]: #85
+#82 := (= #29 #81)
+#83 := [rewrite]: #82
+#89 := [monotonicity #83 #86]: #88
+#78 := (iff #27 #77)
+#75 := (iff #26 #74)
+#60 := (iff #23 #59)
+#61 := [rewrite]: #60
+#67 := (iff #25 #66)
+#71 := (iff #66 #66)
+#69 := (iff #65 #65)
+#70 := [rewrite]: #69
+#72 := [monotonicity #70]: #71
+#68 := [rewrite]: #67
+#73 := [trans #68 #72]: #67
+#76 := [monotonicity #73 #61]: #75
+#63 := (iff #24 #62)
+#56 := (iff #22 #55)
+#57 := [rewrite]: #56
+#64 := [monotonicity #57 #61]: #63
+#79 := [monotonicity #64 #76]: #78
+#92 := [monotonicity #79 #89]: #91
+#95 := [monotonicity #92]: #94
+#98 := [monotonicity #95]: #97
+#101 := [quant-intro #98]: #100
+#49 := [asserted]: #35
+#102 := [mp #49 #101]: #99
+#174 := [mp #102 #173]: #171
+#148 := [mp~ #174 #194]: #171
+#222 := [mp #148 #221]: #219
+#253 := [mp #222 #252]: #250
+#689 := [mp #253 #688]: #684
+#639 := (not #684)
+#640 := (or #639 #645)
+#346 := (* -1::Int 1::Int)
+#678 := (div #345 #346)
+#679 := (* -1::Int #678)
+#680 := (+ #11 #679)
+#681 := (= #680 0::Int)
+#358 := (<= 1::Int 0::Int)
+#361 := (or #357 #358)
+#340 := (not #361)
+#359 := (or #347 #358)
+#360 := (not #359)
+#675 := (or #360 #340)
+#676 := (if #675 #671 #681)
+#354 := (= 1::Int 0::Int)
+#355 := (or #270 #354)
+#682 := (if #355 #356 #676)
+#635 := (or #639 #682)
+#641 := (iff #635 #640)
+#637 := (iff #640 #640)
+#643 := [rewrite]: #637
+#649 := (iff #682 #645)
+#644 := (iff #676 #362)
+#646 := (iff #681 #368)
+#366 := (= #680 #365)
+#651 := (= #679 #654)
+#376 := (= #678 #375)
+#652 := (= #346 -1::Int)
+#653 := [rewrite]: #652
+#650 := [monotonicity #653]: #376
+#655 := [monotonicity #650]: #651
+#367 := [monotonicity #655]: #366
+#647 := [monotonicity #367]: #646
+#382 := (iff #675 #381)
+#379 := (iff #340 #657)
+#670 := (iff #361 #357)
+#668 := (or #357 false)
+#669 := (iff #668 #357)
+#667 := [rewrite]: #669
+#308 := (iff #361 #668)
+#322 := (iff #358 false)
+#323 := [rewrite]: #322
+#309 := [monotonicity #323]: #308
+#656 := [trans #309 #667]: #670
+#380 := [monotonicity #656]: #379
+#303 := (iff #360 #665)
+#664 := (iff #359 #347)
+#324 := (or #347 false)
+#662 := (iff #324 #347)
+#663 := [rewrite]: #662
+#660 := (iff #359 #324)
+#661 := [monotonicity #323]: #660
+#659 := [trans #661 #663]: #664
+#666 := [monotonicity #659]: #303
+#276 := [monotonicity #666 #380]: #382
+#648 := [monotonicity #276 #647]: #644
+#658 := (iff #355 #270)
+#337 := (or #270 false)
+#674 := (iff #337 #270)
+#317 := [rewrite]: #674
+#673 := (iff #355 #337)
+#672 := (iff #354 false)
+#332 := [rewrite]: #672
+#333 := [monotonicity #332]: #673
+#321 := [trans #333 #317]: #658
+#638 := [monotonicity #321 #648]: #649
+#642 := [monotonicity #638]: #641
+#484 := [trans #642 #643]: #641
+#636 := [quant-inst #8 #10]: #635
+#485 := [mp #636 #484]: #640
+#597 := [unit-resolution #485 #689]: #645
+#615 := (not #645)
+#616 := (or #615 #270 #362)
+#501 := [def-axiom]: #616
+#602 := [unit-resolution #501 #597]: #601
+#603 := [unit-resolution #602 #607]: #362
+#609 := (or #381 #270)
+#631 := (not #381)
+#614 := [hypothesis]: #631
+#486 := (or #381 #347)
+#628 := [def-axiom]: #486
+#618 := [unit-resolution #628 #614]: #347
+#629 := (or #381 #357)
+#630 := [def-axiom]: #629
+#605 := [unit-resolution #630 #614]: #357
+#599 := (or #270 #665 #657)
+#596 := [th-lemma arith triangle-eq]: #599
+#598 := [unit-resolution #596 #607]: #381
+#608 := [unit-resolution #598 #605 #618]: false
+#610 := [lemma #608]: #609
+#575 := [unit-resolution #610 #607]: #381
+#466 := (not #362)
+#619 := (or #466 #631 #671)
+#620 := [def-axiom]: #619
+#576 := [unit-resolution #620 #575 #603 #510]: false
+#577 := [lemma #576]: #270
+#588 := [symm #577]: #580
+#593 := [monotonicity #588]: #589
+#590 := [symm #593]: #594
+#581 := [monotonicity #590]: #595
+#582 := [mp #48 #581]: #516
+#578 := (or #517 #356)
+#612 := (or #615 #517 #356)
+#613 := [def-axiom]: #612
+#579 := [unit-resolution #613 #597]: #578
+#569 := [unit-resolution #579 #577]: #356
+[unit-resolution #569 #582]: false
+54eadbdaf5a8d862c94033c6a936caca8195fd89 304 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #17 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #15 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
-#16 := (f4 f5 #15)
-#18 := (f3 #16 #17)
-#740 := (pattern #18)
-#19 := 0::Int
-#85 := -1::Int
-#89 := (* -1::Int #17)
-#86 := (* -1::Int #15)
-#92 := (div #86 #89)
-#243 := (* -1::Int #92)
-#244 := (+ #18 #243)
-#245 := (= #244 0::Int)
-#29 := (div #15 #17)
-#240 := (* -1::Int #29)
-#241 := (+ #18 #240)
-#242 := (= #241 0::Int)
-#118 := (>= #15 0::Int)
-#111 := (<= #17 0::Int)
-#203 := (or #111 #118)
-#204 := (not #203)
-#107 := (<= #15 0::Int)
-#201 := (or #107 #111)
-#202 := (not #201)
-#207 := (or #202 #204)
-#246 := (ite #207 #242 #245)
-#239 := (= #18 0::Int)
-#21 := (= #17 0::Int)
-#20 := (= #15 0::Int)
-#22 := (or #20 #21)
-#247 := (ite #22 #239 #246)
-#741 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #740) #247)
-#250 := (forall (vars (?v0 Int) (?v1 Int)) #247)
-#744 := (iff #250 #741)
-#742 := (iff #247 #247)
-#743 := [refl]: #742
-#745 := [quant-intro #743]: #744
-#210 := (ite #207 #29 #92)
-#213 := (ite #22 0::Int #210)
-#216 := (= #18 #213)
-#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
-#251 := (iff #219 #250)
-#248 := (iff #216 #247)
-#249 := [rewrite]: #248
-#252 := [quant-intro #249]: #251
-#119 := (not #118)
-#112 := (not #111)
-#122 := (and #112 #119)
-#108 := (not #107)
-#115 := (and #108 #112)
-#125 := (or #115 #122)
-#128 := (ite #125 #29 #92)
-#131 := (ite #22 0::Int #128)
-#134 := (= #18 #131)
-#137 := (forall (vars (?v0 Int) (?v1 Int)) #134)
-#220 := (iff #137 #219)
-#217 := (iff #134 #216)
-#214 := (= #131 #213)
-#211 := (= #128 #210)
-#208 := (iff #125 #207)
-#205 := (iff #122 #204)
-#206 := [rewrite]: #205
-#195 := (iff #115 #202)
-#196 := [rewrite]: #195
-#209 := [monotonicity #196 #206]: #208
-#212 := [monotonicity #209]: #211
-#215 := [monotonicity #212]: #214
-#218 := [monotonicity #215]: #217
-#221 := [quant-intro #218]: #220
-#199 := (~ #137 #137)
-#197 := (~ #134 #134)
-#198 := [refl]: #197
-#200 := [nnf-pos #198]: #199
-#31 := (- #17)
-#30 := (- #15)
-#32 := (div #30 #31)
-#24 := (< 0::Int #17)
-#26 := (< #15 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #15)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#33 := (ite #28 #29 #32)
-#34 := (ite #22 0::Int #33)
-#35 := (= #18 #34)
-#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
-#140 := (iff #36 #137)
-#79 := (and #24 #26)
-#82 := (or #25 #79)
-#95 := (ite #82 #29 #92)
-#98 := (ite #22 0::Int #95)
-#101 := (= #18 #98)
-#104 := (forall (vars (?v0 Int) (?v1 Int)) #101)
-#138 := (iff #104 #137)
-#135 := (iff #101 #134)
-#132 := (= #98 #131)
-#129 := (= #95 #128)
-#126 := (iff #82 #125)
-#123 := (iff #79 #122)
-#120 := (iff #26 #119)
-#121 := [rewrite]: #120
-#113 := (iff #24 #112)
-#114 := [rewrite]: #113
-#124 := [monotonicity #114 #121]: #123
-#116 := (iff #25 #115)
-#109 := (iff #23 #108)
-#110 := [rewrite]: #109
-#117 := [monotonicity #110 #114]: #116
-#127 := [monotonicity #117 #124]: #126
-#130 := [monotonicity #127]: #129
-#133 := [monotonicity #130]: #132
-#136 := [monotonicity #133]: #135
-#139 := [quant-intro #136]: #138
-#105 := (iff #36 #104)
-#102 := (iff #35 #101)
-#99 := (= #34 #98)
-#96 := (= #33 #95)
-#93 := (= #32 #92)
-#90 := (= #31 #89)
-#91 := [rewrite]: #90
-#87 := (= #30 #86)
-#88 := [rewrite]: #87
-#94 := [monotonicity #88 #91]: #93
-#83 := (iff #28 #82)
-#80 := (iff #27 #79)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#97 := [monotonicity #84 #94]: #96
-#100 := [monotonicity #97]: #99
-#103 := [monotonicity #100]: #102
-#106 := [quant-intro #103]: #105
-#141 := [trans #106 #139]: #140
-#78 := [asserted]: #36
-#142 := [mp #78 #141]: #137
-#191 := [mp~ #142 #200]: #137
-#222 := [mp #191 #221]: #219
-#253 := [mp #222 #252]: #250
-#746 := [mp #253 #745]: #741
-#9 := 3::Int
-#11 := 1::Int
-#10 := (f4 f5 3::Int)
-#12 := (f3 #10 1::Int)
-#13 := (= #12 3::Int)
-#14 := (not #13)
-#67 := [asserted]: #14
-#656 := (not #741)
-#653 := (or #656 #13)
-#327 := (* -1::Int 1::Int)
-#411 := (* -1::Int 3::Int)
-#412 := (div #411 #327)
-#413 := (* -1::Int #412)
-#404 := (+ #12 #413)
-#415 := (= #404 0::Int)
-#416 := (div 3::Int 1::Int)
-#417 := (* -1::Int #416)
-#414 := (+ #12 #417)
-#418 := (= #414 0::Int)
-#397 := (>= 3::Int 0::Int)
-#732 := (<= 1::Int 0::Int)
-#734 := (or #732 #397)
-#391 := (not #734)
-#521 := (<= 3::Int 0::Int)
-#728 := (or #521 #732)
-#402 := (not #728)
-#403 := (or #402 #391)
-#735 := (ite #403 #418 #415)
-#736 := (= #12 0::Int)
-#737 := (= 1::Int 0::Int)
-#738 := (= 3::Int 0::Int)
-#733 := (or #738 #737)
-#739 := (ite #733 #736 #735)
-#655 := (or #656 #739)
-#666 := (iff #655 #653)
-#663 := (iff #653 #653)
-#668 := [rewrite]: #663
-#662 := (iff #739 #13)
-#580 := (ite false #736 #13)
-#671 := (iff #580 #13)
-#675 := [rewrite]: #671
-#581 := (iff #739 #580)
-#578 := (iff #735 #13)
-#1 := true
-#573 := (ite true #13 #13)
-#569 := (iff #573 #13)
-#577 := [rewrite]: #569
-#575 := (iff #735 #573)
-#673 := (iff #415 #13)
-#695 := -3::Int
-#700 := (+ -3::Int #12)
-#686 := (= #700 0::Int)
-#682 := (iff #686 #13)
-#683 := [rewrite]: #682
-#669 := (iff #415 #686)
-#672 := (= #404 #700)
-#698 := (+ #12 -3::Int)
-#541 := (= #698 #700)
-#542 := [rewrite]: #541
-#565 := (= #404 #698)
-#563 := (= #413 -3::Int)
-#696 := (= #411 -3::Int)
-#697 := [rewrite]: #696
-#678 := (= #413 #411)
-#679 := (= #412 3::Int)
-#520 := (div -3::Int -1::Int)
-#676 := (= #520 3::Int)
-#677 := [rewrite]: #676
-#522 := (= #412 #520)
-#684 := (= #327 -1::Int)
-#691 := [rewrite]: #684
-#523 := [monotonicity #697 #691]: #522
-#680 := [trans #523 #677]: #679
-#681 := [monotonicity #680]: #678
-#564 := [trans #681 #697]: #563
-#524 := [monotonicity #564]: #565
-#574 := [trans #524 #542]: #672
-#670 := [monotonicity #574]: #669
-#558 := [trans #670 #683]: #673
-#689 := (iff #418 #13)
-#687 := (iff #418 #686)
-#543 := (= #414 #700)
-#699 := (= #414 #698)
-#692 := (= #417 -3::Int)
-#702 := (= #417 #411)
-#701 := (= #416 3::Int)
-#705 := [rewrite]: #701
-#706 := [monotonicity #705]: #702
-#693 := [trans #706 #697]: #692
-#694 := [monotonicity #693]: #699
-#685 := [trans #694 #542]: #543
-#688 := [monotonicity #685]: #687
-#690 := [trans #688 #683]: #689
-#704 := (iff #403 true)
-#422 := (or true false)
-#425 := (iff #422 true)
-#703 := [rewrite]: #425
-#423 := (iff #403 #422)
-#708 := (iff #391 false)
-#710 := (not true)
-#707 := (iff #710 false)
-#711 := [rewrite]: #707
-#432 := (iff #391 #710)
-#333 := (iff #734 true)
-#714 := (or false true)
-#438 := (iff #714 true)
-#439 := [rewrite]: #438
-#436 := (iff #734 #714)
-#727 := (iff #397 true)
-#713 := [rewrite]: #727
-#718 := (iff #732 false)
-#719 := [rewrite]: #718
-#437 := [monotonicity #719 #713]: #436
-#709 := [trans #437 #439]: #333
-#433 := [monotonicity #709]: #432
-#712 := [trans #433 #711]: #708
-#726 := (iff #402 true)
-#360 := (not false)
-#365 := (iff #360 true)
-#366 := [rewrite]: #365
-#723 := (iff #402 #360)
-#716 := (iff #728 false)
-#390 := (or false false)
-#715 := (iff #390 false)
-#378 := [rewrite]: #715
-#720 := (iff #728 #390)
-#381 := (iff #521 false)
-#717 := [rewrite]: #381
-#721 := [monotonicity #717 #719]: #720
-#722 := [trans #721 #378]: #716
-#725 := [monotonicity #722]: #723
-#724 := [trans #725 #366]: #726
-#424 := [monotonicity #724 #712]: #423
-#419 := [trans #424 #703]: #704
-#576 := [monotonicity #419 #690 #558]: #575
-#579 := [trans #576 #577]: #578
-#379 := (iff #733 false)
-#731 := (iff #733 #390)
-#394 := (iff #737 false)
-#730 := [rewrite]: #394
-#729 := (iff #738 false)
-#389 := [rewrite]: #729
-#374 := [monotonicity #389 #730]: #731
-#380 := [trans #374 #378]: #379
-#674 := [monotonicity #380 #579]: #581
-#664 := [trans #674 #675]: #662
-#667 := [monotonicity #664]: #666
-#657 := [trans #667 #668]: #666
-#665 := [quant-inst #9 #11]: #655
-#658 := [mp #665 #657]: #653
-[unit-resolution #658 #67 #746]: false
-unsat
-4f67493d1061e5182b09035995903ba8d555fcbc 332 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#11 := 1::Int
-decl f4 :: (-> S3 Int S2)
-decl f6 :: Int
-#9 := f6
-decl f5 :: S3
-#8 := f5
-#10 := (f4 f5 f6)
-#12 := (f3 #10 1::Int)
-#68 := (= f6 #12)
-#19 := 0::Int
-#733 := (= #12 0::Int)
-#548 := (iff #733 #68)
-#546 := (iff #68 #733)
-#541 := (= 0::Int #12)
-#544 := (iff #541 #733)
-#545 := [commutativity]: #544
-#542 := (iff #68 #541)
-#735 := (= f6 0::Int)
-#413 := (div f6 1::Int)
-#82 := -1::Int
-#414 := (* -1::Int #413)
-#411 := (+ #12 #414)
-#415 := (= #411 0::Int)
-#521 := (not #415)
-#557 := (= #413 #12)
-#595 := (= #12 #413)
-#520 := (<= #411 0::Int)
-#479 := [hypothesis]: #415
-#590 := (or #521 #520)
-#591 := [th-lemma arith triangle-eq]: #590
-#592 := [unit-resolution #591 #479]: #520
-#673 := (>= #411 0::Int)
-#597 := (or #521 #673)
-#593 := [th-lemma arith triangle-eq]: #597
-#594 := [unit-resolution #593 #479]: #673
-#598 := [th-lemma arith eq-propagate 1 1 #594 #592]: #595
-#564 := [symm #598]: #557
-#583 := (= f6 #413)
-#626 := (+ f6 #414)
-#631 := (<= #626 0::Int)
-#625 := (= #626 0::Int)
-#1 := true
-#65 := [true-axiom]: true
-#599 := (or false #625)
-#600 := [th-lemma arith]: #599
-#596 := [unit-resolution #600 #65]: #625
-#601 := (not #625)
-#581 := (or #601 #631)
-#527 := [th-lemma arith triangle-eq]: #581
-#582 := [unit-resolution #527 #596]: #631
-#632 := (>= #626 0::Int)
-#563 := (or #601 #632)
-#587 := [th-lemma arith triangle-eq]: #563
-#588 := [unit-resolution #587 #596]: #632
-#589 := [th-lemma arith eq-propagate 1 1 #588 #582]: #583
-#523 := [trans #589 #564]: #68
-#71 := (not #68)
-#13 := (= #12 f6)
-#14 := (not #13)
-#72 := (iff #14 #71)
-#69 := (iff #13 #68)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#67 := [asserted]: #14
-#76 := [mp #67 #73]: #71
-#554 := [unit-resolution #76 #523]: false
-#556 := [lemma #554]: #521
-#408 := (* -1::Int f6)
-#709 := (div #408 -1::Int)
-#421 := (* -1::Int #709)
-#701 := (+ #12 #421)
-#702 := (= #701 0::Int)
-#518 := (<= f6 0::Int)
-#719 := (not #518)
-#394 := (>= f6 0::Int)
-#711 := (not #394)
-#706 := (or #711 #719)
-#692 := (ite #706 #415 #702)
-#570 := (not #735)
-#662 := [hypothesis]: #570
-#565 := (or #735 #692)
-#689 := (ite #735 #733 #692)
-#17 := (:var 0 Int)
-#15 := (:var 1 Int)
-#16 := (f4 f5 #15)
-#18 := (f3 #16 #17)
-#737 := (pattern #18)
-#86 := (* -1::Int #17)
-#83 := (* -1::Int #15)
-#89 := (div #83 #86)
-#240 := (* -1::Int #89)
-#241 := (+ #18 #240)
-#242 := (= #241 0::Int)
-#29 := (div #15 #17)
-#237 := (* -1::Int #29)
-#238 := (+ #18 #237)
-#239 := (= #238 0::Int)
-#115 := (>= #15 0::Int)
-#108 := (<= #17 0::Int)
-#200 := (or #108 #115)
-#201 := (not #200)
-#104 := (<= #15 0::Int)
-#198 := (or #104 #108)
-#199 := (not #198)
-#204 := (or #199 #201)
-#243 := (ite #204 #239 #242)
-#236 := (= #18 0::Int)
-#21 := (= #17 0::Int)
-#20 := (= #15 0::Int)
-#22 := (or #20 #21)
-#244 := (ite #22 #236 #243)
-#738 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #737) #244)
-#247 := (forall (vars (?v0 Int) (?v1 Int)) #244)
-#741 := (iff #247 #738)
-#739 := (iff #244 #244)
-#740 := [refl]: #739
-#742 := [quant-intro #740]: #741
-#207 := (ite #204 #29 #89)
-#210 := (ite #22 0::Int #207)
-#213 := (= #18 #210)
-#216 := (forall (vars (?v0 Int) (?v1 Int)) #213)
-#248 := (iff #216 #247)
-#245 := (iff #213 #244)
-#246 := [rewrite]: #245
-#249 := [quant-intro #246]: #248
-#116 := (not #115)
-#109 := (not #108)
-#119 := (and #109 #116)
-#105 := (not #104)
-#112 := (and #105 #109)
-#122 := (or #112 #119)
-#125 := (ite #122 #29 #89)
-#128 := (ite #22 0::Int #125)
-#131 := (= #18 #128)
-#134 := (forall (vars (?v0 Int) (?v1 Int)) #131)
-#217 := (iff #134 #216)
-#214 := (iff #131 #213)
-#211 := (= #128 #210)
-#208 := (= #125 #207)
-#205 := (iff #122 #204)
-#202 := (iff #119 #201)
-#203 := [rewrite]: #202
-#192 := (iff #112 #199)
-#193 := [rewrite]: #192
-#206 := [monotonicity #193 #203]: #205
-#209 := [monotonicity #206]: #208
-#212 := [monotonicity #209]: #211
-#215 := [monotonicity #212]: #214
-#218 := [quant-intro #215]: #217
-#196 := (~ #134 #134)
-#194 := (~ #131 #131)
-#195 := [refl]: #194
-#197 := [nnf-pos #195]: #196
-#31 := (- #17)
-#30 := (- #15)
-#32 := (div #30 #31)
-#24 := (< 0::Int #17)
-#26 := (< #15 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #15)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#33 := (ite #28 #29 #32)
-#34 := (ite #22 0::Int #33)
-#35 := (= #18 #34)
-#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
-#137 := (iff #36 #134)
-#75 := (and #24 #26)
-#79 := (or #25 #75)
-#92 := (ite #79 #29 #89)
-#95 := (ite #22 0::Int #92)
-#98 := (= #18 #95)
-#101 := (forall (vars (?v0 Int) (?v1 Int)) #98)
-#135 := (iff #101 #134)
-#132 := (iff #98 #131)
-#129 := (= #95 #128)
-#126 := (= #92 #125)
-#123 := (iff #79 #122)
-#120 := (iff #75 #119)
-#117 := (iff #26 #116)
-#118 := [rewrite]: #117
-#110 := (iff #24 #109)
-#111 := [rewrite]: #110
-#121 := [monotonicity #111 #118]: #120
-#113 := (iff #25 #112)
-#106 := (iff #23 #105)
-#107 := [rewrite]: #106
-#114 := [monotonicity #107 #111]: #113
-#124 := [monotonicity #114 #121]: #123
-#127 := [monotonicity #124]: #126
-#130 := [monotonicity #127]: #129
-#133 := [monotonicity #130]: #132
-#136 := [quant-intro #133]: #135
-#102 := (iff #36 #101)
-#99 := (iff #35 #98)
-#96 := (= #34 #95)
-#93 := (= #33 #92)
-#90 := (= #32 #89)
-#87 := (= #31 #86)
-#88 := [rewrite]: #87
-#84 := (= #30 #83)
-#85 := [rewrite]: #84
-#91 := [monotonicity #85 #88]: #90
-#80 := (iff #28 #79)
-#77 := (iff #27 #75)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#94 := [monotonicity #81 #91]: #93
-#97 := [monotonicity #94]: #96
-#100 := [monotonicity #97]: #99
-#103 := [quant-intro #100]: #102
-#138 := [trans #103 #136]: #137
-#74 := [asserted]: #36
-#139 := [mp #74 #138]: #134
-#188 := [mp~ #139 #197]: #134
-#219 := [mp #188 #218]: #216
-#250 := [mp #219 #249]: #247
-#743 := [mp #250 #742]: #738
-#696 := (not #738)
-#691 := (or #696 #689)
-#324 := (* -1::Int 1::Int)
-#409 := (div #408 #324)
-#410 := (* -1::Int #409)
-#401 := (+ #12 #410)
-#412 := (= #401 0::Int)
-#729 := (<= 1::Int 0::Int)
-#731 := (or #729 #394)
-#388 := (not #731)
-#725 := (or #518 #729)
-#399 := (not #725)
-#400 := (or #399 #388)
-#732 := (ite #400 #415 #412)
-#734 := (= 1::Int 0::Int)
-#730 := (or #735 #734)
-#736 := (ite #730 #733 #732)
-#697 := (or #696 #736)
-#539 := (iff #697 #691)
-#682 := (iff #691 #691)
-#683 := [rewrite]: #682
-#690 := (iff #736 #689)
-#693 := (iff #732 #692)
-#699 := (iff #412 #702)
-#416 := (= #401 #701)
-#422 := (= #410 #421)
-#419 := (= #409 #709)
-#708 := (= #324 -1::Int)
-#705 := [rewrite]: #708
-#420 := [monotonicity #705]: #419
-#700 := [monotonicity #420]: #422
-#698 := [monotonicity #700]: #416
-#703 := [monotonicity #698]: #699
-#430 := (iff #400 #706)
-#435 := (or #719 #711)
-#707 := (iff #435 #706)
-#429 := [rewrite]: #707
-#436 := (iff #400 #435)
-#433 := (iff #388 #711)
-#724 := (iff #731 #394)
-#722 := (or false #394)
-#723 := (iff #722 #394)
-#721 := [rewrite]: #723
-#362 := (iff #731 #722)
-#376 := (iff #729 false)
-#377 := [rewrite]: #376
-#363 := [monotonicity #377]: #362
-#710 := [trans #363 #721]: #724
-#434 := [monotonicity #710]: #433
-#357 := (iff #399 #719)
-#718 := (iff #725 #518)
-#378 := (or #518 false)
-#716 := (iff #378 #518)
-#717 := [rewrite]: #716
-#714 := (iff #725 #378)
-#715 := [monotonicity #377]: #714
-#713 := [trans #715 #717]: #718
-#720 := [monotonicity #713]: #357
-#330 := [monotonicity #720 #434]: #436
-#704 := [trans #330 #429]: #430
-#694 := [monotonicity #704 #703]: #693
-#712 := (iff #730 #735)
-#391 := (or #735 false)
-#728 := (iff #391 #735)
-#371 := [rewrite]: #728
-#727 := (iff #730 #391)
-#726 := (iff #734 false)
-#386 := [rewrite]: #726
-#387 := [monotonicity #386]: #727
-#375 := [trans #387 #371]: #712
-#695 := [monotonicity #375 #694]: #690
-#540 := [monotonicity #695]: #539
-#684 := [trans #540 #683]: #539
-#538 := [quant-inst #9 #11]: #697
-#685 := [mp #538 #684]: #691
-#558 := [unit-resolution #685 #743]: #689
-#555 := (not #689)
-#566 := (or #555 #735 #692)
-#574 := [def-axiom]: #566
-#567 := [unit-resolution #574 #558]: #565
-#568 := [unit-resolution #567 #662]: #692
-#654 := (or #706 #735)
-#681 := (not #706)
-#653 := [hypothesis]: #681
-#679 := (or #706 #394)
-#680 := [def-axiom]: #679
-#650 := [unit-resolution #680 #653]: #394
-#686 := (or #706 #518)
-#687 := [def-axiom]: #686
-#652 := [unit-resolution #687 #653]: #518
-#663 := (or #735 #719 #711)
-#664 := [th-lemma arith triangle-eq]: #663
-#660 := [unit-resolution #664 #662]: #435
-#665 := [unit-resolution #660 #652 #650]: false
-#655 := [lemma #665]: #654
-#569 := [unit-resolution #655 #662]: #706
-#675 := (not #692)
-#678 := (or #675 #681 #415)
-#560 := [def-axiom]: #678
-#579 := [unit-resolution #560 #569 #568 #556]: false
-#559 := [lemma #579]: #735
-#543 := [monotonicity #559]: #542
-#547 := [trans #543 #545]: #546
-#549 := [symm #547]: #548
-#580 := (or #570 #733)
-#572 := (or #555 #570 #733)
-#573 := [def-axiom]: #572
-#535 := [unit-resolution #573 #558]: #580
-#536 := [unit-resolution #535 #559]: #733
-#550 := [mp #536 #549]: #68
-[unit-resolution #76 #550]: false
-unsat
-e29ee22242a3ef560671b54d7d6c2b7f016db198 321 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#17 := (f4 f5 #16)
-#19 := (f3 #17 #18)
-#769 := (pattern #19)
-#9 := 0::Int
-#68 := -1::Int
-#112 := (* -1::Int #18)
-#109 := (* -1::Int #16)
-#115 := (div #109 #112)
-#272 := (* -1::Int #115)
-#273 := (+ #19 #272)
-#274 := (= #273 0::Int)
-#29 := (div #16 #18)
-#269 := (* -1::Int #29)
-#270 := (+ #19 #269)
-#271 := (= #270 0::Int)
-#147 := (>= #16 0::Int)
-#140 := (<= #18 0::Int)
-#232 := (or #140 #147)
-#233 := (not #232)
-#136 := (<= #16 0::Int)
-#230 := (or #136 #140)
-#231 := (not #230)
-#236 := (or #231 #233)
-#275 := (ite #236 #271 #274)
-#268 := (= #19 0::Int)
-#21 := (= #18 0::Int)
-#20 := (= #16 0::Int)
-#22 := (or #20 #21)
-#276 := (ite #22 #268 #275)
-#770 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #769) #276)
-#279 := (forall (vars (?v0 Int) (?v1 Int)) #276)
-#773 := (iff #279 #770)
-#771 := (iff #276 #276)
-#772 := [refl]: #771
-#774 := [quant-intro #772]: #773
-#239 := (ite #236 #29 #115)
-#242 := (ite #22 0::Int #239)
-#245 := (= #19 #242)
-#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
-#280 := (iff #248 #279)
-#277 := (iff #245 #276)
-#278 := [rewrite]: #277
-#281 := [quant-intro #278]: #280
-#148 := (not #147)
-#141 := (not #140)
-#151 := (and #141 #148)
-#137 := (not #136)
-#144 := (and #137 #141)
-#154 := (or #144 #151)
-#157 := (ite #154 #29 #115)
-#160 := (ite #22 0::Int #157)
-#163 := (= #19 #160)
-#166 := (forall (vars (?v0 Int) (?v1 Int)) #163)
-#249 := (iff #166 #248)
-#246 := (iff #163 #245)
-#243 := (= #160 #242)
-#240 := (= #157 #239)
-#237 := (iff #154 #236)
-#234 := (iff #151 #233)
-#235 := [rewrite]: #234
-#224 := (iff #144 #231)
-#225 := [rewrite]: #224
-#238 := [monotonicity #225 #235]: #237
-#241 := [monotonicity #238]: #240
-#244 := [monotonicity #241]: #243
-#247 := [monotonicity #244]: #246
-#250 := [quant-intro #247]: #249
-#228 := (~ #166 #166)
-#226 := (~ #163 #163)
-#227 := [refl]: #226
-#229 := [nnf-pos #227]: #228
-#31 := (- #18)
-#30 := (- #16)
-#32 := (div #30 #31)
-#24 := (< 0::Int #18)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#33 := (ite #28 #29 #32)
-#34 := (ite #22 0::Int #33)
-#35 := (= #19 #34)
-#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
-#169 := (iff #36 #166)
-#103 := (and #24 #26)
-#106 := (or #25 #103)
-#118 := (ite #106 #29 #115)
-#97 := (= 0::Int #18)
-#94 := (= 0::Int #16)
-#100 := (or #94 #97)
-#121 := (ite #100 0::Int #118)
-#124 := (= #19 #121)
-#127 := (forall (vars (?v0 Int) (?v1 Int)) #124)
-#167 := (iff #127 #166)
-#164 := (iff #124 #163)
-#161 := (= #121 #160)
-#158 := (= #118 #157)
-#155 := (iff #106 #154)
-#152 := (iff #103 #151)
-#149 := (iff #26 #148)
-#150 := [rewrite]: #149
-#142 := (iff #24 #141)
-#143 := [rewrite]: #142
-#153 := [monotonicity #143 #150]: #152
-#145 := (iff #25 #144)
-#138 := (iff #23 #137)
-#139 := [rewrite]: #138
-#146 := [monotonicity #139 #143]: #145
-#156 := [monotonicity #146 #153]: #155
-#159 := [monotonicity #156]: #158
-#134 := (iff #100 #22)
-#132 := (iff #97 #21)
-#133 := [rewrite]: #132
-#130 := (iff #94 #20)
-#131 := [rewrite]: #130
-#135 := [monotonicity #131 #133]: #134
-#162 := [monotonicity #135 #159]: #161
-#165 := [monotonicity #162]: #164
-#168 := [quant-intro #165]: #167
-#128 := (iff #36 #127)
-#125 := (iff #35 #124)
-#122 := (= #34 #121)
-#119 := (= #33 #118)
-#116 := (= #32 #115)
-#113 := (= #31 #112)
-#114 := [rewrite]: #113
-#110 := (= #30 #109)
-#111 := [rewrite]: #110
-#117 := [monotonicity #111 #114]: #116
-#107 := (iff #28 #106)
-#104 := (iff #27 #103)
-#105 := [rewrite]: #104
-#108 := [monotonicity #105]: #107
-#120 := [monotonicity #108 #117]: #119
-#101 := (iff #22 #100)
-#98 := (iff #21 #97)
-#99 := [rewrite]: #98
-#95 := (iff #20 #94)
-#96 := [rewrite]: #95
-#102 := [monotonicity #96 #99]: #101
-#123 := [monotonicity #102 #120]: #122
-#126 := [monotonicity #123]: #125
-#129 := [quant-intro #126]: #128
-#170 := [trans #129 #168]: #169
-#93 := [asserted]: #36
-#171 := [mp #93 #170]: #166
-#220 := [mp~ #171 #229]: #166
-#251 := [mp #220 #250]: #248
-#282 := [mp #251 #281]: #279
-#775 := [mp #282 #774]: #770
-#10 := (f4 f5 0::Int)
-#71 := (f3 #10 -1::Int)
-#74 := (= #71 0::Int)
-#87 := (not #74)
-#11 := 1::Int
-#12 := (- 1::Int)
-#13 := (f3 #10 #12)
-#14 := (= #13 0::Int)
-#15 := (not #14)
-#90 := (iff #15 #87)
-#77 := (= 0::Int #71)
-#82 := (not #77)
-#88 := (iff #82 #87)
-#85 := (iff #77 #74)
-#86 := [rewrite]: #85
-#89 := [monotonicity #86]: #88
-#83 := (iff #15 #82)
-#80 := (iff #14 #77)
-#78 := (iff #74 #77)
-#79 := [rewrite]: #78
-#75 := (iff #14 #74)
-#72 := (= #13 #71)
-#69 := (= #12 -1::Int)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73]: #75
-#81 := [trans #76 #79]: #80
-#84 := [monotonicity #81]: #83
-#91 := [trans #84 #89]: #90
-#67 := [asserted]: #15
-#92 := [mp #67 #91]: #87
-#604 := (not #770)
-#605 := (or #604 #74)
-#356 := (* -1::Int -1::Int)
-#440 := (* -1::Int 0::Int)
-#441 := (div #440 #356)
-#442 := (* -1::Int #441)
-#433 := (+ #71 #442)
-#444 := (= #433 0::Int)
-#445 := (div 0::Int -1::Int)
-#446 := (* -1::Int #445)
-#443 := (+ #71 #446)
-#447 := (= #443 0::Int)
-#426 := (>= 0::Int 0::Int)
-#761 := (<= -1::Int 0::Int)
-#763 := (or #761 #426)
-#420 := (not #763)
-#550 := (<= 0::Int 0::Int)
-#757 := (or #550 #761)
-#431 := (not #757)
-#432 := (or #431 #420)
-#764 := (ite #432 #447 #444)
-#765 := (= -1::Int 0::Int)
-#766 := (= 0::Int 0::Int)
-#767 := (or #766 #765)
-#762 := (ite #767 #74 #764)
-#598 := (or #604 #762)
-#607 := (iff #598 #605)
-#609 := (iff #605 #605)
-#610 := [rewrite]: #609
-#587 := (iff #762 #74)
-#1 := true
-#701 := (ite true #74 #74)
-#699 := (iff #701 #74)
-#702 := [rewrite]: #699
-#603 := (iff #762 #701)
-#594 := (iff #764 #74)
-#709 := (ite false #74 #74)
-#592 := (iff #709 #74)
-#593 := [rewrite]: #592
-#707 := (iff #764 #709)
-#706 := (iff #444 #74)
-#552 := (= #433 #71)
-#724 := (+ #71 0::Int)
-#721 := (= #724 #71)
-#722 := [rewrite]: #721
-#549 := (= #433 #724)
-#713 := (= #442 0::Int)
-#730 := (= #440 0::Int)
-#734 := [rewrite]: #730
-#718 := (= #442 #440)
-#711 := (= #441 0::Int)
-#572 := (div 0::Int 1::Int)
-#716 := (= #572 0::Int)
-#717 := [rewrite]: #716
-#714 := (= #441 #572)
-#570 := (= #356 1::Int)
-#571 := [rewrite]: #570
-#715 := [monotonicity #734 #571]: #714
-#712 := [trans #715 #717]: #711
-#719 := [monotonicity #712]: #718
-#720 := [trans #719 #734]: #713
-#551 := [monotonicity #720]: #549
-#705 := [trans #551 #722]: #552
-#708 := [monotonicity #705]: #706
-#723 := (iff #447 #74)
-#727 := (= #443 #71)
-#725 := (= #443 #724)
-#731 := (= #446 0::Int)
-#733 := (= #446 #440)
-#454 := (= #445 0::Int)
-#732 := [rewrite]: #454
-#448 := [monotonicity #732]: #733
-#735 := [trans #448 #734]: #731
-#726 := [monotonicity #735]: #725
-#728 := [trans #726 #722]: #727
-#729 := [monotonicity #728]: #723
-#452 := (iff #432 false)
-#736 := (or false false)
-#741 := (iff #736 false)
-#451 := [rewrite]: #741
-#740 := (iff #432 #736)
-#461 := (iff #420 false)
-#754 := (not true)
-#755 := (iff #754 false)
-#753 := [rewrite]: #755
-#738 := (iff #420 #754)
-#468 := (iff #763 true)
-#748 := (or true true)
-#745 := (iff #748 true)
-#751 := [rewrite]: #745
-#466 := (iff #763 #748)
-#743 := (iff #426 true)
-#465 := [rewrite]: #743
-#746 := (iff #761 true)
-#747 := [rewrite]: #746
-#467 := [monotonicity #747 #465]: #466
-#362 := [trans #467 #751]: #468
-#739 := [monotonicity #362]: #738
-#462 := [trans #739 #753]: #461
-#756 := (iff #431 false)
-#394 := (iff #431 #754)
-#389 := (iff #757 true)
-#749 := (iff #757 #748)
-#409 := (iff #550 true)
-#410 := [rewrite]: #409
-#750 := [monotonicity #410 #747]: #749
-#752 := [trans #750 #751]: #389
-#395 := [monotonicity #752]: #394
-#742 := [trans #395 #753]: #756
-#737 := [monotonicity #742 #462]: #740
-#453 := [trans #737 #451]: #452
-#710 := [monotonicity #453 #729 #708]: #707
-#553 := [trans #710 #593]: #594
-#407 := (iff #767 true)
-#759 := (or true false)
-#403 := (iff #759 true)
-#744 := [rewrite]: #403
-#419 := (iff #767 #759)
-#418 := (iff #765 false)
-#423 := [rewrite]: #418
-#768 := (iff #766 true)
-#758 := [rewrite]: #768
-#760 := [monotonicity #758 #423]: #419
-#408 := [trans #760 #744]: #407
-#698 := [monotonicity #408 #553]: #603
-#602 := [trans #698 #702]: #587
-#608 := [monotonicity #602]: #607
-#703 := [trans #608 #610]: #607
-#606 := [quant-inst #9 #68]: #598
-#700 := [mp #606 #703]: #605
-[unit-resolution #700 #92 #775]: false
-unsat
-cb905c8736ea11d2932b8d278573ed536358edd4 315 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
+#7 := f5
 #16 := (f4 f5 #15)
 #18 := (f3 #16 #17)
-#754 := (pattern #18)
-#19 := 0::Int
-#68 := -1::Int
-#103 := (* -1::Int #17)
-#100 := (* -1::Int #15)
-#106 := (div #100 #103)
-#257 := (* -1::Int #106)
-#258 := (+ #18 #257)
-#259 := (= #258 0::Int)
-#29 := (div #15 #17)
-#254 := (* -1::Int #29)
-#255 := (+ #18 #254)
-#256 := (= #255 0::Int)
-#132 := (>= #15 0::Int)
-#125 := (<= #17 0::Int)
-#217 := (or #125 #132)
-#218 := (not #217)
-#121 := (<= #15 0::Int)
-#215 := (or #121 #125)
-#216 := (not #215)
-#221 := (or #216 #218)
-#260 := (ite #221 #256 #259)
-#253 := (= #18 0::Int)
-#21 := (= #17 0::Int)
-#20 := (= #15 0::Int)
-#22 := (or #20 #21)
-#261 := (ite #22 #253 #260)
-#755 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #754) #261)
-#264 := (forall (vars (?v0 Int) (?v1 Int)) #261)
-#758 := (iff #264 #755)
-#756 := (iff #261 #261)
-#757 := [refl]: #756
-#759 := [quant-intro #757]: #758
-#224 := (ite #221 #29 #106)
-#227 := (ite #22 0::Int #224)
-#230 := (= #18 #227)
-#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
-#265 := (iff #233 #264)
-#262 := (iff #230 #261)
-#263 := [rewrite]: #262
-#266 := [quant-intro #263]: #265
-#133 := (not #132)
-#126 := (not #125)
-#136 := (and #126 #133)
-#122 := (not #121)
-#129 := (and #122 #126)
-#139 := (or #129 #136)
-#142 := (ite #139 #29 #106)
-#145 := (ite #22 0::Int #142)
-#148 := (= #18 #145)
-#151 := (forall (vars (?v0 Int) (?v1 Int)) #148)
-#234 := (iff #151 #233)
-#231 := (iff #148 #230)
-#228 := (= #145 #227)
-#225 := (= #142 #224)
-#222 := (iff #139 #221)
-#219 := (iff #136 #218)
-#220 := [rewrite]: #219
-#209 := (iff #129 #216)
-#210 := [rewrite]: #209
-#223 := [monotonicity #210 #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [monotonicity #229]: #231
-#235 := [quant-intro #232]: #234
-#213 := (~ #151 #151)
-#211 := (~ #148 #148)
-#212 := [refl]: #211
-#214 := [nnf-pos #212]: #213
-#31 := (- #17)
-#30 := (- #15)
-#32 := (div #30 #31)
-#24 := (< 0::Int #17)
-#26 := (< #15 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #15)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#33 := (ite #28 #29 #32)
-#34 := (ite #22 0::Int #33)
-#35 := (= #18 #34)
-#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
-#154 := (iff #36 #151)
-#94 := (and #24 #26)
-#97 := (or #25 #94)
-#109 := (ite #97 #29 #106)
-#112 := (ite #22 0::Int #109)
-#115 := (= #18 #112)
-#118 := (forall (vars (?v0 Int) (?v1 Int)) #115)
-#152 := (iff #118 #151)
-#149 := (iff #115 #148)
-#146 := (= #112 #145)
-#143 := (= #109 #142)
-#140 := (iff #97 #139)
-#137 := (iff #94 #136)
-#134 := (iff #26 #133)
-#135 := [rewrite]: #134
-#127 := (iff #24 #126)
-#128 := [rewrite]: #127
-#138 := [monotonicity #128 #135]: #137
-#130 := (iff #25 #129)
-#123 := (iff #23 #122)
-#124 := [rewrite]: #123
-#131 := [monotonicity #124 #128]: #130
-#141 := [monotonicity #131 #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [monotonicity #147]: #149
-#153 := [quant-intro #150]: #152
-#119 := (iff #36 #118)
-#116 := (iff #35 #115)
-#113 := (= #34 #112)
-#110 := (= #33 #109)
-#107 := (= #32 #106)
-#104 := (= #31 #103)
-#105 := [rewrite]: #104
-#101 := (= #30 #100)
-#102 := [rewrite]: #101
-#108 := [monotonicity #102 #105]: #107
-#98 := (iff #28 #97)
-#95 := (iff #27 #94)
-#96 := [rewrite]: #95
-#99 := [monotonicity #96]: #98
-#111 := [monotonicity #99 #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [quant-intro #117]: #119
-#155 := [trans #120 #153]: #154
-#93 := [asserted]: #36
-#156 := [mp #93 #155]: #151
-#205 := [mp~ #156 #214]: #151
-#236 := [mp #205 #235]: #233
-#267 := [mp #236 #266]: #264
-#760 := [mp #267 #759]: #755
-#9 := 1::Int
-#10 := (f4 f5 1::Int)
-#71 := (f3 #10 -1::Int)
-#74 := (= #71 -1::Int)
-#87 := (not #74)
-#11 := (- 1::Int)
-#12 := (f3 #10 #11)
-#13 := (= #12 #11)
-#14 := (not #13)
-#90 := (iff #14 #87)
-#77 := (= -1::Int #71)
-#82 := (not #77)
-#88 := (iff #82 #87)
-#85 := (iff #77 #74)
-#86 := [rewrite]: #85
-#89 := [monotonicity #86]: #88
-#83 := (iff #14 #82)
-#80 := (iff #13 #77)
-#78 := (iff #74 #77)
-#79 := [rewrite]: #78
-#75 := (iff #13 #74)
-#69 := (= #11 -1::Int)
-#70 := [rewrite]: #69
-#72 := (= #12 #71)
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73 #70]: #75
-#81 := [trans #76 #79]: #80
-#84 := [monotonicity #81]: #83
-#91 := [trans #84 #89]: #90
-#67 := [asserted]: #14
-#92 := [mp #67 #91]: #87
-#685 := (not #755)
-#689 := (or #685 #74)
-#341 := (* -1::Int -1::Int)
-#425 := (* -1::Int 1::Int)
-#426 := (div #425 #341)
-#427 := (* -1::Int #426)
-#418 := (+ #71 #427)
-#429 := (= #418 0::Int)
-#430 := (div 1::Int -1::Int)
-#431 := (* -1::Int #430)
-#428 := (+ #71 #431)
-#432 := (= #428 0::Int)
-#411 := (>= 1::Int 0::Int)
-#746 := (<= -1::Int 0::Int)
-#748 := (or #746 #411)
-#405 := (not #748)
-#535 := (<= 1::Int 0::Int)
-#742 := (or #535 #746)
-#416 := (not #742)
-#417 := (or #416 #405)
-#749 := (ite #417 #432 #429)
-#750 := (= #71 0::Int)
-#751 := (= -1::Int 0::Int)
-#752 := (= 1::Int 0::Int)
-#747 := (or #752 #751)
-#753 := (ite #747 #750 #749)
-#676 := (or #685 #753)
-#670 := (iff #676 #689)
-#669 := (iff #689 #689)
-#679 := [rewrite]: #669
-#595 := (iff #753 #74)
-#583 := (ite false #750 #74)
-#593 := (iff #583 #74)
-#594 := [rewrite]: #593
-#591 := (iff #753 #583)
-#589 := (iff #749 #74)
-#683 := (ite false #74 #74)
-#572 := (iff #683 #74)
-#587 := [rewrite]: #572
-#684 := (iff #749 #683)
-#686 := (iff #429 #74)
-#707 := (+ 1::Int #71)
-#555 := (= #707 0::Int)
-#699 := (iff #555 #74)
-#700 := [rewrite]: #699
-#579 := (iff #429 #555)
-#577 := (= #418 #707)
-#710 := (+ #71 1::Int)
-#712 := (= #710 #707)
-#713 := [rewrite]: #712
-#692 := (= #418 #710)
-#693 := (= #427 1::Int)
-#719 := (= #341 1::Int)
-#716 := [rewrite]: #719
-#690 := (= #427 #341)
-#536 := (= #426 -1::Int)
-#703 := (div -1::Int 1::Int)
-#705 := (= #703 -1::Int)
-#534 := [rewrite]: #705
-#704 := (= #426 #703)
-#696 := (= #425 -1::Int)
-#697 := [rewrite]: #696
-#698 := [monotonicity #697 #716]: #704
-#537 := [trans #698 #534]: #536
-#691 := [monotonicity #537]: #690
-#694 := [trans #691 #716]: #693
-#695 := [monotonicity #694]: #692
-#578 := [trans #695 #713]: #577
-#538 := [monotonicity #578]: #579
-#588 := [trans #538 #700]: #686
-#701 := (iff #432 #74)
-#556 := (iff #432 #555)
-#708 := (= #428 #707)
-#711 := (= #428 #710)
-#720 := (= #431 1::Int)
-#433 := (= #431 #341)
-#717 := (= #430 -1::Int)
-#718 := [rewrite]: #717
-#715 := [monotonicity #718]: #433
-#709 := [trans #715 #716]: #720
-#706 := [monotonicity #709]: #711
-#714 := [trans #706 #713]: #708
-#557 := [monotonicity #714]: #556
-#702 := [trans #557 #700]: #701
-#438 := (iff #417 false)
-#404 := (or false false)
-#729 := (iff #404 false)
-#392 := [rewrite]: #729
-#436 := (iff #417 #404)
-#722 := (iff #405 false)
-#1 := true
-#379 := (not true)
-#738 := (iff #379 false)
-#741 := [rewrite]: #738
-#721 := (iff #405 #379)
-#446 := (iff #748 true)
-#452 := (or true true)
-#723 := (iff #452 true)
-#724 := [rewrite]: #723
-#453 := (iff #748 #452)
-#450 := (iff #411 true)
-#451 := [rewrite]: #450
-#732 := (iff #746 true)
-#733 := [rewrite]: #732
-#347 := [monotonicity #733 #451]: #453
-#447 := [trans #347 #724]: #446
-#725 := [monotonicity #447]: #721
-#726 := [trans #725 #741]: #722
-#727 := (iff #416 false)
-#380 := (iff #416 #379)
-#737 := (iff #742 true)
-#734 := (or false true)
-#736 := (iff #734 true)
-#374 := [rewrite]: #736
-#735 := (iff #742 #734)
-#395 := (iff #535 false)
-#731 := [rewrite]: #395
-#730 := [monotonicity #731 #733]: #735
-#739 := [trans #730 #374]: #737
-#740 := [monotonicity #739]: #380
-#728 := [trans #740 #741]: #727
-#437 := [monotonicity #728 #726]: #436
-#439 := [trans #437 #392]: #438
-#687 := [monotonicity #439 #702 #588]: #684
-#590 := [trans #687 #587]: #589
-#393 := (iff #747 false)
-#745 := (iff #747 #404)
-#408 := (iff #751 false)
-#744 := [rewrite]: #408
-#743 := (iff #752 false)
-#403 := [rewrite]: #743
-#388 := [monotonicity #403 #744]: #745
-#394 := [trans #388 #392]: #393
-#592 := [monotonicity #394 #590]: #591
-#688 := [trans #592 #594]: #595
-#667 := [monotonicity #688]: #670
-#680 := [trans #667 #679]: #670
-#678 := [quant-inst #9 #68]: #676
-#681 := [mp #678 #680]: #689
-[unit-resolution #681 #92 #760]: false
-unsat
-509cb97799c2b173f188cefbb1ff19fd9cf187f7 311 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#17 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#18 := (f4 f5 #17)
-#20 := (f3 #18 #19)
-#747 := (pattern #20)
-#21 := 0::Int
-#70 := -1::Int
-#96 := (* -1::Int #19)
-#93 := (* -1::Int #17)
+#695 := (pattern #18)
+#8 := 0::Int
+#54 := -1::Int
+#96 := (* -1::Int #17)
+#93 := (* -1::Int #15)
 #99 := (div #93 #96)
-#250 := (* -1::Int #99)
-#251 := (+ #20 #250)
-#252 := (= #251 0::Int)
-#31 := (div #17 #19)
-#247 := (* -1::Int #31)
-#248 := (+ #20 #247)
-#249 := (= #248 0::Int)
-#125 := (>= #17 0::Int)
-#118 := (<= #19 0::Int)
-#210 := (or #118 #125)
-#211 := (not #210)
-#114 := (<= #17 0::Int)
-#208 := (or #114 #118)
-#209 := (not #208)
-#214 := (or #209 #211)
-#253 := (ite #214 #249 #252)
-#246 := (= #20 0::Int)
-#23 := (= #19 0::Int)
-#22 := (= #17 0::Int)
-#24 := (or #22 #23)
-#254 := (ite #24 #246 #253)
-#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #254)
-#257 := (forall (vars (?v0 Int) (?v1 Int)) #254)
-#751 := (iff #257 #748)
-#749 := (iff #254 #254)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#217 := (ite #214 #31 #99)
-#220 := (ite #24 0::Int #217)
-#223 := (= #20 #220)
-#226 := (forall (vars (?v0 Int) (?v1 Int)) #223)
-#258 := (iff #226 #257)
-#255 := (iff #223 #254)
-#256 := [rewrite]: #255
-#259 := [quant-intro #256]: #258
-#126 := (not #125)
-#119 := (not #118)
-#129 := (and #119 #126)
-#115 := (not #114)
-#122 := (and #115 #119)
-#132 := (or #122 #129)
-#135 := (ite #132 #31 #99)
-#138 := (ite #24 0::Int #135)
-#141 := (= #20 #138)
-#144 := (forall (vars (?v0 Int) (?v1 Int)) #141)
-#227 := (iff #144 #226)
-#224 := (iff #141 #223)
-#221 := (= #138 #220)
-#218 := (= #135 #217)
-#215 := (iff #132 #214)
-#212 := (iff #129 #211)
-#213 := [rewrite]: #212
-#202 := (iff #122 #209)
-#203 := [rewrite]: #202
-#216 := [monotonicity #203 #213]: #215
-#219 := [monotonicity #216]: #218
-#222 := [monotonicity #219]: #221
-#225 := [monotonicity #222]: #224
-#228 := [quant-intro #225]: #227
-#206 := (~ #144 #144)
-#204 := (~ #141 #141)
-#205 := [refl]: #204
-#207 := [nnf-pos #205]: #206
-#33 := (- #19)
-#32 := (- #17)
-#34 := (div #32 #33)
-#26 := (< 0::Int #19)
-#28 := (< #17 0::Int)
-#29 := (and #28 #26)
-#25 := (< 0::Int #17)
-#27 := (and #25 #26)
-#30 := (or #27 #29)
-#35 := (ite #30 #31 #34)
-#36 := (ite #24 0::Int #35)
-#37 := (= #20 #36)
-#38 := (forall (vars (?v0 Int) (?v1 Int)) #37)
-#147 := (iff #38 #144)
-#86 := (and #26 #28)
-#90 := (or #27 #86)
-#102 := (ite #90 #31 #99)
-#105 := (ite #24 0::Int #102)
-#108 := (= #20 #105)
-#111 := (forall (vars (?v0 Int) (?v1 Int)) #108)
-#145 := (iff #111 #144)
-#142 := (iff #108 #141)
-#139 := (= #105 #138)
-#136 := (= #102 #135)
-#133 := (iff #90 #132)
-#130 := (iff #86 #129)
-#127 := (iff #28 #126)
-#128 := [rewrite]: #127
-#120 := (iff #26 #119)
-#121 := [rewrite]: #120
-#131 := [monotonicity #121 #128]: #130
-#123 := (iff #27 #122)
-#116 := (iff #25 #115)
-#117 := [rewrite]: #116
-#124 := [monotonicity #117 #121]: #123
-#134 := [monotonicity #124 #131]: #133
-#137 := [monotonicity #134]: #136
-#140 := [monotonicity #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [quant-intro #143]: #145
-#112 := (iff #38 #111)
-#109 := (iff #37 #108)
-#106 := (= #36 #105)
-#103 := (= #35 #102)
-#100 := (= #34 #99)
-#97 := (= #33 #96)
-#98 := [rewrite]: #97
-#94 := (= #32 #93)
-#95 := [rewrite]: #94
-#101 := [monotonicity #95 #98]: #100
-#91 := (iff #30 #90)
-#88 := (iff #29 #86)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#104 := [monotonicity #92 #101]: #103
-#107 := [monotonicity #104]: #106
-#110 := [monotonicity #107]: #109
-#113 := [quant-intro #110]: #112
-#148 := [trans #113 #146]: #147
-#85 := [asserted]: #38
-#149 := [mp #85 #148]: #144
-#198 := [mp~ #149 #207]: #144
-#229 := [mp #198 #228]: #226
-#260 := [mp #229 #259]: #257
-#753 := [mp #260 #752]: #748
-#76 := -3::Int
-#9 := 3::Int
-#10 := (f4 f5 3::Int)
-#73 := (f3 #10 -1::Int)
-#79 := (= #73 -3::Int)
-#82 := (not #79)
-#14 := (- 3::Int)
-#11 := 1::Int
-#12 := (- 1::Int)
-#13 := (f3 #10 #12)
-#15 := (= #13 #14)
-#16 := (not #15)
-#83 := (iff #16 #82)
-#80 := (iff #15 #79)
-#77 := (= #14 -3::Int)
-#78 := [rewrite]: #77
-#74 := (= #13 #73)
-#71 := (= #12 -1::Int)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#81 := [monotonicity #75 #78]: #80
-#84 := [monotonicity #81]: #83
-#69 := [asserted]: #16
-#87 := [mp #69 #84]: #82
-#671 := (not #748)
-#663 := (or #671 #79)
-#334 := (* -1::Int -1::Int)
-#418 := (* -1::Int 3::Int)
-#419 := (div #418 #334)
-#420 := (* -1::Int #419)
-#411 := (+ #73 #420)
-#422 := (= #411 0::Int)
-#423 := (div 3::Int -1::Int)
-#424 := (* -1::Int #423)
-#421 := (+ #73 #424)
-#425 := (= #421 0::Int)
-#404 := (>= 3::Int 0::Int)
-#739 := (<= -1::Int 0::Int)
-#741 := (or #739 #404)
-#398 := (not #741)
-#528 := (<= 3::Int 0::Int)
-#735 := (or #528 #739)
-#409 := (not #735)
-#410 := (or #409 #398)
-#742 := (ite #410 #425 #422)
-#743 := (= #73 0::Int)
-#744 := (= -1::Int 0::Int)
-#745 := (= 3::Int 0::Int)
-#740 := (or #745 #744)
-#746 := (ite #740 #743 #742)
-#660 := (or #671 #746)
-#672 := (iff #660 #663)
-#674 := (iff #663 #663)
-#670 := [rewrite]: #674
-#682 := (iff #746 #79)
-#586 := (ite false #743 #79)
-#681 := (iff #586 #79)
-#678 := [rewrite]: #681
-#587 := (iff #746 #586)
-#584 := (iff #742 #79)
-#565 := (ite false #79 #79)
-#583 := (iff #565 #79)
-#576 := [rewrite]: #583
-#580 := (iff #742 #565)
-#677 := (iff #422 #79)
-#705 := (+ 3::Int #73)
-#549 := (= #705 0::Int)
-#693 := (iff #549 #79)
-#694 := [rewrite]: #693
-#581 := (iff #422 #549)
-#531 := (= #411 #705)
-#704 := (+ #73 3::Int)
-#706 := (= #704 #705)
-#701 := [rewrite]: #706
-#571 := (= #411 #704)
-#688 := (= #420 3::Int)
-#426 := (* -1::Int -3::Int)
-#709 := (= #426 3::Int)
-#713 := [rewrite]: #709
-#687 := (= #420 #426)
-#684 := (= #419 -3::Int)
-#698 := (div -3::Int 1::Int)
-#530 := (= #698 -3::Int)
-#683 := [rewrite]: #530
-#527 := (= #419 #698)
-#697 := (= #334 1::Int)
-#691 := [rewrite]: #697
-#690 := (= #418 -3::Int)
-#696 := [rewrite]: #690
-#529 := [monotonicity #696 #691]: #527
-#686 := [trans #529 #683]: #684
-#685 := [monotonicity #686]: #687
-#570 := [trans #685 #713]: #688
-#572 := [monotonicity #570]: #571
-#679 := [trans #572 #701]: #531
-#676 := [monotonicity #679]: #581
-#680 := [trans #676 #694]: #677
-#695 := (iff #425 #79)
-#550 := (iff #425 #549)
-#707 := (= #421 #705)
-#699 := (= #421 #704)
-#702 := (= #424 3::Int)
-#708 := (= #424 #426)
-#710 := (= #423 -3::Int)
-#711 := [rewrite]: #710
-#712 := [monotonicity #711]: #708
-#703 := [trans #712 #713]: #702
-#700 := [monotonicity #703]: #699
-#548 := [trans #700 #701]: #707
-#692 := [monotonicity #548]: #550
-#689 := [trans #692 #694]: #695
-#431 := (iff #410 false)
-#397 := (or false false)
-#722 := (iff #397 false)
-#385 := [rewrite]: #722
-#429 := (iff #410 #397)
-#715 := (iff #398 false)
-#1 := true
-#372 := (not true)
-#731 := (iff #372 false)
-#734 := [rewrite]: #731
-#714 := (iff #398 #372)
-#439 := (iff #741 true)
-#445 := (or true true)
-#716 := (iff #445 true)
-#717 := [rewrite]: #716
-#446 := (iff #741 #445)
-#443 := (iff #404 true)
-#444 := [rewrite]: #443
-#725 := (iff #739 true)
-#726 := [rewrite]: #725
-#340 := [monotonicity #726 #444]: #446
-#440 := [trans #340 #717]: #439
-#718 := [monotonicity #440]: #714
-#719 := [trans #718 #734]: #715
-#720 := (iff #409 false)
-#373 := (iff #409 #372)
-#730 := (iff #735 true)
-#727 := (or false true)
-#729 := (iff #727 true)
-#367 := [rewrite]: #729
-#728 := (iff #735 #727)
-#388 := (iff #528 false)
-#724 := [rewrite]: #388
-#723 := [monotonicity #724 #726]: #728
-#732 := [trans #723 #367]: #730
-#733 := [monotonicity #732]: #373
-#721 := [trans #733 #734]: #720
-#430 := [monotonicity #721 #719]: #429
-#432 := [trans #430 #385]: #431
-#582 := [monotonicity #432 #689 #680]: #580
-#585 := [trans #582 #576]: #584
-#386 := (iff #740 false)
-#738 := (iff #740 #397)
-#401 := (iff #744 false)
-#737 := [rewrite]: #401
-#736 := (iff #745 false)
-#396 := [rewrite]: #736
-#381 := [monotonicity #396 #737]: #738
-#387 := [trans #381 #385]: #386
-#588 := [monotonicity #387 #585]: #587
-#669 := [trans #588 #678]: #682
-#673 := [monotonicity #669]: #672
-#675 := [trans #673 #670]: #672
-#662 := [quant-inst #9 #70]: #660
-#664 := [mp #662 #675]: #663
-[unit-resolution #664 #87 #753]: false
-unsat
-f7a542d94fa8744cde88643a09f5498259f3785d 355 0
-#2 := false
-#21 := 0::Int
-#11 := 1::Int
-decl f6 :: Int
-#9 := f6
-#70 := -1::Int
-#76 := (* -1::Int f6)
-#719 := (div #76 1::Int)
-#717 := (* -1::Int #719)
-decl f3 :: (-> S2 Int Int)
-decl f4 :: (-> S3 Int S2)
-decl f5 :: S3
-#8 := f5
-#10 := (f4 f5 f6)
-#73 := (f3 #10 -1::Int)
-#722 := (+ #73 #717)
-#696 := (<= #722 0::Int)
-#713 := (= #722 0::Int)
-#749 := (= f6 0::Int)
-#579 := (not #749)
-#744 := (<= f6 0::Int)
-#620 := [hypothesis]: #749
-#600 := (or #579 #744)
-#546 := [th-lemma arith triangle-eq]: #600
-#601 := [unit-resolution #546 #620]: #744
-#85 := (+ f6 #73)
-#343 := (<= #85 0::Int)
-#582 := (not #343)
-#427 := (>= #85 0::Int)
-#748 := (>= f6 0::Int)
-#689 := (not #713)
-#694 := (>= #722 0::Int)
-#626 := (not #694)
-#635 := (not #427)
-#636 := [hypothesis]: #635
-#627 := (or #626 #427)
-#634 := [hypothesis]: #694
-#670 := (+ f6 #719)
-#667 := (>= #670 0::Int)
-#677 := (= #670 0::Int)
-#1 := true
-#67 := [true-axiom]: true
-#637 := (or false #677)
-#638 := [th-lemma arith]: #637
-#633 := [unit-resolution #638 #67]: #677
-#639 := (not #677)
-#625 := (or #639 #667)
-#621 := [th-lemma arith triangle-eq]: #625
-#622 := [unit-resolution #621 #633]: #667
-#623 := [th-lemma arith farkas 1 -1 1 #622 #636 #634]: false
-#628 := [lemma #623]: #627
-#666 := [unit-resolution #628 #636]: #626
-#629 := (or #689 #694)
-#624 := [th-lemma arith triangle-eq]: #629
-#630 := [unit-resolution #624 #666]: #689
-#604 := (or #749 #713)
-#753 := (= #73 0::Int)
-#701 := (ite #749 #753 #713)
-#19 := (:var 0 Int)
-#17 := (:var 1 Int)
-#18 := (f4 f5 #17)
-#20 := (f3 #18 #19)
-#756 := (pattern #20)
-#105 := (* -1::Int #19)
-#102 := (* -1::Int #17)
-#108 := (div #102 #105)
-#259 := (* -1::Int #108)
-#260 := (+ #20 #259)
-#261 := (= #260 0::Int)
-#31 := (div #17 #19)
-#256 := (* -1::Int #31)
-#257 := (+ #20 #256)
-#258 := (= #257 0::Int)
-#134 := (>= #17 0::Int)
-#127 := (<= #19 0::Int)
-#219 := (or #127 #134)
-#220 := (not #219)
-#123 := (<= #17 0::Int)
-#217 := (or #123 #127)
-#218 := (not #217)
-#223 := (or #218 #220)
-#262 := (ite #223 #258 #261)
-#255 := (= #20 0::Int)
-#23 := (= #19 0::Int)
-#22 := (= #17 0::Int)
-#24 := (or #22 #23)
-#263 := (ite #24 #255 #262)
-#757 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #756) #263)
-#266 := (forall (vars (?v0 Int) (?v1 Int)) #263)
-#760 := (iff #266 #757)
-#758 := (iff #263 #263)
-#759 := [refl]: #758
-#761 := [quant-intro #759]: #760
-#226 := (ite #223 #31 #108)
-#229 := (ite #24 0::Int #226)
-#232 := (= #20 #229)
-#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
-#267 := (iff #235 #266)
-#264 := (iff #232 #263)
-#265 := [rewrite]: #264
-#268 := [quant-intro #265]: #267
-#135 := (not #134)
-#128 := (not #127)
-#138 := (and #128 #135)
-#124 := (not #123)
-#131 := (and #124 #128)
-#141 := (or #131 #138)
-#144 := (ite #141 #31 #108)
-#147 := (ite #24 0::Int #144)
-#150 := (= #20 #147)
-#153 := (forall (vars (?v0 Int) (?v1 Int)) #150)
-#236 := (iff #153 #235)
-#233 := (iff #150 #232)
-#230 := (= #147 #229)
-#227 := (= #144 #226)
-#224 := (iff #141 #223)
-#221 := (iff #138 #220)
-#222 := [rewrite]: #221
-#211 := (iff #131 #218)
-#212 := [rewrite]: #211
-#225 := [monotonicity #212 #222]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [quant-intro #234]: #236
-#215 := (~ #153 #153)
-#213 := (~ #150 #150)
-#214 := [refl]: #213
-#216 := [nnf-pos #214]: #215
-#33 := (- #19)
-#32 := (- #17)
-#34 := (div #32 #33)
-#26 := (< 0::Int #19)
-#28 := (< #17 0::Int)
-#29 := (and #28 #26)
-#25 := (< 0::Int #17)
-#27 := (and #25 #26)
-#30 := (or #27 #29)
-#35 := (ite #30 #31 #34)
-#36 := (ite #24 0::Int #35)
-#37 := (= #20 #36)
-#38 := (forall (vars (?v0 Int) (?v1 Int)) #37)
-#156 := (iff #38 #153)
-#96 := (and #26 #28)
-#99 := (or #27 #96)
-#111 := (ite #99 #31 #108)
-#114 := (ite #24 0::Int #111)
-#117 := (= #20 #114)
-#120 := (forall (vars (?v0 Int) (?v1 Int)) #117)
-#154 := (iff #120 #153)
-#151 := (iff #117 #150)
-#148 := (= #114 #147)
-#145 := (= #111 #144)
-#142 := (iff #99 #141)
-#139 := (iff #96 #138)
-#136 := (iff #28 #135)
-#137 := [rewrite]: #136
-#129 := (iff #26 #128)
-#130 := [rewrite]: #129
-#140 := [monotonicity #130 #137]: #139
-#132 := (iff #27 #131)
-#125 := (iff #25 #124)
-#126 := [rewrite]: #125
-#133 := [monotonicity #126 #130]: #132
-#143 := [monotonicity #133 #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [monotonicity #149]: #151
-#155 := [quant-intro #152]: #154
-#121 := (iff #38 #120)
-#118 := (iff #37 #117)
-#115 := (= #36 #114)
-#112 := (= #35 #111)
-#109 := (= #34 #108)
-#106 := (= #33 #105)
-#107 := [rewrite]: #106
-#103 := (= #32 #102)
-#104 := [rewrite]: #103
-#110 := [monotonicity #104 #107]: #109
-#100 := (iff #30 #99)
-#97 := (iff #29 #96)
-#98 := [rewrite]: #97
-#101 := [monotonicity #98]: #100
-#113 := [monotonicity #101 #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [monotonicity #116]: #118
-#122 := [quant-intro #119]: #121
-#157 := [trans #122 #155]: #156
-#95 := [asserted]: #38
-#158 := [mp #95 #157]: #153
-#207 := [mp~ #158 #216]: #153
-#238 := [mp #207 #237]: #235
-#269 := [mp #238 #268]: #266
-#762 := [mp #269 #761]: #757
-#704 := (not #757)
-#698 := (or #704 #701)
-#428 := (* -1::Int -1::Int)
-#429 := (div #76 #428)
-#420 := (* -1::Int #429)
-#431 := (+ #73 #420)
-#432 := (= #431 0::Int)
-#433 := (div f6 -1::Int)
-#430 := (* -1::Int #433)
-#434 := (+ #73 #430)
-#413 := (= #434 0::Int)
-#750 := (<= -1::Int 0::Int)
-#407 := (or #750 #748)
-#537 := (not #407)
-#418 := (or #744 #750)
-#419 := (not #418)
-#751 := (or #419 #537)
-#752 := (ite #751 #413 #432)
-#754 := (= -1::Int 0::Int)
-#755 := (or #749 #754)
-#745 := (ite #755 #753 #752)
-#699 := (or #704 #745)
-#706 := (iff #699 #698)
-#707 := (iff #698 #698)
-#536 := [rewrite]: #707
-#702 := (iff #745 #701)
-#558 := (iff #752 #713)
-#714 := (ite false #413 #713)
-#716 := (iff #714 #713)
-#557 := [rewrite]: #716
-#715 := (iff #752 #714)
-#708 := (iff #432 #713)
-#711 := (= #431 #722)
-#721 := (= #420 #717)
-#720 := (= #429 #719)
-#440 := (= #428 1::Int)
-#441 := [rewrite]: #440
-#435 := [monotonicity #441]: #720
-#718 := [monotonicity #435]: #721
-#712 := [monotonicity #718]: #711
-#709 := [monotonicity #712]: #708
-#438 := (iff #751 false)
-#449 := (or false false)
-#724 := (iff #449 false)
-#728 := [rewrite]: #724
-#723 := (iff #751 #449)
-#726 := (iff #537 false)
-#376 := (not true)
-#381 := (iff #376 false)
-#382 := [rewrite]: #381
-#349 := (iff #537 #376)
-#454 := (iff #407 true)
-#743 := (or true #748)
-#452 := (iff #743 true)
-#453 := [rewrite]: #452
-#729 := (iff #407 #743)
-#396 := (iff #750 true)
-#397 := [rewrite]: #396
-#730 := [monotonicity #397]: #729
-#455 := [trans #730 #453]: #454
-#725 := [monotonicity #455]: #349
-#448 := [trans #725 #382]: #726
-#742 := (iff #419 false)
-#739 := (iff #419 #376)
-#732 := (iff #418 true)
-#733 := (or #744 true)
-#736 := (iff #733 true)
-#737 := [rewrite]: #736
-#734 := (iff #418 #733)
-#735 := [monotonicity #397]: #734
-#738 := [trans #735 #737]: #732
-#741 := [monotonicity #738]: #739
-#740 := [trans #741 #382]: #742
-#727 := [monotonicity #740 #448]: #723
-#439 := [trans #727 #728]: #438
-#710 := [monotonicity #439 #709]: #715
-#559 := [trans #710 #557]: #558
-#394 := (iff #755 #749)
-#746 := (or #749 false)
-#390 := (iff #746 #749)
-#731 := [rewrite]: #390
-#406 := (iff #755 #746)
-#405 := (iff #754 false)
-#410 := [rewrite]: #405
-#747 := [monotonicity #410]: #406
-#395 := [trans #747 #731]: #394
-#703 := [monotonicity #395 #559]: #702
-#700 := [monotonicity #703]: #706
-#538 := [trans #700 #536]: #706
-#705 := [quant-inst #9 #70]: #699
-#539 := [mp #705 #538]: #698
-#603 := [unit-resolution #539 #762]: #701
-#697 := (not #701)
-#540 := (or #697 #749 #713)
-#688 := [def-axiom]: #540
-#605 := [unit-resolution #688 #603]: #604
-#498 := [unit-resolution #605 #630]: #749
-#609 := (or #579 #748)
-#610 := [th-lemma arith triangle-eq]: #609
-#611 := [unit-resolution #610 #498]: #748
-#693 := (>= #73 0::Int)
-#616 := (or #579 #753)
-#580 := (or #697 #579 #753)
-#581 := [def-axiom]: #580
-#612 := [unit-resolution #581 #603]: #616
-#613 := [unit-resolution #612 #498]: #753
-#590 := (not #753)
-#614 := (or #590 #693)
-#617 := [th-lemma arith triangle-eq]: #614
-#618 := [unit-resolution #617 #613]: #693
-#619 := [th-lemma arith farkas 1 -1 1 #618 #636 #611]: false
-#615 := [lemma #619]: #427
-#602 := (or #582 #635)
-#86 := (= #85 0::Int)
-#89 := (not #86)
-#14 := (- f6)
-#12 := (- 1::Int)
-#13 := (f3 #10 #12)
-#15 := (= #13 #14)
-#16 := (not #15)
-#92 := (iff #16 #89)
-#79 := (= #73 #76)
-#82 := (not #79)
-#90 := (iff #82 #89)
-#87 := (iff #79 #86)
-#88 := [rewrite]: #87
-#91 := [monotonicity #88]: #90
-#83 := (iff #16 #82)
-#80 := (iff #15 #79)
-#77 := (= #14 #76)
-#78 := [rewrite]: #77
-#74 := (= #13 #73)
-#71 := (= #12 -1::Int)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#81 := [monotonicity #75 #78]: #80
-#84 := [monotonicity #81]: #83
-#93 := [trans #84 #91]: #92
-#69 := [asserted]: #16
-#94 := [mp #69 #93]: #89
-#606 := (or #86 #582 #635)
-#607 := [th-lemma arith triangle-eq]: #606
-#608 := [unit-resolution #607 #94]: #602
-#576 := [unit-resolution #608 #615]: #582
-#692 := (<= #73 0::Int)
-#583 := [unit-resolution #612 #620]: #753
-#542 := (or #590 #692)
-#573 := [th-lemma arith triangle-eq]: #542
-#575 := [unit-resolution #573 #583]: #692
-#577 := [th-lemma arith farkas 1 -1 1 #575 #576 #601]: false
-#584 := [lemma #577]: #579
-#587 := [unit-resolution #605 #584]: #713
-#588 := (or #689 #696)
-#598 := [th-lemma arith triangle-eq]: #588
-#578 := [unit-resolution #598 #587]: #696
-#586 := (<= #670 0::Int)
-#599 := (or #639 #586)
-#554 := [th-lemma arith triangle-eq]: #599
-#555 := [unit-resolution #554 #633]: #586
-[th-lemma arith farkas 1 -1 1 #555 #576 #578]: false
-unsat
-128c927b2271de8226cec6066dac246457adc1e5 297 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#17 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#15 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#16 := (f4 f5 #15)
-#18 := (f3 #16 #17)
-#755 := (pattern #18)
-#9 := 0::Int
-#93 := -1::Int
-#97 := (* -1::Int #17)
-#94 := (* -1::Int #15)
-#100 := (div #94 #97)
-#257 := (* -1::Int #100)
-#258 := (+ #18 #257)
-#259 := (= #258 0::Int)
+#255 := (* -1::Int #99)
+#256 := (+ #18 #255)
+#257 := (= #256 0::Int)
 #28 := (div #15 #17)
-#254 := (* -1::Int #28)
-#255 := (+ #18 #254)
-#256 := (= #255 0::Int)
-#132 := (>= #15 0::Int)
-#125 := (<= #17 0::Int)
-#217 := (or #125 #132)
-#218 := (not #217)
-#121 := (<= #15 0::Int)
-#215 := (or #121 #125)
+#252 := (* -1::Int #28)
+#253 := (+ #18 #252)
+#254 := (= #253 0::Int)
+#71 := (<= #17 0::Int)
+#162 := (>= #15 0::Int)
+#215 := (or #162 #71)
 #216 := (not #215)
-#221 := (or #216 #218)
-#260 := (ite #221 #256 #259)
-#253 := (= #18 0::Int)
+#67 := (<= #15 0::Int)
+#211 := (or #67 #71)
+#212 := (not #211)
+#219 := (or #212 #216)
+#258 := (if #219 #254 #257)
+#251 := (= #18 0::Int)
 #20 := (= #17 0::Int)
 #19 := (= #15 0::Int)
 #21 := (or #19 #20)
-#261 := (ite #21 #253 #260)
-#756 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #755) #261)
-#264 := (forall (vars (?v0 Int) (?v1 Int)) #261)
-#759 := (iff #264 #756)
-#757 := (iff #261 #261)
-#758 := [refl]: #757
-#760 := [quant-intro #758]: #759
-#224 := (ite #221 #28 #100)
-#227 := (ite #21 0::Int #224)
-#230 := (= #18 #227)
-#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
-#265 := (iff #233 #264)
-#262 := (iff #230 #261)
-#263 := [rewrite]: #262
-#266 := [quant-intro #263]: #265
-#133 := (not #132)
-#126 := (not #125)
-#136 := (and #126 #133)
-#122 := (not #121)
-#129 := (and #122 #126)
-#139 := (or #129 #136)
-#142 := (ite #139 #28 #100)
-#145 := (ite #21 0::Int #142)
-#148 := (= #18 #145)
-#151 := (forall (vars (?v0 Int) (?v1 Int)) #148)
-#234 := (iff #151 #233)
-#231 := (iff #148 #230)
-#228 := (= #145 #227)
-#225 := (= #142 #224)
-#222 := (iff #139 #221)
-#219 := (iff #136 #218)
-#220 := [rewrite]: #219
-#209 := (iff #129 #216)
-#210 := [rewrite]: #209
-#223 := [monotonicity #210 #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [monotonicity #229]: #231
-#235 := [quant-intro #232]: #234
-#213 := (~ #151 #151)
-#211 := (~ #148 #148)
-#212 := [refl]: #211
-#214 := [nnf-pos #212]: #213
+#259 := (if #21 #251 #258)
+#696 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #695) #259)
+#262 := (forall (vars (?v0 Int) (?v1 Int)) #259)
+#699 := (iff #262 #696)
+#697 := (iff #259 #259)
+#698 := [refl]: #697
+#700 := [quant-intro #698]: #699
+#222 := (if #219 #28 #99)
+#225 := (if #21 0::Int #222)
+#228 := (= #18 #225)
+#231 := (forall (vars (?v0 Int) (?v1 Int)) #228)
+#263 := (iff #231 #262)
+#260 := (iff #228 #259)
+#261 := [rewrite]: #260
+#264 := [quant-intro #261]: #263
+#72 := (not #71)
+#165 := (not #162)
+#168 := (and #165 #72)
+#68 := (not #67)
+#75 := (and #68 #72)
+#171 := (or #75 #168)
+#174 := (if #171 #28 #99)
+#177 := (if #21 0::Int #174)
+#180 := (= #18 #177)
+#183 := (forall (vars (?v0 Int) (?v1 Int)) #180)
+#232 := (iff #183 #231)
+#229 := (iff #180 #228)
+#226 := (= #177 #225)
+#223 := (= #174 #222)
+#220 := (iff #171 #219)
+#217 := (iff #168 #216)
+#218 := [rewrite]: #217
+#213 := (iff #75 #212)
+#214 := [rewrite]: #213
+#221 := [monotonicity #214 #218]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [quant-intro #230]: #232
+#203 := (~ #183 #183)
+#205 := (~ #180 #180)
+#206 := [refl]: #205
+#204 := [nnf-pos #206]: #203
+#78 := (<= 0::Int #15)
+#79 := (not #78)
+#87 := (and #79 #72)
+#90 := (or #75 #87)
+#102 := (if #90 #28 #99)
+#105 := (if #21 0::Int #102)
+#108 := (= #18 #105)
+#111 := (forall (vars (?v0 Int) (?v1 Int)) #108)
+#184 := (iff #111 #183)
+#181 := (iff #108 #180)
+#178 := (= #105 #177)
+#175 := (= #102 #174)
+#172 := (iff #90 #171)
+#169 := (iff #87 #168)
+#166 := (iff #79 #165)
+#163 := (iff #78 #162)
+#164 := [rewrite]: #163
+#167 := [monotonicity #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [monotonicity #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [monotonicity #176]: #178
+#182 := [monotonicity #179]: #181
+#185 := [quant-intro #182]: #184
 #30 := (- #17)
 #29 := (- #15)
 #31 := (div #29 #30)
@@ -30284,46 +27836,1606 @@
 #22 := (< 0::Int #15)
 #24 := (and #22 #23)
 #27 := (or #24 #26)
-#32 := (ite #27 #28 #31)
-#33 := (ite #21 0::Int #32)
+#32 := (if #27 #28 #31)
+#33 := (if #21 0::Int #32)
 #34 := (= #18 #33)
 #35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
-#154 := (iff #35 #151)
-#87 := (and #23 #25)
-#90 := (or #24 #87)
-#103 := (ite #90 #28 #100)
-#81 := (= 0::Int #17)
-#78 := (= 0::Int #15)
-#84 := (or #78 #81)
-#106 := (ite #84 0::Int #103)
+#112 := (iff #35 #111)
+#109 := (iff #34 #108)
+#106 := (= #33 #105)
+#103 := (= #32 #102)
+#100 := (= #31 #99)
+#97 := (= #30 #96)
+#98 := [rewrite]: #97
+#94 := (= #29 #93)
+#95 := [rewrite]: #94
+#101 := [monotonicity #95 #98]: #100
+#91 := (iff #27 #90)
+#88 := (iff #26 #87)
+#73 := (iff #23 #72)
+#74 := [rewrite]: #73
+#80 := (iff #25 #79)
+#84 := (iff #79 #79)
+#82 := (iff #78 #78)
+#83 := [rewrite]: #82
+#85 := [monotonicity #83]: #84
+#81 := [rewrite]: #80
+#86 := [trans #81 #85]: #80
+#89 := [monotonicity #86 #74]: #88
+#76 := (iff #24 #75)
+#69 := (iff #22 #68)
+#70 := [rewrite]: #69
+#77 := [monotonicity #70 #74]: #76
+#92 := [monotonicity #77 #89]: #91
+#104 := [monotonicity #92 #101]: #103
+#107 := [monotonicity #104]: #106
+#110 := [monotonicity #107]: #109
+#113 := [quant-intro #110]: #112
+#49 := [asserted]: #35
+#114 := [mp #49 #113]: #111
+#186 := [mp #114 #185]: #183
+#160 := [mp~ #186 #204]: #183
+#234 := [mp #160 #233]: #231
+#265 := [mp #234 #264]: #262
+#701 := [mp #265 #700]: #696
+#9 := (f4 f5 0::Int)
+#57 := (f3 #9 -1::Int)
+#60 := (= #57 0::Int)
+#63 := (not #60)
+#10 := 1::Int
+#11 := (- 1::Int)
+#12 := (f3 #9 #11)
+#13 := (= #12 0::Int)
+#14 := (not #13)
+#64 := (iff #14 #63)
+#61 := (iff #13 #60)
+#58 := (= #12 #57)
+#55 := (= #11 -1::Int)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#62 := [monotonicity #59]: #61
+#65 := [monotonicity #62]: #64
+#48 := [asserted]: #14
+#66 := [mp #48 #65]: #63
+#530 := (not #696)
+#531 := (or #530 #60)
+#357 := (* -1::Int -1::Int)
+#683 := (* -1::Int 0::Int)
+#358 := (div #683 #357)
+#690 := (* -1::Int #358)
+#691 := (+ #57 #690)
+#692 := (= #691 0::Int)
+#687 := (div 0::Int -1::Int)
+#689 := (* -1::Int #687)
+#346 := (+ #57 #689)
+#476 := (= #346 0::Int)
+#359 := (<= -1::Int 0::Int)
+#372 := (>= 0::Int 0::Int)
+#369 := (or #372 #359)
+#373 := (not #369)
+#368 := (<= 0::Int 0::Int)
+#370 := (or #368 #359)
+#371 := (not #370)
+#352 := (or #371 #373)
+#693 := (if #352 #476 #692)
+#366 := (= -1::Int 0::Int)
+#282 := (= 0::Int 0::Int)
+#367 := (or #282 #366)
+#688 := (if #367 #60 #693)
+#524 := (or #530 #688)
+#533 := (iff #524 #531)
+#535 := (iff #531 #531)
+#536 := [rewrite]: #535
+#513 := (iff #688 #60)
+#1 := true
+#627 := (if true #60 #60)
+#625 := (iff #627 #60)
+#628 := [rewrite]: #625
+#529 := (iff #688 #627)
+#520 := (iff #693 #60)
+#635 := (if false #60 #60)
+#518 := (iff #635 #60)
+#519 := [rewrite]: #518
+#633 := (iff #693 #635)
+#632 := (iff #692 #60)
+#478 := (= #691 #57)
+#650 := (+ #57 0::Int)
+#647 := (= #650 #57)
+#648 := [rewrite]: #647
+#475 := (= #691 #650)
+#639 := (= #690 0::Int)
+#656 := (= #683 0::Int)
+#660 := [rewrite]: #656
+#644 := (= #690 #683)
+#637 := (= #358 0::Int)
+#498 := (div 0::Int 1::Int)
+#642 := (= #498 0::Int)
+#643 := [rewrite]: #642
+#640 := (= #358 #498)
+#496 := (= #357 1::Int)
+#497 := [rewrite]: #496
+#641 := [monotonicity #660 #497]: #640
+#638 := [trans #641 #643]: #637
+#645 := [monotonicity #638]: #644
+#646 := [trans #645 #660]: #639
+#477 := [monotonicity #646]: #475
+#631 := [trans #477 #648]: #478
+#634 := [monotonicity #631]: #632
+#649 := (iff #476 #60)
+#653 := (= #346 #57)
+#651 := (= #346 #650)
+#657 := (= #689 0::Int)
+#659 := (= #689 #683)
+#380 := (= #687 0::Int)
+#658 := [rewrite]: #380
+#374 := [monotonicity #658]: #659
+#661 := [trans #374 #660]: #657
+#652 := [monotonicity #661]: #651
+#654 := [trans #652 #648]: #653
+#655 := [monotonicity #654]: #649
+#378 := (iff #352 false)
+#662 := (or false false)
+#667 := (iff #662 false)
+#377 := [rewrite]: #667
+#666 := (iff #352 #662)
+#387 := (iff #373 false)
+#680 := (not true)
+#681 := (iff #680 false)
+#679 := [rewrite]: #681
+#664 := (iff #373 #680)
+#394 := (iff #369 true)
+#674 := (or true true)
+#671 := (iff #674 true)
+#677 := [rewrite]: #671
+#392 := (iff #369 #674)
+#672 := (iff #359 true)
+#673 := [rewrite]: #672
+#669 := (iff #372 true)
+#391 := [rewrite]: #669
+#393 := [monotonicity #391 #673]: #392
+#288 := [trans #393 #677]: #394
+#665 := [monotonicity #288]: #664
+#388 := [trans #665 #679]: #387
+#682 := (iff #371 false)
+#320 := (iff #371 #680)
+#315 := (iff #370 true)
+#675 := (iff #370 #674)
+#335 := (iff #368 true)
+#336 := [rewrite]: #335
+#676 := [monotonicity #336 #673]: #675
+#678 := [trans #676 #677]: #315
+#321 := [monotonicity #678]: #320
+#668 := [trans #321 #679]: #682
+#663 := [monotonicity #668 #388]: #666
+#379 := [trans #663 #377]: #378
+#636 := [monotonicity #379 #655 #634]: #633
+#479 := [trans #636 #519]: #520
+#333 := (iff #367 true)
+#685 := (or true false)
+#329 := (iff #685 true)
+#670 := [rewrite]: #329
+#345 := (iff #367 #685)
+#344 := (iff #366 false)
+#349 := [rewrite]: #344
+#694 := (iff #282 true)
+#684 := [rewrite]: #694
+#686 := [monotonicity #684 #349]: #345
+#334 := [trans #686 #670]: #333
+#624 := [monotonicity #334 #479]: #529
+#528 := [trans #624 #628]: #513
+#534 := [monotonicity #528]: #533
+#629 := [trans #534 #536]: #533
+#532 := [quant-inst #8 #54]: #524
+#626 := [mp #532 #629]: #531
+[unit-resolution #626 #66 #701]: false
+cf9d6de6ed3e36f7abf849890c513c16e310195c 313 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#16 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#14 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#15 := (f4 f5 #14)
+#17 := (f3 #15 #16)
+#695 := (pattern #17)
+#18 := 0::Int
+#54 := -1::Int
+#96 := (* -1::Int #16)
+#93 := (* -1::Int #14)
+#99 := (div #93 #96)
+#255 := (* -1::Int #99)
+#256 := (+ #17 #255)
+#257 := (= #256 0::Int)
+#28 := (div #14 #16)
+#252 := (* -1::Int #28)
+#253 := (+ #17 #252)
+#254 := (= #253 0::Int)
+#71 := (<= #16 0::Int)
+#162 := (>= #14 0::Int)
+#215 := (or #162 #71)
+#216 := (not #215)
+#67 := (<= #14 0::Int)
+#211 := (or #67 #71)
+#212 := (not #211)
+#219 := (or #212 #216)
+#258 := (if #219 #254 #257)
+#251 := (= #17 0::Int)
+#20 := (= #16 0::Int)
+#19 := (= #14 0::Int)
+#21 := (or #19 #20)
+#259 := (if #21 #251 #258)
+#696 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #695) #259)
+#262 := (forall (vars (?v0 Int) (?v1 Int)) #259)
+#699 := (iff #262 #696)
+#697 := (iff #259 #259)
+#698 := [refl]: #697
+#700 := [quant-intro #698]: #699
+#222 := (if #219 #28 #99)
+#225 := (if #21 0::Int #222)
+#228 := (= #17 #225)
+#231 := (forall (vars (?v0 Int) (?v1 Int)) #228)
+#263 := (iff #231 #262)
+#260 := (iff #228 #259)
+#261 := [rewrite]: #260
+#264 := [quant-intro #261]: #263
+#72 := (not #71)
+#165 := (not #162)
+#168 := (and #165 #72)
+#68 := (not #67)
+#75 := (and #68 #72)
+#171 := (or #75 #168)
+#174 := (if #171 #28 #99)
+#177 := (if #21 0::Int #174)
+#180 := (= #17 #177)
+#183 := (forall (vars (?v0 Int) (?v1 Int)) #180)
+#232 := (iff #183 #231)
+#229 := (iff #180 #228)
+#226 := (= #177 #225)
+#223 := (= #174 #222)
+#220 := (iff #171 #219)
+#217 := (iff #168 #216)
+#218 := [rewrite]: #217
+#213 := (iff #75 #212)
+#214 := [rewrite]: #213
+#221 := [monotonicity #214 #218]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [quant-intro #230]: #232
+#160 := (~ #183 #183)
+#203 := (~ #180 #180)
+#204 := [refl]: #203
+#161 := [nnf-pos #204]: #160
+#78 := (<= 0::Int #14)
+#79 := (not #78)
+#87 := (and #79 #72)
+#90 := (or #75 #87)
+#102 := (if #90 #28 #99)
+#105 := (if #21 0::Int #102)
+#108 := (= #17 #105)
+#111 := (forall (vars (?v0 Int) (?v1 Int)) #108)
+#184 := (iff #111 #183)
+#181 := (iff #108 #180)
+#178 := (= #105 #177)
+#175 := (= #102 #174)
+#172 := (iff #90 #171)
+#169 := (iff #87 #168)
+#166 := (iff #79 #165)
+#163 := (iff #78 #162)
+#164 := [rewrite]: #163
+#167 := [monotonicity #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [monotonicity #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [monotonicity #176]: #178
+#182 := [monotonicity #179]: #181
+#185 := [quant-intro #182]: #184
+#30 := (- #16)
+#29 := (- #14)
+#31 := (div #29 #30)
+#23 := (< 0::Int #16)
+#25 := (< #14 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #14)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#32 := (if #27 #28 #31)
+#33 := (if #21 0::Int #32)
+#34 := (= #17 #33)
+#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
+#112 := (iff #35 #111)
+#109 := (iff #34 #108)
+#106 := (= #33 #105)
+#103 := (= #32 #102)
+#100 := (= #31 #99)
+#97 := (= #30 #96)
+#98 := [rewrite]: #97
+#94 := (= #29 #93)
+#95 := [rewrite]: #94
+#101 := [monotonicity #95 #98]: #100
+#91 := (iff #27 #90)
+#88 := (iff #26 #87)
+#73 := (iff #23 #72)
+#74 := [rewrite]: #73
+#80 := (iff #25 #79)
+#84 := (iff #79 #79)
+#82 := (iff #78 #78)
+#83 := [rewrite]: #82
+#85 := [monotonicity #83]: #84
+#81 := [rewrite]: #80
+#86 := [trans #81 #85]: #80
+#89 := [monotonicity #86 #74]: #88
+#76 := (iff #24 #75)
+#69 := (iff #22 #68)
+#70 := [rewrite]: #69
+#77 := [monotonicity #70 #74]: #76
+#92 := [monotonicity #77 #89]: #91
+#104 := [monotonicity #92 #101]: #103
+#107 := [monotonicity #104]: #106
+#110 := [monotonicity #107]: #109
+#113 := [quant-intro #110]: #112
+#49 := [asserted]: #35
+#114 := [mp #49 #113]: #111
+#186 := [mp #114 #185]: #183
+#207 := [mp~ #186 #161]: #183
+#234 := [mp #207 #233]: #231
+#265 := [mp #234 #264]: #262
+#701 := [mp #265 #700]: #696
+#8 := 1::Int
+#9 := (f4 f5 1::Int)
+#57 := (f3 #9 -1::Int)
+#60 := (= #57 -1::Int)
+#63 := (not #60)
+#10 := (- 1::Int)
+#11 := (f3 #9 #10)
+#12 := (= #11 #10)
+#13 := (not #12)
+#64 := (iff #13 #63)
+#61 := (iff #12 #60)
+#55 := (= #10 -1::Int)
+#56 := [rewrite]: #55
+#58 := (= #11 #57)
+#59 := [monotonicity #56]: #58
+#62 := [monotonicity #59 #56]: #61
+#65 := [monotonicity #62]: #64
+#48 := [asserted]: #13
+#66 := [mp #48 #65]: #63
+#626 := (not #696)
+#630 := (or #626 #60)
+#358 := (* -1::Int -1::Int)
+#357 := (* -1::Int 1::Int)
+#690 := (div #357 #358)
+#691 := (* -1::Int #690)
+#692 := (+ #57 #691)
+#693 := (= #692 0::Int)
+#689 := (div 1::Int -1::Int)
+#346 := (* -1::Int #689)
+#476 := (+ #57 #346)
+#683 := (= #476 0::Int)
+#370 := (<= -1::Int 0::Int)
+#369 := (>= 1::Int 0::Int)
+#373 := (or #369 #370)
+#352 := (not #373)
+#359 := (<= 1::Int 0::Int)
+#371 := (or #359 #370)
+#372 := (not #371)
+#687 := (or #372 #352)
+#688 := (if #687 #683 #693)
+#368 := (= #57 0::Int)
+#366 := (= -1::Int 0::Int)
+#282 := (= 1::Int 0::Int)
+#367 := (or #282 #366)
+#694 := (if #367 #368 #688)
+#617 := (or #626 #694)
+#611 := (iff #617 #630)
+#610 := (iff #630 #630)
+#620 := [rewrite]: #610
+#536 := (iff #694 #60)
+#524 := (if false #368 #60)
+#534 := (iff #524 #60)
+#535 := [rewrite]: #534
+#532 := (iff #694 #524)
+#530 := (iff #688 #60)
+#624 := (if false #60 #60)
+#513 := (iff #624 #60)
+#528 := [rewrite]: #513
+#625 := (iff #688 #624)
+#627 := (iff #693 #60)
+#648 := (+ 1::Int #57)
+#496 := (= #648 0::Int)
+#640 := (iff #496 #60)
+#641 := [rewrite]: #640
+#520 := (iff #693 #496)
+#518 := (= #692 #648)
+#651 := (+ #57 1::Int)
+#653 := (= #651 #648)
+#654 := [rewrite]: #653
+#633 := (= #692 #651)
+#634 := (= #691 1::Int)
+#660 := (= #358 1::Int)
+#657 := [rewrite]: #660
+#631 := (= #691 #358)
+#477 := (= #690 -1::Int)
+#644 := (div -1::Int 1::Int)
+#646 := (= #644 -1::Int)
+#475 := [rewrite]: #646
+#645 := (= #690 #644)
+#637 := (= #357 -1::Int)
+#638 := [rewrite]: #637
+#639 := [monotonicity #638 #657]: #645
+#478 := [trans #639 #475]: #477
+#632 := [monotonicity #478]: #631
+#635 := [trans #632 #657]: #634
+#636 := [monotonicity #635]: #633
+#519 := [trans #636 #654]: #518
+#479 := [monotonicity #519]: #520
+#529 := [trans #479 #641]: #627
+#642 := (iff #683 #60)
+#497 := (iff #683 #496)
+#649 := (= #476 #648)
+#652 := (= #476 #651)
+#661 := (= #346 1::Int)
+#374 := (= #346 #358)
+#658 := (= #689 -1::Int)
+#659 := [rewrite]: #658
+#656 := [monotonicity #659]: #374
+#650 := [trans #656 #657]: #661
+#647 := [monotonicity #650]: #652
+#655 := [trans #647 #654]: #649
+#498 := [monotonicity #655]: #497
+#643 := [trans #498 #641]: #642
+#379 := (iff #687 false)
+#345 := (or false false)
+#670 := (iff #345 false)
+#333 := [rewrite]: #670
+#377 := (iff #687 #345)
+#663 := (iff #352 false)
+#1 := true
+#320 := (not true)
+#679 := (iff #320 false)
+#682 := [rewrite]: #679
+#662 := (iff #352 #320)
+#387 := (iff #373 true)
+#393 := (or true true)
+#664 := (iff #393 true)
+#665 := [rewrite]: #664
+#394 := (iff #373 #393)
+#673 := (iff #370 true)
+#674 := [rewrite]: #673
+#391 := (iff #369 true)
+#392 := [rewrite]: #391
+#288 := [monotonicity #392 #674]: #394
+#388 := [trans #288 #665]: #387
+#666 := [monotonicity #388]: #662
+#667 := [trans #666 #682]: #663
+#668 := (iff #372 false)
+#321 := (iff #372 #320)
+#678 := (iff #371 true)
+#675 := (or false true)
+#677 := (iff #675 true)
+#315 := [rewrite]: #677
+#676 := (iff #371 #675)
+#336 := (iff #359 false)
+#672 := [rewrite]: #336
+#671 := [monotonicity #672 #674]: #676
+#680 := [trans #671 #315]: #678
+#681 := [monotonicity #680]: #321
+#669 := [trans #681 #682]: #668
+#378 := [monotonicity #669 #667]: #377
+#380 := [trans #378 #333]: #379
+#628 := [monotonicity #380 #643 #529]: #625
+#531 := [trans #628 #528]: #530
+#334 := (iff #367 false)
+#686 := (iff #367 #345)
+#349 := (iff #366 false)
+#685 := [rewrite]: #349
+#684 := (iff #282 false)
+#344 := [rewrite]: #684
+#329 := [monotonicity #344 #685]: #686
+#335 := [trans #329 #333]: #334
+#533 := [monotonicity #335 #531]: #532
+#629 := [trans #533 #535]: #536
+#608 := [monotonicity #629]: #611
+#621 := [trans #608 #620]: #611
+#619 := [quant-inst #8 #54]: #617
+#622 := [mp #619 #621]: #630
+[unit-resolution #622 #66 #701]: false
+4a771fcb3bc990f914da773b60610eba4dcd1715 321 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#18 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#16 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#17 := (f4 f5 #16)
+#19 := (f3 #17 #18)
+#700 := (pattern #19)
+#20 := 0::Int
+#56 := -1::Int
+#101 := (* -1::Int #18)
+#98 := (* -1::Int #16)
+#104 := (div #98 #101)
+#260 := (* -1::Int #104)
+#261 := (+ #19 #260)
+#262 := (= #261 0::Int)
+#30 := (div #16 #18)
+#257 := (* -1::Int #30)
+#258 := (+ #19 #257)
+#259 := (= #258 0::Int)
+#76 := (<= #18 0::Int)
+#167 := (>= #16 0::Int)
+#220 := (or #167 #76)
+#221 := (not #220)
+#72 := (<= #16 0::Int)
+#216 := (or #72 #76)
+#217 := (not #216)
+#224 := (or #217 #221)
+#263 := (if #224 #259 #262)
+#256 := (= #19 0::Int)
+#22 := (= #18 0::Int)
+#21 := (= #16 0::Int)
+#23 := (or #21 #22)
+#264 := (if #23 #256 #263)
+#701 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #700) #264)
+#267 := (forall (vars (?v0 Int) (?v1 Int)) #264)
+#704 := (iff #267 #701)
+#702 := (iff #264 #264)
+#703 := [refl]: #702
+#705 := [quant-intro #703]: #704
+#227 := (if #224 #30 #104)
+#230 := (if #23 0::Int #227)
+#233 := (= #19 #230)
+#236 := (forall (vars (?v0 Int) (?v1 Int)) #233)
+#268 := (iff #236 #267)
+#265 := (iff #233 #264)
+#266 := [rewrite]: #265
+#269 := [quant-intro #266]: #268
+#77 := (not #76)
+#170 := (not #167)
+#173 := (and #170 #77)
+#73 := (not #72)
+#80 := (and #73 #77)
+#176 := (or #80 #173)
+#179 := (if #176 #30 #104)
+#182 := (if #23 0::Int #179)
+#185 := (= #19 #182)
+#188 := (forall (vars (?v0 Int) (?v1 Int)) #185)
+#237 := (iff #188 #236)
+#234 := (iff #185 #233)
+#231 := (= #182 #230)
+#228 := (= #179 #227)
+#225 := (iff #176 #224)
+#222 := (iff #173 #221)
+#223 := [rewrite]: #222
+#218 := (iff #80 #217)
+#219 := [rewrite]: #218
+#226 := [monotonicity #219 #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#235 := [monotonicity #232]: #234
+#238 := [quant-intro #235]: #237
+#165 := (~ #188 #188)
+#208 := (~ #185 #185)
+#209 := [refl]: #208
+#166 := [nnf-pos #209]: #165
+#83 := (<= 0::Int #16)
+#84 := (not #83)
+#92 := (and #84 #77)
+#95 := (or #80 #92)
+#107 := (if #95 #30 #104)
+#110 := (if #23 0::Int #107)
+#113 := (= #19 #110)
+#116 := (forall (vars (?v0 Int) (?v1 Int)) #113)
+#189 := (iff #116 #188)
+#186 := (iff #113 #185)
+#183 := (= #110 #182)
+#180 := (= #107 #179)
+#177 := (iff #95 #176)
+#174 := (iff #92 #173)
+#171 := (iff #84 #170)
+#168 := (iff #83 #167)
+#169 := [rewrite]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [monotonicity #178]: #180
+#184 := [monotonicity #181]: #183
+#187 := [monotonicity #184]: #186
+#190 := [quant-intro #187]: #189
+#32 := (- #18)
+#31 := (- #16)
+#33 := (div #31 #32)
+#25 := (< 0::Int #18)
+#27 := (< #16 0::Int)
+#28 := (and #27 #25)
+#24 := (< 0::Int #16)
+#26 := (and #24 #25)
+#29 := (or #26 #28)
+#34 := (if #29 #30 #33)
+#35 := (if #23 0::Int #34)
+#36 := (= #19 #35)
+#37 := (forall (vars (?v0 Int) (?v1 Int)) #36)
+#117 := (iff #37 #116)
+#114 := (iff #36 #113)
+#111 := (= #35 #110)
+#108 := (= #34 #107)
+#105 := (= #33 #104)
+#102 := (= #32 #101)
+#103 := [rewrite]: #102
+#99 := (= #31 #98)
+#100 := [rewrite]: #99
+#106 := [monotonicity #100 #103]: #105
+#96 := (iff #29 #95)
+#93 := (iff #28 #92)
+#78 := (iff #25 #77)
+#79 := [rewrite]: #78
+#85 := (iff #27 #84)
+#89 := (iff #84 #84)
+#87 := (iff #83 #83)
+#88 := [rewrite]: #87
+#90 := [monotonicity #88]: #89
+#86 := [rewrite]: #85
+#91 := [trans #86 #90]: #85
+#94 := [monotonicity #91 #79]: #93
+#81 := (iff #26 #80)
+#74 := (iff #24 #73)
+#75 := [rewrite]: #74
+#82 := [monotonicity #75 #79]: #81
+#97 := [monotonicity #82 #94]: #96
+#109 := [monotonicity #97 #106]: #108
+#112 := [monotonicity #109]: #111
+#115 := [monotonicity #112]: #114
+#118 := [quant-intro #115]: #117
+#51 := [asserted]: #37
+#119 := [mp #51 #118]: #116
+#191 := [mp #119 #190]: #188
+#210 := [mp~ #191 #166]: #188
+#239 := [mp #210 #238]: #236
+#270 := [mp #239 #269]: #267
+#706 := [mp #270 #705]: #701
+#62 := -3::Int
+#8 := 3::Int
+#9 := (f4 f5 3::Int)
+#59 := (f3 #9 -1::Int)
+#65 := (= #59 -3::Int)
+#68 := (not #65)
+#13 := (- 3::Int)
+#10 := 1::Int
+#11 := (- 1::Int)
+#12 := (f3 #9 #11)
+#14 := (= #12 #13)
+#15 := (not #14)
+#69 := (iff #15 #68)
+#66 := (iff #14 #65)
+#63 := (= #13 -3::Int)
+#64 := [rewrite]: #63
+#60 := (= #12 #59)
+#57 := (= #11 -1::Int)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#67 := [monotonicity #61 #64]: #66
+#70 := [monotonicity #67]: #69
+#50 := [asserted]: #15
+#71 := [mp #50 #70]: #68
+#624 := (not #701)
+#616 := (or #624 #65)
+#363 := (* -1::Int -1::Int)
+#362 := (* -1::Int 3::Int)
+#695 := (div #362 #363)
+#696 := (* -1::Int #695)
+#697 := (+ #59 #696)
+#698 := (= #697 0::Int)
+#694 := (div 3::Int -1::Int)
+#351 := (* -1::Int #694)
+#481 := (+ #59 #351)
+#688 := (= #481 0::Int)
+#375 := (<= -1::Int 0::Int)
+#374 := (>= 3::Int 0::Int)
+#378 := (or #374 #375)
+#357 := (not #378)
+#364 := (<= 3::Int 0::Int)
+#376 := (or #364 #375)
+#377 := (not #376)
+#692 := (or #377 #357)
+#693 := (if #692 #688 #698)
+#373 := (= #59 0::Int)
+#371 := (= -1::Int 0::Int)
+#287 := (= 3::Int 0::Int)
+#372 := (or #287 #371)
+#699 := (if #372 #373 #693)
+#613 := (or #624 #699)
+#625 := (iff #613 #616)
+#627 := (iff #616 #616)
+#623 := [rewrite]: #627
+#635 := (iff #699 #65)
+#539 := (if false #373 #65)
+#634 := (iff #539 #65)
+#631 := [rewrite]: #634
+#540 := (iff #699 #539)
+#537 := (iff #693 #65)
+#518 := (if false #65 #65)
+#536 := (iff #518 #65)
+#529 := [rewrite]: #536
+#533 := (iff #693 #518)
+#630 := (iff #698 #65)
+#658 := (+ 3::Int #59)
+#502 := (= #658 0::Int)
+#646 := (iff #502 #65)
+#647 := [rewrite]: #646
+#534 := (iff #698 #502)
+#484 := (= #697 #658)
+#657 := (+ #59 3::Int)
+#659 := (= #657 #658)
+#654 := [rewrite]: #659
+#524 := (= #697 #657)
+#641 := (= #696 3::Int)
+#379 := (* -1::Int -3::Int)
+#662 := (= #379 3::Int)
+#666 := [rewrite]: #662
+#640 := (= #696 #379)
+#637 := (= #695 -3::Int)
+#651 := (div -3::Int 1::Int)
+#483 := (= #651 -3::Int)
+#636 := [rewrite]: #483
+#480 := (= #695 #651)
+#650 := (= #363 1::Int)
+#644 := [rewrite]: #650
+#643 := (= #362 -3::Int)
+#649 := [rewrite]: #643
+#482 := [monotonicity #649 #644]: #480
+#639 := [trans #482 #636]: #637
+#638 := [monotonicity #639]: #640
+#523 := [trans #638 #666]: #641
+#525 := [monotonicity #523]: #524
+#632 := [trans #525 #654]: #484
+#629 := [monotonicity #632]: #534
+#633 := [trans #629 #647]: #630
+#648 := (iff #688 #65)
+#503 := (iff #688 #502)
+#660 := (= #481 #658)
+#652 := (= #481 #657)
+#655 := (= #351 3::Int)
+#661 := (= #351 #379)
+#663 := (= #694 -3::Int)
+#664 := [rewrite]: #663
+#665 := [monotonicity #664]: #661
+#656 := [trans #665 #666]: #655
+#653 := [monotonicity #656]: #652
+#501 := [trans #653 #654]: #660
+#645 := [monotonicity #501]: #503
+#642 := [trans #645 #647]: #648
+#384 := (iff #692 false)
+#350 := (or false false)
+#675 := (iff #350 false)
+#338 := [rewrite]: #675
+#382 := (iff #692 #350)
+#668 := (iff #357 false)
+#1 := true
+#325 := (not true)
+#684 := (iff #325 false)
+#687 := [rewrite]: #684
+#667 := (iff #357 #325)
+#392 := (iff #378 true)
+#398 := (or true true)
+#669 := (iff #398 true)
+#670 := [rewrite]: #669
+#399 := (iff #378 #398)
+#678 := (iff #375 true)
+#679 := [rewrite]: #678
+#396 := (iff #374 true)
+#397 := [rewrite]: #396
+#293 := [monotonicity #397 #679]: #399
+#393 := [trans #293 #670]: #392
+#671 := [monotonicity #393]: #667
+#672 := [trans #671 #687]: #668
+#673 := (iff #377 false)
+#326 := (iff #377 #325)
+#683 := (iff #376 true)
+#680 := (or false true)
+#682 := (iff #680 true)
+#320 := [rewrite]: #682
+#681 := (iff #376 #680)
+#341 := (iff #364 false)
+#677 := [rewrite]: #341
+#676 := [monotonicity #677 #679]: #681
+#685 := [trans #676 #320]: #683
+#686 := [monotonicity #685]: #326
+#674 := [trans #686 #687]: #673
+#383 := [monotonicity #674 #672]: #382
+#385 := [trans #383 #338]: #384
+#535 := [monotonicity #385 #642 #633]: #533
+#538 := [trans #535 #529]: #537
+#339 := (iff #372 false)
+#691 := (iff #372 #350)
+#354 := (iff #371 false)
+#690 := [rewrite]: #354
+#689 := (iff #287 false)
+#349 := [rewrite]: #689
+#334 := [monotonicity #349 #690]: #691
+#340 := [trans #334 #338]: #339
+#541 := [monotonicity #340 #538]: #540
+#622 := [trans #541 #631]: #635
+#626 := [monotonicity #622]: #625
+#628 := [trans #626 #623]: #625
+#615 := [quant-inst #8 #56]: #613
+#617 := [mp #615 #628]: #616
+[unit-resolution #617 #71 #706]: false
+fa2287cb3b9cb63c17ef33b8c249637d75072d26 364 0
+unsat
+#2 := false
+#20 := 0::Int
+#10 := 1::Int
+decl f6 :: Int
+#8 := f6
+#56 := -1::Int
+#62 := (* -1::Int f6)
+#671 := (div #62 1::Int)
+#669 := (* -1::Int #671)
+decl f3 :: (-> S2 Int Int)
+decl f4 :: (-> S3 Int S2)
+decl f5 :: S3
+#7 := f5
+#9 := (f4 f5 f6)
+#59 := (f3 #9 -1::Int)
+#674 := (+ #59 #669)
+#648 := (<= #674 0::Int)
+#665 := (= #674 0::Int)
+#380 := (= f6 0::Int)
+#531 := (not #380)
+#384 := (<= f6 0::Int)
+#635 := [hypothesis]: #380
+#631 := (or #531 #384)
+#636 := [th-lemma arith triangle-eq]: #631
+#625 := [unit-resolution #636 #635]: #384
+#167 := (+ f6 #59)
+#295 := (<= #167 0::Int)
+#626 := (not #295)
+#379 := (>= #167 0::Int)
+#365 := (>= f6 0::Int)
+#641 := (not #665)
+#646 := (>= #674 0::Int)
+#578 := (not #646)
+#587 := (not #379)
+#588 := [hypothesis]: #587
+#579 := (or #578 #379)
+#586 := [hypothesis]: #646
+#622 := (+ f6 #671)
+#619 := (>= #622 0::Int)
+#629 := (= #622 0::Int)
+#1 := true
+#164 := [true-axiom]: true
+#589 := (or false #629)
+#590 := [th-lemma arith]: #589
+#585 := [unit-resolution #590 #164]: #629
+#591 := (not #629)
+#577 := (or #591 #619)
+#573 := [th-lemma arith triangle-eq]: #577
+#574 := [unit-resolution #573 #585]: #619
+#575 := [th-lemma arith farkas 1 -1 1 #574 #588 #586]: false
+#580 := [lemma #575]: #579
+#545 := [unit-resolution #580 #588]: #578
+#549 := (or #641 #646)
+#546 := [th-lemma arith triangle-eq]: #549
+#547 := [unit-resolution #546 #545]: #641
+#639 := (or #380 #665)
+#383 := (= #59 0::Int)
+#653 := (if #380 #383 #665)
+#18 := (:var 0 Int)
+#16 := (:var 1 Int)
+#17 := (f4 f5 #16)
+#19 := (f3 #17 #18)
+#708 := (pattern #19)
+#101 := (* -1::Int #18)
+#98 := (* -1::Int #16)
+#104 := (div #98 #101)
+#268 := (* -1::Int #104)
+#269 := (+ #19 #268)
+#270 := (= #269 0::Int)
+#30 := (div #16 #18)
+#265 := (* -1::Int #30)
+#266 := (+ #19 #265)
+#267 := (= #266 0::Int)
+#76 := (<= #18 0::Int)
+#175 := (>= #16 0::Int)
+#228 := (or #175 #76)
+#229 := (not #228)
+#72 := (<= #16 0::Int)
+#224 := (or #72 #76)
+#225 := (not #224)
+#232 := (or #225 #229)
+#271 := (if #232 #267 #270)
+#264 := (= #19 0::Int)
+#22 := (= #18 0::Int)
+#21 := (= #16 0::Int)
+#23 := (or #21 #22)
+#272 := (if #23 #264 #271)
+#709 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #708) #272)
+#275 := (forall (vars (?v0 Int) (?v1 Int)) #272)
+#712 := (iff #275 #709)
+#710 := (iff #272 #272)
+#711 := [refl]: #710
+#713 := [quant-intro #711]: #712
+#235 := (if #232 #30 #104)
+#238 := (if #23 0::Int #235)
+#241 := (= #19 #238)
+#244 := (forall (vars (?v0 Int) (?v1 Int)) #241)
+#276 := (iff #244 #275)
+#273 := (iff #241 #272)
+#274 := [rewrite]: #273
+#277 := [quant-intro #274]: #276
+#77 := (not #76)
+#178 := (not #175)
+#181 := (and #178 #77)
+#73 := (not #72)
+#80 := (and #73 #77)
+#184 := (or #80 #181)
+#187 := (if #184 #30 #104)
+#190 := (if #23 0::Int #187)
+#193 := (= #19 #190)
+#196 := (forall (vars (?v0 Int) (?v1 Int)) #193)
+#245 := (iff #196 #244)
+#242 := (iff #193 #241)
+#239 := (= #190 #238)
+#236 := (= #187 #235)
+#233 := (iff #184 #232)
+#230 := (iff #181 #229)
+#231 := [rewrite]: #230
+#226 := (iff #80 #225)
+#227 := [rewrite]: #226
+#234 := [monotonicity #227 #231]: #233
+#237 := [monotonicity #234]: #236
+#240 := [monotonicity #237]: #239
+#243 := [monotonicity #240]: #242
+#246 := [quant-intro #243]: #245
+#218 := (~ #196 #196)
+#220 := (~ #193 #193)
+#221 := [refl]: #220
+#219 := [nnf-pos #221]: #218
+#83 := (<= 0::Int #16)
+#84 := (not #83)
+#92 := (and #84 #77)
+#95 := (or #80 #92)
+#107 := (if #95 #30 #104)
+#110 := (if #23 0::Int #107)
+#113 := (= #19 #110)
+#116 := (forall (vars (?v0 Int) (?v1 Int)) #113)
+#197 := (iff #116 #196)
+#194 := (iff #113 #193)
+#191 := (= #110 #190)
+#188 := (= #107 #187)
+#185 := (iff #95 #184)
+#182 := (iff #92 #181)
+#179 := (iff #84 #178)
+#176 := (iff #83 #175)
+#177 := [rewrite]: #176
+#180 := [monotonicity #177]: #179
+#183 := [monotonicity #180]: #182
+#186 := [monotonicity #183]: #185
+#189 := [monotonicity #186]: #188
+#192 := [monotonicity #189]: #191
+#195 := [monotonicity #192]: #194
+#198 := [quant-intro #195]: #197
+#32 := (- #18)
+#31 := (- #16)
+#33 := (div #31 #32)
+#25 := (< 0::Int #18)
+#27 := (< #16 0::Int)
+#28 := (and #27 #25)
+#24 := (< 0::Int #16)
+#26 := (and #24 #25)
+#29 := (or #26 #28)
+#34 := (if #29 #30 #33)
+#35 := (if #23 0::Int #34)
+#36 := (= #19 #35)
+#37 := (forall (vars (?v0 Int) (?v1 Int)) #36)
+#117 := (iff #37 #116)
+#114 := (iff #36 #113)
+#111 := (= #35 #110)
+#108 := (= #34 #107)
+#105 := (= #33 #104)
+#102 := (= #32 #101)
+#103 := [rewrite]: #102
+#99 := (= #31 #98)
+#100 := [rewrite]: #99
+#106 := [monotonicity #100 #103]: #105
+#96 := (iff #29 #95)
+#93 := (iff #28 #92)
+#78 := (iff #25 #77)
+#79 := [rewrite]: #78
+#85 := (iff #27 #84)
+#89 := (iff #84 #84)
+#87 := (iff #83 #83)
+#88 := [rewrite]: #87
+#90 := [monotonicity #88]: #89
+#86 := [rewrite]: #85
+#91 := [trans #86 #90]: #85
+#94 := [monotonicity #91 #79]: #93
+#81 := (iff #26 #80)
+#74 := (iff #24 #73)
+#75 := [rewrite]: #74
+#82 := [monotonicity #75 #79]: #81
+#97 := [monotonicity #82 #94]: #96
+#109 := [monotonicity #97 #106]: #108
+#112 := [monotonicity #109]: #111
+#115 := [monotonicity #112]: #114
+#118 := [quant-intro #115]: #117
+#51 := [asserted]: #37
+#119 := [mp #51 #118]: #116
+#199 := [mp #119 #198]: #196
+#165 := [mp~ #199 #219]: #196
+#247 := [mp #165 #246]: #244
+#278 := [mp #247 #277]: #275
+#714 := [mp #278 #713]: #709
+#656 := (not #709)
+#650 := (or #656 #653)
+#703 := (* -1::Int -1::Int)
+#704 := (div #62 #703)
+#705 := (* -1::Int #704)
+#706 := (+ #59 #705)
+#701 := (= #706 0::Int)
+#489 := (div f6 -1::Int)
+#696 := (* -1::Int #489)
+#370 := (+ #59 #696)
+#371 := (= #370 0::Int)
+#385 := (<= -1::Int 0::Int)
+#700 := (or #365 #385)
+#702 := (not #700)
+#382 := (or #384 #385)
+#386 := (not #382)
+#359 := (or #386 #702)
+#707 := (if #359 #371 #701)
+#381 := (= -1::Int 0::Int)
+#372 := (or #380 #381)
+#697 := (if #372 #383 #707)
+#651 := (or #656 #697)
+#658 := (iff #651 #650)
+#659 := (iff #650 #650)
+#488 := [rewrite]: #659
+#654 := (iff #697 #653)
+#510 := (iff #707 #665)
+#666 := (if false #371 #665)
+#668 := (iff #666 #665)
+#509 := [rewrite]: #668
+#667 := (iff #707 #666)
+#660 := (iff #701 #665)
+#663 := (= #706 #674)
+#673 := (= #705 #669)
+#672 := (= #704 #671)
+#392 := (= #703 1::Int)
+#393 := [rewrite]: #392
+#387 := [monotonicity #393]: #672
+#670 := [monotonicity #387]: #673
+#664 := [monotonicity #670]: #663
+#661 := [monotonicity #664]: #660
+#390 := (iff #359 false)
+#401 := (or false false)
+#676 := (iff #401 false)
+#680 := [rewrite]: #676
+#675 := (iff #359 #401)
+#678 := (iff #702 false)
+#328 := (not true)
+#333 := (iff #328 false)
+#334 := [rewrite]: #333
+#301 := (iff #702 #328)
+#406 := (iff #700 true)
+#695 := (or #365 true)
+#404 := (iff #695 true)
+#405 := [rewrite]: #404
+#681 := (iff #700 #695)
+#348 := (iff #385 true)
+#349 := [rewrite]: #348
+#682 := [monotonicity #349]: #681
+#407 := [trans #682 #405]: #406
+#677 := [monotonicity #407]: #301
+#400 := [trans #677 #334]: #678
+#694 := (iff #386 false)
+#691 := (iff #386 #328)
+#684 := (iff #382 true)
+#685 := (or #384 true)
+#688 := (iff #685 true)
+#689 := [rewrite]: #688
+#686 := (iff #382 #685)
+#687 := [monotonicity #349]: #686
+#690 := [trans #687 #689]: #684
+#693 := [monotonicity #690]: #691
+#692 := [trans #693 #334]: #694
+#679 := [monotonicity #692 #400]: #675
+#391 := [trans #679 #680]: #390
+#662 := [monotonicity #391 #661]: #667
+#511 := [trans #662 #509]: #510
+#346 := (iff #372 #380)
+#698 := (or #380 false)
+#342 := (iff #698 #380)
+#683 := [rewrite]: #342
+#358 := (iff #372 #698)
+#357 := (iff #381 false)
+#362 := [rewrite]: #357
+#699 := [monotonicity #362]: #358
+#347 := [trans #699 #683]: #346
+#655 := [monotonicity #347 #511]: #654
+#652 := [monotonicity #655]: #658
+#490 := [trans #652 #488]: #658
+#657 := [quant-inst #8 #56]: #651
+#491 := [mp #657 #490]: #650
+#548 := [unit-resolution #491 #714]: #653
+#649 := (not #653)
+#492 := (or #649 #380 #665)
+#640 := [def-axiom]: #492
+#643 := [unit-resolution #640 #548]: #639
+#615 := [unit-resolution #643 #547]: #380
+#620 := (or #531 #365)
+#606 := [th-lemma arith triangle-eq]: #620
+#607 := [unit-resolution #606 #615]: #365
+#645 := (>= #59 0::Int)
+#609 := (or #531 #383)
+#532 := (or #649 #531 #383)
+#533 := [def-axiom]: #532
+#610 := [unit-resolution #533 #548]: #609
+#611 := [unit-resolution #610 #615]: #383
+#542 := (not #383)
+#630 := (or #542 #645)
+#632 := [th-lemma arith triangle-eq]: #630
+#623 := [unit-resolution #632 #611]: #645
+#633 := [th-lemma arith farkas 1 -1 1 #623 #588 #607]: false
+#634 := [lemma #633]: #379
+#613 := (or #626 #587)
+#168 := (= #167 0::Int)
+#171 := (not #168)
+#65 := (= #59 #62)
+#68 := (not #65)
+#172 := (iff #68 #171)
+#169 := (iff #65 #168)
+#170 := [rewrite]: #169
+#173 := [monotonicity #170]: #172
+#13 := (- f6)
+#11 := (- 1::Int)
+#12 := (f3 #9 #11)
+#14 := (= #12 #13)
+#15 := (not #14)
+#69 := (iff #15 #68)
+#66 := (iff #14 #65)
+#63 := (= #13 #62)
+#64 := [rewrite]: #63
+#60 := (= #12 #59)
+#57 := (= #11 -1::Int)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#67 := [monotonicity #61 #64]: #66
+#70 := [monotonicity #67]: #69
+#50 := [asserted]: #15
+#71 := [mp #50 #70]: #68
+#174 := [mp #71 #173]: #171
+#627 := (or #168 #626 #587)
+#628 := [th-lemma arith triangle-eq]: #627
+#614 := [unit-resolution #628 #174]: #613
+#616 := [unit-resolution #614 #634]: #626
+#644 := (<= #59 0::Int)
+#617 := [unit-resolution #610 #635]: #383
+#618 := (or #542 #644)
+#581 := [th-lemma arith triangle-eq]: #618
+#576 := [unit-resolution #581 #617]: #644
+#582 := [th-lemma arith farkas 1 -1 1 #576 #616 #625]: false
+#555 := [lemma #582]: #531
+#539 := [unit-resolution #643 #555]: #665
+#540 := (or #641 #648)
+#550 := [th-lemma arith triangle-eq]: #540
+#530 := [unit-resolution #550 #539]: #648
+#563 := (<= #622 0::Int)
+#551 := (or #591 #563)
+#506 := [th-lemma arith triangle-eq]: #551
+#507 := [unit-resolution #506 #585]: #563
+[th-lemma arith farkas 1 -1 1 #507 #616 #530]: false
+0fa0312c612ec397b0cce6b0237bbb9cfd628037 289 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#16 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#14 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#15 := (f4 f5 #14)
+#17 := (f3 #15 #16)
+#683 := (pattern #17)
+#8 := 0::Int
+#79 := -1::Int
+#83 := (* -1::Int #16)
+#80 := (* -1::Int #14)
+#86 := (div #80 #83)
+#242 := (* -1::Int #86)
+#243 := (+ #17 #242)
+#244 := (= #243 0::Int)
+#27 := (div #14 #16)
+#239 := (* -1::Int #27)
+#240 := (+ #17 #239)
+#241 := (= #240 0::Int)
+#57 := (<= #16 0::Int)
+#149 := (>= #14 0::Int)
+#202 := (or #149 #57)
+#203 := (not #202)
+#53 := (<= #14 0::Int)
+#198 := (or #53 #57)
+#199 := (not #198)
+#206 := (or #199 #203)
+#245 := (if #206 #241 #244)
+#238 := (= #17 0::Int)
+#19 := (= #16 0::Int)
+#18 := (= #14 0::Int)
+#20 := (or #18 #19)
+#246 := (if #20 #238 #245)
+#684 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #683) #246)
+#249 := (forall (vars (?v0 Int) (?v1 Int)) #246)
+#687 := (iff #249 #684)
+#685 := (iff #246 #246)
+#686 := [refl]: #685
+#688 := [quant-intro #686]: #687
+#209 := (if #206 #27 #86)
+#212 := (if #20 0::Int #209)
+#215 := (= #17 #212)
+#218 := (forall (vars (?v0 Int) (?v1 Int)) #215)
+#250 := (iff #218 #249)
+#247 := (iff #215 #246)
+#248 := [rewrite]: #247
+#251 := [quant-intro #248]: #250
+#58 := (not #57)
+#152 := (not #149)
+#155 := (and #152 #58)
+#54 := (not #53)
+#61 := (and #54 #58)
+#158 := (or #61 #155)
+#161 := (if #158 #27 #86)
+#164 := (if #20 0::Int #161)
+#167 := (= #17 #164)
+#170 := (forall (vars (?v0 Int) (?v1 Int)) #167)
+#219 := (iff #170 #218)
+#216 := (iff #167 #215)
+#213 := (= #164 #212)
+#210 := (= #161 #209)
+#207 := (iff #158 #206)
+#204 := (iff #155 #203)
+#205 := [rewrite]: #204
+#200 := (iff #61 #199)
+#201 := [rewrite]: #200
+#208 := [monotonicity #201 #205]: #207
+#211 := [monotonicity #208]: #210
+#214 := [monotonicity #211]: #213
+#217 := [monotonicity #214]: #216
+#220 := [quant-intro #217]: #219
+#194 := (~ #170 #170)
+#192 := (~ #167 #167)
+#193 := [refl]: #192
+#195 := [nnf-pos #193]: #194
+#64 := (<= 0::Int #14)
+#65 := (not #64)
+#73 := (and #65 #58)
+#76 := (or #61 #73)
+#89 := (if #76 #27 #86)
+#92 := (if #20 0::Int #89)
+#95 := (= #17 #92)
+#98 := (forall (vars (?v0 Int) (?v1 Int)) #95)
+#171 := (iff #98 #170)
+#168 := (iff #95 #167)
+#165 := (= #92 #164)
+#162 := (= #89 #161)
+#159 := (iff #76 #158)
+#156 := (iff #73 #155)
+#153 := (iff #65 #152)
+#150 := (iff #64 #149)
+#151 := [rewrite]: #150
+#154 := [monotonicity #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [monotonicity #163]: #165
+#169 := [monotonicity #166]: #168
+#172 := [quant-intro #169]: #171
+#29 := (- #16)
+#28 := (- #14)
+#30 := (div #28 #29)
+#22 := (< 0::Int #16)
+#24 := (< #14 0::Int)
+#25 := (and #24 #22)
+#21 := (< 0::Int #14)
+#23 := (and #21 #22)
+#26 := (or #23 #25)
+#31 := (if #26 #27 #30)
+#32 := (if #20 0::Int #31)
+#33 := (= #17 #32)
+#34 := (forall (vars (?v0 Int) (?v1 Int)) #33)
+#99 := (iff #34 #98)
+#96 := (iff #33 #95)
+#93 := (= #32 #92)
+#90 := (= #31 #89)
+#87 := (= #30 #86)
+#84 := (= #29 #83)
+#85 := [rewrite]: #84
+#81 := (= #28 #80)
+#82 := [rewrite]: #81
+#88 := [monotonicity #82 #85]: #87
+#77 := (iff #26 #76)
+#74 := (iff #25 #73)
+#59 := (iff #22 #58)
+#60 := [rewrite]: #59
+#66 := (iff #24 #65)
+#70 := (iff #65 #65)
+#68 := (iff #64 #64)
+#69 := [rewrite]: #68
+#71 := [monotonicity #69]: #70
+#67 := [rewrite]: #66
+#72 := [trans #67 #71]: #66
+#75 := [monotonicity #72 #60]: #74
+#62 := (iff #23 #61)
+#55 := (iff #21 #54)
+#56 := [rewrite]: #55
+#63 := [monotonicity #56 #60]: #62
+#78 := [monotonicity #63 #75]: #77
+#91 := [monotonicity #78 #88]: #90
+#94 := [monotonicity #91]: #93
+#97 := [monotonicity #94]: #96
+#100 := [quant-intro #97]: #99
+#48 := [asserted]: #34
+#101 := [mp #48 #100]: #98
+#173 := [mp #101 #172]: #170
+#147 := [mp~ #173 #195]: #170
+#221 := [mp #147 #220]: #218
+#252 := [mp #221 #251]: #249
+#689 := [mp #252 #688]: #684
+#10 := 3::Int
+#9 := (f4 f5 0::Int)
+#11 := (f3 #9 3::Int)
+#12 := (= #11 0::Int)
+#13 := (not #12)
+#47 := [asserted]: #13
+#501 := (not #684)
+#516 := (or #501 #12)
+#345 := (* -1::Int 3::Int)
+#671 := (* -1::Int 0::Int)
+#346 := (div #671 #345)
+#678 := (* -1::Int #346)
+#679 := (+ #11 #678)
+#680 := (= #679 0::Int)
+#675 := (div 0::Int 3::Int)
+#677 := (* -1::Int #675)
+#334 := (+ #11 #677)
+#464 := (= #334 0::Int)
+#347 := (<= 3::Int 0::Int)
+#360 := (>= 0::Int 0::Int)
+#357 := (or #360 #347)
+#361 := (not #357)
+#356 := (<= 0::Int 0::Int)
+#358 := (or #356 #347)
+#359 := (not #358)
+#340 := (or #359 #361)
+#681 := (if #340 #464 #680)
+#354 := (= 3::Int 0::Int)
+#269 := (= 0::Int 0::Int)
+#355 := (or #269 #354)
+#676 := (if #355 #12 #681)
+#518 := (or #501 #676)
+#512 := (iff #518 #516)
+#521 := (iff #516 #516)
+#522 := [rewrite]: #521
+#613 := (iff #676 #12)
+#1 := true
+#508 := (if true #12 #12)
+#517 := (iff #508 #12)
+#612 := [rewrite]: #517
+#467 := (iff #676 #508)
+#506 := (iff #681 #12)
+#620 := (if false #12 #12)
+#621 := (iff #620 #12)
+#624 := [rewrite]: #621
+#622 := (iff #681 #620)
+#466 := (iff #680 #12)
+#463 := (= #679 #11)
+#648 := (+ #11 0::Int)
+#638 := (= #648 #11)
+#639 := [rewrite]: #638
+#627 := (= #679 #648)
+#632 := (= #678 0::Int)
+#646 := (= #671 0::Int)
+#647 := [rewrite]: #646
+#625 := (= #678 #671)
+#630 := (= #346 0::Int)
+#642 := -3::Int
+#484 := (div 0::Int -3::Int)
+#628 := (= #484 0::Int)
+#629 := [rewrite]: #628
+#485 := (= #346 #484)
+#637 := (= #345 -3::Int)
+#643 := [rewrite]: #637
+#486 := [monotonicity #647 #643]: #485
+#631 := [trans #486 #629]: #630
+#626 := [monotonicity #631]: #625
+#633 := [trans #626 #647]: #632
+#634 := [monotonicity #633]: #627
+#465 := [trans #634 #639]: #463
+#619 := [monotonicity #465]: #466
+#636 := (iff #464 #12)
+#640 := (= #334 #11)
+#645 := (= #334 #648)
+#362 := (= #677 0::Int)
+#367 := (= #677 #671)
+#365 := (= #675 0::Int)
+#366 := [rewrite]: #365
+#368 := [monotonicity #366]: #367
+#644 := [trans #368 #647]: #362
+#649 := [monotonicity #644]: #645
+#635 := [trans #649 #639]: #640
+#641 := [monotonicity #635]: #636
+#651 := (iff #340 false)
+#653 := (or false false)
+#650 := (iff #653 false)
+#654 := [rewrite]: #650
+#375 := (iff #340 #653)
+#275 := (iff #361 false)
+#665 := (not true)
+#668 := (iff #665 false)
+#308 := [rewrite]: #668
+#381 := (iff #361 #665)
+#379 := (iff #357 true)
+#673 := (or true false)
+#317 := (iff #673 true)
+#658 := [rewrite]: #317
+#656 := (iff #357 #673)
+#660 := (iff #347 false)
+#661 := [rewrite]: #660
+#667 := (iff #360 true)
+#670 := [rewrite]: #667
+#657 := [monotonicity #670 #661]: #656
+#380 := [trans #657 #658]: #379
+#382 := [monotonicity #380]: #381
+#652 := [trans #382 #308]: #275
+#309 := (iff #359 false)
+#303 := (iff #359 #665)
+#664 := (iff #358 true)
+#662 := (iff #358 #673)
+#323 := (iff #356 true)
+#324 := [rewrite]: #323
+#663 := [monotonicity #324 #661]: #662
+#659 := [trans #663 #658]: #664
+#666 := [monotonicity #659]: #303
+#669 := [trans #666 #308]: #309
+#376 := [monotonicity #669 #652]: #375
+#655 := [trans #376 #654]: #651
+#623 := [monotonicity #655 #641 #619]: #622
+#507 := [trans #623 #624]: #506
+#321 := (iff #355 true)
+#333 := (iff #355 #673)
+#332 := (iff #354 false)
+#337 := [rewrite]: #332
+#682 := (iff #269 true)
+#672 := [rewrite]: #682
+#674 := [monotonicity #672 #337]: #333
+#322 := [trans #674 #658]: #321
+#615 := [monotonicity #322 #507]: #467
+#616 := [trans #615 #612]: #613
+#520 := [monotonicity #616]: #512
+#523 := [trans #520 #522]: #512
+#519 := [quant-inst #8 #10]: #518
+#524 := [mp #519 #523]: #516
+[unit-resolution #524 #47 #689]: false
+1b013ef09ce577cd8e25f770ced5ed59077a626b 305 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#17 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#15 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#16 := (f4 f5 #15)
+#18 := (f3 #16 #17)
+#697 := (pattern #18)
+#8 := 0::Int
+#93 := -1::Int
+#97 := (* -1::Int #17)
+#94 := (* -1::Int #15)
+#100 := (div #94 #97)
+#256 := (* -1::Int #100)
+#257 := (+ #18 #256)
+#258 := (= #257 0::Int)
+#28 := (div #15 #17)
+#253 := (* -1::Int #28)
+#254 := (+ #18 #253)
+#255 := (= #254 0::Int)
+#71 := (<= #17 0::Int)
+#163 := (>= #15 0::Int)
+#216 := (or #163 #71)
+#217 := (not #216)
+#67 := (<= #15 0::Int)
+#212 := (or #67 #71)
+#213 := (not #212)
+#220 := (or #213 #217)
+#259 := (if #220 #255 #258)
+#252 := (= #18 0::Int)
+#20 := (= #17 0::Int)
+#19 := (= #15 0::Int)
+#21 := (or #19 #20)
+#260 := (if #21 #252 #259)
+#698 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #697) #260)
+#263 := (forall (vars (?v0 Int) (?v1 Int)) #260)
+#701 := (iff #263 #698)
+#699 := (iff #260 #260)
+#700 := [refl]: #699
+#702 := [quant-intro #700]: #701
+#223 := (if #220 #28 #100)
+#226 := (if #21 0::Int #223)
+#229 := (= #18 #226)
+#232 := (forall (vars (?v0 Int) (?v1 Int)) #229)
+#264 := (iff #232 #263)
+#261 := (iff #229 #260)
+#262 := [rewrite]: #261
+#265 := [quant-intro #262]: #264
+#72 := (not #71)
+#166 := (not #163)
+#169 := (and #166 #72)
+#68 := (not #67)
+#75 := (and #68 #72)
+#172 := (or #75 #169)
+#175 := (if #172 #28 #100)
+#178 := (if #21 0::Int #175)
+#181 := (= #18 #178)
+#184 := (forall (vars (?v0 Int) (?v1 Int)) #181)
+#233 := (iff #184 #232)
+#230 := (iff #181 #229)
+#227 := (= #178 #226)
+#224 := (= #175 #223)
+#221 := (iff #172 #220)
+#218 := (iff #169 #217)
+#219 := [rewrite]: #218
+#214 := (iff #75 #213)
+#215 := [rewrite]: #214
+#222 := [monotonicity #215 #219]: #221
+#225 := [monotonicity #222]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [quant-intro #231]: #233
+#206 := (~ #184 #184)
+#208 := (~ #181 #181)
+#209 := [refl]: #208
+#207 := [nnf-pos #209]: #206
+#78 := (<= 0::Int #15)
+#79 := (not #78)
+#87 := (and #79 #72)
+#90 := (or #75 #87)
+#103 := (if #90 #28 #100)
+#106 := (if #21 0::Int #103)
 #109 := (= #18 #106)
 #112 := (forall (vars (?v0 Int) (?v1 Int)) #109)
-#152 := (iff #112 #151)
-#149 := (iff #109 #148)
-#146 := (= #106 #145)
-#143 := (= #103 #142)
-#140 := (iff #90 #139)
-#137 := (iff #87 #136)
-#134 := (iff #25 #133)
-#135 := [rewrite]: #134
-#127 := (iff #23 #126)
-#128 := [rewrite]: #127
-#138 := [monotonicity #128 #135]: #137
-#130 := (iff #24 #129)
-#123 := (iff #22 #122)
-#124 := [rewrite]: #123
-#131 := [monotonicity #124 #128]: #130
-#141 := [monotonicity #131 #138]: #140
-#144 := [monotonicity #141]: #143
-#119 := (iff #84 #21)
-#117 := (iff #81 #20)
-#118 := [rewrite]: #117
-#115 := (iff #78 #19)
-#116 := [rewrite]: #115
-#120 := [monotonicity #116 #118]: #119
-#147 := [monotonicity #120 #144]: #146
-#150 := [monotonicity #147]: #149
-#153 := [quant-intro #150]: #152
+#185 := (iff #112 #184)
+#182 := (iff #109 #181)
+#179 := (= #106 #178)
+#176 := (= #103 #175)
+#173 := (iff #90 #172)
+#170 := (iff #87 #169)
+#167 := (iff #79 #166)
+#164 := (iff #78 #163)
+#165 := [rewrite]: #164
+#168 := [monotonicity #165]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#180 := [monotonicity #177]: #179
+#183 := [monotonicity #180]: #182
+#186 := [quant-intro #183]: #185
+#30 := (- #17)
+#29 := (- #15)
+#31 := (div #29 #30)
+#23 := (< 0::Int #17)
+#25 := (< #15 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #15)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#32 := (if #27 #28 #31)
+#33 := (if #21 0::Int #32)
+#34 := (= #18 #33)
+#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
 #113 := (iff #35 #112)
 #110 := (iff #34 #109)
 #107 := (= #33 #106)
@@ -30336,881 +29448,891 @@
 #102 := [monotonicity #96 #99]: #101
 #91 := (iff #27 #90)
 #88 := (iff #26 #87)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
+#73 := (iff #23 #72)
+#74 := [rewrite]: #73
+#80 := (iff #25 #79)
+#84 := (iff #79 #79)
+#82 := (iff #78 #78)
+#83 := [rewrite]: #82
+#85 := [monotonicity #83]: #84
+#81 := [rewrite]: #80
+#86 := [trans #81 #85]: #80
+#89 := [monotonicity #86 #74]: #88
+#76 := (iff #24 #75)
+#69 := (iff #22 #68)
+#70 := [rewrite]: #69
+#77 := [monotonicity #70 #74]: #76
+#92 := [monotonicity #77 #89]: #91
 #105 := [monotonicity #92 #102]: #104
-#85 := (iff #21 #84)
-#82 := (iff #20 #81)
-#83 := [rewrite]: #82
-#79 := (iff #19 #78)
-#80 := [rewrite]: #79
-#86 := [monotonicity #80 #83]: #85
-#108 := [monotonicity #86 #105]: #107
+#108 := [monotonicity #105]: #107
 #111 := [monotonicity #108]: #110
 #114 := [quant-intro #111]: #113
-#155 := [trans #114 #153]: #154
-#77 := [asserted]: #35
-#156 := [mp #77 #155]: #151
-#205 := [mp~ #156 #214]: #151
-#236 := [mp #205 #235]: #233
-#267 := [mp #236 #266]: #264
-#761 := [mp #267 #760]: #756
-#11 := 3::Int
-#10 := (f4 f5 0::Int)
-#12 := (f3 #10 3::Int)
+#49 := [asserted]: #35
+#115 := [mp #49 #114]: #112
+#187 := [mp #115 #186]: #184
+#204 := [mp~ #187 #207]: #184
+#235 := [mp #204 #234]: #232
+#266 := [mp #235 #265]: #263
+#703 := [mp #266 #702]: #698
+#54 := -3::Int
+#9 := (f4 f5 0::Int)
+#57 := (f3 #9 -3::Int)
+#60 := (= #57 0::Int)
+#63 := (not #60)
+#10 := 3::Int
+#11 := (- 3::Int)
+#12 := (f3 #9 #11)
 #13 := (= #12 0::Int)
 #14 := (not #13)
-#66 := [asserted]: #14
-#590 := (not #756)
-#591 := (or #590 #13)
-#341 := (* -1::Int 3::Int)
-#426 := (* -1::Int 0::Int)
-#427 := (div #426 #341)
-#428 := (* -1::Int #427)
-#419 := (+ #12 #428)
-#430 := (= #419 0::Int)
-#431 := (div 0::Int 3::Int)
-#359 := (* -1::Int #431)
-#432 := (+ #12 #359)
-#429 := (= #432 0::Int)
-#433 := (>= 0::Int 0::Int)
-#412 := (<= 3::Int 0::Int)
-#747 := (or #412 #433)
-#749 := (not #747)
-#406 := (<= 0::Int 0::Int)
-#536 := (or #406 #412)
-#743 := (not #536)
-#417 := (or #743 #749)
-#418 := (ite #417 #429 #430)
-#750 := (= 3::Int 0::Int)
-#751 := (= 0::Int 0::Int)
-#752 := (or #751 #750)
-#753 := (ite #752 #13 #418)
-#584 := (or #590 #753)
-#593 := (iff #584 #591)
-#595 := (iff #591 #591)
-#596 := [rewrite]: #595
-#573 := (iff #753 #13)
-#1 := true
-#687 := (ite true #13 #13)
-#685 := (iff #687 #13)
-#688 := [rewrite]: #685
-#589 := (iff #753 #687)
-#580 := (iff #418 #13)
-#695 := (ite false #13 #13)
-#578 := (iff #695 #13)
-#579 := [rewrite]: #578
-#693 := (iff #418 #695)
-#692 := (iff #430 #13)
-#538 := (= #419 #12)
-#721 := (+ #12 0::Int)
-#712 := (= #721 #12)
-#707 := [rewrite]: #712
-#535 := (= #419 #721)
-#699 := (= #428 0::Int)
-#434 := (= #426 0::Int)
-#716 := [rewrite]: #434
-#704 := (= #428 #426)
-#697 := (= #427 0::Int)
-#715 := -3::Int
-#558 := (div 0::Int -3::Int)
-#702 := (= #558 0::Int)
-#703 := [rewrite]: #702
-#700 := (= #427 #558)
-#556 := (= #341 -3::Int)
-#557 := [rewrite]: #556
-#701 := [monotonicity #716 #557]: #700
-#698 := [trans #701 #703]: #697
-#705 := [monotonicity #698]: #704
-#706 := [trans #705 #716]: #699
-#537 := [monotonicity #706]: #535
-#691 := [trans #537 #707]: #538
-#694 := [monotonicity #691]: #692
-#714 := (iff #429 #13)
-#708 := (= #432 #12)
-#710 := (= #432 #721)
-#720 := (= #359 0::Int)
-#718 := (= #359 #426)
-#439 := (= #431 0::Int)
-#440 := [rewrite]: #439
-#719 := [monotonicity #440]: #718
-#717 := [trans #719 #716]: #720
-#711 := [monotonicity #717]: #710
-#713 := [trans #711 #707]: #708
-#709 := [monotonicity #713]: #714
-#437 := (iff #417 false)
-#448 := (or false false)
-#723 := (iff #448 false)
-#727 := [rewrite]: #723
-#722 := (iff #417 #448)
-#725 := (iff #749 false)
-#731 := (not true)
-#738 := (iff #731 false)
-#740 := [rewrite]: #738
-#347 := (iff #749 #731)
-#453 := (iff #747 true)
-#742 := (or false true)
-#451 := (iff #742 true)
-#452 := [rewrite]: #451
-#728 := (iff #747 #742)
-#741 := (iff #433 true)
-#739 := [rewrite]: #741
-#396 := (iff #412 false)
-#732 := [rewrite]: #396
-#729 := [monotonicity #732 #739]: #728
-#454 := [trans #729 #452]: #453
-#724 := [monotonicity #454]: #347
-#447 := [trans #724 #740]: #725
-#380 := (iff #743 false)
-#737 := (iff #743 #731)
-#735 := (iff #536 true)
-#409 := (or true false)
-#746 := (iff #409 true)
-#389 := [rewrite]: #746
-#733 := (iff #536 #409)
-#394 := (iff #406 true)
-#395 := [rewrite]: #394
-#734 := [monotonicity #395 #732]: #733
-#736 := [trans #734 #389]: #735
-#375 := [monotonicity #736]: #737
-#381 := [trans #375 #740]: #380
-#726 := [monotonicity #381 #447]: #722
-#438 := [trans #726 #727]: #437
-#696 := [monotonicity #438 #709 #694]: #693
-#539 := [trans #696 #579]: #580
-#730 := (iff #752 true)
-#745 := (iff #752 #409)
-#744 := (iff #750 false)
-#404 := [rewrite]: #744
-#748 := (iff #751 true)
-#754 := [rewrite]: #748
-#405 := [monotonicity #754 #404]: #745
-#393 := [trans #405 #389]: #730
-#684 := [monotonicity #393 #539]: #589
-#588 := [trans #684 #688]: #573
-#594 := [monotonicity #588]: #593
-#689 := [trans #594 #596]: #593
-#592 := [quant-inst #9 #11]: #584
-#686 := [mp #592 #689]: #591
-[unit-resolution #686 #66 #761]: false
-unsat
-092ba79ab133007633bbd2e87982795a7237ea61 322 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#17 := (f4 f5 #16)
-#19 := (f3 #17 #18)
-#771 := (pattern #19)
-#9 := 0::Int
-#109 := -1::Int
-#113 := (* -1::Int #18)
-#110 := (* -1::Int #16)
-#116 := (div #110 #113)
-#273 := (* -1::Int #116)
-#274 := (+ #19 #273)
-#275 := (= #274 0::Int)
-#29 := (div #16 #18)
-#270 := (* -1::Int #29)
-#271 := (+ #19 #270)
-#272 := (= #271 0::Int)
-#148 := (>= #16 0::Int)
-#141 := (<= #18 0::Int)
-#233 := (or #141 #148)
-#234 := (not #233)
-#137 := (<= #16 0::Int)
-#231 := (or #137 #141)
-#232 := (not #231)
-#237 := (or #232 #234)
-#276 := (ite #237 #272 #275)
-#269 := (= #19 0::Int)
-#21 := (= #18 0::Int)
-#20 := (= #16 0::Int)
-#22 := (or #20 #21)
-#277 := (ite #22 #269 #276)
-#772 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #771) #277)
-#280 := (forall (vars (?v0 Int) (?v1 Int)) #277)
-#775 := (iff #280 #772)
-#773 := (iff #277 #277)
-#774 := [refl]: #773
-#776 := [quant-intro #774]: #775
-#240 := (ite #237 #29 #116)
-#243 := (ite #22 0::Int #240)
-#246 := (= #19 #243)
-#249 := (forall (vars (?v0 Int) (?v1 Int)) #246)
-#281 := (iff #249 #280)
-#278 := (iff #246 #277)
-#279 := [rewrite]: #278
-#282 := [quant-intro #279]: #281
-#149 := (not #148)
-#142 := (not #141)
-#152 := (and #142 #149)
-#138 := (not #137)
-#145 := (and #138 #142)
-#155 := (or #145 #152)
-#158 := (ite #155 #29 #116)
-#161 := (ite #22 0::Int #158)
-#164 := (= #19 #161)
-#167 := (forall (vars (?v0 Int) (?v1 Int)) #164)
-#250 := (iff #167 #249)
-#247 := (iff #164 #246)
-#244 := (= #161 #243)
-#241 := (= #158 #240)
-#238 := (iff #155 #237)
-#235 := (iff #152 #234)
-#236 := [rewrite]: #235
-#225 := (iff #145 #232)
-#226 := [rewrite]: #225
-#239 := [monotonicity #226 #236]: #238
-#242 := [monotonicity #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [monotonicity #245]: #247
-#251 := [quant-intro #248]: #250
-#229 := (~ #167 #167)
-#227 := (~ #164 #164)
-#228 := [refl]: #227
-#230 := [nnf-pos #228]: #229
-#31 := (- #18)
-#30 := (- #16)
-#32 := (div #30 #31)
-#24 := (< 0::Int #18)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#33 := (ite #28 #29 #32)
-#34 := (ite #22 0::Int #33)
-#35 := (= #19 #34)
-#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
-#170 := (iff #36 #167)
-#103 := (and #24 #26)
-#106 := (or #25 #103)
-#119 := (ite #106 #29 #116)
-#97 := (= 0::Int #18)
-#94 := (= 0::Int #16)
-#100 := (or #94 #97)
-#122 := (ite #100 0::Int #119)
-#125 := (= #19 #122)
-#128 := (forall (vars (?v0 Int) (?v1 Int)) #125)
-#168 := (iff #128 #167)
-#165 := (iff #125 #164)
-#162 := (= #122 #161)
-#159 := (= #119 #158)
-#156 := (iff #106 #155)
-#153 := (iff #103 #152)
-#150 := (iff #26 #149)
-#151 := [rewrite]: #150
-#143 := (iff #24 #142)
-#144 := [rewrite]: #143
-#154 := [monotonicity #144 #151]: #153
-#146 := (iff #25 #145)
-#139 := (iff #23 #138)
-#140 := [rewrite]: #139
-#147 := [monotonicity #140 #144]: #146
-#157 := [monotonicity #147 #154]: #156
-#160 := [monotonicity #157]: #159
-#135 := (iff #100 #22)
-#133 := (iff #97 #21)
-#134 := [rewrite]: #133
-#131 := (iff #94 #20)
-#132 := [rewrite]: #131
-#136 := [monotonicity #132 #134]: #135
-#163 := [monotonicity #136 #160]: #162
-#166 := [monotonicity #163]: #165
-#169 := [quant-intro #166]: #168
-#129 := (iff #36 #128)
-#126 := (iff #35 #125)
-#123 := (= #34 #122)
-#120 := (= #33 #119)
-#117 := (= #32 #116)
-#114 := (= #31 #113)
-#115 := [rewrite]: #114
-#111 := (= #30 #110)
-#112 := [rewrite]: #111
-#118 := [monotonicity #112 #115]: #117
-#107 := (iff #28 #106)
-#104 := (iff #27 #103)
-#105 := [rewrite]: #104
-#108 := [monotonicity #105]: #107
-#121 := [monotonicity #108 #118]: #120
-#101 := (iff #22 #100)
-#98 := (iff #21 #97)
-#99 := [rewrite]: #98
-#95 := (iff #20 #94)
-#96 := [rewrite]: #95
-#102 := [monotonicity #96 #99]: #101
-#124 := [monotonicity #102 #121]: #123
-#127 := [monotonicity #124]: #126
-#130 := [quant-intro #127]: #129
-#171 := [trans #130 #169]: #170
-#93 := [asserted]: #36
-#172 := [mp #93 #171]: #167
-#221 := [mp~ #172 #230]: #167
-#252 := [mp #221 #251]: #249
-#283 := [mp #252 #282]: #280
-#777 := [mp #283 #776]: #772
-#68 := -3::Int
-#10 := (f4 f5 0::Int)
-#71 := (f3 #10 -3::Int)
-#74 := (= #71 0::Int)
-#87 := (not #74)
-#11 := 3::Int
-#12 := (- 3::Int)
-#13 := (f3 #10 #12)
-#14 := (= #13 0::Int)
-#15 := (not #14)
-#90 := (iff #15 #87)
-#77 := (= 0::Int #71)
-#82 := (not #77)
-#88 := (iff #82 #87)
-#85 := (iff #77 #74)
-#86 := [rewrite]: #85
-#89 := [monotonicity #86]: #88
-#83 := (iff #15 #82)
-#80 := (iff #14 #77)
-#78 := (iff #74 #77)
-#79 := [rewrite]: #78
-#75 := (iff #14 #74)
-#72 := (= #13 #71)
-#69 := (= #12 -3::Int)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73]: #75
-#81 := [trans #76 #79]: #80
-#84 := [monotonicity #81]: #83
-#91 := [trans #84 #89]: #90
-#67 := [asserted]: #15
-#92 := [mp #67 #91]: #87
-#604 := (not #772)
-#606 := (or #604 #74)
-#357 := (* -1::Int -3::Int)
-#442 := (* -1::Int 0::Int)
-#443 := (div #442 #357)
-#444 := (* -1::Int #443)
-#435 := (+ #71 #444)
-#446 := (= #435 0::Int)
-#447 := (div 0::Int -3::Int)
-#375 := (* -1::Int #447)
-#448 := (+ #71 #375)
-#445 := (= #448 0::Int)
-#449 := (>= 0::Int 0::Int)
-#428 := (<= -3::Int 0::Int)
-#763 := (or #428 #449)
-#765 := (not #763)
-#422 := (<= 0::Int 0::Int)
-#552 := (or #422 #428)
-#759 := (not #552)
-#433 := (or #759 #765)
-#434 := (ite #433 #445 #446)
-#766 := (= -3::Int 0::Int)
-#767 := (= 0::Int 0::Int)
-#768 := (or #767 #766)
-#769 := (ite #768 #74 #434)
-#607 := (or #604 #769)
-#608 := (iff #607 #606)
-#610 := (iff #606 #606)
-#611 := [rewrite]: #610
-#704 := (iff #769 #74)
-#1 := true
-#555 := (ite true #74 #74)
-#700 := (iff #555 #74)
-#701 := [rewrite]: #700
-#703 := (iff #769 #555)
-#595 := (iff #434 #74)
-#710 := (ite false #74 #74)
-#712 := (iff #710 #74)
-#594 := [rewrite]: #712
-#711 := (iff #434 #710)
-#707 := (iff #446 #74)
-#553 := (= #435 #71)
-#737 := (+ #71 0::Int)
-#728 := (= #737 #71)
-#723 := [rewrite]: #728
-#722 := (= #435 #737)
-#721 := (= #444 0::Int)
-#450 := (= #442 0::Int)
-#732 := [rewrite]: #450
-#714 := (= #444 #442)
-#719 := (= #443 0::Int)
-#573 := (div 0::Int 3::Int)
-#717 := (= #573 0::Int)
-#718 := [rewrite]: #717
-#574 := (= #443 #573)
-#731 := (= #357 3::Int)
-#572 := [rewrite]: #731
-#716 := [monotonicity #732 #572]: #574
-#713 := [trans #716 #718]: #719
-#720 := [monotonicity #713]: #714
-#715 := [trans #720 #732]: #721
-#551 := [monotonicity #715]: #722
-#554 := [trans #551 #723]: #553
-#708 := [monotonicity #554]: #707
-#730 := (iff #445 #74)
-#724 := (= #448 #71)
-#726 := (= #448 #737)
-#736 := (= #375 0::Int)
-#734 := (= #375 #442)
-#455 := (= #447 0::Int)
-#456 := [rewrite]: #455
-#735 := [monotonicity #456]: #734
-#733 := [trans #735 #732]: #736
-#727 := [monotonicity #733]: #726
-#729 := [trans #727 #723]: #724
-#725 := [monotonicity #729]: #730
-#453 := (iff #433 false)
-#464 := (or false false)
-#739 := (iff #464 false)
-#743 := [rewrite]: #739
-#738 := (iff #433 #464)
-#741 := (iff #765 false)
-#754 := (not true)
-#397 := (iff #754 false)
-#757 := [rewrite]: #397
-#363 := (iff #765 #754)
-#469 := (iff #763 true)
-#749 := (or true true)
-#752 := (iff #749 true)
-#747 := [rewrite]: #752
-#467 := (iff #763 #749)
-#744 := (iff #449 true)
-#745 := [rewrite]: #744
-#412 := (iff #428 true)
-#748 := [rewrite]: #412
-#468 := [monotonicity #748 #745]: #467
-#470 := [trans #468 #747]: #469
-#740 := [monotonicity #470]: #363
-#463 := [trans #740 #757]: #741
-#755 := (iff #759 false)
-#756 := (iff #759 #754)
-#753 := (iff #552 true)
-#750 := (iff #552 #749)
-#410 := (iff #422 true)
-#411 := [rewrite]: #410
-#751 := [monotonicity #411 #748]: #750
-#391 := [trans #751 #747]: #753
-#396 := [monotonicity #391]: #756
-#758 := [trans #396 #757]: #755
-#742 := [monotonicity #758 #463]: #738
-#454 := [trans #742 #743]: #453
-#709 := [monotonicity #454 #725 #708]: #711
-#596 := [trans #709 #594]: #595
-#746 := (iff #768 true)
-#425 := (or true false)
-#762 := (iff #425 true)
-#405 := [rewrite]: #762
-#761 := (iff #768 #425)
-#760 := (iff #766 false)
-#420 := [rewrite]: #760
-#764 := (iff #767 true)
-#770 := [rewrite]: #764
-#421 := [monotonicity #770 #420]: #761
-#409 := [trans #421 #405]: #746
-#605 := [monotonicity #409 #596]: #703
-#589 := [trans #605 #701]: #704
-#609 := [monotonicity #589]: #608
-#612 := [trans #609 #611]: #608
-#600 := [quant-inst #9 #68]: #607
-#705 := [mp #600 #612]: #606
-[unit-resolution #705 #92 #777]: false
-unsat
-f4ee017fa009ecfb02498b2f74ede18810bd93a3 314 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#17 := (f4 f5 #16)
-#19 := (f3 #17 #18)
-#745 := (pattern #19)
-#13 := 0::Int
-#84 := -1::Int
-#88 := (* -1::Int #18)
-#85 := (* -1::Int #16)
-#91 := (div #85 #88)
-#248 := (* -1::Int #91)
-#249 := (+ #19 #248)
-#250 := (= #249 0::Int)
-#29 := (div #16 #18)
-#245 := (* -1::Int #29)
-#246 := (+ #19 #245)
-#247 := (= #246 0::Int)
-#123 := (>= #16 0::Int)
-#116 := (<= #18 0::Int)
-#208 := (or #116 #123)
-#209 := (not #208)
-#112 := (<= #16 0::Int)
-#206 := (or #112 #116)
-#207 := (not #206)
-#212 := (or #207 #209)
-#251 := (ite #212 #247 #250)
-#244 := (= #19 0::Int)
-#21 := (= #18 0::Int)
-#20 := (= #16 0::Int)
-#22 := (or #20 #21)
-#252 := (ite #22 #244 #251)
-#746 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #745) #252)
-#255 := (forall (vars (?v0 Int) (?v1 Int)) #252)
-#749 := (iff #255 #746)
-#747 := (iff #252 #252)
-#748 := [refl]: #747
-#750 := [quant-intro #748]: #749
-#215 := (ite #212 #29 #91)
-#218 := (ite #22 0::Int #215)
-#221 := (= #19 #218)
-#224 := (forall (vars (?v0 Int) (?v1 Int)) #221)
-#256 := (iff #224 #255)
-#253 := (iff #221 #252)
-#254 := [rewrite]: #253
-#257 := [quant-intro #254]: #256
-#124 := (not #123)
-#117 := (not #116)
-#127 := (and #117 #124)
-#113 := (not #112)
-#120 := (and #113 #117)
-#130 := (or #120 #127)
-#133 := (ite #130 #29 #91)
-#136 := (ite #22 0::Int #133)
-#139 := (= #19 #136)
-#142 := (forall (vars (?v0 Int) (?v1 Int)) #139)
-#225 := (iff #142 #224)
-#222 := (iff #139 #221)
-#219 := (= #136 #218)
-#216 := (= #133 #215)
-#213 := (iff #130 #212)
-#210 := (iff #127 #209)
-#211 := [rewrite]: #210
-#200 := (iff #120 #207)
-#201 := [rewrite]: #200
-#214 := [monotonicity #201 #211]: #213
-#217 := [monotonicity #214]: #216
-#220 := [monotonicity #217]: #219
-#223 := [monotonicity #220]: #222
-#226 := [quant-intro #223]: #225
-#204 := (~ #142 #142)
-#202 := (~ #139 #139)
-#203 := [refl]: #202
-#205 := [nnf-pos #203]: #204
-#31 := (- #18)
-#30 := (- #16)
-#32 := (div #30 #31)
-#24 := (< 0::Int #18)
-#26 := (< #16 0::Int)
-#27 := (and #26 #24)
-#23 := (< 0::Int #16)
-#25 := (and #23 #24)
-#28 := (or #25 #27)
-#33 := (ite #28 #29 #32)
-#34 := (ite #22 0::Int #33)
-#35 := (= #19 #34)
-#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
-#145 := (iff #36 #142)
-#78 := (and #24 #26)
-#81 := (or #25 #78)
-#94 := (ite #81 #29 #91)
-#72 := (= 0::Int #18)
-#69 := (= 0::Int #16)
-#75 := (or #69 #72)
-#97 := (ite #75 0::Int #94)
-#100 := (= #19 #97)
-#103 := (forall (vars (?v0 Int) (?v1 Int)) #100)
-#143 := (iff #103 #142)
-#140 := (iff #100 #139)
-#137 := (= #97 #136)
-#134 := (= #94 #133)
-#131 := (iff #81 #130)
-#128 := (iff #78 #127)
-#125 := (iff #26 #124)
-#126 := [rewrite]: #125
-#118 := (iff #24 #117)
-#119 := [rewrite]: #118
-#129 := [monotonicity #119 #126]: #128
-#121 := (iff #25 #120)
-#114 := (iff #23 #113)
-#115 := [rewrite]: #114
-#122 := [monotonicity #115 #119]: #121
-#132 := [monotonicity #122 #129]: #131
-#135 := [monotonicity #132]: #134
-#110 := (iff #75 #22)
-#108 := (iff #72 #21)
-#109 := [rewrite]: #108
-#106 := (iff #69 #20)
-#107 := [rewrite]: #106
-#111 := [monotonicity #107 #109]: #110
-#138 := [monotonicity #111 #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [quant-intro #141]: #143
-#104 := (iff #36 #103)
-#101 := (iff #35 #100)
-#98 := (= #34 #97)
-#95 := (= #33 #94)
-#92 := (= #32 #91)
-#89 := (= #31 #88)
-#90 := [rewrite]: #89
-#86 := (= #30 #85)
-#87 := [rewrite]: #86
-#93 := [monotonicity #87 #90]: #92
-#82 := (iff #28 #81)
-#79 := (iff #27 #78)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#96 := [monotonicity #83 #93]: #95
-#76 := (iff #22 #75)
-#73 := (iff #21 #72)
-#74 := [rewrite]: #73
-#70 := (iff #20 #69)
-#71 := [rewrite]: #70
-#77 := [monotonicity #71 #74]: #76
-#99 := [monotonicity #77 #96]: #98
-#102 := [monotonicity #99]: #101
-#105 := [quant-intro #102]: #104
-#146 := [trans #105 #144]: #145
-#68 := [asserted]: #36
-#147 := [mp #68 #146]: #142
-#196 := [mp~ #147 #205]: #142
-#227 := [mp #196 #226]: #224
-#258 := [mp #227 #257]: #255
-#751 := [mp #258 #750]: #746
-#11 := 3::Int
-#9 := 1::Int
-#10 := (f4 f5 1::Int)
-#12 := (f3 #10 3::Int)
-#14 := (= #12 0::Int)
-#15 := (not #14)
-#67 := [asserted]: #15
-#671 := (not #746)
-#672 := (or #671 #14)
-#332 := (* -1::Int 3::Int)
-#416 := (* -1::Int 1::Int)
-#417 := (div #416 #332)
-#418 := (* -1::Int #417)
-#409 := (+ #12 #418)
-#420 := (= #409 0::Int)
-#421 := (div 1::Int 3::Int)
-#422 := (* -1::Int #421)
-#419 := (+ #12 #422)
-#423 := (= #419 0::Int)
-#402 := (>= 1::Int 0::Int)
-#737 := (<= 3::Int 0::Int)
-#739 := (or #737 #402)
-#396 := (not #739)
-#526 := (<= 1::Int 0::Int)
-#733 := (or #526 #737)
-#407 := (not #733)
-#408 := (or #407 #396)
-#740 := (ite #408 #423 #420)
-#741 := (= 3::Int 0::Int)
-#742 := (= 1::Int 0::Int)
-#743 := (or #742 #741)
-#738 := (ite #743 #14 #740)
-#668 := (or #671 #738)
-#662 := (iff #668 #672)
-#664 := (iff #672 #672)
-#665 := [rewrite]: #664
-#660 := (iff #738 #14)
-#680 := (ite false #14 #14)
-#661 := (iff #680 #14)
-#658 := [rewrite]: #661
-#667 := (iff #738 #680)
-#679 := (iff #740 #14)
-#563 := (= #12 1::Int)
-#1 := true
-#582 := (ite true #14 #563)
-#585 := (iff #582 #14)
-#586 := [rewrite]: #585
-#583 := (iff #740 #582)
-#581 := (iff #420 #563)
-#569 := (+ -1::Int #12)
-#674 := (= #569 0::Int)
-#578 := (iff #674 #563)
-#580 := [rewrite]: #578
-#675 := (iff #420 #674)
-#677 := (= #409 #569)
-#683 := (+ #12 -1::Int)
-#570 := (= #683 #569)
-#529 := [rewrite]: #570
-#686 := (= #409 #683)
-#684 := (= #418 -1::Int)
-#691 := (= #416 -1::Int)
-#692 := [rewrite]: #691
-#681 := (= #418 #416)
-#527 := (= #417 1::Int)
-#693 := -3::Int
-#694 := (div -1::Int -3::Int)
-#696 := (= #694 1::Int)
-#525 := [rewrite]: #696
-#695 := (= #417 #694)
-#687 := (= #332 -3::Int)
-#688 := [rewrite]: #687
-#689 := [monotonicity #692 #688]: #695
-#528 := [trans #689 #525]: #527
-#682 := [monotonicity #528]: #681
-#685 := [trans #682 #692]: #684
-#568 := [monotonicity #685]: #686
-#579 := [trans #568 #529]: #677
-#678 := [monotonicity #579]: #675
-#574 := [trans #678 #580]: #581
-#548 := (iff #423 #14)
-#546 := (= #419 #12)
-#698 := (+ #12 0::Int)
-#699 := (= #698 #12)
-#705 := [rewrite]: #699
-#703 := (= #419 #698)
-#702 := (= #422 0::Int)
-#710 := (* -1::Int 0::Int)
-#700 := (= #710 0::Int)
-#701 := [rewrite]: #700
-#707 := (= #422 #710)
-#424 := (= #421 0::Int)
-#706 := [rewrite]: #424
-#711 := [monotonicity #706]: #707
-#697 := [trans #711 #701]: #702
-#704 := [monotonicity #697]: #703
-#547 := [trans #704 #705]: #546
-#690 := [monotonicity #547]: #548
-#708 := (iff #408 true)
-#717 := (or true false)
-#429 := (iff #717 true)
-#430 := [rewrite]: #429
-#427 := (iff #408 #717)
-#716 := (iff #396 false)
-#714 := (not true)
-#438 := (iff #714 false)
-#712 := [rewrite]: #438
-#715 := (iff #396 #714)
-#444 := (iff #739 true)
-#718 := (or false true)
-#442 := (iff #718 true)
-#443 := [rewrite]: #442
-#719 := (iff #739 #718)
-#729 := (iff #402 true)
-#732 := [rewrite]: #729
-#722 := (iff #737 false)
-#723 := [rewrite]: #722
-#441 := [monotonicity #723 #732]: #719
-#338 := [trans #441 #443]: #444
-#437 := [monotonicity #338]: #715
-#713 := [trans #437 #712]: #716
-#371 := (iff #407 true)
-#727 := (not false)
-#730 := (iff #727 true)
-#370 := [rewrite]: #730
-#365 := (iff #407 #727)
-#726 := (iff #733 false)
-#735 := (or false false)
-#379 := (iff #735 false)
-#720 := [rewrite]: #379
-#724 := (iff #733 #735)
-#385 := (iff #526 false)
-#386 := [rewrite]: #385
-#725 := [monotonicity #386 #723]: #724
-#721 := [trans #725 #720]: #726
-#728 := [monotonicity #721]: #365
-#731 := [trans #728 #370]: #371
-#428 := [monotonicity #731 #713]: #427
-#709 := [trans #428 #430]: #708
-#584 := [monotonicity #709 #690 #574]: #583
-#676 := [trans #584 #586]: #679
-#383 := (iff #743 false)
-#395 := (iff #743 #735)
-#394 := (iff #741 false)
-#399 := [rewrite]: #394
-#744 := (iff #742 false)
-#734 := [rewrite]: #744
-#736 := [monotonicity #734 #399]: #395
-#384 := [trans #736 #720]: #383
-#669 := [monotonicity #384 #676]: #667
-#670 := [trans #669 #658]: #660
-#663 := [monotonicity #670]: #662
-#659 := [trans #663 #665]: #662
-#673 := [quant-inst #9 #11]: #668
-#666 := [mp #673 #659]: #672
-[unit-resolution #666 #67 #751]: false
-unsat
-7cb12de79ce8da3bfdf6ce2fdc8ec9ed8a8943d3 289 0
+#64 := (iff #14 #63)
+#61 := (iff #13 #60)
+#58 := (= #12 #57)
+#55 := (= #11 -3::Int)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#62 := [monotonicity #59]: #61
+#65 := [monotonicity #62]: #64
+#48 := [asserted]: #14
+#66 := [mp #48 #65]: #63
+#532 := (not #698)
+#533 := (or #532 #60)
+#359 := (* -1::Int -3::Int)
+#685 := (* -1::Int 0::Int)
+#360 := (div #685 #359)
+#692 := (* -1::Int #360)
+#693 := (+ #57 #692)
+#694 := (= #693 0::Int)
+#689 := (div 0::Int -3::Int)
+#691 := (* -1::Int #689)
+#348 := (+ #57 #691)
+#478 := (= #348 0::Int)
+#361 := (<= -3::Int 0::Int)
+#374 := (>= 0::Int 0::Int)
+#371 := (or #374 #361)
+#375 := (not #371)
+#370 := (<= 0::Int 0::Int)
+#372 := (or #370 #361)
+#373 := (not #372)
+#354 := (or #373 #375)
+#695 := (if #354 #478 #694)
+#368 := (= -3::Int 0::Int)
+#283 := (= 0::Int 0::Int)
+#369 := (or #283 #368)
+#690 := (if #369 #60 #695)
+#526 := (or #532 #690)
+#535 := (iff #526 #533)
+#537 := (iff #533 #533)
+#538 := [rewrite]: #537
+#515 := (iff #690 #60)
+#1 := true
+#629 := (if true #60 #60)
+#627 := (iff #629 #60)
+#630 := [rewrite]: #627
+#531 := (iff #690 #629)
+#522 := (iff #695 #60)
+#637 := (if false #60 #60)
+#520 := (iff #637 #60)
+#521 := [rewrite]: #520
+#635 := (iff #695 #637)
+#634 := (iff #694 #60)
+#480 := (= #693 #57)
+#652 := (+ #57 0::Int)
+#649 := (= #652 #57)
+#650 := [rewrite]: #649
+#477 := (= #693 #652)
+#641 := (= #692 0::Int)
+#658 := (= #685 0::Int)
+#662 := [rewrite]: #658
+#646 := (= #692 #685)
+#639 := (= #360 0::Int)
+#500 := (div 0::Int 3::Int)
+#644 := (= #500 0::Int)
+#645 := [rewrite]: #644
+#642 := (= #360 #500)
+#498 := (= #359 3::Int)
+#499 := [rewrite]: #498
+#643 := [monotonicity #662 #499]: #642
+#640 := [trans #643 #645]: #639
+#647 := [monotonicity #640]: #646
+#648 := [trans #647 #662]: #641
+#479 := [monotonicity #648]: #477
+#633 := [trans #479 #650]: #480
+#636 := [monotonicity #633]: #634
+#651 := (iff #478 #60)
+#655 := (= #348 #57)
+#653 := (= #348 #652)
+#659 := (= #691 0::Int)
+#661 := (= #691 #685)
+#382 := (= #689 0::Int)
+#660 := [rewrite]: #382
+#376 := [monotonicity #660]: #661
+#663 := [trans #376 #662]: #659
+#654 := [monotonicity #663]: #653
+#656 := [trans #654 #650]: #655
+#657 := [monotonicity #656]: #651
+#380 := (iff #354 false)
+#664 := (or false false)
+#669 := (iff #664 false)
+#379 := [rewrite]: #669
+#668 := (iff #354 #664)
+#389 := (iff #375 false)
+#682 := (not true)
+#683 := (iff #682 false)
+#681 := [rewrite]: #683
+#666 := (iff #375 #682)
+#396 := (iff #371 true)
+#676 := (or true true)
+#673 := (iff #676 true)
+#679 := [rewrite]: #673
+#394 := (iff #371 #676)
+#674 := (iff #361 true)
+#675 := [rewrite]: #674
+#671 := (iff #374 true)
+#393 := [rewrite]: #671
+#395 := [monotonicity #393 #675]: #394
+#289 := [trans #395 #679]: #396
+#667 := [monotonicity #289]: #666
+#390 := [trans #667 #681]: #389
+#684 := (iff #373 false)
+#322 := (iff #373 #682)
+#317 := (iff #372 true)
+#677 := (iff #372 #676)
+#337 := (iff #370 true)
+#338 := [rewrite]: #337
+#678 := [monotonicity #338 #675]: #677
+#680 := [trans #678 #679]: #317
+#323 := [monotonicity #680]: #322
+#670 := [trans #323 #681]: #684
+#665 := [monotonicity #670 #390]: #668
+#381 := [trans #665 #379]: #380
+#638 := [monotonicity #381 #657 #636]: #635
+#481 := [trans #638 #521]: #522
+#335 := (iff #369 true)
+#687 := (or true false)
+#331 := (iff #687 true)
+#672 := [rewrite]: #331
+#347 := (iff #369 #687)
+#346 := (iff #368 false)
+#351 := [rewrite]: #346
+#696 := (iff #283 true)
+#686 := [rewrite]: #696
+#688 := [monotonicity #686 #351]: #347
+#336 := [trans #688 #672]: #335
+#626 := [monotonicity #336 #481]: #531
+#530 := [trans #626 #630]: #515
+#536 := [monotonicity #530]: #535
+#631 := [trans #536 #538]: #535
+#534 := [quant-inst #8 #54]: #526
+#628 := [mp #534 #631]: #533
+[unit-resolution #628 #66 #703]: false
+6382d5aff89219a8ada90f5d3d58d36cd0bdab6f 306 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #17 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #15 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #16 := (f4 f5 #15)
 #18 := (f3 #16 #17)
-#730 := (pattern #18)
+#683 := (pattern #18)
+#12 := 0::Int
+#80 := -1::Int
+#84 := (* -1::Int #17)
+#81 := (* -1::Int #15)
+#87 := (div #81 #84)
+#243 := (* -1::Int #87)
+#244 := (+ #18 #243)
+#245 := (= #244 0::Int)
+#28 := (div #15 #17)
+#240 := (* -1::Int #28)
+#241 := (+ #18 #240)
+#242 := (= #241 0::Int)
+#58 := (<= #17 0::Int)
+#150 := (>= #15 0::Int)
+#203 := (or #150 #58)
+#204 := (not #203)
+#54 := (<= #15 0::Int)
+#199 := (or #54 #58)
+#200 := (not #199)
+#207 := (or #200 #204)
+#246 := (if #207 #242 #245)
+#239 := (= #18 0::Int)
+#20 := (= #17 0::Int)
+#19 := (= #15 0::Int)
+#21 := (or #19 #20)
+#247 := (if #21 #239 #246)
+#684 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #683) #247)
+#250 := (forall (vars (?v0 Int) (?v1 Int)) #247)
+#687 := (iff #250 #684)
+#685 := (iff #247 #247)
+#686 := [refl]: #685
+#688 := [quant-intro #686]: #687
+#210 := (if #207 #28 #87)
+#213 := (if #21 0::Int #210)
+#216 := (= #18 #213)
+#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
+#251 := (iff #219 #250)
+#248 := (iff #216 #247)
+#249 := [rewrite]: #248
+#252 := [quant-intro #249]: #251
+#59 := (not #58)
+#153 := (not #150)
+#156 := (and #153 #59)
+#55 := (not #54)
+#62 := (and #55 #59)
+#159 := (or #62 #156)
+#162 := (if #159 #28 #87)
+#165 := (if #21 0::Int #162)
+#168 := (= #18 #165)
+#171 := (forall (vars (?v0 Int) (?v1 Int)) #168)
+#220 := (iff #171 #219)
+#217 := (iff #168 #216)
+#214 := (= #165 #213)
+#211 := (= #162 #210)
+#208 := (iff #159 #207)
+#205 := (iff #156 #204)
+#206 := [rewrite]: #205
+#201 := (iff #62 #200)
+#202 := [rewrite]: #201
+#209 := [monotonicity #202 #206]: #208
+#212 := [monotonicity #209]: #211
+#215 := [monotonicity #212]: #214
+#218 := [monotonicity #215]: #217
+#221 := [quant-intro #218]: #220
+#195 := (~ #171 #171)
+#193 := (~ #168 #168)
+#194 := [refl]: #193
+#196 := [nnf-pos #194]: #195
+#65 := (<= 0::Int #15)
+#66 := (not #65)
+#74 := (and #66 #59)
+#77 := (or #62 #74)
+#90 := (if #77 #28 #87)
+#93 := (if #21 0::Int #90)
+#96 := (= #18 #93)
+#99 := (forall (vars (?v0 Int) (?v1 Int)) #96)
+#172 := (iff #99 #171)
+#169 := (iff #96 #168)
+#166 := (= #93 #165)
+#163 := (= #90 #162)
+#160 := (iff #77 #159)
+#157 := (iff #74 #156)
+#154 := (iff #66 #153)
+#151 := (iff #65 #150)
+#152 := [rewrite]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [monotonicity #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [quant-intro #170]: #172
+#30 := (- #17)
+#29 := (- #15)
+#31 := (div #29 #30)
+#23 := (< 0::Int #17)
+#25 := (< #15 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #15)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#32 := (if #27 #28 #31)
+#33 := (if #21 0::Int #32)
+#34 := (= #18 #33)
+#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
+#100 := (iff #35 #99)
+#97 := (iff #34 #96)
+#94 := (= #33 #93)
+#91 := (= #32 #90)
+#88 := (= #31 #87)
+#85 := (= #30 #84)
+#86 := [rewrite]: #85
+#82 := (= #29 #81)
+#83 := [rewrite]: #82
+#89 := [monotonicity #83 #86]: #88
+#78 := (iff #27 #77)
+#75 := (iff #26 #74)
+#60 := (iff #23 #59)
+#61 := [rewrite]: #60
+#67 := (iff #25 #66)
+#71 := (iff #66 #66)
+#69 := (iff #65 #65)
+#70 := [rewrite]: #69
+#72 := [monotonicity #70]: #71
+#68 := [rewrite]: #67
+#73 := [trans #68 #72]: #67
+#76 := [monotonicity #73 #61]: #75
+#63 := (iff #24 #62)
+#56 := (iff #22 #55)
+#57 := [rewrite]: #56
+#64 := [monotonicity #57 #61]: #63
+#79 := [monotonicity #64 #76]: #78
+#92 := [monotonicity #79 #89]: #91
+#95 := [monotonicity #92]: #94
+#98 := [monotonicity #95]: #97
+#101 := [quant-intro #98]: #100
+#49 := [asserted]: #35
+#102 := [mp #49 #101]: #99
+#174 := [mp #102 #173]: #171
+#148 := [mp~ #174 #196]: #171
+#222 := [mp #148 #221]: #219
+#253 := [mp #222 #252]: #250
+#689 := [mp #253 #688]: #684
+#10 := 3::Int
+#8 := 1::Int
+#9 := (f4 f5 1::Int)
+#11 := (f3 #9 3::Int)
+#13 := (= #11 0::Int)
+#14 := (not #13)
+#48 := [asserted]: #14
+#596 := (not #684)
+#598 := (or #596 #13)
+#345 := (* -1::Int 3::Int)
+#671 := (* -1::Int 1::Int)
+#346 := (div #671 #345)
+#678 := (* -1::Int #346)
+#679 := (+ #11 #678)
+#680 := (= #679 0::Int)
+#675 := (div 1::Int 3::Int)
+#677 := (* -1::Int #675)
+#334 := (+ #11 #677)
+#464 := (= #334 0::Int)
+#347 := (<= 3::Int 0::Int)
+#360 := (>= 1::Int 0::Int)
+#357 := (or #360 #347)
+#361 := (not #357)
+#356 := (<= 1::Int 0::Int)
+#358 := (or #356 #347)
+#359 := (not #358)
+#340 := (or #359 #361)
+#681 := (if #340 #464 #680)
+#354 := (= 3::Int 0::Int)
+#270 := (= 1::Int 0::Int)
+#355 := (or #270 #354)
+#676 := (if #355 #13 #681)
+#608 := (or #596 #676)
+#610 := (iff #608 #598)
+#611 := (iff #598 #598)
+#600 := [rewrite]: #611
+#607 := (iff #676 #13)
+#524 := (if false #13 #13)
+#618 := (iff #524 #13)
+#605 := [rewrite]: #618
+#617 := (iff #676 #524)
+#522 := (iff #681 #13)
+#612 := (= #11 1::Int)
+#1 := true
+#518 := (if true #13 #612)
+#520 := (iff #518 #13)
+#521 := [rewrite]: #520
+#519 := (iff #681 #518)
+#501 := (iff #680 #612)
+#621 := (+ -1::Int #11)
+#467 := (= #621 0::Int)
+#613 := (iff #467 #612)
+#616 := [rewrite]: #613
+#615 := (iff #680 #467)
+#507 := (= #679 #621)
+#620 := (+ #11 -1::Int)
+#624 := (= #620 #621)
+#506 := [rewrite]: #624
+#622 := (= #679 #620)
+#466 := (= #678 -1::Int)
+#485 := (= #671 -1::Int)
+#486 := [rewrite]: #485
+#463 := (= #678 #671)
+#627 := (= #346 1::Int)
+#628 := -3::Int
+#631 := (div -1::Int -3::Int)
+#632 := (= #631 1::Int)
+#633 := [rewrite]: #632
+#625 := (= #346 #631)
+#629 := (= #345 -3::Int)
+#630 := [rewrite]: #629
+#626 := [monotonicity #486 #630]: #625
+#634 := [trans #626 #633]: #627
+#465 := [monotonicity #634]: #463
+#619 := [trans #465 #486]: #466
+#623 := [monotonicity #619]: #622
+#508 := [trans #623 #506]: #507
+#517 := [monotonicity #508]: #615
+#516 := [trans #517 #616]: #501
+#643 := (iff #464 #13)
+#642 := (= #334 #11)
+#639 := (+ #11 0::Int)
+#636 := (= #639 #11)
+#641 := [rewrite]: #636
+#640 := (= #334 #639)
+#649 := (= #677 0::Int)
+#647 := (* -1::Int 0::Int)
+#648 := (= #647 0::Int)
+#645 := [rewrite]: #648
+#362 := (= #677 #647)
+#368 := (= #675 0::Int)
+#646 := [rewrite]: #368
+#644 := [monotonicity #646]: #362
+#638 := [trans #644 #645]: #649
+#635 := [monotonicity #638]: #640
+#637 := [trans #635 #641]: #642
+#484 := [monotonicity #637]: #643
+#366 := (iff #340 true)
+#656 := (or true false)
+#380 := (iff #656 true)
+#381 := [rewrite]: #380
+#655 := (iff #340 #656)
+#654 := (iff #361 false)
+#652 := (not true)
+#376 := (iff #652 false)
+#650 := [rewrite]: #376
+#653 := (iff #361 #652)
+#382 := (iff #357 true)
+#657 := (iff #357 #656)
+#660 := (iff #347 false)
+#661 := [rewrite]: #660
+#667 := (iff #360 true)
+#670 := [rewrite]: #667
+#379 := [monotonicity #670 #661]: #657
+#276 := [trans #379 #381]: #382
+#375 := [monotonicity #276]: #653
+#651 := [trans #375 #650]: #654
+#309 := (iff #359 true)
+#665 := (not false)
+#668 := (iff #665 true)
+#308 := [rewrite]: #668
+#303 := (iff #359 #665)
+#664 := (iff #358 false)
+#673 := (or false false)
+#317 := (iff #673 false)
+#658 := [rewrite]: #317
+#662 := (iff #358 #673)
+#323 := (iff #356 false)
+#324 := [rewrite]: #323
+#663 := [monotonicity #324 #661]: #662
+#659 := [trans #663 #658]: #664
+#666 := [monotonicity #659]: #303
+#669 := [trans #666 #308]: #309
+#365 := [monotonicity #669 #651]: #655
+#367 := [trans #365 #381]: #366
+#512 := [monotonicity #367 #484 #516]: #519
+#523 := [trans #512 #521]: #522
+#321 := (iff #355 false)
+#333 := (iff #355 #673)
+#332 := (iff #354 false)
+#337 := [rewrite]: #332
+#682 := (iff #270 false)
+#672 := [rewrite]: #682
+#674 := [monotonicity #672 #337]: #333
+#322 := [trans #674 #658]: #321
+#614 := [monotonicity #322 #523]: #617
+#599 := [trans #614 #605]: #607
+#606 := [monotonicity #599]: #610
+#601 := [trans #606 #600]: #610
+#609 := [quant-inst #8 #10]: #608
+#602 := [mp #609 #601]: #598
+[unit-resolution #602 #48 #689]: false
+edcd41cd053f07265d5fea261f85739d8063959d 296 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#16 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#14 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#15 := (f4 f5 #14)
+#17 := (f3 #15 #16)
+#683 := (pattern #17)
+#18 := 0::Int
+#80 := -1::Int
+#84 := (* -1::Int #16)
+#81 := (* -1::Int #14)
+#87 := (div #81 #84)
+#243 := (* -1::Int #87)
+#244 := (+ #17 #243)
+#245 := (= #244 0::Int)
+#28 := (div #14 #16)
+#240 := (* -1::Int #28)
+#241 := (+ #17 #240)
+#242 := (= #241 0::Int)
+#58 := (<= #16 0::Int)
+#150 := (>= #14 0::Int)
+#203 := (or #150 #58)
+#204 := (not #203)
+#54 := (<= #14 0::Int)
+#199 := (or #54 #58)
+#200 := (not #199)
+#207 := (or #200 #204)
+#246 := (if #207 #242 #245)
+#239 := (= #17 0::Int)
+#20 := (= #16 0::Int)
+#19 := (= #14 0::Int)
+#21 := (or #19 #20)
+#247 := (if #21 #239 #246)
+#684 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #683) #247)
+#250 := (forall (vars (?v0 Int) (?v1 Int)) #247)
+#687 := (iff #250 #684)
+#685 := (iff #247 #247)
+#686 := [refl]: #685
+#688 := [quant-intro #686]: #687
+#210 := (if #207 #28 #87)
+#213 := (if #21 0::Int #210)
+#216 := (= #17 #213)
+#219 := (forall (vars (?v0 Int) (?v1 Int)) #216)
+#251 := (iff #219 #250)
+#248 := (iff #216 #247)
+#249 := [rewrite]: #248
+#252 := [quant-intro #249]: #251
+#59 := (not #58)
+#153 := (not #150)
+#156 := (and #153 #59)
+#55 := (not #54)
+#62 := (and #55 #59)
+#159 := (or #62 #156)
+#162 := (if #159 #28 #87)
+#165 := (if #21 0::Int #162)
+#168 := (= #17 #165)
+#171 := (forall (vars (?v0 Int) (?v1 Int)) #168)
+#220 := (iff #171 #219)
+#217 := (iff #168 #216)
+#214 := (= #165 #213)
+#211 := (= #162 #210)
+#208 := (iff #159 #207)
+#205 := (iff #156 #204)
+#206 := [rewrite]: #205
+#201 := (iff #62 #200)
+#202 := [rewrite]: #201
+#209 := [monotonicity #202 #206]: #208
+#212 := [monotonicity #209]: #211
+#215 := [monotonicity #212]: #214
+#218 := [monotonicity #215]: #217
+#221 := [quant-intro #218]: #220
+#195 := (~ #171 #171)
+#193 := (~ #168 #168)
+#194 := [refl]: #193
+#196 := [nnf-pos #194]: #195
+#65 := (<= 0::Int #14)
+#66 := (not #65)
+#74 := (and #66 #59)
+#77 := (or #62 #74)
+#90 := (if #77 #28 #87)
+#93 := (if #21 0::Int #90)
+#96 := (= #17 #93)
+#99 := (forall (vars (?v0 Int) (?v1 Int)) #96)
+#172 := (iff #99 #171)
+#169 := (iff #96 #168)
+#166 := (= #93 #165)
+#163 := (= #90 #162)
+#160 := (iff #77 #159)
+#157 := (iff #74 #156)
+#154 := (iff #66 #153)
+#151 := (iff #65 #150)
+#152 := [rewrite]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [monotonicity #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [quant-intro #170]: #172
+#30 := (- #16)
+#29 := (- #14)
+#31 := (div #29 #30)
+#23 := (< 0::Int #16)
+#25 := (< #14 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #14)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#32 := (if #27 #28 #31)
+#33 := (if #21 0::Int #32)
+#34 := (= #17 #33)
+#35 := (forall (vars (?v0 Int) (?v1 Int)) #34)
+#100 := (iff #35 #99)
+#97 := (iff #34 #96)
+#94 := (= #33 #93)
+#91 := (= #32 #90)
+#88 := (= #31 #87)
+#85 := (= #30 #84)
+#86 := [rewrite]: #85
+#82 := (= #29 #81)
+#83 := [rewrite]: #82
+#89 := [monotonicity #83 #86]: #88
+#78 := (iff #27 #77)
+#75 := (iff #26 #74)
+#60 := (iff #23 #59)
+#61 := [rewrite]: #60
+#67 := (iff #25 #66)
+#71 := (iff #66 #66)
+#69 := (iff #65 #65)
+#70 := [rewrite]: #69
+#72 := [monotonicity #70]: #71
+#68 := [rewrite]: #67
+#73 := [trans #68 #72]: #67
+#76 := [monotonicity #73 #61]: #75
+#63 := (iff #24 #62)
+#56 := (iff #22 #55)
+#57 := [rewrite]: #56
+#64 := [monotonicity #57 #61]: #63
+#79 := [monotonicity #64 #76]: #78
+#92 := [monotonicity #79 #89]: #91
+#95 := [monotonicity #92]: #94
+#98 := [monotonicity #95]: #97
+#101 := [quant-intro #98]: #100
+#49 := [asserted]: #35
+#102 := [mp #49 #101]: #99
+#174 := [mp #102 #173]: #171
+#148 := [mp~ #174 #196]: #171
+#222 := [mp #148 #221]: #219
+#253 := [mp #222 #252]: #250
+#689 := [mp #253 #688]: #684
+#11 := 1::Int
+#8 := 3::Int
+#9 := (f4 f5 3::Int)
+#10 := (f3 #9 3::Int)
+#12 := (= #10 1::Int)
+#13 := (not #12)
+#48 := [asserted]: #13
+#521 := (not #684)
+#522 := (or #521 #12)
+#464 := (* -1::Int 3::Int)
+#671 := (div #464 #464)
+#345 := (* -1::Int #671)
+#346 := (+ #10 #345)
+#678 := (= #346 0::Int)
+#340 := (div 3::Int 3::Int)
+#675 := (* -1::Int #340)
+#677 := (+ #10 #675)
+#334 := (= #677 0::Int)
+#356 := (<= 3::Int 0::Int)
+#359 := (>= 3::Int 0::Int)
+#360 := (or #359 #356)
+#357 := (not #360)
+#347 := (or #356 #356)
+#358 := (not #347)
+#361 := (or #358 #357)
+#679 := (if #361 #334 #678)
+#355 := (= #10 0::Int)
+#270 := (= 3::Int 0::Int)
+#354 := (or #270 #270)
+#680 := (if #354 #355 #679)
+#523 := (or #521 #680)
+#617 := (iff #523 #522)
+#618 := (iff #522 #522)
+#605 := [rewrite]: #618
+#512 := (iff #680 #12)
+#616 := (if false #355 #12)
+#518 := (iff #616 #12)
+#519 := [rewrite]: #518
+#501 := (iff #680 #616)
+#612 := (iff #679 #12)
+#1 := true
+#507 := (if true #12 #12)
+#615 := (iff #507 #12)
+#517 := [rewrite]: #615
+#508 := (iff #679 #507)
+#624 := (iff #678 #12)
+#645 := (+ -1::Int #10)
+#635 := (= #645 0::Int)
+#642 := (iff #635 #12)
+#637 := [rewrite]: #642
+#623 := (iff #678 #635)
+#620 := (= #346 #645)
+#362 := (+ #10 -1::Int)
+#649 := (= #362 #645)
+#638 := [rewrite]: #649
+#466 := (= #346 #362)
+#463 := (= #345 -1::Int)
+#655 := (* -1::Int 1::Int)
+#367 := (= #655 -1::Int)
+#368 := [rewrite]: #367
+#627 := (= #345 #655)
+#632 := (= #671 1::Int)
+#485 := -3::Int
+#629 := (div -3::Int -3::Int)
+#625 := (= #629 1::Int)
+#626 := [rewrite]: #625
+#630 := (= #671 #629)
+#486 := (= #464 -3::Int)
+#628 := [rewrite]: #486
+#631 := [monotonicity #628 #628]: #630
+#633 := [trans #631 #626]: #632
+#634 := [monotonicity #633]: #627
+#465 := [trans #634 #368]: #463
+#619 := [monotonicity #465]: #466
+#622 := [trans #619 #638]: #620
+#621 := [monotonicity #622]: #623
+#506 := [trans #621 #637]: #624
+#643 := (iff #334 #12)
+#636 := (iff #334 #635)
+#639 := (= #677 #645)
+#644 := (= #677 #362)
+#646 := (= #675 -1::Int)
+#365 := (= #675 #655)
+#654 := (= #340 1::Int)
+#651 := [rewrite]: #654
+#366 := [monotonicity #651]: #365
+#647 := [trans #366 #368]: #646
+#648 := [monotonicity #647]: #644
+#640 := [trans #648 #638]: #639
+#641 := [monotonicity #640]: #636
+#484 := [trans #641 #637]: #643
+#376 := (iff #361 true)
+#668 := (or true false)
+#669 := (iff #668 true)
+#667 := [rewrite]: #669
+#653 := (iff #361 #668)
+#276 := (iff #357 false)
+#657 := (not true)
+#381 := (iff #657 false)
+#382 := [rewrite]: #381
+#379 := (iff #357 #657)
+#670 := (iff #360 true)
+#308 := (iff #360 #668)
+#317 := (iff #356 false)
+#658 := [rewrite]: #317
+#303 := (iff #359 true)
+#666 := [rewrite]: #303
+#309 := [monotonicity #666 #658]: #308
+#656 := [trans #309 #667]: #670
+#380 := [monotonicity #656]: #379
+#652 := [trans #380 #382]: #276
+#659 := (iff #358 true)
+#660 := (not false)
+#663 := (iff #660 true)
+#664 := [rewrite]: #663
+#661 := (iff #358 #660)
+#323 := (iff #347 false)
+#682 := (or false false)
+#337 := (iff #682 false)
+#673 := [rewrite]: #337
+#321 := (iff #347 #682)
+#322 := [monotonicity #658 #658]: #321
+#324 := [trans #322 #673]: #323
+#662 := [monotonicity #324]: #661
+#665 := [trans #662 #664]: #659
+#375 := [monotonicity #665 #652]: #653
+#650 := [trans #375 #667]: #376
+#467 := [monotonicity #650 #484 #506]: #508
+#613 := [trans #467 #517]: #612
+#333 := (iff #354 false)
+#672 := (iff #354 #682)
+#681 := (iff #270 false)
+#676 := [rewrite]: #681
+#332 := [monotonicity #676 #676]: #672
+#674 := [trans #332 #673]: #333
+#516 := [monotonicity #674 #613]: #501
+#520 := [trans #516 #519]: #512
+#614 := [monotonicity #520]: #617
+#607 := [trans #614 #605]: #617
+#524 := [quant-inst #8 #8]: #523
+#599 := [mp #524 #607]: #522
+[unit-resolution #599 #48 #689]: false
+2aeb178d5528960841f3f6a1d0552953e056dd91 320 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#17 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#15 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#16 := (f4 f5 #15)
+#18 := (f3 #16 #17)
+#684 := (pattern #18)
 #19 := 0::Int
-#75 := -1::Int
-#79 := (* -1::Int #17)
-#76 := (* -1::Int #15)
-#82 := (div #76 #79)
-#233 := (* -1::Int #82)
-#234 := (+ #18 #233)
-#235 := (= #234 0::Int)
+#81 := -1::Int
+#85 := (* -1::Int #17)
+#82 := (* -1::Int #15)
+#88 := (div #82 #85)
+#244 := (* -1::Int #88)
+#245 := (+ #18 #244)
+#246 := (= #245 0::Int)
 #29 := (div #15 #17)
-#230 := (* -1::Int #29)
-#231 := (+ #18 #230)
-#232 := (= #231 0::Int)
-#108 := (>= #15 0::Int)
-#101 := (<= #17 0::Int)
-#193 := (or #101 #108)
-#194 := (not #193)
-#97 := (<= #15 0::Int)
-#191 := (or #97 #101)
-#192 := (not #191)
-#197 := (or #192 #194)
-#236 := (ite #197 #232 #235)
-#229 := (= #18 0::Int)
+#241 := (* -1::Int #29)
+#242 := (+ #18 #241)
+#243 := (= #242 0::Int)
+#59 := (<= #17 0::Int)
+#151 := (>= #15 0::Int)
+#204 := (or #151 #59)
+#205 := (not #204)
+#55 := (<= #15 0::Int)
+#200 := (or #55 #59)
+#201 := (not #200)
+#208 := (or #201 #205)
+#247 := (if #208 #243 #246)
+#240 := (= #18 0::Int)
 #21 := (= #17 0::Int)
 #20 := (= #15 0::Int)
 #22 := (or #20 #21)
-#237 := (ite #22 #229 #236)
-#731 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #730) #237)
-#240 := (forall (vars (?v0 Int) (?v1 Int)) #237)
-#734 := (iff #240 #731)
-#732 := (iff #237 #237)
-#733 := [refl]: #732
-#735 := [quant-intro #733]: #734
-#200 := (ite #197 #29 #82)
-#203 := (ite #22 0::Int #200)
-#206 := (= #18 #203)
-#209 := (forall (vars (?v0 Int) (?v1 Int)) #206)
-#241 := (iff #209 #240)
-#238 := (iff #206 #237)
-#239 := [rewrite]: #238
-#242 := [quant-intro #239]: #241
-#109 := (not #108)
-#102 := (not #101)
-#112 := (and #102 #109)
-#98 := (not #97)
-#105 := (and #98 #102)
-#115 := (or #105 #112)
-#118 := (ite #115 #29 #82)
-#121 := (ite #22 0::Int #118)
-#124 := (= #18 #121)
-#127 := (forall (vars (?v0 Int) (?v1 Int)) #124)
-#210 := (iff #127 #209)
-#207 := (iff #124 #206)
-#204 := (= #121 #203)
-#201 := (= #118 #200)
-#198 := (iff #115 #197)
-#195 := (iff #112 #194)
-#196 := [rewrite]: #195
-#185 := (iff #105 #192)
-#186 := [rewrite]: #185
-#199 := [monotonicity #186 #196]: #198
-#202 := [monotonicity #199]: #201
-#205 := [monotonicity #202]: #204
-#208 := [monotonicity #205]: #207
-#211 := [quant-intro #208]: #210
-#189 := (~ #127 #127)
-#187 := (~ #124 #124)
-#188 := [refl]: #187
-#190 := [nnf-pos #188]: #189
+#248 := (if #22 #240 #247)
+#685 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #684) #248)
+#251 := (forall (vars (?v0 Int) (?v1 Int)) #248)
+#688 := (iff #251 #685)
+#686 := (iff #248 #248)
+#687 := [refl]: #686
+#689 := [quant-intro #687]: #688
+#211 := (if #208 #29 #88)
+#214 := (if #22 0::Int #211)
+#217 := (= #18 #214)
+#220 := (forall (vars (?v0 Int) (?v1 Int)) #217)
+#252 := (iff #220 #251)
+#249 := (iff #217 #248)
+#250 := [rewrite]: #249
+#253 := [quant-intro #250]: #252
+#60 := (not #59)
+#154 := (not #151)
+#157 := (and #154 #60)
+#56 := (not #55)
+#63 := (and #56 #60)
+#160 := (or #63 #157)
+#163 := (if #160 #29 #88)
+#166 := (if #22 0::Int #163)
+#169 := (= #18 #166)
+#172 := (forall (vars (?v0 Int) (?v1 Int)) #169)
+#221 := (iff #172 #220)
+#218 := (iff #169 #217)
+#215 := (= #166 #214)
+#212 := (= #163 #211)
+#209 := (iff #160 #208)
+#206 := (iff #157 #205)
+#207 := [rewrite]: #206
+#202 := (iff #63 #201)
+#203 := [rewrite]: #202
+#210 := [monotonicity #203 #207]: #209
+#213 := [monotonicity #210]: #212
+#216 := [monotonicity #213]: #215
+#219 := [monotonicity #216]: #218
+#222 := [quant-intro #219]: #221
+#149 := (~ #172 #172)
+#192 := (~ #169 #169)
+#193 := [refl]: #192
+#150 := [nnf-pos #193]: #149
+#66 := (<= 0::Int #15)
+#67 := (not #66)
+#75 := (and #67 #60)
+#78 := (or #63 #75)
+#91 := (if #78 #29 #88)
+#94 := (if #22 0::Int #91)
+#97 := (= #18 #94)
+#100 := (forall (vars (?v0 Int) (?v1 Int)) #97)
+#173 := (iff #100 #172)
+#170 := (iff #97 #169)
+#167 := (= #94 #166)
+#164 := (= #91 #163)
+#161 := (iff #78 #160)
+#158 := (iff #75 #157)
+#155 := (iff #67 #154)
+#152 := (iff #66 #151)
+#153 := [rewrite]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [monotonicity #162]: #164
+#168 := [monotonicity #165]: #167
+#171 := [monotonicity #168]: #170
+#174 := [quant-intro #171]: #173
 #31 := (- #17)
 #30 := (- #15)
 #32 := (div #30 #31)
@@ -31220,287 +30342,318 @@
 #23 := (< 0::Int #15)
 #25 := (and #23 #24)
 #28 := (or #25 #27)
-#33 := (ite #28 #29 #32)
-#34 := (ite #22 0::Int #33)
+#33 := (if #28 #29 #32)
+#34 := (if #22 0::Int #33)
 #35 := (= #18 #34)
 #36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
-#130 := (iff #36 #127)
-#69 := (and #24 #26)
-#72 := (or #25 #69)
-#85 := (ite #72 #29 #82)
-#88 := (ite #22 0::Int #85)
-#91 := (= #18 #88)
-#94 := (forall (vars (?v0 Int) (?v1 Int)) #91)
-#128 := (iff #94 #127)
-#125 := (iff #91 #124)
-#122 := (= #88 #121)
-#119 := (= #85 #118)
-#116 := (iff #72 #115)
-#113 := (iff #69 #112)
-#110 := (iff #26 #109)
-#111 := [rewrite]: #110
-#103 := (iff #24 #102)
-#104 := [rewrite]: #103
-#114 := [monotonicity #104 #111]: #113
-#106 := (iff #25 #105)
-#99 := (iff #23 #98)
-#100 := [rewrite]: #99
-#107 := [monotonicity #100 #104]: #106
-#117 := [monotonicity #107 #114]: #116
-#120 := [monotonicity #117]: #119
-#123 := [monotonicity #120]: #122
-#126 := [monotonicity #123]: #125
-#129 := [quant-intro #126]: #128
-#95 := (iff #36 #94)
-#92 := (iff #35 #91)
-#89 := (= #34 #88)
-#86 := (= #33 #85)
-#83 := (= #32 #82)
-#80 := (= #31 #79)
-#81 := [rewrite]: #80
-#77 := (= #30 #76)
-#78 := [rewrite]: #77
-#84 := [monotonicity #78 #81]: #83
-#73 := (iff #28 #72)
-#70 := (iff #27 #69)
+#101 := (iff #36 #100)
+#98 := (iff #35 #97)
+#95 := (= #34 #94)
+#92 := (= #33 #91)
+#89 := (= #32 #88)
+#86 := (= #31 #85)
+#87 := [rewrite]: #86
+#83 := (= #30 #82)
+#84 := [rewrite]: #83
+#90 := [monotonicity #84 #87]: #89
+#79 := (iff #28 #78)
+#76 := (iff #27 #75)
+#61 := (iff #24 #60)
+#62 := [rewrite]: #61
+#68 := (iff #26 #67)
+#72 := (iff #67 #67)
+#70 := (iff #66 #66)
 #71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#87 := [monotonicity #74 #84]: #86
-#90 := [monotonicity #87]: #89
-#93 := [monotonicity #90]: #92
-#96 := [quant-intro #93]: #95
-#131 := [trans #96 #129]: #130
-#68 := [asserted]: #36
-#132 := [mp #68 #131]: #127
-#181 := [mp~ #132 #190]: #127
-#212 := [mp #181 #211]: #209
-#243 := [mp #212 #242]: #240
-#736 := [mp #243 #735]: #731
+#73 := [monotonicity #71]: #72
+#69 := [rewrite]: #68
+#74 := [trans #69 #73]: #68
+#77 := [monotonicity #74 #62]: #76
+#64 := (iff #25 #63)
+#57 := (iff #23 #56)
+#58 := [rewrite]: #57
+#65 := [monotonicity #58 #62]: #64
+#80 := [monotonicity #65 #77]: #79
+#93 := [monotonicity #80 #90]: #92
+#96 := [monotonicity #93]: #95
+#99 := [monotonicity #96]: #98
+#102 := [quant-intro #99]: #101
+#50 := [asserted]: #36
+#103 := [mp #50 #102]: #100
+#175 := [mp #103 #174]: #172
+#196 := [mp~ #175 #150]: #172
+#223 := [mp #196 #222]: #220
+#254 := [mp #223 #253]: #251
+#690 := [mp #254 #689]: #685
 #12 := 1::Int
-#9 := 3::Int
-#10 := (f4 f5 3::Int)
-#11 := (f3 #10 3::Int)
+#10 := 3::Int
+#8 := 5::Int
+#9 := (f4 f5 5::Int)
+#11 := (f3 #9 3::Int)
 #13 := (= #11 1::Int)
 #14 := (not #13)
-#67 := [asserted]: #14
-#571 := (not #731)
-#664 := (or #571 #13)
-#317 := (* -1::Int 3::Int)
-#401 := (div #317 #317)
-#402 := (* -1::Int #401)
-#403 := (+ #11 #402)
-#394 := (= #403 0::Int)
-#405 := (div 3::Int 3::Int)
-#406 := (* -1::Int #405)
-#407 := (+ #11 #406)
-#404 := (= #407 0::Int)
-#408 := (>= 3::Int 0::Int)
-#387 := (<= 3::Int 0::Int)
-#722 := (or #387 #408)
-#724 := (not #722)
-#381 := (or #387 #387)
-#511 := (not #381)
-#718 := (or #511 #724)
-#392 := (ite #718 #404 #394)
-#393 := (= #11 0::Int)
-#725 := (= 3::Int 0::Int)
-#726 := (or #725 #725)
-#727 := (ite #726 #393 #392)
-#661 := (or #571 #727)
-#652 := (iff #661 #664)
-#646 := (iff #664 #664)
-#643 := [rewrite]: #646
-#569 := (iff #727 #13)
-#565 := (ite false #393 #13)
-#567 := (iff #565 #13)
-#568 := [rewrite]: #567
-#566 := (iff #727 #565)
-#548 := (iff #392 #13)
-#1 := true
-#662 := (ite true #13 #13)
-#660 := (iff #662 #13)
-#663 := [rewrite]: #660
-#564 := (iff #392 #662)
-#555 := (iff #394 #13)
-#686 := (+ -1::Int #11)
-#689 := (= #686 0::Int)
-#531 := (iff #689 #13)
-#532 := [rewrite]: #531
-#553 := (iff #394 #689)
-#668 := (= #403 #686)
-#692 := (+ #11 -1::Int)
-#687 := (= #692 #686)
-#682 := [rewrite]: #687
-#669 := (= #403 #692)
-#666 := (= #402 -1::Int)
-#414 := (* -1::Int 1::Int)
-#694 := (= #414 -1::Int)
-#409 := [rewrite]: #694
-#512 := (= #402 #414)
-#681 := (= #401 1::Int)
-#676 := -3::Int
-#672 := (div -3::Int -3::Int)
-#680 := (= #672 1::Int)
-#674 := [rewrite]: #680
-#673 := (= #401 #672)
-#677 := (= #317 -3::Int)
-#678 := [rewrite]: #677
-#679 := [monotonicity #678 #678]: #673
-#510 := [trans #679 #674]: #681
-#513 := [monotonicity #510]: #512
-#667 := [trans #513 #409]: #666
-#670 := [monotonicity #667]: #669
-#671 := [trans #670 #682]: #668
-#554 := [monotonicity #671]: #553
-#514 := [trans #554 #532]: #555
-#533 := (iff #404 #13)
-#684 := (iff #404 #689)
-#683 := (= #407 #686)
-#696 := (= #407 #692)
-#691 := (= #406 -1::Int)
-#415 := (= #406 #414)
-#412 := (= #405 1::Int)
-#413 := [rewrite]: #412
-#693 := [monotonicity #413]: #415
-#695 := [trans #693 #409]: #691
-#685 := [monotonicity #695]: #696
-#688 := [trans #685 #682]: #683
-#690 := [monotonicity #688]: #684
-#675 := [trans #690 #532]: #533
-#698 := (iff #718 true)
-#700 := (or true false)
-#697 := (iff #700 true)
-#701 := [rewrite]: #697
-#422 := (iff #718 #700)
-#323 := (iff #724 false)
-#704 := (not true)
-#428 := (iff #704 false)
-#429 := [rewrite]: #428
-#426 := (iff #724 #704)
-#717 := (iff #722 true)
-#715 := (or false true)
-#716 := (iff #715 true)
-#714 := [rewrite]: #716
-#355 := (iff #722 #715)
-#350 := (iff #408 true)
-#713 := [rewrite]: #350
-#364 := (iff #387 false)
-#705 := [rewrite]: #364
-#356 := [monotonicity #705 #713]: #355
-#703 := [trans #356 #714]: #717
-#427 := [monotonicity #703]: #426
-#699 := [trans #427 #429]: #323
-#706 := (iff #511 true)
-#707 := (not false)
-#710 := (iff #707 true)
-#711 := [rewrite]: #710
-#708 := (iff #511 #707)
-#370 := (iff #381 false)
-#729 := (or false false)
-#384 := (iff #729 false)
-#720 := [rewrite]: #384
-#368 := (iff #381 #729)
-#369 := [monotonicity #705 #705]: #368
-#371 := [trans #369 #720]: #370
-#709 := [monotonicity #371]: #708
-#712 := [trans #709 #711]: #706
-#423 := [monotonicity #712 #699]: #422
-#702 := [trans #423 #701]: #698
-#659 := [monotonicity #702 #675 #514]: #564
-#563 := [trans #659 #663]: #548
-#380 := (iff #726 false)
-#719 := (iff #726 #729)
-#728 := (iff #725 false)
-#723 := [rewrite]: #728
-#379 := [monotonicity #723 #723]: #719
-#721 := [trans #379 #720]: #380
-#559 := [monotonicity #721 #563]: #566
-#570 := [trans #559 #568]: #569
-#654 := [monotonicity #570]: #652
-#645 := [trans #654 #643]: #652
-#665 := [quant-inst #9 #9]: #661
-#655 := [mp #665 #645]: #664
-[unit-resolution #655 #67 #736]: false
-unsat
-3738fba1d7898fa560273958052bb4073440cad3 313 0
+#49 := [asserted]: #14
+#589 := (not #685)
+#590 := (or #589 #13)
+#347 := (* -1::Int 3::Int)
+#346 := (* -1::Int 5::Int)
+#679 := (div #346 #347)
+#680 := (* -1::Int #679)
+#681 := (+ #11 #680)
+#682 := (= #681 0::Int)
+#678 := (div 5::Int 3::Int)
+#335 := (* -1::Int #678)
+#465 := (+ #11 #335)
+#672 := (= #465 0::Int)
+#359 := (<= 3::Int 0::Int)
+#358 := (>= 5::Int 0::Int)
+#362 := (or #358 #359)
+#341 := (not #362)
+#348 := (<= 5::Int 0::Int)
+#360 := (or #348 #359)
+#361 := (not #360)
+#676 := (or #361 #341)
+#677 := (if #676 #672 #682)
+#357 := (= #11 0::Int)
+#355 := (= 3::Int 0::Int)
+#271 := (= 5::Int 0::Int)
+#356 := (or #271 #355)
+#683 := (if #356 #357 #677)
+#592 := (or #589 #683)
+#594 := (iff #592 #590)
+#591 := (iff #590 #590)
+#596 := [rewrite]: #591
+#598 := (iff #683 #13)
+#612 := (if false #357 #13)
+#603 := (iff #612 #13)
+#604 := [rewrite]: #603
+#601 := (iff #683 #612)
+#611 := (iff #677 #13)
+#621 := 2::Int
+#618 := (= #11 2::Int)
+#1 := true
+#600 := (if true #13 #618)
+#609 := (iff #600 #13)
+#610 := [rewrite]: #609
+#597 := (iff #677 #600)
+#606 := (iff #682 #618)
+#468 := -2::Int
+#519 := (+ -2::Int #11)
+#523 := (= #519 0::Int)
+#615 := (iff #523 #618)
+#619 := [rewrite]: #615
+#524 := (iff #682 #523)
+#521 := (= #681 #519)
+#617 := (+ #11 -2::Int)
+#520 := (= #617 #519)
+#513 := [rewrite]: #520
+#502 := (= #681 #617)
+#613 := (= #680 -2::Int)
+#507 := (* -1::Int 2::Int)
+#616 := (= #507 -2::Int)
+#518 := [rewrite]: #616
+#508 := (= #680 #507)
+#622 := (= #679 2::Int)
+#628 := -3::Int
+#627 := -5::Int
+#466 := (div -5::Int -3::Int)
+#623 := (= #466 2::Int)
+#624 := [rewrite]: #623
+#467 := (= #679 #466)
+#635 := (= #347 -3::Int)
+#464 := [rewrite]: #635
+#633 := (= #346 -5::Int)
+#634 := [rewrite]: #633
+#620 := [monotonicity #634 #464]: #467
+#625 := [trans #620 #624]: #622
+#509 := [monotonicity #625]: #508
+#614 := [trans #509 #518]: #613
+#517 := [monotonicity #614]: #502
+#522 := [trans #517 #513]: #521
+#525 := [monotonicity #522]: #524
+#608 := [trans #525 #619]: #606
+#632 := (iff #672 #13)
+#642 := (+ -1::Int #11)
+#486 := (= #642 0::Int)
+#630 := (iff #486 #13)
+#631 := [rewrite]: #630
+#487 := (iff #672 #486)
+#644 := (= #465 #642)
+#641 := (+ #11 -1::Int)
+#643 := (= #641 #642)
+#638 := [rewrite]: #643
+#636 := (= #465 #641)
+#639 := (= #335 -1::Int)
+#363 := (* -1::Int 1::Int)
+#646 := (= #363 -1::Int)
+#650 := [rewrite]: #646
+#645 := (= #335 #363)
+#647 := (= #678 1::Int)
+#648 := [rewrite]: #647
+#649 := [monotonicity #648]: #645
+#640 := [trans #649 #650]: #639
+#637 := [monotonicity #640]: #636
+#485 := [trans #637 #638]: #644
+#629 := [monotonicity #485]: #487
+#626 := [trans #629 #631]: #632
+#368 := (iff #676 true)
+#658 := (or true false)
+#382 := (iff #658 true)
+#383 := [rewrite]: #382
+#366 := (iff #676 #658)
+#652 := (iff #341 false)
+#654 := (not true)
+#651 := (iff #654 false)
+#655 := [rewrite]: #651
+#376 := (iff #341 #654)
+#277 := (iff #362 true)
+#380 := (iff #362 #658)
+#662 := (iff #359 false)
+#663 := [rewrite]: #662
+#671 := (iff #358 true)
+#657 := [rewrite]: #671
+#381 := [monotonicity #657 #663]: #380
+#653 := [trans #381 #383]: #277
+#377 := [monotonicity #653]: #376
+#656 := [trans #377 #655]: #652
+#670 := (iff #361 true)
+#304 := (not false)
+#309 := (iff #304 true)
+#310 := [rewrite]: #309
+#667 := (iff #361 #304)
+#660 := (iff #360 false)
+#334 := (or false false)
+#659 := (iff #334 false)
+#322 := [rewrite]: #659
+#664 := (iff #360 #334)
+#325 := (iff #348 false)
+#661 := [rewrite]: #325
+#665 := [monotonicity #661 #663]: #664
+#666 := [trans #665 #322]: #660
+#669 := [monotonicity #666]: #667
+#668 := [trans #669 #310]: #670
+#367 := [monotonicity #668 #656]: #366
+#369 := [trans #367 #383]: #368
+#599 := [monotonicity #369 #626 #608]: #597
+#607 := [trans #599 #610]: #611
+#323 := (iff #356 false)
+#675 := (iff #356 #334)
+#338 := (iff #355 false)
+#674 := [rewrite]: #338
+#673 := (iff #271 false)
+#333 := [rewrite]: #673
+#318 := [monotonicity #333 #674]: #675
+#324 := [trans #318 #322]: #323
+#602 := [monotonicity #324 #607]: #601
+#605 := [trans #602 #604]: #598
+#595 := [monotonicity #605]: #594
+#582 := [trans #595 #596]: #594
+#593 := [quant-inst #8 #10]: #592
+#583 := [mp #593 #582]: #590
+[unit-resolution #583 #49 #690]: false
+07dc79bb7af38a9690966d1d8001aa5e0aaa3f0d 322 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #18 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #16 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #17 := (f4 f5 #16)
 #19 := (f3 #17 #18)
-#731 := (pattern #19)
+#700 := (pattern #19)
 #20 := 0::Int
-#76 := -1::Int
-#80 := (* -1::Int #18)
-#77 := (* -1::Int #16)
-#83 := (div #77 #80)
-#234 := (* -1::Int #83)
-#235 := (+ #19 #234)
-#236 := (= #235 0::Int)
+#62 := -1::Int
+#101 := (* -1::Int #18)
+#98 := (* -1::Int #16)
+#104 := (div #98 #101)
+#260 := (* -1::Int #104)
+#261 := (+ #19 #260)
+#262 := (= #261 0::Int)
 #30 := (div #16 #18)
-#231 := (* -1::Int #30)
-#232 := (+ #19 #231)
-#233 := (= #232 0::Int)
-#109 := (>= #16 0::Int)
-#102 := (<= #18 0::Int)
-#194 := (or #102 #109)
-#195 := (not #194)
-#98 := (<= #16 0::Int)
-#192 := (or #98 #102)
-#193 := (not #192)
-#198 := (or #193 #195)
-#237 := (ite #198 #233 #236)
-#230 := (= #19 0::Int)
+#257 := (* -1::Int #30)
+#258 := (+ #19 #257)
+#259 := (= #258 0::Int)
+#76 := (<= #18 0::Int)
+#167 := (>= #16 0::Int)
+#220 := (or #167 #76)
+#221 := (not #220)
+#72 := (<= #16 0::Int)
+#216 := (or #72 #76)
+#217 := (not #216)
+#224 := (or #217 #221)
+#263 := (if #224 #259 #262)
+#256 := (= #19 0::Int)
 #22 := (= #18 0::Int)
 #21 := (= #16 0::Int)
 #23 := (or #21 #22)
-#238 := (ite #23 #230 #237)
-#732 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #731) #238)
-#241 := (forall (vars (?v0 Int) (?v1 Int)) #238)
-#735 := (iff #241 #732)
-#733 := (iff #238 #238)
-#734 := [refl]: #733
-#736 := [quant-intro #734]: #735
-#201 := (ite #198 #30 #83)
-#204 := (ite #23 0::Int #201)
-#207 := (= #19 #204)
-#210 := (forall (vars (?v0 Int) (?v1 Int)) #207)
-#242 := (iff #210 #241)
-#239 := (iff #207 #238)
-#240 := [rewrite]: #239
-#243 := [quant-intro #240]: #242
-#110 := (not #109)
-#103 := (not #102)
-#113 := (and #103 #110)
-#99 := (not #98)
-#106 := (and #99 #103)
-#116 := (or #106 #113)
-#119 := (ite #116 #30 #83)
-#122 := (ite #23 0::Int #119)
-#125 := (= #19 #122)
-#128 := (forall (vars (?v0 Int) (?v1 Int)) #125)
-#211 := (iff #128 #210)
-#208 := (iff #125 #207)
-#205 := (= #122 #204)
-#202 := (= #119 #201)
-#199 := (iff #116 #198)
-#196 := (iff #113 #195)
-#197 := [rewrite]: #196
-#186 := (iff #106 #193)
-#187 := [rewrite]: #186
-#200 := [monotonicity #187 #197]: #199
-#203 := [monotonicity #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [monotonicity #206]: #208
-#212 := [quant-intro #209]: #211
-#190 := (~ #128 #128)
-#188 := (~ #125 #125)
-#189 := [refl]: #188
-#191 := [nnf-pos #189]: #190
+#264 := (if #23 #256 #263)
+#701 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #700) #264)
+#267 := (forall (vars (?v0 Int) (?v1 Int)) #264)
+#704 := (iff #267 #701)
+#702 := (iff #264 #264)
+#703 := [refl]: #702
+#705 := [quant-intro #703]: #704
+#227 := (if #224 #30 #104)
+#230 := (if #23 0::Int #227)
+#233 := (= #19 #230)
+#236 := (forall (vars (?v0 Int) (?v1 Int)) #233)
+#268 := (iff #236 #267)
+#265 := (iff #233 #264)
+#266 := [rewrite]: #265
+#269 := [quant-intro #266]: #268
+#77 := (not #76)
+#170 := (not #167)
+#173 := (and #170 #77)
+#73 := (not #72)
+#80 := (and #73 #77)
+#176 := (or #80 #173)
+#179 := (if #176 #30 #104)
+#182 := (if #23 0::Int #179)
+#185 := (= #19 #182)
+#188 := (forall (vars (?v0 Int) (?v1 Int)) #185)
+#237 := (iff #188 #236)
+#234 := (iff #185 #233)
+#231 := (= #182 #230)
+#228 := (= #179 #227)
+#225 := (iff #176 #224)
+#222 := (iff #173 #221)
+#223 := [rewrite]: #222
+#218 := (iff #80 #217)
+#219 := [rewrite]: #218
+#226 := [monotonicity #219 #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#235 := [monotonicity #232]: #234
+#238 := [quant-intro #235]: #237
+#208 := (~ #188 #188)
+#210 := (~ #185 #185)
+#211 := [refl]: #210
+#209 := [nnf-pos #211]: #208
+#83 := (<= 0::Int #16)
+#84 := (not #83)
+#92 := (and #84 #77)
+#95 := (or #80 #92)
+#107 := (if #95 #30 #104)
+#110 := (if #23 0::Int #107)
+#113 := (= #19 #110)
+#116 := (forall (vars (?v0 Int) (?v1 Int)) #113)
+#189 := (iff #116 #188)
+#186 := (iff #113 #185)
+#183 := (= #110 #182)
+#180 := (= #107 #179)
+#177 := (iff #95 #176)
+#174 := (iff #92 #173)
+#171 := (iff #84 #170)
+#168 := (iff #83 #167)
+#169 := [rewrite]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [monotonicity #178]: #180
+#184 := [monotonicity #181]: #183
+#187 := [monotonicity #184]: #186
+#190 := [quant-intro #187]: #189
 #32 := (- #18)
 #31 := (- #16)
 #33 := (div #31 #32)
@@ -31510,624 +30663,642 @@
 #24 := (< 0::Int #16)
 #26 := (and #24 #25)
 #29 := (or #26 #28)
-#34 := (ite #29 #30 #33)
-#35 := (ite #23 0::Int #34)
+#34 := (if #29 #30 #33)
+#35 := (if #23 0::Int #34)
 #36 := (= #19 #35)
 #37 := (forall (vars (?v0 Int) (?v1 Int)) #36)
-#131 := (iff #37 #128)
-#70 := (and #25 #27)
-#73 := (or #26 #70)
-#86 := (ite #73 #30 #83)
-#89 := (ite #23 0::Int #86)
-#92 := (= #19 #89)
-#95 := (forall (vars (?v0 Int) (?v1 Int)) #92)
-#129 := (iff #95 #128)
-#126 := (iff #92 #125)
-#123 := (= #89 #122)
-#120 := (= #86 #119)
-#117 := (iff #73 #116)
-#114 := (iff #70 #113)
-#111 := (iff #27 #110)
-#112 := [rewrite]: #111
-#104 := (iff #25 #103)
-#105 := [rewrite]: #104
-#115 := [monotonicity #105 #112]: #114
-#107 := (iff #26 #106)
-#100 := (iff #24 #99)
-#101 := [rewrite]: #100
-#108 := [monotonicity #101 #105]: #107
-#118 := [monotonicity #108 #115]: #117
-#121 := [monotonicity #118]: #120
-#124 := [monotonicity #121]: #123
-#127 := [monotonicity #124]: #126
-#130 := [quant-intro #127]: #129
-#96 := (iff #37 #95)
-#93 := (iff #36 #92)
-#90 := (= #35 #89)
-#87 := (= #34 #86)
-#84 := (= #33 #83)
-#81 := (= #32 #80)
-#82 := [rewrite]: #81
-#78 := (= #31 #77)
+#117 := (iff #37 #116)
+#114 := (iff #36 #113)
+#111 := (= #35 #110)
+#108 := (= #34 #107)
+#105 := (= #33 #104)
+#102 := (= #32 #101)
+#103 := [rewrite]: #102
+#99 := (= #31 #98)
+#100 := [rewrite]: #99
+#106 := [monotonicity #100 #103]: #105
+#96 := (iff #29 #95)
+#93 := (iff #28 #92)
+#78 := (iff #25 #77)
 #79 := [rewrite]: #78
-#85 := [monotonicity #79 #82]: #84
-#74 := (iff #29 #73)
-#71 := (iff #28 #70)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#88 := [monotonicity #75 #85]: #87
-#91 := [monotonicity #88]: #90
-#94 := [monotonicity #91]: #93
-#97 := [quant-intro #94]: #96
-#132 := [trans #97 #130]: #131
-#69 := [asserted]: #37
-#133 := [mp #69 #132]: #128
-#182 := [mp~ #133 #191]: #128
-#213 := [mp #182 #212]: #210
-#244 := [mp #213 #243]: #241
-#737 := [mp #244 #736]: #732
-#13 := 1::Int
-#11 := 3::Int
-#9 := 5::Int
-#10 := (f4 f5 5::Int)
-#12 := (f3 #10 3::Int)
-#14 := (= #12 1::Int)
-#15 := (not #14)
-#68 := [asserted]: #15
-#640 := (not #732)
-#641 := (or #640 #14)
-#318 := (* -1::Int 3::Int)
-#402 := (* -1::Int 5::Int)
-#403 := (div #402 #318)
-#404 := (* -1::Int #403)
-#395 := (+ #12 #404)
-#406 := (= #395 0::Int)
-#407 := (div 5::Int 3::Int)
-#408 := (* -1::Int #407)
-#405 := (+ #12 #408)
-#409 := (= #405 0::Int)
-#388 := (>= 5::Int 0::Int)
-#723 := (<= 3::Int 0::Int)
-#725 := (or #723 #388)
-#382 := (not #725)
-#512 := (<= 5::Int 0::Int)
-#719 := (or #512 #723)
-#393 := (not #719)
-#394 := (or #393 #382)
-#726 := (ite #394 #409 #406)
-#727 := (= #12 0::Int)
-#728 := (= 3::Int 0::Int)
-#729 := (= 5::Int 0::Int)
-#724 := (or #729 #728)
-#730 := (ite #724 #727 #726)
-#642 := (or #640 #730)
-#643 := (iff #642 #641)
-#630 := (iff #641 #641)
-#632 := [rewrite]: #630
-#637 := (iff #730 #14)
-#650 := (ite false #727 #14)
-#652 := (iff #650 #14)
-#636 := [rewrite]: #652
-#651 := (iff #730 #650)
-#648 := (iff #726 #14)
-#669 := 2::Int
-#653 := (= #12 2::Int)
-#1 := true
-#656 := (ite true #14 #653)
-#654 := (iff #656 #14)
-#659 := [rewrite]: #654
-#657 := (iff #726 #656)
-#644 := (iff #406 #653)
-#660 := -2::Int
-#568 := (+ -2::Int #12)
-#665 := (= #568 0::Int)
-#655 := (iff #665 #653)
-#647 := [rewrite]: #655
-#662 := (iff #406 #665)
-#571 := (= #395 #568)
-#566 := (+ #12 -2::Int)
-#569 := (= #566 #568)
-#570 := [rewrite]: #569
-#567 := (= #395 #566)
-#549 := (= #404 -2::Int)
-#515 := (* -1::Int 2::Int)
-#661 := (= #515 -2::Int)
-#664 := [rewrite]: #661
-#663 := (= #404 #515)
-#555 := (= #403 2::Int)
-#513 := -3::Int
-#675 := -5::Int
-#668 := (div -5::Int -3::Int)
-#672 := (= #668 2::Int)
-#554 := [rewrite]: #672
-#670 := (= #403 #668)
-#514 := (= #318 -3::Int)
-#667 := [rewrite]: #514
-#682 := (= #402 -5::Int)
-#511 := [rewrite]: #682
-#671 := [monotonicity #511 #667]: #670
-#556 := [trans #671 #554]: #555
-#565 := [monotonicity #556]: #663
-#564 := [trans #565 #664]: #549
-#560 := [monotonicity #564]: #567
-#572 := [trans #560 #570]: #571
-#666 := [monotonicity #572]: #662
-#646 := [trans #666 #647]: #644
-#680 := (iff #409 #14)
-#691 := (+ -1::Int #12)
-#677 := (= #691 0::Int)
-#673 := (iff #677 #14)
-#674 := [rewrite]: #673
-#678 := (iff #409 #677)
-#534 := (= #405 #691)
-#689 := (+ #12 -1::Int)
-#532 := (= #689 #691)
-#533 := [rewrite]: #532
-#690 := (= #405 #689)
-#683 := (= #408 -1::Int)
-#693 := (* -1::Int 1::Int)
-#687 := (= #693 -1::Int)
-#688 := [rewrite]: #687
-#697 := (= #408 #693)
-#692 := (= #407 1::Int)
-#696 := [rewrite]: #692
-#686 := [monotonicity #696]: #697
-#684 := [trans #686 #688]: #683
-#685 := [monotonicity #684]: #690
-#676 := [trans #685 #533]: #534
-#679 := [monotonicity #676]: #678
-#681 := [trans #679 #674]: #680
-#695 := (iff #394 true)
-#413 := (or true false)
-#416 := (iff #413 true)
-#694 := [rewrite]: #416
-#414 := (iff #394 #413)
-#699 := (iff #382 false)
-#701 := (not true)
-#698 := (iff #701 false)
-#702 := [rewrite]: #698
-#423 := (iff #382 #701)
-#324 := (iff #725 true)
-#705 := (or false true)
-#429 := (iff #705 true)
-#430 := [rewrite]: #429
-#427 := (iff #725 #705)
-#718 := (iff #388 true)
-#704 := [rewrite]: #718
-#709 := (iff #723 false)
-#710 := [rewrite]: #709
-#428 := [monotonicity #710 #704]: #427
-#700 := [trans #428 #430]: #324
-#424 := [monotonicity #700]: #423
-#703 := [trans #424 #702]: #699
-#717 := (iff #393 true)
-#351 := (not false)
-#356 := (iff #351 true)
-#357 := [rewrite]: #356
-#714 := (iff #393 #351)
-#707 := (iff #719 false)
-#381 := (or false false)
-#706 := (iff #381 false)
-#369 := [rewrite]: #706
-#711 := (iff #719 #381)
-#372 := (iff #512 false)
-#708 := [rewrite]: #372
-#712 := [monotonicity #708 #710]: #711
-#713 := [trans #712 #369]: #707
-#716 := [monotonicity #713]: #714
-#715 := [trans #716 #357]: #717
-#415 := [monotonicity #715 #703]: #414
-#410 := [trans #415 #694]: #695
-#658 := [monotonicity #410 #681 #646]: #657
-#649 := [trans #658 #659]: #648
-#370 := (iff #724 false)
-#722 := (iff #724 #381)
-#385 := (iff #728 false)
-#721 := [rewrite]: #385
-#720 := (iff #729 false)
-#380 := [rewrite]: #720
-#365 := [monotonicity #380 #721]: #722
-#371 := [trans #365 #369]: #370
-#645 := [monotonicity #371 #649]: #651
-#639 := [trans #645 #636]: #637
-#629 := [monotonicity #639]: #643
-#633 := [trans #629 #632]: #643
-#638 := [quant-inst #9 #11]: #642
-#634 := [mp #638 #633]: #641
-[unit-resolution #634 #68 #737]: false
-unsat
-b0632c3adf15c421ca3bfe276f81b5b084a9fb12 312 0
+#85 := (iff #27 #84)
+#89 := (iff #84 #84)
+#87 := (iff #83 #83)
+#88 := [rewrite]: #87
+#90 := [monotonicity #88]: #89
+#86 := [rewrite]: #85
+#91 := [trans #86 #90]: #85
+#94 := [monotonicity #91 #79]: #93
+#81 := (iff #26 #80)
+#74 := (iff #24 #73)
+#75 := [rewrite]: #74
+#82 := [monotonicity #75 #79]: #81
+#97 := [monotonicity #82 #94]: #96
+#109 := [monotonicity #97 #106]: #108
+#112 := [monotonicity #109]: #111
+#115 := [monotonicity #112]: #114
+#118 := [quant-intro #115]: #117
+#51 := [asserted]: #37
+#119 := [mp #51 #118]: #116
+#191 := [mp #119 #190]: #188
+#165 := [mp~ #191 #209]: #188
+#239 := [mp #165 #238]: #236
+#270 := [mp #239 #269]: #267
+#706 := [mp #270 #705]: #701
+#56 := -3::Int
+#8 := 1::Int
+#9 := (f4 f5 1::Int)
+#59 := (f3 #9 -3::Int)
+#65 := (= #59 -1::Int)
+#68 := (not #65)
+#13 := (- 1::Int)
+#10 := 3::Int
+#11 := (- 3::Int)
+#12 := (f3 #9 #11)
+#14 := (= #12 #13)
+#15 := (not #14)
+#69 := (iff #15 #68)
+#66 := (iff #14 #65)
+#63 := (= #13 -1::Int)
+#64 := [rewrite]: #63
+#60 := (= #12 #59)
+#57 := (= #11 -3::Int)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#67 := [monotonicity #61 #64]: #66
+#70 := [monotonicity #67]: #69
+#50 := [asserted]: #15
+#71 := [mp #50 #70]: #68
+#616 := (not #701)
+#613 := (or #616 #65)
+#363 := (* -1::Int -3::Int)
+#362 := (* -1::Int 1::Int)
+#695 := (div #362 #363)
+#696 := (* -1::Int #695)
+#697 := (+ #59 #696)
+#698 := (= #697 0::Int)
+#694 := (div 1::Int -3::Int)
+#351 := (* -1::Int #694)
+#481 := (+ #59 #351)
+#688 := (= #481 0::Int)
+#375 := (<= -3::Int 0::Int)
+#374 := (>= 1::Int 0::Int)
+#378 := (or #374 #375)
+#357 := (not #378)
+#364 := (<= 1::Int 0::Int)
+#376 := (or #364 #375)
+#377 := (not #376)
+#692 := (or #377 #357)
+#693 := (if #692 #688 #698)
+#373 := (= #59 0::Int)
+#371 := (= -3::Int 0::Int)
+#287 := (= 1::Int 0::Int)
+#372 := (or #287 #371)
+#699 := (if #372 #373 #693)
+#615 := (or #616 #699)
+#626 := (iff #615 #613)
+#623 := (iff #613 #613)
+#628 := [rewrite]: #623
+#622 := (iff #699 #65)
+#529 := (if false #373 #65)
+#539 := (iff #529 #65)
+#540 := [rewrite]: #539
+#631 := (iff #699 #529)
+#541 := (iff #693 #65)
+#537 := (iff #693 #529)
+#535 := (iff #698 #65)
+#524 := (+ 1::Int #59)
+#629 := (= #524 0::Int)
+#518 := (iff #629 #65)
+#533 := [rewrite]: #518
+#630 := (iff #698 #629)
+#632 := (= #697 #524)
+#638 := (+ #59 1::Int)
+#525 := (= #638 #524)
+#484 := [rewrite]: #525
+#641 := (= #697 #638)
+#639 := (= #696 1::Int)
+#480 := (* -1::Int -1::Int)
+#636 := (= #480 1::Int)
+#637 := [rewrite]: #636
+#482 := (= #696 #480)
+#644 := (= #695 -1::Int)
+#648 := (div -1::Int 3::Int)
+#649 := (= #648 -1::Int)
+#650 := [rewrite]: #649
+#642 := (= #695 #648)
+#646 := (= #363 3::Int)
+#647 := [rewrite]: #646
+#503 := (= #362 -1::Int)
+#645 := [rewrite]: #503
+#643 := [monotonicity #645 #647]: #642
+#651 := [trans #643 #650]: #644
+#483 := [monotonicity #651]: #482
+#640 := [trans #483 #637]: #639
+#523 := [monotonicity #640]: #641
+#534 := [trans #523 #484]: #632
+#633 := [monotonicity #534]: #630
+#536 := [trans #633 #533]: #535
+#501 := (iff #688 #373)
+#654 := (= #481 #59)
+#657 := (+ #59 0::Int)
+#658 := (= #657 #59)
+#659 := [rewrite]: #658
+#652 := (= #481 #657)
+#655 := (= #351 0::Int)
+#379 := (* -1::Int 0::Int)
+#662 := (= #379 0::Int)
+#666 := [rewrite]: #662
+#661 := (= #351 #379)
+#663 := (= #694 0::Int)
+#664 := [rewrite]: #663
+#665 := [monotonicity #664]: #661
+#656 := [trans #665 #666]: #655
+#653 := [monotonicity #656]: #652
+#660 := [trans #653 #659]: #654
+#502 := [monotonicity #660]: #501
+#384 := (iff #692 false)
+#350 := (or false false)
+#675 := (iff #350 false)
+#338 := [rewrite]: #675
+#382 := (iff #692 #350)
+#668 := (iff #357 false)
+#1 := true
+#325 := (not true)
+#684 := (iff #325 false)
+#687 := [rewrite]: #684
+#667 := (iff #357 #325)
+#392 := (iff #378 true)
+#398 := (or true true)
+#669 := (iff #398 true)
+#670 := [rewrite]: #669
+#399 := (iff #378 #398)
+#678 := (iff #375 true)
+#679 := [rewrite]: #678
+#396 := (iff #374 true)
+#397 := [rewrite]: #396
+#293 := [monotonicity #397 #679]: #399
+#393 := [trans #293 #670]: #392
+#671 := [monotonicity #393]: #667
+#672 := [trans #671 #687]: #668
+#673 := (iff #377 false)
+#326 := (iff #377 #325)
+#683 := (iff #376 true)
+#680 := (or false true)
+#682 := (iff #680 true)
+#320 := [rewrite]: #682
+#681 := (iff #376 #680)
+#341 := (iff #364 false)
+#677 := [rewrite]: #341
+#676 := [monotonicity #677 #679]: #681
+#685 := [trans #676 #320]: #683
+#686 := [monotonicity #685]: #326
+#674 := [trans #686 #687]: #673
+#383 := [monotonicity #674 #672]: #382
+#385 := [trans #383 #338]: #384
+#538 := [monotonicity #385 #502 #536]: #537
+#634 := [trans #538 #540]: #541
+#339 := (iff #372 false)
+#691 := (iff #372 #350)
+#354 := (iff #371 false)
+#690 := [rewrite]: #354
+#689 := (iff #287 false)
+#349 := [rewrite]: #689
+#334 := [monotonicity #349 #690]: #691
+#340 := [trans #334 #338]: #339
+#635 := [monotonicity #340 #634]: #631
+#624 := [trans #635 #540]: #622
+#627 := [monotonicity #624]: #626
+#617 := [trans #627 #628]: #626
+#625 := [quant-inst #8 #56]: #615
+#618 := [mp #625 #617]: #613
+[unit-resolution #618 #71 #706]: false
+2724efda4c32efbff1ae699cb7c49583d776fd69 321 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#18 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#16 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#17 := (f4 f5 #16)
+#19 := (f3 #17 #18)
+#700 := (pattern #19)
+#20 := 0::Int
+#62 := -1::Int
+#101 := (* -1::Int #18)
+#98 := (* -1::Int #16)
+#104 := (div #98 #101)
+#260 := (* -1::Int #104)
+#261 := (+ #19 #260)
+#262 := (= #261 0::Int)
+#30 := (div #16 #18)
+#257 := (* -1::Int #30)
+#258 := (+ #19 #257)
+#259 := (= #258 0::Int)
+#76 := (<= #18 0::Int)
+#167 := (>= #16 0::Int)
+#220 := (or #167 #76)
+#221 := (not #220)
+#72 := (<= #16 0::Int)
+#216 := (or #72 #76)
+#217 := (not #216)
+#224 := (or #217 #221)
+#263 := (if #224 #259 #262)
+#256 := (= #19 0::Int)
+#22 := (= #18 0::Int)
+#21 := (= #16 0::Int)
+#23 := (or #21 #22)
+#264 := (if #23 #256 #263)
+#701 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #700) #264)
+#267 := (forall (vars (?v0 Int) (?v1 Int)) #264)
+#704 := (iff #267 #701)
+#702 := (iff #264 #264)
+#703 := [refl]: #702
+#705 := [quant-intro #703]: #704
+#227 := (if #224 #30 #104)
+#230 := (if #23 0::Int #227)
+#233 := (= #19 #230)
+#236 := (forall (vars (?v0 Int) (?v1 Int)) #233)
+#268 := (iff #236 #267)
+#265 := (iff #233 #264)
+#266 := [rewrite]: #265
+#269 := [quant-intro #266]: #268
+#77 := (not #76)
+#170 := (not #167)
+#173 := (and #170 #77)
+#73 := (not #72)
+#80 := (and #73 #77)
+#176 := (or #80 #173)
+#179 := (if #176 #30 #104)
+#182 := (if #23 0::Int #179)
+#185 := (= #19 #182)
+#188 := (forall (vars (?v0 Int) (?v1 Int)) #185)
+#237 := (iff #188 #236)
+#234 := (iff #185 #233)
+#231 := (= #182 #230)
+#228 := (= #179 #227)
+#225 := (iff #176 #224)
+#222 := (iff #173 #221)
+#223 := [rewrite]: #222
+#218 := (iff #80 #217)
+#219 := [rewrite]: #218
+#226 := [monotonicity #219 #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#235 := [monotonicity #232]: #234
+#238 := [quant-intro #235]: #237
+#165 := (~ #188 #188)
+#208 := (~ #185 #185)
+#209 := [refl]: #208
+#166 := [nnf-pos #209]: #165
+#83 := (<= 0::Int #16)
+#84 := (not #83)
+#92 := (and #84 #77)
+#95 := (or #80 #92)
+#107 := (if #95 #30 #104)
+#110 := (if #23 0::Int #107)
+#113 := (= #19 #110)
+#116 := (forall (vars (?v0 Int) (?v1 Int)) #113)
+#189 := (iff #116 #188)
+#186 := (iff #113 #185)
+#183 := (= #110 #182)
+#180 := (= #107 #179)
+#177 := (iff #95 #176)
+#174 := (iff #92 #173)
+#171 := (iff #84 #170)
+#168 := (iff #83 #167)
+#169 := [rewrite]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [monotonicity #178]: #180
+#184 := [monotonicity #181]: #183
+#187 := [monotonicity #184]: #186
+#190 := [quant-intro #187]: #189
+#32 := (- #18)
+#31 := (- #16)
+#33 := (div #31 #32)
+#25 := (< 0::Int #18)
+#27 := (< #16 0::Int)
+#28 := (and #27 #25)
+#24 := (< 0::Int #16)
+#26 := (and #24 #25)
+#29 := (or #26 #28)
+#34 := (if #29 #30 #33)
+#35 := (if #23 0::Int #34)
+#36 := (= #19 #35)
+#37 := (forall (vars (?v0 Int) (?v1 Int)) #36)
+#117 := (iff #37 #116)
+#114 := (iff #36 #113)
+#111 := (= #35 #110)
+#108 := (= #34 #107)
+#105 := (= #33 #104)
+#102 := (= #32 #101)
+#103 := [rewrite]: #102
+#99 := (= #31 #98)
+#100 := [rewrite]: #99
+#106 := [monotonicity #100 #103]: #105
+#96 := (iff #29 #95)
+#93 := (iff #28 #92)
+#78 := (iff #25 #77)
+#79 := [rewrite]: #78
+#85 := (iff #27 #84)
+#89 := (iff #84 #84)
+#87 := (iff #83 #83)
+#88 := [rewrite]: #87
+#90 := [monotonicity #88]: #89
+#86 := [rewrite]: #85
+#91 := [trans #86 #90]: #85
+#94 := [monotonicity #91 #79]: #93
+#81 := (iff #26 #80)
+#74 := (iff #24 #73)
+#75 := [rewrite]: #74
+#82 := [monotonicity #75 #79]: #81
+#97 := [monotonicity #82 #94]: #96
+#109 := [monotonicity #97 #106]: #108
+#112 := [monotonicity #109]: #111
+#115 := [monotonicity #112]: #114
+#118 := [quant-intro #115]: #117
+#51 := [asserted]: #37
+#119 := [mp #51 #118]: #116
+#191 := [mp #119 #190]: #188
+#210 := [mp~ #191 #166]: #188
+#239 := [mp #210 #238]: #236
+#270 := [mp #239 #269]: #267
+#706 := [mp #270 #705]: #701
+#56 := -3::Int
+#8 := 3::Int
+#9 := (f4 f5 3::Int)
+#59 := (f3 #9 -3::Int)
+#65 := (= #59 -1::Int)
+#68 := (not #65)
+#12 := 1::Int
+#13 := (- 1::Int)
+#10 := (- 3::Int)
+#11 := (f3 #9 #10)
+#14 := (= #11 #13)
+#15 := (not #14)
+#69 := (iff #15 #68)
+#66 := (iff #14 #65)
+#63 := (= #13 -1::Int)
+#64 := [rewrite]: #63
+#60 := (= #11 #59)
+#57 := (= #10 -3::Int)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#67 := [monotonicity #61 #64]: #66
+#70 := [monotonicity #67]: #69
+#50 := [asserted]: #15
+#71 := [mp #50 #70]: #68
+#624 := (not #701)
+#616 := (or #624 #65)
+#363 := (* -1::Int -3::Int)
+#362 := (* -1::Int 3::Int)
+#695 := (div #362 #363)
+#696 := (* -1::Int #695)
+#697 := (+ #59 #696)
+#698 := (= #697 0::Int)
+#694 := (div 3::Int -3::Int)
+#351 := (* -1::Int #694)
+#481 := (+ #59 #351)
+#688 := (= #481 0::Int)
+#375 := (<= -3::Int 0::Int)
+#374 := (>= 3::Int 0::Int)
+#378 := (or #374 #375)
+#357 := (not #378)
+#364 := (<= 3::Int 0::Int)
+#376 := (or #364 #375)
+#377 := (not #376)
+#692 := (or #377 #357)
+#693 := (if #692 #688 #698)
+#373 := (= #59 0::Int)
+#371 := (= -3::Int 0::Int)
+#287 := (= 3::Int 0::Int)
+#372 := (or #287 #371)
+#699 := (if #372 #373 #693)
+#613 := (or #624 #699)
+#625 := (iff #613 #616)
+#627 := (iff #616 #616)
+#623 := [rewrite]: #627
+#635 := (iff #699 #65)
+#539 := (if false #373 #65)
+#634 := (iff #539 #65)
+#631 := [rewrite]: #634
+#540 := (iff #699 #539)
+#537 := (iff #693 #65)
+#518 := (if false #65 #65)
+#536 := (iff #518 #65)
+#529 := [rewrite]: #536
+#533 := (iff #693 #518)
+#630 := (iff #698 #65)
+#658 := (+ 1::Int #59)
+#502 := (= #658 0::Int)
+#646 := (iff #502 #65)
+#647 := [rewrite]: #646
+#534 := (iff #698 #502)
+#484 := (= #697 #658)
+#657 := (+ #59 1::Int)
+#659 := (= #657 #658)
+#654 := [rewrite]: #659
+#524 := (= #697 #657)
+#641 := (= #696 1::Int)
+#379 := (* -1::Int -1::Int)
+#662 := (= #379 1::Int)
+#666 := [rewrite]: #662
+#640 := (= #696 #379)
+#637 := (= #695 -1::Int)
+#651 := (div -3::Int 3::Int)
+#483 := (= #651 -1::Int)
+#636 := [rewrite]: #483
+#480 := (= #695 #651)
+#650 := (= #363 3::Int)
+#644 := [rewrite]: #650
+#643 := (= #362 -3::Int)
+#649 := [rewrite]: #643
+#482 := [monotonicity #649 #644]: #480
+#639 := [trans #482 #636]: #637
+#638 := [monotonicity #639]: #640
+#523 := [trans #638 #666]: #641
+#525 := [monotonicity #523]: #524
+#632 := [trans #525 #654]: #484
+#629 := [monotonicity #632]: #534
+#633 := [trans #629 #647]: #630
+#648 := (iff #688 #65)
+#503 := (iff #688 #502)
+#660 := (= #481 #658)
+#652 := (= #481 #657)
+#655 := (= #351 1::Int)
+#661 := (= #351 #379)
+#663 := (= #694 -1::Int)
+#664 := [rewrite]: #663
+#665 := [monotonicity #664]: #661
+#656 := [trans #665 #666]: #655
+#653 := [monotonicity #656]: #652
+#501 := [trans #653 #654]: #660
+#645 := [monotonicity #501]: #503
+#642 := [trans #645 #647]: #648
+#384 := (iff #692 false)
+#350 := (or false false)
+#675 := (iff #350 false)
+#338 := [rewrite]: #675
+#382 := (iff #692 #350)
+#668 := (iff #357 false)
+#1 := true
+#325 := (not true)
+#684 := (iff #325 false)
+#687 := [rewrite]: #684
+#667 := (iff #357 #325)
+#392 := (iff #378 true)
+#398 := (or true true)
+#669 := (iff #398 true)
+#670 := [rewrite]: #669
+#399 := (iff #378 #398)
+#678 := (iff #375 true)
+#679 := [rewrite]: #678
+#396 := (iff #374 true)
+#397 := [rewrite]: #396
+#293 := [monotonicity #397 #679]: #399
+#393 := [trans #293 #670]: #392
+#671 := [monotonicity #393]: #667
+#672 := [trans #671 #687]: #668
+#673 := (iff #377 false)
+#326 := (iff #377 #325)
+#683 := (iff #376 true)
+#680 := (or false true)
+#682 := (iff #680 true)
+#320 := [rewrite]: #682
+#681 := (iff #376 #680)
+#341 := (iff #364 false)
+#677 := [rewrite]: #341
+#676 := [monotonicity #677 #679]: #681
+#685 := [trans #676 #320]: #683
+#686 := [monotonicity #685]: #326
+#674 := [trans #686 #687]: #673
+#383 := [monotonicity #674 #672]: #382
+#385 := [trans #383 #338]: #384
+#535 := [monotonicity #385 #642 #633]: #533
+#538 := [trans #535 #529]: #537
+#339 := (iff #372 false)
+#691 := (iff #372 #350)
+#354 := (iff #371 false)
+#690 := [rewrite]: #354
+#689 := (iff #287 false)
+#349 := [rewrite]: #689
+#334 := [monotonicity #349 #690]: #691
+#340 := [trans #334 #338]: #339
+#541 := [monotonicity #340 #538]: #540
+#622 := [trans #541 #631]: #635
+#626 := [monotonicity #622]: #625
+#628 := [trans #626 #623]: #625
+#615 := [quant-inst #8 #56]: #613
+#617 := [mp #615 #628]: #616
+[unit-resolution #617 #71 #706]: false
+b17d0a5f28b546cd2d43a494f2d86e3a5351ba17 336 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #19 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #17 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #18 := (f4 f5 #17)
 #20 := (f3 #18 #19)
-#747 := (pattern #20)
+#703 := (pattern #20)
 #21 := 0::Int
-#76 := -1::Int
-#96 := (* -1::Int #19)
-#93 := (* -1::Int #17)
-#99 := (div #93 #96)
-#250 := (* -1::Int #99)
-#251 := (+ #20 #250)
-#252 := (= #251 0::Int)
+#99 := -1::Int
+#103 := (* -1::Int #19)
+#100 := (* -1::Int #17)
+#106 := (div #100 #103)
+#262 := (* -1::Int #106)
+#263 := (+ #20 #262)
+#264 := (= #263 0::Int)
 #31 := (div #17 #19)
-#247 := (* -1::Int #31)
-#248 := (+ #20 #247)
-#249 := (= #248 0::Int)
-#125 := (>= #17 0::Int)
-#118 := (<= #19 0::Int)
-#210 := (or #118 #125)
-#211 := (not #210)
-#114 := (<= #17 0::Int)
-#208 := (or #114 #118)
-#209 := (not #208)
-#214 := (or #209 #211)
-#253 := (ite #214 #249 #252)
-#246 := (= #20 0::Int)
+#259 := (* -1::Int #31)
+#260 := (+ #20 #259)
+#261 := (= #260 0::Int)
+#77 := (<= #19 0::Int)
+#169 := (>= #17 0::Int)
+#222 := (or #169 #77)
+#223 := (not #222)
+#73 := (<= #17 0::Int)
+#218 := (or #73 #77)
+#219 := (not #218)
+#226 := (or #219 #223)
+#265 := (if #226 #261 #264)
+#258 := (= #20 0::Int)
 #23 := (= #19 0::Int)
 #22 := (= #17 0::Int)
 #24 := (or #22 #23)
-#254 := (ite #24 #246 #253)
-#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #254)
-#257 := (forall (vars (?v0 Int) (?v1 Int)) #254)
-#751 := (iff #257 #748)
-#749 := (iff #254 #254)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#217 := (ite #214 #31 #99)
-#220 := (ite #24 0::Int #217)
-#223 := (= #20 #220)
-#226 := (forall (vars (?v0 Int) (?v1 Int)) #223)
-#258 := (iff #226 #257)
-#255 := (iff #223 #254)
-#256 := [rewrite]: #255
-#259 := [quant-intro #256]: #258
-#126 := (not #125)
-#119 := (not #118)
-#129 := (and #119 #126)
-#115 := (not #114)
-#122 := (and #115 #119)
-#132 := (or #122 #129)
-#135 := (ite #132 #31 #99)
-#138 := (ite #24 0::Int #135)
-#141 := (= #20 #138)
-#144 := (forall (vars (?v0 Int) (?v1 Int)) #141)
-#227 := (iff #144 #226)
-#224 := (iff #141 #223)
-#221 := (= #138 #220)
-#218 := (= #135 #217)
-#215 := (iff #132 #214)
-#212 := (iff #129 #211)
-#213 := [rewrite]: #212
-#202 := (iff #122 #209)
-#203 := [rewrite]: #202
-#216 := [monotonicity #203 #213]: #215
-#219 := [monotonicity #216]: #218
-#222 := [monotonicity #219]: #221
-#225 := [monotonicity #222]: #224
-#228 := [quant-intro #225]: #227
-#206 := (~ #144 #144)
-#204 := (~ #141 #141)
-#205 := [refl]: #204
-#207 := [nnf-pos #205]: #206
-#33 := (- #19)
-#32 := (- #17)
-#34 := (div #32 #33)
-#26 := (< 0::Int #19)
-#28 := (< #17 0::Int)
-#29 := (and #28 #26)
-#25 := (< 0::Int #17)
-#27 := (and #25 #26)
-#30 := (or #27 #29)
-#35 := (ite #30 #31 #34)
-#36 := (ite #24 0::Int #35)
-#37 := (= #20 #36)
-#38 := (forall (vars (?v0 Int) (?v1 Int)) #37)
-#147 := (iff #38 #144)
-#86 := (and #26 #28)
-#90 := (or #27 #86)
-#102 := (ite #90 #31 #99)
-#105 := (ite #24 0::Int #102)
-#108 := (= #20 #105)
-#111 := (forall (vars (?v0 Int) (?v1 Int)) #108)
-#145 := (iff #111 #144)
-#142 := (iff #108 #141)
-#139 := (= #105 #138)
-#136 := (= #102 #135)
-#133 := (iff #90 #132)
-#130 := (iff #86 #129)
-#127 := (iff #28 #126)
-#128 := [rewrite]: #127
-#120 := (iff #26 #119)
-#121 := [rewrite]: #120
-#131 := [monotonicity #121 #128]: #130
-#123 := (iff #27 #122)
-#116 := (iff #25 #115)
-#117 := [rewrite]: #116
-#124 := [monotonicity #117 #121]: #123
-#134 := [monotonicity #124 #131]: #133
-#137 := [monotonicity #134]: #136
-#140 := [monotonicity #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [quant-intro #143]: #145
-#112 := (iff #38 #111)
-#109 := (iff #37 #108)
-#106 := (= #36 #105)
-#103 := (= #35 #102)
-#100 := (= #34 #99)
-#97 := (= #33 #96)
-#98 := [rewrite]: #97
-#94 := (= #32 #93)
-#95 := [rewrite]: #94
-#101 := [monotonicity #95 #98]: #100
-#91 := (iff #30 #90)
-#88 := (iff #29 #86)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#104 := [monotonicity #92 #101]: #103
-#107 := [monotonicity #104]: #106
-#110 := [monotonicity #107]: #109
-#113 := [quant-intro #110]: #112
-#148 := [trans #113 #146]: #147
-#85 := [asserted]: #38
-#149 := [mp #85 #148]: #144
-#198 := [mp~ #149 #207]: #144
-#229 := [mp #198 #228]: #226
-#260 := [mp #229 #259]: #257
-#753 := [mp #260 #752]: #748
-#70 := -3::Int
-#9 := 1::Int
-#10 := (f4 f5 1::Int)
-#73 := (f3 #10 -3::Int)
-#79 := (= #73 -1::Int)
-#82 := (not #79)
-#14 := (- 1::Int)
-#11 := 3::Int
-#12 := (- 3::Int)
-#13 := (f3 #10 #12)
-#15 := (= #13 #14)
-#16 := (not #15)
-#83 := (iff #16 #82)
-#80 := (iff #15 #79)
-#77 := (= #14 -1::Int)
-#78 := [rewrite]: #77
-#74 := (= #13 #73)
-#71 := (= #12 -3::Int)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#81 := [monotonicity #75 #78]: #80
-#84 := [monotonicity #81]: #83
-#69 := [asserted]: #16
-#87 := [mp #69 #84]: #82
-#663 := (not #748)
-#660 := (or #663 #79)
-#334 := (* -1::Int -3::Int)
-#418 := (* -1::Int 1::Int)
-#419 := (div #418 #334)
-#420 := (* -1::Int #419)
-#411 := (+ #73 #420)
-#422 := (= #411 0::Int)
-#423 := (div 1::Int -3::Int)
-#424 := (* -1::Int #423)
-#421 := (+ #73 #424)
-#425 := (= #421 0::Int)
-#404 := (>= 1::Int 0::Int)
-#739 := (<= -3::Int 0::Int)
-#741 := (or #739 #404)
-#398 := (not #741)
-#528 := (<= 1::Int 0::Int)
-#735 := (or #528 #739)
-#409 := (not #735)
-#410 := (or #409 #398)
-#742 := (ite #410 #425 #422)
-#743 := (= #73 0::Int)
-#744 := (= -3::Int 0::Int)
-#745 := (= 1::Int 0::Int)
-#740 := (or #745 #744)
-#746 := (ite #740 #743 #742)
-#662 := (or #663 #746)
-#673 := (iff #662 #660)
-#670 := (iff #660 #660)
-#675 := [rewrite]: #670
-#669 := (iff #746 #79)
-#576 := (ite false #743 #79)
-#586 := (iff #576 #79)
-#587 := [rewrite]: #586
-#678 := (iff #746 #576)
-#588 := (iff #742 #79)
-#584 := (iff #742 #576)
-#582 := (iff #422 #79)
-#571 := (+ 1::Int #73)
-#676 := (= #571 0::Int)
-#565 := (iff #676 #79)
-#580 := [rewrite]: #565
-#677 := (iff #422 #676)
-#679 := (= #411 #571)
-#685 := (+ #73 1::Int)
-#572 := (= #685 #571)
-#531 := [rewrite]: #572
-#688 := (= #411 #685)
-#686 := (= #420 1::Int)
-#527 := (* -1::Int -1::Int)
-#683 := (= #527 1::Int)
-#684 := [rewrite]: #683
-#529 := (= #420 #527)
-#691 := (= #419 -1::Int)
-#695 := (div -1::Int 3::Int)
-#696 := (= #695 -1::Int)
-#697 := [rewrite]: #696
-#689 := (= #419 #695)
-#693 := (= #334 3::Int)
-#694 := [rewrite]: #693
-#550 := (= #418 -1::Int)
-#692 := [rewrite]: #550
-#690 := [monotonicity #692 #694]: #689
-#698 := [trans #690 #697]: #691
-#530 := [monotonicity #698]: #529
-#687 := [trans #530 #684]: #686
-#570 := [monotonicity #687]: #688
-#581 := [trans #570 #531]: #679
-#680 := [monotonicity #581]: #677
-#583 := [trans #680 #580]: #582
-#548 := (iff #425 #743)
-#701 := (= #421 #73)
-#704 := (+ #73 0::Int)
-#705 := (= #704 #73)
-#706 := [rewrite]: #705
-#699 := (= #421 #704)
-#702 := (= #424 0::Int)
-#426 := (* -1::Int 0::Int)
-#709 := (= #426 0::Int)
-#713 := [rewrite]: #709
-#708 := (= #424 #426)
-#710 := (= #423 0::Int)
-#711 := [rewrite]: #710
-#712 := [monotonicity #711]: #708
-#703 := [trans #712 #713]: #702
-#700 := [monotonicity #703]: #699
-#707 := [trans #700 #706]: #701
-#549 := [monotonicity #707]: #548
-#431 := (iff #410 false)
-#397 := (or false false)
-#722 := (iff #397 false)
-#385 := [rewrite]: #722
-#429 := (iff #410 #397)
-#715 := (iff #398 false)
-#1 := true
-#372 := (not true)
-#731 := (iff #372 false)
-#734 := [rewrite]: #731
-#714 := (iff #398 #372)
-#439 := (iff #741 true)
-#445 := (or true true)
-#716 := (iff #445 true)
-#717 := [rewrite]: #716
-#446 := (iff #741 #445)
-#443 := (iff #404 true)
-#444 := [rewrite]: #443
-#725 := (iff #739 true)
-#726 := [rewrite]: #725
-#340 := [monotonicity #726 #444]: #446
-#440 := [trans #340 #717]: #439
-#718 := [monotonicity #440]: #714
-#719 := [trans #718 #734]: #715
-#720 := (iff #409 false)
-#373 := (iff #409 #372)
-#730 := (iff #735 true)
-#727 := (or false true)
-#729 := (iff #727 true)
-#367 := [rewrite]: #729
-#728 := (iff #735 #727)
-#388 := (iff #528 false)
-#724 := [rewrite]: #388
-#723 := [monotonicity #724 #726]: #728
-#732 := [trans #723 #367]: #730
-#733 := [monotonicity #732]: #373
-#721 := [trans #733 #734]: #720
-#430 := [monotonicity #721 #719]: #429
-#432 := [trans #430 #385]: #431
-#585 := [monotonicity #432 #549 #583]: #584
-#681 := [trans #585 #587]: #588
-#386 := (iff #740 false)
-#738 := (iff #740 #397)
-#401 := (iff #744 false)
-#737 := [rewrite]: #401
-#736 := (iff #745 false)
-#396 := [rewrite]: #736
-#381 := [monotonicity #396 #737]: #738
-#387 := [trans #381 #385]: #386
-#682 := [monotonicity #387 #681]: #678
-#671 := [trans #682 #587]: #669
-#674 := [monotonicity #671]: #673
-#664 := [trans #674 #675]: #673
-#672 := [quant-inst #9 #70]: #662
-#665 := [mp #672 #664]: #660
-[unit-resolution #665 #87 #753]: false
-unsat
-9923768ca3c7be858f0346034e649eacbb6e42b8 311 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#17 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#18 := (f4 f5 #17)
-#20 := (f3 #18 #19)
-#747 := (pattern #20)
-#21 := 0::Int
-#76 := -1::Int
-#96 := (* -1::Int #19)
-#93 := (* -1::Int #17)
-#99 := (div #93 #96)
-#250 := (* -1::Int #99)
-#251 := (+ #20 #250)
-#252 := (= #251 0::Int)
-#31 := (div #17 #19)
-#247 := (* -1::Int #31)
-#248 := (+ #20 #247)
-#249 := (= #248 0::Int)
-#125 := (>= #17 0::Int)
-#118 := (<= #19 0::Int)
-#210 := (or #118 #125)
-#211 := (not #210)
-#114 := (<= #17 0::Int)
-#208 := (or #114 #118)
-#209 := (not #208)
-#214 := (or #209 #211)
-#253 := (ite #214 #249 #252)
-#246 := (= #20 0::Int)
-#23 := (= #19 0::Int)
-#22 := (= #17 0::Int)
-#24 := (or #22 #23)
-#254 := (ite #24 #246 #253)
-#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #254)
-#257 := (forall (vars (?v0 Int) (?v1 Int)) #254)
-#751 := (iff #257 #748)
-#749 := (iff #254 #254)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#217 := (ite #214 #31 #99)
-#220 := (ite #24 0::Int #217)
-#223 := (= #20 #220)
-#226 := (forall (vars (?v0 Int) (?v1 Int)) #223)
-#258 := (iff #226 #257)
-#255 := (iff #223 #254)
-#256 := [rewrite]: #255
-#259 := [quant-intro #256]: #258
-#126 := (not #125)
-#119 := (not #118)
-#129 := (and #119 #126)
-#115 := (not #114)
-#122 := (and #115 #119)
-#132 := (or #122 #129)
-#135 := (ite #132 #31 #99)
-#138 := (ite #24 0::Int #135)
-#141 := (= #20 #138)
-#144 := (forall (vars (?v0 Int) (?v1 Int)) #141)
-#227 := (iff #144 #226)
-#224 := (iff #141 #223)
-#221 := (= #138 #220)
-#218 := (= #135 #217)
-#215 := (iff #132 #214)
-#212 := (iff #129 #211)
-#213 := [rewrite]: #212
-#202 := (iff #122 #209)
-#203 := [rewrite]: #202
-#216 := [monotonicity #203 #213]: #215
-#219 := [monotonicity #216]: #218
-#222 := [monotonicity #219]: #221
-#225 := [monotonicity #222]: #224
-#228 := [quant-intro #225]: #227
-#206 := (~ #144 #144)
-#204 := (~ #141 #141)
-#205 := [refl]: #204
-#207 := [nnf-pos #205]: #206
+#266 := (if #24 #258 #265)
+#704 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #703) #266)
+#269 := (forall (vars (?v0 Int) (?v1 Int)) #266)
+#707 := (iff #269 #704)
+#705 := (iff #266 #266)
+#706 := [refl]: #705
+#708 := [quant-intro #706]: #707
+#229 := (if #226 #31 #106)
+#232 := (if #24 0::Int #229)
+#235 := (= #20 #232)
+#238 := (forall (vars (?v0 Int) (?v1 Int)) #235)
+#270 := (iff #238 #269)
+#267 := (iff #235 #266)
+#268 := [rewrite]: #267
+#271 := [quant-intro #268]: #270
+#78 := (not #77)
+#172 := (not #169)
+#175 := (and #172 #78)
+#74 := (not #73)
+#81 := (and #74 #78)
+#178 := (or #81 #175)
+#181 := (if #178 #31 #106)
+#184 := (if #24 0::Int #181)
+#187 := (= #20 #184)
+#190 := (forall (vars (?v0 Int) (?v1 Int)) #187)
+#239 := (iff #190 #238)
+#236 := (iff #187 #235)
+#233 := (= #184 #232)
+#230 := (= #181 #229)
+#227 := (iff #178 #226)
+#224 := (iff #175 #223)
+#225 := [rewrite]: #224
+#220 := (iff #81 #219)
+#221 := [rewrite]: #220
+#228 := [monotonicity #221 #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [monotonicity #234]: #236
+#240 := [quant-intro #237]: #239
+#214 := (~ #190 #190)
+#212 := (~ #187 #187)
+#213 := [refl]: #212
+#215 := [nnf-pos #213]: #214
+#84 := (<= 0::Int #17)
+#85 := (not #84)
+#93 := (and #85 #78)
+#96 := (or #81 #93)
+#109 := (if #96 #31 #106)
+#112 := (if #24 0::Int #109)
+#115 := (= #20 #112)
+#118 := (forall (vars (?v0 Int) (?v1 Int)) #115)
+#191 := (iff #118 #190)
+#188 := (iff #115 #187)
+#185 := (= #112 #184)
+#182 := (= #109 #181)
+#179 := (iff #96 #178)
+#176 := (iff #93 #175)
+#173 := (iff #85 #172)
+#170 := (iff #84 #169)
+#171 := [rewrite]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#180 := [monotonicity #177]: #179
+#183 := [monotonicity #180]: #182
+#186 := [monotonicity #183]: #185
+#189 := [monotonicity #186]: #188
+#192 := [quant-intro #189]: #191
 #33 := (- #19)
 #32 := (- #17)
 #34 := (div #32 #33)
@@ -32137,636 +31308,660 @@
 #25 := (< 0::Int #17)
 #27 := (and #25 #26)
 #30 := (or #27 #29)
-#35 := (ite #30 #31 #34)
-#36 := (ite #24 0::Int #35)
+#35 := (if #30 #31 #34)
+#36 := (if #24 0::Int #35)
 #37 := (= #20 #36)
 #38 := (forall (vars (?v0 Int) (?v1 Int)) #37)
-#147 := (iff #38 #144)
-#86 := (and #26 #28)
-#90 := (or #27 #86)
-#102 := (ite #90 #31 #99)
-#105 := (ite #24 0::Int #102)
-#108 := (= #20 #105)
-#111 := (forall (vars (?v0 Int) (?v1 Int)) #108)
-#145 := (iff #111 #144)
-#142 := (iff #108 #141)
-#139 := (= #105 #138)
-#136 := (= #102 #135)
-#133 := (iff #90 #132)
-#130 := (iff #86 #129)
-#127 := (iff #28 #126)
-#128 := [rewrite]: #127
-#120 := (iff #26 #119)
-#121 := [rewrite]: #120
-#131 := [monotonicity #121 #128]: #130
-#123 := (iff #27 #122)
-#116 := (iff #25 #115)
-#117 := [rewrite]: #116
-#124 := [monotonicity #117 #121]: #123
-#134 := [monotonicity #124 #131]: #133
-#137 := [monotonicity #134]: #136
-#140 := [monotonicity #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [quant-intro #143]: #145
-#112 := (iff #38 #111)
-#109 := (iff #37 #108)
-#106 := (= #36 #105)
-#103 := (= #35 #102)
-#100 := (= #34 #99)
-#97 := (= #33 #96)
-#98 := [rewrite]: #97
-#94 := (= #32 #93)
-#95 := [rewrite]: #94
-#101 := [monotonicity #95 #98]: #100
-#91 := (iff #30 #90)
-#88 := (iff #29 #86)
+#119 := (iff #38 #118)
+#116 := (iff #37 #115)
+#113 := (= #36 #112)
+#110 := (= #35 #109)
+#107 := (= #34 #106)
+#104 := (= #33 #103)
+#105 := [rewrite]: #104
+#101 := (= #32 #100)
+#102 := [rewrite]: #101
+#108 := [monotonicity #102 #105]: #107
+#97 := (iff #30 #96)
+#94 := (iff #29 #93)
+#79 := (iff #26 #78)
+#80 := [rewrite]: #79
+#86 := (iff #28 #85)
+#90 := (iff #85 #85)
+#88 := (iff #84 #84)
 #89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#104 := [monotonicity #92 #101]: #103
-#107 := [monotonicity #104]: #106
-#110 := [monotonicity #107]: #109
-#113 := [quant-intro #110]: #112
-#148 := [trans #113 #146]: #147
-#85 := [asserted]: #38
-#149 := [mp #85 #148]: #144
-#198 := [mp~ #149 #207]: #144
-#229 := [mp #198 #228]: #226
-#260 := [mp #229 #259]: #257
-#753 := [mp #260 #752]: #748
-#70 := -3::Int
-#9 := 3::Int
-#10 := (f4 f5 3::Int)
-#73 := (f3 #10 -3::Int)
-#79 := (= #73 -1::Int)
-#82 := (not #79)
-#13 := 1::Int
-#14 := (- 1::Int)
+#91 := [monotonicity #89]: #90
+#87 := [rewrite]: #86
+#92 := [trans #87 #91]: #86
+#95 := [monotonicity #92 #80]: #94
+#82 := (iff #27 #81)
+#75 := (iff #25 #74)
+#76 := [rewrite]: #75
+#83 := [monotonicity #76 #80]: #82
+#98 := [monotonicity #83 #95]: #97
+#111 := [monotonicity #98 #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [quant-intro #117]: #119
+#52 := [asserted]: #38
+#121 := [mp #52 #120]: #118
+#193 := [mp #121 #192]: #190
+#167 := [mp~ #193 #215]: #190
+#241 := [mp #167 #240]: #238
+#272 := [mp #241 #271]: #269
+#709 := [mp #272 #708]: #704
+#63 := -2::Int
+#57 := -3::Int
+#8 := 5::Int
+#9 := (f4 f5 5::Int)
+#60 := (f3 #9 -3::Int)
+#66 := (= #60 -2::Int)
+#69 := (not #66)
+#13 := 2::Int
+#14 := (- 2::Int)
+#10 := 3::Int
 #11 := (- 3::Int)
-#12 := (f3 #10 #11)
+#12 := (f3 #9 #11)
 #15 := (= #12 #14)
 #16 := (not #15)
-#83 := (iff #16 #82)
-#80 := (iff #15 #79)
-#77 := (= #14 -1::Int)
+#70 := (iff #16 #69)
+#67 := (iff #15 #66)
+#64 := (= #14 -2::Int)
+#65 := [rewrite]: #64
+#61 := (= #12 #60)
+#58 := (= #11 -3::Int)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#68 := [monotonicity #62 #65]: #67
+#71 := [monotonicity #68]: #70
+#51 := [asserted]: #16
+#72 := [mp #51 #71]: #69
+#623 := (not #704)
+#617 := (or #623 #66)
+#366 := (* -1::Int -3::Int)
+#365 := (* -1::Int 5::Int)
+#698 := (div #365 #366)
+#699 := (* -1::Int #698)
+#700 := (+ #60 #699)
+#701 := (= #700 0::Int)
+#697 := (div 5::Int -3::Int)
+#354 := (* -1::Int #697)
+#484 := (+ #60 #354)
+#691 := (= #484 0::Int)
+#378 := (<= -3::Int 0::Int)
+#377 := (>= 5::Int 0::Int)
+#381 := (or #377 #378)
+#360 := (not #381)
+#367 := (<= 5::Int 0::Int)
+#379 := (or #367 #378)
+#380 := (not #379)
+#695 := (or #380 #360)
+#696 := (if #695 #691 #701)
+#376 := (= #60 0::Int)
+#374 := (= -3::Int 0::Int)
+#289 := (= 5::Int 0::Int)
+#375 := (or #289 #374)
+#702 := (if #375 #376 #696)
+#624 := (or #623 #702)
+#609 := (iff #624 #617)
+#612 := (iff #617 #617)
+#613 := [rewrite]: #612
+#621 := (iff #702 #66)
+#629 := (if false #376 #66)
+#631 := (iff #629 #66)
+#620 := [rewrite]: #631
+#630 := (iff #702 #629)
+#618 := (iff #696 #66)
+#649 := (= #60 -1::Int)
+#638 := (if false #649 #66)
+#619 := (iff #638 #66)
+#616 := [rewrite]: #619
+#625 := (iff #696 #638)
+#637 := (iff #701 #66)
+#521 := (+ 2::Int #60)
+#540 := (= #521 0::Int)
+#543 := (iff #540 #66)
+#544 := [rewrite]: #543
+#541 := (iff #701 #540)
+#539 := (= #700 #521)
+#632 := (+ #60 2::Int)
+#536 := (= #632 #521)
+#538 := [rewrite]: #536
+#633 := (= #700 #632)
+#635 := (= #699 2::Int)
+#644 := (* -1::Int -2::Int)
+#528 := (= #644 2::Int)
+#487 := [rewrite]: #528
+#526 := (= #699 #644)
+#643 := (= #698 -2::Int)
+#652 := -5::Int
+#485 := (div -5::Int 3::Int)
+#640 := (= #485 -2::Int)
+#642 := [rewrite]: #640
+#486 := (= #698 #485)
+#654 := (= #366 3::Int)
+#483 := [rewrite]: #654
+#653 := (= #365 -5::Int)
+#647 := [rewrite]: #653
+#639 := [monotonicity #647 #483]: #486
+#641 := [trans #639 #642]: #643
+#527 := [monotonicity #641]: #526
+#537 := [trans #527 #487]: #635
+#636 := [monotonicity #537]: #633
+#532 := [trans #636 #538]: #539
+#542 := [monotonicity #532]: #541
+#634 := [trans #542 #544]: #637
+#645 := (iff #691 #649)
+#307 := 1::Int
+#661 := (+ 1::Int #60)
+#505 := (= #661 0::Int)
+#650 := (iff #505 #649)
+#651 := [rewrite]: #650
+#506 := (iff #691 #505)
+#663 := (= #484 #661)
+#660 := (+ #60 1::Int)
+#662 := (= #660 #661)
+#657 := [rewrite]: #662
+#655 := (= #484 #660)
+#658 := (= #354 1::Int)
+#382 := (* -1::Int -1::Int)
+#665 := (= #382 1::Int)
+#669 := [rewrite]: #665
+#664 := (= #354 #382)
+#666 := (= #697 -1::Int)
+#667 := [rewrite]: #666
+#668 := [monotonicity #667]: #664
+#659 := [trans #668 #669]: #658
+#656 := [monotonicity #659]: #655
+#504 := [trans #656 #657]: #663
+#648 := [monotonicity #504]: #506
+#646 := [trans #648 #651]: #645
+#387 := (iff #695 false)
+#353 := (or false false)
+#678 := (iff #353 false)
+#341 := [rewrite]: #678
+#385 := (iff #695 #353)
+#671 := (iff #360 false)
+#1 := true
+#328 := (not true)
+#687 := (iff #328 false)
+#690 := [rewrite]: #687
+#670 := (iff #360 #328)
+#395 := (iff #381 true)
+#401 := (or true true)
+#672 := (iff #401 true)
+#673 := [rewrite]: #672
+#402 := (iff #381 #401)
+#681 := (iff #378 true)
+#682 := [rewrite]: #681
+#399 := (iff #377 true)
+#400 := [rewrite]: #399
+#295 := [monotonicity #400 #682]: #402
+#396 := [trans #295 #673]: #395
+#674 := [monotonicity #396]: #670
+#675 := [trans #674 #690]: #671
+#676 := (iff #380 false)
+#329 := (iff #380 #328)
+#686 := (iff #379 true)
+#683 := (or false true)
+#685 := (iff #683 true)
+#323 := [rewrite]: #685
+#684 := (iff #379 #683)
+#344 := (iff #367 false)
+#680 := [rewrite]: #344
+#679 := [monotonicity #680 #682]: #684
+#688 := [trans #679 #323]: #686
+#689 := [monotonicity #688]: #329
+#677 := [trans #689 #690]: #676
+#386 := [monotonicity #677 #675]: #385
+#388 := [trans #386 #341]: #387
+#627 := [monotonicity #388 #646 #634]: #625
+#628 := [trans #627 #616]: #618
+#342 := (iff #375 false)
+#694 := (iff #375 #353)
+#357 := (iff #374 false)
+#693 := [rewrite]: #357
+#692 := (iff #289 false)
+#352 := [rewrite]: #692
+#337 := [monotonicity #352 #693]: #694
+#343 := [trans #337 #341]: #342
+#626 := [monotonicity #343 #628]: #630
+#622 := [trans #626 #620]: #621
+#611 := [monotonicity #622]: #609
+#614 := [trans #611 #613]: #609
+#608 := [quant-inst #8 #57]: #624
+#610 := [mp #608 #614]: #617
+[unit-resolution #610 #72 #709]: false
+f1eea19af20531a11f6cccfddc40aec123007d40 325 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#17 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#15 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#16 := (f4 f5 #15)
+#18 := (f3 #16 #17)
+#699 := (pattern #18)
+#19 := 0::Int
+#55 := -1::Int
+#100 := (* -1::Int #17)
+#97 := (* -1::Int #15)
+#103 := (div #97 #100)
+#259 := (* -1::Int #103)
+#260 := (+ #18 #259)
+#261 := (= #260 0::Int)
+#29 := (div #15 #17)
+#256 := (* -1::Int #29)
+#257 := (+ #18 #256)
+#258 := (= #257 0::Int)
+#75 := (<= #17 0::Int)
+#166 := (>= #15 0::Int)
+#219 := (or #166 #75)
+#220 := (not #219)
+#71 := (<= #15 0::Int)
+#215 := (or #71 #75)
+#216 := (not #215)
+#223 := (or #216 #220)
+#262 := (if #223 #258 #261)
+#255 := (= #18 0::Int)
+#21 := (= #17 0::Int)
+#20 := (= #15 0::Int)
+#22 := (or #20 #21)
+#263 := (if #22 #255 #262)
+#700 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #699) #263)
+#266 := (forall (vars (?v0 Int) (?v1 Int)) #263)
+#703 := (iff #266 #700)
+#701 := (iff #263 #263)
+#702 := [refl]: #701
+#704 := [quant-intro #702]: #703
+#226 := (if #223 #29 #103)
+#229 := (if #22 0::Int #226)
+#232 := (= #18 #229)
+#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
+#267 := (iff #235 #266)
+#264 := (iff #232 #263)
+#265 := [rewrite]: #264
+#268 := [quant-intro #265]: #267
+#76 := (not #75)
+#169 := (not #166)
+#172 := (and #169 #76)
+#72 := (not #71)
+#79 := (and #72 #76)
+#175 := (or #79 #172)
+#178 := (if #175 #29 #103)
+#181 := (if #22 0::Int #178)
+#184 := (= #18 #181)
+#187 := (forall (vars (?v0 Int) (?v1 Int)) #184)
+#236 := (iff #187 #235)
+#233 := (iff #184 #232)
+#230 := (= #181 #229)
+#227 := (= #178 #226)
+#224 := (iff #175 #223)
+#221 := (iff #172 #220)
+#222 := [rewrite]: #221
+#217 := (iff #79 #216)
+#218 := [rewrite]: #217
+#225 := [monotonicity #218 #222]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [quant-intro #234]: #236
+#209 := (~ #187 #187)
+#211 := (~ #184 #184)
+#212 := [refl]: #211
+#210 := [nnf-pos #212]: #209
+#82 := (<= 0::Int #15)
+#83 := (not #82)
+#91 := (and #83 #76)
+#94 := (or #79 #91)
+#106 := (if #94 #29 #103)
+#109 := (if #22 0::Int #106)
+#112 := (= #18 #109)
+#115 := (forall (vars (?v0 Int) (?v1 Int)) #112)
+#188 := (iff #115 #187)
+#185 := (iff #112 #184)
+#182 := (= #109 #181)
+#179 := (= #106 #178)
+#176 := (iff #94 #175)
+#173 := (iff #91 #172)
+#170 := (iff #83 #169)
+#167 := (iff #82 #166)
+#168 := [rewrite]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#180 := [monotonicity #177]: #179
+#183 := [monotonicity #180]: #182
+#186 := [monotonicity #183]: #185
+#189 := [quant-intro #186]: #188
+#31 := (- #17)
+#30 := (- #15)
+#32 := (div #30 #31)
+#24 := (< 0::Int #17)
+#26 := (< #15 0::Int)
+#27 := (and #26 #24)
+#23 := (< 0::Int #15)
+#25 := (and #23 #24)
+#28 := (or #25 #27)
+#33 := (if #28 #29 #32)
+#34 := (if #22 0::Int #33)
+#35 := (= #18 #34)
+#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
+#116 := (iff #36 #115)
+#113 := (iff #35 #112)
+#110 := (= #34 #109)
+#107 := (= #33 #106)
+#104 := (= #32 #103)
+#101 := (= #31 #100)
+#102 := [rewrite]: #101
+#98 := (= #30 #97)
+#99 := [rewrite]: #98
+#105 := [monotonicity #99 #102]: #104
+#95 := (iff #28 #94)
+#92 := (iff #27 #91)
+#77 := (iff #24 #76)
 #78 := [rewrite]: #77
-#74 := (= #12 #73)
-#71 := (= #11 -3::Int)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#81 := [monotonicity #75 #78]: #80
-#84 := [monotonicity #81]: #83
-#69 := [asserted]: #16
-#87 := [mp #69 #84]: #82
-#671 := (not #748)
-#663 := (or #671 #79)
-#334 := (* -1::Int -3::Int)
-#418 := (* -1::Int 3::Int)
-#419 := (div #418 #334)
-#420 := (* -1::Int #419)
-#411 := (+ #73 #420)
-#422 := (= #411 0::Int)
-#423 := (div 3::Int -3::Int)
-#424 := (* -1::Int #423)
-#421 := (+ #73 #424)
-#425 := (= #421 0::Int)
-#404 := (>= 3::Int 0::Int)
-#739 := (<= -3::Int 0::Int)
-#741 := (or #739 #404)
-#398 := (not #741)
-#528 := (<= 3::Int 0::Int)
-#735 := (or #528 #739)
-#409 := (not #735)
-#410 := (or #409 #398)
-#742 := (ite #410 #425 #422)
-#743 := (= #73 0::Int)
-#744 := (= -3::Int 0::Int)
-#745 := (= 3::Int 0::Int)
-#740 := (or #745 #744)
-#746 := (ite #740 #743 #742)
-#660 := (or #671 #746)
-#672 := (iff #660 #663)
-#674 := (iff #663 #663)
-#670 := [rewrite]: #674
-#682 := (iff #746 #79)
-#586 := (ite false #743 #79)
-#681 := (iff #586 #79)
-#678 := [rewrite]: #681
-#587 := (iff #746 #586)
-#584 := (iff #742 #79)
-#565 := (ite false #79 #79)
-#583 := (iff #565 #79)
-#576 := [rewrite]: #583
-#580 := (iff #742 #565)
-#677 := (iff #422 #79)
-#705 := (+ 1::Int #73)
-#549 := (= #705 0::Int)
-#693 := (iff #549 #79)
-#694 := [rewrite]: #693
-#581 := (iff #422 #549)
-#531 := (= #411 #705)
-#704 := (+ #73 1::Int)
-#706 := (= #704 #705)
-#701 := [rewrite]: #706
-#571 := (= #411 #704)
-#688 := (= #420 1::Int)
-#426 := (* -1::Int -1::Int)
-#709 := (= #426 1::Int)
-#713 := [rewrite]: #709
-#687 := (= #420 #426)
-#684 := (= #419 -1::Int)
-#698 := (div -3::Int 3::Int)
-#530 := (= #698 -1::Int)
-#683 := [rewrite]: #530
-#527 := (= #419 #698)
-#697 := (= #334 3::Int)
-#691 := [rewrite]: #697
-#690 := (= #418 -3::Int)
-#696 := [rewrite]: #690
-#529 := [monotonicity #696 #691]: #527
-#686 := [trans #529 #683]: #684
-#685 := [monotonicity #686]: #687
-#570 := [trans #685 #713]: #688
-#572 := [monotonicity #570]: #571
-#679 := [trans #572 #701]: #531
-#676 := [monotonicity #679]: #581
-#680 := [trans #676 #694]: #677
-#695 := (iff #425 #79)
-#550 := (iff #425 #549)
-#707 := (= #421 #705)
-#699 := (= #421 #704)
-#702 := (= #424 1::Int)
-#708 := (= #424 #426)
-#710 := (= #423 -1::Int)
-#711 := [rewrite]: #710
-#712 := [monotonicity #711]: #708
-#703 := [trans #712 #713]: #702
-#700 := [monotonicity #703]: #699
-#548 := [trans #700 #701]: #707
-#692 := [monotonicity #548]: #550
-#689 := [trans #692 #694]: #695
-#431 := (iff #410 false)
-#397 := (or false false)
-#722 := (iff #397 false)
-#385 := [rewrite]: #722
-#429 := (iff #410 #397)
-#715 := (iff #398 false)
-#1 := true
-#372 := (not true)
-#731 := (iff #372 false)
-#734 := [rewrite]: #731
-#714 := (iff #398 #372)
-#439 := (iff #741 true)
-#445 := (or true true)
-#716 := (iff #445 true)
-#717 := [rewrite]: #716
-#446 := (iff #741 #445)
-#443 := (iff #404 true)
-#444 := [rewrite]: #443
-#725 := (iff #739 true)
-#726 := [rewrite]: #725
-#340 := [monotonicity #726 #444]: #446
-#440 := [trans #340 #717]: #439
-#718 := [monotonicity #440]: #714
-#719 := [trans #718 #734]: #715
-#720 := (iff #409 false)
-#373 := (iff #409 #372)
-#730 := (iff #735 true)
-#727 := (or false true)
-#729 := (iff #727 true)
-#367 := [rewrite]: #729
-#728 := (iff #735 #727)
-#388 := (iff #528 false)
-#724 := [rewrite]: #388
-#723 := [monotonicity #724 #726]: #728
-#732 := [trans #723 #367]: #730
-#733 := [monotonicity #732]: #373
-#721 := [trans #733 #734]: #720
-#430 := [monotonicity #721 #719]: #429
-#432 := [trans #430 #385]: #431
-#582 := [monotonicity #432 #689 #680]: #580
-#585 := [trans #582 #576]: #584
-#386 := (iff #740 false)
-#738 := (iff #740 #397)
-#401 := (iff #744 false)
-#737 := [rewrite]: #401
-#736 := (iff #745 false)
-#396 := [rewrite]: #736
-#381 := [monotonicity #396 #737]: #738
-#387 := [trans #381 #385]: #386
-#588 := [monotonicity #387 #585]: #587
-#669 := [trans #588 #678]: #682
-#673 := [monotonicity #669]: #672
-#675 := [trans #673 #670]: #672
-#662 := [quant-inst #9 #70]: #660
-#664 := [mp #662 #675]: #663
-[unit-resolution #664 #87 #753]: false
-unsat
-0d7678af8cbb5c17b0aa826f273a0694a47c1519 326 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#20 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#18 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#19 := (f4 f5 #18)
-#21 := (f3 #19 #20)
-#750 := (pattern #21)
-#22 := 0::Int
-#94 := -1::Int
-#98 := (* -1::Int #20)
-#95 := (* -1::Int #18)
-#101 := (div #95 #98)
-#252 := (* -1::Int #101)
-#253 := (+ #21 #252)
-#254 := (= #253 0::Int)
-#32 := (div #18 #20)
-#249 := (* -1::Int #32)
-#250 := (+ #21 #249)
-#251 := (= #250 0::Int)
-#127 := (>= #18 0::Int)
-#120 := (<= #20 0::Int)
-#212 := (or #120 #127)
-#213 := (not #212)
-#116 := (<= #18 0::Int)
-#210 := (or #116 #120)
-#211 := (not #210)
-#216 := (or #211 #213)
-#255 := (ite #216 #251 #254)
-#248 := (= #21 0::Int)
-#24 := (= #20 0::Int)
-#23 := (= #18 0::Int)
-#25 := (or #23 #24)
-#256 := (ite #25 #248 #255)
-#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #256)
-#259 := (forall (vars (?v0 Int) (?v1 Int)) #256)
-#754 := (iff #259 #751)
-#752 := (iff #256 #256)
-#753 := [refl]: #752
-#755 := [quant-intro #753]: #754
-#219 := (ite #216 #32 #101)
-#222 := (ite #25 0::Int #219)
-#225 := (= #21 #222)
-#228 := (forall (vars (?v0 Int) (?v1 Int)) #225)
-#260 := (iff #228 #259)
-#257 := (iff #225 #256)
-#258 := [rewrite]: #257
-#261 := [quant-intro #258]: #260
-#128 := (not #127)
-#121 := (not #120)
-#131 := (and #121 #128)
-#117 := (not #116)
-#124 := (and #117 #121)
-#134 := (or #124 #131)
-#137 := (ite #134 #32 #101)
-#140 := (ite #25 0::Int #137)
-#143 := (= #21 #140)
-#146 := (forall (vars (?v0 Int) (?v1 Int)) #143)
-#229 := (iff #146 #228)
-#226 := (iff #143 #225)
-#223 := (= #140 #222)
-#220 := (= #137 #219)
-#217 := (iff #134 #216)
-#214 := (iff #131 #213)
-#215 := [rewrite]: #214
-#204 := (iff #124 #211)
-#205 := [rewrite]: #204
-#218 := [monotonicity #205 #215]: #217
-#221 := [monotonicity #218]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [quant-intro #227]: #229
-#208 := (~ #146 #146)
-#206 := (~ #143 #143)
-#207 := [refl]: #206
-#209 := [nnf-pos #207]: #208
-#34 := (- #20)
-#33 := (- #18)
-#35 := (div #33 #34)
-#27 := (< 0::Int #20)
-#29 := (< #18 0::Int)
-#30 := (and #29 #27)
-#26 := (< 0::Int #18)
-#28 := (and #26 #27)
-#31 := (or #28 #30)
-#36 := (ite #31 #32 #35)
-#37 := (ite #25 0::Int #36)
-#38 := (= #21 #37)
-#39 := (forall (vars (?v0 Int) (?v1 Int)) #38)
-#149 := (iff #39 #146)
-#87 := (and #27 #29)
-#91 := (or #28 #87)
-#104 := (ite #91 #32 #101)
-#107 := (ite #25 0::Int #104)
-#110 := (= #21 #107)
-#113 := (forall (vars (?v0 Int) (?v1 Int)) #110)
-#147 := (iff #113 #146)
-#144 := (iff #110 #143)
-#141 := (= #107 #140)
-#138 := (= #104 #137)
-#135 := (iff #91 #134)
-#132 := (iff #87 #131)
-#129 := (iff #29 #128)
-#130 := [rewrite]: #129
-#122 := (iff #27 #121)
-#123 := [rewrite]: #122
-#133 := [monotonicity #123 #130]: #132
-#125 := (iff #28 #124)
-#118 := (iff #26 #117)
-#119 := [rewrite]: #118
-#126 := [monotonicity #119 #123]: #125
-#136 := [monotonicity #126 #133]: #135
-#139 := [monotonicity #136]: #138
-#142 := [monotonicity #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [quant-intro #145]: #147
-#114 := (iff #39 #113)
-#111 := (iff #38 #110)
-#108 := (= #37 #107)
-#105 := (= #36 #104)
-#102 := (= #35 #101)
-#99 := (= #34 #98)
-#100 := [rewrite]: #99
-#96 := (= #33 #95)
-#97 := [rewrite]: #96
-#103 := [monotonicity #97 #100]: #102
-#92 := (iff #31 #91)
-#89 := (iff #30 #87)
-#90 := [rewrite]: #89
-#93 := [monotonicity #90]: #92
-#106 := [monotonicity #93 #103]: #105
-#109 := [monotonicity #106]: #108
-#112 := [monotonicity #109]: #111
-#115 := [quant-intro #112]: #114
-#150 := [trans #115 #148]: #149
-#86 := [asserted]: #39
-#151 := [mp #86 #150]: #146
-#200 := [mp~ #151 #209]: #146
-#231 := [mp #200 #230]: #228
-#262 := [mp #231 #261]: #259
-#756 := [mp #262 #755]: #751
-#77 := -2::Int
-#71 := -3::Int
-#9 := 5::Int
-#10 := (f4 f5 5::Int)
-#74 := (f3 #10 -3::Int)
-#80 := (= #74 -2::Int)
-#83 := (not #80)
-#14 := 2::Int
-#15 := (- 2::Int)
+#84 := (iff #26 #83)
+#88 := (iff #83 #83)
+#86 := (iff #82 #82)
+#87 := [rewrite]: #86
+#89 := [monotonicity #87]: #88
+#85 := [rewrite]: #84
+#90 := [trans #85 #89]: #84
+#93 := [monotonicity #90 #78]: #92
+#80 := (iff #25 #79)
+#73 := (iff #23 #72)
+#74 := [rewrite]: #73
+#81 := [monotonicity #74 #78]: #80
+#96 := [monotonicity #81 #93]: #95
+#108 := [monotonicity #96 #105]: #107
+#111 := [monotonicity #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [quant-intro #114]: #116
+#50 := [asserted]: #36
+#118 := [mp #50 #117]: #115
+#190 := [mp #118 #189]: #187
+#207 := [mp~ #190 #210]: #187
+#238 := [mp #207 #237]: #235
+#269 := [mp #238 #268]: #266
+#705 := [mp #269 #704]: #700
 #11 := 3::Int
-#12 := (- 3::Int)
-#13 := (f3 #10 #12)
-#16 := (= #13 #15)
-#17 := (not #16)
-#84 := (iff #17 #83)
-#81 := (iff #16 #80)
-#78 := (= #15 -2::Int)
-#79 := [rewrite]: #78
-#75 := (= #13 #74)
-#72 := (= #12 -3::Int)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#82 := [monotonicity #76 #79]: #81
-#85 := [monotonicity #82]: #84
-#70 := [asserted]: #17
-#88 := [mp #70 #85]: #83
-#670 := (not #751)
-#664 := (or #670 #80)
-#336 := (* -1::Int -3::Int)
-#421 := (* -1::Int 5::Int)
-#422 := (div #421 #336)
-#423 := (* -1::Int #422)
-#414 := (+ #74 #423)
-#425 := (= #414 0::Int)
-#426 := (div 5::Int -3::Int)
-#354 := (* -1::Int #426)
-#427 := (+ #74 #354)
-#424 := (= #427 0::Int)
-#428 := (>= 5::Int 0::Int)
-#407 := (<= -3::Int 0::Int)
-#742 := (or #407 #428)
-#744 := (not #742)
-#401 := (<= 5::Int 0::Int)
-#531 := (or #401 #407)
-#738 := (not #531)
-#412 := (or #738 #744)
-#413 := (ite #412 #424 #425)
-#745 := (= #74 0::Int)
-#746 := (= -3::Int 0::Int)
-#747 := (= 5::Int 0::Int)
-#748 := (or #747 #746)
-#743 := (ite #748 #745 #413)
-#671 := (or #670 #743)
-#656 := (iff #671 #664)
-#659 := (iff #664 #664)
-#660 := [rewrite]: #659
-#668 := (iff #743 #80)
-#676 := (ite false #745 #80)
-#678 := (iff #676 #80)
-#667 := [rewrite]: #678
-#677 := (iff #743 #676)
-#665 := (iff #413 #80)
-#696 := (= #74 -1::Int)
-#685 := (ite false #696 #80)
-#666 := (iff #685 #80)
-#663 := [rewrite]: #666
-#672 := (iff #413 #685)
-#684 := (iff #425 #80)
-#568 := (+ 2::Int #74)
-#587 := (= #568 0::Int)
-#590 := (iff #587 #80)
-#591 := [rewrite]: #590
-#588 := (iff #425 #587)
-#586 := (= #414 #568)
-#679 := (+ #74 2::Int)
-#583 := (= #679 #568)
-#585 := [rewrite]: #583
-#680 := (= #414 #679)
-#682 := (= #423 2::Int)
-#691 := (* -1::Int -2::Int)
-#575 := (= #691 2::Int)
-#534 := [rewrite]: #575
-#573 := (= #423 #691)
-#690 := (= #422 -2::Int)
-#699 := -5::Int
-#532 := (div -5::Int 3::Int)
-#687 := (= #532 -2::Int)
-#689 := [rewrite]: #687
-#533 := (= #422 #532)
-#701 := (= #336 3::Int)
-#530 := [rewrite]: #701
-#700 := (= #421 -5::Int)
-#694 := [rewrite]: #700
-#686 := [monotonicity #694 #530]: #533
-#688 := [trans #686 #689]: #690
-#574 := [monotonicity #688]: #573
-#584 := [trans #574 #534]: #682
-#683 := [monotonicity #584]: #680
-#579 := [trans #683 #585]: #586
-#589 := [monotonicity #579]: #588
-#681 := [trans #589 #591]: #684
-#692 := (iff #424 #696)
-#715 := 1::Int
-#708 := (+ 1::Int #74)
-#552 := (= #708 0::Int)
-#697 := (iff #552 #696)
-#698 := [rewrite]: #697
-#553 := (iff #424 #552)
-#710 := (= #427 #708)
-#707 := (+ #74 1::Int)
-#709 := (= #707 #708)
-#704 := [rewrite]: #709
-#702 := (= #427 #707)
-#705 := (= #354 1::Int)
-#714 := (* -1::Int -1::Int)
-#712 := (= #714 1::Int)
-#716 := [rewrite]: #712
-#429 := (= #354 #714)
-#435 := (= #426 -1::Int)
-#713 := [rewrite]: #435
-#711 := [monotonicity #713]: #429
-#706 := [trans #711 #716]: #705
-#703 := [monotonicity #706]: #702
-#551 := [trans #703 #704]: #710
-#695 := [monotonicity #551]: #553
-#693 := [trans #695 #698]: #692
-#433 := (iff #412 false)
-#740 := (or false false)
-#384 := (iff #740 false)
-#725 := [rewrite]: #384
-#722 := (iff #412 #740)
-#721 := (iff #744 false)
-#1 := true
-#735 := (not true)
-#736 := (iff #735 false)
-#734 := [rewrite]: #736
-#443 := (iff #744 #735)
-#720 := (iff #742 true)
-#447 := (or true true)
-#342 := (iff #447 true)
-#719 := [rewrite]: #342
-#448 := (iff #742 #447)
-#724 := (iff #428 true)
-#446 := [rewrite]: #724
-#727 := (iff #407 true)
-#728 := [rewrite]: #727
-#449 := [monotonicity #728 #446]: #448
-#442 := [trans #449 #719]: #720
-#717 := [monotonicity #442]: #443
-#718 := [trans #717 #734]: #721
-#737 := (iff #738 false)
-#375 := (iff #738 #735)
-#370 := (iff #531 true)
-#729 := (or false true)
-#726 := (iff #729 true)
-#732 := [rewrite]: #726
-#730 := (iff #531 #729)
-#390 := (iff #401 false)
-#391 := [rewrite]: #390
-#731 := [monotonicity #391 #728]: #730
-#733 := [trans #731 #732]: #370
-#376 := [monotonicity #733]: #375
-#723 := [trans #376 #734]: #737
-#432 := [monotonicity #723 #718]: #722
-#434 := [trans #432 #725]: #433
-#674 := [monotonicity #434 #693 #681]: #672
-#675 := [trans #674 #663]: #665
-#388 := (iff #748 false)
-#400 := (iff #748 #740)
-#399 := (iff #746 false)
-#404 := [rewrite]: #399
-#749 := (iff #747 false)
-#739 := [rewrite]: #749
-#741 := [monotonicity #739 #404]: #400
-#389 := [trans #741 #725]: #388
-#673 := [monotonicity #389 #675]: #677
-#669 := [trans #673 #667]: #668
-#658 := [monotonicity #669]: #656
-#661 := [trans #658 #660]: #656
-#655 := [quant-inst #9 #71]: #671
-#657 := [mp #655 #661]: #664
-[unit-resolution #657 #88 #756]: false
-unsat
-ca8fe38f3d2a99215e3a097c3b452207a271c445 327 0
+#58 := (f4 f5 -1::Int)
+#61 := (f3 #58 3::Int)
+#64 := (= #61 -1::Int)
+#67 := (not #64)
+#8 := 1::Int
+#9 := (- 1::Int)
+#10 := (f4 f5 #9)
+#12 := (f3 #10 3::Int)
+#13 := (= #12 #9)
+#14 := (not #13)
+#68 := (iff #14 #67)
+#65 := (iff #13 #64)
+#56 := (= #9 -1::Int)
+#57 := [rewrite]: #56
+#62 := (= #12 #61)
+#59 := (= #10 #58)
+#60 := [monotonicity #57]: #59
+#63 := [monotonicity #60]: #62
+#66 := [monotonicity #63 #57]: #65
+#69 := [monotonicity #66]: #68
+#49 := [asserted]: #14
+#70 := [mp #49 #69]: #67
+#625 := (not #700)
+#626 := (or #625 #64)
+#362 := (* -1::Int 3::Int)
+#361 := (* -1::Int -1::Int)
+#694 := (div #361 #362)
+#695 := (* -1::Int #694)
+#696 := (+ #61 #695)
+#697 := (= #696 0::Int)
+#693 := (div -1::Int 3::Int)
+#350 := (* -1::Int #693)
+#480 := (+ #61 #350)
+#687 := (= #480 0::Int)
+#374 := (<= 3::Int 0::Int)
+#373 := (>= -1::Int 0::Int)
+#377 := (or #373 #374)
+#356 := (not #377)
+#363 := (<= -1::Int 0::Int)
+#375 := (or #363 #374)
+#376 := (not #375)
+#691 := (or #376 #356)
+#692 := (if #691 #687 #697)
+#372 := (= #61 0::Int)
+#370 := (= 3::Int 0::Int)
+#286 := (= -1::Int 0::Int)
+#371 := (or #286 #370)
+#698 := (if #371 #372 #692)
+#622 := (or #625 #698)
+#616 := (iff #622 #626)
+#618 := (iff #626 #626)
+#619 := [rewrite]: #618
+#614 := (iff #698 #64)
+#634 := (if false #372 #64)
+#615 := (iff #634 #64)
+#612 := [rewrite]: #615
+#621 := (iff #698 #634)
+#633 := (iff #692 #64)
+#1 := true
+#536 := (if true #64 #372)
+#539 := (iff #536 #64)
+#540 := [rewrite]: #539
+#537 := (iff #692 #536)
+#535 := (iff #697 #372)
+#532 := (= #696 #61)
+#533 := (+ #61 0::Int)
+#632 := (= #533 #61)
+#517 := [rewrite]: #632
+#628 := (= #696 #533)
+#483 := (= #695 0::Int)
+#637 := (* -1::Int 0::Int)
+#523 := (= #637 0::Int)
+#524 := [rewrite]: #523
+#640 := (= #695 #637)
+#638 := (= #694 0::Int)
+#649 := -3::Int
+#479 := (div 1::Int -3::Int)
+#635 := (= #479 0::Int)
+#636 := [rewrite]: #635
+#481 := (= #694 #479)
+#643 := (= #362 -3::Int)
+#650 := [rewrite]: #643
+#654 := (= #361 1::Int)
+#655 := [rewrite]: #654
+#482 := [monotonicity #655 #650]: #481
+#639 := [trans #482 #636]: #638
+#522 := [monotonicity #639]: #640
+#631 := [trans #522 #524]: #483
+#629 := [monotonicity #631]: #628
+#534 := [trans #629 #517]: #532
+#528 := [monotonicity #534]: #535
+#642 := (iff #687 #64)
+#653 := (+ 1::Int #61)
+#644 := (= #653 0::Int)
+#647 := (iff #644 #64)
+#641 := [rewrite]: #647
+#645 := (iff #687 #644)
+#501 := (= #480 #653)
+#652 := (+ #61 1::Int)
+#659 := (= #652 #653)
+#500 := [rewrite]: #659
+#657 := (= #480 #652)
+#656 := (= #350 1::Int)
+#661 := (= #350 #361)
+#660 := (= #693 -1::Int)
+#664 := [rewrite]: #660
+#665 := [monotonicity #664]: #661
+#651 := [trans #665 #655]: #656
+#658 := [monotonicity #651]: #657
+#502 := [trans #658 #500]: #501
+#646 := [monotonicity #502]: #645
+#648 := [trans #646 #641]: #642
+#663 := (iff #691 true)
+#381 := (or false true)
+#384 := (iff #381 true)
+#662 := [rewrite]: #384
+#382 := (iff #691 #381)
+#667 := (iff #356 true)
+#669 := (not false)
+#666 := (iff #669 true)
+#670 := [rewrite]: #666
+#391 := (iff #356 #669)
+#292 := (iff #377 false)
+#349 := (or false false)
+#674 := (iff #349 false)
+#337 := [rewrite]: #674
+#397 := (iff #377 #349)
+#677 := (iff #374 false)
+#678 := [rewrite]: #677
+#395 := (iff #373 false)
+#396 := [rewrite]: #395
+#398 := [monotonicity #396 #678]: #397
+#668 := [trans #398 #337]: #292
+#392 := [monotonicity #668]: #391
+#671 := [trans #392 #670]: #667
+#672 := (iff #376 false)
+#324 := (not true)
+#683 := (iff #324 false)
+#686 := [rewrite]: #683
+#325 := (iff #376 #324)
+#682 := (iff #375 true)
+#679 := (or true false)
+#681 := (iff #679 true)
+#319 := [rewrite]: #681
+#680 := (iff #375 #679)
+#340 := (iff #363 true)
+#676 := [rewrite]: #340
+#675 := [monotonicity #676 #678]: #680
+#684 := [trans #675 #319]: #682
+#685 := [monotonicity #684]: #325
+#673 := [trans #685 #686]: #672
+#383 := [monotonicity #673 #671]: #382
+#378 := [trans #383 #662]: #663
+#538 := [monotonicity #378 #648 #528]: #537
+#630 := [trans #538 #540]: #633
+#338 := (iff #371 false)
+#690 := (iff #371 #349)
+#353 := (iff #370 false)
+#689 := [rewrite]: #353
+#688 := (iff #286 false)
+#348 := [rewrite]: #688
+#333 := [monotonicity #348 #689]: #690
+#339 := [trans #333 #337]: #338
+#623 := [monotonicity #339 #630]: #621
+#624 := [trans #623 #612]: #614
+#617 := [monotonicity #624]: #616
+#613 := [trans #617 #619]: #616
+#627 := [quant-inst #55 #11]: #622
+#620 := [mp #627 #613]: #626
+[unit-resolution #620 #70 #705]: false
+b3b7ec77601c17fd899065a2138ddfd9bb069c98 327 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #18 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #16 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #17 := (f4 f5 #16)
 #19 := (f3 #17 #18)
-#758 := (pattern #19)
+#703 := (pattern #19)
 #20 := 0::Int
-#69 := -1::Int
-#107 := (* -1::Int #18)
-#104 := (* -1::Int #16)
-#110 := (div #104 #107)
-#261 := (* -1::Int #110)
-#262 := (+ #19 #261)
-#263 := (= #262 0::Int)
+#65 := -1::Int
+#104 := (* -1::Int #18)
+#101 := (* -1::Int #16)
+#107 := (div #101 #104)
+#263 := (* -1::Int #107)
+#264 := (+ #19 #263)
+#265 := (= #264 0::Int)
 #30 := (div #16 #18)
-#258 := (* -1::Int #30)
-#259 := (+ #19 #258)
-#260 := (= #259 0::Int)
-#136 := (>= #16 0::Int)
-#129 := (<= #18 0::Int)
-#221 := (or #129 #136)
-#222 := (not #221)
-#125 := (<= #16 0::Int)
-#219 := (or #125 #129)
+#260 := (* -1::Int #30)
+#261 := (+ #19 #260)
+#262 := (= #261 0::Int)
+#79 := (<= #18 0::Int)
+#170 := (>= #16 0::Int)
+#223 := (or #170 #79)
+#224 := (not #223)
+#75 := (<= #16 0::Int)
+#219 := (or #75 #79)
 #220 := (not #219)
-#225 := (or #220 #222)
-#264 := (ite #225 #260 #263)
-#257 := (= #19 0::Int)
+#227 := (or #220 #224)
+#266 := (if #227 #262 #265)
+#259 := (= #19 0::Int)
 #22 := (= #18 0::Int)
 #21 := (= #16 0::Int)
 #23 := (or #21 #22)
-#265 := (ite #23 #257 #264)
-#759 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #758) #265)
-#268 := (forall (vars (?v0 Int) (?v1 Int)) #265)
-#762 := (iff #268 #759)
-#760 := (iff #265 #265)
-#761 := [refl]: #760
-#763 := [quant-intro #761]: #762
-#228 := (ite #225 #30 #110)
-#231 := (ite #23 0::Int #228)
-#234 := (= #19 #231)
-#237 := (forall (vars (?v0 Int) (?v1 Int)) #234)
-#269 := (iff #237 #268)
-#266 := (iff #234 #265)
-#267 := [rewrite]: #266
-#270 := [quant-intro #267]: #269
-#137 := (not #136)
-#130 := (not #129)
-#140 := (and #130 #137)
-#126 := (not #125)
-#133 := (and #126 #130)
-#143 := (or #133 #140)
-#146 := (ite #143 #30 #110)
-#149 := (ite #23 0::Int #146)
-#152 := (= #19 #149)
-#155 := (forall (vars (?v0 Int) (?v1 Int)) #152)
-#238 := (iff #155 #237)
-#235 := (iff #152 #234)
-#232 := (= #149 #231)
-#229 := (= #146 #228)
-#226 := (iff #143 #225)
-#223 := (iff #140 #222)
-#224 := [rewrite]: #223
-#213 := (iff #133 #220)
-#214 := [rewrite]: #213
-#227 := [monotonicity #214 #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [monotonicity #233]: #235
-#239 := [quant-intro #236]: #238
-#217 := (~ #155 #155)
-#215 := (~ #152 #152)
-#216 := [refl]: #215
-#218 := [nnf-pos #216]: #217
+#267 := (if #23 #259 #266)
+#704 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #703) #267)
+#270 := (forall (vars (?v0 Int) (?v1 Int)) #267)
+#707 := (iff #270 #704)
+#705 := (iff #267 #267)
+#706 := [refl]: #705
+#708 := [quant-intro #706]: #707
+#230 := (if #227 #30 #107)
+#233 := (if #23 0::Int #230)
+#236 := (= #19 #233)
+#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
+#271 := (iff #239 #270)
+#268 := (iff #236 #267)
+#269 := [rewrite]: #268
+#272 := [quant-intro #269]: #271
+#80 := (not #79)
+#173 := (not #170)
+#176 := (and #173 #80)
+#76 := (not #75)
+#83 := (and #76 #80)
+#179 := (or #83 #176)
+#182 := (if #179 #30 #107)
+#185 := (if #23 0::Int #182)
+#188 := (= #19 #185)
+#191 := (forall (vars (?v0 Int) (?v1 Int)) #188)
+#240 := (iff #191 #239)
+#237 := (iff #188 #236)
+#234 := (= #185 #233)
+#231 := (= #182 #230)
+#228 := (iff #179 #227)
+#225 := (iff #176 #224)
+#226 := [rewrite]: #225
+#221 := (iff #83 #220)
+#222 := [rewrite]: #221
+#229 := [monotonicity #222 #226]: #228
+#232 := [monotonicity #229]: #231
+#235 := [monotonicity #232]: #234
+#238 := [monotonicity #235]: #237
+#241 := [quant-intro #238]: #240
+#215 := (~ #191 #191)
+#213 := (~ #188 #188)
+#214 := [refl]: #213
+#216 := [nnf-pos #214]: #215
+#86 := (<= 0::Int #16)
+#87 := (not #86)
+#95 := (and #87 #80)
+#98 := (or #83 #95)
+#110 := (if #98 #30 #107)
+#113 := (if #23 0::Int #110)
+#116 := (= #19 #113)
+#119 := (forall (vars (?v0 Int) (?v1 Int)) #116)
+#192 := (iff #119 #191)
+#189 := (iff #116 #188)
+#186 := (= #113 #185)
+#183 := (= #110 #182)
+#180 := (iff #98 #179)
+#177 := (iff #95 #176)
+#174 := (iff #87 #173)
+#171 := (iff #86 #170)
+#172 := [rewrite]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [monotonicity #178]: #180
+#184 := [monotonicity #181]: #183
+#187 := [monotonicity #184]: #186
+#190 := [monotonicity #187]: #189
+#193 := [quant-intro #190]: #192
 #32 := (- #18)
 #31 := (- #16)
 #33 := (div #31 #32)
@@ -32776,325 +31971,325 @@
 #24 := (< 0::Int #16)
 #26 := (and #24 #25)
 #29 := (or #26 #28)
-#34 := (ite #29 #30 #33)
-#35 := (ite #23 0::Int #34)
+#34 := (if #29 #30 #33)
+#35 := (if #23 0::Int #34)
 #36 := (= #19 #35)
 #37 := (forall (vars (?v0 Int) (?v1 Int)) #36)
-#158 := (iff #37 #155)
-#98 := (and #25 #27)
-#101 := (or #26 #98)
-#113 := (ite #101 #30 #110)
-#116 := (ite #23 0::Int #113)
-#119 := (= #19 #116)
-#122 := (forall (vars (?v0 Int) (?v1 Int)) #119)
-#156 := (iff #122 #155)
-#153 := (iff #119 #152)
-#150 := (= #116 #149)
-#147 := (= #113 #146)
-#144 := (iff #101 #143)
-#141 := (iff #98 #140)
-#138 := (iff #27 #137)
-#139 := [rewrite]: #138
-#131 := (iff #25 #130)
-#132 := [rewrite]: #131
-#142 := [monotonicity #132 #139]: #141
-#134 := (iff #26 #133)
-#127 := (iff #24 #126)
-#128 := [rewrite]: #127
-#135 := [monotonicity #128 #132]: #134
-#145 := [monotonicity #135 #142]: #144
-#148 := [monotonicity #145]: #147
-#151 := [monotonicity #148]: #150
-#154 := [monotonicity #151]: #153
-#157 := [quant-intro #154]: #156
-#123 := (iff #37 #122)
-#120 := (iff #36 #119)
-#117 := (= #35 #116)
-#114 := (= #34 #113)
-#111 := (= #33 #110)
-#108 := (= #32 #107)
-#109 := [rewrite]: #108
-#105 := (= #31 #104)
+#120 := (iff #37 #119)
+#117 := (iff #36 #116)
+#114 := (= #35 #113)
+#111 := (= #34 #110)
+#108 := (= #33 #107)
+#105 := (= #32 #104)
 #106 := [rewrite]: #105
-#112 := [monotonicity #106 #109]: #111
-#102 := (iff #29 #101)
-#99 := (iff #28 #98)
-#100 := [rewrite]: #99
-#103 := [monotonicity #100]: #102
-#115 := [monotonicity #103 #112]: #114
+#102 := (= #31 #101)
+#103 := [rewrite]: #102
+#109 := [monotonicity #103 #106]: #108
+#99 := (iff #29 #98)
+#96 := (iff #28 #95)
+#81 := (iff #25 #80)
+#82 := [rewrite]: #81
+#88 := (iff #27 #87)
+#92 := (iff #87 #87)
+#90 := (iff #86 #86)
+#91 := [rewrite]: #90
+#93 := [monotonicity #91]: #92
+#89 := [rewrite]: #88
+#94 := [trans #89 #93]: #88
+#97 := [monotonicity #94 #82]: #96
+#84 := (iff #26 #83)
+#77 := (iff #24 #76)
+#78 := [rewrite]: #77
+#85 := [monotonicity #78 #82]: #84
+#100 := [monotonicity #85 #97]: #99
+#112 := [monotonicity #100 #109]: #111
+#115 := [monotonicity #112]: #114
 #118 := [monotonicity #115]: #117
-#121 := [monotonicity #118]: #120
-#124 := [quant-intro #121]: #123
-#159 := [trans #124 #157]: #158
-#97 := [asserted]: #37
-#160 := [mp #97 #159]: #155
-#209 := [mp~ #160 #218]: #155
-#240 := [mp #209 #239]: #237
-#271 := [mp #240 #270]: #268
-#764 := [mp #271 #763]: #759
-#12 := 3::Int
-#72 := (f4 f5 -1::Int)
-#75 := (f3 #72 3::Int)
-#78 := (= #75 -1::Int)
-#91 := (not #78)
-#9 := 1::Int
-#10 := (- 1::Int)
-#11 := (f4 f5 #10)
-#13 := (f3 #11 3::Int)
-#14 := (= #13 #10)
-#15 := (not #14)
-#94 := (iff #15 #91)
-#81 := (= -1::Int #75)
-#86 := (not #81)
-#92 := (iff #86 #91)
-#89 := (iff #81 #78)
-#90 := [rewrite]: #89
-#93 := [monotonicity #90]: #92
-#87 := (iff #15 #86)
-#84 := (iff #14 #81)
-#82 := (iff #78 #81)
-#83 := [rewrite]: #82
-#79 := (iff #14 #78)
-#70 := (= #10 -1::Int)
-#71 := [rewrite]: #70
-#76 := (= #13 #75)
-#73 := (= #11 #72)
-#74 := [monotonicity #71]: #73
-#77 := [monotonicity #74]: #76
-#80 := [monotonicity #77 #71]: #79
-#85 := [trans #80 #83]: #84
-#88 := [monotonicity #85]: #87
-#95 := [trans #88 #93]: #94
-#68 := [asserted]: #15
-#96 := [mp #68 #95]: #91
-#684 := (not #759)
-#685 := (or #684 #78)
-#345 := (* -1::Int 3::Int)
-#429 := (* -1::Int -1::Int)
-#430 := (div #429 #345)
-#431 := (* -1::Int #430)
-#422 := (+ #75 #431)
-#433 := (= #422 0::Int)
-#434 := (div -1::Int 3::Int)
-#435 := (* -1::Int #434)
-#432 := (+ #75 #435)
-#436 := (= #432 0::Int)
-#415 := (>= -1::Int 0::Int)
-#750 := (<= 3::Int 0::Int)
-#752 := (or #750 #415)
-#409 := (not #752)
-#539 := (<= -1::Int 0::Int)
-#746 := (or #539 #750)
-#420 := (not #746)
-#421 := (or #420 #409)
-#753 := (ite #421 #436 #433)
-#754 := (= #75 0::Int)
-#755 := (= 3::Int 0::Int)
-#756 := (= -1::Int 0::Int)
-#751 := (or #756 #755)
-#757 := (ite #751 #754 #753)
-#681 := (or #684 #757)
-#675 := (iff #681 #685)
-#677 := (iff #685 #685)
-#678 := [rewrite]: #677
-#673 := (iff #757 #78)
-#693 := (ite false #754 #78)
-#674 := (iff #693 #78)
-#671 := [rewrite]: #674
-#680 := (iff #757 #693)
-#692 := (iff #753 #78)
-#1 := true
-#595 := (ite true #78 #754)
-#598 := (iff #595 #78)
-#599 := [rewrite]: #598
-#596 := (iff #753 #595)
-#594 := (iff #433 #754)
-#591 := (= #422 #75)
-#592 := (+ #75 0::Int)
-#691 := (= #592 #75)
-#576 := [rewrite]: #691
-#687 := (= #422 #592)
-#542 := (= #431 0::Int)
-#696 := (* -1::Int 0::Int)
-#582 := (= #696 0::Int)
-#583 := [rewrite]: #582
-#699 := (= #431 #696)
-#697 := (= #430 0::Int)
-#708 := -3::Int
-#538 := (div 1::Int -3::Int)
-#694 := (= #538 0::Int)
-#695 := [rewrite]: #694
-#540 := (= #430 #538)
-#702 := (= #345 -3::Int)
-#709 := [rewrite]: #702
-#713 := (= #429 1::Int)
-#714 := [rewrite]: #713
-#541 := [monotonicity #714 #709]: #540
-#698 := [trans #541 #695]: #697
-#581 := [monotonicity #698]: #699
-#690 := [trans #581 #583]: #542
-#688 := [monotonicity #690]: #687
-#593 := [trans #688 #576]: #591
-#587 := [monotonicity #593]: #594
-#701 := (iff #436 #78)
-#712 := (+ 1::Int #75)
-#703 := (= #712 0::Int)
-#706 := (iff #703 #78)
-#700 := [rewrite]: #706
-#704 := (iff #436 #703)
-#560 := (= #432 #712)
-#711 := (+ #75 1::Int)
-#718 := (= #711 #712)
-#559 := [rewrite]: #718
-#716 := (= #432 #711)
-#715 := (= #435 1::Int)
-#720 := (= #435 #429)
-#719 := (= #434 -1::Int)
-#723 := [rewrite]: #719
-#724 := [monotonicity #723]: #720
-#710 := [trans #724 #714]: #715
-#717 := [monotonicity #710]: #716
-#561 := [trans #717 #559]: #560
-#705 := [monotonicity #561]: #704
-#707 := [trans #705 #700]: #701
-#722 := (iff #421 true)
-#440 := (or false true)
-#443 := (iff #440 true)
-#721 := [rewrite]: #443
-#441 := (iff #421 #440)
-#726 := (iff #409 true)
-#728 := (not false)
-#725 := (iff #728 true)
-#729 := [rewrite]: #725
-#450 := (iff #409 #728)
-#351 := (iff #752 false)
-#408 := (or false false)
-#733 := (iff #408 false)
-#396 := [rewrite]: #733
-#456 := (iff #752 #408)
-#454 := (iff #415 false)
-#455 := [rewrite]: #454
-#736 := (iff #750 false)
-#737 := [rewrite]: #736
-#457 := [monotonicity #737 #455]: #456
-#727 := [trans #457 #396]: #351
-#451 := [monotonicity #727]: #450
-#730 := [trans #451 #729]: #726
-#731 := (iff #420 false)
-#383 := (not true)
-#742 := (iff #383 false)
-#745 := [rewrite]: #742
-#384 := (iff #420 #383)
-#741 := (iff #746 true)
-#738 := (or true false)
-#740 := (iff #738 true)
-#378 := [rewrite]: #740
-#739 := (iff #746 #738)
-#399 := (iff #539 true)
-#735 := [rewrite]: #399
-#734 := [monotonicity #735 #737]: #739
-#743 := [trans #734 #378]: #741
-#744 := [monotonicity #743]: #384
-#732 := [trans #744 #745]: #731
-#442 := [monotonicity #732 #730]: #441
-#437 := [trans #442 #721]: #722
-#597 := [monotonicity #437 #707 #587]: #596
-#689 := [trans #597 #599]: #692
-#397 := (iff #751 false)
-#749 := (iff #751 #408)
-#412 := (iff #755 false)
-#748 := [rewrite]: #412
-#747 := (iff #756 false)
-#407 := [rewrite]: #747
-#392 := [monotonicity #407 #748]: #749
-#398 := [trans #392 #396]: #397
-#682 := [monotonicity #398 #689]: #680
-#683 := [trans #682 #671]: #673
-#676 := [monotonicity #683]: #675
-#672 := [trans #676 #678]: #675
-#686 := [quant-inst #69 #12]: #681
-#679 := [mp #686 #672]: #685
-[unit-resolution #679 #96 #764]: false
-unsat
-95ce555aaa4ba313bd33402001355ba151fdf57d 317 0
+#121 := [quant-intro #118]: #120
+#51 := [asserted]: #37
+#122 := [mp #51 #121]: #119
+#194 := [mp #122 #193]: #191
+#168 := [mp~ #194 #216]: #191
+#242 := [mp #168 #241]: #239
+#273 := [mp #242 #272]: #270
+#709 := [mp #273 #708]: #704
+#8 := 3::Int
+#56 := -3::Int
+#59 := (f4 f5 -3::Int)
+#62 := (f3 #59 3::Int)
+#68 := (= #62 -1::Int)
+#71 := (not #68)
+#12 := 1::Int
+#13 := (- 1::Int)
+#9 := (- 3::Int)
+#10 := (f4 f5 #9)
+#11 := (f3 #10 3::Int)
+#14 := (= #11 #13)
+#15 := (not #14)
+#72 := (iff #15 #71)
+#69 := (iff #14 #68)
+#66 := (= #13 -1::Int)
+#67 := [rewrite]: #66
+#63 := (= #11 #62)
+#60 := (= #10 #59)
+#57 := (= #9 -3::Int)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#64 := [monotonicity #61]: #63
+#70 := [monotonicity #64 #67]: #69
+#73 := [monotonicity #70]: #72
+#50 := [asserted]: #15
+#74 := [mp #50 #73]: #71
+#618 := (not #704)
+#628 := (or #618 #68)
+#366 := (* -1::Int 3::Int)
+#365 := (* -1::Int -3::Int)
+#698 := (div #365 #366)
+#699 := (* -1::Int #698)
+#700 := (+ #62 #699)
+#701 := (= #700 0::Int)
+#697 := (div -3::Int 3::Int)
+#354 := (* -1::Int #697)
+#484 := (+ #62 #354)
+#691 := (= #484 0::Int)
+#378 := (<= 3::Int 0::Int)
+#377 := (>= -3::Int 0::Int)
+#381 := (or #377 #378)
+#360 := (not #381)
+#367 := (<= -3::Int 0::Int)
+#379 := (or #367 #378)
+#380 := (not #379)
+#695 := (or #380 #360)
+#696 := (if #695 #691 #701)
+#376 := (= #62 0::Int)
+#374 := (= 3::Int 0::Int)
+#290 := (= -3::Int 0::Int)
+#375 := (or #290 #374)
+#702 := (if #375 #376 #696)
+#629 := (or #618 #702)
+#626 := (iff #629 #628)
+#620 := (iff #628 #628)
+#621 := [rewrite]: #620
+#619 := (iff #702 #68)
+#637 := (if false #376 #68)
+#625 := (iff #637 #68)
+#627 := [rewrite]: #625
+#634 := (iff #702 #637)
+#543 := (iff #696 #68)
+#1 := true
+#539 := (if true #68 #68)
+#541 := (iff #539 #68)
+#542 := [rewrite]: #541
+#532 := (iff #696 #539)
+#536 := (iff #701 #68)
+#663 := (+ 1::Int #62)
+#649 := (= #663 0::Int)
+#645 := (iff #649 #68)
+#646 := [rewrite]: #645
+#636 := (iff #701 #649)
+#632 := (= #700 #663)
+#661 := (+ #62 1::Int)
+#504 := (= #661 #663)
+#505 := [rewrite]: #504
+#635 := (= #700 #661)
+#528 := (= #699 1::Int)
+#665 := (* -1::Int -1::Int)
+#659 := (= #665 1::Int)
+#660 := [rewrite]: #659
+#526 := (= #699 #665)
+#641 := (= #698 -1::Int)
+#486 := (div 3::Int -3::Int)
+#642 := (= #486 -1::Int)
+#643 := [rewrite]: #642
+#639 := (= #698 #486)
+#483 := (= #366 -3::Int)
+#485 := [rewrite]: #483
+#647 := (= #365 3::Int)
+#654 := [rewrite]: #647
+#640 := [monotonicity #654 #485]: #639
+#644 := [trans #640 #643]: #641
+#527 := [monotonicity #644]: #526
+#487 := [trans #527 #660]: #528
+#537 := [monotonicity #487]: #635
+#633 := [trans #537 #505]: #632
+#521 := [monotonicity #633]: #636
+#538 := [trans #521 #646]: #536
+#652 := (iff #691 #68)
+#650 := (iff #691 #649)
+#506 := (= #484 #663)
+#662 := (= #484 #661)
+#655 := (= #354 1::Int)
+#669 := (= #354 #665)
+#664 := (= #697 -1::Int)
+#668 := [rewrite]: #664
+#658 := [monotonicity #668]: #669
+#656 := [trans #658 #660]: #655
+#657 := [monotonicity #656]: #662
+#648 := [trans #657 #505]: #506
+#651 := [monotonicity #648]: #650
+#653 := [trans #651 #646]: #652
+#667 := (iff #695 true)
+#385 := (or false true)
+#388 := (iff #385 true)
+#666 := [rewrite]: #388
+#386 := (iff #695 #385)
+#671 := (iff #360 true)
+#673 := (not false)
+#670 := (iff #673 true)
+#674 := [rewrite]: #670
+#395 := (iff #360 #673)
+#296 := (iff #381 false)
+#353 := (or false false)
+#678 := (iff #353 false)
+#341 := [rewrite]: #678
+#401 := (iff #381 #353)
+#681 := (iff #378 false)
+#682 := [rewrite]: #681
+#399 := (iff #377 false)
+#400 := [rewrite]: #399
+#402 := [monotonicity #400 #682]: #401
+#672 := [trans #402 #341]: #296
+#396 := [monotonicity #672]: #395
+#675 := [trans #396 #674]: #671
+#676 := (iff #380 false)
+#328 := (not true)
+#687 := (iff #328 false)
+#690 := [rewrite]: #687
+#329 := (iff #380 #328)
+#686 := (iff #379 true)
+#683 := (or true false)
+#685 := (iff #683 true)
+#323 := [rewrite]: #685
+#684 := (iff #379 #683)
+#344 := (iff #367 true)
+#680 := [rewrite]: #344
+#679 := [monotonicity #680 #682]: #684
+#688 := [trans #679 #323]: #686
+#689 := [monotonicity #688]: #329
+#677 := [trans #689 #690]: #676
+#387 := [monotonicity #677 #675]: #386
+#382 := [trans #387 #666]: #667
+#540 := [monotonicity #382 #653 #538]: #532
+#544 := [trans #540 #542]: #543
+#342 := (iff #375 false)
+#694 := (iff #375 #353)
+#357 := (iff #374 false)
+#693 := [rewrite]: #357
+#692 := (iff #290 false)
+#352 := [rewrite]: #692
+#337 := [monotonicity #352 #693]: #694
+#343 := [trans #337 #341]: #342
+#638 := [monotonicity #343 #544]: #634
+#616 := [trans #638 #627]: #619
+#631 := [monotonicity #616]: #626
+#622 := [trans #631 #621]: #626
+#630 := [quant-inst #56 #8]: #629
+#623 := [mp #630 #622]: #628
+[unit-resolution #623 #74 #709]: false
+ce73a3cbcbb282ad675c6218053260f8ce5ee783 342 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #19 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #17 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #18 := (f4 f5 #17)
 #20 := (f3 #18 #19)
-#750 := (pattern #20)
+#706 := (pattern #20)
 #21 := 0::Int
-#79 := -1::Int
-#99 := (* -1::Int #19)
-#96 := (* -1::Int #17)
-#102 := (div #96 #99)
-#253 := (* -1::Int #102)
-#254 := (+ #20 #253)
-#255 := (= #254 0::Int)
+#102 := -1::Int
+#106 := (* -1::Int #19)
+#103 := (* -1::Int #17)
+#109 := (div #103 #106)
+#265 := (* -1::Int #109)
+#266 := (+ #20 #265)
+#267 := (= #266 0::Int)
 #31 := (div #17 #19)
-#250 := (* -1::Int #31)
-#251 := (+ #20 #250)
-#252 := (= #251 0::Int)
-#128 := (>= #17 0::Int)
-#121 := (<= #19 0::Int)
-#213 := (or #121 #128)
-#214 := (not #213)
-#117 := (<= #17 0::Int)
-#211 := (or #117 #121)
-#212 := (not #211)
-#217 := (or #212 #214)
-#256 := (ite #217 #252 #255)
-#249 := (= #20 0::Int)
+#262 := (* -1::Int #31)
+#263 := (+ #20 #262)
+#264 := (= #263 0::Int)
+#80 := (<= #19 0::Int)
+#172 := (>= #17 0::Int)
+#225 := (or #172 #80)
+#226 := (not #225)
+#76 := (<= #17 0::Int)
+#221 := (or #76 #80)
+#222 := (not #221)
+#229 := (or #222 #226)
+#268 := (if #229 #264 #267)
+#261 := (= #20 0::Int)
 #23 := (= #19 0::Int)
 #22 := (= #17 0::Int)
 #24 := (or #22 #23)
-#257 := (ite #24 #249 #256)
-#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #257)
-#260 := (forall (vars (?v0 Int) (?v1 Int)) #257)
-#754 := (iff #260 #751)
-#752 := (iff #257 #257)
-#753 := [refl]: #752
-#755 := [quant-intro #753]: #754
-#220 := (ite #217 #31 #102)
-#223 := (ite #24 0::Int #220)
-#226 := (= #20 #223)
-#229 := (forall (vars (?v0 Int) (?v1 Int)) #226)
-#261 := (iff #229 #260)
-#258 := (iff #226 #257)
-#259 := [rewrite]: #258
-#262 := [quant-intro #259]: #261
-#129 := (not #128)
-#122 := (not #121)
-#132 := (and #122 #129)
-#118 := (not #117)
-#125 := (and #118 #122)
-#135 := (or #125 #132)
-#138 := (ite #135 #31 #102)
-#141 := (ite #24 0::Int #138)
-#144 := (= #20 #141)
-#147 := (forall (vars (?v0 Int) (?v1 Int)) #144)
-#230 := (iff #147 #229)
-#227 := (iff #144 #226)
-#224 := (= #141 #223)
-#221 := (= #138 #220)
-#218 := (iff #135 #217)
-#215 := (iff #132 #214)
-#216 := [rewrite]: #215
-#205 := (iff #125 #212)
-#206 := [rewrite]: #205
-#219 := [monotonicity #206 #216]: #218
-#222 := [monotonicity #219]: #221
-#225 := [monotonicity #222]: #224
-#228 := [monotonicity #225]: #227
-#231 := [quant-intro #228]: #230
-#209 := (~ #147 #147)
-#207 := (~ #144 #144)
-#208 := [refl]: #207
-#210 := [nnf-pos #208]: #209
+#269 := (if #24 #261 #268)
+#707 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #706) #269)
+#272 := (forall (vars (?v0 Int) (?v1 Int)) #269)
+#710 := (iff #272 #707)
+#708 := (iff #269 #269)
+#709 := [refl]: #708
+#711 := [quant-intro #709]: #710
+#232 := (if #229 #31 #109)
+#235 := (if #24 0::Int #232)
+#238 := (= #20 #235)
+#241 := (forall (vars (?v0 Int) (?v1 Int)) #238)
+#273 := (iff #241 #272)
+#270 := (iff #238 #269)
+#271 := [rewrite]: #270
+#274 := [quant-intro #271]: #273
+#81 := (not #80)
+#175 := (not #172)
+#178 := (and #175 #81)
+#77 := (not #76)
+#84 := (and #77 #81)
+#181 := (or #84 #178)
+#184 := (if #181 #31 #109)
+#187 := (if #24 0::Int #184)
+#190 := (= #20 #187)
+#193 := (forall (vars (?v0 Int) (?v1 Int)) #190)
+#242 := (iff #193 #241)
+#239 := (iff #190 #238)
+#236 := (= #187 #235)
+#233 := (= #184 #232)
+#230 := (iff #181 #229)
+#227 := (iff #178 #226)
+#228 := [rewrite]: #227
+#223 := (iff #84 #222)
+#224 := [rewrite]: #223
+#231 := [monotonicity #224 #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [monotonicity #234]: #236
+#240 := [monotonicity #237]: #239
+#243 := [quant-intro #240]: #242
+#213 := (~ #193 #193)
+#215 := (~ #190 #190)
+#216 := [refl]: #215
+#214 := [nnf-pos #216]: #213
+#87 := (<= 0::Int #17)
+#88 := (not #87)
+#96 := (and #88 #81)
+#99 := (or #84 #96)
+#112 := (if #99 #31 #109)
+#115 := (if #24 0::Int #112)
+#118 := (= #20 #115)
+#121 := (forall (vars (?v0 Int) (?v1 Int)) #118)
+#194 := (iff #121 #193)
+#191 := (iff #118 #190)
+#188 := (= #115 #187)
+#185 := (= #112 #184)
+#182 := (iff #99 #181)
+#179 := (iff #96 #178)
+#176 := (iff #88 #175)
+#173 := (iff #87 #172)
+#174 := [rewrite]: #173
+#177 := [monotonicity #174]: #176
+#180 := [monotonicity #177]: #179
+#183 := [monotonicity #180]: #182
+#186 := [monotonicity #183]: #185
+#189 := [monotonicity #186]: #188
+#192 := [monotonicity #189]: #191
+#195 := [quant-intro #192]: #194
 #33 := (- #19)
 #32 := (- #17)
 #34 := (div #32 #33)
@@ -33104,1656 +32299,1606 @@
 #25 := (< 0::Int #17)
 #27 := (and #25 #26)
 #30 := (or #27 #29)
-#35 := (ite #30 #31 #34)
-#36 := (ite #24 0::Int #35)
+#35 := (if #30 #31 #34)
+#36 := (if #24 0::Int #35)
 #37 := (= #20 #36)
 #38 := (forall (vars (?v0 Int) (?v1 Int)) #37)
-#150 := (iff #38 #147)
-#89 := (and #26 #28)
-#93 := (or #27 #89)
-#105 := (ite #93 #31 #102)
-#108 := (ite #24 0::Int #105)
-#111 := (= #20 #108)
-#114 := (forall (vars (?v0 Int) (?v1 Int)) #111)
-#148 := (iff #114 #147)
-#145 := (iff #111 #144)
-#142 := (= #108 #141)
-#139 := (= #105 #138)
-#136 := (iff #93 #135)
-#133 := (iff #89 #132)
-#130 := (iff #28 #129)
-#131 := [rewrite]: #130
-#123 := (iff #26 #122)
-#124 := [rewrite]: #123
-#134 := [monotonicity #124 #131]: #133
-#126 := (iff #27 #125)
-#119 := (iff #25 #118)
-#120 := [rewrite]: #119
-#127 := [monotonicity #120 #124]: #126
-#137 := [monotonicity #127 #134]: #136
-#140 := [monotonicity #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [quant-intro #146]: #148
-#115 := (iff #38 #114)
-#112 := (iff #37 #111)
-#109 := (= #36 #108)
-#106 := (= #35 #105)
-#103 := (= #34 #102)
-#100 := (= #33 #99)
-#101 := [rewrite]: #100
-#97 := (= #32 #96)
-#98 := [rewrite]: #97
-#104 := [monotonicity #98 #101]: #103
-#94 := (iff #30 #93)
-#91 := (iff #29 #89)
+#122 := (iff #38 #121)
+#119 := (iff #37 #118)
+#116 := (= #36 #115)
+#113 := (= #35 #112)
+#110 := (= #34 #109)
+#107 := (= #33 #106)
+#108 := [rewrite]: #107
+#104 := (= #32 #103)
+#105 := [rewrite]: #104
+#111 := [monotonicity #105 #108]: #110
+#100 := (iff #30 #99)
+#97 := (iff #29 #96)
+#82 := (iff #26 #81)
+#83 := [rewrite]: #82
+#89 := (iff #28 #88)
+#93 := (iff #88 #88)
+#91 := (iff #87 #87)
 #92 := [rewrite]: #91
-#95 := [monotonicity #92]: #94
-#107 := [monotonicity #95 #104]: #106
-#110 := [monotonicity #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [quant-intro #113]: #115
-#151 := [trans #116 #149]: #150
-#88 := [asserted]: #38
-#152 := [mp #88 #151]: #147
-#201 := [mp~ #152 #210]: #147
-#232 := [mp #201 #231]: #229
-#263 := [mp #232 #262]: #260
-#756 := [mp #263 #755]: #751
-#9 := 3::Int
-#70 := -3::Int
-#73 := (f4 f5 -3::Int)
-#76 := (f3 #73 3::Int)
-#82 := (= #76 -1::Int)
-#85 := (not #82)
-#13 := 1::Int
-#14 := (- 1::Int)
-#10 := (- 3::Int)
-#11 := (f4 f5 #10)
-#12 := (f3 #11 3::Int)
+#94 := [monotonicity #92]: #93
+#90 := [rewrite]: #89
+#95 := [trans #90 #94]: #89
+#98 := [monotonicity #95 #83]: #97
+#85 := (iff #27 #84)
+#78 := (iff #25 #77)
+#79 := [rewrite]: #78
+#86 := [monotonicity #79 #83]: #85
+#101 := [monotonicity #86 #98]: #100
+#114 := [monotonicity #101 #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [monotonicity #117]: #119
+#123 := [quant-intro #120]: #122
+#52 := [asserted]: #38
+#124 := [mp #52 #123]: #121
+#196 := [mp #124 #195]: #193
+#170 := [mp~ #196 #214]: #193
+#244 := [mp #170 #243]: #241
+#275 := [mp #244 #274]: #272
+#712 := [mp #275 #711]: #707
+#66 := -2::Int
+#11 := 3::Int
+#57 := -5::Int
+#60 := (f4 f5 -5::Int)
+#63 := (f3 #60 3::Int)
+#69 := (= #63 -2::Int)
+#72 := (not #69)
+#13 := 2::Int
+#14 := (- 2::Int)
+#8 := 5::Int
+#9 := (- 5::Int)
+#10 := (f4 f5 #9)
+#12 := (f3 #10 3::Int)
 #15 := (= #12 #14)
 #16 := (not #15)
-#86 := (iff #16 #85)
-#83 := (iff #15 #82)
-#80 := (= #14 -1::Int)
-#81 := [rewrite]: #80
-#77 := (= #12 #76)
-#74 := (= #11 #73)
-#71 := (= #10 -3::Int)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#84 := [monotonicity #78 #81]: #83
-#87 := [monotonicity #84]: #86
-#69 := [asserted]: #16
-#90 := [mp #69 #87]: #85
-#665 := (not #751)
-#675 := (or #665 #82)
-#337 := (* -1::Int 3::Int)
-#421 := (* -1::Int -3::Int)
-#422 := (div #421 #337)
-#423 := (* -1::Int #422)
-#414 := (+ #76 #423)
-#425 := (= #414 0::Int)
-#426 := (div -3::Int 3::Int)
-#427 := (* -1::Int #426)
-#424 := (+ #76 #427)
-#428 := (= #424 0::Int)
-#407 := (>= -3::Int 0::Int)
-#742 := (<= 3::Int 0::Int)
-#744 := (or #742 #407)
-#401 := (not #744)
-#531 := (<= -3::Int 0::Int)
-#738 := (or #531 #742)
-#412 := (not #738)
-#413 := (or #412 #401)
-#745 := (ite #413 #428 #425)
-#746 := (= #76 0::Int)
-#747 := (= 3::Int 0::Int)
-#748 := (= -3::Int 0::Int)
-#743 := (or #748 #747)
-#749 := (ite #743 #746 #745)
-#676 := (or #665 #749)
-#673 := (iff #676 #675)
-#667 := (iff #675 #675)
-#668 := [rewrite]: #667
-#666 := (iff #749 #82)
-#684 := (ite false #746 #82)
-#672 := (iff #684 #82)
-#674 := [rewrite]: #672
-#681 := (iff #749 #684)
-#590 := (iff #745 #82)
-#1 := true
-#586 := (ite true #82 #82)
-#588 := (iff #586 #82)
-#589 := [rewrite]: #588
-#579 := (iff #745 #586)
-#583 := (iff #425 #82)
-#710 := (+ 1::Int #76)
-#696 := (= #710 0::Int)
-#692 := (iff #696 #82)
-#693 := [rewrite]: #692
-#683 := (iff #425 #696)
-#679 := (= #414 #710)
-#708 := (+ #76 1::Int)
-#551 := (= #708 #710)
-#552 := [rewrite]: #551
-#682 := (= #414 #708)
-#575 := (= #423 1::Int)
-#712 := (* -1::Int -1::Int)
-#706 := (= #712 1::Int)
-#707 := [rewrite]: #706
-#573 := (= #423 #712)
-#688 := (= #422 -1::Int)
-#533 := (div 3::Int -3::Int)
-#689 := (= #533 -1::Int)
-#690 := [rewrite]: #689
-#686 := (= #422 #533)
-#530 := (= #337 -3::Int)
-#532 := [rewrite]: #530
-#694 := (= #421 3::Int)
-#701 := [rewrite]: #694
-#687 := [monotonicity #701 #532]: #686
-#691 := [trans #687 #690]: #688
-#574 := [monotonicity #691]: #573
-#534 := [trans #574 #707]: #575
-#584 := [monotonicity #534]: #682
-#680 := [trans #584 #552]: #679
-#568 := [monotonicity #680]: #683
-#585 := [trans #568 #693]: #583
-#699 := (iff #428 #82)
-#697 := (iff #428 #696)
-#553 := (= #424 #710)
-#709 := (= #424 #708)
-#702 := (= #427 1::Int)
-#716 := (= #427 #712)
-#711 := (= #426 -1::Int)
-#715 := [rewrite]: #711
-#705 := [monotonicity #715]: #716
-#703 := [trans #705 #707]: #702
-#704 := [monotonicity #703]: #709
-#695 := [trans #704 #552]: #553
-#698 := [monotonicity #695]: #697
-#700 := [trans #698 #693]: #699
-#714 := (iff #413 true)
-#432 := (or false true)
-#435 := (iff #432 true)
-#713 := [rewrite]: #435
-#433 := (iff #413 #432)
-#718 := (iff #401 true)
-#720 := (not false)
-#717 := (iff #720 true)
-#721 := [rewrite]: #717
-#442 := (iff #401 #720)
-#343 := (iff #744 false)
-#400 := (or false false)
-#725 := (iff #400 false)
-#388 := [rewrite]: #725
-#448 := (iff #744 #400)
-#446 := (iff #407 false)
-#447 := [rewrite]: #446
-#728 := (iff #742 false)
-#729 := [rewrite]: #728
-#449 := [monotonicity #729 #447]: #448
-#719 := [trans #449 #388]: #343
-#443 := [monotonicity #719]: #442
-#722 := [trans #443 #721]: #718
-#723 := (iff #412 false)
-#375 := (not true)
-#734 := (iff #375 false)
-#737 := [rewrite]: #734
-#376 := (iff #412 #375)
-#733 := (iff #738 true)
-#730 := (or true false)
-#732 := (iff #730 true)
-#370 := [rewrite]: #732
-#731 := (iff #738 #730)
-#391 := (iff #531 true)
-#727 := [rewrite]: #391
-#726 := [monotonicity #727 #729]: #731
-#735 := [trans #726 #370]: #733
-#736 := [monotonicity #735]: #376
-#724 := [trans #736 #737]: #723
-#434 := [monotonicity #724 #722]: #433
-#429 := [trans #434 #713]: #714
-#587 := [monotonicity #429 #700 #585]: #579
-#591 := [trans #587 #589]: #590
-#389 := (iff #743 false)
-#741 := (iff #743 #400)
-#404 := (iff #747 false)
-#740 := [rewrite]: #404
-#739 := (iff #748 false)
-#399 := [rewrite]: #739
-#384 := [monotonicity #399 #740]: #741
-#390 := [trans #384 #388]: #389
-#685 := [monotonicity #390 #591]: #681
-#663 := [trans #685 #674]: #666
-#678 := [monotonicity #663]: #673
-#669 := [trans #678 #668]: #673
-#677 := [quant-inst #70 #9]: #676
-#670 := [mp #677 #669]: #675
-[unit-resolution #670 #90 #756]: false
-unsat
-b727e2bb2818b6309ef23720490cb0c379a73f89 332 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#20 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#18 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#19 := (f4 f5 #18)
-#21 := (f3 #19 #20)
-#753 := (pattern #21)
-#22 := 0::Int
-#97 := -1::Int
-#101 := (* -1::Int #20)
-#98 := (* -1::Int #18)
-#104 := (div #98 #101)
-#255 := (* -1::Int #104)
-#256 := (+ #21 #255)
-#257 := (= #256 0::Int)
-#32 := (div #18 #20)
-#252 := (* -1::Int #32)
-#253 := (+ #21 #252)
-#254 := (= #253 0::Int)
-#130 := (>= #18 0::Int)
-#123 := (<= #20 0::Int)
-#215 := (or #123 #130)
-#216 := (not #215)
-#119 := (<= #18 0::Int)
-#213 := (or #119 #123)
-#214 := (not #213)
-#219 := (or #214 #216)
-#258 := (ite #219 #254 #257)
-#251 := (= #21 0::Int)
-#24 := (= #20 0::Int)
-#23 := (= #18 0::Int)
-#25 := (or #23 #24)
-#259 := (ite #25 #251 #258)
-#754 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #753) #259)
-#262 := (forall (vars (?v0 Int) (?v1 Int)) #259)
-#757 := (iff #262 #754)
-#755 := (iff #259 #259)
-#756 := [refl]: #755
-#758 := [quant-intro #756]: #757
-#222 := (ite #219 #32 #104)
-#225 := (ite #25 0::Int #222)
-#228 := (= #21 #225)
-#231 := (forall (vars (?v0 Int) (?v1 Int)) #228)
-#263 := (iff #231 #262)
-#260 := (iff #228 #259)
-#261 := [rewrite]: #260
-#264 := [quant-intro #261]: #263
-#131 := (not #130)
-#124 := (not #123)
-#134 := (and #124 #131)
-#120 := (not #119)
-#127 := (and #120 #124)
-#137 := (or #127 #134)
-#140 := (ite #137 #32 #104)
-#143 := (ite #25 0::Int #140)
-#146 := (= #21 #143)
-#149 := (forall (vars (?v0 Int) (?v1 Int)) #146)
-#232 := (iff #149 #231)
-#229 := (iff #146 #228)
-#226 := (= #143 #225)
-#223 := (= #140 #222)
-#220 := (iff #137 #219)
-#217 := (iff #134 #216)
-#218 := [rewrite]: #217
-#207 := (iff #127 #214)
-#208 := [rewrite]: #207
-#221 := [monotonicity #208 #218]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [quant-intro #230]: #232
-#211 := (~ #149 #149)
-#209 := (~ #146 #146)
-#210 := [refl]: #209
-#212 := [nnf-pos #210]: #211
-#34 := (- #20)
-#33 := (- #18)
-#35 := (div #33 #34)
-#27 := (< 0::Int #20)
-#29 := (< #18 0::Int)
-#30 := (and #29 #27)
-#26 := (< 0::Int #18)
-#28 := (and #26 #27)
-#31 := (or #28 #30)
-#36 := (ite #31 #32 #35)
-#37 := (ite #25 0::Int #36)
-#38 := (= #21 #37)
-#39 := (forall (vars (?v0 Int) (?v1 Int)) #38)
-#152 := (iff #39 #149)
-#90 := (and #27 #29)
-#94 := (or #28 #90)
-#107 := (ite #94 #32 #104)
-#110 := (ite #25 0::Int #107)
-#113 := (= #21 #110)
-#116 := (forall (vars (?v0 Int) (?v1 Int)) #113)
-#150 := (iff #116 #149)
-#147 := (iff #113 #146)
-#144 := (= #110 #143)
-#141 := (= #107 #140)
-#138 := (iff #94 #137)
-#135 := (iff #90 #134)
-#132 := (iff #29 #131)
-#133 := [rewrite]: #132
-#125 := (iff #27 #124)
-#126 := [rewrite]: #125
-#136 := [monotonicity #126 #133]: #135
-#128 := (iff #28 #127)
-#121 := (iff #26 #120)
-#122 := [rewrite]: #121
-#129 := [monotonicity #122 #126]: #128
-#139 := [monotonicity #129 #136]: #138
-#142 := [monotonicity #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [monotonicity #145]: #147
-#151 := [quant-intro #148]: #150
-#117 := (iff #39 #116)
-#114 := (iff #38 #113)
-#111 := (= #37 #110)
-#108 := (= #36 #107)
-#105 := (= #35 #104)
-#102 := (= #34 #101)
-#103 := [rewrite]: #102
-#99 := (= #33 #98)
-#100 := [rewrite]: #99
-#106 := [monotonicity #100 #103]: #105
-#95 := (iff #31 #94)
-#92 := (iff #30 #90)
-#93 := [rewrite]: #92
-#96 := [monotonicity #93]: #95
-#109 := [monotonicity #96 #106]: #108
-#112 := [monotonicity #109]: #111
-#115 := [monotonicity #112]: #114
-#118 := [quant-intro #115]: #117
-#153 := [trans #118 #151]: #152
-#89 := [asserted]: #39
-#154 := [mp #89 #153]: #149
-#203 := [mp~ #154 #212]: #149
-#234 := [mp #203 #233]: #231
-#265 := [mp #234 #264]: #262
-#759 := [mp #265 #758]: #754
-#80 := -2::Int
-#12 := 3::Int
-#71 := -5::Int
-#74 := (f4 f5 -5::Int)
-#77 := (f3 #74 3::Int)
-#83 := (= #77 -2::Int)
-#86 := (not #83)
-#14 := 2::Int
-#15 := (- 2::Int)
-#9 := 5::Int
-#10 := (- 5::Int)
-#11 := (f4 f5 #10)
-#13 := (f3 #11 3::Int)
-#16 := (= #13 #15)
-#17 := (not #16)
-#87 := (iff #17 #86)
-#84 := (iff #16 #83)
-#81 := (= #15 -2::Int)
-#82 := [rewrite]: #81
-#78 := (= #13 #77)
-#75 := (= #11 #74)
-#72 := (= #10 -5::Int)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#79 := [monotonicity #76]: #78
-#85 := [monotonicity #79 #82]: #84
-#88 := [monotonicity #85]: #87
-#70 := [asserted]: #17
-#91 := [mp #70 #88]: #86
-#658 := (not #754)
-#659 := (or #658 #83)
-#339 := (* -1::Int 3::Int)
-#424 := (* -1::Int -5::Int)
-#425 := (div #424 #339)
-#426 := (* -1::Int #425)
-#417 := (+ #77 #426)
-#428 := (= #417 0::Int)
-#429 := (div -5::Int 3::Int)
-#357 := (* -1::Int #429)
-#430 := (+ #77 #357)
-#427 := (= #430 0::Int)
-#431 := (>= -5::Int 0::Int)
-#410 := (<= 3::Int 0::Int)
-#745 := (or #410 #431)
-#747 := (not #745)
-#404 := (<= -5::Int 0::Int)
-#534 := (or #404 #410)
-#741 := (not #534)
-#415 := (or #741 #747)
-#416 := (ite #415 #427 #428)
-#748 := (= #77 0::Int)
-#749 := (= 3::Int 0::Int)
-#750 := (= -5::Int 0::Int)
-#751 := (or #750 #749)
-#746 := (ite #751 #748 #416)
-#661 := (or #658 #746)
-#663 := (iff #661 #659)
-#660 := (iff #659 #659)
-#665 := [rewrite]: #660
-#667 := (iff #746 #83)
-#681 := (ite false #748 #83)
-#672 := (iff #681 #83)
-#673 := [rewrite]: #672
-#670 := (iff #746 #681)
-#680 := (iff #416 #83)
-#687 := (= #77 -1::Int)
-#1 := true
-#669 := (ite true #83 #687)
-#678 := (iff #669 #83)
-#679 := [rewrite]: #678
-#666 := (iff #416 #669)
-#675 := (iff #428 #687)
-#537 := 1::Int
-#588 := (+ 1::Int #77)
-#592 := (= #588 0::Int)
-#684 := (iff #592 #687)
-#688 := [rewrite]: #684
-#593 := (iff #428 #592)
-#590 := (= #417 #588)
-#686 := (+ #77 1::Int)
-#589 := (= #686 #588)
-#582 := [rewrite]: #589
-#571 := (= #417 #686)
-#682 := (= #426 1::Int)
-#576 := (* -1::Int -1::Int)
-#685 := (= #576 1::Int)
-#587 := [rewrite]: #685
-#577 := (= #426 #576)
-#691 := (= #425 -1::Int)
-#704 := -3::Int
-#536 := (div 5::Int -3::Int)
-#692 := (= #536 -1::Int)
-#693 := [rewrite]: #692
-#689 := (= #425 #536)
-#533 := (= #339 -3::Int)
-#535 := [rewrite]: #533
-#703 := (= #424 5::Int)
-#697 := [rewrite]: #703
-#690 := [monotonicity #697 #535]: #689
-#694 := [trans #690 #693]: #691
-#578 := [monotonicity #694]: #577
-#683 := [trans #578 #587]: #682
-#586 := [monotonicity #683]: #571
-#591 := [trans #586 #582]: #590
-#594 := [monotonicity #591]: #593
-#677 := [trans #594 #688]: #675
-#696 := (iff #427 #83)
-#707 := (+ 2::Int #77)
-#698 := (= #707 0::Int)
-#701 := (iff #698 #83)
-#695 := [rewrite]: #701
-#699 := (iff #427 #698)
-#555 := (= #430 #707)
-#706 := (+ #77 2::Int)
-#713 := (= #706 #707)
-#554 := [rewrite]: #713
-#711 := (= #430 #706)
-#710 := (= #357 2::Int)
-#718 := (* -1::Int -2::Int)
-#708 := (= #718 2::Int)
-#709 := [rewrite]: #708
-#715 := (= #357 #718)
-#432 := (= #429 -2::Int)
-#714 := [rewrite]: #432
-#719 := [monotonicity #714]: #715
-#705 := [trans #719 #709]: #710
-#712 := [monotonicity #705]: #711
-#556 := [trans #712 #554]: #555
-#700 := [monotonicity #556]: #699
-#702 := [trans #700 #695]: #696
-#716 := (iff #415 true)
-#725 := (or false true)
-#437 := (iff #725 true)
-#438 := [rewrite]: #437
-#435 := (iff #415 #725)
-#724 := (iff #747 true)
-#722 := (not false)
-#446 := (iff #722 true)
-#720 := [rewrite]: #446
-#723 := (iff #747 #722)
-#452 := (iff #745 false)
-#743 := (or false false)
-#387 := (iff #743 false)
-#728 := [rewrite]: #387
-#450 := (iff #745 #743)
-#727 := (iff #431 false)
-#449 := [rewrite]: #727
-#730 := (iff #410 false)
-#731 := [rewrite]: #730
-#451 := [monotonicity #731 #449]: #450
-#345 := [trans #451 #728]: #452
-#445 := [monotonicity #345]: #723
-#721 := [trans #445 #720]: #724
-#740 := (iff #741 false)
-#738 := (not true)
-#739 := (iff #738 false)
-#737 := [rewrite]: #739
-#378 := (iff #741 #738)
-#373 := (iff #534 true)
-#732 := (or true false)
-#729 := (iff #732 true)
-#735 := [rewrite]: #729
-#733 := (iff #534 #732)
-#393 := (iff #404 true)
-#394 := [rewrite]: #393
-#734 := [monotonicity #394 #731]: #733
-#736 := [trans #734 #735]: #373
-#379 := [monotonicity #736]: #378
-#726 := [trans #379 #737]: #740
-#436 := [monotonicity #726 #721]: #435
-#717 := [trans #436 #438]: #716
-#668 := [monotonicity #717 #702 #677]: #666
-#676 := [trans #668 #679]: #680
-#391 := (iff #751 false)
-#403 := (iff #751 #743)
-#402 := (iff #749 false)
-#407 := [rewrite]: #402
-#752 := (iff #750 false)
-#742 := [rewrite]: #752
-#744 := [monotonicity #742 #407]: #403
-#392 := [trans #744 #728]: #391
-#671 := [monotonicity #392 #676]: #670
-#674 := [trans #671 #673]: #667
-#664 := [monotonicity #674]: #663
-#651 := [trans #664 #665]: #663
-#662 := [quant-inst #71 #12]: #661
-#652 := [mp #662 #651]: #659
-[unit-resolution #652 #91 #759]: false
-unsat
-6a8f77a157d7a4aa5835bfb290984ca56f4fde4e 345 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#20 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#18 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#19 := (f4 f5 #18)
-#21 := (f3 #19 #20)
-#777 := (pattern #21)
-#15 := 0::Int
-#70 := -1::Int
-#120 := (* -1::Int #20)
-#117 := (* -1::Int #18)
-#123 := (div #117 #120)
-#280 := (* -1::Int #123)
-#281 := (+ #21 #280)
-#282 := (= #281 0::Int)
-#31 := (div #18 #20)
-#277 := (* -1::Int #31)
-#278 := (+ #21 #277)
-#279 := (= #278 0::Int)
-#155 := (>= #18 0::Int)
-#148 := (<= #20 0::Int)
-#240 := (or #148 #155)
-#241 := (not #240)
-#144 := (<= #18 0::Int)
-#238 := (or #144 #148)
-#239 := (not #238)
-#244 := (or #239 #241)
-#283 := (ite #244 #279 #282)
-#276 := (= #21 0::Int)
-#23 := (= #20 0::Int)
-#22 := (= #18 0::Int)
-#24 := (or #22 #23)
-#284 := (ite #24 #276 #283)
-#778 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #777) #284)
-#287 := (forall (vars (?v0 Int) (?v1 Int)) #284)
-#781 := (iff #287 #778)
-#779 := (iff #284 #284)
-#780 := [refl]: #779
-#782 := [quant-intro #780]: #781
-#247 := (ite #244 #31 #123)
-#250 := (ite #24 0::Int #247)
-#253 := (= #21 #250)
-#256 := (forall (vars (?v0 Int) (?v1 Int)) #253)
-#288 := (iff #256 #287)
-#285 := (iff #253 #284)
-#286 := [rewrite]: #285
-#289 := [quant-intro #286]: #288
-#156 := (not #155)
-#149 := (not #148)
-#159 := (and #149 #156)
-#145 := (not #144)
-#152 := (and #145 #149)
-#162 := (or #152 #159)
-#165 := (ite #162 #31 #123)
-#168 := (ite #24 0::Int #165)
-#171 := (= #21 #168)
-#174 := (forall (vars (?v0 Int) (?v1 Int)) #171)
-#257 := (iff #174 #256)
-#254 := (iff #171 #253)
-#251 := (= #168 #250)
-#248 := (= #165 #247)
-#245 := (iff #162 #244)
-#242 := (iff #159 #241)
-#243 := [rewrite]: #242
-#232 := (iff #152 #239)
-#233 := [rewrite]: #232
-#246 := [monotonicity #233 #243]: #245
-#249 := [monotonicity #246]: #248
-#252 := [monotonicity #249]: #251
-#255 := [monotonicity #252]: #254
-#258 := [quant-intro #255]: #257
-#236 := (~ #174 #174)
-#234 := (~ #171 #171)
-#235 := [refl]: #234
-#237 := [nnf-pos #235]: #236
-#33 := (- #20)
-#32 := (- #18)
-#34 := (div #32 #33)
-#26 := (< 0::Int #20)
-#28 := (< #18 0::Int)
-#29 := (and #28 #26)
-#25 := (< 0::Int #18)
-#27 := (and #25 #26)
-#30 := (or #27 #29)
-#35 := (ite #30 #31 #34)
-#36 := (ite #24 0::Int #35)
-#37 := (= #21 #36)
-#38 := (forall (vars (?v0 Int) (?v1 Int)) #37)
-#177 := (iff #38 #174)
-#111 := (and #26 #28)
-#114 := (or #27 #111)
-#126 := (ite #114 #31 #123)
-#105 := (= 0::Int #20)
-#102 := (= 0::Int #18)
-#108 := (or #102 #105)
-#129 := (ite #108 0::Int #126)
-#132 := (= #21 #129)
-#135 := (forall (vars (?v0 Int) (?v1 Int)) #132)
-#175 := (iff #135 #174)
-#172 := (iff #132 #171)
-#169 := (= #129 #168)
-#166 := (= #126 #165)
-#163 := (iff #114 #162)
-#160 := (iff #111 #159)
-#157 := (iff #28 #156)
-#158 := [rewrite]: #157
-#150 := (iff #26 #149)
-#151 := [rewrite]: #150
-#161 := [monotonicity #151 #158]: #160
-#153 := (iff #27 #152)
-#146 := (iff #25 #145)
-#147 := [rewrite]: #146
-#154 := [monotonicity #147 #151]: #153
-#164 := [monotonicity #154 #161]: #163
-#167 := [monotonicity #164]: #166
-#142 := (iff #108 #24)
-#140 := (iff #105 #23)
-#141 := [rewrite]: #140
-#138 := (iff #102 #22)
-#139 := [rewrite]: #138
-#143 := [monotonicity #139 #141]: #142
-#170 := [monotonicity #143 #167]: #169
-#173 := [monotonicity #170]: #172
-#176 := [quant-intro #173]: #175
-#136 := (iff #38 #135)
-#133 := (iff #37 #132)
-#130 := (= #36 #129)
-#127 := (= #35 #126)
-#124 := (= #34 #123)
-#121 := (= #33 #120)
-#122 := [rewrite]: #121
-#118 := (= #32 #117)
-#119 := [rewrite]: #118
-#125 := [monotonicity #119 #122]: #124
-#115 := (iff #30 #114)
-#112 := (iff #29 #111)
-#113 := [rewrite]: #112
-#116 := [monotonicity #113]: #115
-#128 := [monotonicity #116 #125]: #127
-#109 := (iff #24 #108)
-#106 := (iff #23 #105)
-#107 := [rewrite]: #106
-#103 := (iff #22 #102)
-#104 := [rewrite]: #103
-#110 := [monotonicity #104 #107]: #109
-#131 := [monotonicity #110 #128]: #130
-#134 := [monotonicity #131]: #133
-#137 := [quant-intro #134]: #136
-#178 := [trans #137 #176]: #177
-#101 := [asserted]: #38
-#179 := [mp #101 #178]: #174
-#228 := [mp~ #179 #237]: #174
-#259 := [mp #228 #258]: #256
-#290 := [mp #259 #289]: #287
-#783 := [mp #290 #782]: #778
-#76 := -3::Int
-#73 := (f4 f5 -1::Int)
-#79 := (f3 #73 -3::Int)
-#82 := (= #79 0::Int)
-#95 := (not #82)
-#12 := 3::Int
-#13 := (- 3::Int)
-#9 := 1::Int
-#10 := (- 1::Int)
-#11 := (f4 f5 #10)
-#14 := (f3 #11 #13)
-#16 := (= #14 0::Int)
-#17 := (not #16)
-#98 := (iff #17 #95)
-#85 := (= 0::Int #79)
-#90 := (not #85)
-#96 := (iff #90 #95)
-#93 := (iff #85 #82)
-#94 := [rewrite]: #93
-#97 := [monotonicity #94]: #96
-#91 := (iff #17 #90)
-#88 := (iff #16 #85)
-#86 := (iff #82 #85)
-#87 := [rewrite]: #86
-#83 := (iff #16 #82)
-#80 := (= #14 #79)
-#77 := (= #13 -3::Int)
-#78 := [rewrite]: #77
-#74 := (= #11 #73)
-#71 := (= #10 -1::Int)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#81 := [monotonicity #75 #78]: #80
-#84 := [monotonicity #81]: #83
-#89 := [trans #84 #87]: #88
-#92 := [monotonicity #89]: #91
-#99 := [trans #92 #97]: #98
-#69 := [asserted]: #17
-#100 := [mp #69 #99]: #95
-#702 := (not #778)
-#703 := (or #702 #82)
-#364 := (* -1::Int -3::Int)
-#448 := (* -1::Int -1::Int)
-#449 := (div #448 #364)
-#450 := (* -1::Int #449)
-#441 := (+ #79 #450)
-#452 := (= #441 0::Int)
-#453 := (div -1::Int -3::Int)
-#454 := (* -1::Int #453)
-#451 := (+ #79 #454)
-#455 := (= #451 0::Int)
-#434 := (>= -1::Int 0::Int)
-#769 := (<= -3::Int 0::Int)
-#771 := (or #769 #434)
-#428 := (not #771)
-#558 := (<= -1::Int 0::Int)
-#765 := (or #558 #769)
-#439 := (not #765)
-#440 := (or #439 #428)
-#772 := (ite #440 #455 #452)
-#773 := (= -3::Int 0::Int)
-#774 := (= -1::Int 0::Int)
-#775 := (or #774 #773)
-#770 := (ite #775 #82 #772)
-#704 := (or #702 #770)
-#705 := (iff #704 #703)
-#695 := (iff #703 #703)
-#696 := [rewrite]: #695
-#690 := (iff #770 #82)
-#708 := (ite false #82 #82)
-#701 := (iff #708 #82)
-#693 := [rewrite]: #701
-#712 := (iff #770 #708)
-#618 := (iff #772 #82)
-#722 := (= #79 1::Int)
-#606 := (ite false #722 #82)
-#616 := (iff #606 #82)
-#617 := [rewrite]: #616
-#614 := (iff #772 #606)
-#612 := (iff #452 #82)
-#595 := (= #441 #79)
-#709 := (+ #79 0::Int)
-#707 := (= #709 #79)
-#710 := [rewrite]: #707
-#611 := (= #441 #709)
-#602 := (= #450 0::Int)
-#717 := (* -1::Int 0::Int)
-#600 := (= #717 0::Int)
-#601 := [rewrite]: #600
-#715 := (= #450 #717)
-#714 := (= #449 0::Int)
-#728 := (div 1::Int 3::Int)
-#560 := (= #728 0::Int)
-#713 := [rewrite]: #560
-#557 := (= #449 #728)
-#727 := (= #364 3::Int)
-#721 := [rewrite]: #727
-#720 := (= #448 1::Int)
-#726 := [rewrite]: #720
-#559 := [monotonicity #726 #721]: #557
-#716 := [trans #559 #713]: #714
-#718 := [monotonicity #716]: #715
-#561 := [trans #718 #601]: #602
-#706 := [monotonicity #561]: #611
-#610 := [trans #706 #710]: #595
-#613 := [monotonicity #610]: #612
-#725 := (iff #455 #722)
-#730 := (+ -1::Int #79)
-#578 := (= #730 0::Int)
-#723 := (iff #578 #722)
-#724 := [rewrite]: #723
-#579 := (iff #455 #578)
-#731 := (= #451 #730)
-#733 := (+ #79 -1::Int)
-#735 := (= #733 #730)
-#736 := [rewrite]: #735
-#734 := (= #451 #733)
-#743 := (= #454 -1::Int)
-#741 := (* -1::Int 1::Int)
-#742 := (= #741 -1::Int)
-#739 := [rewrite]: #742
-#456 := (= #454 #741)
-#462 := (= #453 1::Int)
-#740 := [rewrite]: #462
-#738 := [monotonicity #740]: #456
-#732 := [trans #738 #739]: #743
-#729 := [monotonicity #732]: #734
-#737 := [trans #729 #736]: #731
-#580 := [monotonicity #737]: #579
-#719 := [trans #580 #724]: #725
-#460 := (iff #440 false)
-#767 := (or false false)
-#411 := (iff #767 false)
-#752 := [rewrite]: #411
-#749 := (iff #440 #767)
-#748 := (iff #428 false)
-#1 := true
-#762 := (not true)
-#763 := (iff #762 false)
-#761 := [rewrite]: #763
-#470 := (iff #428 #762)
-#747 := (iff #771 true)
-#474 := (or true false)
-#370 := (iff #474 true)
-#746 := [rewrite]: #370
-#475 := (iff #771 #474)
-#751 := (iff #434 false)
-#473 := [rewrite]: #751
-#754 := (iff #769 true)
-#755 := [rewrite]: #754
-#476 := [monotonicity #755 #473]: #475
-#469 := [trans #476 #746]: #747
-#744 := [monotonicity #469]: #470
-#745 := [trans #744 #761]: #748
-#764 := (iff #439 false)
-#402 := (iff #439 #762)
-#397 := (iff #765 true)
-#756 := (or true true)
-#753 := (iff #756 true)
-#759 := [rewrite]: #753
-#757 := (iff #765 #756)
-#417 := (iff #558 true)
-#418 := [rewrite]: #417
-#758 := [monotonicity #418 #755]: #757
-#760 := [trans #758 #759]: #397
-#403 := [monotonicity #760]: #402
-#750 := [trans #403 #761]: #764
-#459 := [monotonicity #750 #745]: #749
-#461 := [trans #459 #752]: #460
-#615 := [monotonicity #461 #719 #613]: #614
-#711 := [trans #615 #617]: #618
-#415 := (iff #775 false)
-#427 := (iff #775 #767)
-#426 := (iff #773 false)
-#431 := [rewrite]: #426
-#776 := (iff #774 false)
-#766 := [rewrite]: #776
-#768 := [monotonicity #766 #431]: #427
-#416 := [trans #768 #752]: #415
-#699 := [monotonicity #416 #711]: #712
-#692 := [trans #699 #693]: #690
-#694 := [monotonicity #692]: #705
-#697 := [trans #694 #696]: #705
-#700 := [quant-inst #70 #76]: #704
-#691 := [mp #700 #697]: #703
-[unit-resolution #691 #100 #783]: false
-unsat
-42d7b09a76594ba9de59690fd4e89ad80ae41c2d 314 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#18 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#16 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#17 := (f4 f5 #16)
-#19 := (f3 #17 #18)
-#759 := (pattern #19)
-#20 := 0::Int
-#104 := -1::Int
-#108 := (* -1::Int #18)
-#105 := (* -1::Int #16)
-#111 := (div #105 #108)
-#262 := (* -1::Int #111)
-#263 := (+ #19 #262)
-#264 := (= #263 0::Int)
-#30 := (div #16 #18)
-#259 := (* -1::Int #30)
-#260 := (+ #19 #259)
-#261 := (= #260 0::Int)
-#137 := (>= #16 0::Int)
-#130 := (<= #18 0::Int)
-#222 := (or #130 #137)
-#223 := (not #222)
-#126 := (<= #16 0::Int)
-#220 := (or #126 #130)
-#221 := (not #220)
-#226 := (or #221 #223)
-#265 := (ite #226 #261 #264)
-#258 := (= #19 0::Int)
-#22 := (= #18 0::Int)
-#21 := (= #16 0::Int)
+#73 := (iff #16 #72)
+#70 := (iff #15 #69)
+#67 := (= #14 -2::Int)
+#68 := [rewrite]: #67
+#64 := (= #12 #63)
+#61 := (= #10 #60)
+#58 := (= #9 -5::Int)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#65 := [monotonicity #62]: #64
+#71 := [monotonicity #65 #68]: #70
+#74 := [monotonicity #71]: #73
+#51 := [asserted]: #16
+#75 := [mp #51 #74]: #72
+#611 := (not #707)
+#612 := (or #611 #69)
+#369 := (* -1::Int 3::Int)
+#368 := (* -1::Int -5::Int)
+#701 := (div #368 #369)
+#702 := (* -1::Int #701)
+#703 := (+ #63 #702)
+#704 := (= #703 0::Int)
+#700 := (div -5::Int 3::Int)
+#357 := (* -1::Int #700)
+#487 := (+ #63 #357)
+#694 := (= #487 0::Int)
+#381 := (<= 3::Int 0::Int)
+#380 := (>= -5::Int 0::Int)
+#384 := (or #380 #381)
+#363 := (not #384)
+#370 := (<= -5::Int 0::Int)
+#382 := (or #370 #381)
+#383 := (not #382)
+#698 := (or #383 #363)
+#699 := (if #698 #694 #704)
+#379 := (= #63 0::Int)
+#377 := (= 3::Int 0::Int)
+#292 := (= -5::Int 0::Int)
+#378 := (or #292 #377)
+#705 := (if #378 #379 #699)
+#614 := (or #611 #705)
+#616 := (iff #614 #612)
+#613 := (iff #612 #612)
+#618 := [rewrite]: #613
+#620 := (iff #705 #69)
+#634 := (if false #379 #69)
+#625 := (iff #634 #69)
+#626 := [rewrite]: #625
+#623 := (iff #705 #634)
+#633 := (iff #699 #69)
+#640 := (= #63 -1::Int)
+#1 := true
+#622 := (if true #69 #640)
+#631 := (iff #622 #69)
+#632 := [rewrite]: #631
+#619 := (iff #699 #622)
+#628 := (iff #704 #640)
+#310 := 1::Int
+#541 := (+ 1::Int #63)
+#545 := (= #541 0::Int)
+#637 := (iff #545 #640)
+#641 := [rewrite]: #637
+#546 := (iff #704 #545)
+#543 := (= #703 #541)
+#639 := (+ #63 1::Int)
+#542 := (= #639 #541)
+#535 := [rewrite]: #542
+#524 := (= #703 #639)
+#635 := (= #702 1::Int)
+#530 := (* -1::Int -1::Int)
+#638 := (= #530 1::Int)
+#540 := [rewrite]: #638
+#531 := (= #702 #530)
+#647 := (= #701 -1::Int)
+#486 := -3::Int
+#642 := (div 5::Int -3::Int)
+#646 := (= #642 -1::Int)
+#644 := [rewrite]: #646
+#643 := (= #701 #642)
+#488 := (= #369 -3::Int)
+#489 := [rewrite]: #488
+#650 := (= #368 5::Int)
+#657 := [rewrite]: #650
+#645 := [monotonicity #657 #489]: #643
+#529 := [trans #645 #644]: #647
+#490 := [monotonicity #529]: #531
+#636 := [trans #490 #540]: #635
+#539 := [monotonicity #636]: #524
+#544 := [trans #539 #535]: #543
+#547 := [monotonicity #544]: #546
+#630 := [trans #547 #641]: #628
+#655 := (iff #694 #69)
+#666 := (+ 2::Int #63)
+#652 := (= #666 0::Int)
+#648 := (iff #652 #69)
+#649 := [rewrite]: #648
+#653 := (iff #694 #652)
+#509 := (= #487 #666)
+#664 := (+ #63 2::Int)
+#507 := (= #664 #666)
+#508 := [rewrite]: #507
+#665 := (= #487 #664)
+#658 := (= #357 2::Int)
+#668 := (* -1::Int -2::Int)
+#662 := (= #668 2::Int)
+#663 := [rewrite]: #662
+#672 := (= #357 #668)
+#667 := (= #700 -2::Int)
+#671 := [rewrite]: #667
+#661 := [monotonicity #671]: #672
+#659 := [trans #661 #663]: #658
+#660 := [monotonicity #659]: #665
+#651 := [trans #660 #508]: #509
+#654 := [monotonicity #651]: #653
+#656 := [trans #654 #649]: #655
+#670 := (iff #698 true)
+#388 := (or false true)
+#391 := (iff #388 true)
+#669 := [rewrite]: #391
+#389 := (iff #698 #388)
+#674 := (iff #363 true)
+#676 := (not false)
+#673 := (iff #676 true)
+#677 := [rewrite]: #673
+#398 := (iff #363 #676)
+#298 := (iff #384 false)
+#356 := (or false false)
+#681 := (iff #356 false)
+#344 := [rewrite]: #681
+#404 := (iff #384 #356)
+#684 := (iff #381 false)
+#685 := [rewrite]: #684
+#402 := (iff #380 false)
+#403 := [rewrite]: #402
+#405 := [monotonicity #403 #685]: #404
+#675 := [trans #405 #344]: #298
+#399 := [monotonicity #675]: #398
+#678 := [trans #399 #677]: #674
+#679 := (iff #383 false)
+#331 := (not true)
+#690 := (iff #331 false)
+#693 := [rewrite]: #690
+#332 := (iff #383 #331)
+#689 := (iff #382 true)
+#686 := (or true false)
+#688 := (iff #686 true)
+#326 := [rewrite]: #688
+#687 := (iff #382 #686)
+#347 := (iff #370 true)
+#683 := [rewrite]: #347
+#682 := [monotonicity #683 #685]: #687
+#691 := [trans #682 #326]: #689
+#692 := [monotonicity #691]: #332
+#680 := [trans #692 #693]: #679
+#390 := [monotonicity #680 #678]: #389
+#385 := [trans #390 #669]: #670
+#621 := [monotonicity #385 #656 #630]: #619
+#629 := [trans #621 #632]: #633
+#345 := (iff #378 false)
+#697 := (iff #378 #356)
+#360 := (iff #377 false)
+#696 := [rewrite]: #360
+#695 := (iff #292 false)
+#355 := [rewrite]: #695
+#340 := [monotonicity #355 #696]: #697
+#346 := [trans #340 #344]: #345
+#624 := [monotonicity #346 #629]: #623
+#627 := [trans #624 #626]: #620
+#617 := [monotonicity #627]: #616
+#604 := [trans #617 #618]: #616
+#615 := [quant-inst #57 #11]: #614
+#605 := [mp #615 #604]: #612
+[unit-resolution #605 #75 #712]: false
+b9e2cb2587eedfa83c2fb391ad520d91b8574998 328 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#19 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#17 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#18 := (f4 f5 #17)
+#20 := (f3 #18 #19)
+#703 := (pattern #20)
+#14 := 0::Int
+#56 := -1::Int
+#104 := (* -1::Int #19)
+#101 := (* -1::Int #17)
+#107 := (div #101 #104)
+#263 := (* -1::Int #107)
+#264 := (+ #20 #263)
+#265 := (= #264 0::Int)
+#30 := (div #17 #19)
+#260 := (* -1::Int #30)
+#261 := (+ #20 #260)
+#262 := (= #261 0::Int)
+#79 := (<= #19 0::Int)
+#170 := (>= #17 0::Int)
+#223 := (or #170 #79)
+#224 := (not #223)
+#75 := (<= #17 0::Int)
+#219 := (or #75 #79)
+#220 := (not #219)
+#227 := (or #220 #224)
+#266 := (if #227 #262 #265)
+#259 := (= #20 0::Int)
+#22 := (= #19 0::Int)
+#21 := (= #17 0::Int)
 #23 := (or #21 #22)
-#266 := (ite #23 #258 #265)
-#760 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #759) #266)
-#269 := (forall (vars (?v0 Int) (?v1 Int)) #266)
-#763 := (iff #269 #760)
-#761 := (iff #266 #266)
-#762 := [refl]: #761
-#764 := [quant-intro #762]: #763
-#229 := (ite #226 #30 #111)
-#232 := (ite #23 0::Int #229)
-#235 := (= #19 #232)
-#238 := (forall (vars (?v0 Int) (?v1 Int)) #235)
-#270 := (iff #238 #269)
-#267 := (iff #235 #266)
-#268 := [rewrite]: #267
-#271 := [quant-intro #268]: #270
-#138 := (not #137)
-#131 := (not #130)
-#141 := (and #131 #138)
-#127 := (not #126)
-#134 := (and #127 #131)
-#144 := (or #134 #141)
-#147 := (ite #144 #30 #111)
-#150 := (ite #23 0::Int #147)
-#153 := (= #19 #150)
-#156 := (forall (vars (?v0 Int) (?v1 Int)) #153)
-#239 := (iff #156 #238)
-#236 := (iff #153 #235)
-#233 := (= #150 #232)
-#230 := (= #147 #229)
-#227 := (iff #144 #226)
-#224 := (iff #141 #223)
-#225 := [rewrite]: #224
-#214 := (iff #134 #221)
-#215 := [rewrite]: #214
-#228 := [monotonicity #215 #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [monotonicity #234]: #236
-#240 := [quant-intro #237]: #239
-#218 := (~ #156 #156)
-#216 := (~ #153 #153)
-#217 := [refl]: #216
-#219 := [nnf-pos #217]: #218
-#32 := (- #18)
-#31 := (- #16)
+#267 := (if #23 #259 #266)
+#704 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #703) #267)
+#270 := (forall (vars (?v0 Int) (?v1 Int)) #267)
+#707 := (iff #270 #704)
+#705 := (iff #267 #267)
+#706 := [refl]: #705
+#708 := [quant-intro #706]: #707
+#230 := (if #227 #30 #107)
+#233 := (if #23 0::Int #230)
+#236 := (= #20 #233)
+#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
+#271 := (iff #239 #270)
+#268 := (iff #236 #267)
+#269 := [rewrite]: #268
+#272 := [quant-intro #269]: #271
+#80 := (not #79)
+#173 := (not #170)
+#176 := (and #173 #80)
+#76 := (not #75)
+#83 := (and #76 #80)
+#179 := (or #83 #176)
+#182 := (if #179 #30 #107)
+#185 := (if #23 0::Int #182)
+#188 := (= #20 #185)
+#191 := (forall (vars (?v0 Int) (?v1 Int)) #188)
+#240 := (iff #191 #239)
+#237 := (iff #188 #236)
+#234 := (= #185 #233)
+#231 := (= #182 #230)
+#228 := (iff #179 #227)
+#225 := (iff #176 #224)
+#226 := [rewrite]: #225
+#221 := (iff #83 #220)
+#222 := [rewrite]: #221
+#229 := [monotonicity #222 #226]: #228
+#232 := [monotonicity #229]: #231
+#235 := [monotonicity #232]: #234
+#238 := [monotonicity #235]: #237
+#241 := [quant-intro #238]: #240
+#211 := (~ #191 #191)
+#213 := (~ #188 #188)
+#214 := [refl]: #213
+#212 := [nnf-pos #214]: #211
+#86 := (<= 0::Int #17)
+#87 := (not #86)
+#95 := (and #87 #80)
+#98 := (or #83 #95)
+#110 := (if #98 #30 #107)
+#113 := (if #23 0::Int #110)
+#116 := (= #20 #113)
+#119 := (forall (vars (?v0 Int) (?v1 Int)) #116)
+#192 := (iff #119 #191)
+#189 := (iff #116 #188)
+#186 := (= #113 #185)
+#183 := (= #110 #182)
+#180 := (iff #98 #179)
+#177 := (iff #95 #176)
+#174 := (iff #87 #173)
+#171 := (iff #86 #170)
+#172 := [rewrite]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [monotonicity #178]: #180
+#184 := [monotonicity #181]: #183
+#187 := [monotonicity #184]: #186
+#190 := [monotonicity #187]: #189
+#193 := [quant-intro #190]: #192
+#32 := (- #19)
+#31 := (- #17)
 #33 := (div #31 #32)
-#25 := (< 0::Int #18)
-#27 := (< #16 0::Int)
+#25 := (< 0::Int #19)
+#27 := (< #17 0::Int)
 #28 := (and #27 #25)
-#24 := (< 0::Int #16)
+#24 := (< 0::Int #17)
 #26 := (and #24 #25)
 #29 := (or #26 #28)
-#34 := (ite #29 #30 #33)
-#35 := (ite #23 0::Int #34)
-#36 := (= #19 #35)
+#34 := (if #29 #30 #33)
+#35 := (if #23 0::Int #34)
+#36 := (= #20 #35)
 #37 := (forall (vars (?v0 Int) (?v1 Int)) #36)
-#159 := (iff #37 #156)
-#98 := (and #25 #27)
-#101 := (or #26 #98)
-#114 := (ite #101 #30 #111)
-#117 := (ite #23 0::Int #114)
-#120 := (= #19 #117)
-#123 := (forall (vars (?v0 Int) (?v1 Int)) #120)
-#157 := (iff #123 #156)
-#154 := (iff #120 #153)
-#151 := (= #117 #150)
-#148 := (= #114 #147)
-#145 := (iff #101 #144)
-#142 := (iff #98 #141)
-#139 := (iff #27 #138)
-#140 := [rewrite]: #139
-#132 := (iff #25 #131)
-#133 := [rewrite]: #132
-#143 := [monotonicity #133 #140]: #142
-#135 := (iff #26 #134)
-#128 := (iff #24 #127)
-#129 := [rewrite]: #128
-#136 := [monotonicity #129 #133]: #135
-#146 := [monotonicity #136 #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [monotonicity #149]: #151
-#155 := [monotonicity #152]: #154
-#158 := [quant-intro #155]: #157
-#124 := (iff #37 #123)
-#121 := (iff #36 #120)
-#118 := (= #35 #117)
-#115 := (= #34 #114)
-#112 := (= #33 #111)
-#109 := (= #32 #108)
-#110 := [rewrite]: #109
-#106 := (= #31 #105)
-#107 := [rewrite]: #106
-#113 := [monotonicity #107 #110]: #112
-#102 := (iff #29 #101)
-#99 := (iff #28 #98)
-#100 := [rewrite]: #99
-#103 := [monotonicity #100]: #102
-#116 := [monotonicity #103 #113]: #115
-#119 := [monotonicity #116]: #118
-#122 := [monotonicity #119]: #121
-#125 := [quant-intro #122]: #124
-#160 := [trans #125 #158]: #159
-#97 := [asserted]: #37
-#161 := [mp #97 #160]: #156
-#210 := [mp~ #161 #219]: #156
-#241 := [mp #210 #240]: #238
-#272 := [mp #241 #271]: #269
-#765 := [mp #272 #764]: #760
-#13 := 1::Int
-#69 := -3::Int
-#72 := (f4 f5 -3::Int)
-#75 := (f3 #72 -3::Int)
-#78 := (= #75 1::Int)
-#91 := (not #78)
-#9 := 3::Int
-#10 := (- 3::Int)
-#11 := (f4 f5 #10)
-#12 := (f3 #11 #10)
-#14 := (= #12 1::Int)
-#15 := (not #14)
-#94 := (iff #15 #91)
-#81 := (= 1::Int #75)
-#86 := (not #81)
-#92 := (iff #86 #91)
-#89 := (iff #81 #78)
-#90 := [rewrite]: #89
-#93 := [monotonicity #90]: #92
-#87 := (iff #15 #86)
-#84 := (iff #14 #81)
-#82 := (iff #78 #81)
-#83 := [rewrite]: #82
-#79 := (iff #14 #78)
-#76 := (= #12 #75)
-#70 := (= #10 -3::Int)
-#71 := [rewrite]: #70
-#73 := (= #11 #72)
-#74 := [monotonicity #71]: #73
-#77 := [monotonicity #74 #71]: #76
-#80 := [monotonicity #77]: #79
-#85 := [trans #80 #83]: #84
-#88 := [monotonicity #85]: #87
-#95 := [trans #88 #93]: #94
-#68 := [asserted]: #15
-#96 := [mp #68 #95]: #91
-#596 := (not #760)
-#597 := (or #596 #78)
-#346 := (* -1::Int -3::Int)
-#430 := (div #346 #346)
-#431 := (* -1::Int #430)
-#432 := (+ #75 #431)
-#423 := (= #432 0::Int)
-#434 := (div -3::Int -3::Int)
-#435 := (* -1::Int #434)
-#436 := (+ #75 #435)
-#433 := (= #436 0::Int)
-#437 := (>= -3::Int 0::Int)
-#416 := (<= -3::Int 0::Int)
-#751 := (or #416 #437)
-#753 := (not #751)
-#410 := (or #416 #416)
-#540 := (not #410)
-#747 := (or #540 #753)
-#421 := (ite #747 #433 #423)
-#422 := (= #75 0::Int)
-#754 := (= -3::Int 0::Int)
-#755 := (or #754 #754)
-#756 := (ite #755 #422 #421)
-#598 := (or #596 #756)
-#600 := (iff #598 #597)
-#690 := (iff #597 #597)
-#694 := [rewrite]: #690
-#595 := (iff #756 #78)
-#689 := (ite false #422 #78)
-#592 := (iff #689 #78)
-#594 := [rewrite]: #592
-#692 := (iff #756 #689)
-#593 := (iff #421 #78)
-#582 := (ite false #78 #78)
-#543 := (iff #582 #78)
-#691 := [rewrite]: #543
-#583 := (iff #421 #582)
-#697 := (iff #423 #78)
-#721 := (+ -1::Int #75)
-#711 := (= #721 0::Int)
-#718 := (iff #711 #78)
-#713 := [rewrite]: #718
-#698 := (iff #423 #711)
-#695 := (= #432 #721)
-#438 := (+ #75 -1::Int)
-#725 := (= #438 #721)
-#714 := [rewrite]: #725
-#541 := (= #432 #438)
-#710 := (= #431 -1::Int)
-#731 := (* -1::Int 1::Int)
-#443 := (= #731 -1::Int)
-#444 := [rewrite]: #443
-#709 := (= #431 #731)
-#702 := (= #430 1::Int)
-#704 := (div 3::Int 3::Int)
-#707 := (= #704 1::Int)
-#701 := [rewrite]: #707
-#705 := (= #430 #704)
-#561 := (= #346 3::Int)
-#562 := [rewrite]: #561
-#706 := [monotonicity #562 #562]: #705
-#708 := [trans #706 #701]: #702
-#703 := [monotonicity #708]: #709
-#539 := [trans #703 #444]: #710
-#542 := [monotonicity #539]: #541
-#696 := [trans #542 #714]: #695
-#699 := [monotonicity #696]: #698
-#700 := [trans #699 #713]: #697
-#719 := (iff #433 #78)
-#712 := (iff #433 #711)
-#715 := (= #436 #721)
-#720 := (= #436 #438)
-#722 := (= #435 -1::Int)
-#441 := (= #435 #731)
-#730 := (= #434 1::Int)
-#727 := [rewrite]: #730
-#442 := [monotonicity #727]: #441
-#723 := [trans #442 #444]: #722
-#724 := [monotonicity #723]: #720
-#716 := [trans #724 #714]: #715
-#717 := [monotonicity #716]: #712
-#560 := [trans #717 #713]: #719
-#452 := (iff #747 false)
-#758 := (or false false)
-#413 := (iff #758 false)
-#749 := [rewrite]: #413
-#729 := (iff #747 #758)
-#352 := (iff #753 false)
-#1 := true
-#739 := (not true)
-#741 := (iff #739 false)
-#379 := [rewrite]: #741
-#457 := (iff #753 #739)
-#455 := (iff #751 true)
-#745 := (or true false)
-#732 := (iff #745 true)
-#733 := [rewrite]: #732
-#743 := (iff #751 #745)
-#384 := (iff #437 false)
-#385 := [rewrite]: #384
-#393 := (iff #416 true)
-#734 := [rewrite]: #393
-#746 := [monotonicity #734 #385]: #743
-#456 := [trans #746 #733]: #455
-#458 := [monotonicity #456]: #457
-#728 := [trans #458 #379]: #352
-#742 := (iff #540 false)
-#740 := (iff #540 #739)
-#737 := (iff #410 true)
-#397 := (or true true)
-#400 := (iff #397 true)
-#736 := [rewrite]: #400
-#398 := (iff #410 #397)
-#399 := [monotonicity #734 #734]: #398
-#738 := [trans #399 #736]: #737
-#735 := [monotonicity #738]: #740
-#744 := [trans #735 #379]: #742
-#451 := [monotonicity #744 #728]: #729
-#726 := [trans #451 #749]: #452
-#584 := [monotonicity #726 #560 #700]: #583
-#688 := [trans #584 #691]: #593
-#409 := (iff #755 false)
-#748 := (iff #755 #758)
-#757 := (iff #754 false)
-#752 := [rewrite]: #757
-#408 := [monotonicity #752 #752]: #748
-#750 := [trans #408 #749]: #409
-#577 := [monotonicity #750 #688]: #692
-#588 := [trans #577 #594]: #595
-#693 := [monotonicity #588]: #600
-#681 := [trans #693 #694]: #600
-#599 := [quant-inst #69 #69]: #598
-#683 := [mp #599 #681]: #597
-[unit-resolution #683 #96 #765]: false
-unsat
-661d623240b7a8e55ac7487a194ea82048a9383e 341 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#20 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#18 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#19 := (f4 f5 #18)
-#21 := (f3 #19 #20)
-#764 := (pattern #21)
-#22 := 0::Int
-#109 := -1::Int
-#113 := (* -1::Int #20)
-#110 := (* -1::Int #18)
-#116 := (div #110 #113)
-#267 := (* -1::Int #116)
-#268 := (+ #21 #267)
-#269 := (= #268 0::Int)
-#32 := (div #18 #20)
-#264 := (* -1::Int #32)
-#265 := (+ #21 #264)
-#266 := (= #265 0::Int)
-#142 := (>= #18 0::Int)
-#135 := (<= #20 0::Int)
-#227 := (or #135 #142)
-#228 := (not #227)
-#131 := (<= #18 0::Int)
-#225 := (or #131 #135)
-#226 := (not #225)
-#231 := (or #226 #228)
-#270 := (ite #231 #266 #269)
-#263 := (= #21 0::Int)
-#24 := (= #20 0::Int)
-#23 := (= #18 0::Int)
-#25 := (or #23 #24)
-#271 := (ite #25 #263 #270)
-#765 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #764) #271)
-#274 := (forall (vars (?v0 Int) (?v1 Int)) #271)
-#768 := (iff #274 #765)
-#766 := (iff #271 #271)
-#767 := [refl]: #766
-#769 := [quant-intro #767]: #768
-#234 := (ite #231 #32 #116)
-#237 := (ite #25 0::Int #234)
-#240 := (= #21 #237)
-#243 := (forall (vars (?v0 Int) (?v1 Int)) #240)
-#275 := (iff #243 #274)
-#272 := (iff #240 #271)
-#273 := [rewrite]: #272
-#276 := [quant-intro #273]: #275
-#143 := (not #142)
-#136 := (not #135)
-#146 := (and #136 #143)
-#132 := (not #131)
-#139 := (and #132 #136)
-#149 := (or #139 #146)
-#152 := (ite #149 #32 #116)
-#155 := (ite #25 0::Int #152)
-#158 := (= #21 #155)
-#161 := (forall (vars (?v0 Int) (?v1 Int)) #158)
-#244 := (iff #161 #243)
-#241 := (iff #158 #240)
-#238 := (= #155 #237)
-#235 := (= #152 #234)
-#232 := (iff #149 #231)
-#229 := (iff #146 #228)
-#230 := [rewrite]: #229
-#219 := (iff #139 #226)
-#220 := [rewrite]: #219
-#233 := [monotonicity #220 #230]: #232
-#236 := [monotonicity #233]: #235
-#239 := [monotonicity #236]: #238
-#242 := [monotonicity #239]: #241
-#245 := [quant-intro #242]: #244
-#223 := (~ #161 #161)
-#221 := (~ #158 #158)
-#222 := [refl]: #221
-#224 := [nnf-pos #222]: #223
-#34 := (- #20)
-#33 := (- #18)
-#35 := (div #33 #34)
-#27 := (< 0::Int #20)
-#29 := (< #18 0::Int)
-#30 := (and #29 #27)
-#26 := (< 0::Int #18)
-#28 := (and #26 #27)
-#31 := (or #28 #30)
-#36 := (ite #31 #32 #35)
-#37 := (ite #25 0::Int #36)
-#38 := (= #21 #37)
-#39 := (forall (vars (?v0 Int) (?v1 Int)) #38)
-#164 := (iff #39 #161)
-#103 := (and #27 #29)
-#106 := (or #28 #103)
-#119 := (ite #106 #32 #116)
-#122 := (ite #25 0::Int #119)
-#125 := (= #21 #122)
-#128 := (forall (vars (?v0 Int) (?v1 Int)) #125)
-#162 := (iff #128 #161)
-#159 := (iff #125 #158)
-#156 := (= #122 #155)
-#153 := (= #119 #152)
-#150 := (iff #106 #149)
-#147 := (iff #103 #146)
-#144 := (iff #29 #143)
-#145 := [rewrite]: #144
-#137 := (iff #27 #136)
-#138 := [rewrite]: #137
-#148 := [monotonicity #138 #145]: #147
-#140 := (iff #28 #139)
-#133 := (iff #26 #132)
-#134 := [rewrite]: #133
-#141 := [monotonicity #134 #138]: #140
-#151 := [monotonicity #141 #148]: #150
-#154 := [monotonicity #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [quant-intro #160]: #162
-#129 := (iff #39 #128)
-#126 := (iff #38 #125)
-#123 := (= #37 #122)
-#120 := (= #36 #119)
-#117 := (= #35 #116)
-#114 := (= #34 #113)
-#115 := [rewrite]: #114
-#111 := (= #33 #110)
-#112 := [rewrite]: #111
-#118 := [monotonicity #112 #115]: #117
-#107 := (iff #31 #106)
-#104 := (iff #30 #103)
-#105 := [rewrite]: #104
-#108 := [monotonicity #105]: #107
-#121 := [monotonicity #108 #118]: #120
-#124 := [monotonicity #121]: #123
-#127 := [monotonicity #124]: #126
-#130 := [quant-intro #127]: #129
-#165 := [trans #130 #163]: #164
-#102 := [asserted]: #39
-#166 := [mp #102 #165]: #161
-#215 := [mp~ #166 #224]: #161
-#246 := [mp #215 #245]: #243
-#277 := [mp #246 #276]: #274
-#770 := [mp #277 #769]: #765
-#15 := 1::Int
-#77 := -3::Int
-#71 := -5::Int
-#74 := (f4 f5 -5::Int)
-#80 := (f3 #74 -3::Int)
-#83 := (= #80 1::Int)
-#96 := (not #83)
-#12 := 3::Int
-#13 := (- 3::Int)
-#9 := 5::Int
-#10 := (- 5::Int)
-#11 := (f4 f5 #10)
-#14 := (f3 #11 #13)
-#16 := (= #14 1::Int)
-#17 := (not #16)
-#99 := (iff #17 #96)
-#86 := (= 1::Int #80)
-#91 := (not #86)
-#97 := (iff #91 #96)
-#94 := (iff #86 #83)
-#95 := [rewrite]: #94
-#98 := [monotonicity #95]: #97
-#92 := (iff #17 #91)
-#89 := (iff #16 #86)
-#87 := (iff #83 #86)
-#88 := [rewrite]: #87
-#84 := (iff #16 #83)
-#81 := (= #14 #80)
-#78 := (= #13 -3::Int)
-#79 := [rewrite]: #78
-#75 := (= #11 #74)
-#72 := (= #10 -5::Int)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#82 := [monotonicity #76 #79]: #81
-#85 := [monotonicity #82]: #84
-#90 := [trans #85 #88]: #89
-#93 := [monotonicity #90]: #92
-#100 := [trans #93 #98]: #99
-#70 := [asserted]: #17
-#101 := [mp #70 #100]: #96
-#678 := (not #765)
-#685 := (or #678 #83)
-#351 := (* -1::Int -3::Int)
-#435 := (* -1::Int -5::Int)
-#436 := (div #435 #351)
-#437 := (* -1::Int #436)
-#428 := (+ #80 #437)
-#439 := (= #428 0::Int)
-#440 := (div -5::Int -3::Int)
-#441 := (* -1::Int #440)
-#438 := (+ #80 #441)
-#442 := (= #438 0::Int)
-#421 := (>= -5::Int 0::Int)
-#756 := (<= -3::Int 0::Int)
-#758 := (or #756 #421)
-#415 := (not #758)
-#545 := (<= -5::Int 0::Int)
-#752 := (or #545 #756)
-#426 := (not #752)
-#427 := (or #426 #415)
-#759 := (ite #427 #442 #439)
-#760 := (= #80 0::Int)
-#761 := (= -3::Int 0::Int)
-#762 := (= -5::Int 0::Int)
-#757 := (or #762 #761)
-#763 := (ite #757 #760 #759)
-#669 := (or #678 #763)
-#672 := (iff #669 #685)
-#674 := (iff #685 #685)
-#675 := [rewrite]: #674
-#683 := (iff #763 #83)
-#691 := (ite false #760 #83)
-#681 := (iff #691 #83)
-#682 := [rewrite]: #681
-#687 := (iff #763 #691)
-#689 := (iff #759 #83)
-#727 := 2::Int
-#712 := (= #80 2::Int)
-#686 := (ite false #712 #83)
-#677 := (iff #686 #83)
-#679 := [rewrite]: #677
-#688 := (iff #759 #686)
-#695 := (iff #439 #83)
-#597 := (+ -1::Int #80)
-#602 := (= #597 0::Int)
-#605 := (iff #602 #83)
-#698 := [rewrite]: #605
-#603 := (iff #439 #602)
-#593 := (= #428 #597)
-#694 := (+ #80 -1::Int)
-#599 := (= #694 #597)
-#600 := [rewrite]: #599
-#697 := (= #428 #694)
-#598 := (= #437 -1::Int)
-#587 := (* -1::Int 1::Int)
-#548 := (= #587 -1::Int)
-#696 := [rewrite]: #548
-#588 := (= #437 #587)
-#702 := (= #436 1::Int)
-#547 := (div 5::Int 3::Int)
-#703 := (= #547 1::Int)
-#704 := [rewrite]: #703
-#700 := (= #436 #547)
-#544 := (= #351 3::Int)
-#546 := [rewrite]: #544
-#708 := (= #435 5::Int)
-#715 := [rewrite]: #708
-#701 := [monotonicity #715 #546]: #700
-#705 := [trans #701 #704]: #702
-#589 := [monotonicity #705]: #588
-#693 := [trans #589 #696]: #598
-#582 := [monotonicity #693]: #697
-#601 := [trans #582 #600]: #593
-#604 := [monotonicity #601]: #603
-#699 := [trans #604 #698]: #695
-#713 := (iff #442 #712)
-#730 := -2::Int
-#718 := (+ -2::Int #80)
-#709 := (= #718 0::Int)
-#706 := (iff #709 #712)
-#707 := [rewrite]: #706
-#710 := (iff #442 #709)
-#566 := (= #438 #718)
-#717 := (+ #80 -2::Int)
-#724 := (= #717 #718)
-#565 := [rewrite]: #724
-#722 := (= #438 #717)
-#721 := (= #441 -2::Int)
-#725 := (* -1::Int 2::Int)
-#719 := (= #725 -2::Int)
-#720 := [rewrite]: #719
-#729 := (= #441 #725)
-#728 := (= #440 2::Int)
-#443 := [rewrite]: #728
-#726 := [monotonicity #443]: #729
-#716 := [trans #726 #720]: #721
-#723 := [monotonicity #716]: #722
-#567 := [trans #723 #565]: #566
-#711 := [monotonicity #567]: #710
-#714 := [trans #711 #707]: #713
-#448 := (iff #427 false)
-#414 := (or false false)
-#739 := (iff #414 false)
-#402 := [rewrite]: #739
-#446 := (iff #427 #414)
-#732 := (iff #415 false)
-#1 := true
-#389 := (not true)
-#748 := (iff #389 false)
-#751 := [rewrite]: #748
-#731 := (iff #415 #389)
-#456 := (iff #758 true)
-#462 := (or true false)
-#733 := (iff #462 true)
-#734 := [rewrite]: #733
-#463 := (iff #758 #462)
-#460 := (iff #421 false)
-#461 := [rewrite]: #460
-#742 := (iff #756 true)
-#743 := [rewrite]: #742
-#357 := [monotonicity #743 #461]: #463
-#457 := [trans #357 #734]: #456
-#735 := [monotonicity #457]: #731
-#736 := [trans #735 #751]: #732
-#737 := (iff #426 false)
-#390 := (iff #426 #389)
-#747 := (iff #752 true)
-#744 := (or true true)
-#746 := (iff #744 true)
-#384 := [rewrite]: #746
-#745 := (iff #752 #744)
-#405 := (iff #545 true)
-#741 := [rewrite]: #405
-#740 := [monotonicity #741 #743]: #745
-#749 := [trans #740 #384]: #747
-#750 := [monotonicity #749]: #390
-#738 := [trans #750 #751]: #737
-#447 := [monotonicity #738 #736]: #446
-#449 := [trans #447 #402]: #448
-#680 := [monotonicity #449 #714 #699]: #688
-#690 := [trans #680 #679]: #689
-#403 := (iff #757 false)
-#755 := (iff #757 #414)
-#418 := (iff #761 false)
-#754 := [rewrite]: #418
-#753 := (iff #762 false)
-#413 := [rewrite]: #753
-#398 := [monotonicity #413 #754]: #755
-#404 := [trans #398 #402]: #403
-#692 := [monotonicity #404 #690]: #687
-#684 := [trans #692 #682]: #683
-#673 := [monotonicity #684]: #672
-#671 := [trans #673 #675]: #672
-#670 := [quant-inst #71 #77]: #669
-#676 := [mp #670 #671]: #685
-[unit-resolution #676 #101 #770]: false
-unsat
-aab5c4c0313de0fd03391587f807d1eea6cbc4ca 278 0
+#120 := (iff #37 #119)
+#117 := (iff #36 #116)
+#114 := (= #35 #113)
+#111 := (= #34 #110)
+#108 := (= #33 #107)
+#105 := (= #32 #104)
+#106 := [rewrite]: #105
+#102 := (= #31 #101)
+#103 := [rewrite]: #102
+#109 := [monotonicity #103 #106]: #108
+#99 := (iff #29 #98)
+#96 := (iff #28 #95)
+#81 := (iff #25 #80)
+#82 := [rewrite]: #81
+#88 := (iff #27 #87)
+#92 := (iff #87 #87)
+#90 := (iff #86 #86)
+#91 := [rewrite]: #90
+#93 := [monotonicity #91]: #92
+#89 := [rewrite]: #88
+#94 := [trans #89 #93]: #88
+#97 := [monotonicity #94 #82]: #96
+#84 := (iff #26 #83)
+#77 := (iff #24 #76)
+#78 := [rewrite]: #77
+#85 := [monotonicity #78 #82]: #84
+#100 := [monotonicity #85 #97]: #99
+#112 := [monotonicity #100 #109]: #111
+#115 := [monotonicity #112]: #114
+#118 := [monotonicity #115]: #117
+#121 := [quant-intro #118]: #120
+#51 := [asserted]: #37
+#122 := [mp #51 #121]: #119
+#194 := [mp #122 #193]: #191
+#168 := [mp~ #194 #212]: #191
+#242 := [mp #168 #241]: #239
+#273 := [mp #242 #272]: #270
+#709 := [mp #273 #708]: #704
+#62 := -3::Int
+#59 := (f4 f5 -1::Int)
+#65 := (f3 #59 -3::Int)
+#68 := (= #65 0::Int)
+#71 := (not #68)
+#11 := 3::Int
+#12 := (- 3::Int)
+#8 := 1::Int
+#9 := (- 1::Int)
+#10 := (f4 f5 #9)
+#13 := (f3 #10 #12)
+#15 := (= #13 0::Int)
+#16 := (not #15)
+#72 := (iff #16 #71)
+#69 := (iff #15 #68)
+#66 := (= #13 #65)
+#63 := (= #12 -3::Int)
+#64 := [rewrite]: #63
+#60 := (= #10 #59)
+#57 := (= #9 -1::Int)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#67 := [monotonicity #61 #64]: #66
+#70 := [monotonicity #67]: #69
+#73 := [monotonicity #70]: #72
+#50 := [asserted]: #16
+#74 := [mp #50 #73]: #71
+#628 := (not #704)
+#629 := (or #628 #68)
+#365 := (* -1::Int -3::Int)
+#691 := (* -1::Int -1::Int)
+#366 := (div #691 #365)
+#698 := (* -1::Int #366)
+#699 := (+ #65 #698)
+#700 := (= #699 0::Int)
+#695 := (div -1::Int -3::Int)
+#697 := (* -1::Int #695)
+#354 := (+ #65 #697)
+#484 := (= #354 0::Int)
+#367 := (<= -3::Int 0::Int)
+#380 := (>= -1::Int 0::Int)
+#377 := (or #380 #367)
+#381 := (not #377)
+#376 := (<= -1::Int 0::Int)
+#378 := (or #376 #367)
+#379 := (not #378)
+#360 := (or #379 #381)
+#701 := (if #360 #484 #700)
+#374 := (= -3::Int 0::Int)
+#290 := (= -1::Int 0::Int)
+#375 := (or #290 #374)
+#696 := (if #375 #68 #701)
+#630 := (or #628 #696)
+#631 := (iff #630 #629)
+#621 := (iff #629 #629)
+#622 := [rewrite]: #621
+#616 := (iff #696 #68)
+#634 := (if false #68 #68)
+#627 := (iff #634 #68)
+#619 := [rewrite]: #627
+#638 := (iff #696 #634)
+#544 := (iff #701 #68)
+#648 := (= #65 1::Int)
+#532 := (if false #648 #68)
+#542 := (iff #532 #68)
+#543 := [rewrite]: #542
+#540 := (iff #701 #532)
+#538 := (iff #700 #68)
+#521 := (= #699 #65)
+#635 := (+ #65 0::Int)
+#633 := (= #635 #65)
+#636 := [rewrite]: #633
+#537 := (= #699 #635)
+#528 := (= #698 0::Int)
+#643 := (* -1::Int 0::Int)
+#526 := (= #643 0::Int)
+#527 := [rewrite]: #526
+#641 := (= #698 #643)
+#640 := (= #366 0::Int)
+#654 := (div 1::Int 3::Int)
+#486 := (= #654 0::Int)
+#639 := [rewrite]: #486
+#483 := (= #366 #654)
+#653 := (= #365 3::Int)
+#647 := [rewrite]: #653
+#646 := (= #691 1::Int)
+#652 := [rewrite]: #646
+#485 := [monotonicity #652 #647]: #483
+#642 := [trans #485 #639]: #640
+#644 := [monotonicity #642]: #641
+#487 := [trans #644 #527]: #528
+#632 := [monotonicity #487]: #537
+#536 := [trans #632 #636]: #521
+#539 := [monotonicity #536]: #538
+#651 := (iff #484 #648)
+#656 := (+ -1::Int #65)
+#504 := (= #656 0::Int)
+#649 := (iff #504 #648)
+#650 := [rewrite]: #649
+#505 := (iff #484 #504)
+#657 := (= #354 #656)
+#659 := (+ #65 -1::Int)
+#661 := (= #659 #656)
+#662 := [rewrite]: #661
+#660 := (= #354 #659)
+#669 := (= #697 -1::Int)
+#667 := (* -1::Int 1::Int)
+#668 := (= #667 -1::Int)
+#665 := [rewrite]: #668
+#382 := (= #697 #667)
+#388 := (= #695 1::Int)
+#666 := [rewrite]: #388
+#664 := [monotonicity #666]: #382
+#658 := [trans #664 #665]: #669
+#655 := [monotonicity #658]: #660
+#663 := [trans #655 #662]: #657
+#506 := [monotonicity #663]: #505
+#645 := [trans #506 #650]: #651
+#386 := (iff #360 false)
+#693 := (or false false)
+#337 := (iff #693 false)
+#678 := [rewrite]: #337
+#675 := (iff #360 #693)
+#674 := (iff #381 false)
+#1 := true
+#688 := (not true)
+#689 := (iff #688 false)
+#687 := [rewrite]: #689
+#396 := (iff #381 #688)
+#673 := (iff #377 true)
+#400 := (or false true)
+#296 := (iff #400 true)
+#672 := [rewrite]: #296
+#401 := (iff #377 #400)
+#680 := (iff #367 true)
+#681 := [rewrite]: #680
+#677 := (iff #380 false)
+#399 := [rewrite]: #677
+#402 := [monotonicity #399 #681]: #401
+#395 := [trans #402 #672]: #673
+#670 := [monotonicity #395]: #396
+#671 := [trans #670 #687]: #674
+#690 := (iff #379 false)
+#328 := (iff #379 #688)
+#323 := (iff #378 true)
+#682 := (or true true)
+#679 := (iff #682 true)
+#685 := [rewrite]: #679
+#683 := (iff #378 #682)
+#343 := (iff #376 true)
+#344 := [rewrite]: #343
+#684 := [monotonicity #344 #681]: #683
+#686 := [trans #684 #685]: #323
+#329 := [monotonicity #686]: #328
+#676 := [trans #329 #687]: #690
+#385 := [monotonicity #676 #671]: #675
+#387 := [trans #385 #678]: #386
+#541 := [monotonicity #387 #645 #539]: #540
+#637 := [trans #541 #543]: #544
+#341 := (iff #375 false)
+#353 := (iff #375 #693)
+#352 := (iff #374 false)
+#357 := [rewrite]: #352
+#702 := (iff #290 false)
+#692 := [rewrite]: #702
+#694 := [monotonicity #692 #357]: #353
+#342 := [trans #694 #678]: #341
+#625 := [monotonicity #342 #637]: #638
+#618 := [trans #625 #619]: #616
+#620 := [monotonicity #618]: #631
+#623 := [trans #620 #622]: #631
+#626 := [quant-inst #56 #62]: #630
+#617 := [mp #626 #623]: #629
+[unit-resolution #617 #74 #709]: false
+166dc257eef9fb9bbbf145be894cbe683831674b 312 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #17 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #15 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
+#16 := (f4 f5 #15)
+#18 := (f3 #16 #17)
+#700 := (pattern #18)
+#19 := 0::Int
+#97 := -1::Int
+#101 := (* -1::Int #17)
+#98 := (* -1::Int #15)
+#104 := (div #98 #101)
+#260 := (* -1::Int #104)
+#261 := (+ #18 #260)
+#262 := (= #261 0::Int)
+#29 := (div #15 #17)
+#257 := (* -1::Int #29)
+#258 := (+ #18 #257)
+#259 := (= #258 0::Int)
+#75 := (<= #17 0::Int)
+#167 := (>= #15 0::Int)
+#220 := (or #167 #75)
+#221 := (not #220)
+#71 := (<= #15 0::Int)
+#216 := (or #71 #75)
+#217 := (not #216)
+#224 := (or #217 #221)
+#263 := (if #224 #259 #262)
+#256 := (= #18 0::Int)
+#21 := (= #17 0::Int)
+#20 := (= #15 0::Int)
+#22 := (or #20 #21)
+#264 := (if #22 #256 #263)
+#701 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #700) #264)
+#267 := (forall (vars (?v0 Int) (?v1 Int)) #264)
+#704 := (iff #267 #701)
+#702 := (iff #264 #264)
+#703 := [refl]: #702
+#705 := [quant-intro #703]: #704
+#227 := (if #224 #29 #104)
+#230 := (if #22 0::Int #227)
+#233 := (= #18 #230)
+#236 := (forall (vars (?v0 Int) (?v1 Int)) #233)
+#268 := (iff #236 #267)
+#265 := (iff #233 #264)
+#266 := [rewrite]: #265
+#269 := [quant-intro #266]: #268
+#76 := (not #75)
+#170 := (not #167)
+#173 := (and #170 #76)
+#72 := (not #71)
+#79 := (and #72 #76)
+#176 := (or #79 #173)
+#179 := (if #176 #29 #104)
+#182 := (if #22 0::Int #179)
+#185 := (= #18 #182)
+#188 := (forall (vars (?v0 Int) (?v1 Int)) #185)
+#237 := (iff #188 #236)
+#234 := (iff #185 #233)
+#231 := (= #182 #230)
+#228 := (= #179 #227)
+#225 := (iff #176 #224)
+#222 := (iff #173 #221)
+#223 := [rewrite]: #222
+#218 := (iff #79 #217)
+#219 := [rewrite]: #218
+#226 := [monotonicity #219 #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#235 := [monotonicity #232]: #234
+#238 := [quant-intro #235]: #237
+#210 := (~ #188 #188)
+#212 := (~ #185 #185)
+#213 := [refl]: #212
+#211 := [nnf-pos #213]: #210
+#82 := (<= 0::Int #15)
+#83 := (not #82)
+#91 := (and #83 #76)
+#94 := (or #79 #91)
+#107 := (if #94 #29 #104)
+#110 := (if #22 0::Int #107)
+#113 := (= #18 #110)
+#116 := (forall (vars (?v0 Int) (?v1 Int)) #113)
+#189 := (iff #116 #188)
+#186 := (iff #113 #185)
+#183 := (= #110 #182)
+#180 := (= #107 #179)
+#177 := (iff #94 #176)
+#174 := (iff #91 #173)
+#171 := (iff #83 #170)
+#168 := (iff #82 #167)
+#169 := [rewrite]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [monotonicity #178]: #180
+#184 := [monotonicity #181]: #183
+#187 := [monotonicity #184]: #186
+#190 := [quant-intro #187]: #189
+#31 := (- #17)
+#30 := (- #15)
+#32 := (div #30 #31)
+#24 := (< 0::Int #17)
+#26 := (< #15 0::Int)
+#27 := (and #26 #24)
+#23 := (< 0::Int #15)
+#25 := (and #23 #24)
+#28 := (or #25 #27)
+#33 := (if #28 #29 #32)
+#34 := (if #22 0::Int #33)
+#35 := (= #18 #34)
+#36 := (forall (vars (?v0 Int) (?v1 Int)) #35)
+#117 := (iff #36 #116)
+#114 := (iff #35 #113)
+#111 := (= #34 #110)
+#108 := (= #33 #107)
+#105 := (= #32 #104)
+#102 := (= #31 #101)
+#103 := [rewrite]: #102
+#99 := (= #30 #98)
+#100 := [rewrite]: #99
+#106 := [monotonicity #100 #103]: #105
+#95 := (iff #28 #94)
+#92 := (iff #27 #91)
+#77 := (iff #24 #76)
+#78 := [rewrite]: #77
+#84 := (iff #26 #83)
+#88 := (iff #83 #83)
+#86 := (iff #82 #82)
+#87 := [rewrite]: #86
+#89 := [monotonicity #87]: #88
+#85 := [rewrite]: #84
+#90 := [trans #85 #89]: #84
+#93 := [monotonicity #90 #78]: #92
+#80 := (iff #25 #79)
+#73 := (iff #23 #72)
+#74 := [rewrite]: #73
+#81 := [monotonicity #74 #78]: #80
+#96 := [monotonicity #81 #93]: #95
+#109 := [monotonicity #96 #106]: #108
+#112 := [monotonicity #109]: #111
+#115 := [monotonicity #112]: #114
+#118 := [quant-intro #115]: #117
+#50 := [asserted]: #36
+#119 := [mp #50 #118]: #116
+#191 := [mp #119 #190]: #188
+#208 := [mp~ #191 #211]: #188
+#239 := [mp #208 #238]: #236
+#270 := [mp #239 #269]: #267
+#706 := [mp #270 #705]: #701
+#12 := 1::Int
+#55 := -3::Int
+#58 := (f4 f5 -3::Int)
+#61 := (f3 #58 -3::Int)
+#64 := (= #61 1::Int)
+#67 := (not #64)
+#8 := 3::Int
+#9 := (- 3::Int)
+#10 := (f4 f5 #9)
+#11 := (f3 #10 #9)
+#13 := (= #11 1::Int)
+#14 := (not #13)
+#68 := (iff #14 #67)
+#65 := (iff #13 #64)
+#62 := (= #11 #61)
+#56 := (= #9 -3::Int)
+#57 := [rewrite]: #56
+#59 := (= #10 #58)
+#60 := [monotonicity #57]: #59
+#63 := [monotonicity #60 #57]: #62
+#66 := [monotonicity #63]: #65
+#69 := [monotonicity #66]: #68
+#49 := [asserted]: #14
+#70 := [mp #49 #69]: #67
+#537 := (not #701)
+#538 := (or #537 #64)
+#481 := (* -1::Int -3::Int)
+#688 := (div #481 #481)
+#362 := (* -1::Int #688)
+#363 := (+ #61 #362)
+#695 := (= #363 0::Int)
+#357 := (div -3::Int -3::Int)
+#692 := (* -1::Int #357)
+#694 := (+ #61 #692)
+#351 := (= #694 0::Int)
+#373 := (<= -3::Int 0::Int)
+#376 := (>= -3::Int 0::Int)
+#377 := (or #376 #373)
+#374 := (not #377)
+#364 := (or #373 #373)
+#375 := (not #364)
+#378 := (or #375 #374)
+#696 := (if #378 #351 #695)
+#372 := (= #61 0::Int)
+#287 := (= -3::Int 0::Int)
+#371 := (or #287 #287)
+#697 := (if #371 #372 #696)
+#539 := (or #537 #697)
+#541 := (iff #539 #538)
+#631 := (iff #538 #538)
+#635 := [rewrite]: #631
+#536 := (iff #697 #64)
+#630 := (if false #372 #64)
+#533 := (iff #630 #64)
+#535 := [rewrite]: #533
+#633 := (iff #697 #630)
+#534 := (iff #696 #64)
+#523 := (if false #64 #64)
+#484 := (iff #523 #64)
+#632 := [rewrite]: #484
+#524 := (iff #696 #523)
+#638 := (iff #695 #64)
+#662 := (+ -1::Int #61)
+#652 := (= #662 0::Int)
+#659 := (iff #652 #64)
+#654 := [rewrite]: #659
+#639 := (iff #695 #652)
+#636 := (= #363 #662)
+#379 := (+ #61 -1::Int)
+#666 := (= #379 #662)
+#655 := [rewrite]: #666
+#482 := (= #363 #379)
+#651 := (= #362 -1::Int)
+#672 := (* -1::Int 1::Int)
+#384 := (= #672 -1::Int)
+#385 := [rewrite]: #384
+#650 := (= #362 #672)
+#643 := (= #688 1::Int)
+#645 := (div 3::Int 3::Int)
+#648 := (= #645 1::Int)
+#642 := [rewrite]: #648
+#646 := (= #688 #645)
+#502 := (= #481 3::Int)
+#503 := [rewrite]: #502
+#647 := [monotonicity #503 #503]: #646
+#649 := [trans #647 #642]: #643
+#644 := [monotonicity #649]: #650
+#480 := [trans #644 #385]: #651
+#483 := [monotonicity #480]: #482
+#637 := [trans #483 #655]: #636
+#640 := [monotonicity #637]: #639
+#641 := [trans #640 #654]: #638
+#660 := (iff #351 #64)
+#653 := (iff #351 #652)
+#656 := (= #694 #662)
+#661 := (= #694 #379)
+#663 := (= #692 -1::Int)
+#382 := (= #692 #672)
+#671 := (= #357 1::Int)
+#668 := [rewrite]: #671
+#383 := [monotonicity #668]: #382
+#664 := [trans #383 #385]: #663
+#665 := [monotonicity #664]: #661
+#657 := [trans #665 #655]: #656
+#658 := [monotonicity #657]: #653
+#501 := [trans #658 #654]: #660
+#393 := (iff #378 false)
+#699 := (or false false)
+#354 := (iff #699 false)
+#690 := [rewrite]: #354
+#670 := (iff #378 #699)
+#293 := (iff #374 false)
+#1 := true
+#680 := (not true)
+#682 := (iff #680 false)
+#320 := [rewrite]: #682
+#398 := (iff #374 #680)
+#396 := (iff #377 true)
+#686 := (or false true)
+#673 := (iff #686 true)
+#674 := [rewrite]: #673
+#684 := (iff #377 #686)
+#334 := (iff #373 true)
+#675 := [rewrite]: #334
+#325 := (iff #376 false)
+#326 := [rewrite]: #325
+#687 := [monotonicity #326 #675]: #684
+#397 := [trans #687 #674]: #396
+#399 := [monotonicity #397]: #398
+#669 := [trans #399 #320]: #293
+#683 := (iff #375 false)
+#681 := (iff #375 #680)
+#678 := (iff #364 true)
+#338 := (or true true)
+#341 := (iff #338 true)
+#677 := [rewrite]: #341
+#339 := (iff #364 #338)
+#340 := [monotonicity #675 #675]: #339
+#679 := [trans #340 #677]: #678
+#676 := [monotonicity #679]: #681
+#685 := [trans #676 #320]: #683
+#392 := [monotonicity #685 #669]: #670
+#667 := [trans #392 #690]: #393
+#525 := [monotonicity #667 #501 #641]: #524
+#629 := [trans #525 #632]: #534
+#350 := (iff #371 false)
+#689 := (iff #371 #699)
+#698 := (iff #287 false)
+#693 := [rewrite]: #698
+#349 := [monotonicity #693 #693]: #689
+#691 := [trans #349 #690]: #350
+#518 := [monotonicity #691 #629]: #633
+#529 := [trans #518 #535]: #536
+#634 := [monotonicity #529]: #541
+#622 := [trans #634 #635]: #541
+#540 := [quant-inst #55 #55]: #539
+#624 := [mp #540 #622]: #538
+[unit-resolution #624 #70 #706]: false
+ac847d4d96ab393b411eb8572de1bfa41757e40d 339 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#19 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#17 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#18 := (f4 f5 #17)
+#20 := (f3 #18 #19)
+#705 := (pattern #20)
+#21 := 0::Int
+#102 := -1::Int
+#106 := (* -1::Int #19)
+#103 := (* -1::Int #17)
+#109 := (div #103 #106)
+#265 := (* -1::Int #109)
+#266 := (+ #20 #265)
+#267 := (= #266 0::Int)
+#31 := (div #17 #19)
+#262 := (* -1::Int #31)
+#263 := (+ #20 #262)
+#264 := (= #263 0::Int)
+#80 := (<= #19 0::Int)
+#172 := (>= #17 0::Int)
+#225 := (or #172 #80)
+#226 := (not #225)
+#76 := (<= #17 0::Int)
+#221 := (or #76 #80)
+#222 := (not #221)
+#229 := (or #222 #226)
+#268 := (if #229 #264 #267)
+#261 := (= #20 0::Int)
+#23 := (= #19 0::Int)
+#22 := (= #17 0::Int)
+#24 := (or #22 #23)
+#269 := (if #24 #261 #268)
+#706 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #705) #269)
+#272 := (forall (vars (?v0 Int) (?v1 Int)) #269)
+#709 := (iff #272 #706)
+#707 := (iff #269 #269)
+#708 := [refl]: #707
+#710 := [quant-intro #708]: #709
+#232 := (if #229 #31 #109)
+#235 := (if #24 0::Int #232)
+#238 := (= #20 #235)
+#241 := (forall (vars (?v0 Int) (?v1 Int)) #238)
+#273 := (iff #241 #272)
+#270 := (iff #238 #269)
+#271 := [rewrite]: #270
+#274 := [quant-intro #271]: #273
+#81 := (not #80)
+#175 := (not #172)
+#178 := (and #175 #81)
+#77 := (not #76)
+#84 := (and #77 #81)
+#181 := (or #84 #178)
+#184 := (if #181 #31 #109)
+#187 := (if #24 0::Int #184)
+#190 := (= #20 #187)
+#193 := (forall (vars (?v0 Int) (?v1 Int)) #190)
+#242 := (iff #193 #241)
+#239 := (iff #190 #238)
+#236 := (= #187 #235)
+#233 := (= #184 #232)
+#230 := (iff #181 #229)
+#227 := (iff #178 #226)
+#228 := [rewrite]: #227
+#223 := (iff #84 #222)
+#224 := [rewrite]: #223
+#231 := [monotonicity #224 #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [monotonicity #234]: #236
+#240 := [monotonicity #237]: #239
+#243 := [quant-intro #240]: #242
+#213 := (~ #193 #193)
+#215 := (~ #190 #190)
+#216 := [refl]: #215
+#214 := [nnf-pos #216]: #213
+#87 := (<= 0::Int #17)
+#88 := (not #87)
+#96 := (and #88 #81)
+#99 := (or #84 #96)
+#112 := (if #99 #31 #109)
+#115 := (if #24 0::Int #112)
+#118 := (= #20 #115)
+#121 := (forall (vars (?v0 Int) (?v1 Int)) #118)
+#194 := (iff #121 #193)
+#191 := (iff #118 #190)
+#188 := (= #115 #187)
+#185 := (= #112 #184)
+#182 := (iff #99 #181)
+#179 := (iff #96 #178)
+#176 := (iff #88 #175)
+#173 := (iff #87 #172)
+#174 := [rewrite]: #173
+#177 := [monotonicity #174]: #176
+#180 := [monotonicity #177]: #179
+#183 := [monotonicity #180]: #182
+#186 := [monotonicity #183]: #185
+#189 := [monotonicity #186]: #188
+#192 := [monotonicity #189]: #191
+#195 := [quant-intro #192]: #194
+#33 := (- #19)
+#32 := (- #17)
+#34 := (div #32 #33)
+#26 := (< 0::Int #19)
+#28 := (< #17 0::Int)
+#29 := (and #28 #26)
+#25 := (< 0::Int #17)
+#27 := (and #25 #26)
+#30 := (or #27 #29)
+#35 := (if #30 #31 #34)
+#36 := (if #24 0::Int #35)
+#37 := (= #20 #36)
+#38 := (forall (vars (?v0 Int) (?v1 Int)) #37)
+#122 := (iff #38 #121)
+#119 := (iff #37 #118)
+#116 := (= #36 #115)
+#113 := (= #35 #112)
+#110 := (= #34 #109)
+#107 := (= #33 #106)
+#108 := [rewrite]: #107
+#104 := (= #32 #103)
+#105 := [rewrite]: #104
+#111 := [monotonicity #105 #108]: #110
+#100 := (iff #30 #99)
+#97 := (iff #29 #96)
+#82 := (iff #26 #81)
+#83 := [rewrite]: #82
+#89 := (iff #28 #88)
+#93 := (iff #88 #88)
+#91 := (iff #87 #87)
+#92 := [rewrite]: #91
+#94 := [monotonicity #92]: #93
+#90 := [rewrite]: #89
+#95 := [trans #90 #94]: #89
+#98 := [monotonicity #95 #83]: #97
+#85 := (iff #27 #84)
+#78 := (iff #25 #77)
+#79 := [rewrite]: #78
+#86 := [monotonicity #79 #83]: #85
+#101 := [monotonicity #86 #98]: #100
+#114 := [monotonicity #101 #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [monotonicity #117]: #119
+#123 := [quant-intro #120]: #122
+#52 := [asserted]: #38
+#124 := [mp #52 #123]: #121
+#196 := [mp #124 #195]: #193
+#170 := [mp~ #196 #214]: #193
+#244 := [mp #170 #243]: #241
+#275 := [mp #244 #274]: #272
+#711 := [mp #275 #710]: #706
+#14 := 1::Int
+#63 := -3::Int
+#57 := -5::Int
+#60 := (f4 f5 -5::Int)
+#66 := (f3 #60 -3::Int)
+#69 := (= #66 1::Int)
+#72 := (not #69)
+#11 := 3::Int
+#12 := (- 3::Int)
+#8 := 5::Int
+#9 := (- 5::Int)
+#10 := (f4 f5 #9)
+#13 := (f3 #10 #12)
+#15 := (= #13 1::Int)
+#16 := (not #15)
+#73 := (iff #16 #72)
+#70 := (iff #15 #69)
+#67 := (= #13 #66)
+#64 := (= #12 -3::Int)
+#65 := [rewrite]: #64
+#61 := (= #10 #60)
+#58 := (= #9 -5::Int)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#68 := [monotonicity #62 #65]: #67
+#71 := [monotonicity #68]: #70
+#74 := [monotonicity #71]: #73
+#51 := [asserted]: #16
+#75 := [mp #51 #74]: #72
+#619 := (not #706)
+#626 := (or #619 #69)
+#368 := (* -1::Int -3::Int)
+#367 := (* -1::Int -5::Int)
+#700 := (div #367 #368)
+#701 := (* -1::Int #700)
+#702 := (+ #66 #701)
+#703 := (= #702 0::Int)
+#699 := (div -5::Int -3::Int)
+#356 := (* -1::Int #699)
+#486 := (+ #66 #356)
+#693 := (= #486 0::Int)
+#380 := (<= -3::Int 0::Int)
+#379 := (>= -5::Int 0::Int)
+#383 := (or #379 #380)
+#362 := (not #383)
+#369 := (<= -5::Int 0::Int)
+#381 := (or #369 #380)
+#382 := (not #381)
+#697 := (or #382 #362)
+#698 := (if #697 #693 #703)
+#378 := (= #66 0::Int)
+#376 := (= -3::Int 0::Int)
+#292 := (= -5::Int 0::Int)
+#377 := (or #292 #376)
+#704 := (if #377 #378 #698)
+#610 := (or #619 #704)
+#613 := (iff #610 #626)
+#615 := (iff #626 #626)
+#616 := [rewrite]: #615
+#624 := (iff #704 #69)
+#632 := (if false #378 #69)
+#622 := (iff #632 #69)
+#623 := [rewrite]: #622
+#628 := (iff #704 #632)
+#630 := (iff #698 #69)
+#668 := 2::Int
+#653 := (= #66 2::Int)
+#627 := (if false #653 #69)
+#618 := (iff #627 #69)
+#620 := [rewrite]: #618
+#629 := (iff #698 #627)
+#636 := (iff #703 #69)
+#538 := (+ -1::Int #66)
+#543 := (= #538 0::Int)
+#546 := (iff #543 #69)
+#639 := [rewrite]: #546
+#544 := (iff #703 #543)
+#534 := (= #702 #538)
+#635 := (+ #66 -1::Int)
+#540 := (= #635 #538)
+#541 := [rewrite]: #540
+#638 := (= #702 #635)
+#539 := (= #701 -1::Int)
+#528 := (* -1::Int 1::Int)
+#489 := (= #528 -1::Int)
+#637 := [rewrite]: #489
+#529 := (= #701 #528)
+#643 := (= #700 1::Int)
+#488 := (div 5::Int 3::Int)
+#644 := (= #488 1::Int)
+#645 := [rewrite]: #644
+#641 := (= #700 #488)
+#485 := (= #368 3::Int)
+#487 := [rewrite]: #485
+#649 := (= #367 5::Int)
+#656 := [rewrite]: #649
+#642 := [monotonicity #656 #487]: #641
+#646 := [trans #642 #645]: #643
+#530 := [monotonicity #646]: #529
+#634 := [trans #530 #637]: #539
+#523 := [monotonicity #634]: #638
+#542 := [trans #523 #541]: #534
+#545 := [monotonicity #542]: #544
+#640 := [trans #545 #639]: #636
+#654 := (iff #693 #653)
+#671 := -2::Int
+#659 := (+ -2::Int #66)
+#650 := (= #659 0::Int)
+#647 := (iff #650 #653)
+#648 := [rewrite]: #647
+#651 := (iff #693 #650)
+#507 := (= #486 #659)
+#658 := (+ #66 -2::Int)
+#665 := (= #658 #659)
+#506 := [rewrite]: #665
+#663 := (= #486 #658)
+#662 := (= #356 -2::Int)
+#666 := (* -1::Int 2::Int)
+#660 := (= #666 -2::Int)
+#661 := [rewrite]: #660
+#670 := (= #356 #666)
+#669 := (= #699 2::Int)
+#384 := [rewrite]: #669
+#667 := [monotonicity #384]: #670
+#657 := [trans #667 #661]: #662
+#664 := [monotonicity #657]: #663
+#508 := [trans #664 #506]: #507
+#652 := [monotonicity #508]: #651
+#655 := [trans #652 #648]: #654
+#389 := (iff #697 false)
+#355 := (or false false)
+#680 := (iff #355 false)
+#343 := [rewrite]: #680
+#387 := (iff #697 #355)
+#673 := (iff #362 false)
+#1 := true
+#330 := (not true)
+#689 := (iff #330 false)
+#692 := [rewrite]: #689
+#672 := (iff #362 #330)
+#397 := (iff #383 true)
+#403 := (or false true)
+#674 := (iff #403 true)
+#675 := [rewrite]: #674
+#404 := (iff #383 #403)
+#683 := (iff #380 true)
+#684 := [rewrite]: #683
+#401 := (iff #379 false)
+#402 := [rewrite]: #401
+#298 := [monotonicity #402 #684]: #404
+#398 := [trans #298 #675]: #397
+#676 := [monotonicity #398]: #672
+#677 := [trans #676 #692]: #673
+#678 := (iff #382 false)
+#331 := (iff #382 #330)
+#688 := (iff #381 true)
+#685 := (or true true)
+#687 := (iff #685 true)
+#325 := [rewrite]: #687
+#686 := (iff #381 #685)
+#346 := (iff #369 true)
+#682 := [rewrite]: #346
+#681 := [monotonicity #682 #684]: #686
+#690 := [trans #681 #325]: #688
+#691 := [monotonicity #690]: #331
+#679 := [trans #691 #692]: #678
+#388 := [monotonicity #679 #677]: #387
+#390 := [trans #388 #343]: #389
+#621 := [monotonicity #390 #655 #640]: #629
+#631 := [trans #621 #620]: #630
+#344 := (iff #377 false)
+#696 := (iff #377 #355)
+#359 := (iff #376 false)
+#695 := [rewrite]: #359
+#694 := (iff #292 false)
+#354 := [rewrite]: #694
+#339 := [monotonicity #354 #695]: #696
+#345 := [trans #339 #343]: #344
+#633 := [monotonicity #345 #631]: #628
+#625 := [trans #633 #623]: #624
+#614 := [monotonicity #625]: #613
+#612 := [trans #614 #616]: #613
+#611 := [quant-inst #57 #63]: #610
+#617 := [mp #611 #612]: #626
+[unit-resolution #617 #75 #711]: false
+ce1a28b0de5b74c56978e7de07c2e3640f9fb87f 275 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#16 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#14 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#35 := (f4 f5 #14)
+#36 := (f3 #35 #16)
+#689 := (pattern #36)
+#8 := 0::Int
+#78 := -1::Int
+#82 := (* -1::Int #16)
+#79 := (* -1::Int #14)
+#101 := (mod #79 #82)
+#257 := (+ #36 #101)
+#258 := (= #257 0::Int)
+#37 := (mod #14 #16)
+#254 := (* -1::Int #37)
+#255 := (+ #36 #254)
+#256 := (= #255 0::Int)
+#56 := (<= #16 0::Int)
+#148 := (>= #14 0::Int)
+#201 := (or #148 #56)
+#202 := (not #201)
+#52 := (<= #14 0::Int)
+#197 := (or #52 #56)
+#198 := (not #197)
+#205 := (or #198 #202)
+#259 := (if #205 #256 #258)
+#253 := (= #36 0::Int)
+#18 := (= #14 0::Int)
+#260 := (if #18 #253 #259)
+#252 := (= #36 #14)
+#19 := (= #16 0::Int)
+#261 := (if #19 #252 #260)
+#690 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #689) #261)
+#264 := (forall (vars (?v0 Int) (?v1 Int)) #261)
+#693 := (iff #264 #690)
+#691 := (iff #261 #261)
+#692 := [refl]: #691
+#694 := [quant-intro #692]: #693
+#107 := (* -1::Int #101)
+#221 := (if #205 #37 #107)
+#224 := (if #18 0::Int #221)
+#227 := (if #19 #14 #224)
+#230 := (= #36 #227)
+#233 := (forall (vars (?v0 Int) (?v1 Int)) #230)
+#265 := (iff #233 #264)
+#262 := (iff #230 #261)
+#263 := [rewrite]: #262
+#266 := [quant-intro #263]: #265
+#57 := (not #56)
+#151 := (not #148)
+#154 := (and #151 #57)
+#53 := (not #52)
+#60 := (and #53 #57)
+#157 := (or #60 #154)
+#173 := (if #157 #37 #107)
+#176 := (if #18 0::Int #173)
+#179 := (if #19 #14 #176)
+#182 := (= #36 #179)
+#185 := (forall (vars (?v0 Int) (?v1 Int)) #182)
+#234 := (iff #185 #233)
+#231 := (iff #182 #230)
+#228 := (= #179 #227)
+#225 := (= #176 #224)
+#222 := (= #173 #221)
+#206 := (iff #157 #205)
+#203 := (iff #154 #202)
+#204 := [rewrite]: #203
+#199 := (iff #60 #198)
+#200 := [rewrite]: #199
+#207 := [monotonicity #200 #204]: #206
+#223 := [monotonicity #207]: #222
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#235 := [quant-intro #232]: #234
+#192 := (~ #185 #185)
+#147 := (~ #182 #182)
+#191 := [refl]: #147
+#195 := [nnf-pos #191]: #192
+#63 := (<= 0::Int #14)
+#64 := (not #63)
+#72 := (and #64 #57)
+#75 := (or #60 #72)
+#112 := (if #75 #37 #107)
+#115 := (if #18 0::Int #112)
+#118 := (if #19 #14 #115)
+#121 := (= #36 #118)
+#124 := (forall (vars (?v0 Int) (?v1 Int)) #121)
+#186 := (iff #124 #185)
+#183 := (iff #121 #182)
+#180 := (= #118 #179)
+#177 := (= #115 #176)
+#174 := (= #112 #173)
+#158 := (iff #75 #157)
+#155 := (iff #72 #154)
+#152 := (iff #64 #151)
+#149 := (iff #63 #148)
+#150 := [rewrite]: #149
+#153 := [monotonicity #150]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#175 := [monotonicity #159]: #174
+#178 := [monotonicity #175]: #177
+#181 := [monotonicity #178]: #180
+#184 := [monotonicity #181]: #183
+#187 := [quant-intro #184]: #186
+#29 := (- #16)
+#28 := (- #14)
+#38 := (mod #28 #29)
+#39 := (- #38)
+#22 := (< 0::Int #16)
+#24 := (< #14 0::Int)
+#25 := (and #24 #22)
+#21 := (< 0::Int #14)
+#23 := (and #21 #22)
+#26 := (or #23 #25)
+#40 := (if #26 #37 #39)
+#41 := (if #18 0::Int #40)
+#42 := (if #19 #14 #41)
+#43 := (= #36 #42)
+#44 := (forall (vars (?v0 Int) (?v1 Int)) #43)
+#125 := (iff #44 #124)
+#122 := (iff #43 #121)
+#119 := (= #42 #118)
+#116 := (= #41 #115)
+#113 := (= #40 #112)
+#110 := (= #39 #107)
+#104 := (- #101)
+#108 := (= #104 #107)
+#109 := [rewrite]: #108
+#105 := (= #39 #104)
+#102 := (= #38 #101)
+#83 := (= #29 #82)
+#84 := [rewrite]: #83
+#80 := (= #28 #79)
+#81 := [rewrite]: #80
+#103 := [monotonicity #81 #84]: #102
+#106 := [monotonicity #103]: #105
+#111 := [trans #106 #109]: #110
+#76 := (iff #26 #75)
+#73 := (iff #25 #72)
+#58 := (iff #22 #57)
+#59 := [rewrite]: #58
+#65 := (iff #24 #64)
+#69 := (iff #64 #64)
+#67 := (iff #63 #63)
+#68 := [rewrite]: #67
+#70 := [monotonicity #68]: #69
+#66 := [rewrite]: #65
+#71 := [trans #66 #70]: #65
+#74 := [monotonicity #71 #59]: #73
+#61 := (iff #23 #60)
+#54 := (iff #21 #53)
+#55 := [rewrite]: #54
+#62 := [monotonicity #55 #59]: #61
+#77 := [monotonicity #62 #74]: #76
+#114 := [monotonicity #77 #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [monotonicity #117]: #119
+#123 := [monotonicity #120]: #122
+#126 := [quant-intro #123]: #125
+#48 := [asserted]: #44
+#127 := [mp #48 #126]: #124
+#188 := [mp #127 #187]: #185
+#196 := [mp~ #188 #195]: #185
+#236 := [mp #196 #235]: #233
+#267 := [mp #236 #266]: #264
+#695 := [mp #267 #694]: #690
+#9 := (f4 f5 0::Int)
+#10 := (f3 #9 0::Int)
+#11 := (= #10 0::Int)
+#12 := (not #11)
+#46 := [asserted]: #12
+#642 := (not #690)
+#483 := (or #642 #11)
+#676 := (* -1::Int 0::Int)
+#333 := (mod #676 #676)
+#463 := (+ #10 #333)
+#670 := (= #463 0::Int)
+#356 := (mod 0::Int 0::Int)
+#360 := (* -1::Int #356)
+#339 := (+ #10 #360)
+#674 := (= #339 0::Int)
+#353 := (<= 0::Int 0::Int)
+#346 := (>= 0::Int 0::Int)
+#357 := (or #346 #353)
+#358 := (not #357)
+#354 := (or #353 #353)
+#355 := (not #354)
+#359 := (or #355 #358)
+#344 := (if #359 #674 #670)
+#268 := (= 0::Int 0::Int)
+#345 := (if #268 #11 #344)
+#677 := (if #268 #11 #345)
+#484 := (or #642 #677)
+#627 := (iff #484 #483)
+#629 := (iff #483 #483)
+#630 := [rewrite]: #629
+#641 := (iff #677 #11)
+#1 := true
+#638 := (if true #11 #11)
+#635 := (iff #638 #11)
+#640 := [rewrite]: #635
+#639 := (iff #677 #638)
+#648 := (iff #345 #11)
+#651 := (+ #10 #356)
+#375 := (= #651 0::Int)
+#646 := (if true #11 #375)
+#647 := (iff #646 #11)
+#644 := [rewrite]: #647
+#361 := (iff #345 #646)
+#367 := (iff #344 #375)
+#650 := (if false #674 #375)
+#365 := (iff #650 #375)
+#366 := [rewrite]: #365
+#654 := (iff #344 #650)
+#649 := (iff #670 #375)
+#652 := (= #463 #651)
+#381 := (= #333 #356)
+#379 := (= #676 0::Int)
+#380 := [rewrite]: #379
+#274 := [monotonicity #380 #380]: #381
+#374 := [monotonicity #274]: #652
+#653 := [monotonicity #374]: #649
+#656 := (iff #359 false)
+#308 := (or false false)
+#669 := (iff #308 false)
+#655 := [rewrite]: #669
+#668 := (iff #359 #308)
+#667 := (iff #358 false)
+#316 := (not true)
+#321 := (iff #316 false)
+#322 := [rewrite]: #321
+#302 := (iff #358 #316)
+#658 := (iff #357 true)
+#681 := (or true true)
+#336 := (iff #681 true)
+#672 := [rewrite]: #336
+#662 := (iff #357 #681)
+#680 := (iff #353 true)
+#675 := [rewrite]: #680
+#660 := (iff #346 true)
+#661 := [rewrite]: #660
+#663 := [monotonicity #661 #675]: #662
+#664 := [trans #663 #672]: #658
+#665 := [monotonicity #664]: #302
+#307 := [trans #665 #322]: #667
+#323 := (iff #355 false)
+#657 := (iff #355 #316)
+#332 := (iff #354 true)
+#671 := (iff #354 #681)
+#331 := [monotonicity #675 #675]: #671
+#673 := [trans #331 #672]: #332
+#320 := [monotonicity #673]: #657
+#659 := [trans #320 #322]: #323
+#666 := [monotonicity #659 #307]: #668
+#378 := [trans #666 #655]: #656
+#364 := [monotonicity #378 #653]: #654
+#645 := [trans #364 #366]: #367
+#678 := (iff #268 true)
+#679 := [rewrite]: #678
+#643 := [monotonicity #679 #645]: #361
+#637 := [trans #643 #644]: #648
+#634 := [monotonicity #679 #637]: #639
+#636 := [trans #634 #640]: #641
+#628 := [monotonicity #636]: #627
+#624 := [trans #628 #630]: #627
+#485 := [quant-inst #8 #8]: #484
+#625 := [mp #485 #624]: #483
+[unit-resolution #625 #46 #695]: false
+01e092dd4a496cce0a16abf4e555c06c4ce61922 279 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#17 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#15 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
 #36 := (f4 f5 #15)
 #37 := (f3 #36 #17)
-#761 := (pattern #37)
-#9 := 0::Int
-#92 := -1::Int
-#96 := (* -1::Int #17)
-#93 := (* -1::Int #15)
-#157 := (mod #93 #96)
-#272 := (+ #37 #157)
-#273 := (= #272 0::Int)
+#690 := (pattern #37)
+#10 := 0::Int
+#79 := -1::Int
+#83 := (* -1::Int #17)
+#80 := (* -1::Int #15)
+#102 := (mod #80 #83)
+#258 := (+ #37 #102)
+#259 := (= #258 0::Int)
 #38 := (mod #15 #17)
-#269 := (* -1::Int #38)
-#270 := (+ #37 #269)
-#271 := (= #270 0::Int)
-#131 := (>= #15 0::Int)
-#124 := (<= #17 0::Int)
-#216 := (or #124 #131)
-#217 := (not #216)
-#120 := (<= #15 0::Int)
-#214 := (or #120 #124)
-#215 := (not #214)
-#220 := (or #215 #217)
-#274 := (ite #220 #271 #273)
-#268 := (= #37 0::Int)
+#255 := (* -1::Int #38)
+#256 := (+ #37 #255)
+#257 := (= #256 0::Int)
+#57 := (<= #17 0::Int)
+#149 := (>= #15 0::Int)
+#202 := (or #149 #57)
+#203 := (not #202)
+#53 := (<= #15 0::Int)
+#198 := (or #53 #57)
+#199 := (not #198)
+#206 := (or #199 #203)
+#260 := (if #206 #257 #259)
+#254 := (= #37 0::Int)
 #19 := (= #15 0::Int)
-#275 := (ite #19 #268 #274)
-#267 := (= #15 #37)
+#261 := (if #19 #254 #260)
+#253 := (= #37 #15)
 #20 := (= #17 0::Int)
-#276 := (ite #20 #267 #275)
-#762 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #761) #276)
-#279 := (forall (vars (?v0 Int) (?v1 Int)) #276)
-#765 := (iff #279 #762)
-#763 := (iff #276 #276)
-#764 := [refl]: #763
-#766 := [quant-intro #764]: #765
-#163 := (* -1::Int #157)
-#236 := (ite #220 #38 #163)
-#239 := (ite #19 0::Int #236)
-#242 := (ite #20 #15 #239)
-#245 := (= #37 #242)
-#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
-#280 := (iff #248 #279)
-#277 := (iff #245 #276)
-#278 := [rewrite]: #277
-#281 := [quant-intro #278]: #280
-#132 := (not #131)
-#125 := (not #124)
-#135 := (and #125 #132)
-#121 := (not #120)
-#128 := (and #121 #125)
-#138 := (or #128 #135)
-#183 := (ite #138 #38 #163)
-#186 := (ite #19 0::Int #183)
-#189 := (ite #20 #15 #186)
-#192 := (= #37 #189)
-#195 := (forall (vars (?v0 Int) (?v1 Int)) #192)
-#249 := (iff #195 #248)
-#246 := (iff #192 #245)
-#243 := (= #189 #242)
-#240 := (= #186 #239)
-#237 := (= #183 #236)
-#221 := (iff #138 #220)
-#218 := (iff #135 #217)
-#219 := [rewrite]: #218
-#208 := (iff #128 #215)
-#209 := [rewrite]: #208
-#222 := [monotonicity #209 #219]: #221
-#238 := [monotonicity #222]: #237
-#241 := [monotonicity #238]: #240
-#244 := [monotonicity #241]: #243
-#247 := [monotonicity #244]: #246
-#250 := [quant-intro #247]: #249
-#206 := (~ #195 #195)
-#205 := (~ #192 #192)
-#202 := [refl]: #205
-#207 := [nnf-pos #202]: #206
+#262 := (if #20 #253 #261)
+#691 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #690) #262)
+#265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
+#694 := (iff #265 #691)
+#692 := (iff #262 #262)
+#693 := [refl]: #692
+#695 := [quant-intro #693]: #694
+#108 := (* -1::Int #102)
+#222 := (if #206 #38 #108)
+#225 := (if #19 0::Int #222)
+#228 := (if #20 #15 #225)
+#231 := (= #37 #228)
+#234 := (forall (vars (?v0 Int) (?v1 Int)) #231)
+#266 := (iff #234 #265)
+#263 := (iff #231 #262)
+#264 := [rewrite]: #263
+#267 := [quant-intro #264]: #266
+#58 := (not #57)
+#152 := (not #149)
+#155 := (and #152 #58)
+#54 := (not #53)
+#61 := (and #54 #58)
+#158 := (or #61 #155)
+#174 := (if #158 #38 #108)
+#177 := (if #19 0::Int #174)
+#180 := (if #20 #15 #177)
+#183 := (= #37 #180)
+#186 := (forall (vars (?v0 Int) (?v1 Int)) #183)
+#235 := (iff #186 #234)
+#232 := (iff #183 #231)
+#229 := (= #180 #228)
+#226 := (= #177 #225)
+#223 := (= #174 #222)
+#207 := (iff #158 #206)
+#204 := (iff #155 #203)
+#205 := [rewrite]: #204
+#200 := (iff #61 #199)
+#201 := [rewrite]: #200
+#208 := [monotonicity #201 #205]: #207
+#224 := [monotonicity #208]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [quant-intro #233]: #235
+#195 := (~ #186 #186)
+#191 := (~ #183 #183)
+#194 := [refl]: #191
+#196 := [nnf-pos #194]: #195
+#64 := (<= 0::Int #15)
+#65 := (not #64)
+#73 := (and #65 #58)
+#76 := (or #61 #73)
+#113 := (if #76 #38 #108)
+#116 := (if #19 0::Int #113)
+#119 := (if #20 #15 #116)
+#122 := (= #37 #119)
+#125 := (forall (vars (?v0 Int) (?v1 Int)) #122)
+#187 := (iff #125 #186)
+#184 := (iff #122 #183)
+#181 := (= #119 #180)
+#178 := (= #116 #177)
+#175 := (= #113 #174)
+#159 := (iff #76 #158)
+#156 := (iff #73 #155)
+#153 := (iff #65 #152)
+#150 := (iff #64 #149)
+#151 := [rewrite]: #150
+#154 := [monotonicity #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#176 := [monotonicity #160]: #175
+#179 := [monotonicity #176]: #178
+#182 := [monotonicity #179]: #181
+#185 := [monotonicity #182]: #184
+#188 := [quant-intro #185]: #187
 #30 := (- #17)
 #29 := (- #15)
 #39 := (mod #29 #30)
@@ -34764,275 +33909,1217 @@
 #22 := (< 0::Int #15)
 #24 := (and #22 #23)
 #27 := (or #24 #26)
-#41 := (ite #27 #38 #40)
-#42 := (ite #19 0::Int #41)
-#43 := (ite #20 #15 #42)
+#41 := (if #27 #38 #40)
+#42 := (if #19 0::Int #41)
+#43 := (if #20 #15 #42)
 #44 := (= #37 #43)
 #45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
-#198 := (iff #45 #195)
-#86 := (and #23 #25)
-#89 := (or #24 #86)
-#168 := (ite #89 #38 #163)
-#77 := (= 0::Int #15)
-#171 := (ite #77 0::Int #168)
-#80 := (= 0::Int #17)
-#174 := (ite #80 #15 #171)
-#177 := (= #37 #174)
-#180 := (forall (vars (?v0 Int) (?v1 Int)) #177)
-#196 := (iff #180 #195)
-#193 := (iff #177 #192)
-#190 := (= #174 #189)
-#187 := (= #171 #186)
-#184 := (= #168 #183)
-#139 := (iff #89 #138)
-#136 := (iff #86 #135)
-#133 := (iff #25 #132)
-#134 := [rewrite]: #133
-#126 := (iff #23 #125)
-#127 := [rewrite]: #126
-#137 := [monotonicity #127 #134]: #136
-#129 := (iff #24 #128)
-#122 := (iff #22 #121)
-#123 := [rewrite]: #122
-#130 := [monotonicity #123 #127]: #129
-#140 := [monotonicity #130 #137]: #139
-#185 := [monotonicity #140]: #184
-#114 := (iff #77 #19)
-#115 := [rewrite]: #114
-#188 := [monotonicity #115 #185]: #187
-#116 := (iff #80 #20)
-#117 := [rewrite]: #116
-#191 := [monotonicity #117 #188]: #190
-#194 := [monotonicity #191]: #193
-#197 := [quant-intro #194]: #196
-#181 := (iff #45 #180)
-#178 := (iff #44 #177)
-#175 := (= #43 #174)
-#172 := (= #42 #171)
-#169 := (= #41 #168)
-#166 := (= #40 #163)
-#160 := (- #157)
-#164 := (= #160 #163)
-#165 := [rewrite]: #164
-#161 := (= #40 #160)
-#158 := (= #39 #157)
-#97 := (= #30 #96)
-#98 := [rewrite]: #97
-#94 := (= #29 #93)
-#95 := [rewrite]: #94
-#159 := [monotonicity #95 #98]: #158
-#162 := [monotonicity #159]: #161
-#167 := [trans #162 #165]: #166
-#90 := (iff #27 #89)
-#87 := (iff #26 #86)
-#88 := [rewrite]: #87
-#91 := [monotonicity #88]: #90
-#170 := [monotonicity #91 #167]: #169
-#78 := (iff #19 #77)
-#79 := [rewrite]: #78
-#173 := [monotonicity #79 #170]: #172
-#81 := (iff #20 #80)
+#126 := (iff #45 #125)
+#123 := (iff #44 #122)
+#120 := (= #43 #119)
+#117 := (= #42 #116)
+#114 := (= #41 #113)
+#111 := (= #40 #108)
+#105 := (- #102)
+#109 := (= #105 #108)
+#110 := [rewrite]: #109
+#106 := (= #40 #105)
+#103 := (= #39 #102)
+#84 := (= #30 #83)
+#85 := [rewrite]: #84
+#81 := (= #29 #80)
 #82 := [rewrite]: #81
-#176 := [monotonicity #82 #173]: #175
+#104 := [monotonicity #82 #85]: #103
+#107 := [monotonicity #104]: #106
+#112 := [trans #107 #110]: #111
+#77 := (iff #27 #76)
+#74 := (iff #26 #73)
+#59 := (iff #23 #58)
+#60 := [rewrite]: #59
+#66 := (iff #25 #65)
+#70 := (iff #65 #65)
+#68 := (iff #64 #64)
+#69 := [rewrite]: #68
+#71 := [monotonicity #69]: #70
+#67 := [rewrite]: #66
+#72 := [trans #67 #71]: #66
+#75 := [monotonicity #72 #60]: #74
+#62 := (iff #24 #61)
+#55 := (iff #22 #54)
+#56 := [rewrite]: #55
+#63 := [monotonicity #56 #60]: #62
+#78 := [monotonicity #63 #75]: #77
+#115 := [monotonicity #78 #112]: #114
+#118 := [monotonicity #115]: #117
+#121 := [monotonicity #118]: #120
+#124 := [monotonicity #121]: #123
+#127 := [quant-intro #124]: #126
+#49 := [asserted]: #45
+#128 := [mp #49 #127]: #125
+#189 := [mp #128 #188]: #186
+#197 := [mp~ #189 #196]: #186
+#237 := [mp #197 #236]: #234
+#268 := [mp #237 #267]: #265
+#696 := [mp #268 #695]: #691
+decl f6 :: Int
+#8 := f6
+#9 := (f4 f5 f6)
+#11 := (f3 #9 0::Int)
+#12 := (= #11 f6)
+#13 := (not #12)
+#47 := [asserted]: #13
+#485 := (not #691)
+#486 := (or #485 #12)
+#345 := (* -1::Int 0::Int)
+#671 := (* -1::Int f6)
+#346 := (mod #671 #345)
+#678 := (+ #11 #346)
+#679 := (= #678 0::Int)
+#675 := (mod f6 0::Int)
+#677 := (* -1::Int #675)
+#334 := (+ #11 #677)
+#464 := (= #334 0::Int)
+#347 := (<= 0::Int 0::Int)
+#360 := (>= f6 0::Int)
+#357 := (or #360 #347)
+#361 := (not #357)
+#356 := (<= f6 0::Int)
+#358 := (or #356 #347)
+#359 := (not #358)
+#340 := (or #359 #361)
+#680 := (if #340 #464 #679)
+#355 := (= #11 0::Int)
+#354 := (= f6 0::Int)
+#681 := (if #354 #355 #680)
+#269 := (= 0::Int 0::Int)
+#676 := (if #269 #12 #681)
+#628 := (or #485 #676)
+#630 := (iff #628 #486)
+#625 := (iff #486 #486)
+#626 := [rewrite]: #625
+#643 := (iff #676 #12)
+#376 := (mod #671 0::Int)
+#651 := (+ #11 #376)
+#366 := (= #651 0::Int)
+#638 := (if #354 #355 #366)
+#1 := true
+#635 := (if true #12 #638)
+#642 := (iff #635 #12)
+#637 := [rewrite]: #642
+#636 := (iff #676 #635)
+#639 := (iff #681 #638)
+#645 := (iff #680 #366)
+#646 := (if false #464 #366)
+#644 := (iff #646 #366)
+#648 := [rewrite]: #644
+#647 := (iff #680 #646)
+#367 := (iff #679 #366)
+#655 := (= #678 #651)
+#650 := (= #346 #376)
+#653 := (= #345 0::Int)
+#375 := [rewrite]: #653
+#654 := [monotonicity #375]: #650
+#365 := [monotonicity #654]: #655
+#368 := [monotonicity #365]: #367
+#275 := (iff #340 false)
+#657 := (or false false)
+#381 := (iff #657 false)
+#382 := [rewrite]: #381
+#379 := (iff #340 #657)
+#670 := (iff #361 false)
+#323 := (not true)
+#661 := (iff #323 false)
+#662 := [rewrite]: #661
+#669 := (iff #361 #323)
+#308 := (iff #357 true)
+#659 := (or #360 true)
+#666 := (iff #659 true)
+#668 := [rewrite]: #666
+#665 := (iff #357 #659)
+#332 := (iff #347 true)
+#337 := [rewrite]: #332
+#303 := [monotonicity #337]: #665
+#309 := [trans #303 #668]: #308
+#667 := [monotonicity #309]: #669
+#656 := [trans #667 #662]: #670
+#663 := (iff #359 false)
+#324 := (iff #359 #323)
+#321 := (iff #358 true)
+#673 := (or #356 true)
+#317 := (iff #673 true)
+#658 := [rewrite]: #317
+#333 := (iff #358 #673)
+#674 := [monotonicity #337]: #333
+#322 := [trans #674 #658]: #321
+#660 := [monotonicity #322]: #324
+#664 := [trans #660 #662]: #663
+#380 := [monotonicity #664 #656]: #379
+#652 := [trans #380 #382]: #275
+#362 := [monotonicity #652 #368]: #647
+#649 := [trans #362 #648]: #645
+#640 := [monotonicity #649]: #639
+#682 := (iff #269 true)
+#672 := [rewrite]: #682
+#641 := [monotonicity #672 #640]: #636
+#484 := [trans #641 #637]: #643
+#631 := [monotonicity #484]: #630
+#632 := [trans #631 #626]: #630
+#629 := [quant-inst #8 #10]: #628
+#633 := [mp #629 #632]: #486
+[unit-resolution #633 #47 #696]: false
+eac86f8245b94dc0d52cdc4d9e88e042a740d116 302 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#17 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#15 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#36 := (f4 f5 #15)
+#37 := (f3 #36 #17)
+#689 := (pattern #37)
+#8 := 0::Int
+#79 := -1::Int
+#83 := (* -1::Int #17)
+#80 := (* -1::Int #15)
+#102 := (mod #80 #83)
+#258 := (+ #37 #102)
+#259 := (= #258 0::Int)
+#38 := (mod #15 #17)
+#255 := (* -1::Int #38)
+#256 := (+ #37 #255)
+#257 := (= #256 0::Int)
+#57 := (<= #17 0::Int)
+#149 := (>= #15 0::Int)
+#202 := (or #149 #57)
+#203 := (not #202)
+#53 := (<= #15 0::Int)
+#198 := (or #53 #57)
+#199 := (not #198)
+#206 := (or #199 #203)
+#260 := (if #206 #257 #259)
+#254 := (= #37 0::Int)
+#19 := (= #15 0::Int)
+#261 := (if #19 #254 #260)
+#253 := (= #37 #15)
+#20 := (= #17 0::Int)
+#262 := (if #20 #253 #261)
+#690 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #689) #262)
+#265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
+#693 := (iff #265 #690)
+#691 := (iff #262 #262)
+#692 := [refl]: #691
+#694 := [quant-intro #692]: #693
+#108 := (* -1::Int #102)
+#222 := (if #206 #38 #108)
+#225 := (if #19 0::Int #222)
+#228 := (if #20 #15 #225)
+#231 := (= #37 #228)
+#234 := (forall (vars (?v0 Int) (?v1 Int)) #231)
+#266 := (iff #234 #265)
+#263 := (iff #231 #262)
+#264 := [rewrite]: #263
+#267 := [quant-intro #264]: #266
+#58 := (not #57)
+#152 := (not #149)
+#155 := (and #152 #58)
+#54 := (not #53)
+#61 := (and #54 #58)
+#158 := (or #61 #155)
+#174 := (if #158 #38 #108)
+#177 := (if #19 0::Int #174)
+#180 := (if #20 #15 #177)
+#183 := (= #37 #180)
+#186 := (forall (vars (?v0 Int) (?v1 Int)) #183)
+#235 := (iff #186 #234)
+#232 := (iff #183 #231)
+#229 := (= #180 #228)
+#226 := (= #177 #225)
+#223 := (= #174 #222)
+#207 := (iff #158 #206)
+#204 := (iff #155 #203)
+#205 := [rewrite]: #204
+#200 := (iff #61 #199)
+#201 := [rewrite]: #200
+#208 := [monotonicity #201 #205]: #207
+#224 := [monotonicity #208]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [quant-intro #233]: #235
+#193 := (~ #186 #186)
+#148 := (~ #183 #183)
+#192 := [refl]: #148
+#196 := [nnf-pos #192]: #193
+#64 := (<= 0::Int #15)
+#65 := (not #64)
+#73 := (and #65 #58)
+#76 := (or #61 #73)
+#113 := (if #76 #38 #108)
+#116 := (if #19 0::Int #113)
+#119 := (if #20 #15 #116)
+#122 := (= #37 #119)
+#125 := (forall (vars (?v0 Int) (?v1 Int)) #122)
+#187 := (iff #125 #186)
+#184 := (iff #122 #183)
+#181 := (= #119 #180)
+#178 := (= #116 #177)
+#175 := (= #113 #174)
+#159 := (iff #76 #158)
+#156 := (iff #73 #155)
+#153 := (iff #65 #152)
+#150 := (iff #64 #149)
+#151 := [rewrite]: #150
+#154 := [monotonicity #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#176 := [monotonicity #160]: #175
 #179 := [monotonicity #176]: #178
-#182 := [quant-intro #179]: #181
-#199 := [trans #182 #197]: #198
-#156 := [asserted]: #45
-#200 := [mp #156 #199]: #195
-#203 := [mp~ #200 #207]: #195
-#251 := [mp #203 #250]: #248
-#282 := [mp #251 #281]: #279
-#767 := [mp #282 #766]: #762
-#10 := (f4 f5 0::Int)
-#11 := (f3 #10 0::Int)
+#182 := [monotonicity #179]: #181
+#185 := [monotonicity #182]: #184
+#188 := [quant-intro #185]: #187
+#30 := (- #17)
+#29 := (- #15)
+#39 := (mod #29 #30)
+#40 := (- #39)
+#23 := (< 0::Int #17)
+#25 := (< #15 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #15)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#41 := (if #27 #38 #40)
+#42 := (if #19 0::Int #41)
+#43 := (if #20 #15 #42)
+#44 := (= #37 #43)
+#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
+#126 := (iff #45 #125)
+#123 := (iff #44 #122)
+#120 := (= #43 #119)
+#117 := (= #42 #116)
+#114 := (= #41 #113)
+#111 := (= #40 #108)
+#105 := (- #102)
+#109 := (= #105 #108)
+#110 := [rewrite]: #109
+#106 := (= #40 #105)
+#103 := (= #39 #102)
+#84 := (= #30 #83)
+#85 := [rewrite]: #84
+#81 := (= #29 #80)
+#82 := [rewrite]: #81
+#104 := [monotonicity #82 #85]: #103
+#107 := [monotonicity #104]: #106
+#112 := [trans #107 #110]: #111
+#77 := (iff #27 #76)
+#74 := (iff #26 #73)
+#59 := (iff #23 #58)
+#60 := [rewrite]: #59
+#66 := (iff #25 #65)
+#70 := (iff #65 #65)
+#68 := (iff #64 #64)
+#69 := [rewrite]: #68
+#71 := [monotonicity #69]: #70
+#67 := [rewrite]: #66
+#72 := [trans #67 #71]: #66
+#75 := [monotonicity #72 #60]: #74
+#62 := (iff #24 #61)
+#55 := (iff #22 #54)
+#56 := [rewrite]: #55
+#63 := [monotonicity #56 #60]: #62
+#78 := [monotonicity #63 #75]: #77
+#115 := [monotonicity #78 #112]: #114
+#118 := [monotonicity #115]: #117
+#121 := [monotonicity #118]: #120
+#124 := [monotonicity #121]: #123
+#127 := [quant-intro #124]: #126
+#49 := [asserted]: #45
+#128 := [mp #49 #127]: #125
+#189 := [mp #128 #188]: #186
+#197 := [mp~ #189 #196]: #186
+#237 := [mp #197 #236]: #234
+#268 := [mp #237 #267]: #265
+#695 := [mp #268 #694]: #690
+#10 := 1::Int
+#9 := (f4 f5 0::Int)
+#11 := (f3 #9 1::Int)
 #12 := (= #11 0::Int)
 #13 := (not #12)
-#65 := [asserted]: #13
-#708 := (not #762)
-#714 := (or #708 #12)
-#340 := (* -1::Int 0::Int)
-#425 := (mod #340 #340)
-#426 := (+ #11 #425)
-#427 := (= #426 0::Int)
-#418 := (mod 0::Int 0::Int)
-#429 := (* -1::Int #418)
-#430 := (+ #11 #429)
-#358 := (= #430 0::Int)
-#431 := (>= 0::Int 0::Int)
-#428 := (<= 0::Int 0::Int)
-#432 := (or #428 #431)
-#411 := (not #432)
-#746 := (or #428 #428)
-#748 := (not #746)
-#405 := (or #748 #411)
-#535 := (ite #405 #358 #427)
-#742 := (= 0::Int 0::Int)
-#416 := (ite #742 #12 #535)
-#66 := (= 0::Int #11)
-#417 := (ite #742 #66 #416)
-#555 := (or #708 #417)
-#557 := (iff #555 #714)
-#700 := (iff #714 #714)
-#701 := [rewrite]: #700
-#712 := (iff #417 #12)
-#1 := true
-#709 := (ite true #12 #12)
-#706 := (iff #709 #12)
-#707 := [rewrite]: #706
-#710 := (iff #417 #709)
-#716 := (iff #416 #12)
-#346 := (+ #11 #418)
-#446 := (= #346 0::Int)
-#717 := (ite true #12 #446)
-#715 := (iff #717 #12)
-#719 := [rewrite]: #715
-#718 := (iff #416 #717)
-#438 := (iff #535 #446)
-#725 := (ite false #358 #446)
-#436 := (iff #725 #446)
-#437 := [rewrite]: #436
-#722 := (iff #535 #725)
-#447 := (iff #427 #446)
-#723 := (= #426 #346)
-#452 := (= #425 #418)
-#450 := (= #340 0::Int)
-#451 := [rewrite]: #450
-#453 := [monotonicity #451 #451]: #452
-#724 := [monotonicity #453]: #723
-#721 := [monotonicity #724]: #447
-#727 := (iff #405 false)
+#47 := [asserted]: #13
+#466 := (not #690)
+#614 := (or #466 #12)
+#670 := (* -1::Int 1::Int)
+#463 := (* -1::Int 0::Int)
+#344 := (mod #463 #670)
+#345 := (+ #11 #344)
+#677 := (= #345 0::Int)
+#339 := (mod 0::Int 1::Int)
+#674 := (* -1::Int #339)
+#676 := (+ #11 #674)
+#333 := (= #676 0::Int)
+#355 := (<= 1::Int 0::Int)
+#358 := (>= 0::Int 0::Int)
+#359 := (or #358 #355)
+#356 := (not #359)
+#354 := (<= 0::Int 0::Int)
+#346 := (or #354 #355)
+#357 := (not #346)
+#360 := (or #357 #356)
+#678 := (if #360 #333 #677)
+#353 := (= 0::Int 0::Int)
+#679 := (if #353 #12 #678)
+#269 := (= 1::Int 0::Int)
+#680 := (if #269 #12 #679)
+#516 := (or #466 #680)
+#612 := (iff #516 #614)
+#500 := (iff #614 #614)
+#515 := [rewrite]: #500
+#506 := (iff #680 #12)
+#624 := (if false #12 #12)
+#632 := (iff #624 #12)
+#626 := [rewrite]: #632
+#623 := (iff #680 #624)
+#622 := (iff #679 #12)
+#1 := true
+#464 := (if true #12 #12)
+#619 := (iff #464 #12)
+#621 := [rewrite]: #619
+#465 := (iff #679 #464)
+#633 := (iff #678 #12)
+#625 := (iff #678 #624)
+#629 := (iff #677 #12)
+#627 := (= #345 #11)
+#367 := (+ #11 0::Int)
+#361 := (= #367 #11)
+#643 := [rewrite]: #361
+#484 := (= #345 #367)
+#642 := (= #344 0::Int)
+#634 := (mod 0::Int -1::Int)
+#641 := (= #634 0::Int)
+#636 := [rewrite]: #641
+#635 := (= #344 #634)
+#638 := (= #670 -1::Int)
+#639 := [rewrite]: #638
+#654 := (= #463 0::Int)
+#364 := [rewrite]: #654
+#640 := [monotonicity #364 #639]: #635
+#483 := [trans #640 #636]: #642
+#485 := [monotonicity #483]: #484
+#628 := [trans #485 #643]: #627
+#630 := [monotonicity #628]: #629
+#648 := (iff #333 #12)
+#647 := (= #676 #11)
+#645 := (= #676 #367)
+#365 := (= #674 0::Int)
+#653 := (= #674 #463)
+#375 := (= #339 0::Int)
+#649 := [rewrite]: #375
+#650 := [monotonicity #649]: #653
+#366 := [trans #650 #364]: #365
+#646 := [monotonicity #366]: #645
+#644 := [trans #646 #643]: #647
+#637 := [monotonicity #644]: #648
+#652 := (iff #360 false)
 #379 := (or false false)
-#738 := (iff #379 false)
-#741 := [rewrite]: #738
-#380 := (iff #405 #379)
-#737 := (iff #411 false)
-#745 := (not true)
-#392 := (iff #745 false)
-#393 := [rewrite]: #392
-#736 := (iff #411 #745)
-#735 := (iff #432 true)
-#747 := (or true true)
-#403 := (iff #747 true)
-#408 := [rewrite]: #403
-#733 := (iff #432 #747)
-#731 := (iff #431 true)
-#732 := [rewrite]: #731
-#751 := (iff #428 true)
-#752 := [rewrite]: #751
-#734 := [monotonicity #752 #732]: #733
-#730 := [trans #734 #408]: #735
-#374 := [monotonicity #730]: #736
-#739 := [trans #374 #393]: #737
-#394 := (iff #748 false)
-#388 := (iff #748 #745)
-#744 := (iff #746 true)
-#753 := (iff #746 #747)
-#743 := [monotonicity #752 #752]: #753
-#404 := [trans #743 #408]: #744
-#729 := [monotonicity #404]: #388
-#395 := [trans #729 #393]: #394
-#740 := [monotonicity #395 #739]: #380
-#728 := [trans #740 #741]: #727
-#726 := [monotonicity #728 #721]: #722
-#439 := [trans #726 #437]: #438
-#749 := (iff #742 true)
-#750 := [rewrite]: #749
-#433 := [monotonicity #750 #439]: #718
-#720 := [trans #433 #719]: #716
-#72 := (iff #66 #12)
-#73 := [rewrite]: #72
-#711 := [monotonicity #750 #73 #720]: #710
-#713 := [trans #711 #707]: #712
-#699 := [monotonicity #713]: #557
-#702 := [trans #699 #701]: #557
-#556 := [quant-inst #9 #9]: #555
-#696 := [mp #556 #702]: #714
-[unit-resolution #696 #65 #767]: false
-unsat
-3f080b795c6233af5c4422b10a1f955ad6c02a32 286 0
+#275 := (iff #379 false)
+#651 := [rewrite]: #275
+#380 := (iff #360 #379)
+#656 := (iff #356 false)
+#660 := (not true)
+#663 := (iff #660 false)
+#658 := [rewrite]: #663
+#669 := (iff #356 #660)
+#668 := (iff #359 true)
+#316 := (or true false)
+#321 := (iff #316 true)
+#322 := [rewrite]: #321
+#307 := (iff #359 #316)
+#332 := (iff #355 false)
+#673 := [rewrite]: #332
+#665 := (iff #358 true)
+#667 := [rewrite]: #665
+#308 := [monotonicity #667 #673]: #307
+#666 := [trans #308 #322]: #668
+#655 := [monotonicity #666]: #669
+#378 := [trans #655 #658]: #656
+#664 := (iff #357 false)
+#661 := (iff #357 #660)
+#323 := (iff #346 true)
+#657 := (iff #346 #316)
+#336 := (iff #354 true)
+#672 := [rewrite]: #336
+#320 := [monotonicity #672 #673]: #657
+#659 := [trans #320 #322]: #323
+#662 := [monotonicity #659]: #661
+#302 := [trans #662 #658]: #664
+#381 := [monotonicity #302 #378]: #380
+#374 := [trans #381 #651]: #652
+#631 := [monotonicity #374 #637 #630]: #625
+#462 := [trans #631 #626]: #633
+#671 := (iff #353 true)
+#331 := [rewrite]: #671
+#618 := [monotonicity #331 #462]: #465
+#620 := [trans #618 #621]: #622
+#675 := (iff #269 false)
+#681 := [rewrite]: #675
+#505 := [monotonicity #681 #620]: #623
+#507 := [trans #505 #626]: #506
+#615 := [monotonicity #507]: #612
+#517 := [trans #615 #515]: #612
+#611 := [quant-inst #8 #10]: #516
+#518 := [mp #611 #517]: #614
+[unit-resolution #518 #47 #695]: false
+b328a65166639bc9762c0041f148bc92847217f4 303 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#17 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#15 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#36 := (f4 f5 #15)
+#37 := (f3 #36 #17)
+#689 := (pattern #37)
+#11 := 0::Int
+#79 := -1::Int
+#83 := (* -1::Int #17)
+#80 := (* -1::Int #15)
+#102 := (mod #80 #83)
+#258 := (+ #37 #102)
+#259 := (= #258 0::Int)
+#38 := (mod #15 #17)
+#255 := (* -1::Int #38)
+#256 := (+ #37 #255)
+#257 := (= #256 0::Int)
+#57 := (<= #17 0::Int)
+#149 := (>= #15 0::Int)
+#202 := (or #149 #57)
+#203 := (not #202)
+#53 := (<= #15 0::Int)
+#198 := (or #53 #57)
+#199 := (not #198)
+#206 := (or #199 #203)
+#260 := (if #206 #257 #259)
+#254 := (= #37 0::Int)
+#19 := (= #15 0::Int)
+#261 := (if #19 #254 #260)
+#253 := (= #37 #15)
+#20 := (= #17 0::Int)
+#262 := (if #20 #253 #261)
+#690 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #689) #262)
+#265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
+#693 := (iff #265 #690)
+#691 := (iff #262 #262)
+#692 := [refl]: #691
+#694 := [quant-intro #692]: #693
+#108 := (* -1::Int #102)
+#222 := (if #206 #38 #108)
+#225 := (if #19 0::Int #222)
+#228 := (if #20 #15 #225)
+#231 := (= #37 #228)
+#234 := (forall (vars (?v0 Int) (?v1 Int)) #231)
+#266 := (iff #234 #265)
+#263 := (iff #231 #262)
+#264 := [rewrite]: #263
+#267 := [quant-intro #264]: #266
+#58 := (not #57)
+#152 := (not #149)
+#155 := (and #152 #58)
+#54 := (not #53)
+#61 := (and #54 #58)
+#158 := (or #61 #155)
+#174 := (if #158 #38 #108)
+#177 := (if #19 0::Int #174)
+#180 := (if #20 #15 #177)
+#183 := (= #37 #180)
+#186 := (forall (vars (?v0 Int) (?v1 Int)) #183)
+#235 := (iff #186 #234)
+#232 := (iff #183 #231)
+#229 := (= #180 #228)
+#226 := (= #177 #225)
+#223 := (= #174 #222)
+#207 := (iff #158 #206)
+#204 := (iff #155 #203)
+#205 := [rewrite]: #204
+#200 := (iff #61 #199)
+#201 := [rewrite]: #200
+#208 := [monotonicity #201 #205]: #207
+#224 := [monotonicity #208]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [quant-intro #233]: #235
+#193 := (~ #186 #186)
+#148 := (~ #183 #183)
+#192 := [refl]: #148
+#196 := [nnf-pos #192]: #193
+#64 := (<= 0::Int #15)
+#65 := (not #64)
+#73 := (and #65 #58)
+#76 := (or #61 #73)
+#113 := (if #76 #38 #108)
+#116 := (if #19 0::Int #113)
+#119 := (if #20 #15 #116)
+#122 := (= #37 #119)
+#125 := (forall (vars (?v0 Int) (?v1 Int)) #122)
+#187 := (iff #125 #186)
+#184 := (iff #122 #183)
+#181 := (= #119 #180)
+#178 := (= #116 #177)
+#175 := (= #113 #174)
+#159 := (iff #76 #158)
+#156 := (iff #73 #155)
+#153 := (iff #65 #152)
+#150 := (iff #64 #149)
+#151 := [rewrite]: #150
+#154 := [monotonicity #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#176 := [monotonicity #160]: #175
+#179 := [monotonicity #176]: #178
+#182 := [monotonicity #179]: #181
+#185 := [monotonicity #182]: #184
+#188 := [quant-intro #185]: #187
+#30 := (- #17)
+#29 := (- #15)
+#39 := (mod #29 #30)
+#40 := (- #39)
+#23 := (< 0::Int #17)
+#25 := (< #15 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #15)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#41 := (if #27 #38 #40)
+#42 := (if #19 0::Int #41)
+#43 := (if #20 #15 #42)
+#44 := (= #37 #43)
+#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
+#126 := (iff #45 #125)
+#123 := (iff #44 #122)
+#120 := (= #43 #119)
+#117 := (= #42 #116)
+#114 := (= #41 #113)
+#111 := (= #40 #108)
+#105 := (- #102)
+#109 := (= #105 #108)
+#110 := [rewrite]: #109
+#106 := (= #40 #105)
+#103 := (= #39 #102)
+#84 := (= #30 #83)
+#85 := [rewrite]: #84
+#81 := (= #29 #80)
+#82 := [rewrite]: #81
+#104 := [monotonicity #82 #85]: #103
+#107 := [monotonicity #104]: #106
+#112 := [trans #107 #110]: #111
+#77 := (iff #27 #76)
+#74 := (iff #26 #73)
+#59 := (iff #23 #58)
+#60 := [rewrite]: #59
+#66 := (iff #25 #65)
+#70 := (iff #65 #65)
+#68 := (iff #64 #64)
+#69 := [rewrite]: #68
+#71 := [monotonicity #69]: #70
+#67 := [rewrite]: #66
+#72 := [trans #67 #71]: #66
+#75 := [monotonicity #72 #60]: #74
+#62 := (iff #24 #61)
+#55 := (iff #22 #54)
+#56 := [rewrite]: #55
+#63 := [monotonicity #56 #60]: #62
+#78 := [monotonicity #63 #75]: #77
+#115 := [monotonicity #78 #112]: #114
+#118 := [monotonicity #115]: #117
+#121 := [monotonicity #118]: #120
+#124 := [monotonicity #121]: #123
+#127 := [quant-intro #124]: #126
+#49 := [asserted]: #45
+#128 := [mp #49 #127]: #125
+#189 := [mp #128 #188]: #186
+#197 := [mp~ #189 #196]: #186
+#237 := [mp #197 #236]: #234
+#268 := [mp #237 #267]: #265
+#695 := [mp #268 #694]: #690
+#8 := 1::Int
+#9 := (f4 f5 1::Int)
+#10 := (f3 #9 1::Int)
+#12 := (= #10 0::Int)
+#13 := (not #12)
+#47 := [asserted]: #13
+#614 := (not #690)
+#516 := (or #614 #12)
+#333 := (* -1::Int 1::Int)
+#463 := (mod #333 #333)
+#670 := (+ #10 #463)
+#344 := (= #670 0::Int)
+#360 := (mod 1::Int 1::Int)
+#339 := (* -1::Int #360)
+#674 := (+ #10 #339)
+#676 := (= #674 0::Int)
+#354 := (<= 1::Int 0::Int)
+#357 := (>= 1::Int 0::Int)
+#358 := (or #357 #354)
+#359 := (not #358)
+#355 := (or #354 #354)
+#346 := (not #355)
+#356 := (or #346 #359)
+#345 := (if #356 #676 #344)
+#269 := (= 1::Int 0::Int)
+#677 := (if #269 #12 #345)
+#353 := (= #10 1::Int)
+#678 := (if #269 #353 #677)
+#611 := (or #614 #678)
+#615 := (iff #611 #516)
+#515 := (iff #516 #516)
+#517 := [rewrite]: #515
+#507 := (iff #678 #12)
+#622 := (if false #353 #12)
+#505 := (iff #622 #12)
+#506 := [rewrite]: #505
+#620 := (iff #678 #622)
+#619 := (iff #677 #12)
+#633 := (if false #12 #12)
+#465 := (iff #633 #12)
+#618 := [rewrite]: #465
+#462 := (iff #677 #633)
+#632 := (iff #345 #12)
+#1 := true
+#629 := (if true #12 #12)
+#625 := (iff #629 #12)
+#631 := [rewrite]: #625
+#630 := (iff #345 #629)
+#627 := (iff #344 #12)
+#484 := (= #670 #10)
+#365 := (+ #10 0::Int)
+#645 := (= #365 #10)
+#646 := [rewrite]: #645
+#642 := (= #670 #365)
+#641 := (= #463 0::Int)
+#638 := (mod -1::Int -1::Int)
+#635 := (= #638 0::Int)
+#640 := [rewrite]: #635
+#639 := (= #463 #638)
+#648 := (= #333 -1::Int)
+#637 := [rewrite]: #648
+#634 := [monotonicity #637 #637]: #639
+#636 := [trans #634 #640]: #641
+#483 := [monotonicity #636]: #642
+#485 := [trans #483 #646]: #484
+#628 := [monotonicity #485]: #627
+#647 := (iff #676 #12)
+#361 := (= #674 #10)
+#366 := (= #674 #365)
+#654 := (= #339 0::Int)
+#374 := (* -1::Int 0::Int)
+#653 := (= #374 0::Int)
+#650 := [rewrite]: #653
+#375 := (= #339 #374)
+#651 := (= #360 0::Int)
+#652 := [rewrite]: #651
+#649 := [monotonicity #652]: #375
+#364 := [trans #649 #650]: #654
+#367 := [monotonicity #364]: #366
+#643 := [trans #367 #646]: #361
+#644 := [monotonicity #643]: #647
+#381 := (iff #356 true)
+#663 := (or true false)
+#302 := (iff #663 true)
+#665 := [rewrite]: #302
+#379 := (iff #356 #663)
+#656 := (iff #359 false)
+#308 := (not true)
+#669 := (iff #308 false)
+#655 := [rewrite]: #669
+#668 := (iff #359 #308)
+#667 := (iff #358 true)
+#658 := (iff #358 #663)
+#675 := (iff #354 false)
+#681 := [rewrite]: #675
+#661 := (iff #357 true)
+#662 := [rewrite]: #661
+#664 := [monotonicity #662 #681]: #658
+#307 := [trans #664 #665]: #667
+#666 := [monotonicity #307]: #668
+#378 := [trans #666 #655]: #656
+#659 := (iff #346 true)
+#657 := (not false)
+#322 := (iff #657 true)
+#323 := [rewrite]: #322
+#320 := (iff #346 #657)
+#673 := (iff #355 false)
+#671 := (or false false)
+#672 := (iff #671 false)
+#332 := [rewrite]: #672
+#331 := (iff #355 #671)
+#336 := [monotonicity #681 #681]: #331
+#316 := [trans #336 #332]: #673
+#321 := [monotonicity #316]: #320
+#660 := [trans #321 #323]: #659
+#380 := [monotonicity #660 #378]: #379
+#275 := [trans #380 #665]: #381
+#624 := [monotonicity #275 #644 #628]: #630
+#626 := [trans #624 #631]: #632
+#679 := (iff #269 false)
+#680 := [rewrite]: #679
+#464 := [monotonicity #680 #626]: #462
+#621 := [trans #464 #618]: #619
+#623 := [monotonicity #680 #621]: #620
+#466 := [trans #623 #506]: #507
+#500 := [monotonicity #466]: #615
+#518 := [trans #500 #517]: #615
+#612 := [quant-inst #8 #8]: #611
+#511 := [mp #612 #518]: #516
+[unit-resolution #511 #47 #695]: false
+c12283e59631fb6e4322b03bf5696f9cba81cc99 314 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #18 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #16 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #37 := (f4 f5 #16)
 #38 := (f3 #37 #18)
-#759 := (pattern #38)
-#11 := 0::Int
-#90 := -1::Int
-#94 := (* -1::Int #18)
-#91 := (* -1::Int #16)
-#155 := (mod #91 #94)
-#270 := (+ #38 #155)
-#271 := (= #270 0::Int)
+#690 := (pattern #38)
+#12 := 0::Int
+#80 := -1::Int
+#84 := (* -1::Int #18)
+#81 := (* -1::Int #16)
+#103 := (mod #81 #84)
+#259 := (+ #38 #103)
+#260 := (= #259 0::Int)
 #39 := (mod #16 #18)
-#267 := (* -1::Int #39)
-#268 := (+ #38 #267)
-#269 := (= #268 0::Int)
-#129 := (>= #16 0::Int)
-#122 := (<= #18 0::Int)
-#214 := (or #122 #129)
-#215 := (not #214)
-#118 := (<= #16 0::Int)
-#212 := (or #118 #122)
-#213 := (not #212)
-#218 := (or #213 #215)
-#272 := (ite #218 #269 #271)
-#266 := (= #38 0::Int)
+#256 := (* -1::Int #39)
+#257 := (+ #38 #256)
+#258 := (= #257 0::Int)
+#58 := (<= #18 0::Int)
+#150 := (>= #16 0::Int)
+#203 := (or #150 #58)
+#204 := (not #203)
+#54 := (<= #16 0::Int)
+#199 := (or #54 #58)
+#200 := (not #199)
+#207 := (or #200 #204)
+#261 := (if #207 #258 #260)
+#255 := (= #38 0::Int)
 #20 := (= #16 0::Int)
-#273 := (ite #20 #266 #272)
-#265 := (= #16 #38)
+#262 := (if #20 #255 #261)
+#254 := (= #38 #16)
 #21 := (= #18 0::Int)
-#274 := (ite #21 #265 #273)
-#760 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #759) #274)
-#277 := (forall (vars (?v0 Int) (?v1 Int)) #274)
-#763 := (iff #277 #760)
-#761 := (iff #274 #274)
-#762 := [refl]: #761
-#764 := [quant-intro #762]: #763
-#161 := (* -1::Int #155)
-#234 := (ite #218 #39 #161)
-#237 := (ite #20 0::Int #234)
-#240 := (ite #21 #16 #237)
-#243 := (= #38 #240)
-#246 := (forall (vars (?v0 Int) (?v1 Int)) #243)
-#278 := (iff #246 #277)
-#275 := (iff #243 #274)
-#276 := [rewrite]: #275
-#279 := [quant-intro #276]: #278
-#130 := (not #129)
-#123 := (not #122)
-#133 := (and #123 #130)
-#119 := (not #118)
-#126 := (and #119 #123)
-#136 := (or #126 #133)
-#181 := (ite #136 #39 #161)
-#184 := (ite #20 0::Int #181)
-#187 := (ite #21 #16 #184)
-#190 := (= #38 #187)
-#193 := (forall (vars (?v0 Int) (?v1 Int)) #190)
-#247 := (iff #193 #246)
-#244 := (iff #190 #243)
-#241 := (= #187 #240)
-#238 := (= #184 #237)
-#235 := (= #181 #234)
-#219 := (iff #136 #218)
-#216 := (iff #133 #215)
-#217 := [rewrite]: #216
-#206 := (iff #126 #213)
-#207 := [rewrite]: #206
-#220 := [monotonicity #207 #217]: #219
-#236 := [monotonicity #220]: #235
-#239 := [monotonicity #236]: #238
-#242 := [monotonicity #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [quant-intro #245]: #247
-#204 := (~ #193 #193)
-#203 := (~ #190 #190)
-#200 := [refl]: #203
-#205 := [nnf-pos #200]: #204
+#263 := (if #21 #254 #262)
+#691 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #690) #263)
+#266 := (forall (vars (?v0 Int) (?v1 Int)) #263)
+#694 := (iff #266 #691)
+#692 := (iff #263 #263)
+#693 := [refl]: #692
+#695 := [quant-intro #693]: #694
+#109 := (* -1::Int #103)
+#223 := (if #207 #39 #109)
+#226 := (if #20 0::Int #223)
+#229 := (if #21 #16 #226)
+#232 := (= #38 #229)
+#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
+#267 := (iff #235 #266)
+#264 := (iff #232 #263)
+#265 := [rewrite]: #264
+#268 := [quant-intro #265]: #267
+#59 := (not #58)
+#153 := (not #150)
+#156 := (and #153 #59)
+#55 := (not #54)
+#62 := (and #55 #59)
+#159 := (or #62 #156)
+#175 := (if #159 #39 #109)
+#178 := (if #20 0::Int #175)
+#181 := (if #21 #16 #178)
+#184 := (= #38 #181)
+#187 := (forall (vars (?v0 Int) (?v1 Int)) #184)
+#236 := (iff #187 #235)
+#233 := (iff #184 #232)
+#230 := (= #181 #229)
+#227 := (= #178 #226)
+#224 := (= #175 #223)
+#208 := (iff #159 #207)
+#205 := (iff #156 #204)
+#206 := [rewrite]: #205
+#201 := (iff #62 #200)
+#202 := [rewrite]: #201
+#209 := [monotonicity #202 #206]: #208
+#225 := [monotonicity #209]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [quant-intro #234]: #236
+#149 := (~ #187 #187)
+#194 := (~ #184 #184)
+#148 := [refl]: #194
+#197 := [nnf-pos #148]: #149
+#65 := (<= 0::Int #16)
+#66 := (not #65)
+#74 := (and #66 #59)
+#77 := (or #62 #74)
+#114 := (if #77 #39 #109)
+#117 := (if #20 0::Int #114)
+#120 := (if #21 #16 #117)
+#123 := (= #38 #120)
+#126 := (forall (vars (?v0 Int) (?v1 Int)) #123)
+#188 := (iff #126 #187)
+#185 := (iff #123 #184)
+#182 := (= #120 #181)
+#179 := (= #117 #178)
+#176 := (= #114 #175)
+#160 := (iff #77 #159)
+#157 := (iff #74 #156)
+#154 := (iff #66 #153)
+#151 := (iff #65 #150)
+#152 := [rewrite]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#177 := [monotonicity #161]: #176
+#180 := [monotonicity #177]: #179
+#183 := [monotonicity #180]: #182
+#186 := [monotonicity #183]: #185
+#189 := [quant-intro #186]: #188
+#31 := (- #18)
+#30 := (- #16)
+#40 := (mod #30 #31)
+#41 := (- #40)
+#24 := (< 0::Int #18)
+#26 := (< #16 0::Int)
+#27 := (and #26 #24)
+#23 := (< 0::Int #16)
+#25 := (and #23 #24)
+#28 := (or #25 #27)
+#42 := (if #28 #39 #41)
+#43 := (if #20 0::Int #42)
+#44 := (if #21 #16 #43)
+#45 := (= #38 #44)
+#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
+#127 := (iff #46 #126)
+#124 := (iff #45 #123)
+#121 := (= #44 #120)
+#118 := (= #43 #117)
+#115 := (= #42 #114)
+#112 := (= #41 #109)
+#106 := (- #103)
+#110 := (= #106 #109)
+#111 := [rewrite]: #110
+#107 := (= #41 #106)
+#104 := (= #40 #103)
+#85 := (= #31 #84)
+#86 := [rewrite]: #85
+#82 := (= #30 #81)
+#83 := [rewrite]: #82
+#105 := [monotonicity #83 #86]: #104
+#108 := [monotonicity #105]: #107
+#113 := [trans #108 #111]: #112
+#78 := (iff #28 #77)
+#75 := (iff #27 #74)
+#60 := (iff #24 #59)
+#61 := [rewrite]: #60
+#67 := (iff #26 #66)
+#71 := (iff #66 #66)
+#69 := (iff #65 #65)
+#70 := [rewrite]: #69
+#72 := [monotonicity #70]: #71
+#68 := [rewrite]: #67
+#73 := [trans #68 #72]: #67
+#76 := [monotonicity #73 #61]: #75
+#63 := (iff #25 #62)
+#56 := (iff #23 #55)
+#57 := [rewrite]: #56
+#64 := [monotonicity #57 #61]: #63
+#79 := [monotonicity #64 #76]: #78
+#116 := [monotonicity #79 #113]: #115
+#119 := [monotonicity #116]: #118
+#122 := [monotonicity #119]: #121
+#125 := [monotonicity #122]: #124
+#128 := [quant-intro #125]: #127
+#50 := [asserted]: #46
+#129 := [mp #50 #128]: #126
+#190 := [mp #129 #189]: #187
+#198 := [mp~ #190 #197]: #187
+#238 := [mp #198 #237]: #235
+#269 := [mp #238 #268]: #266
+#696 := [mp #269 #695]: #691
+#10 := 1::Int
+#8 := 3::Int
+#9 := (f4 f5 3::Int)
+#11 := (f3 #9 1::Int)
+#13 := (= #11 0::Int)
+#14 := (not #13)
+#48 := [asserted]: #14
+#520 := (not #691)
+#521 := (or #520 #13)
+#345 := (* -1::Int 1::Int)
+#671 := (* -1::Int 3::Int)
+#346 := (mod #671 #345)
+#678 := (+ #11 #346)
+#679 := (= #678 0::Int)
+#675 := (mod 3::Int 1::Int)
+#677 := (* -1::Int #675)
+#334 := (+ #11 #677)
+#464 := (= #334 0::Int)
+#347 := (<= 1::Int 0::Int)
+#360 := (>= 3::Int 0::Int)
+#357 := (or #360 #347)
+#361 := (not #357)
+#356 := (<= 3::Int 0::Int)
+#358 := (or #356 #347)
+#359 := (not #358)
+#340 := (or #359 #361)
+#680 := (if #340 #464 #679)
+#355 := (= 3::Int 0::Int)
+#681 := (if #355 #13 #680)
+#354 := (= #11 3::Int)
+#270 := (= 1::Int 0::Int)
+#676 := (if #270 #354 #681)
+#522 := (or #520 #676)
+#524 := (iff #522 #521)
+#614 := (iff #521 #521)
+#618 := [rewrite]: #614
+#519 := (iff #676 #13)
+#613 := (if false #354 #13)
+#516 := (iff #613 #13)
+#518 := [rewrite]: #516
+#616 := (iff #676 #613)
+#517 := (iff #681 #13)
+#506 := (if false #13 #13)
+#467 := (iff #506 #13)
+#615 := [rewrite]: #467
+#507 := (iff #681 #506)
+#621 := (iff #680 #13)
+#1 := true
+#466 := (if true #13 #13)
+#622 := (iff #466 #13)
+#623 := [rewrite]: #622
+#619 := (iff #680 #466)
+#463 := (iff #679 #13)
+#627 := (= #678 #11)
+#648 := (+ #11 0::Int)
+#638 := (= #648 #11)
+#639 := [rewrite]: #638
+#632 := (= #678 #648)
+#625 := (= #346 0::Int)
+#642 := -3::Int
+#486 := (mod -3::Int -1::Int)
+#630 := (= #486 0::Int)
+#631 := [rewrite]: #630
+#628 := (= #346 #486)
+#484 := (= #345 -1::Int)
+#485 := [rewrite]: #484
+#637 := (= #671 -3::Int)
+#643 := [rewrite]: #637
+#629 := [monotonicity #643 #485]: #628
+#626 := [trans #629 #631]: #625
+#633 := [monotonicity #626]: #632
+#634 := [trans #633 #639]: #627
+#465 := [monotonicity #634]: #463
+#636 := (iff #464 #13)
+#640 := (= #334 #11)
+#645 := (= #334 #648)
+#362 := (= #677 0::Int)
+#366 := (* -1::Int 0::Int)
+#646 := (= #366 0::Int)
+#647 := [rewrite]: #646
+#367 := (= #677 #366)
+#655 := (= #675 0::Int)
+#365 := [rewrite]: #655
+#368 := [monotonicity #365]: #367
+#644 := [trans #368 #647]: #362
+#649 := [monotonicity #644]: #645
+#635 := [trans #649 #639]: #640
+#641 := [monotonicity #635]: #636
+#654 := (iff #340 true)
+#309 := (or true false)
+#670 := (iff #309 true)
+#656 := [rewrite]: #670
+#376 := (iff #340 #309)
+#653 := (iff #361 false)
+#380 := (not true)
+#276 := (iff #380 false)
+#652 := [rewrite]: #276
+#381 := (iff #361 #380)
+#657 := (iff #357 true)
+#669 := (iff #357 #309)
+#674 := (iff #347 false)
+#317 := [rewrite]: #674
+#668 := (iff #360 true)
+#308 := [rewrite]: #668
+#667 := [monotonicity #308 #317]: #669
+#379 := [trans #667 #656]: #657
+#382 := [monotonicity #379]: #381
+#375 := [trans #382 #652]: #653
+#303 := (iff #359 true)
+#662 := (not false)
+#659 := (iff #662 true)
+#665 := [rewrite]: #659
+#663 := (iff #359 #662)
+#660 := (iff #358 false)
+#658 := (or false false)
+#323 := (iff #658 false)
+#324 := [rewrite]: #323
+#321 := (iff #358 #658)
+#673 := (iff #356 false)
+#333 := [rewrite]: #673
+#322 := [monotonicity #333 #317]: #321
+#661 := [trans #322 #324]: #660
+#664 := [monotonicity #661]: #663
+#666 := [trans #664 #665]: #303
+#650 := [monotonicity #666 #375]: #376
+#651 := [trans #650 #656]: #654
+#620 := [monotonicity #651 #641 #465]: #619
+#624 := [trans #620 #623]: #621
+#332 := (iff #355 false)
+#337 := [rewrite]: #332
+#508 := [monotonicity #337 #624]: #507
+#612 := [trans #508 #615]: #517
+#682 := (iff #270 false)
+#672 := [rewrite]: #682
+#501 := [monotonicity #672 #612]: #616
+#512 := [trans #501 #518]: #519
+#617 := [monotonicity #512]: #524
+#605 := [trans #617 #618]: #524
+#523 := [quant-inst #8 #10]: #522
+#607 := [mp #523 #605]: #521
+[unit-resolution #607 #48 #696]: false
+13a0ef36b0a684e9e6fa65ca4317572de1110ac0 310 0
+unsat
+#2 := false
+#12 := 0::Int
+decl f6 :: Int
+#8 := f6
+#360 := (>= f6 0::Int)
+#666 := (not #360)
+#356 := (<= f6 0::Int)
+#323 := (not #356)
+#309 := (or #323 #666)
+#621 := (not #309)
+#80 := -1::Int
+#671 := (* -1::Int f6)
+#646 := (mod #671 -1::Int)
+decl f3 :: (-> S2 Int Int)
+#10 := 1::Int
+decl f4 :: (-> S3 Int S2)
+decl f5 :: S3
+#7 := f5
+#9 := (f4 f5 f6)
+#11 := (f3 #9 1::Int)
+#644 := (+ #11 #646)
+#649 := (= #644 0::Int)
+#13 := (= #11 0::Int)
+#640 := (if #309 #13 #649)
+#355 := (= f6 0::Int)
+#641 := (if #355 #13 #640)
+#18 := (:var 0 Int)
+#16 := (:var 1 Int)
+#37 := (f4 f5 #16)
+#38 := (f3 #37 #18)
+#690 := (pattern #38)
+#84 := (* -1::Int #18)
+#81 := (* -1::Int #16)
+#103 := (mod #81 #84)
+#259 := (+ #38 #103)
+#260 := (= #259 0::Int)
+#39 := (mod #16 #18)
+#256 := (* -1::Int #39)
+#257 := (+ #38 #256)
+#258 := (= #257 0::Int)
+#58 := (<= #18 0::Int)
+#150 := (>= #16 0::Int)
+#203 := (or #150 #58)
+#204 := (not #203)
+#54 := (<= #16 0::Int)
+#199 := (or #54 #58)
+#200 := (not #199)
+#207 := (or #200 #204)
+#261 := (if #207 #258 #260)
+#255 := (= #38 0::Int)
+#20 := (= #16 0::Int)
+#262 := (if #20 #255 #261)
+#254 := (= #38 #16)
+#21 := (= #18 0::Int)
+#263 := (if #21 #254 #262)
+#691 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #690) #263)
+#266 := (forall (vars (?v0 Int) (?v1 Int)) #263)
+#694 := (iff #266 #691)
+#692 := (iff #263 #263)
+#693 := [refl]: #692
+#695 := [quant-intro #693]: #694
+#109 := (* -1::Int #103)
+#223 := (if #207 #39 #109)
+#226 := (if #20 0::Int #223)
+#229 := (if #21 #16 #226)
+#232 := (= #38 #229)
+#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
+#267 := (iff #235 #266)
+#264 := (iff #232 #263)
+#265 := [rewrite]: #264
+#268 := [quant-intro #265]: #267
+#59 := (not #58)
+#153 := (not #150)
+#156 := (and #153 #59)
+#55 := (not #54)
+#62 := (and #55 #59)
+#159 := (or #62 #156)
+#175 := (if #159 #39 #109)
+#178 := (if #20 0::Int #175)
+#181 := (if #21 #16 #178)
+#184 := (= #38 #181)
+#187 := (forall (vars (?v0 Int) (?v1 Int)) #184)
+#236 := (iff #187 #235)
+#233 := (iff #184 #232)
+#230 := (= #181 #229)
+#227 := (= #178 #226)
+#224 := (= #175 #223)
+#208 := (iff #159 #207)
+#205 := (iff #156 #204)
+#206 := [rewrite]: #205
+#201 := (iff #62 #200)
+#202 := [rewrite]: #201
+#209 := [monotonicity #202 #206]: #208
+#225 := [monotonicity #209]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [quant-intro #234]: #236
+#149 := (~ #187 #187)
+#192 := (~ #184 #184)
+#148 := [refl]: #192
+#197 := [nnf-pos #148]: #149
+#65 := (<= 0::Int #16)
+#66 := (not #65)
+#74 := (and #66 #59)
+#77 := (or #62 #74)
+#114 := (if #77 #39 #109)
+#117 := (if #20 0::Int #114)
+#120 := (if #21 #16 #117)
+#123 := (= #38 #120)
+#126 := (forall (vars (?v0 Int) (?v1 Int)) #123)
+#188 := (iff #126 #187)
+#185 := (iff #123 #184)
+#182 := (= #120 #181)
+#179 := (= #117 #178)
+#176 := (= #114 #175)
+#160 := (iff #77 #159)
+#157 := (iff #74 #156)
+#154 := (iff #66 #153)
+#151 := (iff #65 #150)
+#152 := [rewrite]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#177 := [monotonicity #161]: #176
+#180 := [monotonicity #177]: #179
+#183 := [monotonicity #180]: #182
+#186 := [monotonicity #183]: #185
+#189 := [quant-intro #186]: #188
 #31 := (- #18)
 #30 := (- #16)
 #40 := (mod #30 #31)
@@ -35043,283 +35130,288 @@
 #23 := (< 0::Int #16)
 #25 := (and #23 #24)
 #28 := (or #25 #27)
-#42 := (ite #28 #39 #41)
-#43 := (ite #20 0::Int #42)
-#44 := (ite #21 #16 #43)
+#42 := (if #28 #39 #41)
+#43 := (if #20 0::Int #42)
+#44 := (if #21 #16 #43)
 #45 := (= #38 #44)
 #46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#196 := (iff #46 #193)
-#84 := (and #24 #26)
-#87 := (or #25 #84)
-#166 := (ite #87 #39 #161)
-#74 := (= 0::Int #16)
-#169 := (ite #74 0::Int #166)
-#78 := (= 0::Int #18)
-#172 := (ite #78 #16 #169)
-#175 := (= #38 #172)
-#178 := (forall (vars (?v0 Int) (?v1 Int)) #175)
-#194 := (iff #178 #193)
-#191 := (iff #175 #190)
-#188 := (= #172 #187)
-#185 := (= #169 #184)
-#182 := (= #166 #181)
-#137 := (iff #87 #136)
-#134 := (iff #84 #133)
-#131 := (iff #26 #130)
-#132 := [rewrite]: #131
-#124 := (iff #24 #123)
-#125 := [rewrite]: #124
-#135 := [monotonicity #125 #132]: #134
-#127 := (iff #25 #126)
-#120 := (iff #23 #119)
-#121 := [rewrite]: #120
-#128 := [monotonicity #121 #125]: #127
-#138 := [monotonicity #128 #135]: #137
-#183 := [monotonicity #138]: #182
-#112 := (iff #74 #20)
-#113 := [rewrite]: #112
-#186 := [monotonicity #113 #183]: #185
-#114 := (iff #78 #21)
-#115 := [rewrite]: #114
-#189 := [monotonicity #115 #186]: #188
-#192 := [monotonicity #189]: #191
-#195 := [quant-intro #192]: #194
-#179 := (iff #46 #178)
-#176 := (iff #45 #175)
-#173 := (= #44 #172)
-#170 := (= #43 #169)
-#167 := (= #42 #166)
-#164 := (= #41 #161)
-#158 := (- #155)
-#162 := (= #158 #161)
-#163 := [rewrite]: #162
-#159 := (= #41 #158)
-#156 := (= #40 #155)
-#95 := (= #31 #94)
-#96 := [rewrite]: #95
-#92 := (= #30 #91)
-#93 := [rewrite]: #92
-#157 := [monotonicity #93 #96]: #156
-#160 := [monotonicity #157]: #159
-#165 := [trans #160 #163]: #164
-#88 := (iff #28 #87)
-#85 := (iff #27 #84)
+#127 := (iff #46 #126)
+#124 := (iff #45 #123)
+#121 := (= #44 #120)
+#118 := (= #43 #117)
+#115 := (= #42 #114)
+#112 := (= #41 #109)
+#106 := (- #103)
+#110 := (= #106 #109)
+#111 := [rewrite]: #110
+#107 := (= #41 #106)
+#104 := (= #40 #103)
+#85 := (= #31 #84)
 #86 := [rewrite]: #85
-#89 := [monotonicity #86]: #88
-#168 := [monotonicity #89 #165]: #167
-#76 := (iff #20 #74)
-#77 := [rewrite]: #76
-#171 := [monotonicity #77 #168]: #170
-#79 := (iff #21 #78)
-#80 := [rewrite]: #79
-#174 := [monotonicity #80 #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [quant-intro #177]: #179
-#197 := [trans #180 #195]: #196
-#154 := [asserted]: #46
-#198 := [mp #154 #197]: #193
-#201 := [mp~ #198 #205]: #193
-#249 := [mp #201 #248]: #246
-#280 := [mp #249 #279]: #277
-#765 := [mp #280 #764]: #760
-decl f6 :: Int
-#9 := f6
-#10 := (f4 f5 f6)
-#12 := (f3 #10 0::Int)
-#67 := (= f6 #12)
-#70 := (not #67)
-#13 := (= #12 f6)
+#82 := (= #30 #81)
+#83 := [rewrite]: #82
+#105 := [monotonicity #83 #86]: #104
+#108 := [monotonicity #105]: #107
+#113 := [trans #108 #111]: #112
+#78 := (iff #28 #77)
+#75 := (iff #27 #74)
+#60 := (iff #24 #59)
+#61 := [rewrite]: #60
+#67 := (iff #26 #66)
+#71 := (iff #66 #66)
+#69 := (iff #65 #65)
+#70 := [rewrite]: #69
+#72 := [monotonicity #70]: #71
+#68 := [rewrite]: #67
+#73 := [trans #68 #72]: #67
+#76 := [monotonicity #73 #61]: #75
+#63 := (iff #25 #62)
+#56 := (iff #23 #55)
+#57 := [rewrite]: #56
+#64 := [monotonicity #57 #61]: #63
+#79 := [monotonicity #64 #76]: #78
+#116 := [monotonicity #79 #113]: #115
+#119 := [monotonicity #116]: #118
+#122 := [monotonicity #119]: #121
+#125 := [monotonicity #122]: #124
+#128 := [quant-intro #125]: #127
+#50 := [asserted]: #46
+#129 := [mp #50 #128]: #126
+#190 := [mp #129 #189]: #187
+#198 := [mp~ #190 #197]: #187
+#238 := [mp #198 #237]: #235
+#269 := [mp #238 #268]: #266
+#696 := [mp #269 #695]: #691
+#631 := (not #691)
+#625 := (or #631 #641)
+#345 := (* -1::Int 1::Int)
+#346 := (mod #671 #345)
+#678 := (+ #11 #346)
+#679 := (= #678 0::Int)
+#675 := (mod f6 1::Int)
+#677 := (* -1::Int #675)
+#334 := (+ #11 #677)
+#464 := (= #334 0::Int)
+#347 := (<= 1::Int 0::Int)
+#357 := (or #360 #347)
+#361 := (not #357)
+#358 := (or #356 #347)
+#359 := (not #358)
+#340 := (or #359 #361)
+#680 := (if #340 #464 #679)
+#681 := (if #355 #13 #680)
+#354 := (= #11 f6)
+#270 := (= 1::Int 0::Int)
+#676 := (if #270 #354 #681)
+#626 := (or #631 #676)
+#633 := (iff #626 #625)
+#634 := (iff #625 #625)
+#463 := [rewrite]: #634
+#629 := (iff #676 #641)
+#643 := (if false #354 #641)
+#486 := (iff #643 #641)
+#628 := [rewrite]: #486
+#484 := (iff #676 #643)
+#642 := (iff #681 #641)
+#635 := (iff #680 #640)
+#638 := (iff #679 #649)
+#648 := (= #678 #644)
+#647 := (= #346 #646)
+#367 := (= #345 -1::Int)
+#368 := [rewrite]: #367
+#362 := [monotonicity #368]: #647
+#645 := [monotonicity #362]: #648
+#639 := [monotonicity #645]: #638
+#365 := (iff #464 #13)
+#651 := (= #334 #11)
+#653 := (+ #11 0::Int)
+#650 := (= #653 #11)
+#654 := [rewrite]: #650
+#375 := (= #334 #653)
+#276 := (= #677 0::Int)
+#657 := (* -1::Int 0::Int)
+#381 := (= #657 0::Int)
+#382 := [rewrite]: #381
+#379 := (= #677 #657)
+#670 := (= #675 0::Int)
+#656 := [rewrite]: #670
+#380 := [monotonicity #656]: #379
+#652 := [trans #380 #382]: #276
+#376 := [monotonicity #652]: #375
+#655 := [trans #376 #654]: #651
+#366 := [monotonicity #655]: #365
+#669 := (iff #340 #309)
+#668 := (iff #361 #666)
+#665 := (iff #357 #360)
+#661 := (or #360 false)
+#664 := (iff #661 #360)
+#659 := [rewrite]: #664
+#662 := (iff #357 #661)
+#332 := (iff #347 false)
+#337 := [rewrite]: #332
+#663 := [monotonicity #337]: #662
+#303 := [trans #663 #659]: #665
+#308 := [monotonicity #303]: #668
+#324 := (iff #359 #323)
+#321 := (iff #358 #356)
+#673 := (or #356 false)
+#317 := (iff #673 #356)
+#658 := [rewrite]: #317
+#333 := (iff #358 #673)
+#674 := [monotonicity #337]: #333
+#322 := [trans #674 #658]: #321
+#660 := [monotonicity #322]: #324
+#667 := [monotonicity #660 #308]: #669
+#636 := [monotonicity #667 #366 #639]: #635
+#637 := [monotonicity #636]: #642
+#682 := (iff #270 false)
+#672 := [rewrite]: #682
+#485 := [monotonicity #672 #637]: #484
+#630 := [trans #485 #628]: #629
+#627 := [monotonicity #630]: #633
+#465 := [trans #627 #463]: #633
+#632 := [quant-inst #8 #10]: #626
+#466 := [mp #632 #465]: #625
+#563 := [unit-resolution #466 #696]: #641
+#520 := (not #355)
+#512 := (not #641)
+#564 := (or #512 #520)
 #14 := (not #13)
-#71 := (iff #14 #70)
-#68 := (iff #13 #67)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#66 := [asserted]: #14
-#75 := [mp #66 #72]: #70
-#553 := (not #760)
-#554 := (or #553 #67)
-#338 := (* -1::Int 0::Int)
-#423 := (* -1::Int f6)
-#424 := (mod #423 #338)
-#425 := (+ #12 #424)
-#416 := (= #425 0::Int)
-#427 := (mod f6 0::Int)
-#428 := (* -1::Int #427)
-#356 := (+ #12 #428)
-#429 := (= #356 0::Int)
-#426 := (>= f6 0::Int)
-#430 := (<= 0::Int 0::Int)
-#409 := (or #430 #426)
-#744 := (not #409)
-#746 := (<= f6 0::Int)
-#403 := (or #746 #430)
-#533 := (not #403)
-#740 := (or #533 #744)
-#414 := (ite #740 #429 #416)
-#415 := (= #12 0::Int)
-#747 := (= f6 0::Int)
-#748 := (ite #747 #415 #414)
-#749 := (= 0::Int 0::Int)
-#750 := (ite #749 #67 #748)
-#555 := (or #553 #750)
-#698 := (iff #555 #554)
-#700 := (iff #554 #554)
-#694 := [rewrite]: #700
-#706 := (iff #750 #67)
-#444 := (mod #423 0::Int)
-#723 := (+ #12 #444)
-#434 := (= #723 0::Int)
-#718 := (ite #747 #415 #434)
-#1 := true
-#709 := (ite true #67 #718)
-#710 := (iff #709 #67)
-#711 := [rewrite]: #710
-#704 := (iff #750 #709)
-#707 := (iff #748 #718)
-#717 := (iff #414 #434)
-#437 := (ite false #429 #434)
-#431 := (iff #437 #434)
-#713 := [rewrite]: #431
-#715 := (iff #414 #437)
-#435 := (iff #416 #434)
-#720 := (= #425 #723)
-#445 := (= #424 #444)
-#721 := (= #338 0::Int)
-#722 := [rewrite]: #721
-#719 := [monotonicity #722]: #445
-#724 := [monotonicity #719]: #720
-#436 := [monotonicity #724]: #435
-#451 := (iff #740 false)
-#725 := (or false false)
-#449 := (iff #725 false)
-#450 := [rewrite]: #449
-#726 := (iff #740 #725)
-#736 := (iff #744 false)
-#391 := (not true)
-#729 := (iff #391 false)
-#730 := [rewrite]: #729
-#378 := (iff #744 #391)
-#737 := (iff #409 true)
-#733 := (or true #426)
-#372 := (iff #733 true)
-#735 := [rewrite]: #372
-#728 := (iff #409 #733)
-#741 := (iff #430 true)
-#401 := [rewrite]: #741
-#734 := [monotonicity #401]: #728
-#377 := [trans #734 #735]: #737
-#738 := [monotonicity #377]: #378
-#739 := [trans #738 #730]: #736
-#731 := (iff #533 false)
-#392 := (iff #533 #391)
-#727 := (iff #403 true)
-#406 := (or #746 true)
-#743 := (iff #406 true)
-#386 := [rewrite]: #743
-#742 := (iff #403 #406)
-#402 := [monotonicity #401]: #742
-#390 := [trans #402 #386]: #727
-#393 := [monotonicity #390]: #392
-#732 := [trans #393 #730]: #731
-#448 := [monotonicity #732 #739]: #726
-#344 := [trans #448 #450]: #451
-#716 := [monotonicity #344 #436]: #715
-#714 := [trans #716 #713]: #717
-#708 := [monotonicity #714]: #707
-#745 := (iff #749 true)
-#751 := [rewrite]: #745
-#705 := [monotonicity #751 #708]: #704
-#712 := [trans #705 #711]: #706
-#699 := [monotonicity #712]: #698
-#695 := [trans #699 #694]: #698
-#697 := [quant-inst #9 #11]: #555
-#701 := [mp #697 #695]: #554
-[unit-resolution #701 #75 #765]: false
-unsat
-92fe8b3236e9b683646a61d1edaeb4be3eebbe17 308 0
+#48 := [asserted]: #14
+#521 := (or #512 #520 #13)
+#522 := [def-axiom]: #521
+#565 := [unit-resolution #522 #48]: #564
+#560 := [unit-resolution #565 #563]: #520
+#523 := (or #512 #355 #640)
+#524 := [def-axiom]: #523
+#566 := [unit-resolution #524 #560 #563]: #640
+#467 := (not #640)
+#552 := (or #467 #621)
+#615 := (or #467 #621 #13)
+#517 := [def-axiom]: #615
+#548 := [unit-resolution #517 #48]: #552
+#549 := [unit-resolution #548 #566]: #621
+#622 := (or #309 #360)
+#623 := [def-axiom]: #622
+#550 := [unit-resolution #623 #549]: #360
+#619 := (or #309 #356)
+#620 := [def-axiom]: #619
+#553 := [unit-resolution #620 #549]: #356
+#554 := (or #355 #323 #666)
+#555 := [th-lemma arith triangle-eq]: #554
+[unit-resolution #555 #560 #553 #550]: false
+1408c1de56e4c2eda00e3072d30651f219cea591 315 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #18 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #16 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #37 := (f4 f5 #16)
 #38 := (f3 #37 #18)
-#761 := (pattern #38)
-#9 := 0::Int
-#93 := -1::Int
-#97 := (* -1::Int #18)
-#94 := (* -1::Int #16)
-#158 := (mod #94 #97)
-#273 := (+ #38 #158)
-#274 := (= #273 0::Int)
-#39 := (mod #16 #18)
-#270 := (* -1::Int #39)
-#271 := (+ #38 #270)
+#702 := (pattern #38)
+#8 := 0::Int
+#54 := -1::Int
+#96 := (* -1::Int #18)
+#93 := (* -1::Int #16)
+#115 := (mod #93 #96)
+#271 := (+ #38 #115)
 #272 := (= #271 0::Int)
-#132 := (>= #16 0::Int)
-#125 := (<= #18 0::Int)
-#217 := (or #125 #132)
-#218 := (not #217)
-#121 := (<= #16 0::Int)
-#215 := (or #121 #125)
+#39 := (mod #16 #18)
+#268 := (* -1::Int #39)
+#269 := (+ #38 #268)
+#270 := (= #269 0::Int)
+#71 := (<= #18 0::Int)
+#162 := (>= #16 0::Int)
+#215 := (or #162 #71)
 #216 := (not #215)
-#221 := (or #216 #218)
-#275 := (ite #221 #272 #274)
-#269 := (= #38 0::Int)
+#67 := (<= #16 0::Int)
+#211 := (or #67 #71)
+#212 := (not #211)
+#219 := (or #212 #216)
+#273 := (if #219 #270 #272)
+#267 := (= #38 0::Int)
 #20 := (= #16 0::Int)
-#276 := (ite #20 #269 #275)
-#268 := (= #16 #38)
+#274 := (if #20 #267 #273)
+#266 := (= #38 #16)
 #21 := (= #18 0::Int)
-#277 := (ite #21 #268 #276)
-#762 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #761) #277)
-#280 := (forall (vars (?v0 Int) (?v1 Int)) #277)
-#765 := (iff #280 #762)
-#763 := (iff #277 #277)
-#764 := [refl]: #763
-#766 := [quant-intro #764]: #765
-#164 := (* -1::Int #158)
-#237 := (ite #221 #39 #164)
-#240 := (ite #20 0::Int #237)
-#243 := (ite #21 #16 #240)
-#246 := (= #38 #243)
-#249 := (forall (vars (?v0 Int) (?v1 Int)) #246)
-#281 := (iff #249 #280)
-#278 := (iff #246 #277)
-#279 := [rewrite]: #278
-#282 := [quant-intro #279]: #281
-#133 := (not #132)
-#126 := (not #125)
-#136 := (and #126 #133)
-#122 := (not #121)
-#129 := (and #122 #126)
-#139 := (or #129 #136)
-#184 := (ite #139 #39 #164)
-#187 := (ite #20 0::Int #184)
-#190 := (ite #21 #16 #187)
-#193 := (= #38 #190)
-#196 := (forall (vars (?v0 Int) (?v1 Int)) #193)
-#250 := (iff #196 #249)
-#247 := (iff #193 #246)
-#244 := (= #190 #243)
-#241 := (= #187 #240)
-#238 := (= #184 #237)
-#222 := (iff #139 #221)
-#219 := (iff #136 #218)
-#220 := [rewrite]: #219
-#209 := (iff #129 #216)
-#210 := [rewrite]: #209
-#223 := [monotonicity #210 #220]: #222
-#239 := [monotonicity #223]: #238
-#242 := [monotonicity #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [monotonicity #245]: #247
-#251 := [quant-intro #248]: #250
-#207 := (~ #196 #196)
-#206 := (~ #193 #193)
-#203 := [refl]: #206
-#208 := [nnf-pos #203]: #207
+#275 := (if #21 #266 #274)
+#703 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #702) #275)
+#278 := (forall (vars (?v0 Int) (?v1 Int)) #275)
+#706 := (iff #278 #703)
+#704 := (iff #275 #275)
+#705 := [refl]: #704
+#707 := [quant-intro #705]: #706
+#121 := (* -1::Int #115)
+#235 := (if #219 #39 #121)
+#238 := (if #20 0::Int #235)
+#241 := (if #21 #16 #238)
+#244 := (= #38 #241)
+#247 := (forall (vars (?v0 Int) (?v1 Int)) #244)
+#279 := (iff #247 #278)
+#276 := (iff #244 #275)
+#277 := [rewrite]: #276
+#280 := [quant-intro #277]: #279
+#72 := (not #71)
+#165 := (not #162)
+#168 := (and #165 #72)
+#68 := (not #67)
+#75 := (and #68 #72)
+#171 := (or #75 #168)
+#187 := (if #171 #39 #121)
+#190 := (if #20 0::Int #187)
+#193 := (if #21 #16 #190)
+#196 := (= #38 #193)
+#199 := (forall (vars (?v0 Int) (?v1 Int)) #196)
+#248 := (iff #199 #247)
+#245 := (iff #196 #244)
+#242 := (= #193 #241)
+#239 := (= #190 #238)
+#236 := (= #187 #235)
+#220 := (iff #171 #219)
+#217 := (iff #168 #216)
+#218 := [rewrite]: #217
+#213 := (iff #75 #212)
+#214 := [rewrite]: #213
+#221 := [monotonicity #214 #218]: #220
+#237 := [monotonicity #221]: #236
+#240 := [monotonicity #237]: #239
+#243 := [monotonicity #240]: #242
+#246 := [monotonicity #243]: #245
+#249 := [quant-intro #246]: #248
+#208 := (~ #199 #199)
+#204 := (~ #196 #196)
+#207 := [refl]: #204
+#209 := [nnf-pos #207]: #208
+#78 := (<= 0::Int #16)
+#79 := (not #78)
+#87 := (and #79 #72)
+#90 := (or #75 #87)
+#126 := (if #90 #39 #121)
+#129 := (if #20 0::Int #126)
+#132 := (if #21 #16 #129)
+#135 := (= #38 #132)
+#138 := (forall (vars (?v0 Int) (?v1 Int)) #135)
+#200 := (iff #138 #199)
+#197 := (iff #135 #196)
+#194 := (= #132 #193)
+#191 := (= #129 #190)
+#188 := (= #126 #187)
+#172 := (iff #90 #171)
+#169 := (iff #87 #168)
+#166 := (iff #79 #165)
+#163 := (iff #78 #162)
+#164 := [rewrite]: #163
+#167 := [monotonicity #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [monotonicity #170]: #172
+#189 := [monotonicity #173]: #188
+#192 := [monotonicity #189]: #191
+#195 := [monotonicity #192]: #194
+#198 := [monotonicity #195]: #197
+#201 := [quant-intro #198]: #200
 #31 := (- #18)
 #30 := (- #16)
 #40 := (mod #30 #31)
@@ -35330,305 +35422,312 @@
 #23 := (< 0::Int #16)
 #25 := (and #23 #24)
 #28 := (or #25 #27)
-#42 := (ite #28 #39 #41)
-#43 := (ite #20 0::Int #42)
-#44 := (ite #21 #16 #43)
+#42 := (if #28 #39 #41)
+#43 := (if #20 0::Int #42)
+#44 := (if #21 #16 #43)
 #45 := (= #38 #44)
 #46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#199 := (iff #46 #196)
-#87 := (and #24 #26)
-#90 := (or #25 #87)
-#169 := (ite #90 #39 #164)
-#78 := (= 0::Int #16)
-#172 := (ite #78 0::Int #169)
-#81 := (= 0::Int #18)
-#175 := (ite #81 #16 #172)
-#178 := (= #38 #175)
-#181 := (forall (vars (?v0 Int) (?v1 Int)) #178)
-#197 := (iff #181 #196)
-#194 := (iff #178 #193)
-#191 := (= #175 #190)
-#188 := (= #172 #187)
-#185 := (= #169 #184)
-#140 := (iff #90 #139)
-#137 := (iff #87 #136)
-#134 := (iff #26 #133)
-#135 := [rewrite]: #134
-#127 := (iff #24 #126)
-#128 := [rewrite]: #127
-#138 := [monotonicity #128 #135]: #137
-#130 := (iff #25 #129)
-#123 := (iff #23 #122)
-#124 := [rewrite]: #123
-#131 := [monotonicity #124 #128]: #130
-#141 := [monotonicity #131 #138]: #140
-#186 := [monotonicity #141]: #185
-#115 := (iff #78 #20)
-#116 := [rewrite]: #115
-#189 := [monotonicity #116 #186]: #188
-#117 := (iff #81 #21)
-#118 := [rewrite]: #117
-#192 := [monotonicity #118 #189]: #191
-#195 := [monotonicity #192]: #194
-#198 := [quant-intro #195]: #197
-#182 := (iff #46 #181)
-#179 := (iff #45 #178)
-#176 := (= #44 #175)
-#173 := (= #43 #172)
-#170 := (= #42 #169)
-#167 := (= #41 #164)
-#161 := (- #158)
-#165 := (= #161 #164)
-#166 := [rewrite]: #165
-#162 := (= #41 #161)
-#159 := (= #40 #158)
-#98 := (= #31 #97)
-#99 := [rewrite]: #98
-#95 := (= #30 #94)
-#96 := [rewrite]: #95
-#160 := [monotonicity #96 #99]: #159
-#163 := [monotonicity #160]: #162
-#168 := [trans #163 #166]: #167
+#139 := (iff #46 #138)
+#136 := (iff #45 #135)
+#133 := (= #44 #132)
+#130 := (= #43 #129)
+#127 := (= #42 #126)
+#124 := (= #41 #121)
+#118 := (- #115)
+#122 := (= #118 #121)
+#123 := [rewrite]: #122
+#119 := (= #41 #118)
+#116 := (= #40 #115)
+#97 := (= #31 #96)
+#98 := [rewrite]: #97
+#94 := (= #30 #93)
+#95 := [rewrite]: #94
+#117 := [monotonicity #95 #98]: #116
+#120 := [monotonicity #117]: #119
+#125 := [trans #120 #123]: #124
 #91 := (iff #28 #90)
 #88 := (iff #27 #87)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#171 := [monotonicity #92 #168]: #170
-#79 := (iff #20 #78)
-#80 := [rewrite]: #79
-#174 := [monotonicity #80 #171]: #173
-#82 := (iff #21 #81)
+#73 := (iff #24 #72)
+#74 := [rewrite]: #73
+#80 := (iff #26 #79)
+#84 := (iff #79 #79)
+#82 := (iff #78 #78)
 #83 := [rewrite]: #82
-#177 := [monotonicity #83 #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [quant-intro #180]: #182
-#200 := [trans #183 #198]: #199
-#157 := [asserted]: #46
-#201 := [mp #157 #200]: #196
-#204 := [mp~ #201 #208]: #196
-#252 := [mp #204 #251]: #249
-#283 := [mp #252 #282]: #280
-#767 := [mp #283 #766]: #762
-#11 := 1::Int
-#10 := (f4 f5 0::Int)
-#12 := (f3 #10 1::Int)
+#85 := [monotonicity #83]: #84
+#81 := [rewrite]: #80
+#86 := [trans #81 #85]: #80
+#89 := [monotonicity #86 #74]: #88
+#76 := (iff #25 #75)
+#69 := (iff #23 #68)
+#70 := [rewrite]: #69
+#77 := [monotonicity #70 #74]: #76
+#92 := [monotonicity #77 #89]: #91
+#128 := [monotonicity #92 #125]: #127
+#131 := [monotonicity #128]: #130
+#134 := [monotonicity #131]: #133
+#137 := [monotonicity #134]: #136
+#140 := [quant-intro #137]: #139
+#50 := [asserted]: #46
+#141 := [mp #50 #140]: #138
+#202 := [mp #141 #201]: #199
+#210 := [mp~ #202 #209]: #199
+#250 := [mp #210 #249]: #247
+#281 := [mp #250 #280]: #278
+#708 := [mp #281 #707]: #703
+#9 := (f4 f5 0::Int)
+#57 := (f3 #9 -1::Int)
+#60 := (= #57 0::Int)
+#63 := (not #60)
+#10 := 1::Int
+#11 := (- 1::Int)
+#12 := (f3 #9 #11)
 #13 := (= #12 0::Int)
 #14 := (not #13)
-#66 := [asserted]: #14
-#683 := (not #762)
-#684 := (or #683 #13)
-#341 := (* -1::Int 1::Int)
-#425 := (* -1::Int 0::Int)
-#426 := (mod #425 #341)
-#427 := (+ #12 #426)
-#418 := (= #427 0::Int)
-#429 := (mod 0::Int 1::Int)
-#430 := (* -1::Int #429)
-#431 := (+ #12 #430)
-#428 := (= #431 0::Int)
-#432 := (>= 0::Int 0::Int)
-#411 := (<= 1::Int 0::Int)
-#746 := (or #411 #432)
-#748 := (not #746)
-#405 := (<= 0::Int 0::Int)
-#535 := (or #405 #411)
-#742 := (not #535)
-#416 := (or #742 #748)
-#417 := (ite #416 #428 #418)
-#749 := (= 0::Int 0::Int)
-#750 := (ite #749 #13 #417)
-#67 := (= 0::Int #12)
-#751 := (= 1::Int 0::Int)
-#752 := (ite #751 #67 #750)
-#687 := (or #683 #752)
-#587 := (iff #687 #684)
-#590 := (iff #684 #684)
-#583 := [rewrite]: #590
-#686 := (iff #752 #13)
-#704 := (ite false #13 #13)
-#534 := (iff #704 #13)
-#536 := [rewrite]: #534
-#579 := (iff #752 #704)
-#577 := (iff #750 #13)
-#1 := true
-#691 := (ite true #13 #13)
-#692 := (iff #691 #13)
-#695 := [rewrite]: #692
-#693 := (iff #750 #691)
-#537 := (iff #417 #13)
-#698 := (iff #417 #704)
-#697 := (iff #418 #13)
-#702 := (= #427 #12)
-#433 := (+ #12 0::Int)
-#716 := (= #433 #12)
-#720 := [rewrite]: #716
-#700 := (= #427 #433)
-#557 := (= #426 0::Int)
-#713 := (mod 0::Int -1::Int)
-#555 := (= #713 0::Int)
-#556 := [rewrite]: #555
-#708 := (= #426 #713)
-#707 := (= #341 -1::Int)
-#712 := [rewrite]: #707
-#438 := (= #425 0::Int)
-#439 := [rewrite]: #438
-#714 := [monotonicity #439 #712]: #708
-#699 := [trans #714 #556]: #557
-#701 := [monotonicity #699]: #700
-#696 := [trans #701 #720]: #702
-#703 := [monotonicity #696]: #697
-#711 := (iff #428 #13)
-#709 := (= #431 #12)
-#715 := (= #431 #433)
-#717 := (= #430 0::Int)
-#436 := (= #430 #425)
-#722 := (= #429 0::Int)
-#726 := [rewrite]: #722
-#437 := [monotonicity #726]: #436
-#718 := [trans #437 #439]: #717
-#719 := [monotonicity #718]: #715
-#710 := [trans #719 #720]: #709
-#706 := [monotonicity #710]: #711
-#721 := (iff #416 false)
-#347 := (or false false)
-#446 := (iff #347 false)
-#447 := [rewrite]: #446
-#723 := (iff #416 #347)
-#452 := (iff #748 false)
-#732 := (not true)
-#735 := (iff #732 false)
-#730 := [rewrite]: #735
-#450 := (iff #748 #732)
-#727 := (iff #746 true)
-#379 := (or false true)
-#738 := (iff #379 true)
-#741 := [rewrite]: #738
-#380 := (iff #746 #379)
-#737 := (iff #432 true)
-#739 := [rewrite]: #737
-#404 := (iff #411 false)
-#745 := [rewrite]: #404
-#740 := [monotonicity #745 #739]: #380
-#728 := [trans #740 #741]: #727
-#451 := [monotonicity #728]: #450
-#453 := [trans #451 #730]: #452
-#736 := (iff #742 false)
-#733 := (iff #742 #732)
-#395 := (iff #535 true)
-#388 := (or true false)
-#393 := (iff #388 true)
-#394 := [rewrite]: #393
-#729 := (iff #535 #388)
-#408 := (iff #405 true)
-#744 := [rewrite]: #408
-#392 := [monotonicity #744 #745]: #729
-#731 := [trans #392 #394]: #395
-#734 := [monotonicity #731]: #733
-#374 := [trans #734 #730]: #736
-#724 := [monotonicity #374 #453]: #723
-#725 := [trans #724 #447]: #721
-#705 := [monotonicity #725 #706 #703]: #698
-#690 := [trans #705 #536]: #537
-#743 := (iff #749 true)
-#403 := [rewrite]: #743
-#694 := [monotonicity #403 #690]: #693
-#578 := [trans #694 #695]: #577
-#73 := (iff #67 #13)
-#74 := [rewrite]: #73
-#747 := (iff #751 false)
-#753 := [rewrite]: #747
-#538 := [monotonicity #753 #74 #578]: #579
-#588 := [trans #538 #536]: #686
-#589 := [monotonicity #588]: #587
-#591 := [trans #589 #583]: #587
-#572 := [quant-inst #9 #11]: #687
-#592 := [mp #572 #591]: #684
-[unit-resolution #592 #66 #767]: false
-unsat
-dbfbec508dfad574448ad70185c575b9e410bcdb 309 0
+#64 := (iff #14 #63)
+#61 := (iff #13 #60)
+#58 := (= #12 #57)
+#55 := (= #11 -1::Int)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#62 := [monotonicity #59]: #61
+#65 := [monotonicity #62]: #64
+#48 := [asserted]: #14
+#66 := [mp #48 #65]: #63
+#479 := (not #703)
+#627 := (or #479 #60)
+#683 := (* -1::Int -1::Int)
+#476 := (* -1::Int 0::Int)
+#357 := (mod #476 #683)
+#358 := (+ #57 #357)
+#690 := (= #358 0::Int)
+#352 := (mod 0::Int -1::Int)
+#687 := (* -1::Int #352)
+#689 := (+ #57 #687)
+#346 := (= #689 0::Int)
+#368 := (<= -1::Int 0::Int)
+#371 := (>= 0::Int 0::Int)
+#372 := (or #371 #368)
+#369 := (not #372)
+#367 := (<= 0::Int 0::Int)
+#359 := (or #367 #368)
+#370 := (not #359)
+#373 := (or #370 #369)
+#691 := (if #373 #346 #690)
+#366 := (= 0::Int 0::Int)
+#692 := (if #366 #60 #691)
+#282 := (= -1::Int 0::Int)
+#693 := (if #282 #60 #692)
+#529 := (or #479 #693)
+#625 := (iff #529 #627)
+#513 := (iff #627 #627)
+#528 := [rewrite]: #513
+#519 := (iff #693 #60)
+#637 := (if false #60 #60)
+#645 := (iff #637 #60)
+#639 := [rewrite]: #645
+#636 := (iff #693 #637)
+#635 := (iff #692 #60)
+#1 := true
+#477 := (if true #60 #60)
+#632 := (iff #477 #60)
+#634 := [rewrite]: #632
+#478 := (iff #692 #477)
+#646 := (iff #691 #60)
+#638 := (iff #691 #637)
+#642 := (iff #690 #60)
+#640 := (= #358 #57)
+#380 := (+ #57 0::Int)
+#374 := (= #380 #57)
+#656 := [rewrite]: #374
+#497 := (= #358 #380)
+#655 := (= #357 0::Int)
+#647 := (mod 0::Int 1::Int)
+#654 := (= #647 0::Int)
+#649 := [rewrite]: #654
+#648 := (= #357 #647)
+#651 := (= #683 1::Int)
+#652 := [rewrite]: #651
+#667 := (= #476 0::Int)
+#377 := [rewrite]: #667
+#653 := [monotonicity #377 #652]: #648
+#496 := [trans #653 #649]: #655
+#498 := [monotonicity #496]: #497
+#641 := [trans #498 #656]: #640
+#643 := [monotonicity #641]: #642
+#661 := (iff #346 #60)
+#660 := (= #689 #57)
+#658 := (= #689 #380)
+#378 := (= #687 0::Int)
+#666 := (= #687 #476)
+#388 := (= #352 0::Int)
+#662 := [rewrite]: #388
+#663 := [monotonicity #662]: #666
+#379 := [trans #663 #377]: #378
+#659 := [monotonicity #379]: #658
+#657 := [trans #659 #656]: #660
+#650 := [monotonicity #657]: #661
+#665 := (iff #373 false)
+#392 := (or false false)
+#288 := (iff #392 false)
+#664 := [rewrite]: #288
+#393 := (iff #373 #392)
+#669 := (iff #369 false)
+#673 := (not true)
+#676 := (iff #673 false)
+#671 := [rewrite]: #676
+#682 := (iff #369 #673)
+#681 := (iff #372 true)
+#329 := (or true true)
+#334 := (iff #329 true)
+#335 := [rewrite]: #334
+#320 := (iff #372 #329)
+#345 := (iff #368 true)
+#686 := [rewrite]: #345
+#678 := (iff #371 true)
+#680 := [rewrite]: #678
+#321 := [monotonicity #680 #686]: #320
+#679 := [trans #321 #335]: #681
+#668 := [monotonicity #679]: #682
+#391 := [trans #668 #671]: #669
+#677 := (iff #370 false)
+#674 := (iff #370 #673)
+#336 := (iff #359 true)
+#670 := (iff #359 #329)
+#349 := (iff #367 true)
+#685 := [rewrite]: #349
+#333 := [monotonicity #685 #686]: #670
+#672 := [trans #333 #335]: #336
+#675 := [monotonicity #672]: #674
+#315 := [trans #675 #671]: #677
+#394 := [monotonicity #315 #391]: #393
+#387 := [trans #394 #664]: #665
+#644 := [monotonicity #387 #650 #643]: #638
+#475 := [trans #644 #639]: #646
+#684 := (iff #366 true)
+#344 := [rewrite]: #684
+#631 := [monotonicity #344 #475]: #478
+#633 := [trans #631 #634]: #635
+#688 := (iff #282 false)
+#694 := [rewrite]: #688
+#518 := [monotonicity #694 #633]: #636
+#520 := [trans #518 #639]: #519
+#628 := [monotonicity #520]: #625
+#530 := [trans #628 #528]: #625
+#624 := [quant-inst #8 #54]: #529
+#531 := [mp #624 #530]: #627
+[unit-resolution #531 #66 #708]: false
+d3eb3a34e82f6e4956530fdf12a1b5f1a3da5b8d 322 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #18 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #16 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #37 := (f4 f5 #16)
 #38 := (f3 #37 #18)
-#751 := (pattern #38)
+#702 := (pattern #38)
 #12 := 0::Int
-#83 := -1::Int
-#87 := (* -1::Int #18)
-#84 := (* -1::Int #16)
-#148 := (mod #84 #87)
-#263 := (+ #38 #148)
-#264 := (= #263 0::Int)
+#54 := -1::Int
+#96 := (* -1::Int #18)
+#93 := (* -1::Int #16)
+#115 := (mod #93 #96)
+#271 := (+ #38 #115)
+#272 := (= #271 0::Int)
 #39 := (mod #16 #18)
-#260 := (* -1::Int #39)
-#261 := (+ #38 #260)
-#262 := (= #261 0::Int)
-#122 := (>= #16 0::Int)
-#115 := (<= #18 0::Int)
-#207 := (or #115 #122)
-#208 := (not #207)
-#111 := (<= #16 0::Int)
-#205 := (or #111 #115)
-#206 := (not #205)
-#211 := (or #206 #208)
-#265 := (ite #211 #262 #264)
-#259 := (= #38 0::Int)
+#268 := (* -1::Int #39)
+#269 := (+ #38 #268)
+#270 := (= #269 0::Int)
+#71 := (<= #18 0::Int)
+#162 := (>= #16 0::Int)
+#215 := (or #162 #71)
+#216 := (not #215)
+#67 := (<= #16 0::Int)
+#211 := (or #67 #71)
+#212 := (not #211)
+#219 := (or #212 #216)
+#273 := (if #219 #270 #272)
+#267 := (= #38 0::Int)
 #20 := (= #16 0::Int)
-#266 := (ite #20 #259 #265)
-#258 := (= #16 #38)
+#274 := (if #20 #267 #273)
+#266 := (= #38 #16)
 #21 := (= #18 0::Int)
-#267 := (ite #21 #258 #266)
-#752 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #751) #267)
-#270 := (forall (vars (?v0 Int) (?v1 Int)) #267)
-#755 := (iff #270 #752)
-#753 := (iff #267 #267)
-#754 := [refl]: #753
-#756 := [quant-intro #754]: #755
-#154 := (* -1::Int #148)
-#227 := (ite #211 #39 #154)
-#230 := (ite #20 0::Int #227)
-#233 := (ite #21 #16 #230)
-#236 := (= #38 #233)
-#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
-#271 := (iff #239 #270)
-#268 := (iff #236 #267)
-#269 := [rewrite]: #268
-#272 := [quant-intro #269]: #271
-#123 := (not #122)
-#116 := (not #115)
-#126 := (and #116 #123)
-#112 := (not #111)
-#119 := (and #112 #116)
-#129 := (or #119 #126)
-#174 := (ite #129 #39 #154)
-#177 := (ite #20 0::Int #174)
-#180 := (ite #21 #16 #177)
-#183 := (= #38 #180)
-#186 := (forall (vars (?v0 Int) (?v1 Int)) #183)
-#240 := (iff #186 #239)
-#237 := (iff #183 #236)
-#234 := (= #180 #233)
-#231 := (= #177 #230)
-#228 := (= #174 #227)
-#212 := (iff #129 #211)
-#209 := (iff #126 #208)
-#210 := [rewrite]: #209
-#199 := (iff #119 #206)
-#200 := [rewrite]: #199
-#213 := [monotonicity #200 #210]: #212
-#229 := [monotonicity #213]: #228
-#232 := [monotonicity #229]: #231
-#235 := [monotonicity #232]: #234
-#238 := [monotonicity #235]: #237
-#241 := [quant-intro #238]: #240
-#197 := (~ #186 #186)
-#196 := (~ #183 #183)
-#193 := [refl]: #196
-#198 := [nnf-pos #193]: #197
+#275 := (if #21 #266 #274)
+#703 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #702) #275)
+#278 := (forall (vars (?v0 Int) (?v1 Int)) #275)
+#706 := (iff #278 #703)
+#704 := (iff #275 #275)
+#705 := [refl]: #704
+#707 := [quant-intro #705]: #706
+#121 := (* -1::Int #115)
+#235 := (if #219 #39 #121)
+#238 := (if #20 0::Int #235)
+#241 := (if #21 #16 #238)
+#244 := (= #38 #241)
+#247 := (forall (vars (?v0 Int) (?v1 Int)) #244)
+#279 := (iff #247 #278)
+#276 := (iff #244 #275)
+#277 := [rewrite]: #276
+#280 := [quant-intro #277]: #279
+#72 := (not #71)
+#165 := (not #162)
+#168 := (and #165 #72)
+#68 := (not #67)
+#75 := (and #68 #72)
+#171 := (or #75 #168)
+#187 := (if #171 #39 #121)
+#190 := (if #20 0::Int #187)
+#193 := (if #21 #16 #190)
+#196 := (= #38 #193)
+#199 := (forall (vars (?v0 Int) (?v1 Int)) #196)
+#248 := (iff #199 #247)
+#245 := (iff #196 #244)
+#242 := (= #193 #241)
+#239 := (= #190 #238)
+#236 := (= #187 #235)
+#220 := (iff #171 #219)
+#217 := (iff #168 #216)
+#218 := [rewrite]: #217
+#213 := (iff #75 #212)
+#214 := [rewrite]: #213
+#221 := [monotonicity #214 #218]: #220
+#237 := [monotonicity #221]: #236
+#240 := [monotonicity #237]: #239
+#243 := [monotonicity #240]: #242
+#246 := [monotonicity #243]: #245
+#249 := [quant-intro #246]: #248
+#208 := (~ #199 #199)
+#204 := (~ #196 #196)
+#207 := [refl]: #204
+#209 := [nnf-pos #207]: #208
+#78 := (<= 0::Int #16)
+#79 := (not #78)
+#87 := (and #79 #72)
+#90 := (or #75 #87)
+#126 := (if #90 #39 #121)
+#129 := (if #20 0::Int #126)
+#132 := (if #21 #16 #129)
+#135 := (= #38 #132)
+#138 := (forall (vars (?v0 Int) (?v1 Int)) #135)
+#200 := (iff #138 #199)
+#197 := (iff #135 #196)
+#194 := (= #132 #193)
+#191 := (= #129 #190)
+#188 := (= #126 #187)
+#172 := (iff #90 #171)
+#169 := (iff #87 #168)
+#166 := (iff #79 #165)
+#163 := (iff #78 #162)
+#164 := [rewrite]: #163
+#167 := [monotonicity #164]: #166
+#170 := [monotonicity #167]: #169
+#173 := [monotonicity #170]: #172
+#189 := [monotonicity #173]: #188
+#192 := [monotonicity #189]: #191
+#195 := [monotonicity #192]: #194
+#198 := [monotonicity #195]: #197
+#201 := [quant-intro #198]: #200
 #31 := (- #18)
 #30 := (- #16)
 #40 := (mod #30 #31)
@@ -35639,306 +35738,319 @@
 #23 := (< 0::Int #16)
 #25 := (and #23 #24)
 #28 := (or #25 #27)
-#42 := (ite #28 #39 #41)
-#43 := (ite #20 0::Int #42)
-#44 := (ite #21 #16 #43)
+#42 := (if #28 #39 #41)
+#43 := (if #20 0::Int #42)
+#44 := (if #21 #16 #43)
 #45 := (= #38 #44)
 #46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#189 := (iff #46 #186)
-#77 := (and #24 #26)
-#80 := (or #25 #77)
-#159 := (ite #80 #39 #154)
-#68 := (= 0::Int #16)
-#162 := (ite #68 0::Int #159)
-#71 := (= 0::Int #18)
-#165 := (ite #71 #16 #162)
-#168 := (= #38 #165)
-#171 := (forall (vars (?v0 Int) (?v1 Int)) #168)
-#187 := (iff #171 #186)
-#184 := (iff #168 #183)
-#181 := (= #165 #180)
-#178 := (= #162 #177)
-#175 := (= #159 #174)
-#130 := (iff #80 #129)
-#127 := (iff #77 #126)
-#124 := (iff #26 #123)
-#125 := [rewrite]: #124
-#117 := (iff #24 #116)
-#118 := [rewrite]: #117
-#128 := [monotonicity #118 #125]: #127
-#120 := (iff #25 #119)
-#113 := (iff #23 #112)
-#114 := [rewrite]: #113
-#121 := [monotonicity #114 #118]: #120
-#131 := [monotonicity #121 #128]: #130
-#176 := [monotonicity #131]: #175
-#105 := (iff #68 #20)
-#106 := [rewrite]: #105
-#179 := [monotonicity #106 #176]: #178
-#107 := (iff #71 #21)
-#108 := [rewrite]: #107
-#182 := [monotonicity #108 #179]: #181
-#185 := [monotonicity #182]: #184
-#188 := [quant-intro #185]: #187
-#172 := (iff #46 #171)
-#169 := (iff #45 #168)
-#166 := (= #44 #165)
-#163 := (= #43 #162)
-#160 := (= #42 #159)
-#157 := (= #41 #154)
-#151 := (- #148)
-#155 := (= #151 #154)
-#156 := [rewrite]: #155
-#152 := (= #41 #151)
-#149 := (= #40 #148)
-#88 := (= #31 #87)
-#89 := [rewrite]: #88
-#85 := (= #30 #84)
-#86 := [rewrite]: #85
-#150 := [monotonicity #86 #89]: #149
-#153 := [monotonicity #150]: #152
-#158 := [trans #153 #156]: #157
-#81 := (iff #28 #80)
-#78 := (iff #27 #77)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#161 := [monotonicity #82 #158]: #160
-#69 := (iff #20 #68)
+#139 := (iff #46 #138)
+#136 := (iff #45 #135)
+#133 := (= #44 #132)
+#130 := (= #43 #129)
+#127 := (= #42 #126)
+#124 := (= #41 #121)
+#118 := (- #115)
+#122 := (= #118 #121)
+#123 := [rewrite]: #122
+#119 := (= #41 #118)
+#116 := (= #40 #115)
+#97 := (= #31 #96)
+#98 := [rewrite]: #97
+#94 := (= #30 #93)
+#95 := [rewrite]: #94
+#117 := [monotonicity #95 #98]: #116
+#120 := [monotonicity #117]: #119
+#125 := [trans #120 #123]: #124
+#91 := (iff #28 #90)
+#88 := (iff #27 #87)
+#73 := (iff #24 #72)
+#74 := [rewrite]: #73
+#80 := (iff #26 #79)
+#84 := (iff #79 #79)
+#82 := (iff #78 #78)
+#83 := [rewrite]: #82
+#85 := [monotonicity #83]: #84
+#81 := [rewrite]: #80
+#86 := [trans #81 #85]: #80
+#89 := [monotonicity #86 #74]: #88
+#76 := (iff #25 #75)
+#69 := (iff #23 #68)
 #70 := [rewrite]: #69
-#164 := [monotonicity #70 #161]: #163
-#72 := (iff #21 #71)
-#73 := [rewrite]: #72
-#167 := [monotonicity #73 #164]: #166
-#170 := [monotonicity #167]: #169
-#173 := [quant-intro #170]: #172
-#190 := [trans #173 #188]: #189
-#147 := [asserted]: #46
-#191 := [mp #147 #190]: #186
-#194 := [mp~ #191 #198]: #186
-#242 := [mp #194 #241]: #239
-#273 := [mp #242 #272]: #270
-#757 := [mp #273 #756]: #752
-#9 := 1::Int
-#10 := (f4 f5 1::Int)
-#11 := (f3 #10 1::Int)
+#77 := [monotonicity #70 #74]: #76
+#92 := [monotonicity #77 #89]: #91
+#128 := [monotonicity #92 #125]: #127
+#131 := [monotonicity #128]: #130
+#134 := [monotonicity #131]: #133
+#137 := [monotonicity #134]: #136
+#140 := [quant-intro #137]: #139
+#50 := [asserted]: #46
+#141 := [mp #50 #140]: #138
+#202 := [mp #141 #201]: #199
+#210 := [mp~ #202 #209]: #199
+#250 := [mp #210 #249]: #247
+#281 := [mp #250 #280]: #278
+#708 := [mp #281 #707]: #703
+#8 := 1::Int
+#9 := (f4 f5 1::Int)
+#57 := (f3 #9 -1::Int)
+#60 := (= #57 0::Int)
+#63 := (not #60)
+#10 := (- 1::Int)
+#11 := (f3 #9 #10)
 #13 := (= #11 0::Int)
 #14 := (not #13)
-#66 := [asserted]: #14
-#577 := (not #752)
-#579 := (or #577 #13)
-#331 := (* -1::Int 1::Int)
-#415 := (mod #331 #331)
-#416 := (+ #11 #415)
-#417 := (= #416 0::Int)
-#408 := (mod 1::Int 1::Int)
-#419 := (* -1::Int #408)
-#420 := (+ #11 #419)
-#421 := (= #420 0::Int)
-#418 := (>= 1::Int 0::Int)
-#422 := (<= 1::Int 0::Int)
-#401 := (or #422 #418)
-#736 := (not #401)
-#738 := (or #422 #422)
-#395 := (not #738)
-#525 := (or #395 #736)
-#732 := (ite #525 #421 #417)
-#406 := (= 1::Int 0::Int)
-#407 := (ite #406 #13 #732)
-#739 := (= 1::Int #11)
-#740 := (ite #406 #739 #407)
-#580 := (or #577 #740)
-#581 := (iff #580 #579)
-#583 := (iff #579 #579)
-#584 := [rewrite]: #583
-#677 := (iff #740 #13)
-#743 := (= #11 1::Int)
-#528 := (ite false #743 #13)
-#673 := (iff #528 #13)
-#674 := [rewrite]: #673
-#676 := (iff #740 #528)
-#568 := (iff #407 #13)
-#683 := (ite false #13 #13)
-#685 := (iff #683 #13)
-#567 := [rewrite]: #685
-#684 := (iff #407 #683)
-#680 := (iff #732 #13)
-#1 := true
-#688 := (ite true #13 #13)
-#526 := (iff #688 #13)
-#527 := [rewrite]: #526
-#695 := (iff #732 #688)
-#693 := (iff #417 #13)
-#686 := (= #416 #11)
-#705 := (+ #11 0::Int)
-#710 := (= #705 #11)
-#699 := [rewrite]: #710
-#691 := (= #416 #705)
-#689 := (= #415 0::Int)
-#698 := (mod -1::Int -1::Int)
-#546 := (= #698 0::Int)
-#547 := [rewrite]: #546
-#704 := (= #415 #698)
-#702 := (= #331 -1::Int)
-#703 := [rewrite]: #702
-#545 := [monotonicity #703 #703]: #704
-#690 := [trans #545 #547]: #689
-#692 := [monotonicity #690]: #691
-#687 := [trans #692 #699]: #686
-#694 := [monotonicity #687]: #693
-#696 := (iff #421 #13)
-#700 := (= #420 #11)
-#709 := (= #420 #705)
-#708 := (= #419 0::Int)
-#426 := (* -1::Int 0::Int)
-#429 := (= #426 0::Int)
-#707 := [rewrite]: #429
-#427 := (= #419 #426)
-#712 := (= #408 0::Int)
-#716 := [rewrite]: #712
-#428 := [monotonicity #716]: #427
-#423 := [trans #428 #707]: #708
-#706 := [monotonicity #423]: #709
-#701 := [trans #706 #699]: #700
-#697 := [monotonicity #701]: #696
-#711 := (iff #525 true)
-#337 := (or true false)
-#436 := (iff #337 true)
-#437 := [rewrite]: #436
-#713 := (iff #525 #337)
-#442 := (iff #736 false)
-#731 := (not true)
-#440 := (iff #731 false)
-#441 := [rewrite]: #440
-#717 := (iff #736 #731)
-#730 := (iff #401 true)
-#364 := (or false true)
-#369 := (iff #364 true)
-#370 := [rewrite]: #369
-#727 := (iff #401 #364)
-#720 := (iff #418 true)
-#726 := [rewrite]: #720
-#393 := (iff #422 false)
-#398 := [rewrite]: #393
-#729 := [monotonicity #398 #726]: #727
-#728 := [trans #729 #370]: #730
-#718 := [monotonicity #728]: #717
-#443 := [trans #718 #441]: #442
-#724 := (iff #395 true)
-#384 := (not false)
-#722 := (iff #384 true)
-#723 := [rewrite]: #722
-#385 := (iff #395 #384)
-#382 := (iff #738 false)
-#734 := (or false false)
-#378 := (iff #734 false)
-#719 := [rewrite]: #378
-#394 := (iff #738 #734)
-#735 := [monotonicity #398 #398]: #394
-#383 := [trans #735 #719]: #382
-#721 := [monotonicity #383]: #385
-#725 := [trans #721 #723]: #724
-#714 := [monotonicity #725 #443]: #713
-#715 := [trans #714 #437]: #711
-#524 := [monotonicity #715 #697 #694]: #695
-#681 := [trans #524 #527]: #680
-#741 := (iff #406 false)
-#742 := [rewrite]: #741
-#682 := [monotonicity #742 #681]: #684
-#569 := [trans #682 #567]: #568
-#737 := (iff #739 #743)
-#733 := [rewrite]: #737
-#578 := [monotonicity #742 #733 #569]: #676
-#562 := [trans #578 #674]: #677
-#582 := [monotonicity #562]: #581
-#585 := [trans #582 #584]: #581
-#573 := [quant-inst #9 #9]: #580
-#678 := [mp #573 #585]: #579
-[unit-resolution #678 #66 #757]: false
-unsat
-85bd77bcf683d302943eca4a8f60f76dd09e8863 320 0
+#64 := (iff #14 #63)
+#61 := (iff #13 #60)
+#58 := (= #11 #57)
+#55 := (= #10 -1::Int)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#62 := [monotonicity #59]: #61
+#65 := [monotonicity #62]: #64
+#48 := [asserted]: #14
+#66 := [mp #48 #65]: #63
+#528 := (not #703)
+#530 := (or #528 #60)
+#357 := (* -1::Int -1::Int)
+#683 := (* -1::Int 1::Int)
+#358 := (mod #683 #357)
+#690 := (+ #57 #358)
+#691 := (= #690 0::Int)
+#687 := (mod 1::Int -1::Int)
+#689 := (* -1::Int #687)
+#346 := (+ #57 #689)
+#476 := (= #346 0::Int)
+#359 := (<= -1::Int 0::Int)
+#372 := (>= 1::Int 0::Int)
+#369 := (or #372 #359)
+#373 := (not #369)
+#368 := (<= 1::Int 0::Int)
+#370 := (or #368 #359)
+#371 := (not #370)
+#352 := (or #371 #373)
+#692 := (if #352 #476 #691)
+#367 := (= 1::Int 0::Int)
+#693 := (if #367 #60 #692)
+#366 := (= #57 1::Int)
+#282 := (= -1::Int 0::Int)
+#688 := (if #282 #366 #693)
+#531 := (or #528 #688)
+#532 := (iff #531 #530)
+#534 := (iff #530 #530)
+#535 := [rewrite]: #534
+#628 := (iff #688 #60)
+#479 := (if false #366 #60)
+#624 := (iff #479 #60)
+#625 := [rewrite]: #624
+#627 := (iff #688 #479)
+#519 := (iff #693 #60)
+#477 := (if false #60 #60)
+#632 := (iff #477 #60)
+#634 := [rewrite]: #632
+#636 := (iff #693 #477)
+#635 := (iff #692 #60)
+#478 := (iff #692 #477)
+#646 := (iff #691 #60)
+#645 := (= #690 #57)
+#660 := (+ #57 0::Int)
+#650 := (= #660 #57)
+#651 := [rewrite]: #650
+#638 := (= #690 #660)
+#643 := (= #358 0::Int)
+#497 := (mod -1::Int 1::Int)
+#641 := (= #497 0::Int)
+#642 := [rewrite]: #641
+#498 := (= #358 #497)
+#655 := (= #357 1::Int)
+#496 := [rewrite]: #655
+#654 := (= #683 -1::Int)
+#649 := [rewrite]: #654
+#640 := [monotonicity #649 #496]: #498
+#637 := [trans #640 #642]: #643
+#644 := [monotonicity #637]: #638
+#639 := [trans #644 #651]: #645
+#475 := [monotonicity #639]: #646
+#648 := (iff #476 #60)
+#652 := (= #346 #57)
+#657 := (= #346 #660)
+#374 := (= #689 0::Int)
+#378 := (* -1::Int 0::Int)
+#658 := (= #378 0::Int)
+#659 := [rewrite]: #658
+#379 := (= #689 #378)
+#667 := (= #687 0::Int)
+#377 := [rewrite]: #667
+#380 := [monotonicity #377]: #379
+#656 := [trans #380 #659]: #374
+#661 := [monotonicity #656]: #657
+#647 := [trans #661 #651]: #652
+#653 := [monotonicity #647]: #648
+#666 := (iff #352 false)
+#664 := (or false false)
+#388 := (iff #664 false)
+#662 := [rewrite]: #388
+#665 := (iff #352 #664)
+#394 := (iff #373 false)
+#1 := true
+#674 := (not true)
+#671 := (iff #674 false)
+#677 := [rewrite]: #671
+#392 := (iff #373 #674)
+#669 := (iff #369 true)
+#321 := (or true true)
+#682 := (iff #321 true)
+#668 := [rewrite]: #682
+#681 := (iff #369 #321)
+#686 := (iff #359 true)
+#329 := [rewrite]: #686
+#680 := (iff #372 true)
+#320 := [rewrite]: #680
+#679 := [monotonicity #320 #329]: #681
+#391 := [trans #679 #668]: #669
+#393 := [monotonicity #391]: #392
+#288 := [trans #393 #677]: #394
+#315 := (iff #371 false)
+#675 := (iff #371 #674)
+#672 := (iff #370 true)
+#670 := (or false true)
+#335 := (iff #670 true)
+#336 := [rewrite]: #335
+#333 := (iff #370 #670)
+#685 := (iff #368 false)
+#345 := [rewrite]: #685
+#334 := [monotonicity #345 #329]: #333
+#673 := [trans #334 #336]: #672
+#676 := [monotonicity #673]: #675
+#678 := [trans #676 #677]: #315
+#387 := [monotonicity #678 #288]: #665
+#663 := [trans #387 #662]: #666
+#631 := [monotonicity #663 #653 #475]: #478
+#633 := [trans #631 #634]: #635
+#344 := (iff #367 false)
+#349 := [rewrite]: #344
+#518 := [monotonicity #349 #633]: #636
+#520 := [trans #518 #634]: #519
+#694 := (iff #282 false)
+#684 := [rewrite]: #694
+#529 := [monotonicity #684 #520]: #627
+#513 := [trans #529 #625]: #628
+#533 := [monotonicity #513]: #532
+#536 := [trans #533 #535]: #532
+#524 := [quant-inst #8 #54]: #531
+#629 := [mp #524 #536]: #530
+[unit-resolution #629 #66 #708]: false
+4aa0b6a1a9a2558065eff1ba9f7dadbceeb2b883 324 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #19 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #17 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #38 := (f4 f5 #17)
 #39 := (f3 #38 #19)
-#752 := (pattern #39)
+#703 := (pattern #39)
 #13 := 0::Int
-#84 := -1::Int
-#88 := (* -1::Int #19)
-#85 := (* -1::Int #17)
-#149 := (mod #85 #88)
-#264 := (+ #39 #149)
-#265 := (= #264 0::Int)
+#55 := -1::Int
+#97 := (* -1::Int #19)
+#94 := (* -1::Int #17)
+#116 := (mod #94 #97)
+#272 := (+ #39 #116)
+#273 := (= #272 0::Int)
 #40 := (mod #17 #19)
-#261 := (* -1::Int #40)
-#262 := (+ #39 #261)
-#263 := (= #262 0::Int)
-#123 := (>= #17 0::Int)
-#116 := (<= #19 0::Int)
-#208 := (or #116 #123)
-#209 := (not #208)
-#112 := (<= #17 0::Int)
-#206 := (or #112 #116)
-#207 := (not #206)
-#212 := (or #207 #209)
-#266 := (ite #212 #263 #265)
-#260 := (= #39 0::Int)
+#269 := (* -1::Int #40)
+#270 := (+ #39 #269)
+#271 := (= #270 0::Int)
+#72 := (<= #19 0::Int)
+#163 := (>= #17 0::Int)
+#216 := (or #163 #72)
+#217 := (not #216)
+#68 := (<= #17 0::Int)
+#212 := (or #68 #72)
+#213 := (not #212)
+#220 := (or #213 #217)
+#274 := (if #220 #271 #273)
+#268 := (= #39 0::Int)
 #21 := (= #17 0::Int)
-#267 := (ite #21 #260 #266)
-#259 := (= #17 #39)
+#275 := (if #21 #268 #274)
+#267 := (= #39 #17)
 #22 := (= #19 0::Int)
-#268 := (ite #22 #259 #267)
-#753 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #752) #268)
-#271 := (forall (vars (?v0 Int) (?v1 Int)) #268)
-#756 := (iff #271 #753)
-#754 := (iff #268 #268)
-#755 := [refl]: #754
-#757 := [quant-intro #755]: #756
-#155 := (* -1::Int #149)
-#228 := (ite #212 #40 #155)
-#231 := (ite #21 0::Int #228)
-#234 := (ite #22 #17 #231)
-#237 := (= #39 #234)
-#240 := (forall (vars (?v0 Int) (?v1 Int)) #237)
-#272 := (iff #240 #271)
-#269 := (iff #237 #268)
-#270 := [rewrite]: #269
-#273 := [quant-intro #270]: #272
-#124 := (not #123)
-#117 := (not #116)
-#127 := (and #117 #124)
-#113 := (not #112)
-#120 := (and #113 #117)
-#130 := (or #120 #127)
-#175 := (ite #130 #40 #155)
-#178 := (ite #21 0::Int #175)
-#181 := (ite #22 #17 #178)
-#184 := (= #39 #181)
-#187 := (forall (vars (?v0 Int) (?v1 Int)) #184)
-#241 := (iff #187 #240)
-#238 := (iff #184 #237)
-#235 := (= #181 #234)
-#232 := (= #178 #231)
-#229 := (= #175 #228)
-#213 := (iff #130 #212)
-#210 := (iff #127 #209)
-#211 := [rewrite]: #210
-#200 := (iff #120 #207)
-#201 := [rewrite]: #200
-#214 := [monotonicity #201 #211]: #213
-#230 := [monotonicity #214]: #229
-#233 := [monotonicity #230]: #232
-#236 := [monotonicity #233]: #235
-#239 := [monotonicity #236]: #238
-#242 := [quant-intro #239]: #241
-#198 := (~ #187 #187)
-#197 := (~ #184 #184)
-#194 := [refl]: #197
-#199 := [nnf-pos #194]: #198
+#276 := (if #22 #267 #275)
+#704 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #703) #276)
+#279 := (forall (vars (?v0 Int) (?v1 Int)) #276)
+#707 := (iff #279 #704)
+#705 := (iff #276 #276)
+#706 := [refl]: #705
+#708 := [quant-intro #706]: #707
+#122 := (* -1::Int #116)
+#236 := (if #220 #40 #122)
+#239 := (if #21 0::Int #236)
+#242 := (if #22 #17 #239)
+#245 := (= #39 #242)
+#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
+#280 := (iff #248 #279)
+#277 := (iff #245 #276)
+#278 := [rewrite]: #277
+#281 := [quant-intro #278]: #280
+#73 := (not #72)
+#166 := (not #163)
+#169 := (and #166 #73)
+#69 := (not #68)
+#76 := (and #69 #73)
+#172 := (or #76 #169)
+#188 := (if #172 #40 #122)
+#191 := (if #21 0::Int #188)
+#194 := (if #22 #17 #191)
+#197 := (= #39 #194)
+#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
+#249 := (iff #200 #248)
+#246 := (iff #197 #245)
+#243 := (= #194 #242)
+#240 := (= #191 #239)
+#237 := (= #188 #236)
+#221 := (iff #172 #220)
+#218 := (iff #169 #217)
+#219 := [rewrite]: #218
+#214 := (iff #76 #213)
+#215 := [rewrite]: #214
+#222 := [monotonicity #215 #219]: #221
+#238 := [monotonicity #222]: #237
+#241 := [monotonicity #238]: #240
+#244 := [monotonicity #241]: #243
+#247 := [monotonicity #244]: #246
+#250 := [quant-intro #247]: #249
+#162 := (~ #200 #200)
+#207 := (~ #197 #197)
+#161 := [refl]: #207
+#210 := [nnf-pos #161]: #162
+#79 := (<= 0::Int #17)
+#80 := (not #79)
+#88 := (and #80 #73)
+#91 := (or #76 #88)
+#127 := (if #91 #40 #122)
+#130 := (if #21 0::Int #127)
+#133 := (if #22 #17 #130)
+#136 := (= #39 #133)
+#139 := (forall (vars (?v0 Int) (?v1 Int)) #136)
+#201 := (iff #139 #200)
+#198 := (iff #136 #197)
+#195 := (= #133 #194)
+#192 := (= #130 #191)
+#189 := (= #127 #188)
+#173 := (iff #91 #172)
+#170 := (iff #88 #169)
+#167 := (iff #80 #166)
+#164 := (iff #79 #163)
+#165 := [rewrite]: #164
+#168 := [monotonicity #165]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #171]: #173
+#190 := [monotonicity #174]: #189
+#193 := [monotonicity #190]: #192
+#196 := [monotonicity #193]: #195
+#199 := [monotonicity #196]: #198
+#202 := [quant-intro #199]: #201
 #32 := (- #19)
 #31 := (- #17)
 #41 := (mod #31 #32)
@@ -35949,964 +36061,321 @@
 #24 := (< 0::Int #17)
 #26 := (and #24 #25)
 #29 := (or #26 #28)
-#43 := (ite #29 #40 #42)
-#44 := (ite #21 0::Int #43)
-#45 := (ite #22 #17 #44)
+#43 := (if #29 #40 #42)
+#44 := (if #21 0::Int #43)
+#45 := (if #22 #17 #44)
 #46 := (= #39 #45)
 #47 := (forall (vars (?v0 Int) (?v1 Int)) #46)
-#190 := (iff #47 #187)
-#78 := (and #25 #27)
-#81 := (or #26 #78)
-#160 := (ite #81 #40 #155)
-#69 := (= 0::Int #17)
-#163 := (ite #69 0::Int #160)
-#72 := (= 0::Int #19)
-#166 := (ite #72 #17 #163)
-#169 := (= #39 #166)
-#172 := (forall (vars (?v0 Int) (?v1 Int)) #169)
-#188 := (iff #172 #187)
-#185 := (iff #169 #184)
-#182 := (= #166 #181)
-#179 := (= #163 #178)
-#176 := (= #160 #175)
-#131 := (iff #81 #130)
-#128 := (iff #78 #127)
-#125 := (iff #27 #124)
-#126 := [rewrite]: #125
-#118 := (iff #25 #117)
-#119 := [rewrite]: #118
-#129 := [monotonicity #119 #126]: #128
-#121 := (iff #26 #120)
-#114 := (iff #24 #113)
-#115 := [rewrite]: #114
-#122 := [monotonicity #115 #119]: #121
-#132 := [monotonicity #122 #129]: #131
-#177 := [monotonicity #132]: #176
-#106 := (iff #69 #21)
-#107 := [rewrite]: #106
-#180 := [monotonicity #107 #177]: #179
-#108 := (iff #72 #22)
-#109 := [rewrite]: #108
-#183 := [monotonicity #109 #180]: #182
-#186 := [monotonicity #183]: #185
-#189 := [quant-intro #186]: #188
-#173 := (iff #47 #172)
-#170 := (iff #46 #169)
-#167 := (= #45 #166)
-#164 := (= #44 #163)
-#161 := (= #43 #160)
-#158 := (= #42 #155)
-#152 := (- #149)
-#156 := (= #152 #155)
-#157 := [rewrite]: #156
-#153 := (= #42 #152)
-#150 := (= #41 #149)
-#89 := (= #32 #88)
-#90 := [rewrite]: #89
-#86 := (= #31 #85)
-#87 := [rewrite]: #86
-#151 := [monotonicity #87 #90]: #150
-#154 := [monotonicity #151]: #153
-#159 := [trans #154 #157]: #158
-#82 := (iff #29 #81)
-#79 := (iff #28 #78)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#162 := [monotonicity #83 #159]: #161
-#70 := (iff #21 #69)
+#140 := (iff #47 #139)
+#137 := (iff #46 #136)
+#134 := (= #45 #133)
+#131 := (= #44 #130)
+#128 := (= #43 #127)
+#125 := (= #42 #122)
+#119 := (- #116)
+#123 := (= #119 #122)
+#124 := [rewrite]: #123
+#120 := (= #42 #119)
+#117 := (= #41 #116)
+#98 := (= #32 #97)
+#99 := [rewrite]: #98
+#95 := (= #31 #94)
+#96 := [rewrite]: #95
+#118 := [monotonicity #96 #99]: #117
+#121 := [monotonicity #118]: #120
+#126 := [trans #121 #124]: #125
+#92 := (iff #29 #91)
+#89 := (iff #28 #88)
+#74 := (iff #25 #73)
+#75 := [rewrite]: #74
+#81 := (iff #27 #80)
+#85 := (iff #80 #80)
+#83 := (iff #79 #79)
+#84 := [rewrite]: #83
+#86 := [monotonicity #84]: #85
+#82 := [rewrite]: #81
+#87 := [trans #82 #86]: #81
+#90 := [monotonicity #87 #75]: #89
+#77 := (iff #26 #76)
+#70 := (iff #24 #69)
 #71 := [rewrite]: #70
-#165 := [monotonicity #71 #162]: #164
-#73 := (iff #22 #72)
-#74 := [rewrite]: #73
-#168 := [monotonicity #74 #165]: #167
-#171 := [monotonicity #168]: #170
-#174 := [quant-intro #171]: #173
-#191 := [trans #174 #189]: #190
-#148 := [asserted]: #47
-#192 := [mp #148 #191]: #187
-#195 := [mp~ #192 #199]: #187
-#243 := [mp #195 #242]: #240
-#274 := [mp #243 #273]: #271
-#758 := [mp #274 #757]: #753
-#11 := 1::Int
-#9 := 3::Int
-#10 := (f4 f5 3::Int)
-#12 := (f3 #10 1::Int)
-#14 := (= #12 0::Int)
-#15 := (not #14)
-#67 := [asserted]: #15
-#676 := (not #753)
-#680 := (or #676 #14)
-#332 := (* -1::Int 1::Int)
-#416 := (* -1::Int 3::Int)
-#417 := (mod #416 #332)
-#418 := (+ #12 #417)
-#409 := (= #418 0::Int)
-#420 := (mod 3::Int 1::Int)
-#421 := (* -1::Int #420)
-#422 := (+ #12 #421)
-#419 := (= #422 0::Int)
-#423 := (>= 3::Int 0::Int)
-#402 := (<= 1::Int 0::Int)
-#737 := (or #402 #423)
-#739 := (not #737)
-#396 := (<= 3::Int 0::Int)
-#526 := (or #396 #402)
-#733 := (not #526)
-#407 := (or #733 #739)
-#408 := (ite #407 #419 #409)
-#740 := (= 3::Int 0::Int)
-#741 := (ite #740 #14 #408)
-#742 := (= 3::Int #12)
-#743 := (= 1::Int 0::Int)
-#738 := (ite #743 #742 #741)
-#667 := (or #676 #738)
-#661 := (iff #667 #680)
-#660 := (iff #680 #680)
-#670 := [rewrite]: #660
-#586 := (iff #738 #14)
-#399 := (= #12 3::Int)
-#574 := (ite false #399 #14)
-#584 := (iff #574 #14)
-#585 := [rewrite]: #584
-#582 := (iff #738 #574)
-#580 := (iff #741 #14)
-#674 := (ite false #14 #14)
-#563 := (iff #674 #14)
-#578 := [rewrite]: #563
-#675 := (iff #741 #674)
-#677 := (iff #408 #14)
-#1 := true
-#686 := (ite true #14 #14)
-#570 := (iff #686 #14)
-#529 := [rewrite]: #570
-#568 := (iff #408 #686)
-#685 := (iff #409 #14)
-#682 := (= #418 #12)
-#697 := (+ #12 0::Int)
-#704 := (= #697 #12)
-#699 := [rewrite]: #704
-#528 := (= #418 #697)
-#525 := (= #417 0::Int)
-#690 := -3::Int
-#688 := (mod -3::Int -1::Int)
-#689 := (= #688 0::Int)
-#696 := [rewrite]: #689
-#694 := (= #417 #688)
-#693 := (= #332 -1::Int)
-#687 := [rewrite]: #693
-#691 := (= #416 -3::Int)
-#692 := [rewrite]: #691
-#695 := [monotonicity #692 #687]: #694
-#527 := [trans #695 #696]: #525
-#681 := [monotonicity #527]: #528
-#684 := [trans #681 #699]: #682
-#683 := [monotonicity #684]: #685
-#547 := (iff #419 #14)
-#705 := (= #422 #12)
-#698 := (= #422 #697)
-#701 := (= #421 0::Int)
-#706 := (* -1::Int 0::Int)
-#711 := (= #706 0::Int)
-#700 := [rewrite]: #711
-#710 := (= #421 #706)
-#709 := (= #420 0::Int)
-#424 := [rewrite]: #709
-#707 := [monotonicity #424]: #710
-#702 := [trans #707 #700]: #701
-#703 := [monotonicity #702]: #698
-#546 := [trans #703 #699]: #705
-#548 := [monotonicity #546]: #547
-#430 := (iff #407 true)
-#713 := (or true false)
-#428 := (iff #713 true)
-#429 := [rewrite]: #428
-#717 := (iff #407 #713)
-#712 := (iff #739 false)
-#338 := (not true)
-#437 := (iff #338 false)
-#438 := [rewrite]: #437
-#714 := (iff #739 #338)
-#443 := (iff #737 true)
-#732 := (or false true)
-#441 := (iff #732 true)
-#442 := [rewrite]: #441
-#718 := (iff #737 #732)
-#731 := (iff #423 true)
-#729 := [rewrite]: #731
-#383 := (iff #402 false)
-#384 := [rewrite]: #383
-#719 := [monotonicity #384 #729]: #718
-#444 := [trans #719 #442]: #443
-#715 := [monotonicity #444]: #714
-#716 := [trans #715 #438]: #712
-#370 := (iff #733 true)
-#721 := (not false)
-#728 := (iff #721 true)
-#730 := [rewrite]: #728
-#727 := (iff #733 #721)
-#725 := (iff #526 false)
-#385 := (or false false)
-#723 := (iff #385 false)
-#724 := [rewrite]: #723
-#386 := (iff #526 #385)
-#379 := (iff #396 false)
-#720 := [rewrite]: #379
-#722 := [monotonicity #720 #384]: #386
-#726 := [trans #722 #724]: #725
-#365 := [monotonicity #726]: #727
-#371 := [trans #365 #730]: #370
-#427 := [monotonicity #371 #716]: #717
-#708 := [trans #427 #429]: #430
-#569 := [monotonicity #708 #548 #683]: #568
-#579 := [trans #569 #529]: #677
-#395 := (iff #740 false)
-#736 := [rewrite]: #395
-#678 := [monotonicity #736 #579]: #675
-#581 := [trans #678 #578]: #580
-#394 := (iff #742 #399)
-#735 := [rewrite]: #394
-#744 := (iff #743 false)
-#734 := [rewrite]: #744
-#583 := [monotonicity #734 #735 #581]: #582
-#679 := [trans #583 #585]: #586
-#658 := [monotonicity #679]: #661
-#671 := [trans #658 #670]: #661
-#669 := [quant-inst #9 #11]: #667
-#672 := [mp #669 #671]: #680
-[unit-resolution #672 #67 #758]: false
-unsat
-6be2ef74dd3e2bf3bb35431b62b3251c3cb851ce 318 0
-#2 := false
-#13 := 0::Int
-decl f6 :: Int
-#9 := f6
-#740 := (= f6 0::Int)
-#581 := (not #740)
-#423 := (>= f6 0::Int)
-#728 := (not #423)
-#396 := (<= f6 0::Int)
-#385 := (not #396)
-#696 := (or #385 #728 #740)
-#583 := (not #696)
-#84 := -1::Int
-#416 := (* -1::Int f6)
-#708 := (mod #416 -1::Int)
-decl f3 :: (-> S2 Int Int)
-#11 := 1::Int
-decl f4 :: (-> S3 Int S2)
-decl f5 :: S3
-#8 := f5
-#10 := (f4 f5 f6)
-#12 := (f3 #10 1::Int)
-#706 := (+ #12 #708)
-#711 := (= #706 0::Int)
+#78 := [monotonicity #71 #75]: #77
+#93 := [monotonicity #78 #90]: #92
+#129 := [monotonicity #93 #126]: #128
+#132 := [monotonicity #129]: #131
+#135 := [monotonicity #132]: #134
+#138 := [monotonicity #135]: #137
+#141 := [quant-intro #138]: #140
+#51 := [asserted]: #47
+#142 := [mp #51 #141]: #139
+#203 := [mp #142 #202]: #200
+#211 := [mp~ #203 #210]: #200
+#251 := [mp #211 #250]: #248
+#282 := [mp #251 #281]: #279
+#709 := [mp #282 #708]: #704
+#8 := 3::Int
+#9 := (f4 f5 3::Int)
+#58 := (f3 #9 -1::Int)
+#61 := (= #58 0::Int)
+#64 := (not #61)
+#10 := 1::Int
+#11 := (- 1::Int)
+#12 := (f3 #9 #11)
 #14 := (= #12 0::Int)
-#528 := (ite #696 #14 #711)
-#19 := (:var 0 Int)
-#17 := (:var 1 Int)
-#38 := (f4 f5 #17)
-#39 := (f3 #38 #19)
-#752 := (pattern #39)
-#88 := (* -1::Int #19)
-#85 := (* -1::Int #17)
-#149 := (mod #85 #88)
-#264 := (+ #39 #149)
-#265 := (= #264 0::Int)
-#40 := (mod #17 #19)
-#261 := (* -1::Int #40)
-#262 := (+ #39 #261)
-#263 := (= #262 0::Int)
-#123 := (>= #17 0::Int)
-#116 := (<= #19 0::Int)
-#208 := (or #116 #123)
-#209 := (not #208)
-#112 := (<= #17 0::Int)
-#206 := (or #112 #116)
-#207 := (not #206)
-#212 := (or #207 #209)
-#266 := (ite #212 #263 #265)
-#260 := (= #39 0::Int)
-#21 := (= #17 0::Int)
-#267 := (ite #21 #260 #266)
-#259 := (= #17 #39)
-#22 := (= #19 0::Int)
-#268 := (ite #22 #259 #267)
-#753 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #752) #268)
-#271 := (forall (vars (?v0 Int) (?v1 Int)) #268)
-#756 := (iff #271 #753)
-#754 := (iff #268 #268)
-#755 := [refl]: #754
-#757 := [quant-intro #755]: #756
-#155 := (* -1::Int #149)
-#228 := (ite #212 #40 #155)
-#231 := (ite #21 0::Int #228)
-#234 := (ite #22 #17 #231)
-#237 := (= #39 #234)
-#240 := (forall (vars (?v0 Int) (?v1 Int)) #237)
-#272 := (iff #240 #271)
-#269 := (iff #237 #268)
-#270 := [rewrite]: #269
-#273 := [quant-intro #270]: #272
-#124 := (not #123)
-#117 := (not #116)
-#127 := (and #117 #124)
-#113 := (not #112)
-#120 := (and #113 #117)
-#130 := (or #120 #127)
-#175 := (ite #130 #40 #155)
-#178 := (ite #21 0::Int #175)
-#181 := (ite #22 #17 #178)
-#184 := (= #39 #181)
-#187 := (forall (vars (?v0 Int) (?v1 Int)) #184)
-#241 := (iff #187 #240)
-#238 := (iff #184 #237)
-#235 := (= #181 #234)
-#232 := (= #178 #231)
-#229 := (= #175 #228)
-#213 := (iff #130 #212)
-#210 := (iff #127 #209)
-#211 := [rewrite]: #210
-#200 := (iff #120 #207)
-#201 := [rewrite]: #200
-#214 := [monotonicity #201 #211]: #213
-#230 := [monotonicity #214]: #229
-#233 := [monotonicity #230]: #232
-#236 := [monotonicity #233]: #235
-#239 := [monotonicity #236]: #238
-#242 := [quant-intro #239]: #241
-#198 := (~ #187 #187)
-#197 := (~ #184 #184)
-#194 := [refl]: #197
-#199 := [nnf-pos #194]: #198
-#32 := (- #19)
-#31 := (- #17)
-#41 := (mod #31 #32)
-#42 := (- #41)
-#25 := (< 0::Int #19)
-#27 := (< #17 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #17)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#43 := (ite #29 #40 #42)
-#44 := (ite #21 0::Int #43)
-#45 := (ite #22 #17 #44)
-#46 := (= #39 #45)
-#47 := (forall (vars (?v0 Int) (?v1 Int)) #46)
-#190 := (iff #47 #187)
-#78 := (and #25 #27)
-#81 := (or #26 #78)
-#160 := (ite #81 #40 #155)
-#69 := (= 0::Int #17)
-#163 := (ite #69 0::Int #160)
-#72 := (= 0::Int #19)
-#166 := (ite #72 #17 #163)
-#169 := (= #39 #166)
-#172 := (forall (vars (?v0 Int) (?v1 Int)) #169)
-#188 := (iff #172 #187)
-#185 := (iff #169 #184)
-#182 := (= #166 #181)
-#179 := (= #163 #178)
-#176 := (= #160 #175)
-#131 := (iff #81 #130)
-#128 := (iff #78 #127)
-#125 := (iff #27 #124)
-#126 := [rewrite]: #125
-#118 := (iff #25 #117)
-#119 := [rewrite]: #118
-#129 := [monotonicity #119 #126]: #128
-#121 := (iff #26 #120)
-#114 := (iff #24 #113)
-#115 := [rewrite]: #114
-#122 := [monotonicity #115 #119]: #121
-#132 := [monotonicity #122 #129]: #131
-#177 := [monotonicity #132]: #176
-#106 := (iff #69 #21)
-#107 := [rewrite]: #106
-#180 := [monotonicity #107 #177]: #179
-#108 := (iff #72 #22)
-#109 := [rewrite]: #108
-#183 := [monotonicity #109 #180]: #182
-#186 := [monotonicity #183]: #185
-#189 := [quant-intro #186]: #188
-#173 := (iff #47 #172)
-#170 := (iff #46 #169)
-#167 := (= #45 #166)
-#164 := (= #44 #163)
-#161 := (= #43 #160)
-#158 := (= #42 #155)
-#152 := (- #149)
-#156 := (= #152 #155)
-#157 := [rewrite]: #156
-#153 := (= #42 #152)
-#150 := (= #41 #149)
-#89 := (= #32 #88)
-#90 := [rewrite]: #89
-#86 := (= #31 #85)
-#87 := [rewrite]: #86
-#151 := [monotonicity #87 #90]: #150
-#154 := [monotonicity #151]: #153
-#159 := [trans #154 #157]: #158
-#82 := (iff #29 #81)
-#79 := (iff #28 #78)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#162 := [monotonicity #83 #159]: #161
-#70 := (iff #21 #69)
-#71 := [rewrite]: #70
-#165 := [monotonicity #71 #162]: #164
-#73 := (iff #22 #72)
-#74 := [rewrite]: #73
-#168 := [monotonicity #74 #165]: #167
-#171 := [monotonicity #168]: #170
-#174 := [quant-intro #171]: #173
-#191 := [trans #174 #189]: #190
-#148 := [asserted]: #47
-#192 := [mp #148 #191]: #187
-#195 := [mp~ #192 #199]: #187
-#243 := [mp #195 #242]: #240
-#274 := [mp #243 #273]: #271
-#758 := [mp #274 #757]: #753
-#683 := (not #753)
-#686 := (or #683 #528)
-#332 := (* -1::Int 1::Int)
-#417 := (mod #416 #332)
-#418 := (+ #12 #417)
-#409 := (= #418 0::Int)
-#420 := (mod f6 1::Int)
-#421 := (* -1::Int #420)
-#422 := (+ #12 #421)
-#419 := (= #422 0::Int)
-#402 := (<= 1::Int 0::Int)
-#737 := (or #402 #423)
-#739 := (not #737)
-#526 := (or #396 #402)
-#733 := (not #526)
-#407 := (or #733 #739)
-#408 := (ite #407 #419 #409)
-#741 := (ite #740 #14 #408)
-#742 := (= f6 #12)
-#743 := (= 1::Int 0::Int)
-#738 := (ite #743 #742 #741)
-#568 := (or #683 #738)
-#570 := (iff #568 #686)
-#677 := (iff #686 #686)
-#579 := [rewrite]: #677
-#684 := (iff #738 #528)
-#371 := (or #385 #728)
-#705 := (or #371 #740)
-#546 := (ite #705 #14 #711)
-#681 := (iff #546 #528)
-#525 := (iff #705 #696)
-#527 := [rewrite]: #525
-#682 := [monotonicity #527]: #681
-#695 := (iff #738 #546)
-#692 := (ite false #742 #546)
-#688 := (iff #692 #546)
-#694 := [rewrite]: #688
-#693 := (iff #738 #692)
-#690 := (iff #741 #546)
-#702 := (ite #371 #14 #711)
-#703 := (ite #740 #14 #702)
-#547 := (iff #703 #546)
-#548 := [rewrite]: #547
-#704 := (iff #741 #703)
-#697 := (iff #408 #702)
-#700 := (iff #409 #711)
-#710 := (= #418 #706)
-#709 := (= #417 #708)
-#429 := (= #332 -1::Int)
-#430 := [rewrite]: #429
-#424 := [monotonicity #430]: #709
-#707 := [monotonicity #424]: #710
-#701 := [monotonicity #707]: #700
-#427 := (iff #419 #14)
-#713 := (= #422 #12)
-#715 := (+ #12 0::Int)
-#712 := (= #715 #12)
-#716 := [rewrite]: #712
-#437 := (= #422 #715)
-#338 := (= #421 0::Int)
-#719 := (* -1::Int 0::Int)
-#443 := (= #719 0::Int)
-#444 := [rewrite]: #443
-#441 := (= #421 #719)
-#732 := (= #420 0::Int)
-#718 := [rewrite]: #732
-#442 := [monotonicity #718]: #441
-#714 := [trans #442 #444]: #338
-#438 := [monotonicity #714]: #437
-#717 := [trans #438 #716]: #713
-#428 := [monotonicity #717]: #427
-#731 := (iff #407 #371)
-#730 := (iff #739 #728)
-#727 := (iff #737 #423)
-#723 := (or false #423)
-#726 := (iff #723 #423)
-#721 := [rewrite]: #726
-#724 := (iff #737 #723)
-#394 := (iff #402 false)
-#399 := [rewrite]: #394
-#725 := [monotonicity #399]: #724
-#365 := [trans #725 #721]: #727
-#370 := [monotonicity #365]: #730
-#386 := (iff #733 #385)
-#383 := (iff #526 #396)
-#735 := (or #396 false)
-#379 := (iff #735 #396)
-#720 := [rewrite]: #379
-#395 := (iff #526 #735)
-#736 := [monotonicity #399]: #395
-#384 := [trans #736 #720]: #383
-#722 := [monotonicity #384]: #386
-#729 := [monotonicity #722 #370]: #731
-#698 := [monotonicity #729 #428 #701]: #697
-#699 := [monotonicity #698]: #704
-#691 := [trans #699 #548]: #690
-#744 := (iff #743 false)
-#734 := [rewrite]: #744
-#687 := [monotonicity #734 #691]: #693
-#689 := [trans #687 #694]: #695
-#685 := [trans #689 #682]: #684
-#529 := [monotonicity #685]: #570
-#674 := [trans #529 #579]: #570
-#569 := [quant-inst #9 #11]: #568
-#675 := [mp #569 #674]: #686
-#668 := [unit-resolution #675 #758]: #528
-#676 := (not #528)
-#673 := (or #676 #583)
-#15 := (not #14)
-#67 := [asserted]: #15
-#680 := (or #676 #583 #14)
-#667 := [def-axiom]: #680
-#662 := [unit-resolution #667 #67]: #673
-#663 := [unit-resolution #662 #668]: #583
-#574 := (or #696 #581)
-#582 := [def-axiom]: #574
-#664 := [unit-resolution #582 #663]: #581
-#678 := (or #696 #396)
-#563 := [def-axiom]: #678
-#665 := [unit-resolution #563 #663]: #396
-#578 := (or #696 #423)
-#580 := [def-axiom]: #578
-#659 := [unit-resolution #580 #663]: #423
-#666 := (or #740 #385 #728)
-#650 := [th-lemma arith triangle-eq]: #666
-[unit-resolution #650 #659 #665 #664]: false
-unsat
-e7d5b6ef2ab2beae18b5430bef94875f7e4823b1 327 0
+#15 := (not #14)
+#65 := (iff #15 #64)
+#62 := (iff #14 #61)
+#59 := (= #12 #58)
+#56 := (= #11 -1::Int)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#63 := [monotonicity #60]: #62
+#66 := [monotonicity #63]: #65
+#49 := [asserted]: #15
+#67 := [mp #49 #66]: #64
+#531 := (not #704)
+#532 := (or #531 #61)
+#358 := (* -1::Int -1::Int)
+#684 := (* -1::Int 3::Int)
+#359 := (mod #684 #358)
+#691 := (+ #58 #359)
+#692 := (= #691 0::Int)
+#688 := (mod 3::Int -1::Int)
+#690 := (* -1::Int #688)
+#347 := (+ #58 #690)
+#477 := (= #347 0::Int)
+#360 := (<= -1::Int 0::Int)
+#373 := (>= 3::Int 0::Int)
+#370 := (or #373 #360)
+#374 := (not #370)
+#369 := (<= 3::Int 0::Int)
+#371 := (or #369 #360)
+#372 := (not #371)
+#353 := (or #372 #374)
+#693 := (if #353 #477 #692)
+#368 := (= 3::Int 0::Int)
+#694 := (if #368 #61 #693)
+#367 := (= #58 3::Int)
+#283 := (= -1::Int 0::Int)
+#689 := (if #283 #367 #694)
+#525 := (or #531 #689)
+#534 := (iff #525 #532)
+#536 := (iff #532 #532)
+#537 := [rewrite]: #536
+#514 := (iff #689 #61)
+#628 := (if false #367 #61)
+#626 := (iff #628 #61)
+#629 := [rewrite]: #626
+#530 := (iff #689 #628)
+#521 := (iff #694 #61)
+#479 := (if false #61 #61)
+#635 := (iff #479 #61)
+#636 := [rewrite]: #635
+#519 := (iff #694 #479)
+#634 := (iff #693 #61)
+#632 := (iff #693 #479)
+#476 := (iff #692 #61)
+#640 := (= #691 #58)
+#661 := (+ #58 0::Int)
+#651 := (= #661 #58)
+#652 := [rewrite]: #651
+#645 := (= #691 #661)
+#638 := (= #359 0::Int)
+#655 := -3::Int
+#499 := (mod -3::Int 1::Int)
+#643 := (= #499 0::Int)
+#644 := [rewrite]: #643
+#641 := (= #359 #499)
+#497 := (= #358 1::Int)
+#498 := [rewrite]: #497
+#650 := (= #684 -3::Int)
+#656 := [rewrite]: #650
+#642 := [monotonicity #656 #498]: #641
+#639 := [trans #642 #644]: #638
+#646 := [monotonicity #639]: #645
+#647 := [trans #646 #652]: #640
+#478 := [monotonicity #647]: #476
+#649 := (iff #477 #61)
+#653 := (= #347 #58)
+#658 := (= #347 #661)
+#375 := (= #690 0::Int)
+#379 := (* -1::Int 0::Int)
+#659 := (= #379 0::Int)
+#660 := [rewrite]: #659
+#380 := (= #690 #379)
+#668 := (= #688 0::Int)
+#378 := [rewrite]: #668
+#381 := [monotonicity #378]: #380
+#657 := [trans #381 #660]: #375
+#662 := [monotonicity #657]: #658
+#648 := [trans #662 #652]: #653
+#654 := [monotonicity #648]: #649
+#667 := (iff #353 false)
+#665 := (or false false)
+#389 := (iff #665 false)
+#663 := [rewrite]: #389
+#666 := (iff #353 #665)
+#395 := (iff #374 false)
+#1 := true
+#675 := (not true)
+#672 := (iff #675 false)
+#678 := [rewrite]: #672
+#393 := (iff #374 #675)
+#670 := (iff #370 true)
+#322 := (or true true)
+#683 := (iff #322 true)
+#669 := [rewrite]: #683
+#682 := (iff #370 #322)
+#687 := (iff #360 true)
+#330 := [rewrite]: #687
+#681 := (iff #373 true)
+#321 := [rewrite]: #681
+#680 := [monotonicity #321 #330]: #682
+#392 := [trans #680 #669]: #670
+#394 := [monotonicity #392]: #393
+#289 := [trans #394 #678]: #395
+#316 := (iff #372 false)
+#676 := (iff #372 #675)
+#673 := (iff #371 true)
+#671 := (or false true)
+#336 := (iff #671 true)
+#337 := [rewrite]: #336
+#334 := (iff #371 #671)
+#686 := (iff #369 false)
+#346 := [rewrite]: #686
+#335 := [monotonicity #346 #330]: #334
+#674 := [trans #335 #337]: #673
+#677 := [monotonicity #674]: #676
+#679 := [trans #677 #678]: #316
+#388 := [monotonicity #679 #289]: #666
+#664 := [trans #388 #663]: #667
+#633 := [monotonicity #664 #654 #478]: #632
+#637 := [trans #633 #636]: #634
+#345 := (iff #368 false)
+#350 := [rewrite]: #345
+#520 := [monotonicity #350 #637]: #519
+#480 := [trans #520 #636]: #521
+#695 := (iff #283 false)
+#685 := [rewrite]: #695
+#625 := [monotonicity #685 #480]: #530
+#529 := [trans #625 #629]: #514
+#535 := [monotonicity #529]: #534
+#630 := [trans #535 #537]: #534
+#533 := [quant-inst #8 #55]: #525
+#627 := [mp #533 #630]: #532
+[unit-resolution #627 #67 #709]: false
+6ed556159a25d6cb7b0afc89ba7e23c5523c8b63 304 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #19 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #17 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #38 := (f4 f5 #17)
 #39 := (f3 #38 #19)
-#776 := (pattern #39)
-#9 := 0::Int
-#68 := -1::Int
-#112 := (* -1::Int #19)
-#109 := (* -1::Int #17)
-#173 := (mod #109 #112)
-#288 := (+ #39 #173)
-#289 := (= #288 0::Int)
+#703 := (pattern #39)
+#13 := 0::Int
+#55 := -1::Int
+#97 := (* -1::Int #19)
+#94 := (* -1::Int #17)
+#116 := (mod #94 #97)
+#272 := (+ #39 #116)
+#273 := (= #272 0::Int)
 #40 := (mod #17 #19)
-#285 := (* -1::Int #40)
-#286 := (+ #39 #285)
-#287 := (= #286 0::Int)
-#147 := (>= #17 0::Int)
-#140 := (<= #19 0::Int)
-#232 := (or #140 #147)
-#233 := (not #232)
-#136 := (<= #17 0::Int)
-#230 := (or #136 #140)
-#231 := (not #230)
-#236 := (or #231 #233)
-#290 := (ite #236 #287 #289)
-#284 := (= #39 0::Int)
+#269 := (* -1::Int #40)
+#270 := (+ #39 #269)
+#271 := (= #270 0::Int)
+#72 := (<= #19 0::Int)
+#163 := (>= #17 0::Int)
+#216 := (or #163 #72)
+#217 := (not #216)
+#68 := (<= #17 0::Int)
+#212 := (or #68 #72)
+#213 := (not #212)
+#220 := (or #213 #217)
+#274 := (if #220 #271 #273)
+#268 := (= #39 0::Int)
 #21 := (= #17 0::Int)
-#291 := (ite #21 #284 #290)
-#283 := (= #17 #39)
+#275 := (if #21 #268 #274)
+#267 := (= #39 #17)
 #22 := (= #19 0::Int)
-#292 := (ite #22 #283 #291)
-#777 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #776) #292)
-#295 := (forall (vars (?v0 Int) (?v1 Int)) #292)
-#780 := (iff #295 #777)
-#778 := (iff #292 #292)
-#779 := [refl]: #778
-#781 := [quant-intro #779]: #780
-#179 := (* -1::Int #173)
-#252 := (ite #236 #40 #179)
-#255 := (ite #21 0::Int #252)
-#258 := (ite #22 #17 #255)
-#261 := (= #39 #258)
-#264 := (forall (vars (?v0 Int) (?v1 Int)) #261)
-#296 := (iff #264 #295)
-#293 := (iff #261 #292)
-#294 := [rewrite]: #293
-#297 := [quant-intro #294]: #296
-#148 := (not #147)
-#141 := (not #140)
-#151 := (and #141 #148)
-#137 := (not #136)
-#144 := (and #137 #141)
-#154 := (or #144 #151)
-#199 := (ite #154 #40 #179)
-#202 := (ite #21 0::Int #199)
-#205 := (ite #22 #17 #202)
-#208 := (= #39 #205)
-#211 := (forall (vars (?v0 Int) (?v1 Int)) #208)
-#265 := (iff #211 #264)
-#262 := (iff #208 #261)
-#259 := (= #205 #258)
-#256 := (= #202 #255)
-#253 := (= #199 #252)
-#237 := (iff #154 #236)
-#234 := (iff #151 #233)
-#235 := [rewrite]: #234
-#224 := (iff #144 #231)
-#225 := [rewrite]: #224
-#238 := [monotonicity #225 #235]: #237
-#254 := [monotonicity #238]: #253
-#257 := [monotonicity #254]: #256
-#260 := [monotonicity #257]: #259
-#263 := [monotonicity #260]: #262
-#266 := [quant-intro #263]: #265
-#222 := (~ #211 #211)
-#221 := (~ #208 #208)
-#218 := [refl]: #221
-#223 := [nnf-pos #218]: #222
-#32 := (- #19)
-#31 := (- #17)
-#41 := (mod #31 #32)
-#42 := (- #41)
-#25 := (< 0::Int #19)
-#27 := (< #17 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #17)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#43 := (ite #29 #40 #42)
-#44 := (ite #21 0::Int #43)
-#45 := (ite #22 #17 #44)
-#46 := (= #39 #45)
-#47 := (forall (vars (?v0 Int) (?v1 Int)) #46)
-#214 := (iff #47 #211)
-#103 := (and #25 #27)
-#106 := (or #26 #103)
-#184 := (ite #106 #40 #179)
-#94 := (= 0::Int #17)
-#187 := (ite #94 0::Int #184)
-#97 := (= 0::Int #19)
-#190 := (ite #97 #17 #187)
-#193 := (= #39 #190)
-#196 := (forall (vars (?v0 Int) (?v1 Int)) #193)
-#212 := (iff #196 #211)
-#209 := (iff #193 #208)
-#206 := (= #190 #205)
-#203 := (= #187 #202)
-#200 := (= #184 #199)
-#155 := (iff #106 #154)
-#152 := (iff #103 #151)
-#149 := (iff #27 #148)
-#150 := [rewrite]: #149
-#142 := (iff #25 #141)
-#143 := [rewrite]: #142
-#153 := [monotonicity #143 #150]: #152
-#145 := (iff #26 #144)
-#138 := (iff #24 #137)
-#139 := [rewrite]: #138
-#146 := [monotonicity #139 #143]: #145
-#156 := [monotonicity #146 #153]: #155
-#201 := [monotonicity #156]: #200
-#130 := (iff #94 #21)
-#131 := [rewrite]: #130
-#204 := [monotonicity #131 #201]: #203
-#132 := (iff #97 #22)
-#133 := [rewrite]: #132
-#207 := [monotonicity #133 #204]: #206
-#210 := [monotonicity #207]: #209
-#213 := [quant-intro #210]: #212
-#197 := (iff #47 #196)
-#194 := (iff #46 #193)
-#191 := (= #45 #190)
-#188 := (= #44 #187)
-#185 := (= #43 #184)
-#182 := (= #42 #179)
-#176 := (- #173)
-#180 := (= #176 #179)
-#181 := [rewrite]: #180
-#177 := (= #42 #176)
-#174 := (= #41 #173)
-#113 := (= #32 #112)
-#114 := [rewrite]: #113
-#110 := (= #31 #109)
-#111 := [rewrite]: #110
-#175 := [monotonicity #111 #114]: #174
-#178 := [monotonicity #175]: #177
-#183 := [trans #178 #181]: #182
-#107 := (iff #29 #106)
-#104 := (iff #28 #103)
-#105 := [rewrite]: #104
-#108 := [monotonicity #105]: #107
-#186 := [monotonicity #108 #183]: #185
-#95 := (iff #21 #94)
-#96 := [rewrite]: #95
-#189 := [monotonicity #96 #186]: #188
-#98 := (iff #22 #97)
-#99 := [rewrite]: #98
-#192 := [monotonicity #99 #189]: #191
-#195 := [monotonicity #192]: #194
-#198 := [quant-intro #195]: #197
-#215 := [trans #198 #213]: #214
-#172 := [asserted]: #47
-#216 := [mp #172 #215]: #211
-#219 := [mp~ #216 #223]: #211
-#267 := [mp #219 #266]: #264
-#298 := [mp #267 #297]: #295
-#782 := [mp #298 #781]: #777
-#10 := (f4 f5 0::Int)
-#71 := (f3 #10 -1::Int)
-#74 := (= #71 0::Int)
-#87 := (not #74)
-#11 := 1::Int
-#12 := (- 1::Int)
-#13 := (f3 #10 #12)
-#14 := (= #13 0::Int)
-#15 := (not #14)
-#90 := (iff #15 #87)
-#77 := (= 0::Int #71)
-#82 := (not #77)
-#88 := (iff #82 #87)
-#85 := (iff #77 #74)
-#86 := [rewrite]: #85
-#89 := [monotonicity #86]: #88
-#83 := (iff #15 #82)
-#80 := (iff #14 #77)
-#78 := (iff #74 #77)
-#79 := [rewrite]: #78
-#75 := (iff #14 #74)
-#72 := (= #13 #71)
-#69 := (= #12 -1::Int)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73]: #75
-#81 := [trans #76 #79]: #80
-#84 := [monotonicity #81]: #83
-#91 := [trans #84 #89]: #90
-#67 := [asserted]: #15
-#92 := [mp #67 #91]: #87
-#553 := (not #777)
-#701 := (or #553 #74)
-#356 := (* -1::Int -1::Int)
-#440 := (* -1::Int 0::Int)
-#441 := (mod #440 #356)
-#442 := (+ #71 #441)
-#433 := (= #442 0::Int)
-#444 := (mod 0::Int -1::Int)
-#445 := (* -1::Int #444)
-#446 := (+ #71 #445)
-#443 := (= #446 0::Int)
-#447 := (>= 0::Int 0::Int)
-#426 := (<= -1::Int 0::Int)
-#761 := (or #426 #447)
-#763 := (not #761)
-#420 := (<= 0::Int 0::Int)
-#550 := (or #420 #426)
-#757 := (not #550)
-#431 := (or #757 #763)
-#432 := (ite #431 #443 #433)
-#764 := (= 0::Int 0::Int)
-#765 := (ite #764 #74 #432)
-#766 := (= -1::Int 0::Int)
-#767 := (ite #766 #77 #765)
-#603 := (or #553 #767)
-#699 := (iff #603 #701)
-#587 := (iff #701 #701)
-#602 := [rewrite]: #587
-#593 := (iff #767 #74)
-#711 := (ite false #74 #74)
-#719 := (iff #711 #74)
-#713 := [rewrite]: #719
-#710 := (iff #767 #711)
-#709 := (iff #765 #74)
-#1 := true
-#551 := (ite true #74 #74)
-#706 := (iff #551 #74)
-#708 := [rewrite]: #706
-#552 := (iff #765 #551)
-#720 := (iff #432 #74)
-#712 := (iff #432 #711)
-#716 := (iff #433 #74)
-#714 := (= #442 #71)
-#454 := (+ #71 0::Int)
-#448 := (= #454 #71)
-#730 := [rewrite]: #448
-#571 := (= #442 #454)
-#729 := (= #441 0::Int)
-#721 := (mod 0::Int 1::Int)
-#728 := (= #721 0::Int)
-#723 := [rewrite]: #728
-#722 := (= #441 #721)
-#725 := (= #356 1::Int)
-#726 := [rewrite]: #725
-#741 := (= #440 0::Int)
-#451 := [rewrite]: #741
-#727 := [monotonicity #451 #726]: #722
-#570 := [trans #727 #723]: #729
-#572 := [monotonicity #570]: #571
-#715 := [trans #572 #730]: #714
-#717 := [monotonicity #715]: #716
-#735 := (iff #443 #74)
-#734 := (= #446 #71)
-#732 := (= #446 #454)
-#452 := (= #445 0::Int)
-#740 := (= #445 #440)
-#462 := (= #444 0::Int)
-#736 := [rewrite]: #462
-#737 := [monotonicity #736]: #740
-#453 := [trans #737 #451]: #452
-#733 := [monotonicity #453]: #732
-#731 := [trans #733 #730]: #734
-#724 := [monotonicity #731]: #735
-#739 := (iff #431 false)
-#466 := (or false false)
-#362 := (iff #466 false)
-#738 := [rewrite]: #362
-#467 := (iff #431 #466)
-#743 := (iff #763 false)
-#747 := (not true)
-#750 := (iff #747 false)
-#745 := [rewrite]: #750
-#756 := (iff #763 #747)
-#755 := (iff #761 true)
-#403 := (or true true)
-#408 := (iff #403 true)
-#409 := [rewrite]: #408
-#394 := (iff #761 #403)
-#752 := (iff #447 true)
-#754 := [rewrite]: #752
-#419 := (iff #426 true)
-#760 := [rewrite]: #419
-#395 := [monotonicity #760 #754]: #394
-#753 := [trans #395 #409]: #755
-#742 := [monotonicity #753]: #756
-#465 := [trans #742 #745]: #743
-#751 := (iff #757 false)
-#748 := (iff #757 #747)
-#410 := (iff #550 true)
-#744 := (iff #550 #403)
-#423 := (iff #420 true)
-#759 := [rewrite]: #423
-#407 := [monotonicity #759 #760]: #744
-#746 := [trans #407 #409]: #410
-#749 := [monotonicity #746]: #748
-#389 := [trans #749 #745]: #751
-#468 := [monotonicity #389 #465]: #467
-#461 := [trans #468 #738]: #739
-#718 := [monotonicity #461 #724 #717]: #712
-#549 := [trans #718 #713]: #720
-#758 := (iff #764 true)
-#418 := [rewrite]: #758
-#705 := [monotonicity #418 #549]: #552
-#707 := [trans #705 #708]: #709
-#762 := (iff #766 false)
-#768 := [rewrite]: #762
-#592 := [monotonicity #768 #86 #707]: #710
-#594 := [trans #592 #713]: #593
-#702 := [monotonicity #594]: #699
-#604 := [trans #702 #602]: #699
-#698 := [quant-inst #9 #68]: #603
-#605 := [mp #698 #604]: #701
-[unit-resolution #605 #92 #782]: false
-unsat
-53e960c63036f749bc0e8a6a50570c720042f356 337 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#17 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#38 := (f4 f5 #17)
-#39 := (f3 #38 #19)
-#776 := (pattern #39)
-#13 := 0::Int
-#68 := -1::Int
-#112 := (* -1::Int #19)
-#109 := (* -1::Int #17)
-#173 := (mod #109 #112)
-#288 := (+ #39 #173)
-#289 := (= #288 0::Int)
-#40 := (mod #17 #19)
-#285 := (* -1::Int #40)
-#286 := (+ #39 #285)
-#287 := (= #286 0::Int)
-#147 := (>= #17 0::Int)
-#140 := (<= #19 0::Int)
-#232 := (or #140 #147)
-#233 := (not #232)
-#136 := (<= #17 0::Int)
-#230 := (or #136 #140)
-#231 := (not #230)
-#236 := (or #231 #233)
-#290 := (ite #236 #287 #289)
-#284 := (= #39 0::Int)
-#21 := (= #17 0::Int)
-#291 := (ite #21 #284 #290)
-#283 := (= #17 #39)
-#22 := (= #19 0::Int)
-#292 := (ite #22 #283 #291)
-#777 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #776) #292)
-#295 := (forall (vars (?v0 Int) (?v1 Int)) #292)
-#780 := (iff #295 #777)
-#778 := (iff #292 #292)
-#779 := [refl]: #778
-#781 := [quant-intro #779]: #780
-#179 := (* -1::Int #173)
-#252 := (ite #236 #40 #179)
-#255 := (ite #21 0::Int #252)
-#258 := (ite #22 #17 #255)
-#261 := (= #39 #258)
-#264 := (forall (vars (?v0 Int) (?v1 Int)) #261)
-#296 := (iff #264 #295)
-#293 := (iff #261 #292)
-#294 := [rewrite]: #293
-#297 := [quant-intro #294]: #296
-#148 := (not #147)
-#141 := (not #140)
-#151 := (and #141 #148)
-#137 := (not #136)
-#144 := (and #137 #141)
-#154 := (or #144 #151)
-#199 := (ite #154 #40 #179)
-#202 := (ite #21 0::Int #199)
-#205 := (ite #22 #17 #202)
-#208 := (= #39 #205)
-#211 := (forall (vars (?v0 Int) (?v1 Int)) #208)
-#265 := (iff #211 #264)
-#262 := (iff #208 #261)
-#259 := (= #205 #258)
-#256 := (= #202 #255)
-#253 := (= #199 #252)
-#237 := (iff #154 #236)
-#234 := (iff #151 #233)
-#235 := [rewrite]: #234
-#224 := (iff #144 #231)
-#225 := [rewrite]: #224
-#238 := [monotonicity #225 #235]: #237
-#254 := [monotonicity #238]: #253
-#257 := [monotonicity #254]: #256
-#260 := [monotonicity #257]: #259
-#263 := [monotonicity #260]: #262
-#266 := [quant-intro #263]: #265
-#222 := (~ #211 #211)
-#221 := (~ #208 #208)
-#218 := [refl]: #221
-#223 := [nnf-pos #218]: #222
+#276 := (if #22 #267 #275)
+#704 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #703) #276)
+#279 := (forall (vars (?v0 Int) (?v1 Int)) #276)
+#707 := (iff #279 #704)
+#705 := (iff #276 #276)
+#706 := [refl]: #705
+#708 := [quant-intro #706]: #707
+#122 := (* -1::Int #116)
+#236 := (if #220 #40 #122)
+#239 := (if #21 0::Int #236)
+#242 := (if #22 #17 #239)
+#245 := (= #39 #242)
+#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
+#280 := (iff #248 #279)
+#277 := (iff #245 #276)
+#278 := [rewrite]: #277
+#281 := [quant-intro #278]: #280
+#73 := (not #72)
+#166 := (not #163)
+#169 := (and #166 #73)
+#69 := (not #68)
+#76 := (and #69 #73)
+#172 := (or #76 #169)
+#188 := (if #172 #40 #122)
+#191 := (if #21 0::Int #188)
+#194 := (if #22 #17 #191)
+#197 := (= #39 #194)
+#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
+#249 := (iff #200 #248)
+#246 := (iff #197 #245)
+#243 := (= #194 #242)
+#240 := (= #191 #239)
+#237 := (= #188 #236)
+#221 := (iff #172 #220)
+#218 := (iff #169 #217)
+#219 := [rewrite]: #218
+#214 := (iff #76 #213)
+#215 := [rewrite]: #214
+#222 := [monotonicity #215 #219]: #221
+#238 := [monotonicity #222]: #237
+#241 := [monotonicity #238]: #240
+#244 := [monotonicity #241]: #243
+#247 := [monotonicity #244]: #246
+#250 := [quant-intro #247]: #249
+#205 := (~ #200 #200)
+#209 := (~ #197 #197)
+#204 := [refl]: #209
+#210 := [nnf-pos #204]: #205
+#79 := (<= 0::Int #17)
+#80 := (not #79)
+#88 := (and #80 #73)
+#91 := (or #76 #88)
+#127 := (if #91 #40 #122)
+#130 := (if #21 0::Int #127)
+#133 := (if #22 #17 #130)
+#136 := (= #39 #133)
+#139 := (forall (vars (?v0 Int) (?v1 Int)) #136)
+#201 := (iff #139 #200)
+#198 := (iff #136 #197)
+#195 := (= #133 #194)
+#192 := (= #130 #191)
+#189 := (= #127 #188)
+#173 := (iff #91 #172)
+#170 := (iff #88 #169)
+#167 := (iff #80 #166)
+#164 := (iff #79 #163)
+#165 := [rewrite]: #164
+#168 := [monotonicity #165]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #171]: #173
+#190 := [monotonicity #174]: #189
+#193 := [monotonicity #190]: #192
+#196 := [monotonicity #193]: #195
+#199 := [monotonicity #196]: #198
+#202 := [quant-intro #199]: #201
 #32 := (- #19)
 #31 := (- #17)
 #41 := (mod #31 #32)
@@ -36917,991 +36386,605 @@
 #24 := (< 0::Int #17)
 #26 := (and #24 #25)
 #29 := (or #26 #28)
-#43 := (ite #29 #40 #42)
-#44 := (ite #21 0::Int #43)
-#45 := (ite #22 #17 #44)
+#43 := (if #29 #40 #42)
+#44 := (if #21 0::Int #43)
+#45 := (if #22 #17 #44)
 #46 := (= #39 #45)
 #47 := (forall (vars (?v0 Int) (?v1 Int)) #46)
-#214 := (iff #47 #211)
-#103 := (and #25 #27)
-#106 := (or #26 #103)
-#184 := (ite #106 #40 #179)
-#94 := (= 0::Int #17)
-#187 := (ite #94 0::Int #184)
-#97 := (= 0::Int #19)
-#190 := (ite #97 #17 #187)
-#193 := (= #39 #190)
-#196 := (forall (vars (?v0 Int) (?v1 Int)) #193)
-#212 := (iff #196 #211)
-#209 := (iff #193 #208)
-#206 := (= #190 #205)
-#203 := (= #187 #202)
-#200 := (= #184 #199)
-#155 := (iff #106 #154)
-#152 := (iff #103 #151)
-#149 := (iff #27 #148)
-#150 := [rewrite]: #149
-#142 := (iff #25 #141)
-#143 := [rewrite]: #142
-#153 := [monotonicity #143 #150]: #152
-#145 := (iff #26 #144)
-#138 := (iff #24 #137)
-#139 := [rewrite]: #138
-#146 := [monotonicity #139 #143]: #145
-#156 := [monotonicity #146 #153]: #155
-#201 := [monotonicity #156]: #200
-#130 := (iff #94 #21)
-#131 := [rewrite]: #130
-#204 := [monotonicity #131 #201]: #203
-#132 := (iff #97 #22)
-#133 := [rewrite]: #132
-#207 := [monotonicity #133 #204]: #206
-#210 := [monotonicity #207]: #209
-#213 := [quant-intro #210]: #212
-#197 := (iff #47 #196)
-#194 := (iff #46 #193)
-#191 := (= #45 #190)
-#188 := (= #44 #187)
-#185 := (= #43 #184)
-#182 := (= #42 #179)
-#176 := (- #173)
-#180 := (= #176 #179)
-#181 := [rewrite]: #180
-#177 := (= #42 #176)
-#174 := (= #41 #173)
-#113 := (= #32 #112)
-#114 := [rewrite]: #113
-#110 := (= #31 #109)
-#111 := [rewrite]: #110
-#175 := [monotonicity #111 #114]: #174
-#178 := [monotonicity #175]: #177
-#183 := [trans #178 #181]: #182
-#107 := (iff #29 #106)
-#104 := (iff #28 #103)
-#105 := [rewrite]: #104
-#108 := [monotonicity #105]: #107
-#186 := [monotonicity #108 #183]: #185
-#95 := (iff #21 #94)
-#96 := [rewrite]: #95
-#189 := [monotonicity #96 #186]: #188
-#98 := (iff #22 #97)
+#140 := (iff #47 #139)
+#137 := (iff #46 #136)
+#134 := (= #45 #133)
+#131 := (= #44 #130)
+#128 := (= #43 #127)
+#125 := (= #42 #122)
+#119 := (- #116)
+#123 := (= #119 #122)
+#124 := [rewrite]: #123
+#120 := (= #42 #119)
+#117 := (= #41 #116)
+#98 := (= #32 #97)
 #99 := [rewrite]: #98
-#192 := [monotonicity #99 #189]: #191
-#195 := [monotonicity #192]: #194
-#198 := [quant-intro #195]: #197
-#215 := [trans #198 #213]: #214
-#172 := [asserted]: #47
-#216 := [mp #172 #215]: #211
-#219 := [mp~ #216 #223]: #211
-#267 := [mp #219 #266]: #264
-#298 := [mp #267 #297]: #295
-#782 := [mp #298 #781]: #777
-#9 := 1::Int
-#10 := (f4 f5 1::Int)
-#71 := (f3 #10 -1::Int)
-#74 := (= #71 0::Int)
-#87 := (not #74)
-#11 := (- 1::Int)
-#12 := (f3 #10 #11)
-#14 := (= #12 0::Int)
-#15 := (not #14)
-#90 := (iff #15 #87)
-#77 := (= 0::Int #71)
-#82 := (not #77)
-#88 := (iff #82 #87)
-#85 := (iff #77 #74)
-#86 := [rewrite]: #85
-#89 := [monotonicity #86]: #88
-#83 := (iff #15 #82)
-#80 := (iff #14 #77)
-#78 := (iff #74 #77)
-#79 := [rewrite]: #78
-#75 := (iff #14 #74)
-#72 := (= #12 #71)
-#69 := (= #11 -1::Int)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73]: #75
-#81 := [trans #76 #79]: #80
-#84 := [monotonicity #81]: #83
-#91 := [trans #84 #89]: #90
-#67 := [asserted]: #15
-#92 := [mp #67 #91]: #87
-#598 := (not #777)
-#606 := (or #598 #74)
-#356 := (* -1::Int -1::Int)
-#440 := (* -1::Int 1::Int)
-#441 := (mod #440 #356)
-#442 := (+ #71 #441)
-#433 := (= #442 0::Int)
-#444 := (mod 1::Int -1::Int)
-#445 := (* -1::Int #444)
-#446 := (+ #71 #445)
-#443 := (= #446 0::Int)
-#447 := (>= 1::Int 0::Int)
-#426 := (<= -1::Int 0::Int)
-#761 := (or #426 #447)
-#763 := (not #761)
-#420 := (<= 1::Int 0::Int)
-#550 := (or #420 #426)
-#757 := (not #550)
-#431 := (or #757 #763)
-#432 := (ite #431 #443 #433)
-#764 := (= 1::Int 0::Int)
-#765 := (ite #764 #74 #432)
-#766 := (= 1::Int #71)
-#767 := (= -1::Int 0::Int)
-#762 := (ite #767 #766 #765)
-#607 := (or #598 #762)
-#609 := (iff #607 #606)
-#703 := (iff #606 #606)
-#700 := [rewrite]: #703
-#604 := (iff #762 #74)
-#423 := (= #71 1::Int)
-#698 := (ite false #423 #74)
-#587 := (iff #698 #74)
-#602 := [rewrite]: #587
-#699 := (iff #762 #698)
-#701 := (iff #765 #74)
-#706 := (ite false #74 #74)
-#707 := (iff #706 #74)
-#710 := [rewrite]: #707
-#594 := (iff #765 #706)
-#592 := (iff #432 #74)
-#708 := (iff #432 #706)
-#552 := (iff #433 #74)
-#549 := (= #442 #71)
-#724 := (+ #71 0::Int)
-#721 := (= #724 #71)
-#722 := [rewrite]: #721
-#713 := (= #442 #724)
-#718 := (= #441 0::Int)
-#715 := (mod -1::Int 1::Int)
-#711 := (= #715 0::Int)
-#712 := [rewrite]: #711
-#716 := (= #441 #715)
-#572 := (= #356 1::Int)
-#714 := [rewrite]: #572
-#570 := (= #440 -1::Int)
-#571 := [rewrite]: #570
-#717 := [monotonicity #571 #714]: #716
-#719 := [trans #717 #712]: #718
-#720 := [monotonicity #719]: #713
-#551 := [trans #720 #722]: #549
-#705 := [monotonicity #551]: #552
-#723 := (iff #443 #74)
-#727 := (= #446 #71)
-#725 := (= #446 #724)
-#731 := (= #445 0::Int)
-#732 := (* -1::Int 0::Int)
-#730 := (= #732 0::Int)
-#734 := [rewrite]: #730
-#733 := (= #445 #732)
-#453 := (= #444 0::Int)
-#454 := [rewrite]: #453
-#448 := [monotonicity #454]: #733
-#735 := [trans #448 #734]: #731
-#726 := [monotonicity #735]: #725
-#728 := [trans #726 #722]: #727
-#729 := [monotonicity #728]: #723
-#451 := (iff #431 false)
-#462 := (or false false)
-#737 := (iff #462 false)
-#741 := [rewrite]: #737
-#736 := (iff #431 #462)
-#739 := (iff #763 false)
-#1 := true
-#745 := (not true)
-#752 := (iff #745 false)
-#754 := [rewrite]: #752
-#362 := (iff #763 #745)
-#467 := (iff #761 true)
-#756 := (or true true)
-#465 := (iff #756 true)
-#466 := [rewrite]: #465
-#742 := (iff #761 #756)
-#755 := (iff #447 true)
-#753 := [rewrite]: #755
-#407 := (iff #426 true)
-#408 := [rewrite]: #407
-#743 := [monotonicity #408 #753]: #742
-#468 := [trans #743 #466]: #467
-#738 := [monotonicity #468]: #362
-#461 := [trans #738 #754]: #739
-#394 := (iff #757 false)
-#751 := (iff #757 #745)
-#749 := (iff #550 true)
-#409 := (or false true)
-#747 := (iff #409 true)
-#748 := [rewrite]: #747
-#410 := (iff #550 #409)
-#403 := (iff #420 false)
-#744 := [rewrite]: #403
-#746 := [monotonicity #744 #408]: #410
-#750 := [trans #746 #748]: #749
-#389 := [monotonicity #750]: #751
-#395 := [trans #389 #754]: #394
-#740 := [monotonicity #395 #461]: #736
-#452 := [trans #740 #741]: #451
-#709 := [monotonicity #452 #729 #705]: #708
-#593 := [trans #709 #710]: #592
-#419 := (iff #764 false)
-#760 := [rewrite]: #419
-#553 := [monotonicity #760 #593]: #594
-#603 := [trans #553 #710]: #701
-#418 := (iff #766 #423)
-#759 := [rewrite]: #418
-#768 := (iff #767 false)
-#758 := [rewrite]: #768
-#702 := [monotonicity #758 #759 #603]: #699
-#605 := [trans #702 #602]: #604
-#610 := [monotonicity #605]: #609
-#704 := [trans #610 #700]: #609
-#608 := [quant-inst #9 #68]: #607
-#691 := [mp #608 #704]: #606
-[unit-resolution #691 #92 #782]: false
-unsat
-46dff7eaa6576ae6594696f52887db6fa7375f00 339 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#20 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#18 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#39 := (f4 f5 #18)
-#40 := (f3 #39 #20)
-#777 := (pattern #40)
-#14 := 0::Int
-#69 := -1::Int
-#113 := (* -1::Int #20)
-#110 := (* -1::Int #18)
-#174 := (mod #110 #113)
-#289 := (+ #40 #174)
-#290 := (= #289 0::Int)
-#41 := (mod #18 #20)
-#286 := (* -1::Int #41)
-#287 := (+ #40 #286)
-#288 := (= #287 0::Int)
-#148 := (>= #18 0::Int)
-#141 := (<= #20 0::Int)
-#233 := (or #141 #148)
-#234 := (not #233)
-#137 := (<= #18 0::Int)
-#231 := (or #137 #141)
-#232 := (not #231)
-#237 := (or #232 #234)
-#291 := (ite #237 #288 #290)
-#285 := (= #40 0::Int)
-#22 := (= #18 0::Int)
-#292 := (ite #22 #285 #291)
-#284 := (= #18 #40)
-#23 := (= #20 0::Int)
-#293 := (ite #23 #284 #292)
-#778 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #777) #293)
-#296 := (forall (vars (?v0 Int) (?v1 Int)) #293)
-#781 := (iff #296 #778)
-#779 := (iff #293 #293)
-#780 := [refl]: #779
-#782 := [quant-intro #780]: #781
-#180 := (* -1::Int #174)
-#253 := (ite #237 #41 #180)
-#256 := (ite #22 0::Int #253)
-#259 := (ite #23 #18 #256)
-#262 := (= #40 #259)
-#265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
-#297 := (iff #265 #296)
-#294 := (iff #262 #293)
-#295 := [rewrite]: #294
-#298 := [quant-intro #295]: #297
-#149 := (not #148)
-#142 := (not #141)
-#152 := (and #142 #149)
-#138 := (not #137)
-#145 := (and #138 #142)
-#155 := (or #145 #152)
-#200 := (ite #155 #41 #180)
-#203 := (ite #22 0::Int #200)
-#206 := (ite #23 #18 #203)
-#209 := (= #40 #206)
-#212 := (forall (vars (?v0 Int) (?v1 Int)) #209)
-#266 := (iff #212 #265)
-#263 := (iff #209 #262)
-#260 := (= #206 #259)
-#257 := (= #203 #256)
-#254 := (= #200 #253)
-#238 := (iff #155 #237)
-#235 := (iff #152 #234)
-#236 := [rewrite]: #235
-#225 := (iff #145 #232)
-#226 := [rewrite]: #225
-#239 := [monotonicity #226 #236]: #238
-#255 := [monotonicity #239]: #254
-#258 := [monotonicity #255]: #257
-#261 := [monotonicity #258]: #260
-#264 := [monotonicity #261]: #263
-#267 := [quant-intro #264]: #266
-#223 := (~ #212 #212)
-#222 := (~ #209 #209)
-#219 := [refl]: #222
-#224 := [nnf-pos #219]: #223
-#33 := (- #20)
-#32 := (- #18)
-#42 := (mod #32 #33)
-#43 := (- #42)
-#26 := (< 0::Int #20)
-#28 := (< #18 0::Int)
-#29 := (and #28 #26)
-#25 := (< 0::Int #18)
-#27 := (and #25 #26)
-#30 := (or #27 #29)
-#44 := (ite #30 #41 #43)
-#45 := (ite #22 0::Int #44)
-#46 := (ite #23 #18 #45)
-#47 := (= #40 #46)
-#48 := (forall (vars (?v0 Int) (?v1 Int)) #47)
-#215 := (iff #48 #212)
-#104 := (and #26 #28)
-#107 := (or #27 #104)
-#185 := (ite #107 #41 #180)
-#95 := (= 0::Int #18)
-#188 := (ite #95 0::Int #185)
-#98 := (= 0::Int #20)
-#191 := (ite #98 #18 #188)
-#194 := (= #40 #191)
-#197 := (forall (vars (?v0 Int) (?v1 Int)) #194)
-#213 := (iff #197 #212)
-#210 := (iff #194 #209)
-#207 := (= #191 #206)
-#204 := (= #188 #203)
-#201 := (= #185 #200)
-#156 := (iff #107 #155)
-#153 := (iff #104 #152)
-#150 := (iff #28 #149)
-#151 := [rewrite]: #150
-#143 := (iff #26 #142)
-#144 := [rewrite]: #143
-#154 := [monotonicity #144 #151]: #153
-#146 := (iff #27 #145)
-#139 := (iff #25 #138)
-#140 := [rewrite]: #139
-#147 := [monotonicity #140 #144]: #146
-#157 := [monotonicity #147 #154]: #156
-#202 := [monotonicity #157]: #201
-#131 := (iff #95 #22)
-#132 := [rewrite]: #131
-#205 := [monotonicity #132 #202]: #204
-#133 := (iff #98 #23)
-#134 := [rewrite]: #133
-#208 := [monotonicity #134 #205]: #207
-#211 := [monotonicity #208]: #210
-#214 := [quant-intro #211]: #213
-#198 := (iff #48 #197)
-#195 := (iff #47 #194)
-#192 := (= #46 #191)
-#189 := (= #45 #188)
-#186 := (= #44 #185)
-#183 := (= #43 #180)
-#177 := (- #174)
-#181 := (= #177 #180)
-#182 := [rewrite]: #181
-#178 := (= #43 #177)
-#175 := (= #42 #174)
-#114 := (= #33 #113)
-#115 := [rewrite]: #114
-#111 := (= #32 #110)
-#112 := [rewrite]: #111
-#176 := [monotonicity #112 #115]: #175
-#179 := [monotonicity #176]: #178
-#184 := [trans #179 #182]: #183
-#108 := (iff #30 #107)
-#105 := (iff #29 #104)
-#106 := [rewrite]: #105
-#109 := [monotonicity #106]: #108
-#187 := [monotonicity #109 #184]: #186
-#96 := (iff #22 #95)
-#97 := [rewrite]: #96
-#190 := [monotonicity #97 #187]: #189
-#99 := (iff #23 #98)
-#100 := [rewrite]: #99
-#193 := [monotonicity #100 #190]: #192
-#196 := [monotonicity #193]: #195
-#199 := [quant-intro #196]: #198
-#216 := [trans #199 #214]: #215
-#173 := [asserted]: #48
-#217 := [mp #173 #216]: #212
-#220 := [mp~ #217 #224]: #212
-#268 := [mp #220 #267]: #265
-#299 := [mp #268 #298]: #296
-#783 := [mp #299 #782]: #778
-#9 := 3::Int
-#10 := (f4 f5 3::Int)
-#72 := (f3 #10 -1::Int)
-#75 := (= #72 0::Int)
-#88 := (not #75)
-#11 := 1::Int
-#12 := (- 1::Int)
-#13 := (f3 #10 #12)
-#15 := (= #13 0::Int)
-#16 := (not #15)
-#91 := (iff #16 #88)
-#78 := (= 0::Int #72)
-#83 := (not #78)
-#89 := (iff #83 #88)
-#86 := (iff #78 #75)
-#87 := [rewrite]: #86
-#90 := [monotonicity #87]: #89
-#84 := (iff #16 #83)
-#81 := (iff #15 #78)
-#79 := (iff #75 #78)
-#80 := [rewrite]: #79
-#76 := (iff #15 #75)
-#73 := (= #13 #72)
-#70 := (= #12 -1::Int)
+#95 := (= #31 #94)
+#96 := [rewrite]: #95
+#118 := [monotonicity #96 #99]: #117
+#121 := [monotonicity #118]: #120
+#126 := [trans #121 #124]: #125
+#92 := (iff #29 #91)
+#89 := (iff #28 #88)
+#74 := (iff #25 #73)
+#75 := [rewrite]: #74
+#81 := (iff #27 #80)
+#85 := (iff #80 #80)
+#83 := (iff #79 #79)
+#84 := [rewrite]: #83
+#86 := [monotonicity #84]: #85
+#82 := [rewrite]: #81
+#87 := [trans #82 #86]: #81
+#90 := [monotonicity #87 #75]: #89
+#77 := (iff #26 #76)
+#70 := (iff #24 #69)
 #71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#77 := [monotonicity #74]: #76
-#82 := [trans #77 #80]: #81
-#85 := [monotonicity #82]: #84
-#92 := [trans #85 #90]: #91
-#68 := [asserted]: #16
-#93 := [mp #68 #92]: #88
-#607 := (not #778)
-#608 := (or #607 #75)
-#357 := (* -1::Int -1::Int)
-#441 := (* -1::Int 3::Int)
-#442 := (mod #441 #357)
-#443 := (+ #72 #442)
-#434 := (= #443 0::Int)
-#445 := (mod 3::Int -1::Int)
-#446 := (* -1::Int #445)
-#447 := (+ #72 #446)
-#444 := (= #447 0::Int)
-#448 := (>= 3::Int 0::Int)
-#427 := (<= -1::Int 0::Int)
-#762 := (or #427 #448)
-#764 := (not #762)
-#421 := (<= 3::Int 0::Int)
-#551 := (or #421 #427)
-#758 := (not #551)
-#432 := (or #758 #764)
-#433 := (ite #432 #444 #434)
-#765 := (= 3::Int 0::Int)
-#766 := (ite #765 #75 #433)
-#767 := (= 3::Int #72)
-#768 := (= -1::Int 0::Int)
-#763 := (ite #768 #767 #766)
-#609 := (or #607 #763)
-#611 := (iff #609 #608)
-#701 := (iff #608 #608)
-#705 := [rewrite]: #701
-#606 := (iff #763 #75)
-#424 := (= #72 3::Int)
-#700 := (ite false #424 #75)
-#603 := (iff #700 #75)
-#605 := [rewrite]: #603
-#703 := (iff #763 #700)
-#604 := (iff #766 #75)
-#709 := (ite false #75 #75)
-#711 := (iff #709 #75)
-#593 := [rewrite]: #711
-#554 := (iff #766 #709)
-#594 := (iff #433 #75)
-#710 := (iff #433 #709)
-#706 := (iff #434 #75)
-#552 := (= #443 #72)
-#725 := (+ #72 0::Int)
-#722 := (= #725 #72)
-#723 := [rewrite]: #722
-#721 := (= #443 #725)
-#720 := (= #442 0::Int)
-#571 := -3::Int
-#717 := (mod -3::Int 1::Int)
-#713 := (= #717 0::Int)
-#719 := [rewrite]: #713
-#718 := (= #442 #717)
-#715 := (= #357 1::Int)
-#716 := [rewrite]: #715
-#572 := (= #441 -3::Int)
-#573 := [rewrite]: #572
-#712 := [monotonicity #573 #716]: #718
-#714 := [trans #712 #719]: #720
-#550 := [monotonicity #714]: #721
-#553 := [trans #550 #723]: #552
-#707 := [monotonicity #553]: #706
-#724 := (iff #444 #75)
-#728 := (= #447 #72)
-#726 := (= #447 #725)
-#732 := (= #446 0::Int)
-#733 := (* -1::Int 0::Int)
-#731 := (= #733 0::Int)
-#735 := [rewrite]: #731
-#734 := (= #446 #733)
-#454 := (= #445 0::Int)
-#455 := [rewrite]: #454
-#449 := [monotonicity #455]: #734
-#736 := [trans #449 #735]: #732
-#727 := [monotonicity #736]: #726
-#729 := [trans #727 #723]: #728
-#730 := [monotonicity #729]: #724
-#452 := (iff #432 false)
-#463 := (or false false)
-#738 := (iff #463 false)
-#742 := [rewrite]: #738
-#737 := (iff #432 #463)
-#740 := (iff #764 false)
-#1 := true
-#746 := (not true)
-#753 := (iff #746 false)
-#755 := [rewrite]: #753
-#363 := (iff #764 #746)
-#468 := (iff #762 true)
-#757 := (or true true)
-#466 := (iff #757 true)
-#467 := [rewrite]: #466
-#743 := (iff #762 #757)
-#756 := (iff #448 true)
-#754 := [rewrite]: #756
-#408 := (iff #427 true)
-#409 := [rewrite]: #408
-#744 := [monotonicity #409 #754]: #743
-#469 := [trans #744 #467]: #468
-#739 := [monotonicity #469]: #363
-#462 := [trans #739 #755]: #740
-#395 := (iff #758 false)
-#752 := (iff #758 #746)
-#750 := (iff #551 true)
-#410 := (or false true)
-#748 := (iff #410 true)
-#749 := [rewrite]: #748
-#411 := (iff #551 #410)
-#404 := (iff #421 false)
-#745 := [rewrite]: #404
-#747 := [monotonicity #745 #409]: #411
-#751 := [trans #747 #749]: #750
-#390 := [monotonicity #751]: #752
-#396 := [trans #390 #755]: #395
-#741 := [monotonicity #396 #462]: #737
-#453 := [trans #741 #742]: #452
-#708 := [monotonicity #453 #730 #707]: #710
-#595 := [trans #708 #593]: #594
-#420 := (iff #765 false)
-#761 := [rewrite]: #420
-#702 := [monotonicity #761 #595]: #554
-#699 := [trans #702 #593]: #604
-#419 := (iff #767 #424)
-#760 := [rewrite]: #419
-#769 := (iff #768 false)
-#759 := [rewrite]: #769
-#588 := [monotonicity #759 #760 #699]: #703
-#599 := [trans #588 #605]: #606
-#704 := [monotonicity #599]: #611
-#692 := [trans #704 #705]: #611
-#610 := [quant-inst #9 #69]: #609
-#694 := [mp #610 #692]: #608
-[unit-resolution #694 #93 #783]: false
-unsat
-9887f50578ea703040a91b60b0f2bf0bf6647706 316 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#20 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#18 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#39 := (f4 f5 #18)
-#40 := (f3 #39 #20)
-#777 := (pattern #40)
-#14 := 0::Int
-#69 := -1::Int
-#113 := (* -1::Int #20)
-#110 := (* -1::Int #18)
-#174 := (mod #110 #113)
-#289 := (+ #40 #174)
-#290 := (= #289 0::Int)
-#41 := (mod #18 #20)
-#286 := (* -1::Int #41)
-#287 := (+ #40 #286)
-#288 := (= #287 0::Int)
-#148 := (>= #18 0::Int)
-#141 := (<= #20 0::Int)
-#233 := (or #141 #148)
-#234 := (not #233)
-#137 := (<= #18 0::Int)
-#231 := (or #137 #141)
-#232 := (not #231)
-#237 := (or #232 #234)
-#291 := (ite #237 #288 #290)
-#285 := (= #40 0::Int)
-#22 := (= #18 0::Int)
-#292 := (ite #22 #285 #291)
-#284 := (= #18 #40)
-#23 := (= #20 0::Int)
-#293 := (ite #23 #284 #292)
-#778 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #777) #293)
-#296 := (forall (vars (?v0 Int) (?v1 Int)) #293)
-#781 := (iff #296 #778)
-#779 := (iff #293 #293)
-#780 := [refl]: #779
-#782 := [quant-intro #780]: #781
-#180 := (* -1::Int #174)
-#253 := (ite #237 #41 #180)
-#256 := (ite #22 0::Int #253)
-#259 := (ite #23 #18 #256)
-#262 := (= #40 #259)
+#78 := [monotonicity #71 #75]: #77
+#93 := [monotonicity #78 #90]: #92
+#129 := [monotonicity #93 #126]: #128
+#132 := [monotonicity #129]: #131
+#135 := [monotonicity #132]: #134
+#138 := [monotonicity #135]: #137
+#141 := [quant-intro #138]: #140
+#51 := [asserted]: #47
+#142 := [mp #51 #141]: #139
+#203 := [mp #142 #202]: #200
+#211 := [mp~ #203 #210]: #200
+#251 := [mp #211 #250]: #248
+#282 := [mp #251 #281]: #279
+#709 := [mp #282 #708]: #704
+decl f6 :: Int
+#8 := f6
+#9 := (f4 f5 f6)
+#58 := (f3 #9 -1::Int)
+#61 := (= #58 0::Int)
+#64 := (not #61)
+#10 := 1::Int
+#11 := (- 1::Int)
+#12 := (f3 #9 #11)
+#14 := (= #12 0::Int)
+#15 := (not #14)
+#65 := (iff #15 #64)
+#62 := (iff #14 #61)
+#59 := (= #12 #58)
+#56 := (= #11 -1::Int)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#63 := [monotonicity #60]: #62
+#66 := [monotonicity #63]: #65
+#49 := [asserted]: #15
+#67 := [mp #49 #66]: #64
+#647 := (not #704)
+#476 := (or #647 #61)
+#358 := (* -1::Int -1::Int)
+#684 := (* -1::Int f6)
+#359 := (mod #684 #358)
+#691 := (+ #58 #359)
+#692 := (= #691 0::Int)
+#688 := (mod f6 -1::Int)
+#690 := (* -1::Int #688)
+#347 := (+ #58 #690)
+#477 := (= #347 0::Int)
+#360 := (<= -1::Int 0::Int)
+#373 := (>= f6 0::Int)
+#370 := (or #373 #360)
+#374 := (not #370)
+#369 := (<= f6 0::Int)
+#371 := (or #369 #360)
+#372 := (not #371)
+#353 := (or #372 #374)
+#693 := (if #353 #477 #692)
+#368 := (= f6 0::Int)
+#694 := (if #368 #61 #693)
+#367 := (= #58 f6)
+#283 := (= -1::Int 0::Int)
+#689 := (if #283 #367 #694)
+#478 := (or #647 #689)
+#632 := (iff #478 #476)
+#635 := (iff #476 #476)
+#636 := [rewrite]: #635
+#646 := (iff #689 #61)
+#643 := (if false #367 #61)
+#639 := (iff #643 #61)
+#645 := [rewrite]: #639
+#644 := (iff #689 #643)
+#641 := (iff #694 #61)
+#650 := (if #368 #61 #61)
+#498 := (iff #650 #61)
+#499 := [rewrite]: #498
+#656 := (iff #694 #650)
+#654 := (iff #693 #61)
+#651 := (if false #477 #61)
+#648 := (iff #651 #61)
+#649 := [rewrite]: #648
+#652 := (iff #693 #651)
+#658 := (iff #692 #61)
+#657 := (= #691 #58)
+#380 := (+ #58 0::Int)
+#660 := (= #380 #58)
+#375 := [rewrite]: #660
+#381 := (= #691 #380)
+#378 := (= #359 0::Int)
+#389 := (mod #684 1::Int)
+#664 := (= #389 0::Int)
+#668 := [rewrite]: #664
+#663 := (= #359 #389)
+#666 := (= #358 1::Int)
+#388 := [rewrite]: #666
+#667 := [monotonicity #388]: #663
+#379 := [trans #667 #668]: #378
+#659 := [monotonicity #379]: #381
+#661 := [trans #659 #375]: #657
+#662 := [monotonicity #661]: #658
+#289 := (iff #353 false)
+#670 := (or false false)
+#394 := (iff #670 false)
+#395 := [rewrite]: #394
+#392 := (iff #353 #670)
+#683 := (iff #374 false)
+#1 := true
+#336 := (not true)
+#674 := (iff #336 false)
+#675 := [rewrite]: #674
+#682 := (iff #374 #336)
+#321 := (iff #370 true)
+#672 := (or #373 true)
+#679 := (iff #672 true)
+#681 := [rewrite]: #679
+#678 := (iff #370 #672)
+#345 := (iff #360 true)
+#350 := [rewrite]: #345
+#316 := [monotonicity #350]: #678
+#322 := [trans #316 #681]: #321
+#680 := [monotonicity #322]: #682
+#669 := [trans #680 #675]: #683
+#676 := (iff #372 false)
+#337 := (iff #372 #336)
+#334 := (iff #371 true)
+#686 := (or #369 true)
+#330 := (iff #686 true)
+#671 := [rewrite]: #330
+#346 := (iff #371 #686)
+#687 := [monotonicity #350]: #346
+#335 := [trans #687 #671]: #334
+#673 := [monotonicity #335]: #337
+#677 := [trans #673 #675]: #676
+#393 := [monotonicity #677 #669]: #392
+#665 := [trans #393 #395]: #289
+#653 := [monotonicity #665 #662]: #652
+#655 := [trans #653 #649]: #654
+#497 := [monotonicity #655]: #656
+#642 := [trans #497 #499]: #641
+#695 := (iff #283 false)
+#685 := [rewrite]: #695
+#638 := [monotonicity #685 #642]: #644
+#640 := [trans #638 #645]: #646
+#633 := [monotonicity #640]: #632
+#634 := [trans #633 #636]: #632
+#479 := [quant-inst #8 #55]: #478
+#637 := [mp #479 #634]: #476
+[unit-resolution #637 #67 #709]: false
+9c9742a1f9e5b5feb0bee490cb17aea9c87b53db 303 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#17 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#15 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#36 := (f4 f5 #15)
+#37 := (f3 #36 #17)
+#690 := (pattern #37)
+#8 := 0::Int
+#79 := -1::Int
+#83 := (* -1::Int #17)
+#80 := (* -1::Int #15)
+#102 := (mod #80 #83)
+#258 := (+ #37 #102)
+#259 := (= #258 0::Int)
+#38 := (mod #15 #17)
+#255 := (* -1::Int #38)
+#256 := (+ #37 #255)
+#257 := (= #256 0::Int)
+#57 := (<= #17 0::Int)
+#149 := (>= #15 0::Int)
+#202 := (or #149 #57)
+#203 := (not #202)
+#53 := (<= #15 0::Int)
+#198 := (or #53 #57)
+#199 := (not #198)
+#206 := (or #199 #203)
+#260 := (if #206 #257 #259)
+#254 := (= #37 0::Int)
+#19 := (= #15 0::Int)
+#261 := (if #19 #254 #260)
+#253 := (= #37 #15)
+#20 := (= #17 0::Int)
+#262 := (if #20 #253 #261)
+#691 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #690) #262)
 #265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
-#297 := (iff #265 #296)
-#294 := (iff #262 #293)
-#295 := [rewrite]: #294
-#298 := [quant-intro #295]: #297
-#149 := (not #148)
-#142 := (not #141)
-#152 := (and #142 #149)
-#138 := (not #137)
-#145 := (and #138 #142)
-#155 := (or #145 #152)
-#200 := (ite #155 #41 #180)
-#203 := (ite #22 0::Int #200)
-#206 := (ite #23 #18 #203)
-#209 := (= #40 #206)
-#212 := (forall (vars (?v0 Int) (?v1 Int)) #209)
-#266 := (iff #212 #265)
-#263 := (iff #209 #262)
-#260 := (= #206 #259)
-#257 := (= #203 #256)
-#254 := (= #200 #253)
-#238 := (iff #155 #237)
-#235 := (iff #152 #234)
-#236 := [rewrite]: #235
-#225 := (iff #145 #232)
-#226 := [rewrite]: #225
-#239 := [monotonicity #226 #236]: #238
-#255 := [monotonicity #239]: #254
-#258 := [monotonicity #255]: #257
-#261 := [monotonicity #258]: #260
-#264 := [monotonicity #261]: #263
+#694 := (iff #265 #691)
+#692 := (iff #262 #262)
+#693 := [refl]: #692
+#695 := [quant-intro #693]: #694
+#108 := (* -1::Int #102)
+#222 := (if #206 #38 #108)
+#225 := (if #19 0::Int #222)
+#228 := (if #20 #15 #225)
+#231 := (= #37 #228)
+#234 := (forall (vars (?v0 Int) (?v1 Int)) #231)
+#266 := (iff #234 #265)
+#263 := (iff #231 #262)
+#264 := [rewrite]: #263
 #267 := [quant-intro #264]: #266
-#223 := (~ #212 #212)
-#222 := (~ #209 #209)
-#219 := [refl]: #222
-#224 := [nnf-pos #219]: #223
-#33 := (- #20)
-#32 := (- #18)
-#42 := (mod #32 #33)
-#43 := (- #42)
-#26 := (< 0::Int #20)
-#28 := (< #18 0::Int)
-#29 := (and #28 #26)
-#25 := (< 0::Int #18)
-#27 := (and #25 #26)
-#30 := (or #27 #29)
-#44 := (ite #30 #41 #43)
-#45 := (ite #22 0::Int #44)
-#46 := (ite #23 #18 #45)
-#47 := (= #40 #46)
-#48 := (forall (vars (?v0 Int) (?v1 Int)) #47)
-#215 := (iff #48 #212)
-#104 := (and #26 #28)
-#107 := (or #27 #104)
-#185 := (ite #107 #41 #180)
-#95 := (= 0::Int #18)
-#188 := (ite #95 0::Int #185)
-#98 := (= 0::Int #20)
-#191 := (ite #98 #18 #188)
-#194 := (= #40 #191)
-#197 := (forall (vars (?v0 Int) (?v1 Int)) #194)
-#213 := (iff #197 #212)
-#210 := (iff #194 #209)
-#207 := (= #191 #206)
-#204 := (= #188 #203)
-#201 := (= #185 #200)
-#156 := (iff #107 #155)
-#153 := (iff #104 #152)
-#150 := (iff #28 #149)
+#58 := (not #57)
+#152 := (not #149)
+#155 := (and #152 #58)
+#54 := (not #53)
+#61 := (and #54 #58)
+#158 := (or #61 #155)
+#174 := (if #158 #38 #108)
+#177 := (if #19 0::Int #174)
+#180 := (if #20 #15 #177)
+#183 := (= #37 #180)
+#186 := (forall (vars (?v0 Int) (?v1 Int)) #183)
+#235 := (iff #186 #234)
+#232 := (iff #183 #231)
+#229 := (= #180 #228)
+#226 := (= #177 #225)
+#223 := (= #174 #222)
+#207 := (iff #158 #206)
+#204 := (iff #155 #203)
+#205 := [rewrite]: #204
+#200 := (iff #61 #199)
+#201 := [rewrite]: #200
+#208 := [monotonicity #201 #205]: #207
+#224 := [monotonicity #208]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [quant-intro #233]: #235
+#148 := (~ #186 #186)
+#193 := (~ #183 #183)
+#147 := [refl]: #193
+#196 := [nnf-pos #147]: #148
+#64 := (<= 0::Int #15)
+#65 := (not #64)
+#73 := (and #65 #58)
+#76 := (or #61 #73)
+#113 := (if #76 #38 #108)
+#116 := (if #19 0::Int #113)
+#119 := (if #20 #15 #116)
+#122 := (= #37 #119)
+#125 := (forall (vars (?v0 Int) (?v1 Int)) #122)
+#187 := (iff #125 #186)
+#184 := (iff #122 #183)
+#181 := (= #119 #180)
+#178 := (= #116 #177)
+#175 := (= #113 #174)
+#159 := (iff #76 #158)
+#156 := (iff #73 #155)
+#153 := (iff #65 #152)
+#150 := (iff #64 #149)
 #151 := [rewrite]: #150
-#143 := (iff #26 #142)
-#144 := [rewrite]: #143
-#154 := [monotonicity #144 #151]: #153
-#146 := (iff #27 #145)
-#139 := (iff #25 #138)
-#140 := [rewrite]: #139
-#147 := [monotonicity #140 #144]: #146
-#157 := [monotonicity #147 #154]: #156
-#202 := [monotonicity #157]: #201
-#131 := (iff #95 #22)
-#132 := [rewrite]: #131
-#205 := [monotonicity #132 #202]: #204
-#133 := (iff #98 #23)
-#134 := [rewrite]: #133
-#208 := [monotonicity #134 #205]: #207
-#211 := [monotonicity #208]: #210
-#214 := [quant-intro #211]: #213
-#198 := (iff #48 #197)
-#195 := (iff #47 #194)
-#192 := (= #46 #191)
-#189 := (= #45 #188)
-#186 := (= #44 #185)
-#183 := (= #43 #180)
-#177 := (- #174)
-#181 := (= #177 #180)
-#182 := [rewrite]: #181
-#178 := (= #43 #177)
-#175 := (= #42 #174)
-#114 := (= #33 #113)
-#115 := [rewrite]: #114
-#111 := (= #32 #110)
-#112 := [rewrite]: #111
-#176 := [monotonicity #112 #115]: #175
+#154 := [monotonicity #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#176 := [monotonicity #160]: #175
 #179 := [monotonicity #176]: #178
-#184 := [trans #179 #182]: #183
-#108 := (iff #30 #107)
-#105 := (iff #29 #104)
-#106 := [rewrite]: #105
-#109 := [monotonicity #106]: #108
-#187 := [monotonicity #109 #184]: #186
-#96 := (iff #22 #95)
-#97 := [rewrite]: #96
-#190 := [monotonicity #97 #187]: #189
-#99 := (iff #23 #98)
-#100 := [rewrite]: #99
-#193 := [monotonicity #100 #190]: #192
-#196 := [monotonicity #193]: #195
-#199 := [quant-intro #196]: #198
-#216 := [trans #199 #214]: #215
-#173 := [asserted]: #48
-#217 := [mp #173 #216]: #212
-#220 := [mp~ #217 #224]: #212
-#268 := [mp #220 #267]: #265
-#299 := [mp #268 #298]: #296
-#783 := [mp #299 #782]: #778
-decl f6 :: Int
-#9 := f6
-#10 := (f4 f5 f6)
-#72 := (f3 #10 -1::Int)
-#75 := (= #72 0::Int)
-#88 := (not #75)
-#11 := 1::Int
-#12 := (- 1::Int)
-#13 := (f3 #10 #12)
-#15 := (= #13 0::Int)
-#16 := (not #15)
-#91 := (iff #16 #88)
-#78 := (= 0::Int #72)
-#83 := (not #78)
-#89 := (iff #83 #88)
-#86 := (iff #78 #75)
-#87 := [rewrite]: #86
-#90 := [monotonicity #87]: #89
-#84 := (iff #16 #83)
-#81 := (iff #15 #78)
-#79 := (iff #75 #78)
-#80 := [rewrite]: #79
-#76 := (iff #15 #75)
-#73 := (= #13 #72)
-#70 := (= #12 -1::Int)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#77 := [monotonicity #74]: #76
-#82 := [trans #77 #80]: #81
-#85 := [monotonicity #82]: #84
-#92 := [trans #85 #90]: #91
-#68 := [asserted]: #16
-#93 := [mp #68 #92]: #88
-#721 := (not #778)
-#550 := (or #721 #75)
-#357 := (* -1::Int -1::Int)
-#441 := (* -1::Int f6)
-#442 := (mod #441 #357)
-#443 := (+ #72 #442)
-#434 := (= #443 0::Int)
-#445 := (mod f6 -1::Int)
-#446 := (* -1::Int #445)
-#447 := (+ #72 #446)
-#444 := (= #447 0::Int)
-#448 := (>= f6 0::Int)
-#427 := (<= -1::Int 0::Int)
-#762 := (or #427 #448)
-#764 := (not #762)
-#421 := (<= f6 0::Int)
-#551 := (or #421 #427)
-#758 := (not #551)
-#432 := (or #758 #764)
-#433 := (ite #432 #444 #434)
-#765 := (= f6 0::Int)
-#766 := (ite #765 #75 #433)
-#767 := (= f6 #72)
-#768 := (= -1::Int 0::Int)
-#763 := (ite #768 #767 #766)
-#552 := (or #721 #763)
-#706 := (iff #552 #550)
-#709 := (iff #550 #550)
-#710 := [rewrite]: #709
-#720 := (iff #763 #75)
-#717 := (ite false #767 #75)
-#713 := (iff #717 #75)
-#719 := [rewrite]: #713
-#718 := (iff #763 #717)
-#715 := (iff #766 #75)
-#724 := (ite #765 #75 #75)
-#572 := (iff #724 #75)
-#573 := [rewrite]: #572
-#730 := (iff #766 #724)
-#728 := (iff #433 #75)
-#725 := (ite false #444 #75)
-#722 := (iff #725 #75)
-#723 := [rewrite]: #722
-#726 := (iff #433 #725)
-#732 := (iff #434 #75)
-#731 := (= #443 #72)
-#454 := (+ #72 0::Int)
-#734 := (= #454 #72)
-#449 := [rewrite]: #734
-#455 := (= #443 #454)
-#452 := (= #442 0::Int)
-#463 := (mod #441 1::Int)
-#738 := (= #463 0::Int)
-#742 := [rewrite]: #738
-#737 := (= #442 #463)
-#740 := (= #357 1::Int)
-#462 := [rewrite]: #740
-#741 := [monotonicity #462]: #737
-#453 := [trans #741 #742]: #452
-#733 := [monotonicity #453]: #455
-#735 := [trans #733 #449]: #731
-#736 := [monotonicity #735]: #732
-#363 := (iff #432 false)
-#744 := (or false false)
-#468 := (iff #744 false)
-#469 := [rewrite]: #468
-#466 := (iff #432 #744)
-#757 := (iff #764 false)
-#1 := true
-#410 := (not true)
-#748 := (iff #410 false)
-#749 := [rewrite]: #748
-#756 := (iff #764 #410)
-#395 := (iff #762 true)
-#746 := (or true #448)
-#753 := (iff #746 true)
-#755 := [rewrite]: #753
-#752 := (iff #762 #746)
-#419 := (iff #427 true)
-#424 := [rewrite]: #419
-#390 := [monotonicity #424]: #752
-#396 := [trans #390 #755]: #395
-#754 := [monotonicity #396]: #756
-#743 := [trans #754 #749]: #757
-#750 := (iff #758 false)
-#411 := (iff #758 #410)
-#408 := (iff #551 true)
-#760 := (or #421 true)
-#404 := (iff #760 true)
-#745 := [rewrite]: #404
-#420 := (iff #551 #760)
-#761 := [monotonicity #424]: #420
-#409 := [trans #761 #745]: #408
-#747 := [monotonicity #409]: #411
-#751 := [trans #747 #749]: #750
-#467 := [monotonicity #751 #743]: #466
-#739 := [trans #467 #469]: #363
-#727 := [monotonicity #739 #736]: #726
-#729 := [trans #727 #723]: #728
-#571 := [monotonicity #729]: #730
-#716 := [trans #571 #573]: #715
-#769 := (iff #768 false)
-#759 := [rewrite]: #769
-#712 := [monotonicity #759 #716]: #718
-#714 := [trans #712 #719]: #720
-#707 := [monotonicity #714]: #706
-#708 := [trans #707 #710]: #706
-#553 := [quant-inst #9 #69]: #552
-#711 := [mp #553 #708]: #550
-[unit-resolution #711 #93 #783]: false
-unsat
-5eb728f1a53457d95412080a923ac7601ce16a78 309 0
+#182 := [monotonicity #179]: #181
+#185 := [monotonicity #182]: #184
+#188 := [quant-intro #185]: #187
+#30 := (- #17)
+#29 := (- #15)
+#39 := (mod #29 #30)
+#40 := (- #39)
+#23 := (< 0::Int #17)
+#25 := (< #15 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #15)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#41 := (if #27 #38 #40)
+#42 := (if #19 0::Int #41)
+#43 := (if #20 #15 #42)
+#44 := (= #37 #43)
+#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
+#126 := (iff #45 #125)
+#123 := (iff #44 #122)
+#120 := (= #43 #119)
+#117 := (= #42 #116)
+#114 := (= #41 #113)
+#111 := (= #40 #108)
+#105 := (- #102)
+#109 := (= #105 #108)
+#110 := [rewrite]: #109
+#106 := (= #40 #105)
+#103 := (= #39 #102)
+#84 := (= #30 #83)
+#85 := [rewrite]: #84
+#81 := (= #29 #80)
+#82 := [rewrite]: #81
+#104 := [monotonicity #82 #85]: #103
+#107 := [monotonicity #104]: #106
+#112 := [trans #107 #110]: #111
+#77 := (iff #27 #76)
+#74 := (iff #26 #73)
+#59 := (iff #23 #58)
+#60 := [rewrite]: #59
+#66 := (iff #25 #65)
+#70 := (iff #65 #65)
+#68 := (iff #64 #64)
+#69 := [rewrite]: #68
+#71 := [monotonicity #69]: #70
+#67 := [rewrite]: #66
+#72 := [trans #67 #71]: #66
+#75 := [monotonicity #72 #60]: #74
+#62 := (iff #24 #61)
+#55 := (iff #22 #54)
+#56 := [rewrite]: #55
+#63 := [monotonicity #56 #60]: #62
+#78 := [monotonicity #63 #75]: #77
+#115 := [monotonicity #78 #112]: #114
+#118 := [monotonicity #115]: #117
+#121 := [monotonicity #118]: #120
+#124 := [monotonicity #121]: #123
+#127 := [quant-intro #124]: #126
+#49 := [asserted]: #45
+#128 := [mp #49 #127]: #125
+#189 := [mp #128 #188]: #186
+#197 := [mp~ #189 #196]: #186
+#237 := [mp #197 #236]: #234
+#268 := [mp #237 #267]: #265
+#696 := [mp #268 #695]: #691
+#10 := 3::Int
+#9 := (f4 f5 0::Int)
+#11 := (f3 #9 3::Int)
+#12 := (= #11 0::Int)
+#13 := (not #12)
+#47 := [asserted]: #13
+#615 := (not #691)
+#517 := (or #615 #12)
+#671 := (* -1::Int 3::Int)
+#464 := (* -1::Int 0::Int)
+#345 := (mod #464 #671)
+#346 := (+ #11 #345)
+#678 := (= #346 0::Int)
+#340 := (mod 0::Int 3::Int)
+#675 := (* -1::Int #340)
+#677 := (+ #11 #675)
+#334 := (= #677 0::Int)
+#356 := (<= 3::Int 0::Int)
+#359 := (>= 0::Int 0::Int)
+#360 := (or #359 #356)
+#357 := (not #360)
+#355 := (<= 0::Int 0::Int)
+#347 := (or #355 #356)
+#358 := (not #347)
+#361 := (or #358 #357)
+#679 := (if #361 #334 #678)
+#354 := (= 0::Int 0::Int)
+#680 := (if #354 #12 #679)
+#269 := (= 3::Int 0::Int)
+#681 := (if #269 #12 #680)
+#612 := (or #615 #681)
+#616 := (iff #612 #517)
+#516 := (iff #517 #517)
+#518 := [rewrite]: #516
+#508 := (iff #681 #12)
+#626 := (if false #12 #12)
+#627 := (iff #626 #12)
+#634 := [rewrite]: #627
+#506 := (iff #681 #626)
+#621 := (iff #680 #12)
+#1 := true
+#466 := (if true #12 #12)
+#622 := (iff #466 #12)
+#623 := [rewrite]: #622
+#619 := (iff #680 #466)
+#463 := (iff #679 #12)
+#632 := (iff #679 #626)
+#631 := (iff #678 #12)
+#629 := (= #346 #11)
+#368 := (+ #11 0::Int)
+#362 := (= #368 #11)
+#644 := [rewrite]: #362
+#486 := (= #346 #368)
+#484 := (= #345 0::Int)
+#639 := -3::Int
+#636 := (mod 0::Int -3::Int)
+#637 := (= #636 0::Int)
+#643 := [rewrite]: #637
+#641 := (= #345 #636)
+#640 := (= #671 -3::Int)
+#635 := [rewrite]: #640
+#655 := (= #464 0::Int)
+#365 := [rewrite]: #655
+#642 := [monotonicity #365 #635]: #641
+#485 := [trans #642 #643]: #484
+#628 := [monotonicity #485]: #486
+#630 := [trans #628 #644]: #629
+#625 := [monotonicity #630]: #631
+#649 := (iff #334 #12)
+#648 := (= #677 #11)
+#646 := (= #677 #368)
+#366 := (= #675 0::Int)
+#654 := (= #675 #464)
+#376 := (= #340 0::Int)
+#650 := [rewrite]: #376
+#651 := [monotonicity #650]: #654
+#367 := [trans #651 #365]: #366
+#647 := [monotonicity #367]: #646
+#645 := [trans #647 #644]: #648
+#638 := [monotonicity #645]: #649
+#653 := (iff #361 false)
+#380 := (or false false)
+#275 := (iff #380 false)
+#652 := [rewrite]: #275
+#381 := (iff #361 #380)
+#657 := (iff #357 false)
+#661 := (not true)
+#664 := (iff #661 false)
+#659 := [rewrite]: #664
+#670 := (iff #357 #661)
+#669 := (iff #360 true)
+#317 := (or true false)
+#322 := (iff #317 true)
+#323 := [rewrite]: #322
+#308 := (iff #360 #317)
+#333 := (iff #356 false)
+#674 := [rewrite]: #333
+#666 := (iff #359 true)
+#668 := [rewrite]: #666
+#309 := [monotonicity #668 #674]: #308
+#667 := [trans #309 #323]: #669
+#656 := [monotonicity #667]: #670
+#379 := [trans #656 #659]: #657
+#665 := (iff #358 false)
+#662 := (iff #358 #661)
+#324 := (iff #347 true)
+#658 := (iff #347 #317)
+#337 := (iff #355 true)
+#673 := [rewrite]: #337
+#321 := [monotonicity #673 #674]: #658
+#660 := [trans #321 #323]: #324
+#663 := [monotonicity #660]: #662
+#303 := [trans #663 #659]: #665
+#382 := [monotonicity #303 #379]: #381
+#375 := [trans #382 #652]: #653
+#633 := [monotonicity #375 #638 #625]: #632
+#465 := [trans #633 #634]: #463
+#672 := (iff #354 true)
+#332 := [rewrite]: #672
+#620 := [monotonicity #332 #465]: #619
+#624 := [trans #620 #623]: #621
+#676 := (iff #269 false)
+#682 := [rewrite]: #676
+#507 := [monotonicity #682 #624]: #506
+#467 := [trans #507 #634]: #508
+#501 := [monotonicity #467]: #616
+#519 := [trans #501 #518]: #616
+#613 := [quant-inst #8 #10]: #612
+#512 := [mp #613 #519]: #517
+[unit-resolution #512 #47 #696]: false
+20cf39716d0e0864db7d929b914c6a23abc44f49 316 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #18 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #16 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #37 := (f4 f5 #16)
 #38 := (f3 #37 #18)
-#762 := (pattern #38)
-#9 := 0::Int
+#704 := (pattern #38)
+#8 := 0::Int
 #93 := -1::Int
 #97 := (* -1::Int #18)
 #94 := (* -1::Int #16)
-#158 := (mod #94 #97)
-#273 := (+ #38 #158)
-#274 := (= #273 0::Int)
+#116 := (mod #94 #97)
+#272 := (+ #38 #116)
+#273 := (= #272 0::Int)
 #39 := (mod #16 #18)
-#270 := (* -1::Int #39)
-#271 := (+ #38 #270)
-#272 := (= #271 0::Int)
-#132 := (>= #16 0::Int)
-#125 := (<= #18 0::Int)
-#217 := (or #125 #132)
-#218 := (not #217)
-#121 := (<= #16 0::Int)
-#215 := (or #121 #125)
-#216 := (not #215)
-#221 := (or #216 #218)
-#275 := (ite #221 #272 #274)
-#269 := (= #38 0::Int)
+#269 := (* -1::Int #39)
+#270 := (+ #38 #269)
+#271 := (= #270 0::Int)
+#71 := (<= #18 0::Int)
+#163 := (>= #16 0::Int)
+#216 := (or #163 #71)
+#217 := (not #216)
+#67 := (<= #16 0::Int)
+#212 := (or #67 #71)
+#213 := (not #212)
+#220 := (or #213 #217)
+#274 := (if #220 #271 #273)
+#268 := (= #38 0::Int)
 #20 := (= #16 0::Int)
-#276 := (ite #20 #269 #275)
-#268 := (= #16 #38)
+#275 := (if #20 #268 #274)
+#267 := (= #38 #16)
 #21 := (= #18 0::Int)
-#277 := (ite #21 #268 #276)
-#763 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #762) #277)
-#280 := (forall (vars (?v0 Int) (?v1 Int)) #277)
-#766 := (iff #280 #763)
-#764 := (iff #277 #277)
-#765 := [refl]: #764
-#767 := [quant-intro #765]: #766
-#164 := (* -1::Int #158)
-#237 := (ite #221 #39 #164)
-#240 := (ite #20 0::Int #237)
-#243 := (ite #21 #16 #240)
-#246 := (= #38 #243)
-#249 := (forall (vars (?v0 Int) (?v1 Int)) #246)
-#281 := (iff #249 #280)
-#278 := (iff #246 #277)
-#279 := [rewrite]: #278
-#282 := [quant-intro #279]: #281
-#133 := (not #132)
-#126 := (not #125)
-#136 := (and #126 #133)
-#122 := (not #121)
-#129 := (and #122 #126)
-#139 := (or #129 #136)
-#184 := (ite #139 #39 #164)
-#187 := (ite #20 0::Int #184)
-#190 := (ite #21 #16 #187)
-#193 := (= #38 #190)
-#196 := (forall (vars (?v0 Int) (?v1 Int)) #193)
-#250 := (iff #196 #249)
-#247 := (iff #193 #246)
-#244 := (= #190 #243)
-#241 := (= #187 #240)
-#238 := (= #184 #237)
-#222 := (iff #139 #221)
-#219 := (iff #136 #218)
-#220 := [rewrite]: #219
-#209 := (iff #129 #216)
-#210 := [rewrite]: #209
-#223 := [monotonicity #210 #220]: #222
-#239 := [monotonicity #223]: #238
-#242 := [monotonicity #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [monotonicity #245]: #247
-#251 := [quant-intro #248]: #250
-#207 := (~ #196 #196)
-#206 := (~ #193 #193)
-#203 := [refl]: #206
-#208 := [nnf-pos #203]: #207
+#276 := (if #21 #267 #275)
+#705 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #704) #276)
+#279 := (forall (vars (?v0 Int) (?v1 Int)) #276)
+#708 := (iff #279 #705)
+#706 := (iff #276 #276)
+#707 := [refl]: #706
+#709 := [quant-intro #707]: #708
+#122 := (* -1::Int #116)
+#236 := (if #220 #39 #122)
+#239 := (if #20 0::Int #236)
+#242 := (if #21 #16 #239)
+#245 := (= #38 #242)
+#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
+#280 := (iff #248 #279)
+#277 := (iff #245 #276)
+#278 := [rewrite]: #277
+#281 := [quant-intro #278]: #280
+#72 := (not #71)
+#166 := (not #163)
+#169 := (and #166 #72)
+#68 := (not #67)
+#75 := (and #68 #72)
+#172 := (or #75 #169)
+#188 := (if #172 #39 #122)
+#191 := (if #20 0::Int #188)
+#194 := (if #21 #16 #191)
+#197 := (= #38 #194)
+#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
+#249 := (iff #200 #248)
+#246 := (iff #197 #245)
+#243 := (= #194 #242)
+#240 := (= #191 #239)
+#237 := (= #188 #236)
+#221 := (iff #172 #220)
+#218 := (iff #169 #217)
+#219 := [rewrite]: #218
+#214 := (iff #75 #213)
+#215 := [rewrite]: #214
+#222 := [monotonicity #215 #219]: #221
+#238 := [monotonicity #222]: #237
+#241 := [monotonicity #238]: #240
+#244 := [monotonicity #241]: #243
+#247 := [monotonicity #244]: #246
+#250 := [quant-intro #247]: #249
+#207 := (~ #200 #200)
+#162 := (~ #197 #197)
+#206 := [refl]: #162
+#210 := [nnf-pos #206]: #207
+#78 := (<= 0::Int #16)
+#79 := (not #78)
+#87 := (and #79 #72)
+#90 := (or #75 #87)
+#127 := (if #90 #39 #122)
+#130 := (if #20 0::Int #127)
+#133 := (if #21 #16 #130)
+#136 := (= #38 #133)
+#139 := (forall (vars (?v0 Int) (?v1 Int)) #136)
+#201 := (iff #139 #200)
+#198 := (iff #136 #197)
+#195 := (= #133 #194)
+#192 := (= #130 #191)
+#189 := (= #127 #188)
+#173 := (iff #90 #172)
+#170 := (iff #87 #169)
+#167 := (iff #79 #166)
+#164 := (iff #78 #163)
+#165 := [rewrite]: #164
+#168 := [monotonicity #165]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #171]: #173
+#190 := [monotonicity #174]: #189
+#193 := [monotonicity #190]: #192
+#196 := [monotonicity #193]: #195
+#199 := [monotonicity #196]: #198
+#202 := [quant-intro #199]: #201
 #31 := (- #18)
 #30 := (- #16)
 #40 := (mod #30 #31)
@@ -37912,635 +36995,948 @@
 #23 := (< 0::Int #16)
 #25 := (and #23 #24)
 #28 := (or #25 #27)
-#42 := (ite #28 #39 #41)
-#43 := (ite #20 0::Int #42)
-#44 := (ite #21 #16 #43)
+#42 := (if #28 #39 #41)
+#43 := (if #20 0::Int #42)
+#44 := (if #21 #16 #43)
 #45 := (= #38 #44)
 #46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#199 := (iff #46 #196)
-#87 := (and #24 #26)
-#90 := (or #25 #87)
-#169 := (ite #90 #39 #164)
-#78 := (= 0::Int #16)
-#172 := (ite #78 0::Int #169)
-#81 := (= 0::Int #18)
-#175 := (ite #81 #16 #172)
-#178 := (= #38 #175)
-#181 := (forall (vars (?v0 Int) (?v1 Int)) #178)
-#197 := (iff #181 #196)
-#194 := (iff #178 #193)
-#191 := (= #175 #190)
-#188 := (= #172 #187)
-#185 := (= #169 #184)
-#140 := (iff #90 #139)
-#137 := (iff #87 #136)
-#134 := (iff #26 #133)
-#135 := [rewrite]: #134
-#127 := (iff #24 #126)
-#128 := [rewrite]: #127
-#138 := [monotonicity #128 #135]: #137
-#130 := (iff #25 #129)
-#123 := (iff #23 #122)
+#140 := (iff #46 #139)
+#137 := (iff #45 #136)
+#134 := (= #44 #133)
+#131 := (= #43 #130)
+#128 := (= #42 #127)
+#125 := (= #41 #122)
+#119 := (- #116)
+#123 := (= #119 #122)
 #124 := [rewrite]: #123
-#131 := [monotonicity #124 #128]: #130
-#141 := [monotonicity #131 #138]: #140
-#186 := [monotonicity #141]: #185
-#115 := (iff #78 #20)
-#116 := [rewrite]: #115
-#189 := [monotonicity #116 #186]: #188
-#117 := (iff #81 #21)
-#118 := [rewrite]: #117
-#192 := [monotonicity #118 #189]: #191
-#195 := [monotonicity #192]: #194
-#198 := [quant-intro #195]: #197
-#182 := (iff #46 #181)
-#179 := (iff #45 #178)
-#176 := (= #44 #175)
-#173 := (= #43 #172)
-#170 := (= #42 #169)
-#167 := (= #41 #164)
-#161 := (- #158)
-#165 := (= #161 #164)
-#166 := [rewrite]: #165
-#162 := (= #41 #161)
-#159 := (= #40 #158)
+#120 := (= #41 #119)
+#117 := (= #40 #116)
 #98 := (= #31 #97)
 #99 := [rewrite]: #98
 #95 := (= #30 #94)
 #96 := [rewrite]: #95
-#160 := [monotonicity #96 #99]: #159
-#163 := [monotonicity #160]: #162
-#168 := [trans #163 #166]: #167
+#118 := [monotonicity #96 #99]: #117
+#121 := [monotonicity #118]: #120
+#126 := [trans #121 #124]: #125
 #91 := (iff #28 #90)
 #88 := (iff #27 #87)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#171 := [monotonicity #92 #168]: #170
-#79 := (iff #20 #78)
-#80 := [rewrite]: #79
-#174 := [monotonicity #80 #171]: #173
-#82 := (iff #21 #81)
+#73 := (iff #24 #72)
+#74 := [rewrite]: #73
+#80 := (iff #26 #79)
+#84 := (iff #79 #79)
+#82 := (iff #78 #78)
 #83 := [rewrite]: #82
-#177 := [monotonicity #83 #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [quant-intro #180]: #182
-#200 := [trans #183 #198]: #199
-#157 := [asserted]: #46
-#201 := [mp #157 #200]: #196
-#204 := [mp~ #201 #208]: #196
-#252 := [mp #204 #251]: #249
-#283 := [mp #252 #282]: #280
-#768 := [mp #283 #767]: #763
-#11 := 3::Int
-#10 := (f4 f5 0::Int)
-#12 := (f3 #10 3::Int)
+#85 := [monotonicity #83]: #84
+#81 := [rewrite]: #80
+#86 := [trans #81 #85]: #80
+#89 := [monotonicity #86 #74]: #88
+#76 := (iff #25 #75)
+#69 := (iff #23 #68)
+#70 := [rewrite]: #69
+#77 := [monotonicity #70 #74]: #76
+#92 := [monotonicity #77 #89]: #91
+#129 := [monotonicity #92 #126]: #128
+#132 := [monotonicity #129]: #131
+#135 := [monotonicity #132]: #134
+#138 := [monotonicity #135]: #137
+#141 := [quant-intro #138]: #140
+#50 := [asserted]: #46
+#142 := [mp #50 #141]: #139
+#203 := [mp #142 #202]: #200
+#211 := [mp~ #203 #210]: #200
+#251 := [mp #211 #250]: #248
+#282 := [mp #251 #281]: #279
+#710 := [mp #282 #709]: #705
+#54 := -3::Int
+#9 := (f4 f5 0::Int)
+#57 := (f3 #9 -3::Int)
+#60 := (= #57 0::Int)
+#63 := (not #60)
+#10 := 3::Int
+#11 := (- 3::Int)
+#12 := (f3 #9 #11)
 #13 := (= #12 0::Int)
 #14 := (not #13)
-#66 := [asserted]: #14
-#684 := (not #763)
-#685 := (or #684 #13)
-#341 := (* -1::Int 3::Int)
-#426 := (* -1::Int 0::Int)
-#427 := (mod #426 #341)
-#428 := (+ #12 #427)
-#419 := (= #428 0::Int)
-#430 := (mod 0::Int 3::Int)
-#431 := (* -1::Int #430)
-#359 := (+ #12 #431)
-#432 := (= #359 0::Int)
-#429 := (>= 0::Int 0::Int)
-#433 := (<= 3::Int 0::Int)
-#412 := (or #433 #429)
-#747 := (not #412)
-#749 := (<= 0::Int 0::Int)
-#406 := (or #749 #433)
-#536 := (not #406)
-#743 := (or #536 #747)
-#417 := (ite #743 #432 #419)
-#418 := (= 0::Int 0::Int)
-#750 := (ite #418 #13 #417)
-#67 := (= 0::Int #12)
-#751 := (= 3::Int 0::Int)
-#752 := (ite #751 #67 #750)
-#688 := (or #684 #752)
-#588 := (iff #688 #685)
-#591 := (iff #685 #685)
-#584 := [rewrite]: #591
-#687 := (iff #752 #13)
-#705 := (ite false #13 #13)
-#535 := (iff #705 #13)
-#537 := [rewrite]: #535
-#580 := (iff #752 #705)
-#578 := (iff #750 #13)
-#1 := true
-#692 := (ite true #13 #13)
-#693 := (iff #692 #13)
-#696 := [rewrite]: #693
-#694 := (iff #750 #692)
-#538 := (iff #417 #13)
-#699 := (iff #417 #705)
-#698 := (iff #419 #13)
-#703 := (= #428 #12)
-#719 := (+ #12 0::Int)
-#720 := (= #719 #12)
-#717 := [rewrite]: #720
-#701 := (= #428 #719)
-#558 := (= #427 0::Int)
-#707 := -3::Int
-#714 := (mod 0::Int -3::Int)
-#556 := (= #714 0::Int)
-#557 := [rewrite]: #556
-#709 := (= #427 #714)
-#708 := (= #341 -3::Int)
-#713 := [rewrite]: #708
-#438 := (= #426 0::Int)
-#439 := [rewrite]: #438
-#715 := [monotonicity #439 #713]: #709
-#700 := [trans #715 #557]: #558
-#702 := [monotonicity #700]: #701
-#697 := [trans #702 #717]: #703
-#704 := [monotonicity #697]: #698
-#711 := (iff #432 #13)
-#721 := (= #359 #12)
-#434 := (= #359 #719)
-#440 := (= #431 0::Int)
-#727 := (= #431 #426)
-#726 := (= #430 0::Int)
-#723 := [rewrite]: #726
-#437 := [monotonicity #723]: #727
-#718 := [trans #437 #439]: #440
-#716 := [monotonicity #718]: #434
-#710 := [trans #716 #717]: #721
-#712 := [monotonicity #710]: #711
-#448 := (iff #743 false)
-#454 := (or false false)
-#725 := (iff #454 false)
-#447 := [rewrite]: #725
-#347 := (iff #743 #454)
-#452 := (iff #747 false)
-#732 := (not true)
-#735 := (iff #732 false)
-#736 := [rewrite]: #735
-#729 := (iff #747 #732)
-#742 := (iff #412 true)
-#740 := (or false true)
-#741 := (iff #740 true)
-#739 := [rewrite]: #741
-#380 := (iff #412 #740)
-#375 := (iff #429 true)
-#738 := [rewrite]: #375
-#745 := (iff #433 false)
-#405 := [rewrite]: #745
-#381 := [monotonicity #405 #738]: #380
-#728 := [trans #381 #739]: #742
-#451 := [monotonicity #728]: #729
-#453 := [trans #451 #736]: #452
-#731 := (iff #536 false)
-#733 := (iff #536 #732)
-#395 := (iff #406 true)
-#746 := (or true false)
-#393 := (iff #746 true)
-#394 := [rewrite]: #393
-#389 := (iff #406 #746)
-#404 := (iff #749 true)
-#409 := [rewrite]: #404
-#730 := [monotonicity #409 #405]: #389
-#396 := [trans #730 #394]: #395
-#734 := [monotonicity #396]: #733
-#737 := [trans #734 #736]: #731
-#724 := [monotonicity #737 #453]: #347
-#722 := [trans #724 #447]: #448
-#706 := [monotonicity #722 #712 #704]: #699
-#691 := [trans #706 #537]: #538
-#754 := (iff #418 true)
-#744 := [rewrite]: #754
-#695 := [monotonicity #744 #691]: #694
-#579 := [trans #695 #696]: #578
-#73 := (iff #67 #13)
-#74 := [rewrite]: #73
-#753 := (iff #751 false)
-#748 := [rewrite]: #753
-#539 := [monotonicity #748 #74 #579]: #580
-#589 := [trans #539 #537]: #687
-#590 := [monotonicity #589]: #588
-#592 := [trans #590 #584]: #588
-#573 := [quant-inst #9 #11]: #688
-#593 := [mp #573 #592]: #685
-[unit-resolution #593 #66 #768]: false
-unsat
-e2cefcec1679e5c68460de294f66a29521651aff 328 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#17 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#38 := (f4 f5 #17)
-#39 := (f3 #38 #19)
-#778 := (pattern #39)
-#9 := 0::Int
-#109 := -1::Int
-#113 := (* -1::Int #19)
-#110 := (* -1::Int #17)
-#174 := (mod #110 #113)
-#289 := (+ #39 #174)
-#290 := (= #289 0::Int)
-#40 := (mod #17 #19)
-#286 := (* -1::Int #40)
-#287 := (+ #39 #286)
-#288 := (= #287 0::Int)
-#148 := (>= #17 0::Int)
-#141 := (<= #19 0::Int)
-#233 := (or #141 #148)
-#234 := (not #233)
-#137 := (<= #17 0::Int)
-#231 := (or #137 #141)
-#232 := (not #231)
-#237 := (or #232 #234)
-#291 := (ite #237 #288 #290)
-#285 := (= #39 0::Int)
+#64 := (iff #14 #63)
+#61 := (iff #13 #60)
+#58 := (= #12 #57)
+#55 := (= #11 -3::Int)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#62 := [monotonicity #59]: #61
+#65 := [monotonicity #62]: #64
+#48 := [asserted]: #14
+#66 := [mp #48 #65]: #63
+#481 := (not #705)
+#629 := (or #481 #60)
+#685 := (* -1::Int -3::Int)
+#478 := (* -1::Int 0::Int)
+#359 := (mod #478 #685)
+#360 := (+ #57 #359)
+#692 := (= #360 0::Int)
+#354 := (mod 0::Int -3::Int)
+#689 := (* -1::Int #354)
+#691 := (+ #57 #689)
+#348 := (= #691 0::Int)
+#370 := (<= -3::Int 0::Int)
+#373 := (>= 0::Int 0::Int)
+#374 := (or #373 #370)
+#371 := (not #374)
+#369 := (<= 0::Int 0::Int)
+#361 := (or #369 #370)
+#372 := (not #361)
+#375 := (or #372 #371)
+#693 := (if #375 #348 #692)
+#368 := (= 0::Int 0::Int)
+#694 := (if #368 #60 #693)
+#283 := (= -3::Int 0::Int)
+#695 := (if #283 #60 #694)
+#531 := (or #481 #695)
+#627 := (iff #531 #629)
+#515 := (iff #629 #629)
+#530 := [rewrite]: #515
+#521 := (iff #695 #60)
+#639 := (if false #60 #60)
+#647 := (iff #639 #60)
+#641 := [rewrite]: #647
+#638 := (iff #695 #639)
+#637 := (iff #694 #60)
+#1 := true
+#479 := (if true #60 #60)
+#634 := (iff #479 #60)
+#636 := [rewrite]: #634
+#480 := (iff #694 #479)
+#648 := (iff #693 #60)
+#640 := (iff #693 #639)
+#644 := (iff #692 #60)
+#642 := (= #360 #57)
+#382 := (+ #57 0::Int)
+#376 := (= #382 #57)
+#658 := [rewrite]: #376
+#499 := (= #360 #382)
+#657 := (= #359 0::Int)
+#649 := (mod 0::Int 3::Int)
+#656 := (= #649 0::Int)
+#651 := [rewrite]: #656
+#650 := (= #359 #649)
+#653 := (= #685 3::Int)
+#654 := [rewrite]: #653
+#669 := (= #478 0::Int)
+#379 := [rewrite]: #669
+#655 := [monotonicity #379 #654]: #650
+#498 := [trans #655 #651]: #657
+#500 := [monotonicity #498]: #499
+#643 := [trans #500 #658]: #642
+#645 := [monotonicity #643]: #644
+#663 := (iff #348 #60)
+#662 := (= #691 #57)
+#660 := (= #691 #382)
+#380 := (= #689 0::Int)
+#668 := (= #689 #478)
+#390 := (= #354 0::Int)
+#664 := [rewrite]: #390
+#665 := [monotonicity #664]: #668
+#381 := [trans #665 #379]: #380
+#661 := [monotonicity #381]: #660
+#659 := [trans #661 #658]: #662
+#652 := [monotonicity #659]: #663
+#667 := (iff #375 false)
+#394 := (or false false)
+#289 := (iff #394 false)
+#666 := [rewrite]: #289
+#395 := (iff #375 #394)
+#671 := (iff #371 false)
+#675 := (not true)
+#678 := (iff #675 false)
+#673 := [rewrite]: #678
+#684 := (iff #371 #675)
+#683 := (iff #374 true)
+#331 := (or true true)
+#336 := (iff #331 true)
+#337 := [rewrite]: #336
+#322 := (iff #374 #331)
+#347 := (iff #370 true)
+#688 := [rewrite]: #347
+#680 := (iff #373 true)
+#682 := [rewrite]: #680
+#323 := [monotonicity #682 #688]: #322
+#681 := [trans #323 #337]: #683
+#670 := [monotonicity #681]: #684
+#393 := [trans #670 #673]: #671
+#679 := (iff #372 false)
+#676 := (iff #372 #675)
+#338 := (iff #361 true)
+#672 := (iff #361 #331)
+#351 := (iff #369 true)
+#687 := [rewrite]: #351
+#335 := [monotonicity #687 #688]: #672
+#674 := [trans #335 #337]: #338
+#677 := [monotonicity #674]: #676
+#317 := [trans #677 #673]: #679
+#396 := [monotonicity #317 #393]: #395
+#389 := [trans #396 #666]: #667
+#646 := [monotonicity #389 #652 #645]: #640
+#477 := [trans #646 #641]: #648
+#686 := (iff #368 true)
+#346 := [rewrite]: #686
+#633 := [monotonicity #346 #477]: #480
+#635 := [trans #633 #636]: #637
+#690 := (iff #283 false)
+#696 := [rewrite]: #690
+#520 := [monotonicity #696 #635]: #638
+#522 := [trans #520 #641]: #521
+#630 := [monotonicity #522]: #627
+#532 := [trans #630 #530]: #627
+#626 := [quant-inst #8 #54]: #531
+#533 := [mp #626 #532]: #629
+[unit-resolution #533 #66 #710]: false
+3882a63fbf201b6600e36717b769e184385c0d9b 329 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#17 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#15 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#37 := (f4 f5 #15)
+#38 := (f3 #37 #17)
+#690 := (pattern #38)
+#19 := 0::Int
+#80 := -1::Int
+#84 := (* -1::Int #17)
+#81 := (* -1::Int #15)
+#103 := (mod #81 #84)
+#259 := (+ #38 #103)
+#260 := (= #259 0::Int)
+#39 := (mod #15 #17)
+#256 := (* -1::Int #39)
+#257 := (+ #38 #256)
+#258 := (= #257 0::Int)
+#58 := (<= #17 0::Int)
+#150 := (>= #15 0::Int)
+#203 := (or #150 #58)
+#204 := (not #203)
+#54 := (<= #15 0::Int)
+#199 := (or #54 #58)
+#200 := (not #199)
+#207 := (or #200 #204)
+#261 := (if #207 #258 #260)
+#255 := (= #38 0::Int)
+#20 := (= #15 0::Int)
+#262 := (if #20 #255 #261)
+#254 := (= #38 #15)
 #21 := (= #17 0::Int)
-#292 := (ite #21 #285 #291)
-#284 := (= #17 #39)
-#22 := (= #19 0::Int)
-#293 := (ite #22 #284 #292)
-#779 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #778) #293)
-#296 := (forall (vars (?v0 Int) (?v1 Int)) #293)
-#782 := (iff #296 #779)
-#780 := (iff #293 #293)
-#781 := [refl]: #780
-#783 := [quant-intro #781]: #782
-#180 := (* -1::Int #174)
-#253 := (ite #237 #40 #180)
-#256 := (ite #21 0::Int #253)
-#259 := (ite #22 #17 #256)
-#262 := (= #39 #259)
-#265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
-#297 := (iff #265 #296)
-#294 := (iff #262 #293)
-#295 := [rewrite]: #294
-#298 := [quant-intro #295]: #297
-#149 := (not #148)
-#142 := (not #141)
-#152 := (and #142 #149)
-#138 := (not #137)
-#145 := (and #138 #142)
-#155 := (or #145 #152)
-#200 := (ite #155 #40 #180)
-#203 := (ite #21 0::Int #200)
-#206 := (ite #22 #17 #203)
-#209 := (= #39 #206)
-#212 := (forall (vars (?v0 Int) (?v1 Int)) #209)
-#266 := (iff #212 #265)
-#263 := (iff #209 #262)
-#260 := (= #206 #259)
-#257 := (= #203 #256)
-#254 := (= #200 #253)
-#238 := (iff #155 #237)
-#235 := (iff #152 #234)
-#236 := [rewrite]: #235
-#225 := (iff #145 #232)
-#226 := [rewrite]: #225
-#239 := [monotonicity #226 #236]: #238
-#255 := [monotonicity #239]: #254
-#258 := [monotonicity #255]: #257
-#261 := [monotonicity #258]: #260
-#264 := [monotonicity #261]: #263
-#267 := [quant-intro #264]: #266
-#223 := (~ #212 #212)
-#222 := (~ #209 #209)
-#219 := [refl]: #222
-#224 := [nnf-pos #219]: #223
-#32 := (- #19)
+#263 := (if #21 #254 #262)
+#691 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #690) #263)
+#266 := (forall (vars (?v0 Int) (?v1 Int)) #263)
+#694 := (iff #266 #691)
+#692 := (iff #263 #263)
+#693 := [refl]: #692
+#695 := [quant-intro #693]: #694
+#109 := (* -1::Int #103)
+#223 := (if #207 #39 #109)
+#226 := (if #20 0::Int #223)
+#229 := (if #21 #15 #226)
+#232 := (= #38 #229)
+#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
+#267 := (iff #235 #266)
+#264 := (iff #232 #263)
+#265 := [rewrite]: #264
+#268 := [quant-intro #265]: #267
+#59 := (not #58)
+#153 := (not #150)
+#156 := (and #153 #59)
+#55 := (not #54)
+#62 := (and #55 #59)
+#159 := (or #62 #156)
+#175 := (if #159 #39 #109)
+#178 := (if #20 0::Int #175)
+#181 := (if #21 #15 #178)
+#184 := (= #38 #181)
+#187 := (forall (vars (?v0 Int) (?v1 Int)) #184)
+#236 := (iff #187 #235)
+#233 := (iff #184 #232)
+#230 := (= #181 #229)
+#227 := (= #178 #226)
+#224 := (= #175 #223)
+#208 := (iff #159 #207)
+#205 := (iff #156 #204)
+#206 := [rewrite]: #205
+#201 := (iff #62 #200)
+#202 := [rewrite]: #201
+#209 := [monotonicity #202 #206]: #208
+#225 := [monotonicity #209]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [quant-intro #234]: #236
+#149 := (~ #187 #187)
+#194 := (~ #184 #184)
+#148 := [refl]: #194
+#197 := [nnf-pos #148]: #149
+#65 := (<= 0::Int #15)
+#66 := (not #65)
+#74 := (and #66 #59)
+#77 := (or #62 #74)
+#114 := (if #77 #39 #109)
+#117 := (if #20 0::Int #114)
+#120 := (if #21 #15 #117)
+#123 := (= #38 #120)
+#126 := (forall (vars (?v0 Int) (?v1 Int)) #123)
+#188 := (iff #126 #187)
+#185 := (iff #123 #184)
+#182 := (= #120 #181)
+#179 := (= #117 #178)
+#176 := (= #114 #175)
+#160 := (iff #77 #159)
+#157 := (iff #74 #156)
+#154 := (iff #66 #153)
+#151 := (iff #65 #150)
+#152 := [rewrite]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#177 := [monotonicity #161]: #176
+#180 := [monotonicity #177]: #179
+#183 := [monotonicity #180]: #182
+#186 := [monotonicity #183]: #185
+#189 := [quant-intro #186]: #188
 #31 := (- #17)
-#41 := (mod #31 #32)
-#42 := (- #41)
-#25 := (< 0::Int #19)
-#27 := (< #17 0::Int)
-#28 := (and #27 #25)
+#30 := (- #15)
+#40 := (mod #30 #31)
+#41 := (- #40)
 #24 := (< 0::Int #17)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#43 := (ite #29 #40 #42)
-#44 := (ite #21 0::Int #43)
-#45 := (ite #22 #17 #44)
-#46 := (= #39 #45)
-#47 := (forall (vars (?v0 Int) (?v1 Int)) #46)
-#215 := (iff #47 #212)
-#103 := (and #25 #27)
-#106 := (or #26 #103)
-#185 := (ite #106 #40 #180)
-#94 := (= 0::Int #17)
-#188 := (ite #94 0::Int #185)
-#97 := (= 0::Int #19)
-#191 := (ite #97 #17 #188)
-#194 := (= #39 #191)
-#197 := (forall (vars (?v0 Int) (?v1 Int)) #194)
-#213 := (iff #197 #212)
-#210 := (iff #194 #209)
-#207 := (= #191 #206)
-#204 := (= #188 #203)
-#201 := (= #185 #200)
-#156 := (iff #106 #155)
-#153 := (iff #103 #152)
-#150 := (iff #27 #149)
-#151 := [rewrite]: #150
-#143 := (iff #25 #142)
-#144 := [rewrite]: #143
-#154 := [monotonicity #144 #151]: #153
-#146 := (iff #26 #145)
-#139 := (iff #24 #138)
-#140 := [rewrite]: #139
-#147 := [monotonicity #140 #144]: #146
-#157 := [monotonicity #147 #154]: #156
-#202 := [monotonicity #157]: #201
-#131 := (iff #94 #21)
-#132 := [rewrite]: #131
-#205 := [monotonicity #132 #202]: #204
-#133 := (iff #97 #22)
-#134 := [rewrite]: #133
-#208 := [monotonicity #134 #205]: #207
-#211 := [monotonicity #208]: #210
-#214 := [quant-intro #211]: #213
-#198 := (iff #47 #197)
-#195 := (iff #46 #194)
-#192 := (= #45 #191)
-#189 := (= #44 #188)
-#186 := (= #43 #185)
-#183 := (= #42 #180)
-#177 := (- #174)
-#181 := (= #177 #180)
-#182 := [rewrite]: #181
-#178 := (= #42 #177)
-#175 := (= #41 #174)
-#114 := (= #32 #113)
-#115 := [rewrite]: #114
-#111 := (= #31 #110)
-#112 := [rewrite]: #111
-#176 := [monotonicity #112 #115]: #175
-#179 := [monotonicity #176]: #178
-#184 := [trans #179 #182]: #183
-#107 := (iff #29 #106)
-#104 := (iff #28 #103)
-#105 := [rewrite]: #104
+#26 := (< #15 0::Int)
+#27 := (and #26 #24)
+#23 := (< 0::Int #15)
+#25 := (and #23 #24)
+#28 := (or #25 #27)
+#42 := (if #28 #39 #41)
+#43 := (if #20 0::Int #42)
+#44 := (if #21 #15 #43)
+#45 := (= #38 #44)
+#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
+#127 := (iff #46 #126)
+#124 := (iff #45 #123)
+#121 := (= #44 #120)
+#118 := (= #43 #117)
+#115 := (= #42 #114)
+#112 := (= #41 #109)
+#106 := (- #103)
+#110 := (= #106 #109)
+#111 := [rewrite]: #110
+#107 := (= #41 #106)
+#104 := (= #40 #103)
+#85 := (= #31 #84)
+#86 := [rewrite]: #85
+#82 := (= #30 #81)
+#83 := [rewrite]: #82
+#105 := [monotonicity #83 #86]: #104
 #108 := [monotonicity #105]: #107
-#187 := [monotonicity #108 #184]: #186
-#95 := (iff #21 #94)
-#96 := [rewrite]: #95
-#190 := [monotonicity #96 #187]: #189
-#98 := (iff #22 #97)
-#99 := [rewrite]: #98
-#193 := [monotonicity #99 #190]: #192
-#196 := [monotonicity #193]: #195
-#199 := [quant-intro #196]: #198
-#216 := [trans #199 #214]: #215
-#173 := [asserted]: #47
-#217 := [mp #173 #216]: #212
-#220 := [mp~ #217 #224]: #212
-#268 := [mp #220 #267]: #265
-#299 := [mp #268 #298]: #296
-#784 := [mp #299 #783]: #779
-#68 := -3::Int
-#10 := (f4 f5 0::Int)
-#71 := (f3 #10 -3::Int)
-#74 := (= #71 0::Int)
-#87 := (not #74)
-#11 := 3::Int
-#12 := (- 3::Int)
-#13 := (f3 #10 #12)
-#14 := (= #13 0::Int)
-#15 := (not #14)
-#90 := (iff #15 #87)
-#77 := (= 0::Int #71)
-#82 := (not #77)
-#88 := (iff #82 #87)
-#85 := (iff #77 #74)
-#86 := [rewrite]: #85
-#89 := [monotonicity #86]: #88
-#83 := (iff #15 #82)
-#80 := (iff #14 #77)
-#78 := (iff #74 #77)
-#79 := [rewrite]: #78
-#75 := (iff #14 #74)
-#72 := (= #13 #71)
-#69 := (= #12 -3::Int)
+#113 := [trans #108 #111]: #112
+#78 := (iff #28 #77)
+#75 := (iff #27 #74)
+#60 := (iff #24 #59)
+#61 := [rewrite]: #60
+#67 := (iff #26 #66)
+#71 := (iff #66 #66)
+#69 := (iff #65 #65)
 #70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73]: #75
-#81 := [trans #76 #79]: #80
-#84 := [monotonicity #81]: #83
-#91 := [trans #84 #89]: #90
-#67 := [asserted]: #15
-#92 := [mp #67 #91]: #87
-#596 := (not #779)
-#555 := (or #596 #74)
-#357 := (* -1::Int -3::Int)
-#442 := (* -1::Int 0::Int)
-#443 := (mod #442 #357)
-#444 := (+ #71 #443)
-#435 := (= #444 0::Int)
-#446 := (mod 0::Int -3::Int)
-#447 := (* -1::Int #446)
-#375 := (+ #71 #447)
-#448 := (= #375 0::Int)
-#445 := (>= 0::Int 0::Int)
-#449 := (<= -3::Int 0::Int)
-#428 := (or #449 #445)
-#763 := (not #428)
-#765 := (<= 0::Int 0::Int)
-#422 := (or #765 #449)
-#552 := (not #422)
-#759 := (or #552 #763)
-#433 := (ite #759 #448 #435)
-#434 := (= 0::Int 0::Int)
-#766 := (ite #434 #74 #433)
-#767 := (= -3::Int 0::Int)
-#768 := (ite #767 #77 #766)
-#703 := (or #596 #768)
-#700 := (iff #703 #555)
-#704 := (iff #555 #555)
-#589 := [rewrite]: #704
-#594 := (iff #768 #74)
-#719 := (ite false #74 #74)
-#720 := (iff #719 #74)
-#721 := [rewrite]: #720
-#709 := (iff #768 #719)
-#710 := (iff #766 #74)
-#1 := true
-#551 := (ite true #74 #74)
-#707 := (iff #551 #74)
-#708 := [rewrite]: #707
-#553 := (iff #766 #551)
-#715 := (iff #433 #74)
-#713 := (iff #433 #719)
-#717 := (iff #435 #74)
-#574 := (= #444 #71)
-#455 := (+ #71 0::Int)
-#735 := (= #455 #71)
-#450 := [rewrite]: #735
-#572 := (= #444 #455)
-#725 := (= #443 0::Int)
-#728 := (mod 0::Int 3::Int)
-#729 := (= #728 0::Int)
-#730 := [rewrite]: #729
-#723 := (= #443 #728)
-#726 := (= #357 3::Int)
-#727 := [rewrite]: #726
-#739 := (= #442 0::Int)
-#743 := [rewrite]: #739
-#724 := [monotonicity #743 #727]: #723
-#731 := [trans #724 #730]: #725
-#573 := [monotonicity #731]: #572
-#716 := [trans #573 #450]: #574
-#718 := [monotonicity #716]: #717
-#733 := (iff #448 #74)
-#732 := (= #375 #71)
-#456 := (= #375 #455)
-#453 := (= #447 0::Int)
-#738 := (= #447 #442)
-#463 := (= #446 0::Int)
-#464 := [rewrite]: #463
-#742 := [monotonicity #464]: #738
-#454 := [trans #742 #743]: #453
-#734 := [monotonicity #454]: #456
-#736 := [trans #734 #450]: #732
-#737 := [monotonicity #736]: #733
-#740 := (iff #759 false)
-#467 := (or false false)
-#470 := (iff #467 false)
-#363 := [rewrite]: #470
-#468 := (iff #759 #467)
-#744 := (iff #763 false)
-#748 := (not true)
-#751 := (iff #748 false)
-#752 := [rewrite]: #751
-#755 := (iff #763 #748)
-#397 := (iff #428 true)
-#762 := (or true true)
-#409 := (iff #762 true)
-#410 := [rewrite]: #409
-#756 := (iff #428 #762)
-#391 := (iff #445 true)
-#754 := [rewrite]: #391
-#761 := (iff #449 true)
-#421 := [rewrite]: #761
-#396 := [monotonicity #421 #754]: #756
-#757 := [trans #396 #410]: #397
-#758 := [monotonicity #757]: #755
-#745 := [trans #758 #752]: #744
-#747 := (iff #552 false)
-#749 := (iff #552 #748)
-#411 := (iff #422 true)
-#405 := (iff #422 #762)
-#420 := (iff #765 true)
-#425 := [rewrite]: #420
-#746 := [monotonicity #425 #421]: #405
-#412 := [trans #746 #410]: #411
-#750 := [monotonicity #412]: #749
-#753 := [trans #750 #752]: #747
-#469 := [monotonicity #753 #745]: #468
-#741 := [trans #469 #363]: #740
-#714 := [monotonicity #741 #737 #718]: #713
-#722 := [trans #714 #721]: #715
-#770 := (iff #434 true)
-#760 := [rewrite]: #770
-#554 := [monotonicity #760 #722]: #553
-#711 := [trans #554 #708]: #710
-#769 := (iff #767 false)
-#764 := [rewrite]: #769
-#712 := [monotonicity #764 #86 #711]: #709
-#595 := [trans #712 #721]: #594
-#701 := [monotonicity #595]: #700
-#604 := [trans #701 #589]: #700
-#605 := [quant-inst #9 #68]: #703
-#606 := [mp #605 #604]: #555
-[unit-resolution #606 #92 #784]: false
-unsat
-8523f126ec39b5b31cca78036b23ebeb91082249 325 0
+#72 := [monotonicity #70]: #71
+#68 := [rewrite]: #67
+#73 := [trans #68 #72]: #67
+#76 := [monotonicity #73 #61]: #75
+#63 := (iff #25 #62)
+#56 := (iff #23 #55)
+#57 := [rewrite]: #56
+#64 := [monotonicity #57 #61]: #63
+#79 := [monotonicity #64 #76]: #78
+#116 := [monotonicity #79 #113]: #115
+#119 := [monotonicity #116]: #118
+#122 := [monotonicity #119]: #121
+#125 := [monotonicity #122]: #124
+#128 := [quant-intro #125]: #127
+#50 := [asserted]: #46
+#129 := [mp #50 #128]: #126
+#190 := [mp #129 #189]: #187
+#198 := [mp~ #190 #197]: #187
+#238 := [mp #198 #237]: #235
+#269 := [mp #238 #268]: #266
+#696 := [mp #269 #695]: #691
+#8 := 1::Int
+#10 := 3::Int
+#9 := (f4 f5 1::Int)
+#11 := (f3 #9 3::Int)
+#12 := (= #11 1::Int)
+#13 := (not #12)
+#48 := [asserted]: #13
+#610 := (not #691)
+#606 := (or #610 #12)
+#345 := (* -1::Int 3::Int)
+#671 := (* -1::Int 1::Int)
+#346 := (mod #671 #345)
+#678 := (+ #11 #346)
+#679 := (= #678 0::Int)
+#675 := (mod 1::Int 3::Int)
+#677 := (* -1::Int #675)
+#334 := (+ #11 #677)
+#464 := (= #334 0::Int)
+#347 := (<= 3::Int 0::Int)
+#360 := (>= 1::Int 0::Int)
+#357 := (or #360 #347)
+#361 := (not #357)
+#356 := (<= 1::Int 0::Int)
+#358 := (or #356 #347)
+#359 := (not #358)
+#340 := (or #359 #361)
+#680 := (if #340 #464 #679)
+#355 := (= #11 0::Int)
+#354 := (= 1::Int 0::Int)
+#681 := (if #354 #355 #680)
+#270 := (= 3::Int 0::Int)
+#676 := (if #270 #12 #681)
+#611 := (or #610 #676)
+#601 := (iff #611 #606)
+#603 := (iff #606 #606)
+#597 := [rewrite]: #603
+#608 := (iff #676 #12)
+#605 := (if false #12 #12)
+#596 := (iff #605 #12)
+#598 := [rewrite]: #596
+#607 := (iff #676 #605)
+#614 := (iff #681 #12)
+#521 := (if false #355 #12)
+#524 := (iff #521 #12)
+#617 := [rewrite]: #524
+#522 := (iff #681 #521)
+#512 := (iff #680 #12)
+#508 := -2::Int
+#467 := (= #11 -2::Int)
+#1 := true
+#616 := (if true #12 #467)
+#518 := (iff #616 #12)
+#519 := [rewrite]: #518
+#501 := (iff #680 #616)
+#612 := (iff #679 #467)
+#626 := 2::Int
+#619 := (+ 2::Int #11)
+#624 := (= #619 0::Int)
+#615 := (iff #624 #467)
+#517 := [rewrite]: #615
+#506 := (iff #679 #624)
+#623 := (= #678 #619)
+#463 := (+ #11 2::Int)
+#620 := (= #463 #619)
+#622 := [rewrite]: #620
+#465 := (= #678 #463)
+#627 := (= #346 2::Int)
+#486 := -3::Int
+#630 := (mod -1::Int -3::Int)
+#632 := (= #630 2::Int)
+#633 := [rewrite]: #632
+#631 := (= #346 #630)
+#628 := (= #345 -3::Int)
+#629 := [rewrite]: #628
+#368 := (= #671 -1::Int)
+#646 := [rewrite]: #368
+#625 := [monotonicity #646 #629]: #631
+#634 := [trans #625 #633]: #627
+#466 := [monotonicity #634]: #465
+#621 := [trans #466 #622]: #623
+#507 := [monotonicity #621]: #506
+#613 := [trans #507 #517]: #612
+#484 := (iff #464 #12)
+#649 := (+ -1::Int #11)
+#636 := (= #649 0::Int)
+#637 := (iff #636 #12)
+#643 := [rewrite]: #637
+#641 := (iff #464 #636)
+#640 := (= #334 #649)
+#644 := (+ #11 -1::Int)
+#638 := (= #644 #649)
+#639 := [rewrite]: #638
+#648 := (= #334 #644)
+#647 := (= #677 -1::Int)
+#366 := (= #677 #671)
+#655 := (= #675 1::Int)
+#365 := [rewrite]: #655
+#367 := [monotonicity #365]: #366
+#362 := [trans #367 #646]: #647
+#645 := [monotonicity #362]: #648
+#635 := [trans #645 #639]: #640
+#642 := [monotonicity #635]: #641
+#485 := [trans #642 #643]: #484
+#654 := (iff #340 true)
+#309 := (or true false)
+#670 := (iff #309 true)
+#656 := [rewrite]: #670
+#376 := (iff #340 #309)
+#653 := (iff #361 false)
+#380 := (not true)
+#276 := (iff #380 false)
+#652 := [rewrite]: #276
+#381 := (iff #361 #380)
+#657 := (iff #357 true)
+#669 := (iff #357 #309)
+#674 := (iff #347 false)
+#317 := [rewrite]: #674
+#668 := (iff #360 true)
+#308 := [rewrite]: #668
+#667 := [monotonicity #308 #317]: #669
+#379 := [trans #667 #656]: #657
+#382 := [monotonicity #379]: #381
+#375 := [trans #382 #652]: #653
+#303 := (iff #359 true)
+#662 := (not false)
+#659 := (iff #662 true)
+#665 := [rewrite]: #659
+#663 := (iff #359 #662)
+#660 := (iff #358 false)
+#658 := (or false false)
+#323 := (iff #658 false)
+#324 := [rewrite]: #323
+#321 := (iff #358 #658)
+#673 := (iff #356 false)
+#333 := [rewrite]: #673
+#322 := [monotonicity #333 #317]: #321
+#661 := [trans #322 #324]: #660
+#664 := [monotonicity #661]: #663
+#666 := [trans #664 #665]: #303
+#650 := [monotonicity #666 #375]: #376
+#651 := [trans #650 #656]: #654
+#516 := [monotonicity #651 #485 #613]: #501
+#520 := [trans #516 #519]: #512
+#332 := (iff #354 false)
+#337 := [rewrite]: #332
+#523 := [monotonicity #337 #520]: #522
+#618 := [trans #523 #617]: #614
+#682 := (iff #270 false)
+#672 := [rewrite]: #682
+#599 := [monotonicity #672 #618]: #607
+#609 := [trans #599 #598]: #608
+#602 := [monotonicity #609]: #601
+#604 := [trans #602 #597]: #601
+#600 := [quant-inst #8 #10]: #611
+#588 := [mp #600 #604]: #606
+[unit-resolution #588 #48 #696]: false
+8fb8eaf7501da70df2af1f1c31da5641a4aee45b 304 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#17 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#15 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#36 := (f4 f5 #15)
+#37 := (f3 #36 #17)
+#690 := (pattern #37)
+#11 := 0::Int
+#79 := -1::Int
+#83 := (* -1::Int #17)
+#80 := (* -1::Int #15)
+#102 := (mod #80 #83)
+#258 := (+ #37 #102)
+#259 := (= #258 0::Int)
+#38 := (mod #15 #17)
+#255 := (* -1::Int #38)
+#256 := (+ #37 #255)
+#257 := (= #256 0::Int)
+#57 := (<= #17 0::Int)
+#149 := (>= #15 0::Int)
+#202 := (or #149 #57)
+#203 := (not #202)
+#53 := (<= #15 0::Int)
+#198 := (or #53 #57)
+#199 := (not #198)
+#206 := (or #199 #203)
+#260 := (if #206 #257 #259)
+#254 := (= #37 0::Int)
+#19 := (= #15 0::Int)
+#261 := (if #19 #254 #260)
+#253 := (= #37 #15)
+#20 := (= #17 0::Int)
+#262 := (if #20 #253 #261)
+#691 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #690) #262)
+#265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
+#694 := (iff #265 #691)
+#692 := (iff #262 #262)
+#693 := [refl]: #692
+#695 := [quant-intro #693]: #694
+#108 := (* -1::Int #102)
+#222 := (if #206 #38 #108)
+#225 := (if #19 0::Int #222)
+#228 := (if #20 #15 #225)
+#231 := (= #37 #228)
+#234 := (forall (vars (?v0 Int) (?v1 Int)) #231)
+#266 := (iff #234 #265)
+#263 := (iff #231 #262)
+#264 := [rewrite]: #263
+#267 := [quant-intro #264]: #266
+#58 := (not #57)
+#152 := (not #149)
+#155 := (and #152 #58)
+#54 := (not #53)
+#61 := (and #54 #58)
+#158 := (or #61 #155)
+#174 := (if #158 #38 #108)
+#177 := (if #19 0::Int #174)
+#180 := (if #20 #15 #177)
+#183 := (= #37 #180)
+#186 := (forall (vars (?v0 Int) (?v1 Int)) #183)
+#235 := (iff #186 #234)
+#232 := (iff #183 #231)
+#229 := (= #180 #228)
+#226 := (= #177 #225)
+#223 := (= #174 #222)
+#207 := (iff #158 #206)
+#204 := (iff #155 #203)
+#205 := [rewrite]: #204
+#200 := (iff #61 #199)
+#201 := [rewrite]: #200
+#208 := [monotonicity #201 #205]: #207
+#224 := [monotonicity #208]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [quant-intro #233]: #235
+#193 := (~ #186 #186)
+#148 := (~ #183 #183)
+#192 := [refl]: #148
+#196 := [nnf-pos #192]: #193
+#64 := (<= 0::Int #15)
+#65 := (not #64)
+#73 := (and #65 #58)
+#76 := (or #61 #73)
+#113 := (if #76 #38 #108)
+#116 := (if #19 0::Int #113)
+#119 := (if #20 #15 #116)
+#122 := (= #37 #119)
+#125 := (forall (vars (?v0 Int) (?v1 Int)) #122)
+#187 := (iff #125 #186)
+#184 := (iff #122 #183)
+#181 := (= #119 #180)
+#178 := (= #116 #177)
+#175 := (= #113 #174)
+#159 := (iff #76 #158)
+#156 := (iff #73 #155)
+#153 := (iff #65 #152)
+#150 := (iff #64 #149)
+#151 := [rewrite]: #150
+#154 := [monotonicity #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#176 := [monotonicity #160]: #175
+#179 := [monotonicity #176]: #178
+#182 := [monotonicity #179]: #181
+#185 := [monotonicity #182]: #184
+#188 := [quant-intro #185]: #187
+#30 := (- #17)
+#29 := (- #15)
+#39 := (mod #29 #30)
+#40 := (- #39)
+#23 := (< 0::Int #17)
+#25 := (< #15 0::Int)
+#26 := (and #25 #23)
+#22 := (< 0::Int #15)
+#24 := (and #22 #23)
+#27 := (or #24 #26)
+#41 := (if #27 #38 #40)
+#42 := (if #19 0::Int #41)
+#43 := (if #20 #15 #42)
+#44 := (= #37 #43)
+#45 := (forall (vars (?v0 Int) (?v1 Int)) #44)
+#126 := (iff #45 #125)
+#123 := (iff #44 #122)
+#120 := (= #43 #119)
+#117 := (= #42 #116)
+#114 := (= #41 #113)
+#111 := (= #40 #108)
+#105 := (- #102)
+#109 := (= #105 #108)
+#110 := [rewrite]: #109
+#106 := (= #40 #105)
+#103 := (= #39 #102)
+#84 := (= #30 #83)
+#85 := [rewrite]: #84
+#81 := (= #29 #80)
+#82 := [rewrite]: #81
+#104 := [monotonicity #82 #85]: #103
+#107 := [monotonicity #104]: #106
+#112 := [trans #107 #110]: #111
+#77 := (iff #27 #76)
+#74 := (iff #26 #73)
+#59 := (iff #23 #58)
+#60 := [rewrite]: #59
+#66 := (iff #25 #65)
+#70 := (iff #65 #65)
+#68 := (iff #64 #64)
+#69 := [rewrite]: #68
+#71 := [monotonicity #69]: #70
+#67 := [rewrite]: #66
+#72 := [trans #67 #71]: #66
+#75 := [monotonicity #72 #60]: #74
+#62 := (iff #24 #61)
+#55 := (iff #22 #54)
+#56 := [rewrite]: #55
+#63 := [monotonicity #56 #60]: #62
+#78 := [monotonicity #63 #75]: #77
+#115 := [monotonicity #78 #112]: #114
+#118 := [monotonicity #115]: #117
+#121 := [monotonicity #118]: #120
+#124 := [monotonicity #121]: #123
+#127 := [quant-intro #124]: #126
+#49 := [asserted]: #45
+#128 := [mp #49 #127]: #125
+#189 := [mp #128 #188]: #186
+#197 := [mp~ #189 #196]: #186
+#237 := [mp #197 #236]: #234
+#268 := [mp #237 #267]: #265
+#696 := [mp #268 #695]: #691
+#8 := 3::Int
+#9 := (f4 f5 3::Int)
+#10 := (f3 #9 3::Int)
+#12 := (= #10 0::Int)
+#13 := (not #12)
+#47 := [asserted]: #13
+#517 := (not #691)
+#612 := (or #517 #12)
+#334 := (* -1::Int 3::Int)
+#464 := (mod #334 #334)
+#671 := (+ #10 #464)
+#345 := (= #671 0::Int)
+#361 := (mod 3::Int 3::Int)
+#340 := (* -1::Int #361)
+#675 := (+ #10 #340)
+#677 := (= #675 0::Int)
+#355 := (<= 3::Int 0::Int)
+#358 := (>= 3::Int 0::Int)
+#359 := (or #358 #355)
+#360 := (not #359)
+#356 := (or #355 #355)
+#347 := (not #356)
+#357 := (or #347 #360)
+#346 := (if #357 #677 #345)
+#269 := (= 3::Int 0::Int)
+#678 := (if #269 #12 #346)
+#354 := (= #10 3::Int)
+#679 := (if #269 #354 #678)
+#613 := (or #517 #679)
+#501 := (iff #613 #612)
+#518 := (iff #612 #612)
+#519 := [rewrite]: #518
+#467 := (iff #679 #12)
+#621 := (if false #354 #12)
+#507 := (iff #621 #12)
+#508 := [rewrite]: #507
+#624 := (iff #679 #621)
+#622 := (iff #678 #12)
+#463 := (if false #12 #12)
+#619 := (iff #463 #12)
+#620 := [rewrite]: #619
+#465 := (iff #678 #463)
+#627 := (iff #346 #12)
+#1 := true
+#631 := (if true #12 #12)
+#632 := (iff #631 #12)
+#633 := [rewrite]: #632
+#625 := (iff #346 #631)
+#629 := (iff #345 #12)
+#486 := (= #671 #10)
+#366 := (+ #10 0::Int)
+#646 := (= #366 #10)
+#647 := [rewrite]: #646
+#484 := (= #671 #366)
+#637 := (= #464 0::Int)
+#649 := -3::Int
+#640 := (mod -3::Int -3::Int)
+#641 := (= #640 0::Int)
+#642 := [rewrite]: #641
+#635 := (= #464 #640)
+#638 := (= #334 -3::Int)
+#639 := [rewrite]: #638
+#636 := [monotonicity #639 #639]: #635
+#643 := [trans #636 #642]: #637
+#485 := [monotonicity #643]: #484
+#628 := [trans #485 #647]: #486
+#630 := [monotonicity #628]: #629
+#648 := (iff #677 #12)
+#362 := (= #675 #10)
+#367 := (= #675 #366)
+#655 := (= #340 0::Int)
+#375 := (* -1::Int 0::Int)
+#654 := (= #375 0::Int)
+#651 := [rewrite]: #654
+#376 := (= #340 #375)
+#652 := (= #361 0::Int)
+#653 := [rewrite]: #652
+#650 := [monotonicity #653]: #376
+#365 := [trans #650 #651]: #655
+#368 := [monotonicity #365]: #367
+#644 := [trans #368 #647]: #362
+#645 := [monotonicity #644]: #648
+#382 := (iff #357 true)
+#664 := (or true false)
+#303 := (iff #664 true)
+#666 := [rewrite]: #303
+#380 := (iff #357 #664)
+#657 := (iff #360 false)
+#309 := (not true)
+#670 := (iff #309 false)
+#656 := [rewrite]: #670
+#669 := (iff #360 #309)
+#668 := (iff #359 true)
+#659 := (iff #359 #664)
+#676 := (iff #355 false)
+#682 := [rewrite]: #676
+#662 := (iff #358 true)
+#663 := [rewrite]: #662
+#665 := [monotonicity #663 #682]: #659
+#308 := [trans #665 #666]: #668
+#667 := [monotonicity #308]: #669
+#379 := [trans #667 #656]: #657
+#660 := (iff #347 true)
+#658 := (not false)
+#323 := (iff #658 true)
+#324 := [rewrite]: #323
+#321 := (iff #347 #658)
+#674 := (iff #356 false)
+#672 := (or false false)
+#673 := (iff #672 false)
+#333 := [rewrite]: #673
+#332 := (iff #356 #672)
+#337 := [monotonicity #682 #682]: #332
+#317 := [trans #337 #333]: #674
+#322 := [monotonicity #317]: #321
+#661 := [trans #322 #324]: #660
+#381 := [monotonicity #661 #379]: #380
+#275 := [trans #381 #666]: #382
+#626 := [monotonicity #275 #645 #630]: #625
+#634 := [trans #626 #633]: #627
+#680 := (iff #269 false)
+#681 := [rewrite]: #680
+#466 := [monotonicity #681 #634]: #465
+#623 := [trans #466 #620]: #622
+#506 := [monotonicity #681 #623]: #624
+#615 := [trans #506 #508]: #467
+#516 := [monotonicity #615]: #501
+#512 := [trans #516 #519]: #501
+#616 := [quant-inst #8 #8]: #613
+#520 := [mp #616 #512]: #612
+[unit-resolution #520 #47 #696]: false
+02010738b40a0ce955cc2273aa34fc24db09e1c2 335 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #18 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #16 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #38 := (f4 f5 #16)
 #39 := (f3 #38 #18)
-#747 := (pattern #39)
+#692 := (pattern #39)
 #20 := 0::Int
-#85 := -1::Int
-#89 := (* -1::Int #18)
-#86 := (* -1::Int #16)
-#144 := (mod #86 #89)
-#259 := (+ #39 #144)
-#260 := (= #259 0::Int)
+#81 := -1::Int
+#85 := (* -1::Int #18)
+#82 := (* -1::Int #16)
+#104 := (mod #82 #85)
+#260 := (+ #39 #104)
+#261 := (= #260 0::Int)
 #40 := (mod #16 #18)
-#256 := (* -1::Int #40)
-#257 := (+ #39 #256)
-#258 := (= #257 0::Int)
-#118 := (>= #16 0::Int)
-#111 := (<= #18 0::Int)
-#203 := (or #111 #118)
-#204 := (not #203)
-#107 := (<= #16 0::Int)
-#201 := (or #107 #111)
-#202 := (not #201)
-#207 := (or #202 #204)
-#261 := (ite #207 #258 #260)
-#255 := (= #39 0::Int)
+#257 := (* -1::Int #40)
+#258 := (+ #39 #257)
+#259 := (= #258 0::Int)
+#59 := (<= #18 0::Int)
+#151 := (>= #16 0::Int)
+#204 := (or #151 #59)
+#205 := (not #204)
+#55 := (<= #16 0::Int)
+#200 := (or #55 #59)
+#201 := (not #200)
+#208 := (or #201 #205)
+#262 := (if #208 #259 #261)
+#256 := (= #39 0::Int)
 #21 := (= #16 0::Int)
-#262 := (ite #21 #255 #261)
-#254 := (= #16 #39)
+#263 := (if #21 #256 #262)
+#255 := (= #39 #16)
 #22 := (= #18 0::Int)
-#263 := (ite #22 #254 #262)
-#748 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #747) #263)
-#266 := (forall (vars (?v0 Int) (?v1 Int)) #263)
-#751 := (iff #266 #748)
-#749 := (iff #263 #263)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#150 := (* -1::Int #144)
-#223 := (ite #207 #40 #150)
-#226 := (ite #21 0::Int #223)
-#229 := (ite #22 #16 #226)
-#232 := (= #39 #229)
-#235 := (forall (vars (?v0 Int) (?v1 Int)) #232)
-#267 := (iff #235 #266)
-#264 := (iff #232 #263)
-#265 := [rewrite]: #264
-#268 := [quant-intro #265]: #267
-#119 := (not #118)
-#112 := (not #111)
-#122 := (and #112 #119)
-#108 := (not #107)
-#115 := (and #108 #112)
-#125 := (or #115 #122)
-#170 := (ite #125 #40 #150)
-#173 := (ite #21 0::Int #170)
-#176 := (ite #22 #16 #173)
-#179 := (= #39 #176)
-#182 := (forall (vars (?v0 Int) (?v1 Int)) #179)
-#236 := (iff #182 #235)
-#233 := (iff #179 #232)
-#230 := (= #176 #229)
-#227 := (= #173 #226)
-#224 := (= #170 #223)
-#208 := (iff #125 #207)
-#205 := (iff #122 #204)
-#206 := [rewrite]: #205
-#195 := (iff #115 #202)
-#196 := [rewrite]: #195
-#209 := [monotonicity #196 #206]: #208
-#225 := [monotonicity #209]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [quant-intro #234]: #236
-#193 := (~ #182 #182)
-#192 := (~ #179 #179)
-#189 := [refl]: #192
-#194 := [nnf-pos #189]: #193
+#264 := (if #22 #255 #263)
+#693 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #692) #264)
+#267 := (forall (vars (?v0 Int) (?v1 Int)) #264)
+#696 := (iff #267 #693)
+#694 := (iff #264 #264)
+#695 := [refl]: #694
+#697 := [quant-intro #695]: #696
+#110 := (* -1::Int #104)
+#224 := (if #208 #40 #110)
+#227 := (if #21 0::Int #224)
+#230 := (if #22 #16 #227)
+#233 := (= #39 #230)
+#236 := (forall (vars (?v0 Int) (?v1 Int)) #233)
+#268 := (iff #236 #267)
+#265 := (iff #233 #264)
+#266 := [rewrite]: #265
+#269 := [quant-intro #266]: #268
+#60 := (not #59)
+#154 := (not #151)
+#157 := (and #154 #60)
+#56 := (not #55)
+#63 := (and #56 #60)
+#160 := (or #63 #157)
+#176 := (if #160 #40 #110)
+#179 := (if #21 0::Int #176)
+#182 := (if #22 #16 #179)
+#185 := (= #39 #182)
+#188 := (forall (vars (?v0 Int) (?v1 Int)) #185)
+#237 := (iff #188 #236)
+#234 := (iff #185 #233)
+#231 := (= #182 #230)
+#228 := (= #179 #227)
+#225 := (= #176 #224)
+#209 := (iff #160 #208)
+#206 := (iff #157 #205)
+#207 := [rewrite]: #206
+#202 := (iff #63 #201)
+#203 := [rewrite]: #202
+#210 := [monotonicity #203 #207]: #209
+#226 := [monotonicity #210]: #225
+#229 := [monotonicity #226]: #228
+#232 := [monotonicity #229]: #231
+#235 := [monotonicity #232]: #234
+#238 := [quant-intro #235]: #237
+#195 := (~ #188 #188)
+#150 := (~ #185 #185)
+#194 := [refl]: #150
+#198 := [nnf-pos #194]: #195
+#66 := (<= 0::Int #16)
+#67 := (not #66)
+#75 := (and #67 #60)
+#78 := (or #63 #75)
+#115 := (if #78 #40 #110)
+#118 := (if #21 0::Int #115)
+#121 := (if #22 #16 #118)
+#124 := (= #39 #121)
+#127 := (forall (vars (?v0 Int) (?v1 Int)) #124)
+#189 := (iff #127 #188)
+#186 := (iff #124 #185)
+#183 := (= #121 #182)
+#180 := (= #118 #179)
+#177 := (= #115 #176)
+#161 := (iff #78 #160)
+#158 := (iff #75 #157)
+#155 := (iff #67 #154)
+#152 := (iff #66 #151)
+#153 := [rewrite]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#178 := [monotonicity #162]: #177
+#181 := [monotonicity #178]: #180
+#184 := [monotonicity #181]: #183
+#187 := [monotonicity #184]: #186
+#190 := [quant-intro #187]: #189
 #32 := (- #18)
 #31 := (- #16)
 #41 := (mod #31 #32)
@@ -38551,322 +37947,675 @@
 #24 := (< 0::Int #16)
 #26 := (and #24 #25)
 #29 := (or #26 #28)
-#43 := (ite #29 #40 #42)
-#44 := (ite #21 0::Int #43)
-#45 := (ite #22 #16 #44)
+#43 := (if #29 #40 #42)
+#44 := (if #21 0::Int #43)
+#45 := (if #22 #16 #44)
 #46 := (= #39 #45)
 #47 := (forall (vars (?v0 Int) (?v1 Int)) #46)
-#185 := (iff #47 #182)
-#79 := (and #25 #27)
-#82 := (or #26 #79)
-#155 := (ite #82 #40 #150)
-#158 := (ite #21 0::Int #155)
-#161 := (ite #22 #16 #158)
-#164 := (= #39 #161)
-#167 := (forall (vars (?v0 Int) (?v1 Int)) #164)
-#183 := (iff #167 #182)
-#180 := (iff #164 #179)
-#177 := (= #161 #176)
-#174 := (= #158 #173)
-#171 := (= #155 #170)
-#126 := (iff #82 #125)
-#123 := (iff #79 #122)
-#120 := (iff #27 #119)
-#121 := [rewrite]: #120
-#113 := (iff #25 #112)
-#114 := [rewrite]: #113
-#124 := [monotonicity #114 #121]: #123
-#116 := (iff #26 #115)
-#109 := (iff #24 #108)
-#110 := [rewrite]: #109
-#117 := [monotonicity #110 #114]: #116
-#127 := [monotonicity #117 #124]: #126
-#172 := [monotonicity #127]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [monotonicity #178]: #180
-#184 := [quant-intro #181]: #183
-#168 := (iff #47 #167)
-#165 := (iff #46 #164)
-#162 := (= #45 #161)
-#159 := (= #44 #158)
-#156 := (= #43 #155)
-#153 := (= #42 #150)
-#147 := (- #144)
-#151 := (= #147 #150)
-#152 := [rewrite]: #151
-#148 := (= #42 #147)
-#145 := (= #41 #144)
-#90 := (= #32 #89)
-#91 := [rewrite]: #90
-#87 := (= #31 #86)
-#88 := [rewrite]: #87
-#146 := [monotonicity #88 #91]: #145
-#149 := [monotonicity #146]: #148
-#154 := [trans #149 #152]: #153
-#83 := (iff #29 #82)
-#80 := (iff #28 #79)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#157 := [monotonicity #84 #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [monotonicity #163]: #165
-#169 := [quant-intro #166]: #168
-#186 := [trans #169 #184]: #185
-#143 := [asserted]: #47
-#187 := [mp #143 #186]: #182
-#190 := [mp~ #187 #194]: #182
-#238 := [mp #190 #237]: #235
-#269 := [mp #238 #268]: #266
-#753 := [mp #269 #752]: #748
-#9 := 1::Int
-#11 := 3::Int
-#10 := (f4 f5 1::Int)
-#12 := (f3 #10 3::Int)
-#13 := (= #12 1::Int)
+#128 := (iff #47 #127)
+#125 := (iff #46 #124)
+#122 := (= #45 #121)
+#119 := (= #44 #118)
+#116 := (= #43 #115)
+#113 := (= #42 #110)
+#107 := (- #104)
+#111 := (= #107 #110)
+#112 := [rewrite]: #111
+#108 := (= #42 #107)
+#105 := (= #41 #104)
+#86 := (= #32 #85)
+#87 := [rewrite]: #86
+#83 := (= #31 #82)
+#84 := [rewrite]: #83
+#106 := [monotonicity #84 #87]: #105
+#109 := [monotonicity #106]: #108
+#114 := [trans #109 #112]: #113
+#79 := (iff #29 #78)
+#76 := (iff #28 #75)
+#61 := (iff #25 #60)
+#62 := [rewrite]: #61
+#68 := (iff #27 #67)
+#72 := (iff #67 #67)
+#70 := (iff #66 #66)
+#71 := [rewrite]: #70
+#73 := [monotonicity #71]: #72
+#69 := [rewrite]: #68
+#74 := [trans #69 #73]: #68
+#77 := [monotonicity #74 #62]: #76
+#64 := (iff #26 #63)
+#57 := (iff #24 #56)
+#58 := [rewrite]: #57
+#65 := [monotonicity #58 #62]: #64
+#80 := [monotonicity #65 #77]: #79
+#117 := [monotonicity #80 #114]: #116
+#120 := [monotonicity #117]: #119
+#123 := [monotonicity #120]: #122
+#126 := [monotonicity #123]: #125
+#129 := [quant-intro #126]: #128
+#51 := [asserted]: #47
+#130 := [mp #51 #129]: #127
+#191 := [mp #130 #190]: #188
+#199 := [mp~ #191 #198]: #188
+#239 := [mp #199 #238]: #236
+#270 := [mp #239 #269]: #267
+#698 := [mp #270 #697]: #693
+#12 := 2::Int
+#10 := 3::Int
+#8 := 5::Int
+#9 := (f4 f5 5::Int)
+#11 := (f3 #9 3::Int)
+#13 := (= #11 2::Int)
 #14 := (not #13)
-#67 := [asserted]: #14
-#657 := (not #748)
-#658 := (or #657 #13)
-#327 := (* -1::Int 3::Int)
-#411 := (* -1::Int 1::Int)
-#412 := (mod #411 #327)
-#413 := (+ #12 #412)
-#404 := (= #413 0::Int)
-#415 := (mod 1::Int 3::Int)
-#416 := (* -1::Int #415)
-#417 := (+ #12 #416)
-#414 := (= #417 0::Int)
-#418 := (>= 1::Int 0::Int)
-#397 := (<= 3::Int 0::Int)
-#732 := (or #397 #418)
-#734 := (not #732)
-#391 := (<= 1::Int 0::Int)
-#521 := (or #391 #397)
-#728 := (not #521)
-#402 := (or #728 #734)
-#403 := (ite #402 #414 #404)
-#735 := (= #12 0::Int)
-#736 := (= 1::Int 0::Int)
-#737 := (ite #736 #735 #403)
-#68 := (= 1::Int #12)
-#738 := (= 3::Int 0::Int)
-#733 := (ite #738 #68 #737)
-#659 := (or #657 #733)
-#654 := (iff #659 #658)
-#645 := (iff #658 #658)
-#646 := [rewrite]: #645
-#663 := (iff #733 #13)
-#653 := (ite false #13 #13)
-#666 := (iff #653 #13)
-#667 := [rewrite]: #666
-#655 := (iff #733 #653)
-#664 := (iff #737 #13)
-#581 := (ite false #735 #13)
-#675 := (iff #581 #13)
-#662 := [rewrite]: #675
-#674 := (iff #737 #581)
-#579 := (iff #403 #13)
-#574 := -2::Int
-#669 := (= #12 -2::Int)
-#1 := true
-#575 := (ite true #13 #669)
-#577 := (iff #575 #13)
-#578 := [rewrite]: #577
-#576 := (iff #403 #575)
-#558 := (iff #404 #669)
-#684 := 2::Int
-#680 := (+ 2::Int #12)
-#565 := (= #680 0::Int)
-#670 := (iff #565 #669)
-#673 := [rewrite]: #670
-#524 := (iff #404 #565)
-#563 := (= #413 #680)
-#676 := (+ #12 2::Int)
-#678 := (= #676 #680)
-#681 := [rewrite]: #678
-#677 := (= #413 #676)
-#522 := (= #412 2::Int)
-#687 := -3::Int
-#683 := (mod -1::Int -3::Int)
-#691 := (= #683 2::Int)
-#520 := [rewrite]: #691
-#689 := (= #412 #683)
-#688 := (= #327 -3::Int)
-#682 := [rewrite]: #688
-#419 := (= #411 -1::Int)
-#701 := [rewrite]: #419
-#690 := [monotonicity #701 #682]: #689
-#523 := [trans #690 #520]: #522
-#679 := [monotonicity #523]: #677
-#564 := [trans #679 #681]: #563
-#672 := [monotonicity #564]: #524
-#573 := [trans #672 #673]: #558
-#685 := (iff #414 #13)
-#697 := (+ -1::Int #12)
-#694 := (= #697 0::Int)
-#542 := (iff #694 #13)
-#543 := [rewrite]: #542
-#700 := (iff #414 #694)
-#698 := (= #417 #697)
-#706 := (+ #12 -1::Int)
-#692 := (= #706 #697)
-#693 := [rewrite]: #692
-#695 := (= #417 #706)
-#705 := (= #416 -1::Int)
-#703 := (= #416 #411)
-#424 := (= #415 1::Int)
-#425 := [rewrite]: #424
-#704 := [monotonicity #425]: #703
-#702 := [trans #704 #701]: #705
-#696 := [monotonicity #702]: #695
-#699 := [trans #696 #693]: #698
-#541 := [monotonicity #699]: #700
-#686 := [trans #541 #543]: #685
-#422 := (iff #402 true)
-#433 := (or true false)
-#708 := (iff #433 true)
-#712 := [rewrite]: #708
-#707 := (iff #402 #433)
-#710 := (iff #734 false)
-#437 := (not true)
-#333 := (iff #437 false)
-#709 := [rewrite]: #333
-#438 := (iff #734 #437)
-#714 := (iff #732 true)
-#366 := (or false true)
-#727 := (iff #366 true)
-#713 := [rewrite]: #727
-#726 := (iff #732 #366)
-#725 := (iff #418 true)
-#365 := [rewrite]: #725
-#731 := (iff #397 false)
-#374 := [rewrite]: #731
-#724 := [monotonicity #374 #365]: #726
-#436 := [trans #724 #713]: #714
-#439 := [monotonicity #436]: #438
-#432 := [trans #439 #709]: #710
-#360 := (iff #728 true)
-#719 := (not false)
-#716 := (iff #719 true)
-#722 := [rewrite]: #716
-#720 := (iff #728 #719)
-#717 := (iff #521 false)
-#715 := (or false false)
-#380 := (iff #715 false)
-#381 := [rewrite]: #380
-#378 := (iff #521 #715)
-#730 := (iff #391 false)
-#390 := [rewrite]: #730
-#379 := [monotonicity #390 #374]: #378
-#718 := [trans #379 #381]: #717
-#721 := [monotonicity #718]: #720
-#723 := [trans #721 #722]: #360
-#711 := [monotonicity #723 #432]: #707
-#423 := [trans #711 #712]: #422
-#569 := [monotonicity #423 #686 #573]: #576
-#580 := [trans #569 #578]: #579
-#389 := (iff #736 false)
-#394 := [rewrite]: #389
-#671 := [monotonicity #394 #580]: #674
-#656 := [trans #671 #662]: #664
-#74 := (iff #68 #13)
-#75 := [rewrite]: #74
-#739 := (iff #738 false)
-#729 := [rewrite]: #739
-#665 := [monotonicity #729 #75 #656]: #655
-#668 := [trans #665 #667]: #663
-#661 := [monotonicity #668]: #654
-#648 := [trans #661 #646]: #654
-#660 := [quant-inst #9 #11]: #659
-#649 := [mp #660 #648]: #658
-[unit-resolution #649 #67 #753]: false
-unsat
-78bb6b5ca52ee61b969e810f583df52ff03038e8 310 0
+#49 := [asserted]: #14
+#603 := (not #693)
+#604 := (or #603 #13)
+#348 := (* -1::Int 3::Int)
+#347 := (* -1::Int 5::Int)
+#680 := (mod #347 #348)
+#681 := (+ #11 #680)
+#682 := (= #681 0::Int)
+#679 := (mod 5::Int 3::Int)
+#336 := (* -1::Int #679)
+#466 := (+ #11 #336)
+#673 := (= #466 0::Int)
+#360 := (<= 3::Int 0::Int)
+#359 := (>= 5::Int 0::Int)
+#363 := (or #359 #360)
+#342 := (not #363)
+#349 := (<= 5::Int 0::Int)
+#361 := (or #349 #360)
+#362 := (not #361)
+#677 := (or #362 #342)
+#683 := (if #677 #673 #682)
+#358 := (= #11 0::Int)
+#357 := (= 5::Int 0::Int)
+#678 := (if #357 #358 #683)
+#356 := (= #11 5::Int)
+#271 := (= 3::Int 0::Int)
+#684 := (if #271 #356 #678)
+#605 := (or #603 #684)
+#606 := (iff #605 #604)
+#591 := (iff #604 #604)
+#593 := [rewrite]: #591
+#613 := (iff #684 #13)
+#600 := (if false #356 #13)
+#612 := (iff #600 #13)
+#608 := [rewrite]: #612
+#610 := (iff #684 #600)
+#601 := (iff #678 #13)
+#619 := (if false #358 #13)
+#607 := (iff #619 #13)
+#609 := [rewrite]: #607
+#616 := (iff #678 #619)
+#525 := (iff #683 #13)
+#615 := (= #11 -1::Int)
+#1 := true
+#521 := (if true #13 #615)
+#523 := (iff #521 #13)
+#524 := [rewrite]: #523
+#514 := (iff #683 #521)
+#518 := (iff #682 #615)
+#289 := 1::Int
+#626 := (+ 1::Int #11)
+#617 := (= #626 0::Int)
+#618 := (iff #617 #615)
+#503 := [rewrite]: #618
+#519 := (iff #682 #617)
+#510 := (= #681 #626)
+#624 := (+ #11 1::Int)
+#508 := (= #624 #626)
+#509 := [rewrite]: #508
+#625 := (= #681 #624)
+#621 := (= #680 1::Int)
+#628 := -3::Int
+#632 := -5::Int
+#629 := (mod -5::Int -3::Int)
+#467 := (= #629 1::Int)
+#468 := [rewrite]: #467
+#636 := (= #680 #629)
+#634 := (= #348 -3::Int)
+#635 := [rewrite]: #634
+#633 := (= #347 -5::Int)
+#627 := [rewrite]: #633
+#465 := [monotonicity #627 #635]: #636
+#622 := [trans #465 #468]: #621
+#623 := [monotonicity #622]: #625
+#469 := [trans #623 #509]: #510
+#614 := [monotonicity #469]: #519
+#520 := [trans #614 #503]: #518
+#630 := (iff #673 #13)
+#649 := -2::Int
+#642 := (+ -2::Int #11)
+#639 := (= #642 0::Int)
+#487 := (iff #639 #13)
+#488 := [rewrite]: #487
+#645 := (iff #673 #639)
+#643 := (= #466 #642)
+#651 := (+ #11 -2::Int)
+#637 := (= #651 #642)
+#638 := [rewrite]: #637
+#640 := (= #466 #651)
+#650 := (= #336 -2::Int)
+#369 := (* -1::Int 2::Int)
+#364 := (= #369 -2::Int)
+#646 := [rewrite]: #364
+#370 := (= #336 #369)
+#367 := (= #679 2::Int)
+#368 := [rewrite]: #367
+#648 := [monotonicity #368]: #370
+#647 := [trans #648 #646]: #650
+#641 := [monotonicity #647]: #640
+#644 := [trans #641 #638]: #643
+#486 := [monotonicity #644]: #645
+#631 := [trans #486 #488]: #630
+#653 := (iff #677 true)
+#671 := (or true false)
+#658 := (iff #671 true)
+#659 := [rewrite]: #658
+#652 := (iff #677 #671)
+#377 := (iff #342 false)
+#383 := (not true)
+#654 := (iff #383 false)
+#655 := [rewrite]: #654
+#384 := (iff #342 #383)
+#381 := (iff #363 true)
+#669 := (iff #363 #671)
+#319 := (iff #360 false)
+#660 := [rewrite]: #319
+#310 := (iff #359 true)
+#311 := [rewrite]: #310
+#672 := [monotonicity #311 #660]: #669
+#382 := [trans #672 #659]: #381
+#277 := [monotonicity #382]: #384
+#378 := [trans #277 #655]: #377
+#668 := (iff #362 true)
+#665 := (not false)
+#667 := (iff #665 true)
+#305 := [rewrite]: #667
+#666 := (iff #362 #665)
+#663 := (iff #361 false)
+#323 := (or false false)
+#326 := (iff #323 false)
+#662 := [rewrite]: #326
+#324 := (iff #361 #323)
+#335 := (iff #349 false)
+#676 := [rewrite]: #335
+#325 := [monotonicity #676 #660]: #324
+#664 := [trans #325 #662]: #663
+#661 := [monotonicity #664]: #666
+#670 := [trans #661 #305]: #668
+#656 := [monotonicity #670 #378]: #652
+#657 := [trans #656 #659]: #653
+#522 := [monotonicity #657 #631 #520]: #514
+#526 := [trans #522 #524]: #525
+#339 := (iff #357 false)
+#675 := [rewrite]: #339
+#620 := [monotonicity #675 #526]: #616
+#598 := [trans #620 #609]: #601
+#674 := (iff #271 false)
+#334 := [rewrite]: #674
+#611 := [monotonicity #334 #598]: #610
+#602 := [trans #611 #608]: #613
+#590 := [monotonicity #602]: #606
+#594 := [trans #590 #593]: #606
+#599 := [quant-inst #8 #10]: #605
+#595 := [mp #599 #594]: #604
+[unit-resolution #595 #49 #698]: false
+2b60566cabaa3881d0df54c1bbba88b2e72ec302 342 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#20 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#18 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#40 := (f4 f5 #18)
+#41 := (f3 #40 #20)
+#709 := (pattern #41)
+#22 := 0::Int
+#99 := -1::Int
+#103 := (* -1::Int #20)
+#100 := (* -1::Int #18)
+#122 := (mod #100 #103)
+#278 := (+ #41 #122)
+#279 := (= #278 0::Int)
+#42 := (mod #18 #20)
+#275 := (* -1::Int #42)
+#276 := (+ #41 #275)
+#277 := (= #276 0::Int)
+#77 := (<= #20 0::Int)
+#169 := (>= #18 0::Int)
+#222 := (or #169 #77)
+#223 := (not #222)
+#73 := (<= #18 0::Int)
+#218 := (or #73 #77)
+#219 := (not #218)
+#226 := (or #219 #223)
+#280 := (if #226 #277 #279)
+#274 := (= #41 0::Int)
+#23 := (= #18 0::Int)
+#281 := (if #23 #274 #280)
+#273 := (= #41 #18)
+#24 := (= #20 0::Int)
+#282 := (if #24 #273 #281)
+#710 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #709) #282)
+#285 := (forall (vars (?v0 Int) (?v1 Int)) #282)
+#713 := (iff #285 #710)
+#711 := (iff #282 #282)
+#712 := [refl]: #711
+#714 := [quant-intro #712]: #713
+#128 := (* -1::Int #122)
+#242 := (if #226 #42 #128)
+#245 := (if #23 0::Int #242)
+#248 := (if #24 #18 #245)
+#251 := (= #41 #248)
+#254 := (forall (vars (?v0 Int) (?v1 Int)) #251)
+#286 := (iff #254 #285)
+#283 := (iff #251 #282)
+#284 := [rewrite]: #283
+#287 := [quant-intro #284]: #286
+#78 := (not #77)
+#172 := (not #169)
+#175 := (and #172 #78)
+#74 := (not #73)
+#81 := (and #74 #78)
+#178 := (or #81 #175)
+#194 := (if #178 #42 #128)
+#197 := (if #23 0::Int #194)
+#200 := (if #24 #18 #197)
+#203 := (= #41 #200)
+#206 := (forall (vars (?v0 Int) (?v1 Int)) #203)
+#255 := (iff #206 #254)
+#252 := (iff #203 #251)
+#249 := (= #200 #248)
+#246 := (= #197 #245)
+#243 := (= #194 #242)
+#227 := (iff #178 #226)
+#224 := (iff #175 #223)
+#225 := [rewrite]: #224
+#220 := (iff #81 #219)
+#221 := [rewrite]: #220
+#228 := [monotonicity #221 #225]: #227
+#244 := [monotonicity #228]: #243
+#247 := [monotonicity #244]: #246
+#250 := [monotonicity #247]: #249
+#253 := [monotonicity #250]: #252
+#256 := [quant-intro #253]: #255
+#168 := (~ #206 #206)
+#213 := (~ #203 #203)
+#167 := [refl]: #213
+#216 := [nnf-pos #167]: #168
+#84 := (<= 0::Int #18)
+#85 := (not #84)
+#93 := (and #85 #78)
+#96 := (or #81 #93)
+#133 := (if #96 #42 #128)
+#136 := (if #23 0::Int #133)
+#139 := (if #24 #18 #136)
+#142 := (= #41 #139)
+#145 := (forall (vars (?v0 Int) (?v1 Int)) #142)
+#207 := (iff #145 #206)
+#204 := (iff #142 #203)
+#201 := (= #139 #200)
+#198 := (= #136 #197)
+#195 := (= #133 #194)
+#179 := (iff #96 #178)
+#176 := (iff #93 #175)
+#173 := (iff #85 #172)
+#170 := (iff #84 #169)
+#171 := [rewrite]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#180 := [monotonicity #177]: #179
+#196 := [monotonicity #180]: #195
+#199 := [monotonicity #196]: #198
+#202 := [monotonicity #199]: #201
+#205 := [monotonicity #202]: #204
+#208 := [quant-intro #205]: #207
+#34 := (- #20)
+#33 := (- #18)
+#43 := (mod #33 #34)
+#44 := (- #43)
+#27 := (< 0::Int #20)
+#29 := (< #18 0::Int)
+#30 := (and #29 #27)
+#26 := (< 0::Int #18)
+#28 := (and #26 #27)
+#31 := (or #28 #30)
+#45 := (if #31 #42 #44)
+#46 := (if #23 0::Int #45)
+#47 := (if #24 #18 #46)
+#48 := (= #41 #47)
+#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
+#146 := (iff #49 #145)
+#143 := (iff #48 #142)
+#140 := (= #47 #139)
+#137 := (= #46 #136)
+#134 := (= #45 #133)
+#131 := (= #44 #128)
+#125 := (- #122)
+#129 := (= #125 #128)
+#130 := [rewrite]: #129
+#126 := (= #44 #125)
+#123 := (= #43 #122)
+#104 := (= #34 #103)
+#105 := [rewrite]: #104
+#101 := (= #33 #100)
+#102 := [rewrite]: #101
+#124 := [monotonicity #102 #105]: #123
+#127 := [monotonicity #124]: #126
+#132 := [trans #127 #130]: #131
+#97 := (iff #31 #96)
+#94 := (iff #30 #93)
+#79 := (iff #27 #78)
+#80 := [rewrite]: #79
+#86 := (iff #29 #85)
+#90 := (iff #85 #85)
+#88 := (iff #84 #84)
+#89 := [rewrite]: #88
+#91 := [monotonicity #89]: #90
+#87 := [rewrite]: #86
+#92 := [trans #87 #91]: #86
+#95 := [monotonicity #92 #80]: #94
+#82 := (iff #28 #81)
+#75 := (iff #26 #74)
+#76 := [rewrite]: #75
+#83 := [monotonicity #76 #80]: #82
+#98 := [monotonicity #83 #95]: #97
+#135 := [monotonicity #98 #132]: #134
+#138 := [monotonicity #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [quant-intro #144]: #146
+#53 := [asserted]: #49
+#148 := [mp #53 #147]: #145
+#209 := [mp #148 #208]: #206
+#217 := [mp~ #209 #216]: #206
+#257 := [mp #217 #256]: #254
+#288 := [mp #257 #287]: #285
+#715 := [mp #288 #714]: #710
+#63 := -2::Int
+#57 := -3::Int
+#8 := 1::Int
+#9 := (f4 f5 1::Int)
+#60 := (f3 #9 -3::Int)
+#66 := (= #60 -2::Int)
+#69 := (not #66)
+#13 := 2::Int
+#14 := (- 2::Int)
+#10 := 3::Int
+#11 := (- 3::Int)
+#12 := (f3 #9 #11)
+#15 := (= #12 #14)
+#16 := (not #15)
+#70 := (iff #16 #69)
+#67 := (iff #15 #66)
+#64 := (= #14 -2::Int)
+#65 := [rewrite]: #64
+#61 := (= #12 #60)
+#58 := (= #11 -3::Int)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#68 := [monotonicity #62 #65]: #67
+#71 := [monotonicity #68]: #70
+#51 := [asserted]: #16
+#72 := [mp #51 #71]: #69
+#626 := (not #710)
+#618 := (or #626 #66)
+#365 := (* -1::Int -3::Int)
+#364 := (* -1::Int 1::Int)
+#697 := (mod #364 #365)
+#698 := (+ #60 #697)
+#699 := (= #698 0::Int)
+#696 := (mod 1::Int -3::Int)
+#353 := (* -1::Int #696)
+#483 := (+ #60 #353)
+#690 := (= #483 0::Int)
+#377 := (<= -3::Int 0::Int)
+#376 := (>= 1::Int 0::Int)
+#380 := (or #376 #377)
+#359 := (not #380)
+#366 := (<= 1::Int 0::Int)
+#378 := (or #366 #377)
+#379 := (not #378)
+#694 := (or #379 #359)
+#700 := (if #694 #690 #699)
+#375 := (= #60 0::Int)
+#374 := (= 1::Int 0::Int)
+#695 := (if #374 #375 #700)
+#373 := (= #60 1::Int)
+#289 := (= -3::Int 0::Int)
+#701 := (if #289 #373 #695)
+#615 := (or #626 #701)
+#627 := (iff #615 #618)
+#629 := (iff #618 #618)
+#625 := [rewrite]: #629
+#637 := (iff #701 #66)
+#536 := (if false #373 #66)
+#635 := (iff #536 #66)
+#520 := [rewrite]: #635
+#636 := (iff #701 #536)
+#542 := (iff #695 #66)
+#538 := (if false #375 #66)
+#540 := (iff #538 #66)
+#541 := [rewrite]: #540
+#531 := (iff #695 #538)
+#535 := (iff #700 #66)
+#631 := (iff #700 #536)
+#486 := (iff #699 #66)
+#485 := (+ 2::Int #60)
+#640 := (= #485 0::Int)
+#526 := (iff #640 #66)
+#527 := [rewrite]: #526
+#643 := (iff #699 #640)
+#641 := (= #698 #485)
+#653 := (+ #60 2::Int)
+#638 := (= #653 #485)
+#639 := [rewrite]: #638
+#482 := (= #698 #653)
+#652 := (= #697 2::Int)
+#649 := (mod -1::Int 3::Int)
+#645 := (= #649 2::Int)
+#651 := [rewrite]: #645
+#650 := (= #697 #649)
+#647 := (= #365 3::Int)
+#648 := [rewrite]: #647
+#665 := (= #364 -1::Int)
+#666 := [rewrite]: #665
+#644 := [monotonicity #666 #648]: #650
+#646 := [trans #644 #651]: #652
+#484 := [monotonicity #646]: #482
+#642 := [trans #484 #639]: #641
+#525 := [monotonicity #642]: #643
+#634 := [trans #525 #527]: #486
+#504 := (iff #690 #373)
+#657 := (+ -1::Int #60)
+#660 := (= #657 0::Int)
+#662 := (iff #660 #373)
+#503 := [rewrite]: #662
+#661 := (iff #690 #660)
+#654 := (= #483 #657)
+#667 := (+ #60 -1::Int)
+#658 := (= #667 #657)
+#659 := [rewrite]: #658
+#664 := (= #483 #667)
+#381 := (= #353 -1::Int)
+#386 := (= #353 #364)
+#384 := (= #696 1::Int)
+#385 := [rewrite]: #384
+#387 := [monotonicity #385]: #386
+#663 := [trans #387 #666]: #381
+#668 := [monotonicity #663]: #664
+#655 := [trans #668 #659]: #654
+#656 := [monotonicity #655]: #661
+#505 := [trans #656 #503]: #504
+#670 := (iff #694 false)
+#672 := (or false false)
+#669 := (iff #672 false)
+#673 := [rewrite]: #669
+#394 := (iff #694 #672)
+#295 := (iff #359 false)
+#1 := true
+#682 := (not true)
+#684 := (iff #682 false)
+#322 := [rewrite]: #684
+#400 := (iff #359 #682)
+#398 := (iff #380 true)
+#688 := (or true true)
+#675 := (iff #688 true)
+#676 := [rewrite]: #675
+#686 := (iff #380 #688)
+#336 := (iff #377 true)
+#677 := [rewrite]: #336
+#327 := (iff #376 true)
+#328 := [rewrite]: #327
+#689 := [monotonicity #328 #677]: #686
+#399 := [trans #689 #676]: #398
+#401 := [monotonicity #399]: #400
+#671 := [trans #401 #322]: #295
+#685 := (iff #379 false)
+#683 := (iff #379 #682)
+#680 := (iff #378 true)
+#340 := (or false true)
+#343 := (iff #340 true)
+#679 := [rewrite]: #343
+#341 := (iff #378 #340)
+#352 := (iff #366 false)
+#693 := [rewrite]: #352
+#342 := [monotonicity #693 #677]: #341
+#681 := [trans #342 #679]: #680
+#678 := [monotonicity #681]: #683
+#687 := [trans #678 #322]: #685
+#395 := [monotonicity #687 #671]: #394
+#674 := [trans #395 #673]: #670
+#632 := [monotonicity #674 #505 #634]: #631
+#537 := [trans #632 #520]: #535
+#356 := (iff #374 false)
+#692 := [rewrite]: #356
+#539 := [monotonicity #692 #537]: #531
+#543 := [trans #539 #541]: #542
+#691 := (iff #289 false)
+#351 := [rewrite]: #691
+#633 := [monotonicity #351 #543]: #636
+#624 := [trans #633 #520]: #637
+#628 := [monotonicity #624]: #627
+#630 := [trans #628 #625]: #627
+#617 := [quant-inst #8 #57]: #615
+#619 := [mp #617 #630]: #618
+[unit-resolution #619 #72 #715]: false
+30bd922ca9cd199af046cdc457f97af241893e95 323 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #18 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #16 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #37 := (f4 f5 #16)
 #38 := (f3 #37 #18)
-#752 := (pattern #38)
+#704 := (pattern #38)
 #12 := 0::Int
-#83 := -1::Int
-#87 := (* -1::Int #18)
-#84 := (* -1::Int #16)
-#148 := (mod #84 #87)
-#263 := (+ #38 #148)
-#264 := (= #263 0::Int)
+#93 := -1::Int
+#97 := (* -1::Int #18)
+#94 := (* -1::Int #16)
+#116 := (mod #94 #97)
+#272 := (+ #38 #116)
+#273 := (= #272 0::Int)
 #39 := (mod #16 #18)
-#260 := (* -1::Int #39)
-#261 := (+ #38 #260)
-#262 := (= #261 0::Int)
-#122 := (>= #16 0::Int)
-#115 := (<= #18 0::Int)
-#207 := (or #115 #122)
-#208 := (not #207)
-#111 := (<= #16 0::Int)
-#205 := (or #111 #115)
-#206 := (not #205)
-#211 := (or #206 #208)
-#265 := (ite #211 #262 #264)
-#259 := (= #38 0::Int)
+#269 := (* -1::Int #39)
+#270 := (+ #38 #269)
+#271 := (= #270 0::Int)
+#71 := (<= #18 0::Int)
+#163 := (>= #16 0::Int)
+#216 := (or #163 #71)
+#217 := (not #216)
+#67 := (<= #16 0::Int)
+#212 := (or #67 #71)
+#213 := (not #212)
+#220 := (or #213 #217)
+#274 := (if #220 #271 #273)
+#268 := (= #38 0::Int)
 #20 := (= #16 0::Int)
-#266 := (ite #20 #259 #265)
-#258 := (= #16 #38)
+#275 := (if #20 #268 #274)
+#267 := (= #38 #16)
 #21 := (= #18 0::Int)
-#267 := (ite #21 #258 #266)
-#753 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #752) #267)
-#270 := (forall (vars (?v0 Int) (?v1 Int)) #267)
-#756 := (iff #270 #753)
-#754 := (iff #267 #267)
-#755 := [refl]: #754
-#757 := [quant-intro #755]: #756
-#154 := (* -1::Int #148)
-#227 := (ite #211 #39 #154)
-#230 := (ite #20 0::Int #227)
-#233 := (ite #21 #16 #230)
-#236 := (= #38 #233)
-#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
-#271 := (iff #239 #270)
-#268 := (iff #236 #267)
-#269 := [rewrite]: #268
-#272 := [quant-intro #269]: #271
-#123 := (not #122)
-#116 := (not #115)
-#126 := (and #116 #123)
-#112 := (not #111)
-#119 := (and #112 #116)
-#129 := (or #119 #126)
-#174 := (ite #129 #39 #154)
-#177 := (ite #20 0::Int #174)
-#180 := (ite #21 #16 #177)
-#183 := (= #38 #180)
-#186 := (forall (vars (?v0 Int) (?v1 Int)) #183)
-#240 := (iff #186 #239)
-#237 := (iff #183 #236)
-#234 := (= #180 #233)
-#231 := (= #177 #230)
-#228 := (= #174 #227)
-#212 := (iff #129 #211)
-#209 := (iff #126 #208)
-#210 := [rewrite]: #209
-#199 := (iff #119 #206)
-#200 := [rewrite]: #199
-#213 := [monotonicity #200 #210]: #212
-#229 := [monotonicity #213]: #228
-#232 := [monotonicity #229]: #231
-#235 := [monotonicity #232]: #234
-#238 := [monotonicity #235]: #237
-#241 := [quant-intro #238]: #240
-#197 := (~ #186 #186)
-#196 := (~ #183 #183)
-#193 := [refl]: #196
-#198 := [nnf-pos #193]: #197
+#276 := (if #21 #267 #275)
+#705 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #704) #276)
+#279 := (forall (vars (?v0 Int) (?v1 Int)) #276)
+#708 := (iff #279 #705)
+#706 := (iff #276 #276)
+#707 := [refl]: #706
+#709 := [quant-intro #707]: #708
+#122 := (* -1::Int #116)
+#236 := (if #220 #39 #122)
+#239 := (if #20 0::Int #236)
+#242 := (if #21 #16 #239)
+#245 := (= #38 #242)
+#248 := (forall (vars (?v0 Int) (?v1 Int)) #245)
+#280 := (iff #248 #279)
+#277 := (iff #245 #276)
+#278 := [rewrite]: #277
+#281 := [quant-intro #278]: #280
+#72 := (not #71)
+#166 := (not #163)
+#169 := (and #166 #72)
+#68 := (not #67)
+#75 := (and #68 #72)
+#172 := (or #75 #169)
+#188 := (if #172 #39 #122)
+#191 := (if #20 0::Int #188)
+#194 := (if #21 #16 #191)
+#197 := (= #38 #194)
+#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
+#249 := (iff #200 #248)
+#246 := (iff #197 #245)
+#243 := (= #194 #242)
+#240 := (= #191 #239)
+#237 := (= #188 #236)
+#221 := (iff #172 #220)
+#218 := (iff #169 #217)
+#219 := [rewrite]: #218
+#214 := (iff #75 #213)
+#215 := [rewrite]: #214
+#222 := [monotonicity #215 #219]: #221
+#238 := [monotonicity #222]: #237
+#241 := [monotonicity #238]: #240
+#244 := [monotonicity #241]: #243
+#247 := [monotonicity #244]: #246
+#250 := [quant-intro #247]: #249
+#162 := (~ #200 #200)
+#207 := (~ #197 #197)
+#161 := [refl]: #207
+#210 := [nnf-pos #161]: #162
+#78 := (<= 0::Int #16)
+#79 := (not #78)
+#87 := (and #79 #72)
+#90 := (or #75 #87)
+#127 := (if #90 #39 #122)
+#130 := (if #20 0::Int #127)
+#133 := (if #21 #16 #130)
+#136 := (= #38 #133)
+#139 := (forall (vars (?v0 Int) (?v1 Int)) #136)
+#201 := (iff #139 #200)
+#198 := (iff #136 #197)
+#195 := (= #133 #194)
+#192 := (= #130 #191)
+#189 := (= #127 #188)
+#173 := (iff #90 #172)
+#170 := (iff #87 #169)
+#167 := (iff #79 #166)
+#164 := (iff #78 #163)
+#165 := [rewrite]: #164
+#168 := [monotonicity #165]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #171]: #173
+#190 := [monotonicity #174]: #189
+#193 := [monotonicity #190]: #192
+#196 := [monotonicity #193]: #195
+#199 := [monotonicity #196]: #198
+#202 := [quant-intro #199]: #201
 #31 := (- #18)
 #30 := (- #16)
 #40 := (mod #30 #31)
@@ -38877,307 +38626,672 @@
 #23 := (< 0::Int #16)
 #25 := (and #23 #24)
 #28 := (or #25 #27)
-#42 := (ite #28 #39 #41)
-#43 := (ite #20 0::Int #42)
-#44 := (ite #21 #16 #43)
+#42 := (if #28 #39 #41)
+#43 := (if #20 0::Int #42)
+#44 := (if #21 #16 #43)
 #45 := (= #38 #44)
 #46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
-#189 := (iff #46 #186)
-#77 := (and #24 #26)
-#80 := (or #25 #77)
-#159 := (ite #80 #39 #154)
-#68 := (= 0::Int #16)
-#162 := (ite #68 0::Int #159)
-#71 := (= 0::Int #18)
-#165 := (ite #71 #16 #162)
-#168 := (= #38 #165)
-#171 := (forall (vars (?v0 Int) (?v1 Int)) #168)
-#187 := (iff #171 #186)
-#184 := (iff #168 #183)
-#181 := (= #165 #180)
-#178 := (= #162 #177)
-#175 := (= #159 #174)
-#130 := (iff #80 #129)
-#127 := (iff #77 #126)
-#124 := (iff #26 #123)
-#125 := [rewrite]: #124
-#117 := (iff #24 #116)
-#118 := [rewrite]: #117
-#128 := [monotonicity #118 #125]: #127
-#120 := (iff #25 #119)
-#113 := (iff #23 #112)
-#114 := [rewrite]: #113
-#121 := [monotonicity #114 #118]: #120
-#131 := [monotonicity #121 #128]: #130
-#176 := [monotonicity #131]: #175
-#105 := (iff #68 #20)
-#106 := [rewrite]: #105
-#179 := [monotonicity #106 #176]: #178
-#107 := (iff #71 #21)
-#108 := [rewrite]: #107
-#182 := [monotonicity #108 #179]: #181
-#185 := [monotonicity #182]: #184
-#188 := [quant-intro #185]: #187
-#172 := (iff #46 #171)
-#169 := (iff #45 #168)
-#166 := (= #44 #165)
-#163 := (= #43 #162)
-#160 := (= #42 #159)
-#157 := (= #41 #154)
-#151 := (- #148)
-#155 := (= #151 #154)
-#156 := [rewrite]: #155
-#152 := (= #41 #151)
-#149 := (= #40 #148)
-#88 := (= #31 #87)
-#89 := [rewrite]: #88
-#85 := (= #30 #84)
-#86 := [rewrite]: #85
-#150 := [monotonicity #86 #89]: #149
-#153 := [monotonicity #150]: #152
-#158 := [trans #153 #156]: #157
-#81 := (iff #28 #80)
-#78 := (iff #27 #77)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#161 := [monotonicity #82 #158]: #160
-#69 := (iff #20 #68)
+#140 := (iff #46 #139)
+#137 := (iff #45 #136)
+#134 := (= #44 #133)
+#131 := (= #43 #130)
+#128 := (= #42 #127)
+#125 := (= #41 #122)
+#119 := (- #116)
+#123 := (= #119 #122)
+#124 := [rewrite]: #123
+#120 := (= #41 #119)
+#117 := (= #40 #116)
+#98 := (= #31 #97)
+#99 := [rewrite]: #98
+#95 := (= #30 #94)
+#96 := [rewrite]: #95
+#118 := [monotonicity #96 #99]: #117
+#121 := [monotonicity #118]: #120
+#126 := [trans #121 #124]: #125
+#91 := (iff #28 #90)
+#88 := (iff #27 #87)
+#73 := (iff #24 #72)
+#74 := [rewrite]: #73
+#80 := (iff #26 #79)
+#84 := (iff #79 #79)
+#82 := (iff #78 #78)
+#83 := [rewrite]: #82
+#85 := [monotonicity #83]: #84
+#81 := [rewrite]: #80
+#86 := [trans #81 #85]: #80
+#89 := [monotonicity #86 #74]: #88
+#76 := (iff #25 #75)
+#69 := (iff #23 #68)
 #70 := [rewrite]: #69
-#164 := [monotonicity #70 #161]: #163
-#72 := (iff #21 #71)
-#73 := [rewrite]: #72
-#167 := [monotonicity #73 #164]: #166
-#170 := [monotonicity #167]: #169
-#173 := [quant-intro #170]: #172
-#190 := [trans #173 #188]: #189
-#147 := [asserted]: #46
-#191 := [mp #147 #190]: #186
-#194 := [mp~ #191 #198]: #186
-#242 := [mp #194 #241]: #239
-#273 := [mp #242 #272]: #270
-#758 := [mp #273 #757]: #753
-#9 := 3::Int
-#10 := (f4 f5 3::Int)
-#11 := (f3 #10 3::Int)
+#77 := [monotonicity #70 #74]: #76
+#92 := [monotonicity #77 #89]: #91
+#129 := [monotonicity #92 #126]: #128
+#132 := [monotonicity #129]: #131
+#135 := [monotonicity #132]: #134
+#138 := [monotonicity #135]: #137
+#141 := [quant-intro #138]: #140
+#50 := [asserted]: #46
+#142 := [mp #50 #141]: #139
+#203 := [mp #142 #202]: #200
+#211 := [mp~ #203 #210]: #200
+#251 := [mp #211 #250]: #248
+#282 := [mp #251 #281]: #279
+#710 := [mp #282 #709]: #705
+#54 := -3::Int
+#8 := 3::Int
+#9 := (f4 f5 3::Int)
+#57 := (f3 #9 -3::Int)
+#60 := (= #57 0::Int)
+#63 := (not #60)
+#10 := (- 3::Int)
+#11 := (f3 #9 #10)
 #13 := (= #11 0::Int)
 #14 := (not #13)
-#66 := [asserted]: #14
-#578 := (not #753)
-#580 := (or #578 #13)
-#331 := (* -1::Int 3::Int)
-#416 := (mod #331 #331)
-#417 := (+ #11 #416)
-#418 := (= #417 0::Int)
-#409 := (mod 3::Int 3::Int)
-#420 := (* -1::Int #409)
-#421 := (+ #11 #420)
-#349 := (= #421 0::Int)
-#422 := (>= 3::Int 0::Int)
-#419 := (<= 3::Int 0::Int)
-#423 := (or #419 #422)
-#402 := (not #423)
-#737 := (or #419 #419)
-#739 := (not #737)
-#396 := (or #739 #402)
-#526 := (ite #396 #349 #418)
-#733 := (= 3::Int 0::Int)
-#407 := (ite #733 #13 #526)
-#408 := (= 3::Int #11)
-#740 := (ite #733 #408 #407)
-#581 := (or #578 #740)
-#582 := (iff #581 #580)
-#584 := (iff #580 #580)
-#585 := [rewrite]: #584
-#678 := (iff #740 #13)
-#738 := (= #11 3::Int)
-#529 := (ite false #738 #13)
-#674 := (iff #529 #13)
+#64 := (iff #14 #63)
+#61 := (iff #13 #60)
+#58 := (= #11 #57)
+#55 := (= #10 -3::Int)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#62 := [monotonicity #59]: #61
+#65 := [monotonicity #62]: #64
+#48 := [asserted]: #14
+#66 := [mp #48 #65]: #63
+#530 := (not #705)
+#532 := (or #530 #60)
+#359 := (* -1::Int -3::Int)
+#685 := (* -1::Int 3::Int)
+#360 := (mod #685 #359)
+#692 := (+ #57 #360)
+#693 := (= #692 0::Int)
+#689 := (mod 3::Int -3::Int)
+#691 := (* -1::Int #689)
+#348 := (+ #57 #691)
+#478 := (= #348 0::Int)
+#361 := (<= -3::Int 0::Int)
+#374 := (>= 3::Int 0::Int)
+#371 := (or #374 #361)
+#375 := (not #371)
+#370 := (<= 3::Int 0::Int)
+#372 := (or #370 #361)
+#373 := (not #372)
+#354 := (or #373 #375)
+#694 := (if #354 #478 #693)
+#369 := (= 3::Int 0::Int)
+#695 := (if #369 #60 #694)
+#368 := (= #57 3::Int)
+#283 := (= -3::Int 0::Int)
+#690 := (if #283 #368 #695)
+#533 := (or #530 #690)
+#534 := (iff #533 #532)
+#536 := (iff #532 #532)
+#537 := [rewrite]: #536
+#630 := (iff #690 #60)
+#481 := (if false #368 #60)
+#626 := (iff #481 #60)
+#627 := [rewrite]: #626
+#629 := (iff #690 #481)
+#521 := (iff #695 #60)
+#479 := (if false #60 #60)
+#634 := (iff #479 #60)
+#636 := [rewrite]: #634
+#638 := (iff #695 #479)
+#637 := (iff #694 #60)
+#480 := (iff #694 #479)
+#648 := (iff #693 #60)
+#647 := (= #692 #57)
+#662 := (+ #57 0::Int)
+#652 := (= #662 #57)
+#653 := [rewrite]: #652
+#640 := (= #692 #662)
+#645 := (= #360 0::Int)
+#499 := (mod -3::Int 3::Int)
+#643 := (= #499 0::Int)
+#644 := [rewrite]: #643
+#500 := (= #360 #499)
+#657 := (= #359 3::Int)
+#498 := [rewrite]: #657
+#656 := (= #685 -3::Int)
+#651 := [rewrite]: #656
+#642 := [monotonicity #651 #498]: #500
+#639 := [trans #642 #644]: #645
+#646 := [monotonicity #639]: #640
+#641 := [trans #646 #653]: #647
+#477 := [monotonicity #641]: #648
+#650 := (iff #478 #60)
+#654 := (= #348 #57)
+#659 := (= #348 #662)
+#376 := (= #691 0::Int)
+#380 := (* -1::Int 0::Int)
+#660 := (= #380 0::Int)
+#661 := [rewrite]: #660
+#381 := (= #691 #380)
+#669 := (= #689 0::Int)
+#379 := [rewrite]: #669
+#382 := [monotonicity #379]: #381
+#658 := [trans #382 #661]: #376
+#663 := [monotonicity #658]: #659
+#649 := [trans #663 #653]: #654
+#655 := [monotonicity #649]: #650
+#668 := (iff #354 false)
+#666 := (or false false)
+#390 := (iff #666 false)
+#664 := [rewrite]: #390
+#667 := (iff #354 #666)
+#396 := (iff #375 false)
+#1 := true
+#676 := (not true)
+#673 := (iff #676 false)
+#679 := [rewrite]: #673
+#394 := (iff #375 #676)
+#671 := (iff #371 true)
+#323 := (or true true)
+#684 := (iff #323 true)
+#670 := [rewrite]: #684
+#683 := (iff #371 #323)
+#688 := (iff #361 true)
+#331 := [rewrite]: #688
+#682 := (iff #374 true)
+#322 := [rewrite]: #682
+#681 := [monotonicity #322 #331]: #683
+#393 := [trans #681 #670]: #671
+#395 := [monotonicity #393]: #394
+#289 := [trans #395 #679]: #396
+#317 := (iff #373 false)
+#677 := (iff #373 #676)
+#674 := (iff #372 true)
+#672 := (or false true)
+#337 := (iff #672 true)
+#338 := [rewrite]: #337
+#335 := (iff #372 #672)
+#687 := (iff #370 false)
+#347 := [rewrite]: #687
+#336 := [monotonicity #347 #331]: #335
+#675 := [trans #336 #338]: #674
+#678 := [monotonicity #675]: #677
+#680 := [trans #678 #679]: #317
+#389 := [monotonicity #680 #289]: #667
+#665 := [trans #389 #664]: #668
+#633 := [monotonicity #665 #655 #477]: #480
+#635 := [trans #633 #636]: #637
+#346 := (iff #369 false)
+#351 := [rewrite]: #346
+#520 := [monotonicity #351 #635]: #638
+#522 := [trans #520 #636]: #521
+#696 := (iff #283 false)
+#686 := [rewrite]: #696
+#531 := [monotonicity #686 #522]: #629
+#515 := [trans #531 #627]: #630
+#535 := [monotonicity #515]: #534
+#538 := [trans #535 #537]: #534
+#526 := [quant-inst #8 #54]: #533
+#631 := [mp #526 #538]: #532
+[unit-resolution #631 #66 #710]: false
+6eef1290fd4184aa5ca07b83a07cebe5b5459f61 351 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#20 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#18 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#40 := (f4 f5 #18)
+#41 := (f3 #40 #20)
+#708 := (pattern #41)
+#22 := 0::Int
+#63 := -1::Int
+#102 := (* -1::Int #20)
+#99 := (* -1::Int #18)
+#121 := (mod #99 #102)
+#277 := (+ #41 #121)
+#278 := (= #277 0::Int)
+#42 := (mod #18 #20)
+#274 := (* -1::Int #42)
+#275 := (+ #41 #274)
+#276 := (= #275 0::Int)
+#77 := (<= #20 0::Int)
+#168 := (>= #18 0::Int)
+#221 := (or #168 #77)
+#222 := (not #221)
+#73 := (<= #18 0::Int)
+#217 := (or #73 #77)
+#218 := (not #217)
+#225 := (or #218 #222)
+#279 := (if #225 #276 #278)
+#273 := (= #41 0::Int)
+#23 := (= #18 0::Int)
+#280 := (if #23 #273 #279)
+#272 := (= #41 #18)
+#24 := (= #20 0::Int)
+#281 := (if #24 #272 #280)
+#709 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #708) #281)
+#284 := (forall (vars (?v0 Int) (?v1 Int)) #281)
+#712 := (iff #284 #709)
+#710 := (iff #281 #281)
+#711 := [refl]: #710
+#713 := [quant-intro #711]: #712
+#127 := (* -1::Int #121)
+#241 := (if #225 #42 #127)
+#244 := (if #23 0::Int #241)
+#247 := (if #24 #18 #244)
+#250 := (= #41 #247)
+#253 := (forall (vars (?v0 Int) (?v1 Int)) #250)
+#285 := (iff #253 #284)
+#282 := (iff #250 #281)
+#283 := [rewrite]: #282
+#286 := [quant-intro #283]: #285
+#78 := (not #77)
+#171 := (not #168)
+#174 := (and #171 #78)
+#74 := (not #73)
+#81 := (and #74 #78)
+#177 := (or #81 #174)
+#193 := (if #177 #42 #127)
+#196 := (if #23 0::Int #193)
+#199 := (if #24 #18 #196)
+#202 := (= #41 #199)
+#205 := (forall (vars (?v0 Int) (?v1 Int)) #202)
+#254 := (iff #205 #253)
+#251 := (iff #202 #250)
+#248 := (= #199 #247)
+#245 := (= #196 #244)
+#242 := (= #193 #241)
+#226 := (iff #177 #225)
+#223 := (iff #174 #222)
+#224 := [rewrite]: #223
+#219 := (iff #81 #218)
+#220 := [rewrite]: #219
+#227 := [monotonicity #220 #224]: #226
+#243 := [monotonicity #227]: #242
+#246 := [monotonicity #243]: #245
+#249 := [monotonicity #246]: #248
+#252 := [monotonicity #249]: #251
+#255 := [quant-intro #252]: #254
+#167 := (~ #205 #205)
+#212 := (~ #202 #202)
+#166 := [refl]: #212
+#215 := [nnf-pos #166]: #167
+#84 := (<= 0::Int #18)
+#85 := (not #84)
+#93 := (and #85 #78)
+#96 := (or #81 #93)
+#132 := (if #96 #42 #127)
+#135 := (if #23 0::Int #132)
+#138 := (if #24 #18 #135)
+#141 := (= #41 #138)
+#144 := (forall (vars (?v0 Int) (?v1 Int)) #141)
+#206 := (iff #144 #205)
+#203 := (iff #141 #202)
+#200 := (= #138 #199)
+#197 := (= #135 #196)
+#194 := (= #132 #193)
+#178 := (iff #96 #177)
+#175 := (iff #93 #174)
+#172 := (iff #85 #171)
+#169 := (iff #84 #168)
+#170 := [rewrite]: #169
+#173 := [monotonicity #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [monotonicity #176]: #178
+#195 := [monotonicity #179]: #194
+#198 := [monotonicity #195]: #197
+#201 := [monotonicity #198]: #200
+#204 := [monotonicity #201]: #203
+#207 := [quant-intro #204]: #206
+#34 := (- #20)
+#33 := (- #18)
+#43 := (mod #33 #34)
+#44 := (- #43)
+#27 := (< 0::Int #20)
+#29 := (< #18 0::Int)
+#30 := (and #29 #27)
+#26 := (< 0::Int #18)
+#28 := (and #26 #27)
+#31 := (or #28 #30)
+#45 := (if #31 #42 #44)
+#46 := (if #23 0::Int #45)
+#47 := (if #24 #18 #46)
+#48 := (= #41 #47)
+#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
+#145 := (iff #49 #144)
+#142 := (iff #48 #141)
+#139 := (= #47 #138)
+#136 := (= #46 #135)
+#133 := (= #45 #132)
+#130 := (= #44 #127)
+#124 := (- #121)
+#128 := (= #124 #127)
+#129 := [rewrite]: #128
+#125 := (= #44 #124)
+#122 := (= #43 #121)
+#103 := (= #34 #102)
+#104 := [rewrite]: #103
+#100 := (= #33 #99)
+#101 := [rewrite]: #100
+#123 := [monotonicity #101 #104]: #122
+#126 := [monotonicity #123]: #125
+#131 := [trans #126 #129]: #130
+#97 := (iff #31 #96)
+#94 := (iff #30 #93)
+#79 := (iff #27 #78)
+#80 := [rewrite]: #79
+#86 := (iff #29 #85)
+#90 := (iff #85 #85)
+#88 := (iff #84 #84)
+#89 := [rewrite]: #88
+#91 := [monotonicity #89]: #90
+#87 := [rewrite]: #86
+#92 := [trans #87 #91]: #86
+#95 := [monotonicity #92 #80]: #94
+#82 := (iff #28 #81)
+#75 := (iff #26 #74)
+#76 := [rewrite]: #75
+#83 := [monotonicity #76 #80]: #82
+#98 := [monotonicity #83 #95]: #97
+#134 := [monotonicity #98 #131]: #133
+#137 := [monotonicity #134]: #136
+#140 := [monotonicity #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [quant-intro #143]: #145
+#53 := [asserted]: #49
+#147 := [mp #53 #146]: #144
+#208 := [mp #147 #207]: #205
+#216 := [mp~ #208 #215]: #205
+#256 := [mp #216 #255]: #253
+#287 := [mp #256 #286]: #284
+#714 := [mp #287 #713]: #709
+#57 := -3::Int
+#8 := 5::Int
+#9 := (f4 f5 5::Int)
+#60 := (f3 #9 -3::Int)
+#66 := (= #60 -1::Int)
+#69 := (not #66)
+#13 := 1::Int
+#14 := (- 1::Int)
+#10 := 3::Int
+#11 := (- 3::Int)
+#12 := (f3 #9 #11)
+#15 := (= #12 #14)
+#16 := (not #15)
+#70 := (iff #16 #69)
+#67 := (iff #15 #66)
+#64 := (= #14 -1::Int)
+#65 := [rewrite]: #64
+#61 := (= #12 #60)
+#58 := (= #11 -3::Int)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#68 := [monotonicity #62 #65]: #67
+#71 := [monotonicity #68]: #70
+#51 := [asserted]: #16
+#72 := [mp #51 #71]: #69
+#619 := (not #709)
+#620 := (or #619 #66)
+#364 := (* -1::Int -3::Int)
+#363 := (* -1::Int 5::Int)
+#696 := (mod #363 #364)
+#697 := (+ #60 #696)
+#698 := (= #697 0::Int)
+#695 := (mod 5::Int -3::Int)
+#352 := (* -1::Int #695)
+#482 := (+ #60 #352)
+#689 := (= #482 0::Int)
+#376 := (<= -3::Int 0::Int)
+#375 := (>= 5::Int 0::Int)
+#379 := (or #375 #376)
+#358 := (not #379)
+#365 := (<= 5::Int 0::Int)
+#377 := (or #365 #376)
+#378 := (not #377)
+#693 := (or #378 #358)
+#699 := (if #693 #689 #698)
+#374 := (= #60 0::Int)
+#373 := (= 5::Int 0::Int)
+#694 := (if #373 #374 #699)
+#372 := (= #60 5::Int)
+#288 := (= -3::Int 0::Int)
+#700 := (if #288 #372 #694)
+#621 := (or #619 #700)
+#622 := (iff #621 #620)
+#607 := (iff #620 #620)
+#609 := [rewrite]: #607
+#629 := (iff #700 #66)
+#616 := (if false #372 #66)
+#628 := (iff #616 #66)
+#624 := [rewrite]: #628
+#626 := (iff #700 #616)
+#617 := (iff #694 #66)
+#635 := (if false #374 #66)
+#623 := (iff #635 #66)
+#625 := [rewrite]: #623
+#632 := (iff #694 #635)
+#541 := (iff #699 #66)
+#383 := 2::Int
+#504 := (= #60 2::Int)
+#537 := (if false #504 #66)
+#539 := (iff #537 #66)
+#540 := [rewrite]: #539
+#530 := (iff #699 #537)
+#534 := (iff #698 #66)
+#524 := (+ 1::Int #60)
+#535 := (= #524 0::Int)
+#634 := (iff #535 #66)
+#519 := [rewrite]: #634
+#630 := (iff #698 #535)
+#485 := (= #697 #524)
+#641 := (+ #60 1::Int)
+#525 := (= #641 #524)
+#526 := [rewrite]: #525
+#639 := (= #697 #641)
+#638 := (= #696 1::Int)
+#643 := -5::Int
+#652 := (mod -5::Int 3::Int)
+#484 := (= #652 1::Int)
+#637 := [rewrite]: #484
+#481 := (= #696 #652)
+#651 := (= #364 3::Int)
+#645 := [rewrite]: #651
+#644 := (= #363 -5::Int)
+#650 := [rewrite]: #644
+#483 := [monotonicity #650 #645]: #481
+#640 := [trans #483 #637]: #638
+#642 := [monotonicity #640]: #639
+#633 := [trans #642 #526]: #485
+#631 := [monotonicity #633]: #630
+#536 := [trans #631 #519]: #534
+#648 := (iff #689 #504)
+#380 := -2::Int
+#653 := (+ -2::Int #60)
+#661 := (= #653 0::Int)
+#646 := (iff #661 #504)
+#647 := [rewrite]: #646
+#502 := (iff #689 #661)
+#660 := (= #482 #653)
+#656 := (+ #60 -2::Int)
+#654 := (= #656 #653)
+#659 := [rewrite]: #654
+#657 := (= #482 #656)
+#663 := (= #352 -2::Int)
+#386 := (* -1::Int 2::Int)
+#662 := (= #386 -2::Int)
+#666 := [rewrite]: #662
+#664 := (= #352 #386)
+#384 := (= #695 2::Int)
+#385 := [rewrite]: #384
+#665 := [monotonicity #385]: #664
+#667 := [trans #665 #666]: #663
+#658 := [monotonicity #667]: #657
+#655 := [trans #658 #659]: #660
+#503 := [monotonicity #655]: #502
+#649 := [trans #503 #647]: #648
+#669 := (iff #693 false)
+#671 := (or false false)
+#668 := (iff #671 false)
+#672 := [rewrite]: #668
+#393 := (iff #693 #671)
+#294 := (iff #358 false)
+#1 := true
+#681 := (not true)
+#683 := (iff #681 false)
+#321 := [rewrite]: #683
+#399 := (iff #358 #681)
+#397 := (iff #379 true)
+#687 := (or true true)
+#674 := (iff #687 true)
 #675 := [rewrite]: #674
-#677 := (iff #740 #529)
-#569 := (iff #407 #13)
-#684 := (ite false #13 #13)
-#686 := (iff #684 #13)
-#568 := [rewrite]: #686
-#685 := (iff #407 #684)
-#681 := (iff #526 #13)
-#1 := true
-#689 := (ite true #13 #13)
-#527 := (iff #689 #13)
-#528 := [rewrite]: #527
-#696 := (iff #526 #689)
-#694 := (iff #418 #13)
-#687 := (= #417 #11)
-#424 := (+ #11 0::Int)
-#707 := (= #424 #11)
-#711 := [rewrite]: #707
-#692 := (= #417 #424)
-#690 := (= #416 0::Int)
-#698 := -3::Int
-#699 := (mod -3::Int -3::Int)
-#547 := (= #699 0::Int)
-#548 := [rewrite]: #547
-#705 := (= #416 #699)
-#703 := (= #331 -3::Int)
-#704 := [rewrite]: #703
-#546 := [monotonicity #704 #704]: #705
-#691 := [trans #546 #548]: #690
-#693 := [monotonicity #691]: #692
-#688 := [trans #693 #711]: #687
-#695 := [monotonicity #688]: #694
-#702 := (iff #349 #13)
-#700 := (= #421 #11)
-#706 := (= #421 #424)
-#708 := (= #420 0::Int)
-#717 := (* -1::Int 0::Int)
-#429 := (= #717 0::Int)
-#430 := [rewrite]: #429
-#427 := (= #420 #717)
-#716 := (= #409 0::Int)
-#713 := [rewrite]: #716
-#428 := [monotonicity #713]: #427
-#709 := [trans #428 #430]: #708
-#710 := [monotonicity #709]: #706
-#701 := [trans #710 #711]: #700
-#697 := [monotonicity #701]: #702
-#438 := (iff #396 true)
-#444 := (or true false)
-#715 := (iff #444 true)
-#437 := [rewrite]: #715
-#337 := (iff #396 #444)
-#442 := (iff #402 false)
-#729 := (not true)
-#719 := (iff #729 false)
-#441 := [rewrite]: #719
-#732 := (iff #402 #729)
-#371 := (iff #423 true)
-#727 := (or false true)
-#730 := (iff #727 true)
-#370 := [rewrite]: #730
-#365 := (iff #423 #727)
-#726 := (iff #422 true)
-#721 := [rewrite]: #726
-#734 := (iff #419 false)
-#394 := [rewrite]: #734
-#728 := [monotonicity #394 #721]: #365
-#731 := [trans #728 #370]: #371
-#718 := [monotonicity #731]: #732
-#443 := [trans #718 #441]: #442
-#724 := (iff #739 true)
-#384 := (not false)
-#722 := (iff #384 true)
-#723 := [rewrite]: #722
-#385 := (iff #739 #384)
-#720 := (iff #737 false)
-#399 := (or false false)
-#736 := (iff #399 false)
-#379 := [rewrite]: #736
-#735 := (iff #737 #399)
-#395 := [monotonicity #394 #394]: #735
-#383 := [trans #395 #379]: #720
-#386 := [monotonicity #383]: #385
-#725 := [trans #386 #723]: #724
-#714 := [monotonicity #725 #443]: #337
-#712 := [trans #714 #437]: #438
-#525 := [monotonicity #712 #697 #695]: #696
-#682 := [trans #525 #528]: #681
-#741 := (iff #733 false)
-#742 := [rewrite]: #741
-#683 := [monotonicity #742 #682]: #685
-#570 := [trans #683 #568]: #569
-#743 := (iff #408 #738)
-#744 := [rewrite]: #743
-#579 := [monotonicity #742 #744 #570]: #677
-#563 := [trans #579 #675]: #678
-#583 := [monotonicity #563]: #582
-#586 := [trans #583 #585]: #582
-#574 := [quant-inst #9 #9]: #581
-#679 := [mp #574 #586]: #580
-[unit-resolution #679 #66 #758]: false
-unsat
-152b4464bef887bf549316fec07a40602d181255 331 0
+#685 := (iff #379 #687)
+#335 := (iff #376 true)
+#676 := [rewrite]: #335
+#326 := (iff #375 true)
+#327 := [rewrite]: #326
+#688 := [monotonicity #327 #676]: #685
+#398 := [trans #688 #675]: #397
+#400 := [monotonicity #398]: #399
+#670 := [trans #400 #321]: #294
+#684 := (iff #378 false)
+#682 := (iff #378 #681)
+#679 := (iff #377 true)
+#339 := (or false true)
+#342 := (iff #339 true)
+#678 := [rewrite]: #342
+#340 := (iff #377 #339)
+#351 := (iff #365 false)
+#692 := [rewrite]: #351
+#341 := [monotonicity #692 #676]: #340
+#680 := [trans #341 #678]: #679
+#677 := [monotonicity #680]: #682
+#686 := [trans #677 #321]: #684
+#394 := [monotonicity #686 #670]: #393
+#673 := [trans #394 #672]: #669
+#538 := [monotonicity #673 #649 #536]: #530
+#542 := [trans #538 #540]: #541
+#355 := (iff #373 false)
+#691 := [rewrite]: #355
+#636 := [monotonicity #691 #542]: #632
+#614 := [trans #636 #625]: #617
+#690 := (iff #288 false)
+#350 := [rewrite]: #690
+#627 := [monotonicity #350 #614]: #626
+#618 := [trans #627 #624]: #629
+#606 := [monotonicity #618]: #622
+#610 := [trans #606 #609]: #622
+#615 := [quant-inst #8 #57]: #621
+#611 := [mp #615 #610]: #620
+[unit-resolution #611 #72 #714]: false
+6e4e56fbe00a817abbb464ec634b76cfe95ffdd1 351 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #19 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #17 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #39 := (f4 f5 #17)
 #40 := (f3 #39 #19)
-#739 := (pattern #40)
+#707 := (pattern #40)
 #21 := 0::Int
-#76 := -1::Int
-#80 := (* -1::Int #19)
-#77 := (* -1::Int #17)
-#135 := (mod #77 #80)
-#250 := (+ #40 #135)
-#251 := (= #250 0::Int)
+#56 := -1::Int
+#101 := (* -1::Int #19)
+#98 := (* -1::Int #17)
+#120 := (mod #98 #101)
+#276 := (+ #40 #120)
+#277 := (= #276 0::Int)
 #41 := (mod #17 #19)
-#247 := (* -1::Int #41)
-#248 := (+ #40 #247)
-#249 := (= #248 0::Int)
-#109 := (>= #17 0::Int)
-#102 := (<= #19 0::Int)
-#194 := (or #102 #109)
-#195 := (not #194)
-#98 := (<= #17 0::Int)
-#192 := (or #98 #102)
-#193 := (not #192)
-#198 := (or #193 #195)
-#252 := (ite #198 #249 #251)
-#246 := (= #40 0::Int)
+#273 := (* -1::Int #41)
+#274 := (+ #40 #273)
+#275 := (= #274 0::Int)
+#76 := (<= #19 0::Int)
+#167 := (>= #17 0::Int)
+#220 := (or #167 #76)
+#221 := (not #220)
+#72 := (<= #17 0::Int)
+#216 := (or #72 #76)
+#217 := (not #216)
+#224 := (or #217 #221)
+#278 := (if #224 #275 #277)
+#272 := (= #40 0::Int)
 #22 := (= #17 0::Int)
-#253 := (ite #22 #246 #252)
-#245 := (= #17 #40)
+#279 := (if #22 #272 #278)
+#271 := (= #40 #17)
 #23 := (= #19 0::Int)
-#254 := (ite #23 #245 #253)
-#740 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #739) #254)
-#257 := (forall (vars (?v0 Int) (?v1 Int)) #254)
-#743 := (iff #257 #740)
-#741 := (iff #254 #254)
-#742 := [refl]: #741
-#744 := [quant-intro #742]: #743
-#141 := (* -1::Int #135)
-#214 := (ite #198 #41 #141)
-#217 := (ite #22 0::Int #214)
-#220 := (ite #23 #17 #217)
-#223 := (= #40 #220)
-#226 := (forall (vars (?v0 Int) (?v1 Int)) #223)
-#258 := (iff #226 #257)
-#255 := (iff #223 #254)
-#256 := [rewrite]: #255
-#259 := [quant-intro #256]: #258
-#110 := (not #109)
-#103 := (not #102)
-#113 := (and #103 #110)
-#99 := (not #98)
-#106 := (and #99 #103)
-#116 := (or #106 #113)
-#161 := (ite #116 #41 #141)
-#164 := (ite #22 0::Int #161)
-#167 := (ite #23 #17 #164)
-#170 := (= #40 #167)
-#173 := (forall (vars (?v0 Int) (?v1 Int)) #170)
-#227 := (iff #173 #226)
-#224 := (iff #170 #223)
-#221 := (= #167 #220)
-#218 := (= #164 #217)
-#215 := (= #161 #214)
-#199 := (iff #116 #198)
-#196 := (iff #113 #195)
-#197 := [rewrite]: #196
-#186 := (iff #106 #193)
-#187 := [rewrite]: #186
-#200 := [monotonicity #187 #197]: #199
-#216 := [monotonicity #200]: #215
-#219 := [monotonicity #216]: #218
-#222 := [monotonicity #219]: #221
-#225 := [monotonicity #222]: #224
-#228 := [quant-intro #225]: #227
-#184 := (~ #173 #173)
-#183 := (~ #170 #170)
-#180 := [refl]: #183
-#185 := [nnf-pos #180]: #184
+#280 := (if #23 #271 #279)
+#708 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #707) #280)
+#283 := (forall (vars (?v0 Int) (?v1 Int)) #280)
+#711 := (iff #283 #708)
+#709 := (iff #280 #280)
+#710 := [refl]: #709
+#712 := [quant-intro #710]: #711
+#126 := (* -1::Int #120)
+#240 := (if #224 #41 #126)
+#243 := (if #22 0::Int #240)
+#246 := (if #23 #17 #243)
+#249 := (= #40 #246)
+#252 := (forall (vars (?v0 Int) (?v1 Int)) #249)
+#284 := (iff #252 #283)
+#281 := (iff #249 #280)
+#282 := [rewrite]: #281
+#285 := [quant-intro #282]: #284
+#77 := (not #76)
+#170 := (not #167)
+#173 := (and #170 #77)
+#73 := (not #72)
+#80 := (and #73 #77)
+#176 := (or #80 #173)
+#192 := (if #176 #41 #126)
+#195 := (if #22 0::Int #192)
+#198 := (if #23 #17 #195)
+#201 := (= #40 #198)
+#204 := (forall (vars (?v0 Int) (?v1 Int)) #201)
+#253 := (iff #204 #252)
+#250 := (iff #201 #249)
+#247 := (= #198 #246)
+#244 := (= #195 #243)
+#241 := (= #192 #240)
+#225 := (iff #176 #224)
+#222 := (iff #173 #221)
+#223 := [rewrite]: #222
+#218 := (iff #80 #217)
+#219 := [rewrite]: #218
+#226 := [monotonicity #219 #223]: #225
+#242 := [monotonicity #226]: #241
+#245 := [monotonicity #242]: #244
+#248 := [monotonicity #245]: #247
+#251 := [monotonicity #248]: #250
+#254 := [quant-intro #251]: #253
+#166 := (~ #204 #204)
+#211 := (~ #201 #201)
+#165 := [refl]: #211
+#214 := [nnf-pos #165]: #166
+#83 := (<= 0::Int #17)
+#84 := (not #83)
+#92 := (and #84 #77)
+#95 := (or #80 #92)
+#131 := (if #95 #41 #126)
+#134 := (if #22 0::Int #131)
+#137 := (if #23 #17 #134)
+#140 := (= #40 #137)
+#143 := (forall (vars (?v0 Int) (?v1 Int)) #140)
+#205 := (iff #143 #204)
+#202 := (iff #140 #201)
+#199 := (= #137 #198)
+#196 := (= #134 #195)
+#193 := (= #131 #192)
+#177 := (iff #95 #176)
+#174 := (iff #92 #173)
+#171 := (iff #84 #170)
+#168 := (iff #83 #167)
+#169 := [rewrite]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#194 := [monotonicity #178]: #193
+#197 := [monotonicity #194]: #196
+#200 := [monotonicity #197]: #199
+#203 := [monotonicity #200]: #202
+#206 := [quant-intro #203]: #205
 #33 := (- #19)
 #32 := (- #17)
 #42 := (mod #32 #33)
@@ -39188,1003 +39302,1706 @@
 #25 := (< 0::Int #17)
 #27 := (and #25 #26)
 #30 := (or #27 #29)
-#44 := (ite #30 #41 #43)
-#45 := (ite #22 0::Int #44)
-#46 := (ite #23 #17 #45)
+#44 := (if #30 #41 #43)
+#45 := (if #22 0::Int #44)
+#46 := (if #23 #17 #45)
 #47 := (= #40 #46)
 #48 := (forall (vars (?v0 Int) (?v1 Int)) #47)
-#176 := (iff #48 #173)
-#70 := (and #26 #28)
-#73 := (or #27 #70)
-#146 := (ite #73 #41 #141)
-#149 := (ite #22 0::Int #146)
-#152 := (ite #23 #17 #149)
-#155 := (= #40 #152)
-#158 := (forall (vars (?v0 Int) (?v1 Int)) #155)
-#174 := (iff #158 #173)
-#171 := (iff #155 #170)
-#168 := (= #152 #167)
-#165 := (= #149 #164)
-#162 := (= #146 #161)
-#117 := (iff #73 #116)
-#114 := (iff #70 #113)
-#111 := (iff #28 #110)
-#112 := [rewrite]: #111
-#104 := (iff #26 #103)
-#105 := [rewrite]: #104
-#115 := [monotonicity #105 #112]: #114
-#107 := (iff #27 #106)
-#100 := (iff #25 #99)
-#101 := [rewrite]: #100
-#108 := [monotonicity #101 #105]: #107
-#118 := [monotonicity #108 #115]: #117
-#163 := [monotonicity #118]: #162
-#166 := [monotonicity #163]: #165
-#169 := [monotonicity #166]: #168
-#172 := [monotonicity #169]: #171
-#175 := [quant-intro #172]: #174
-#159 := (iff #48 #158)
-#156 := (iff #47 #155)
-#153 := (= #46 #152)
-#150 := (= #45 #149)
-#147 := (= #44 #146)
-#144 := (= #43 #141)
-#138 := (- #135)
-#142 := (= #138 #141)
-#143 := [rewrite]: #142
-#139 := (= #43 #138)
-#136 := (= #42 #135)
-#81 := (= #33 #80)
-#82 := [rewrite]: #81
-#78 := (= #32 #77)
+#144 := (iff #48 #143)
+#141 := (iff #47 #140)
+#138 := (= #46 #137)
+#135 := (= #45 #134)
+#132 := (= #44 #131)
+#129 := (= #43 #126)
+#123 := (- #120)
+#127 := (= #123 #126)
+#128 := [rewrite]: #127
+#124 := (= #43 #123)
+#121 := (= #42 #120)
+#102 := (= #33 #101)
+#103 := [rewrite]: #102
+#99 := (= #32 #98)
+#100 := [rewrite]: #99
+#122 := [monotonicity #100 #103]: #121
+#125 := [monotonicity #122]: #124
+#130 := [trans #125 #128]: #129
+#96 := (iff #30 #95)
+#93 := (iff #29 #92)
+#78 := (iff #26 #77)
 #79 := [rewrite]: #78
-#137 := [monotonicity #79 #82]: #136
-#140 := [monotonicity #137]: #139
-#145 := [trans #140 #143]: #144
-#74 := (iff #30 #73)
-#71 := (iff #29 #70)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#148 := [monotonicity #75 #145]: #147
-#151 := [monotonicity #148]: #150
-#154 := [monotonicity #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [quant-intro #157]: #159
-#177 := [trans #160 #175]: #176
-#134 := [asserted]: #48
-#178 := [mp #134 #177]: #173
-#181 := [mp~ #178 #185]: #173
-#229 := [mp #181 #228]: #226
-#260 := [mp #229 #259]: #257
-#745 := [mp #260 #744]: #740
+#85 := (iff #28 #84)
+#89 := (iff #84 #84)
+#87 := (iff #83 #83)
+#88 := [rewrite]: #87
+#90 := [monotonicity #88]: #89
+#86 := [rewrite]: #85
+#91 := [trans #86 #90]: #85
+#94 := [monotonicity #91 #79]: #93
+#81 := (iff #27 #80)
+#74 := (iff #25 #73)
+#75 := [rewrite]: #74
+#82 := [monotonicity #75 #79]: #81
+#97 := [monotonicity #82 #94]: #96
+#133 := [monotonicity #97 #130]: #132
+#136 := [monotonicity #133]: #135
+#139 := [monotonicity #136]: #138
+#142 := [monotonicity #139]: #141
+#145 := [quant-intro #142]: #144
+#52 := [asserted]: #48
+#146 := [mp #52 #145]: #143
+#207 := [mp #146 #206]: #204
+#215 := [mp~ #207 #214]: #204
+#255 := [mp #215 #254]: #252
+#286 := [mp #255 #285]: #283
+#713 := [mp #286 #712]: #708
 #13 := 2::Int
 #11 := 3::Int
-#9 := 5::Int
-#10 := (f4 f5 5::Int)
+#59 := (f4 f5 -1::Int)
+#62 := (f3 #59 3::Int)
+#65 := (= #62 2::Int)
+#68 := (not #65)
+#8 := 1::Int
+#9 := (- 1::Int)
+#10 := (f4 f5 #9)
 #12 := (f3 #10 3::Int)
 #14 := (= #12 2::Int)
 #15 := (not #14)
-#68 := [asserted]: #15
-#638 := (not #740)
-#640 := (or #638 #14)
-#318 := (* -1::Int 3::Int)
-#403 := (* -1::Int 5::Int)
-#404 := (mod #403 #318)
-#405 := (+ #12 #404)
-#396 := (= #405 0::Int)
-#407 := (mod 5::Int 3::Int)
-#408 := (* -1::Int #407)
-#336 := (+ #12 #408)
-#409 := (= #336 0::Int)
-#406 := (>= 5::Int 0::Int)
-#410 := (<= 3::Int 0::Int)
-#389 := (or #410 #406)
-#724 := (not #389)
-#726 := (<= 5::Int 0::Int)
-#383 := (or #726 #410)
-#513 := (not #383)
-#720 := (or #513 #724)
-#394 := (ite #720 #409 #396)
-#395 := (= #12 0::Int)
-#727 := (= 5::Int 0::Int)
-#728 := (ite #727 #395 #394)
-#729 := (= 5::Int #12)
-#730 := (= 3::Int 0::Int)
-#725 := (ite #730 #729 #728)
-#641 := (or #638 #725)
-#643 := (iff #641 #640)
-#644 := (iff #640 #640)
-#630 := [rewrite]: #644
-#653 := (iff #725 #14)
-#386 := (= #12 5::Int)
-#649 := (ite false #386 #14)
-#652 := (iff #649 #14)
-#646 := [rewrite]: #652
-#650 := (iff #725 #649)
-#655 := (iff #728 #14)
-#645 := (ite false #395 #14)
-#658 := (iff #645 #14)
-#659 := [rewrite]: #658
-#647 := (iff #728 #645)
-#656 := (iff #394 #14)
-#561 := (= #12 -1::Int)
-#1 := true
-#573 := (ite true #14 #561)
-#667 := (iff #573 #14)
-#654 := [rewrite]: #667
-#666 := (iff #394 #573)
-#571 := (iff #396 #561)
-#672 := 1::Int
-#566 := (+ 1::Int #12)
-#565 := (= #566 0::Int)
-#569 := (iff #565 #561)
-#570 := [rewrite]: #569
-#567 := (iff #396 #565)
-#665 := (= #405 #566)
-#557 := (+ #12 1::Int)
-#661 := (= #557 #566)
-#662 := [rewrite]: #661
-#516 := (= #405 #557)
-#555 := (= #404 1::Int)
-#512 := -3::Int
-#682 := -5::Int
-#668 := (mod -5::Int -3::Int)
-#670 := (= #668 1::Int)
-#673 := [rewrite]: #670
-#669 := (= #404 #668)
-#514 := (= #318 -3::Int)
-#515 := [rewrite]: #514
-#676 := (= #403 -5::Int)
-#683 := [rewrite]: #676
-#671 := [monotonicity #683 #515]: #669
-#556 := [trans #671 #673]: #555
-#664 := [monotonicity #556]: #516
-#550 := [trans #664 #662]: #665
-#568 := [monotonicity #550]: #567
-#572 := [trans #568 #570]: #571
-#675 := (iff #409 #14)
-#698 := -2::Int
-#686 := (+ -2::Int #12)
-#677 := (= #686 0::Int)
-#680 := (iff #677 #14)
-#674 := [rewrite]: #680
-#678 := (iff #409 #677)
-#534 := (= #336 #686)
-#685 := (+ #12 -2::Int)
-#692 := (= #685 #686)
-#533 := [rewrite]: #692
-#690 := (= #336 #685)
-#689 := (= #408 -2::Int)
-#693 := (* -1::Int 2::Int)
-#687 := (= #693 -2::Int)
-#688 := [rewrite]: #687
-#697 := (= #408 #693)
-#696 := (= #407 2::Int)
-#411 := [rewrite]: #696
-#694 := [monotonicity #411]: #697
-#684 := [trans #694 #688]: #689
-#691 := [monotonicity #684]: #690
-#535 := [trans #691 #533]: #534
-#679 := [monotonicity #535]: #678
-#681 := [trans #679 #674]: #675
-#417 := (iff #720 true)
-#700 := (or true false)
-#415 := (iff #700 true)
-#416 := [rewrite]: #415
-#704 := (iff #720 #700)
-#699 := (iff #724 false)
-#324 := (not true)
-#424 := (iff #324 false)
-#425 := [rewrite]: #424
-#701 := (iff #724 #324)
-#430 := (iff #389 true)
-#719 := (or false true)
-#428 := (iff #719 true)
-#429 := [rewrite]: #428
-#705 := (iff #389 #719)
-#718 := (iff #406 true)
-#716 := [rewrite]: #718
-#370 := (iff #410 false)
-#371 := [rewrite]: #370
-#706 := [monotonicity #371 #716]: #705
-#431 := [trans #706 #429]: #430
-#702 := [monotonicity #431]: #701
-#703 := [trans #702 #425]: #699
-#357 := (iff #513 true)
-#708 := (not false)
-#715 := (iff #708 true)
-#717 := [rewrite]: #715
-#714 := (iff #513 #708)
-#712 := (iff #383 false)
-#372 := (or false false)
-#710 := (iff #372 false)
-#711 := [rewrite]: #710
-#373 := (iff #383 #372)
-#366 := (iff #726 false)
-#707 := [rewrite]: #366
-#709 := [monotonicity #707 #371]: #373
-#713 := [trans #709 #711]: #712
-#352 := [monotonicity #713]: #714
-#358 := [trans #352 #717]: #357
-#414 := [monotonicity #358 #703]: #704
-#695 := [trans #414 #416]: #417
-#663 := [monotonicity #695 #681 #572]: #666
-#648 := [trans #663 #654]: #656
-#382 := (iff #727 false)
-#723 := [rewrite]: #382
-#657 := [monotonicity #723 #648]: #647
-#660 := [trans #657 #659]: #655
-#381 := (iff #729 #386)
-#722 := [rewrite]: #381
-#731 := (iff #730 false)
-#721 := [rewrite]: #731
-#651 := [monotonicity #721 #722 #660]: #650
-#637 := [trans #651 #646]: #653
-#639 := [monotonicity #637]: #643
-#631 := [trans #639 #630]: #643
-#642 := [quant-inst #9 #11]: #641
-#633 := [mp #642 #631]: #640
-[unit-resolution #633 #68 #745]: false
-unsat
-d63f13b3722fcb24456a709ef1b920eb8e1c1645 335 0
+#69 := (iff #15 #68)
+#66 := (iff #14 #65)
+#63 := (= #12 #62)
+#60 := (= #10 #59)
+#57 := (= #9 -1::Int)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#64 := [monotonicity #61]: #63
+#67 := [monotonicity #64]: #66
+#70 := [monotonicity #67]: #69
+#50 := [asserted]: #15
+#71 := [mp #50 #70]: #68
+#619 := (not #708)
+#620 := (or #619 #65)
+#363 := (* -1::Int 3::Int)
+#362 := (* -1::Int -1::Int)
+#695 := (mod #362 #363)
+#696 := (+ #62 #695)
+#697 := (= #696 0::Int)
+#694 := (mod -1::Int 3::Int)
+#351 := (* -1::Int #694)
+#481 := (+ #62 #351)
+#688 := (= #481 0::Int)
+#375 := (<= 3::Int 0::Int)
+#374 := (>= -1::Int 0::Int)
+#378 := (or #374 #375)
+#357 := (not #378)
+#364 := (<= -1::Int 0::Int)
+#376 := (or #364 #375)
+#377 := (not #376)
+#692 := (or #377 #357)
+#698 := (if #692 #688 #697)
+#373 := (= #62 0::Int)
+#372 := (= -1::Int 0::Int)
+#693 := (if #372 #373 #698)
+#371 := (= #62 -1::Int)
+#287 := (= 3::Int 0::Int)
+#699 := (if #287 #371 #693)
+#614 := (or #619 #699)
+#605 := (iff #614 #620)
+#608 := (iff #620 #620)
+#609 := [rewrite]: #608
+#617 := (iff #699 #65)
+#625 := (if false #371 #65)
+#623 := (iff #625 #65)
+#628 := [rewrite]: #623
+#626 := (iff #699 #625)
+#613 := (iff #693 #65)
+#631 := (if false #373 #65)
+#624 := (iff #631 #65)
+#616 := [rewrite]: #624
+#635 := (iff #693 #631)
+#541 := (iff #698 #65)
+#1 := true
+#529 := (if true #65 #371)
+#539 := (iff #529 #65)
+#540 := [rewrite]: #539
+#537 := (iff #698 #529)
+#535 := (iff #697 #371)
+#524 := (+ 1::Int #62)
+#629 := (= #524 0::Int)
+#518 := (iff #629 #371)
+#533 := [rewrite]: #518
+#630 := (iff #697 #629)
+#632 := (= #696 #524)
+#638 := (+ #62 1::Int)
+#525 := (= #638 #524)
+#484 := [rewrite]: #525
+#641 := (= #696 #638)
+#639 := (= #695 1::Int)
+#650 := -3::Int
+#480 := (mod 1::Int -3::Int)
+#636 := (= #480 1::Int)
+#637 := [rewrite]: #636
+#482 := (= #695 #480)
+#644 := (= #363 -3::Int)
+#651 := [rewrite]: #644
+#643 := (= #362 1::Int)
+#649 := [rewrite]: #643
+#483 := [monotonicity #649 #651]: #482
+#640 := [trans #483 #637]: #639
+#523 := [monotonicity #640]: #641
+#534 := [trans #523 #484]: #632
+#633 := [monotonicity #534]: #630
+#536 := [trans #633 #533]: #535
+#648 := (iff #688 #65)
+#665 := -2::Int
+#658 := (+ -2::Int #62)
+#502 := (= #658 0::Int)
+#646 := (iff #502 #65)
+#647 := [rewrite]: #646
+#503 := (iff #688 #502)
+#660 := (= #481 #658)
+#657 := (+ #62 -2::Int)
+#659 := (= #657 #658)
+#654 := [rewrite]: #659
+#652 := (= #481 #657)
+#655 := (= #351 -2::Int)
+#664 := (* -1::Int 2::Int)
+#662 := (= #664 -2::Int)
+#666 := [rewrite]: #662
+#379 := (= #351 #664)
+#385 := (= #694 2::Int)
+#663 := [rewrite]: #385
+#661 := [monotonicity #663]: #379
+#656 := [trans #661 #666]: #655
+#653 := [monotonicity #656]: #652
+#501 := [trans #653 #654]: #660
+#645 := [monotonicity #501]: #503
+#642 := [trans #645 #647]: #648
+#383 := (iff #692 true)
+#667 := (or false true)
+#672 := (iff #667 true)
+#382 := [rewrite]: #672
+#671 := (iff #692 #667)
+#392 := (iff #357 true)
+#398 := (not false)
+#669 := (iff #398 true)
+#670 := [rewrite]: #669
+#399 := (iff #357 #398)
+#396 := (iff #378 false)
+#686 := (or false false)
+#673 := (iff #686 false)
+#674 := [rewrite]: #673
+#684 := (iff #378 #686)
+#334 := (iff #375 false)
+#675 := [rewrite]: #334
+#325 := (iff #374 false)
+#326 := [rewrite]: #325
+#687 := [monotonicity #326 #675]: #684
+#397 := [trans #687 #674]: #396
+#293 := [monotonicity #397]: #399
+#393 := [trans #293 #670]: #392
+#683 := (iff #377 false)
+#680 := (not true)
+#682 := (iff #680 false)
+#320 := [rewrite]: #682
+#681 := (iff #377 #680)
+#678 := (iff #376 true)
+#338 := (or true false)
+#341 := (iff #338 true)
+#677 := [rewrite]: #341
+#339 := (iff #376 #338)
+#350 := (iff #364 true)
+#691 := [rewrite]: #350
+#340 := [monotonicity #691 #675]: #339
+#679 := [trans #340 #677]: #678
+#676 := [monotonicity #679]: #681
+#685 := [trans #676 #320]: #683
+#668 := [monotonicity #685 #393]: #671
+#384 := [trans #668 #382]: #383
+#538 := [monotonicity #384 #642 #536]: #537
+#634 := [trans #538 #540]: #541
+#354 := (iff #372 false)
+#690 := [rewrite]: #354
+#622 := [monotonicity #690 #634]: #635
+#615 := [trans #622 #616]: #613
+#689 := (iff #287 false)
+#349 := [rewrite]: #689
+#627 := [monotonicity #349 #615]: #626
+#618 := [trans #627 #628]: #617
+#606 := [monotonicity #618]: #605
+#610 := [trans #606 #609]: #605
+#621 := [quant-inst #56 #11]: #614
+#611 := [mp #621 #610]: #620
+[unit-resolution #611 #71 #713]: false
+f9ffecc986aee817cb6d5df5a9e4ebfb5694a737 332 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#18 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#16 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#37 := (f4 f5 #16)
+#38 := (f3 #37 #18)
+#707 := (pattern #38)
+#12 := 0::Int
+#96 := -1::Int
+#100 := (* -1::Int #18)
+#97 := (* -1::Int #16)
+#119 := (mod #97 #100)
+#275 := (+ #38 #119)
+#276 := (= #275 0::Int)
+#39 := (mod #16 #18)
+#272 := (* -1::Int #39)
+#273 := (+ #38 #272)
+#274 := (= #273 0::Int)
+#74 := (<= #18 0::Int)
+#166 := (>= #16 0::Int)
+#219 := (or #166 #74)
+#220 := (not #219)
+#70 := (<= #16 0::Int)
+#215 := (or #70 #74)
+#216 := (not #215)
+#223 := (or #216 #220)
+#277 := (if #223 #274 #276)
+#271 := (= #38 0::Int)
+#20 := (= #16 0::Int)
+#278 := (if #20 #271 #277)
+#270 := (= #38 #16)
+#21 := (= #18 0::Int)
+#279 := (if #21 #270 #278)
+#708 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #707) #279)
+#282 := (forall (vars (?v0 Int) (?v1 Int)) #279)
+#711 := (iff #282 #708)
+#709 := (iff #279 #279)
+#710 := [refl]: #709
+#712 := [quant-intro #710]: #711
+#125 := (* -1::Int #119)
+#239 := (if #223 #39 #125)
+#242 := (if #20 0::Int #239)
+#245 := (if #21 #16 #242)
+#248 := (= #38 #245)
+#251 := (forall (vars (?v0 Int) (?v1 Int)) #248)
+#283 := (iff #251 #282)
+#280 := (iff #248 #279)
+#281 := [rewrite]: #280
+#284 := [quant-intro #281]: #283
+#75 := (not #74)
+#169 := (not #166)
+#172 := (and #169 #75)
+#71 := (not #70)
+#78 := (and #71 #75)
+#175 := (or #78 #172)
+#191 := (if #175 #39 #125)
+#194 := (if #20 0::Int #191)
+#197 := (if #21 #16 #194)
+#200 := (= #38 #197)
+#203 := (forall (vars (?v0 Int) (?v1 Int)) #200)
+#252 := (iff #203 #251)
+#249 := (iff #200 #248)
+#246 := (= #197 #245)
+#243 := (= #194 #242)
+#240 := (= #191 #239)
+#224 := (iff #175 #223)
+#221 := (iff #172 #220)
+#222 := [rewrite]: #221
+#217 := (iff #78 #216)
+#218 := [rewrite]: #217
+#225 := [monotonicity #218 #222]: #224
+#241 := [monotonicity #225]: #240
+#244 := [monotonicity #241]: #243
+#247 := [monotonicity #244]: #246
+#250 := [monotonicity #247]: #249
+#253 := [quant-intro #250]: #252
+#165 := (~ #203 #203)
+#210 := (~ #200 #200)
+#164 := [refl]: #210
+#213 := [nnf-pos #164]: #165
+#81 := (<= 0::Int #16)
+#82 := (not #81)
+#90 := (and #82 #75)
+#93 := (or #78 #90)
+#130 := (if #93 #39 #125)
+#133 := (if #20 0::Int #130)
+#136 := (if #21 #16 #133)
+#139 := (= #38 #136)
+#142 := (forall (vars (?v0 Int) (?v1 Int)) #139)
+#204 := (iff #142 #203)
+#201 := (iff #139 #200)
+#198 := (= #136 #197)
+#195 := (= #133 #194)
+#192 := (= #130 #191)
+#176 := (iff #93 #175)
+#173 := (iff #90 #172)
+#170 := (iff #82 #169)
+#167 := (iff #81 #166)
+#168 := [rewrite]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#193 := [monotonicity #177]: #192
+#196 := [monotonicity #193]: #195
+#199 := [monotonicity #196]: #198
+#202 := [monotonicity #199]: #201
+#205 := [quant-intro #202]: #204
+#31 := (- #18)
+#30 := (- #16)
+#40 := (mod #30 #31)
+#41 := (- #40)
+#24 := (< 0::Int #18)
+#26 := (< #16 0::Int)
+#27 := (and #26 #24)
+#23 := (< 0::Int #16)
+#25 := (and #23 #24)
+#28 := (or #25 #27)
+#42 := (if #28 #39 #41)
+#43 := (if #20 0::Int #42)
+#44 := (if #21 #16 #43)
+#45 := (= #38 #44)
+#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
+#143 := (iff #46 #142)
+#140 := (iff #45 #139)
+#137 := (= #44 #136)
+#134 := (= #43 #133)
+#131 := (= #42 #130)
+#128 := (= #41 #125)
+#122 := (- #119)
+#126 := (= #122 #125)
+#127 := [rewrite]: #126
+#123 := (= #41 #122)
+#120 := (= #40 #119)
+#101 := (= #31 #100)
+#102 := [rewrite]: #101
+#98 := (= #30 #97)
+#99 := [rewrite]: #98
+#121 := [monotonicity #99 #102]: #120
+#124 := [monotonicity #121]: #123
+#129 := [trans #124 #127]: #128
+#94 := (iff #28 #93)
+#91 := (iff #27 #90)
+#76 := (iff #24 #75)
+#77 := [rewrite]: #76
+#83 := (iff #26 #82)
+#87 := (iff #82 #82)
+#85 := (iff #81 #81)
+#86 := [rewrite]: #85
+#88 := [monotonicity #86]: #87
+#84 := [rewrite]: #83
+#89 := [trans #84 #88]: #83
+#92 := [monotonicity #89 #77]: #91
+#79 := (iff #25 #78)
+#72 := (iff #23 #71)
+#73 := [rewrite]: #72
+#80 := [monotonicity #73 #77]: #79
+#95 := [monotonicity #80 #92]: #94
+#132 := [monotonicity #95 #129]: #131
+#135 := [monotonicity #132]: #134
+#138 := [monotonicity #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [quant-intro #141]: #143
+#50 := [asserted]: #46
+#145 := [mp #50 #144]: #142
+#206 := [mp #145 #205]: #203
+#214 := [mp~ #206 #213]: #203
+#254 := [mp #214 #253]: #251
+#285 := [mp #254 #284]: #282
+#713 := [mp #285 #712]: #708
+#8 := 3::Int
+#54 := -3::Int
+#57 := (f4 f5 -3::Int)
+#60 := (f3 #57 3::Int)
+#63 := (= #60 0::Int)
+#66 := (not #63)
+#9 := (- 3::Int)
+#10 := (f4 f5 #9)
+#11 := (f3 #10 3::Int)
+#13 := (= #11 0::Int)
+#14 := (not #13)
+#67 := (iff #14 #66)
+#64 := (iff #13 #63)
+#61 := (= #11 #60)
+#58 := (= #10 #57)
+#55 := (= #9 -3::Int)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#62 := [monotonicity #59]: #61
+#65 := [monotonicity #62]: #64
+#68 := [monotonicity #65]: #67
+#48 := [asserted]: #14
+#69 := [mp #48 #68]: #66
+#539 := (not #708)
+#540 := (or #539 #63)
+#362 := (* -1::Int 3::Int)
+#688 := (* -1::Int -3::Int)
+#363 := (mod #688 #362)
+#695 := (+ #60 #363)
+#696 := (= #695 0::Int)
+#692 := (mod -3::Int 3::Int)
+#694 := (* -1::Int #692)
+#351 := (+ #60 #694)
+#481 := (= #351 0::Int)
+#364 := (<= 3::Int 0::Int)
+#377 := (>= -3::Int 0::Int)
+#374 := (or #377 #364)
+#378 := (not #374)
+#373 := (<= -3::Int 0::Int)
+#375 := (or #373 #364)
+#376 := (not #375)
+#357 := (or #376 #378)
+#697 := (if #357 #481 #696)
+#372 := (= -3::Int 0::Int)
+#698 := (if #372 #63 #697)
+#371 := (= #60 -3::Int)
+#286 := (= 3::Int 0::Int)
+#693 := (if #286 #371 #698)
+#541 := (or #539 #693)
+#631 := (iff #541 #540)
+#622 := (iff #540 #540)
+#624 := [rewrite]: #622
+#537 := (iff #693 #63)
+#518 := (if false #371 #63)
+#536 := (iff #518 #63)
+#529 := [rewrite]: #536
+#533 := (iff #693 #518)
+#630 := (iff #698 #63)
+#525 := (if false #63 #63)
+#534 := (iff #525 #63)
+#629 := [rewrite]: #534
+#484 := (iff #698 #525)
+#523 := (iff #697 #63)
+#1 := true
+#637 := (if true #63 #63)
+#638 := (iff #637 #63)
+#641 := [rewrite]: #638
+#639 := (iff #697 #637)
+#483 := (iff #696 #63)
+#480 := (= #695 #60)
+#655 := (+ #60 0::Int)
+#652 := (= #655 #60)
+#653 := [rewrite]: #652
+#644 := (= #695 #655)
+#649 := (= #363 0::Int)
+#646 := (mod 3::Int -3::Int)
+#642 := (= #646 0::Int)
+#643 := [rewrite]: #642
+#647 := (= #363 #646)
+#503 := (= #362 -3::Int)
+#645 := [rewrite]: #503
+#501 := (= #688 3::Int)
+#502 := [rewrite]: #501
+#648 := [monotonicity #502 #645]: #647
+#650 := [trans #648 #643]: #649
+#651 := [monotonicity #650]: #644
+#482 := [trans #651 #653]: #480
+#636 := [monotonicity #482]: #483
+#654 := (iff #481 #63)
+#658 := (= #351 #60)
+#656 := (= #351 #655)
+#662 := (= #694 0::Int)
+#663 := (* -1::Int 0::Int)
+#661 := (= #663 0::Int)
+#665 := [rewrite]: #661
+#664 := (= #694 #663)
+#384 := (= #692 0::Int)
+#385 := [rewrite]: #384
+#379 := [monotonicity #385]: #664
+#666 := [trans #379 #665]: #662
+#657 := [monotonicity #666]: #656
+#659 := [trans #657 #653]: #658
+#660 := [monotonicity #659]: #654
+#382 := (iff #357 true)
+#393 := (or false true)
+#668 := (iff #393 true)
+#672 := [rewrite]: #668
+#667 := (iff #357 #393)
+#670 := (iff #378 true)
+#397 := (not false)
+#292 := (iff #397 true)
+#669 := [rewrite]: #292
+#398 := (iff #378 #397)
+#674 := (iff #374 false)
+#326 := (or false false)
+#687 := (iff #326 false)
+#673 := [rewrite]: #687
+#686 := (iff #374 #326)
+#691 := (iff #364 false)
+#334 := [rewrite]: #691
+#685 := (iff #377 false)
+#325 := [rewrite]: #685
+#684 := [monotonicity #325 #334]: #686
+#396 := [trans #684 #673]: #674
+#399 := [monotonicity #396]: #398
+#392 := [trans #399 #669]: #670
+#320 := (iff #376 false)
+#679 := (not true)
+#676 := (iff #679 false)
+#682 := [rewrite]: #676
+#680 := (iff #376 #679)
+#677 := (iff #375 true)
+#675 := (or true false)
+#340 := (iff #675 true)
+#341 := [rewrite]: #340
+#338 := (iff #375 #675)
+#690 := (iff #373 true)
+#350 := [rewrite]: #690
+#339 := [monotonicity #350 #334]: #338
+#678 := [trans #339 #341]: #677
+#681 := [monotonicity #678]: #680
+#683 := [trans #681 #682]: #320
+#671 := [monotonicity #683 #392]: #667
+#383 := [trans #671 #672]: #382
+#640 := [monotonicity #383 #660 #636]: #639
+#524 := [trans #640 #641]: #523
+#349 := (iff #372 false)
+#354 := [rewrite]: #349
+#632 := [monotonicity #354 #524]: #484
+#633 := [trans #632 #629]: #630
+#699 := (iff #286 false)
+#689 := [rewrite]: #699
+#535 := [monotonicity #689 #633]: #533
+#538 := [trans #535 #529]: #537
+#635 := [monotonicity #538]: #631
+#616 := [trans #635 #624]: #631
+#634 := [quant-inst #54 #8]: #541
+#613 := [mp #634 #616]: #540
+[unit-resolution #613 #69 #713]: false
+3568b4797a3dd6439c3992352594a4fe4c338953 354 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#19 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#17 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#39 := (f4 f5 #17)
+#40 := (f3 #39 #19)
+#708 := (pattern #40)
+#21 := 0::Int
+#98 := -1::Int
+#102 := (* -1::Int #19)
+#99 := (* -1::Int #17)
+#121 := (mod #99 #102)
+#277 := (+ #40 #121)
+#278 := (= #277 0::Int)
+#41 := (mod #17 #19)
+#274 := (* -1::Int #41)
+#275 := (+ #40 #274)
+#276 := (= #275 0::Int)
+#76 := (<= #19 0::Int)
+#168 := (>= #17 0::Int)
+#221 := (or #168 #76)
+#222 := (not #221)
+#72 := (<= #17 0::Int)
+#217 := (or #72 #76)
+#218 := (not #217)
+#225 := (or #218 #222)
+#279 := (if #225 #276 #278)
+#273 := (= #40 0::Int)
+#22 := (= #17 0::Int)
+#280 := (if #22 #273 #279)
+#272 := (= #40 #17)
+#23 := (= #19 0::Int)
+#281 := (if #23 #272 #280)
+#709 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #708) #281)
+#284 := (forall (vars (?v0 Int) (?v1 Int)) #281)
+#712 := (iff #284 #709)
+#710 := (iff #281 #281)
+#711 := [refl]: #710
+#713 := [quant-intro #711]: #712
+#127 := (* -1::Int #121)
+#241 := (if #225 #41 #127)
+#244 := (if #22 0::Int #241)
+#247 := (if #23 #17 #244)
+#250 := (= #40 #247)
+#253 := (forall (vars (?v0 Int) (?v1 Int)) #250)
+#285 := (iff #253 #284)
+#282 := (iff #250 #281)
+#283 := [rewrite]: #282
+#286 := [quant-intro #283]: #285
+#77 := (not #76)
+#171 := (not #168)
+#174 := (and #171 #77)
+#73 := (not #72)
+#80 := (and #73 #77)
+#177 := (or #80 #174)
+#193 := (if #177 #41 #127)
+#196 := (if #22 0::Int #193)
+#199 := (if #23 #17 #196)
+#202 := (= #40 #199)
+#205 := (forall (vars (?v0 Int) (?v1 Int)) #202)
+#254 := (iff #205 #253)
+#251 := (iff #202 #250)
+#248 := (= #199 #247)
+#245 := (= #196 #244)
+#242 := (= #193 #241)
+#226 := (iff #177 #225)
+#223 := (iff #174 #222)
+#224 := [rewrite]: #223
+#219 := (iff #80 #218)
+#220 := [rewrite]: #219
+#227 := [monotonicity #220 #224]: #226
+#243 := [monotonicity #227]: #242
+#246 := [monotonicity #243]: #245
+#249 := [monotonicity #246]: #248
+#252 := [monotonicity #249]: #251
+#255 := [quant-intro #252]: #254
+#214 := (~ #205 #205)
+#210 := (~ #202 #202)
+#213 := [refl]: #210
+#215 := [nnf-pos #213]: #214
+#83 := (<= 0::Int #17)
+#84 := (not #83)
+#92 := (and #84 #77)
+#95 := (or #80 #92)
+#132 := (if #95 #41 #127)
+#135 := (if #22 0::Int #132)
+#138 := (if #23 #17 #135)
+#141 := (= #40 #138)
+#144 := (forall (vars (?v0 Int) (?v1 Int)) #141)
+#206 := (iff #144 #205)
+#203 := (iff #141 #202)
+#200 := (= #138 #199)
+#197 := (= #135 #196)
+#194 := (= #132 #193)
+#178 := (iff #95 #177)
+#175 := (iff #92 #174)
+#172 := (iff #84 #171)
+#169 := (iff #83 #168)
+#170 := [rewrite]: #169
+#173 := [monotonicity #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [monotonicity #176]: #178
+#195 := [monotonicity #179]: #194
+#198 := [monotonicity #195]: #197
+#201 := [monotonicity #198]: #200
+#204 := [monotonicity #201]: #203
+#207 := [quant-intro #204]: #206
+#33 := (- #19)
+#32 := (- #17)
+#42 := (mod #32 #33)
+#43 := (- #42)
+#26 := (< 0::Int #19)
+#28 := (< #17 0::Int)
+#29 := (and #28 #26)
+#25 := (< 0::Int #17)
+#27 := (and #25 #26)
+#30 := (or #27 #29)
+#44 := (if #30 #41 #43)
+#45 := (if #22 0::Int #44)
+#46 := (if #23 #17 #45)
+#47 := (= #40 #46)
+#48 := (forall (vars (?v0 Int) (?v1 Int)) #47)
+#145 := (iff #48 #144)
+#142 := (iff #47 #141)
+#139 := (= #46 #138)
+#136 := (= #45 #135)
+#133 := (= #44 #132)
+#130 := (= #43 #127)
+#124 := (- #121)
+#128 := (= #124 #127)
+#129 := [rewrite]: #128
+#125 := (= #43 #124)
+#122 := (= #42 #121)
+#103 := (= #33 #102)
+#104 := [rewrite]: #103
+#100 := (= #32 #99)
+#101 := [rewrite]: #100
+#123 := [monotonicity #101 #104]: #122
+#126 := [monotonicity #123]: #125
+#131 := [trans #126 #129]: #130
+#96 := (iff #30 #95)
+#93 := (iff #29 #92)
+#78 := (iff #26 #77)
+#79 := [rewrite]: #78
+#85 := (iff #28 #84)
+#89 := (iff #84 #84)
+#87 := (iff #83 #83)
+#88 := [rewrite]: #87
+#90 := [monotonicity #88]: #89
+#86 := [rewrite]: #85
+#91 := [trans #86 #90]: #85
+#94 := [monotonicity #91 #79]: #93
+#81 := (iff #27 #80)
+#74 := (iff #25 #73)
+#75 := [rewrite]: #74
+#82 := [monotonicity #75 #79]: #81
+#97 := [monotonicity #82 #94]: #96
+#134 := [monotonicity #97 #131]: #133
+#137 := [monotonicity #134]: #136
+#140 := [monotonicity #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [quant-intro #143]: #145
+#52 := [asserted]: #48
+#147 := [mp #52 #146]: #144
+#208 := [mp #147 #207]: #205
+#216 := [mp~ #208 #215]: #205
+#256 := [mp #216 #255]: #253
+#287 := [mp #256 #286]: #284
+#714 := [mp #287 #713]: #709
+#13 := 1::Int
+#11 := 3::Int
+#56 := -5::Int
+#59 := (f4 f5 -5::Int)
+#62 := (f3 #59 3::Int)
+#65 := (= #62 1::Int)
+#68 := (not #65)
+#8 := 5::Int
+#9 := (- 5::Int)
+#10 := (f4 f5 #9)
+#12 := (f3 #10 3::Int)
+#14 := (= #12 1::Int)
+#15 := (not #14)
+#69 := (iff #15 #68)
+#66 := (iff #14 #65)
+#63 := (= #12 #62)
+#60 := (= #10 #59)
+#57 := (= #9 -5::Int)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#64 := [monotonicity #61]: #63
+#67 := [monotonicity #64]: #66
+#70 := [monotonicity #67]: #69
+#50 := [asserted]: #15
+#71 := [mp #50 #70]: #68
+#615 := (not #709)
+#622 := (or #615 #65)
+#364 := (* -1::Int 3::Int)
+#363 := (* -1::Int -5::Int)
+#696 := (mod #363 #364)
+#697 := (+ #62 #696)
+#698 := (= #697 0::Int)
+#695 := (mod -5::Int 3::Int)
+#352 := (* -1::Int #695)
+#482 := (+ #62 #352)
+#689 := (= #482 0::Int)
+#376 := (<= 3::Int 0::Int)
+#375 := (>= -5::Int 0::Int)
+#379 := (or #375 #376)
+#358 := (not #379)
+#365 := (<= -5::Int 0::Int)
+#377 := (or #365 #376)
+#378 := (not #377)
+#693 := (or #378 #358)
+#699 := (if #693 #689 #698)
+#374 := (= #62 0::Int)
+#373 := (= -5::Int 0::Int)
+#694 := (if #373 #374 #699)
+#372 := (= #62 -5::Int)
+#288 := (= 3::Int 0::Int)
+#700 := (if #288 #372 #694)
+#606 := (or #615 #700)
+#609 := (iff #606 #622)
+#611 := (iff #622 #622)
+#612 := [rewrite]: #611
+#620 := (iff #700 #65)
+#628 := (if false #372 #65)
+#618 := (iff #628 #65)
+#619 := [rewrite]: #618
+#624 := (iff #700 #628)
+#626 := (iff #694 #65)
+#623 := (if false #374 #65)
+#614 := (iff #623 #65)
+#616 := [rewrite]: #614
+#625 := (iff #694 #623)
+#632 := (iff #699 #65)
+#519 := -2::Int
+#534 := (= #62 -2::Int)
+#1 := true
+#539 := (if true #65 #534)
+#542 := (iff #539 #65)
+#635 := [rewrite]: #542
+#540 := (iff #699 #539)
+#530 := (iff #698 #534)
+#484 := 2::Int
+#525 := (+ 2::Int #62)
+#630 := (= #525 0::Int)
+#536 := (iff #630 #534)
+#537 := [rewrite]: #536
+#631 := (iff #698 #630)
+#633 := (= #697 #525)
+#639 := (+ #62 2::Int)
+#526 := (= #639 #525)
+#485 := [rewrite]: #526
+#642 := (= #697 #639)
+#640 := (= #696 2::Int)
+#650 := -3::Int
+#652 := (mod 5::Int -3::Int)
+#637 := (= #652 2::Int)
+#638 := [rewrite]: #637
+#481 := (= #696 #652)
+#651 := (= #364 -3::Int)
+#645 := [rewrite]: #651
+#643 := (= #363 5::Int)
+#644 := [rewrite]: #643
+#483 := [monotonicity #644 #645]: #481
+#641 := [trans #483 #638]: #640
+#524 := [monotonicity #641]: #642
+#535 := [trans #524 #485]: #633
+#634 := [monotonicity #535]: #631
+#538 := [trans #634 #537]: #530
+#648 := (iff #689 #65)
+#654 := (+ -1::Int #62)
+#502 := (= #654 0::Int)
+#646 := (iff #502 #65)
+#647 := [rewrite]: #646
+#503 := (iff #689 #502)
+#655 := (= #482 #654)
+#657 := (+ #62 -1::Int)
+#659 := (= #657 #654)
+#660 := [rewrite]: #659
+#658 := (= #482 #657)
+#667 := (= #352 -1::Int)
+#665 := (* -1::Int 1::Int)
+#666 := (= #665 -1::Int)
+#663 := [rewrite]: #666
+#380 := (= #352 #665)
+#386 := (= #695 1::Int)
+#664 := [rewrite]: #386
+#662 := [monotonicity #664]: #380
+#656 := [trans #662 #663]: #667
+#653 := [monotonicity #656]: #658
+#661 := [trans #653 #660]: #655
+#504 := [monotonicity #661]: #503
+#649 := [trans #504 #647]: #648
+#384 := (iff #693 true)
+#668 := (or false true)
+#673 := (iff #668 true)
+#383 := [rewrite]: #673
+#672 := (iff #693 #668)
+#393 := (iff #358 true)
+#399 := (not false)
+#670 := (iff #399 true)
+#671 := [rewrite]: #670
+#400 := (iff #358 #399)
+#397 := (iff #379 false)
+#687 := (or false false)
+#674 := (iff #687 false)
+#675 := [rewrite]: #674
+#685 := (iff #379 #687)
+#335 := (iff #376 false)
+#676 := [rewrite]: #335
+#326 := (iff #375 false)
+#327 := [rewrite]: #326
+#688 := [monotonicity #327 #676]: #685
+#398 := [trans #688 #675]: #397
+#294 := [monotonicity #398]: #400
+#394 := [trans #294 #671]: #393
+#684 := (iff #378 false)
+#681 := (not true)
+#683 := (iff #681 false)
+#321 := [rewrite]: #683
+#682 := (iff #378 #681)
+#679 := (iff #377 true)
+#339 := (or true false)
+#342 := (iff #339 true)
+#678 := [rewrite]: #342
+#340 := (iff #377 #339)
+#351 := (iff #365 true)
+#692 := [rewrite]: #351
+#341 := [monotonicity #692 #676]: #340
+#680 := [trans #341 #678]: #679
+#677 := [monotonicity #680]: #682
+#686 := [trans #677 #321]: #684
+#669 := [monotonicity #686 #394]: #672
+#385 := [trans #669 #383]: #384
+#541 := [monotonicity #385 #649 #538]: #540
+#636 := [trans #541 #635]: #632
+#355 := (iff #373 false)
+#691 := [rewrite]: #355
+#617 := [monotonicity #691 #636]: #625
+#627 := [trans #617 #616]: #626
+#690 := (iff #288 false)
+#350 := [rewrite]: #690
+#629 := [monotonicity #350 #627]: #624
+#621 := [trans #629 #619]: #620
+#610 := [monotonicity #621]: #609
+#608 := [trans #610 #612]: #609
+#607 := [quant-inst #56 #11]: #606
+#613 := [mp #607 #608]: #622
+[unit-resolution #613 #71 #714]: false
+e74a02aac7e3907e33f4c582e7dc7fb7e61206b6 351 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#19 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#17 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#39 := (f4 f5 #17)
+#40 := (f3 #39 #19)
+#710 := (pattern #40)
+#21 := 0::Int
+#56 := -1::Int
+#104 := (* -1::Int #19)
+#101 := (* -1::Int #17)
+#123 := (mod #101 #104)
+#279 := (+ #40 #123)
+#280 := (= #279 0::Int)
+#41 := (mod #17 #19)
+#276 := (* -1::Int #41)
+#277 := (+ #40 #276)
+#278 := (= #277 0::Int)
+#79 := (<= #19 0::Int)
+#170 := (>= #17 0::Int)
+#223 := (or #170 #79)
+#224 := (not #223)
+#75 := (<= #17 0::Int)
+#219 := (or #75 #79)
+#220 := (not #219)
+#227 := (or #220 #224)
+#281 := (if #227 #278 #280)
+#275 := (= #40 0::Int)
+#22 := (= #17 0::Int)
+#282 := (if #22 #275 #281)
+#274 := (= #40 #17)
+#23 := (= #19 0::Int)
+#283 := (if #23 #274 #282)
+#711 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #710) #283)
+#286 := (forall (vars (?v0 Int) (?v1 Int)) #283)
+#714 := (iff #286 #711)
+#712 := (iff #283 #283)
+#713 := [refl]: #712
+#715 := [quant-intro #713]: #714
+#129 := (* -1::Int #123)
+#243 := (if #227 #41 #129)
+#246 := (if #22 0::Int #243)
+#249 := (if #23 #17 #246)
+#252 := (= #40 #249)
+#255 := (forall (vars (?v0 Int) (?v1 Int)) #252)
+#287 := (iff #255 #286)
+#284 := (iff #252 #283)
+#285 := [rewrite]: #284
+#288 := [quant-intro #285]: #287
+#80 := (not #79)
+#173 := (not #170)
+#176 := (and #173 #80)
+#76 := (not #75)
+#83 := (and #76 #80)
+#179 := (or #83 #176)
+#195 := (if #179 #41 #129)
+#198 := (if #22 0::Int #195)
+#201 := (if #23 #17 #198)
+#204 := (= #40 #201)
+#207 := (forall (vars (?v0 Int) (?v1 Int)) #204)
+#256 := (iff #207 #255)
+#253 := (iff #204 #252)
+#250 := (= #201 #249)
+#247 := (= #198 #246)
+#244 := (= #195 #243)
+#228 := (iff #179 #227)
+#225 := (iff #176 #224)
+#226 := [rewrite]: #225
+#221 := (iff #83 #220)
+#222 := [rewrite]: #221
+#229 := [monotonicity #222 #226]: #228
+#245 := [monotonicity #229]: #244
+#248 := [monotonicity #245]: #247
+#251 := [monotonicity #248]: #250
+#254 := [monotonicity #251]: #253
+#257 := [quant-intro #254]: #256
+#169 := (~ #207 #207)
+#214 := (~ #204 #204)
+#168 := [refl]: #214
+#217 := [nnf-pos #168]: #169
+#86 := (<= 0::Int #17)
+#87 := (not #86)
+#95 := (and #87 #80)
+#98 := (or #83 #95)
+#134 := (if #98 #41 #129)
+#137 := (if #22 0::Int #134)
+#140 := (if #23 #17 #137)
+#143 := (= #40 #140)
+#146 := (forall (vars (?v0 Int) (?v1 Int)) #143)
+#208 := (iff #146 #207)
+#205 := (iff #143 #204)
+#202 := (= #140 #201)
+#199 := (= #137 #198)
+#196 := (= #134 #195)
+#180 := (iff #98 #179)
+#177 := (iff #95 #176)
+#174 := (iff #87 #173)
+#171 := (iff #86 #170)
+#172 := [rewrite]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [monotonicity #178]: #180
+#197 := [monotonicity #181]: #196
+#200 := [monotonicity #197]: #199
+#203 := [monotonicity #200]: #202
+#206 := [monotonicity #203]: #205
+#209 := [quant-intro #206]: #208
+#33 := (- #19)
+#32 := (- #17)
+#42 := (mod #32 #33)
+#43 := (- #42)
+#26 := (< 0::Int #19)
+#28 := (< #17 0::Int)
+#29 := (and #28 #26)
+#25 := (< 0::Int #17)
+#27 := (and #25 #26)
+#30 := (or #27 #29)
+#44 := (if #30 #41 #43)
+#45 := (if #22 0::Int #44)
+#46 := (if #23 #17 #45)
+#47 := (= #40 #46)
+#48 := (forall (vars (?v0 Int) (?v1 Int)) #47)
+#147 := (iff #48 #146)
+#144 := (iff #47 #143)
+#141 := (= #46 #140)
+#138 := (= #45 #137)
+#135 := (= #44 #134)
+#132 := (= #43 #129)
+#126 := (- #123)
+#130 := (= #126 #129)
+#131 := [rewrite]: #130
+#127 := (= #43 #126)
+#124 := (= #42 #123)
+#105 := (= #33 #104)
+#106 := [rewrite]: #105
+#102 := (= #32 #101)
+#103 := [rewrite]: #102
+#125 := [monotonicity #103 #106]: #124
+#128 := [monotonicity #125]: #127
+#133 := [trans #128 #131]: #132
+#99 := (iff #30 #98)
+#96 := (iff #29 #95)
+#81 := (iff #26 #80)
+#82 := [rewrite]: #81
+#88 := (iff #28 #87)
+#92 := (iff #87 #87)
+#90 := (iff #86 #86)
+#91 := [rewrite]: #90
+#93 := [monotonicity #91]: #92
+#89 := [rewrite]: #88
+#94 := [trans #89 #93]: #88
+#97 := [monotonicity #94 #82]: #96
+#84 := (iff #27 #83)
+#77 := (iff #25 #76)
+#78 := [rewrite]: #77
+#85 := [monotonicity #78 #82]: #84
+#100 := [monotonicity #85 #97]: #99
+#136 := [monotonicity #100 #133]: #135
+#139 := [monotonicity #136]: #138
+#142 := [monotonicity #139]: #141
+#145 := [monotonicity #142]: #144
+#148 := [quant-intro #145]: #147
+#52 := [asserted]: #48
+#149 := [mp #52 #148]: #146
+#210 := [mp #149 #209]: #207
+#218 := [mp~ #210 #217]: #207
+#258 := [mp #218 #257]: #255
+#289 := [mp #258 #288]: #286
+#716 := [mp #289 #715]: #711
+#62 := -3::Int
+#59 := (f4 f5 -1::Int)
+#65 := (f3 #59 -3::Int)
+#68 := (= #65 -1::Int)
+#71 := (not #68)
+#8 := 1::Int
+#9 := (- 1::Int)
+#11 := 3::Int
+#12 := (- 3::Int)
+#10 := (f4 f5 #9)
+#13 := (f3 #10 #12)
+#14 := (= #13 #9)
+#15 := (not #14)
+#72 := (iff #15 #71)
+#69 := (iff #14 #68)
+#57 := (= #9 -1::Int)
+#58 := [rewrite]: #57
+#66 := (= #13 #65)
+#63 := (= #12 -3::Int)
+#64 := [rewrite]: #63
+#60 := (= #10 #59)
+#61 := [monotonicity #58]: #60
+#67 := [monotonicity #61 #64]: #66
+#70 := [monotonicity #67 #58]: #69
+#73 := [monotonicity #70]: #72
+#50 := [asserted]: #15
+#74 := [mp #50 #73]: #71
+#631 := (not #711)
+#620 := (or #631 #68)
+#365 := (* -1::Int -3::Int)
+#691 := (* -1::Int -1::Int)
+#366 := (mod #691 #365)
+#698 := (+ #65 #366)
+#699 := (= #698 0::Int)
+#695 := (mod -1::Int -3::Int)
+#697 := (* -1::Int #695)
+#354 := (+ #65 #697)
+#484 := (= #354 0::Int)
+#367 := (<= -3::Int 0::Int)
+#380 := (>= -1::Int 0::Int)
+#377 := (or #380 #367)
+#381 := (not #377)
+#376 := (<= -1::Int 0::Int)
+#378 := (or #376 #367)
+#379 := (not #378)
+#360 := (or #379 #381)
+#700 := (if #360 #484 #699)
+#375 := (= #65 0::Int)
+#374 := (= -1::Int 0::Int)
+#701 := (if #374 #375 #700)
+#290 := (= -3::Int 0::Int)
+#696 := (if #290 #68 #701)
+#621 := (or #631 #696)
+#623 := (iff #621 #620)
+#624 := (iff #620 #620)
+#608 := [rewrite]: #624
+#630 := (iff #696 #68)
+#619 := (if false #68 #68)
+#628 := (iff #619 #68)
+#629 := [rewrite]: #628
+#616 := (iff #696 #619)
+#625 := (iff #701 #68)
+#543 := (if false #375 #68)
+#634 := (iff #543 #68)
+#638 := [rewrite]: #634
+#544 := (iff #701 #543)
+#541 := (iff #700 #68)
+#675 := 2::Int
+#505 := (= #65 2::Int)
+#536 := (if false #505 #68)
+#532 := (iff #536 #68)
+#540 := [rewrite]: #532
+#538 := (iff #700 #536)
+#636 := (iff #699 #68)
+#641 := (+ 1::Int #65)
+#487 := (= #641 0::Int)
+#632 := (iff #487 #68)
+#633 := [rewrite]: #632
+#635 := (iff #699 #487)
+#527 := (= #698 #641)
+#640 := (+ #65 1::Int)
+#644 := (= #640 #641)
+#526 := [rewrite]: #644
+#642 := (= #698 #640)
+#486 := (= #366 1::Int)
+#653 := (mod 1::Int 3::Int)
+#483 := (= #653 1::Int)
+#485 := [rewrite]: #483
+#647 := (= #366 #653)
+#646 := (= #365 3::Int)
+#652 := [rewrite]: #646
+#651 := (= #691 1::Int)
+#645 := [rewrite]: #651
+#654 := [monotonicity #645 #652]: #647
+#639 := [trans #654 #485]: #486
+#643 := [monotonicity #639]: #642
+#528 := [trans #643 #526]: #527
+#537 := [monotonicity #528]: #635
+#521 := [trans #537 #633]: #636
+#649 := (iff #484 #505)
+#667 := -2::Int
+#660 := (+ -2::Int #65)
+#657 := (= #660 0::Int)
+#506 := (iff #657 #505)
+#648 := [rewrite]: #506
+#663 := (iff #484 #657)
+#661 := (= #354 #660)
+#669 := (+ #65 -2::Int)
+#655 := (= #669 #660)
+#656 := [rewrite]: #655
+#658 := (= #354 #669)
+#668 := (= #697 -2::Int)
+#387 := (* -1::Int 2::Int)
+#382 := (= #387 -2::Int)
+#664 := [rewrite]: #382
+#388 := (= #697 #387)
+#385 := (= #695 2::Int)
+#386 := [rewrite]: #385
+#666 := [monotonicity #386]: #388
+#665 := [trans #666 #664]: #668
+#659 := [monotonicity #665]: #658
+#662 := [trans #659 #656]: #661
+#504 := [monotonicity #662]: #663
+#650 := [trans #504 #648]: #649
+#674 := (iff #360 false)
+#672 := (or false false)
+#396 := (iff #672 false)
+#670 := [rewrite]: #396
+#673 := (iff #360 #672)
+#402 := (iff #381 false)
+#1 := true
+#682 := (not true)
+#679 := (iff #682 false)
+#685 := [rewrite]: #679
+#400 := (iff #381 #682)
+#677 := (iff #377 true)
+#329 := (or false true)
+#690 := (iff #329 true)
+#676 := [rewrite]: #690
+#689 := (iff #377 #329)
+#694 := (iff #367 true)
+#337 := [rewrite]: #694
+#688 := (iff #380 false)
+#328 := [rewrite]: #688
+#687 := [monotonicity #328 #337]: #689
+#399 := [trans #687 #676]: #677
+#401 := [monotonicity #399]: #400
+#296 := [trans #401 #685]: #402
+#323 := (iff #379 false)
+#683 := (iff #379 #682)
+#680 := (iff #378 true)
+#678 := (or true true)
+#343 := (iff #678 true)
+#344 := [rewrite]: #343
+#341 := (iff #378 #678)
+#693 := (iff #376 true)
+#353 := [rewrite]: #693
+#342 := [monotonicity #353 #337]: #341
+#681 := [trans #342 #344]: #680
+#684 := [monotonicity #681]: #683
+#686 := [trans #684 #685]: #323
+#395 := [monotonicity #686 #296]: #673
+#671 := [trans #395 #670]: #674
+#539 := [monotonicity #671 #650 #521]: #538
+#542 := [trans #539 #540]: #541
+#352 := (iff #374 false)
+#357 := [rewrite]: #352
+#637 := [monotonicity #357 #542]: #544
+#627 := [trans #637 #638]: #625
+#702 := (iff #290 false)
+#692 := [rewrite]: #702
+#618 := [monotonicity #692 #627]: #616
+#626 := [trans #618 #629]: #630
+#617 := [monotonicity #626]: #623
+#609 := [trans #617 #608]: #623
+#622 := [quant-inst #56 #62]: #621
+#611 := [mp #622 #609]: #620
+[unit-resolution #611 #74 #716]: false
+c218d35497e494bce5a56e2b75fd1bf7144c1ade 317 0
+unsat
+#2 := false
+decl f3 :: (-> S2 Int Int)
+#18 := (:var 0 Int)
+decl f4 :: (-> S3 Int S2)
+#16 := (:var 1 Int)
+decl f5 :: S3
+#7 := f5
+#37 := (f4 f5 #16)
+#38 := (f3 #37 #18)
+#707 := (pattern #38)
+#12 := 0::Int
+#96 := -1::Int
+#100 := (* -1::Int #18)
+#97 := (* -1::Int #16)
+#119 := (mod #97 #100)
+#275 := (+ #38 #119)
+#276 := (= #275 0::Int)
+#39 := (mod #16 #18)
+#272 := (* -1::Int #39)
+#273 := (+ #38 #272)
+#274 := (= #273 0::Int)
+#74 := (<= #18 0::Int)
+#166 := (>= #16 0::Int)
+#219 := (or #166 #74)
+#220 := (not #219)
+#70 := (<= #16 0::Int)
+#215 := (or #70 #74)
+#216 := (not #215)
+#223 := (or #216 #220)
+#277 := (if #223 #274 #276)
+#271 := (= #38 0::Int)
+#20 := (= #16 0::Int)
+#278 := (if #20 #271 #277)
+#270 := (= #38 #16)
+#21 := (= #18 0::Int)
+#279 := (if #21 #270 #278)
+#708 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #707) #279)
+#282 := (forall (vars (?v0 Int) (?v1 Int)) #279)
+#711 := (iff #282 #708)
+#709 := (iff #279 #279)
+#710 := [refl]: #709
+#712 := [quant-intro #710]: #711
+#125 := (* -1::Int #119)
+#239 := (if #223 #39 #125)
+#242 := (if #20 0::Int #239)
+#245 := (if #21 #16 #242)
+#248 := (= #38 #245)
+#251 := (forall (vars (?v0 Int) (?v1 Int)) #248)
+#283 := (iff #251 #282)
+#280 := (iff #248 #279)
+#281 := [rewrite]: #280
+#284 := [quant-intro #281]: #283
+#75 := (not #74)
+#169 := (not #166)
+#172 := (and #169 #75)
+#71 := (not #70)
+#78 := (and #71 #75)
+#175 := (or #78 #172)
+#191 := (if #175 #39 #125)
+#194 := (if #20 0::Int #191)
+#197 := (if #21 #16 #194)
+#200 := (= #38 #197)
+#203 := (forall (vars (?v0 Int) (?v1 Int)) #200)
+#252 := (iff #203 #251)
+#249 := (iff #200 #248)
+#246 := (= #197 #245)
+#243 := (= #194 #242)
+#240 := (= #191 #239)
+#224 := (iff #175 #223)
+#221 := (iff #172 #220)
+#222 := [rewrite]: #221
+#217 := (iff #78 #216)
+#218 := [rewrite]: #217
+#225 := [monotonicity #218 #222]: #224
+#241 := [monotonicity #225]: #240
+#244 := [monotonicity #241]: #243
+#247 := [monotonicity #244]: #246
+#250 := [monotonicity #247]: #249
+#253 := [quant-intro #250]: #252
+#210 := (~ #203 #203)
+#165 := (~ #200 #200)
+#209 := [refl]: #165
+#213 := [nnf-pos #209]: #210
+#81 := (<= 0::Int #16)
+#82 := (not #81)
+#90 := (and #82 #75)
+#93 := (or #78 #90)
+#130 := (if #93 #39 #125)
+#133 := (if #20 0::Int #130)
+#136 := (if #21 #16 #133)
+#139 := (= #38 #136)
+#142 := (forall (vars (?v0 Int) (?v1 Int)) #139)
+#204 := (iff #142 #203)
+#201 := (iff #139 #200)
+#198 := (= #136 #197)
+#195 := (= #133 #194)
+#192 := (= #130 #191)
+#176 := (iff #93 #175)
+#173 := (iff #90 #172)
+#170 := (iff #82 #169)
+#167 := (iff #81 #166)
+#168 := [rewrite]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#193 := [monotonicity #177]: #192
+#196 := [monotonicity #193]: #195
+#199 := [monotonicity #196]: #198
+#202 := [monotonicity #199]: #201
+#205 := [quant-intro #202]: #204
+#31 := (- #18)
+#30 := (- #16)
+#40 := (mod #30 #31)
+#41 := (- #40)
+#24 := (< 0::Int #18)
+#26 := (< #16 0::Int)
+#27 := (and #26 #24)
+#23 := (< 0::Int #16)
+#25 := (and #23 #24)
+#28 := (or #25 #27)
+#42 := (if #28 #39 #41)
+#43 := (if #20 0::Int #42)
+#44 := (if #21 #16 #43)
+#45 := (= #38 #44)
+#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
+#143 := (iff #46 #142)
+#140 := (iff #45 #139)
+#137 := (= #44 #136)
+#134 := (= #43 #133)
+#131 := (= #42 #130)
+#128 := (= #41 #125)
+#122 := (- #119)
+#126 := (= #122 #125)
+#127 := [rewrite]: #126
+#123 := (= #41 #122)
+#120 := (= #40 #119)
+#101 := (= #31 #100)
+#102 := [rewrite]: #101
+#98 := (= #30 #97)
+#99 := [rewrite]: #98
+#121 := [monotonicity #99 #102]: #120
+#124 := [monotonicity #121]: #123
+#129 := [trans #124 #127]: #128
+#94 := (iff #28 #93)
+#91 := (iff #27 #90)
+#76 := (iff #24 #75)
+#77 := [rewrite]: #76
+#83 := (iff #26 #82)
+#87 := (iff #82 #82)
+#85 := (iff #81 #81)
+#86 := [rewrite]: #85
+#88 := [monotonicity #86]: #87
+#84 := [rewrite]: #83
+#89 := [trans #84 #88]: #83
+#92 := [monotonicity #89 #77]: #91
+#79 := (iff #25 #78)
+#72 := (iff #23 #71)
+#73 := [rewrite]: #72
+#80 := [monotonicity #73 #77]: #79
+#95 := [monotonicity #80 #92]: #94
+#132 := [monotonicity #95 #129]: #131
+#135 := [monotonicity #132]: #134
+#138 := [monotonicity #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [quant-intro #141]: #143
+#50 := [asserted]: #46
+#145 := [mp #50 #144]: #142
+#206 := [mp #145 #205]: #203
+#214 := [mp~ #206 #213]: #203
+#254 := [mp #214 #253]: #251
+#285 := [mp #254 #284]: #282
+#713 := [mp #285 #712]: #708
+#54 := -3::Int
+#57 := (f4 f5 -3::Int)
+#60 := (f3 #57 -3::Int)
+#63 := (= #60 0::Int)
+#66 := (not #63)
+#8 := 3::Int
+#9 := (- 3::Int)
+#10 := (f4 f5 #9)
+#11 := (f3 #10 #9)
+#13 := (= #11 0::Int)
+#14 := (not #13)
+#67 := (iff #14 #66)
+#64 := (iff #13 #63)
+#61 := (= #11 #60)
+#55 := (= #9 -3::Int)
+#56 := [rewrite]: #55
+#58 := (= #10 #57)
+#59 := [monotonicity #56]: #58
+#62 := [monotonicity #59 #56]: #61
+#65 := [monotonicity #62]: #64
+#68 := [monotonicity #65]: #67
+#48 := [asserted]: #14
+#69 := [mp #48 #68]: #66
+#524 := (not #708)
+#525 := (or #524 #63)
+#351 := (* -1::Int -3::Int)
+#481 := (mod #351 #351)
+#688 := (+ #60 #481)
+#362 := (= #688 0::Int)
+#378 := (mod -3::Int -3::Int)
+#357 := (* -1::Int #378)
+#692 := (+ #60 #357)
+#694 := (= #692 0::Int)
+#372 := (<= -3::Int 0::Int)
+#375 := (>= -3::Int 0::Int)
+#376 := (or #375 #372)
+#377 := (not #376)
+#373 := (or #372 #372)
+#364 := (not #373)
+#374 := (or #364 #377)
+#363 := (if #374 #694 #362)
+#286 := (= -3::Int 0::Int)
+#695 := (if #286 #63 #363)
+#371 := (= #60 -3::Int)
+#696 := (if #286 #371 #695)
+#484 := (or #524 #696)
+#534 := (iff #484 #525)
+#630 := (iff #525 #525)
+#633 := [rewrite]: #630
+#641 := (iff #696 #63)
+#636 := (if false #371 #63)
+#640 := (iff #636 #63)
+#638 := [rewrite]: #640
+#637 := (iff #696 #636)
+#482 := (iff #695 #63)
+#647 := (if false #63 #63)
+#643 := (iff #647 #63)
+#649 := [rewrite]: #643
+#651 := (iff #695 #647)
+#650 := (iff #363 #63)
+#648 := (iff #363 #647)
+#645 := (iff #362 #63)
+#502 := (= #688 #60)
+#383 := (+ #60 0::Int)
+#663 := (= #383 #60)
+#664 := [rewrite]: #663
+#660 := (= #688 #383)
+#659 := (= #481 0::Int)
+#656 := (mod 3::Int 3::Int)
+#653 := (= #656 0::Int)
+#658 := [rewrite]: #653
+#657 := (= #481 #656)
+#666 := (= #351 3::Int)
+#655 := [rewrite]: #666
+#652 := [monotonicity #655 #655]: #657
+#654 := [trans #652 #658]: #659
+#501 := [monotonicity #654]: #660
+#503 := [trans #501 #664]: #502
+#646 := [monotonicity #503]: #645
+#665 := (iff #694 #63)
+#379 := (= #692 #60)
+#384 := (= #692 #383)
+#672 := (= #357 0::Int)
+#392 := (* -1::Int 0::Int)
+#671 := (= #392 0::Int)
+#668 := [rewrite]: #671
+#393 := (= #357 #392)
+#669 := (= #378 0::Int)
+#670 := [rewrite]: #669
+#667 := [monotonicity #670]: #393
+#382 := [trans #667 #668]: #672
+#385 := [monotonicity #382]: #384
+#661 := [trans #385 #664]: #379
+#662 := [monotonicity #661]: #665
+#399 := (iff #374 false)
+#673 := (or false false)
+#397 := (iff #673 false)
+#398 := [rewrite]: #397
+#674 := (iff #374 #673)
+#684 := (iff #377 false)
+#1 := true
+#675 := (not true)
+#340 := (iff #675 false)
+#341 := [rewrite]: #340
+#326 := (iff #377 #675)
+#685 := (iff #376 true)
+#681 := (or false true)
+#320 := (iff #681 true)
+#683 := [rewrite]: #320
+#676 := (iff #376 #681)
+#693 := (iff #372 true)
+#699 := [rewrite]: #693
+#679 := (iff #375 false)
+#680 := [rewrite]: #679
+#682 := [monotonicity #680 #699]: #676
+#325 := [trans #682 #683]: #685
+#686 := [monotonicity #325]: #326
+#687 := [trans #686 #341]: #684
+#677 := (iff #364 false)
+#338 := (iff #364 #675)
+#691 := (iff #373 true)
+#689 := (or true true)
+#690 := (iff #689 true)
+#350 := [rewrite]: #690
+#349 := (iff #373 #689)
+#354 := [monotonicity #699 #699]: #349
+#334 := [trans #354 #350]: #691
+#339 := [monotonicity #334]: #338
+#678 := [trans #339 #341]: #677
+#396 := [monotonicity #678 #687]: #674
+#292 := [trans #396 #398]: #399
+#642 := [monotonicity #292 #662 #646]: #648
+#644 := [trans #642 #649]: #650
+#697 := (iff #286 false)
+#698 := [rewrite]: #697
+#480 := [monotonicity #698 #644]: #651
+#483 := [trans #480 #649]: #482
+#639 := [monotonicity #698 #483]: #637
+#523 := [trans #639 #638]: #641
+#629 := [monotonicity #523]: #534
+#518 := [trans #629 #633]: #534
+#632 := [quant-inst #54 #54]: #484
+#533 := [mp #632 #518]: #525
+[unit-resolution #533 #69 #713]: false
+bf59e99514afc31c08b47ceb56486f223b9d1199 357 0
+unsat
 #2 := false
 decl f3 :: (-> S2 Int Int)
 #21 := (:var 0 Int)
 decl f4 :: (-> S3 Int S2)
 #19 := (:var 1 Int)
 decl f5 :: S3
-#8 := f5
+#7 := f5
 #41 := (f4 f5 #19)
 #42 := (f3 #41 #21)
-#756 := (pattern #42)
+#717 := (pattern #42)
 #23 := 0::Int
-#94 := -1::Int
-#98 := (* -1::Int #21)
-#95 := (* -1::Int #19)
-#153 := (mod #95 #98)
-#268 := (+ #42 #153)
-#269 := (= #268 0::Int)
+#106 := -1::Int
+#110 := (* -1::Int #21)
+#107 := (* -1::Int #19)
+#129 := (mod #107 #110)
+#285 := (+ #42 #129)
+#286 := (= #285 0::Int)
 #43 := (mod #19 #21)
-#265 := (* -1::Int #43)
-#266 := (+ #42 #265)
-#267 := (= #266 0::Int)
-#127 := (>= #19 0::Int)
-#120 := (<= #21 0::Int)
-#212 := (or #120 #127)
-#213 := (not #212)
-#116 := (<= #19 0::Int)
-#210 := (or #116 #120)
-#211 := (not #210)
-#216 := (or #211 #213)
-#270 := (ite #216 #267 #269)
-#264 := (= #42 0::Int)
+#282 := (* -1::Int #43)
+#283 := (+ #42 #282)
+#284 := (= #283 0::Int)
+#84 := (<= #21 0::Int)
+#176 := (>= #19 0::Int)
+#229 := (or #176 #84)
+#230 := (not #229)
+#80 := (<= #19 0::Int)
+#225 := (or #80 #84)
+#226 := (not #225)
+#233 := (or #226 #230)
+#287 := (if #233 #284 #286)
+#281 := (= #42 0::Int)
 #24 := (= #19 0::Int)
-#271 := (ite #24 #264 #270)
-#263 := (= #19 #42)
+#288 := (if #24 #281 #287)
+#280 := (= #42 #19)
 #25 := (= #21 0::Int)
-#272 := (ite #25 #263 #271)
-#757 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #756) #272)
-#275 := (forall (vars (?v0 Int) (?v1 Int)) #272)
-#760 := (iff #275 #757)
-#758 := (iff #272 #272)
-#759 := [refl]: #758
-#761 := [quant-intro #759]: #760
-#159 := (* -1::Int #153)
-#232 := (ite #216 #43 #159)
-#235 := (ite #24 0::Int #232)
-#238 := (ite #25 #19 #235)
-#241 := (= #42 #238)
-#244 := (forall (vars (?v0 Int) (?v1 Int)) #241)
-#276 := (iff #244 #275)
-#273 := (iff #241 #272)
-#274 := [rewrite]: #273
-#277 := [quant-intro #274]: #276
-#128 := (not #127)
-#121 := (not #120)
-#131 := (and #121 #128)
-#117 := (not #116)
-#124 := (and #117 #121)
-#134 := (or #124 #131)
-#179 := (ite #134 #43 #159)
-#182 := (ite #24 0::Int #179)
-#185 := (ite #25 #19 #182)
-#188 := (= #42 #185)
-#191 := (forall (vars (?v0 Int) (?v1 Int)) #188)
-#245 := (iff #191 #244)
-#242 := (iff #188 #241)
-#239 := (= #185 #238)
-#236 := (= #182 #235)
-#233 := (= #179 #232)
-#217 := (iff #134 #216)
-#214 := (iff #131 #213)
-#215 := [rewrite]: #214
-#204 := (iff #124 #211)
-#205 := [rewrite]: #204
-#218 := [monotonicity #205 #215]: #217
-#234 := [monotonicity #218]: #233
-#237 := [monotonicity #234]: #236
-#240 := [monotonicity #237]: #239
-#243 := [monotonicity #240]: #242
-#246 := [quant-intro #243]: #245
-#202 := (~ #191 #191)
-#201 := (~ #188 #188)
-#198 := [refl]: #201
-#203 := [nnf-pos #198]: #202
-#35 := (- #21)
-#34 := (- #19)
-#44 := (mod #34 #35)
-#45 := (- #44)
-#28 := (< 0::Int #21)
-#30 := (< #19 0::Int)
-#31 := (and #30 #28)
-#27 := (< 0::Int #19)
-#29 := (and #27 #28)
-#32 := (or #29 #31)
-#46 := (ite #32 #43 #45)
-#47 := (ite #24 0::Int #46)
-#48 := (ite #25 #19 #47)
-#49 := (= #42 #48)
-#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
-#194 := (iff #50 #191)
-#87 := (and #28 #30)
-#91 := (or #29 #87)
-#164 := (ite #91 #43 #159)
-#167 := (ite #24 0::Int #164)
-#170 := (ite #25 #19 #167)
-#173 := (= #42 #170)
-#176 := (forall (vars (?v0 Int) (?v1 Int)) #173)
-#192 := (iff #176 #191)
-#189 := (iff #173 #188)
-#186 := (= #170 #185)
-#183 := (= #167 #182)
-#180 := (= #164 #179)
-#135 := (iff #91 #134)
-#132 := (iff #87 #131)
-#129 := (iff #30 #128)
-#130 := [rewrite]: #129
-#122 := (iff #28 #121)
-#123 := [rewrite]: #122
-#133 := [monotonicity #123 #130]: #132
-#125 := (iff #29 #124)
-#118 := (iff #27 #117)
-#119 := [rewrite]: #118
-#126 := [monotonicity #119 #123]: #125
-#136 := [monotonicity #126 #133]: #135
-#181 := [monotonicity #136]: #180
+#289 := (if #25 #280 #288)
+#718 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #717) #289)
+#292 := (forall (vars (?v0 Int) (?v1 Int)) #289)
+#721 := (iff #292 #718)
+#719 := (iff #289 #289)
+#720 := [refl]: #719
+#722 := [quant-intro #720]: #721
+#135 := (* -1::Int #129)
+#249 := (if #233 #43 #135)
+#252 := (if #24 0::Int #249)
+#255 := (if #25 #19 #252)
+#258 := (= #42 #255)
+#261 := (forall (vars (?v0 Int) (?v1 Int)) #258)
+#293 := (iff #261 #292)
+#290 := (iff #258 #289)
+#291 := [rewrite]: #290
+#294 := [quant-intro #291]: #293
+#85 := (not #84)
+#179 := (not #176)
+#182 := (and #179 #85)
+#81 := (not #80)
+#88 := (and #81 #85)
+#185 := (or #88 #182)
+#201 := (if #185 #43 #135)
+#204 := (if #24 0::Int #201)
+#207 := (if #25 #19 #204)
+#210 := (= #42 #207)
+#213 := (forall (vars (?v0 Int) (?v1 Int)) #210)
+#262 := (iff #213 #261)
+#259 := (iff #210 #258)
+#256 := (= #207 #255)
+#253 := (= #204 #252)
+#250 := (= #201 #249)
+#234 := (iff #185 #233)
+#231 := (iff #182 #230)
+#232 := [rewrite]: #231
+#227 := (iff #88 #226)
+#228 := [rewrite]: #227
+#235 := [monotonicity #228 #232]: #234
+#251 := [monotonicity #235]: #250
+#254 := [monotonicity #251]: #253
+#257 := [monotonicity #254]: #256
+#260 := [monotonicity #257]: #259
+#263 := [quant-intro #260]: #262
+#175 := (~ #213 #213)
+#220 := (~ #210 #210)
+#174 := [refl]: #220
+#223 := [nnf-pos #174]: #175
+#91 := (<= 0::Int #19)
+#92 := (not #91)
+#100 := (and #92 #85)
+#103 := (or #88 #100)
+#140 := (if #103 #43 #135)
+#143 := (if #24 0::Int #140)
+#146 := (if #25 #19 #143)
+#149 := (= #42 #146)
+#152 := (forall (vars (?v0 Int) (?v1 Int)) #149)
+#214 := (iff #152 #213)
+#211 := (iff #149 #210)
+#208 := (= #146 #207)
+#205 := (= #143 #204)
+#202 := (= #140 #201)
+#186 := (iff #103 #185)
+#183 := (iff #100 #182)
+#180 := (iff #92 #179)
+#177 := (iff #91 #176)
+#178 := [rewrite]: #177
+#181 := [monotonicity #178]: #180
 #184 := [monotonicity #181]: #183
 #187 := [monotonicity #184]: #186
-#190 := [monotonicity #187]: #189
-#193 := [quant-intro #190]: #192
-#177 := (iff #50 #176)
-#174 := (iff #49 #173)
-#171 := (= #48 #170)
-#168 := (= #47 #167)
-#165 := (= #46 #164)
-#162 := (= #45 #159)
-#156 := (- #153)
-#160 := (= #156 #159)
-#161 := [rewrite]: #160
-#157 := (= #45 #156)
-#154 := (= #44 #153)
-#99 := (= #35 #98)
-#100 := [rewrite]: #99
-#96 := (= #34 #95)
-#97 := [rewrite]: #96
-#155 := [monotonicity #97 #100]: #154
-#158 := [monotonicity #155]: #157
-#163 := [trans #158 #161]: #162
-#92 := (iff #32 #91)
-#89 := (iff #31 #87)
-#90 := [rewrite]: #89
-#93 := [monotonicity #90]: #92
-#166 := [monotonicity #93 #163]: #165
-#169 := [monotonicity #166]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [quant-intro #175]: #177
-#195 := [trans #178 #193]: #194
-#152 := [asserted]: #50
-#196 := [mp #152 #195]: #191
-#199 := [mp~ #196 #203]: #191
-#247 := [mp #199 #246]: #244
-#278 := [mp #247 #277]: #275
-#762 := [mp #278 #761]: #757
-#77 := -2::Int
-#71 := -3::Int
-#9 := 1::Int
-#10 := (f4 f5 1::Int)
-#74 := (f3 #10 -3::Int)
-#80 := (= #74 -2::Int)
-#83 := (not #80)
-#14 := 2::Int
-#15 := (- 2::Int)
-#11 := 3::Int
-#12 := (- 3::Int)
-#13 := (f3 #10 #12)
-#16 := (= #13 #15)
-#17 := (not #16)
-#84 := (iff #17 #83)
-#81 := (iff #16 #80)
-#78 := (= #15 -2::Int)
-#79 := [rewrite]: #78
-#75 := (= #13 #74)
-#72 := (= #12 -3::Int)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#82 := [monotonicity #76 #79]: #81
-#85 := [monotonicity #82]: #84
-#70 := [asserted]: #17
-#88 := [mp #70 #85]: #83
-#664 := (not #757)
-#674 := (or #664 #80)
-#336 := (* -1::Int -3::Int)
-#420 := (* -1::Int 1::Int)
-#421 := (mod #420 #336)
-#422 := (+ #74 #421)
-#413 := (= #422 0::Int)
-#424 := (mod 1::Int -3::Int)
-#425 := (* -1::Int #424)
-#426 := (+ #74 #425)
-#423 := (= #426 0::Int)
-#427 := (>= 1::Int 0::Int)
-#406 := (<= -3::Int 0::Int)
-#741 := (or #406 #427)
-#743 := (not #741)
-#400 := (<= 1::Int 0::Int)
-#530 := (or #400 #406)
-#737 := (not #530)
-#411 := (or #737 #743)
-#412 := (ite #411 #423 #413)
-#744 := (= #74 0::Int)
-#745 := (= 1::Int 0::Int)
-#746 := (ite #745 #744 #412)
-#747 := (= 1::Int #74)
-#742 := (= -3::Int 0::Int)
-#748 := (ite #742 #747 #746)
-#675 := (or #664 #748)
-#672 := (iff #675 #674)
-#666 := (iff #674 #674)
-#667 := [rewrite]: #666
-#665 := (iff #748 #80)
-#739 := (= #74 1::Int)
-#682 := (ite false #739 #80)
-#584 := (iff #682 #80)
-#585 := [rewrite]: #584
-#671 := (iff #748 #682)
-#680 := (iff #746 #80)
-#587 := (ite false #744 #80)
-#590 := (iff #587 #80)
-#683 := [rewrite]: #590
-#588 := (iff #746 #587)
-#578 := (iff #412 #80)
-#567 := (iff #412 #682)
-#678 := (iff #413 #80)
-#688 := (+ 2::Int #74)
-#573 := (= #688 0::Int)
-#681 := (iff #573 #80)
-#583 := [rewrite]: #681
-#574 := (iff #413 #573)
-#690 := (= #422 #688)
-#532 := (+ #74 2::Int)
-#689 := (= #532 #688)
-#687 := [rewrite]: #689
-#685 := (= #422 #532)
-#529 := (= #421 2::Int)
-#692 := (mod -1::Int 3::Int)
-#693 := (= #692 2::Int)
-#700 := [rewrite]: #693
-#698 := (= #421 #692)
-#697 := (= #336 3::Int)
-#691 := [rewrite]: #697
-#710 := (= #420 -1::Int)
-#714 := [rewrite]: #710
-#699 := [monotonicity #714 #691]: #698
-#531 := [trans #699 #700]: #529
-#686 := [monotonicity #531]: #685
-#572 := [trans #686 #687]: #690
-#533 := [monotonicity #572]: #574
-#679 := [trans #533 #583]: #678
-#695 := (iff #423 #739)
-#701 := (+ -1::Int #74)
-#709 := (= #701 0::Int)
-#552 := (iff #709 #739)
-#694 := [rewrite]: #552
-#550 := (iff #423 #709)
-#708 := (= #426 #701)
-#704 := (+ #74 -1::Int)
-#702 := (= #704 #701)
-#707 := [rewrite]: #702
-#705 := (= #426 #704)
-#711 := (= #425 -1::Int)
-#713 := (= #425 #420)
-#434 := (= #424 1::Int)
-#712 := [rewrite]: #434
-#428 := [monotonicity #712]: #713
-#715 := [trans #428 #714]: #711
-#706 := [monotonicity #715]: #705
-#703 := [trans #706 #707]: #708
-#551 := [monotonicity #703]: #550
-#696 := [trans #551 #694]: #695
-#432 := (iff #411 false)
-#716 := (or false false)
-#721 := (iff #716 false)
-#431 := [rewrite]: #721
-#720 := (iff #411 #716)
-#441 := (iff #743 false)
-#1 := true
-#731 := (not true)
-#734 := (iff #731 false)
-#374 := [rewrite]: #734
-#718 := (iff #743 #731)
-#448 := (iff #741 true)
-#722 := (or true true)
-#446 := (iff #722 true)
-#447 := [rewrite]: #446
-#723 := (iff #741 #722)
-#733 := (iff #427 true)
-#736 := [rewrite]: #733
-#388 := (iff #406 true)
-#389 := [rewrite]: #388
-#445 := [monotonicity #389 #736]: #723
-#342 := [trans #445 #447]: #448
-#719 := [monotonicity #342]: #718
-#442 := [trans #719 #374]: #441
-#375 := (iff #737 false)
-#369 := (iff #737 #731)
-#730 := (iff #530 true)
-#390 := (or false true)
-#728 := (iff #390 true)
-#729 := [rewrite]: #728
-#726 := (iff #530 #390)
-#724 := (iff #400 false)
-#387 := [rewrite]: #724
-#727 := [monotonicity #387 #389]: #726
-#725 := [trans #727 #729]: #730
-#732 := [monotonicity #725]: #369
-#735 := [trans #732 #374]: #375
-#717 := [monotonicity #735 #442]: #720
-#433 := [trans #717 #431]: #432
-#582 := [monotonicity #433 #696 #679]: #567
-#586 := [trans #582 #585]: #578
-#740 := (iff #745 false)
-#383 := [rewrite]: #740
-#589 := [monotonicity #383 #586]: #588
-#684 := [trans #589 #683]: #680
-#403 := (iff #747 #739)
-#399 := [rewrite]: #403
-#738 := (iff #742 false)
-#398 := [rewrite]: #738
-#673 := [monotonicity #398 #399 #684]: #671
-#662 := [trans #673 #585]: #665
-#677 := [monotonicity #662]: #672
-#668 := [trans #677 #667]: #672
-#676 := [quant-inst #9 #71]: #675
-#669 := [mp #676 #668]: #674
-[unit-resolution #669 #88 #762]: false
-unsat
-77f73bbea5ab8b6fc826eede2973becc83be2b99 338 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#17 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#38 := (f4 f5 #17)
-#39 := (f3 #38 #19)
-#778 := (pattern #39)
-#13 := 0::Int
-#109 := -1::Int
-#113 := (* -1::Int #19)
-#110 := (* -1::Int #17)
-#174 := (mod #110 #113)
-#289 := (+ #39 #174)
-#290 := (= #289 0::Int)
-#40 := (mod #17 #19)
-#286 := (* -1::Int #40)
-#287 := (+ #39 #286)
-#288 := (= #287 0::Int)
-#148 := (>= #17 0::Int)
-#141 := (<= #19 0::Int)
-#233 := (or #141 #148)
-#234 := (not #233)
-#137 := (<= #17 0::Int)
-#231 := (or #137 #141)
-#232 := (not #231)
-#237 := (or #232 #234)
-#291 := (ite #237 #288 #290)
-#285 := (= #39 0::Int)
-#21 := (= #17 0::Int)
-#292 := (ite #21 #285 #291)
-#284 := (= #17 #39)
-#22 := (= #19 0::Int)
-#293 := (ite #22 #284 #292)
-#779 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #778) #293)
-#296 := (forall (vars (?v0 Int) (?v1 Int)) #293)
-#782 := (iff #296 #779)
-#780 := (iff #293 #293)
-#781 := [refl]: #780
-#783 := [quant-intro #781]: #782
-#180 := (* -1::Int #174)
-#253 := (ite #237 #40 #180)
-#256 := (ite #21 0::Int #253)
-#259 := (ite #22 #17 #256)
-#262 := (= #39 #259)
-#265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
-#297 := (iff #265 #296)
-#294 := (iff #262 #293)
-#295 := [rewrite]: #294
-#298 := [quant-intro #295]: #297
-#149 := (not #148)
-#142 := (not #141)
-#152 := (and #142 #149)
-#138 := (not #137)
-#145 := (and #138 #142)
-#155 := (or #145 #152)
-#200 := (ite #155 #40 #180)
-#203 := (ite #21 0::Int #200)
-#206 := (ite #22 #17 #203)
-#209 := (= #39 #206)
-#212 := (forall (vars (?v0 Int) (?v1 Int)) #209)
-#266 := (iff #212 #265)
-#263 := (iff #209 #262)
-#260 := (= #206 #259)
-#257 := (= #203 #256)
-#254 := (= #200 #253)
-#238 := (iff #155 #237)
-#235 := (iff #152 #234)
-#236 := [rewrite]: #235
-#225 := (iff #145 #232)
-#226 := [rewrite]: #225
-#239 := [monotonicity #226 #236]: #238
-#255 := [monotonicity #239]: #254
-#258 := [monotonicity #255]: #257
-#261 := [monotonicity #258]: #260
-#264 := [monotonicity #261]: #263
-#267 := [quant-intro #264]: #266
-#223 := (~ #212 #212)
-#222 := (~ #209 #209)
-#219 := [refl]: #222
-#224 := [nnf-pos #219]: #223
-#32 := (- #19)
-#31 := (- #17)
-#41 := (mod #31 #32)
-#42 := (- #41)
-#25 := (< 0::Int #19)
-#27 := (< #17 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #17)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#43 := (ite #29 #40 #42)
-#44 := (ite #21 0::Int #43)
-#45 := (ite #22 #17 #44)
-#46 := (= #39 #45)
-#47 := (forall (vars (?v0 Int) (?v1 Int)) #46)
-#215 := (iff #47 #212)
-#103 := (and #25 #27)
-#106 := (or #26 #103)
-#185 := (ite #106 #40 #180)
-#94 := (= 0::Int #17)
-#188 := (ite #94 0::Int #185)
-#97 := (= 0::Int #19)
-#191 := (ite #97 #17 #188)
-#194 := (= #39 #191)
-#197 := (forall (vars (?v0 Int) (?v1 Int)) #194)
-#213 := (iff #197 #212)
-#210 := (iff #194 #209)
-#207 := (= #191 #206)
-#204 := (= #188 #203)
-#201 := (= #185 #200)
-#156 := (iff #106 #155)
-#153 := (iff #103 #152)
-#150 := (iff #27 #149)
-#151 := [rewrite]: #150
-#143 := (iff #25 #142)
-#144 := [rewrite]: #143
-#154 := [monotonicity #144 #151]: #153
-#146 := (iff #26 #145)
-#139 := (iff #24 #138)
-#140 := [rewrite]: #139
-#147 := [monotonicity #140 #144]: #146
-#157 := [monotonicity #147 #154]: #156
-#202 := [monotonicity #157]: #201
-#131 := (iff #94 #21)
-#132 := [rewrite]: #131
-#205 := [monotonicity #132 #202]: #204
-#133 := (iff #97 #22)
-#134 := [rewrite]: #133
-#208 := [monotonicity #134 #205]: #207
-#211 := [monotonicity #208]: #210
-#214 := [quant-intro #211]: #213
-#198 := (iff #47 #197)
-#195 := (iff #46 #194)
-#192 := (= #45 #191)
-#189 := (= #44 #188)
-#186 := (= #43 #185)
-#183 := (= #42 #180)
-#177 := (- #174)
-#181 := (= #177 #180)
-#182 := [rewrite]: #181
-#178 := (= #42 #177)
-#175 := (= #41 #174)
-#114 := (= #32 #113)
-#115 := [rewrite]: #114
-#111 := (= #31 #110)
-#112 := [rewrite]: #111
-#176 := [monotonicity #112 #115]: #175
-#179 := [monotonicity #176]: #178
-#184 := [trans #179 #182]: #183
-#107 := (iff #29 #106)
-#104 := (iff #28 #103)
-#105 := [rewrite]: #104
-#108 := [monotonicity #105]: #107
-#187 := [monotonicity #108 #184]: #186
-#95 := (iff #21 #94)
-#96 := [rewrite]: #95
-#190 := [monotonicity #96 #187]: #189
-#98 := (iff #22 #97)
-#99 := [rewrite]: #98
-#193 := [monotonicity #99 #190]: #192
-#196 := [monotonicity #193]: #195
-#199 := [quant-intro #196]: #198
-#216 := [trans #199 #214]: #215
-#173 := [asserted]: #47
-#217 := [mp #173 #216]: #212
-#220 := [mp~ #217 #224]: #212
-#268 := [mp #220 #267]: #265
-#299 := [mp #268 #298]: #296
-#784 := [mp #299 #783]: #779
-#68 := -3::Int
-#9 := 3::Int
-#10 := (f4 f5 3::Int)
-#71 := (f3 #10 -3::Int)
-#74 := (= #71 0::Int)
-#87 := (not #74)
-#11 := (- 3::Int)
-#12 := (f3 #10 #11)
-#14 := (= #12 0::Int)
-#15 := (not #14)
-#90 := (iff #15 #87)
-#77 := (= 0::Int #71)
-#82 := (not #77)
-#88 := (iff #82 #87)
-#85 := (iff #77 #74)
-#86 := [rewrite]: #85
-#89 := [monotonicity #86]: #88
-#83 := (iff #15 #82)
-#80 := (iff #14 #77)
-#78 := (iff #74 #77)
-#79 := [rewrite]: #78
-#75 := (iff #14 #74)
-#72 := (= #12 #71)
-#69 := (= #11 -3::Int)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73]: #75
-#81 := [trans #76 #79]: #80
-#84 := [monotonicity #81]: #83
-#91 := [trans #84 #89]: #90
-#67 := [asserted]: #15
-#92 := [mp #67 #91]: #87
-#607 := (not #779)
-#600 := (or #607 #74)
-#357 := (* -1::Int -3::Int)
-#442 := (* -1::Int 3::Int)
-#443 := (mod #442 #357)
-#444 := (+ #71 #443)
-#435 := (= #444 0::Int)
-#446 := (mod 3::Int -3::Int)
-#447 := (* -1::Int #446)
-#375 := (+ #71 #447)
-#448 := (= #375 0::Int)
-#445 := (>= 3::Int 0::Int)
-#449 := (<= -3::Int 0::Int)
-#428 := (or #449 #445)
-#763 := (not #428)
-#765 := (<= 3::Int 0::Int)
-#422 := (or #765 #449)
-#552 := (not #422)
-#759 := (or #552 #763)
-#433 := (ite #759 #448 #435)
-#434 := (= 3::Int 0::Int)
-#766 := (ite #434 #74 #433)
-#767 := (= 3::Int #71)
-#768 := (= -3::Int 0::Int)
-#769 := (ite #768 #767 #766)
-#608 := (or #607 #769)
-#610 := (iff #608 #600)
-#612 := (iff #600 #600)
-#705 := [rewrite]: #612
-#604 := (iff #769 #74)
-#420 := (= #71 3::Int)
-#605 := (ite false #420 #74)
-#704 := (iff #605 #74)
-#589 := [rewrite]: #704
-#700 := (iff #769 #605)
-#555 := (iff #766 #74)
-#707 := (ite false #74 #74)
-#711 := (iff #707 #74)
-#709 := [rewrite]: #711
-#595 := (iff #766 #707)
-#712 := (iff #433 #74)
-#708 := (iff #433 #707)
-#553 := (iff #435 #74)
-#722 := (= #444 #71)
-#737 := (+ #71 0::Int)
-#728 := (= #737 #71)
-#723 := [rewrite]: #728
-#721 := (= #444 #737)
-#714 := (= #443 0::Int)
-#716 := (mod -3::Int 3::Int)
-#719 := (= #716 0::Int)
-#713 := [rewrite]: #719
-#717 := (= #443 #716)
-#573 := (= #357 3::Int)
-#574 := [rewrite]: #573
-#731 := (= #442 -3::Int)
-#572 := [rewrite]: #731
-#718 := [monotonicity #572 #574]: #717
-#720 := [trans #718 #713]: #714
-#715 := [monotonicity #720]: #721
-#551 := [trans #715 #723]: #722
-#554 := [monotonicity #551]: #553
-#730 := (iff #448 #74)
-#724 := (= #375 #71)
-#726 := (= #375 #737)
-#736 := (= #447 0::Int)
-#456 := (* -1::Int 0::Int)
-#450 := (= #456 0::Int)
-#732 := [rewrite]: #450
-#734 := (= #447 #456)
-#454 := (= #446 0::Int)
-#455 := [rewrite]: #454
-#735 := [monotonicity #455]: #734
-#733 := [trans #735 #732]: #736
-#727 := [monotonicity #733]: #726
-#729 := [trans #727 #723]: #724
-#725 := [monotonicity #729]: #730
-#743 := (iff #759 false)
-#463 := (or false false)
-#742 := (iff #463 false)
-#739 := [rewrite]: #742
-#464 := (iff #759 #463)
-#740 := (iff #763 false)
-#1 := true
-#752 := (not true)
-#391 := (iff #752 false)
-#754 := [rewrite]: #391
-#470 := (iff #763 #752)
-#468 := (iff #428 true)
-#755 := (or true true)
-#745 := (iff #755 true)
-#467 := [rewrite]: #745
-#758 := (iff #428 #755)
-#397 := (iff #445 true)
-#757 := [rewrite]: #397
-#746 := (iff #449 true)
-#409 := [rewrite]: #746
-#744 := [monotonicity #409 #757]: #758
-#469 := [trans #744 #467]: #468
-#363 := [monotonicity #469]: #470
-#741 := [trans #363 #754]: #740
-#756 := (iff #552 false)
-#747 := (iff #552 #752)
-#750 := (iff #422 true)
-#410 := (or false true)
-#748 := (iff #410 true)
-#749 := [rewrite]: #748
-#411 := (iff #422 #410)
-#762 := (iff #765 false)
-#405 := [rewrite]: #762
-#412 := [monotonicity #405 #409]: #411
-#751 := [trans #412 #749]: #750
-#753 := [monotonicity #751]: #747
-#396 := [trans #753 #754]: #756
-#738 := [monotonicity #396 #741]: #464
-#453 := [trans #738 #739]: #743
-#710 := [monotonicity #453 #725 #554]: #708
-#594 := [trans #710 #709]: #712
-#761 := (iff #434 false)
-#421 := [rewrite]: #761
-#596 := [monotonicity #421 #594]: #595
-#703 := [trans #596 #709]: #555
-#760 := (iff #767 #420)
-#425 := [rewrite]: #760
-#764 := (iff #768 false)
-#770 := [rewrite]: #764
-#701 := [monotonicity #770 #425 #703]: #700
-#606 := [trans #701 #589]: #604
-#611 := [monotonicity #606]: #610
-#702 := [trans #611 #705]: #610
-#609 := [quant-inst #9 #68]: #608
-#706 := [mp #609 #702]: #600
-[unit-resolution #706 #92 #784]: false
-unsat
-adc5ede35f5125662d49d00be9296579ea259f42 344 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#21 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#19 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#41 := (f4 f5 #19)
-#42 := (f3 #41 #21)
-#755 := (pattern #42)
-#23 := 0::Int
-#77 := -1::Int
-#97 := (* -1::Int #21)
-#94 := (* -1::Int #19)
-#152 := (mod #94 #97)
-#267 := (+ #42 #152)
-#268 := (= #267 0::Int)
-#43 := (mod #19 #21)
-#264 := (* -1::Int #43)
-#265 := (+ #42 #264)
-#266 := (= #265 0::Int)
-#126 := (>= #19 0::Int)
-#119 := (<= #21 0::Int)
-#211 := (or #119 #126)
-#212 := (not #211)
-#115 := (<= #19 0::Int)
-#209 := (or #115 #119)
-#210 := (not #209)
-#215 := (or #210 #212)
-#269 := (ite #215 #266 #268)
-#263 := (= #42 0::Int)
-#24 := (= #19 0::Int)
-#270 := (ite #24 #263 #269)
-#262 := (= #19 #42)
-#25 := (= #21 0::Int)
-#271 := (ite #25 #262 #270)
-#756 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #755) #271)
-#274 := (forall (vars (?v0 Int) (?v1 Int)) #271)
-#759 := (iff #274 #756)
-#757 := (iff #271 #271)
-#758 := [refl]: #757
-#760 := [quant-intro #758]: #759
-#158 := (* -1::Int #152)
-#231 := (ite #215 #43 #158)
-#234 := (ite #24 0::Int #231)
-#237 := (ite #25 #19 #234)
-#240 := (= #42 #237)
-#243 := (forall (vars (?v0 Int) (?v1 Int)) #240)
-#275 := (iff #243 #274)
-#272 := (iff #240 #271)
-#273 := [rewrite]: #272
-#276 := [quant-intro #273]: #275
-#127 := (not #126)
-#120 := (not #119)
-#130 := (and #120 #127)
-#116 := (not #115)
-#123 := (and #116 #120)
-#133 := (or #123 #130)
-#178 := (ite #133 #43 #158)
-#181 := (ite #24 0::Int #178)
-#184 := (ite #25 #19 #181)
-#187 := (= #42 #184)
-#190 := (forall (vars (?v0 Int) (?v1 Int)) #187)
-#244 := (iff #190 #243)
-#241 := (iff #187 #240)
-#238 := (= #184 #237)
-#235 := (= #181 #234)
-#232 := (= #178 #231)
-#216 := (iff #133 #215)
-#213 := (iff #130 #212)
-#214 := [rewrite]: #213
-#203 := (iff #123 #210)
-#204 := [rewrite]: #203
-#217 := [monotonicity #204 #214]: #216
-#233 := [monotonicity #217]: #232
-#236 := [monotonicity #233]: #235
-#239 := [monotonicity #236]: #238
-#242 := [monotonicity #239]: #241
-#245 := [quant-intro #242]: #244
-#201 := (~ #190 #190)
-#200 := (~ #187 #187)
-#197 := [refl]: #200
-#202 := [nnf-pos #197]: #201
+#203 := [monotonicity #187]: #202
+#206 := [monotonicity #203]: #205
+#209 := [monotonicity #206]: #208
+#212 := [monotonicity #209]: #211
+#215 := [quant-intro #212]: #214
 #35 := (- #21)
 #34 := (- #19)
 #44 := (mod #34 #35)
@@ -40195,6677 +41012,4596 @@
 #27 := (< 0::Int #19)
 #29 := (and #27 #28)
 #32 := (or #29 #31)
-#46 := (ite #32 #43 #45)
-#47 := (ite #24 0::Int #46)
-#48 := (ite #25 #19 #47)
+#46 := (if #32 #43 #45)
+#47 := (if #24 0::Int #46)
+#48 := (if #25 #19 #47)
 #49 := (= #42 #48)
 #50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
-#193 := (iff #50 #190)
-#87 := (and #28 #30)
-#91 := (or #29 #87)
-#163 := (ite #91 #43 #158)
-#166 := (ite #24 0::Int #163)
-#169 := (ite #25 #19 #166)
-#172 := (= #42 #169)
-#175 := (forall (vars (?v0 Int) (?v1 Int)) #172)
-#191 := (iff #175 #190)
-#188 := (iff #172 #187)
-#185 := (= #169 #184)
-#182 := (= #166 #181)
-#179 := (= #163 #178)
-#134 := (iff #91 #133)
-#131 := (iff #87 #130)
-#128 := (iff #30 #127)
-#129 := [rewrite]: #128
-#121 := (iff #28 #120)
-#122 := [rewrite]: #121
-#132 := [monotonicity #122 #129]: #131
-#124 := (iff #29 #123)
-#117 := (iff #27 #116)
-#118 := [rewrite]: #117
-#125 := [monotonicity #118 #122]: #124
-#135 := [monotonicity #125 #132]: #134
-#180 := [monotonicity #135]: #179
-#183 := [monotonicity #180]: #182
-#186 := [monotonicity #183]: #185
-#189 := [monotonicity #186]: #188
-#192 := [quant-intro #189]: #191
-#176 := (iff #50 #175)
-#173 := (iff #49 #172)
-#170 := (= #48 #169)
-#167 := (= #47 #166)
-#164 := (= #46 #163)
-#161 := (= #45 #158)
-#155 := (- #152)
-#159 := (= #155 #158)
-#160 := [rewrite]: #159
-#156 := (= #45 #155)
-#153 := (= #44 #152)
-#98 := (= #35 #97)
-#99 := [rewrite]: #98
-#95 := (= #34 #94)
+#153 := (iff #50 #152)
+#150 := (iff #49 #149)
+#147 := (= #48 #146)
+#144 := (= #47 #143)
+#141 := (= #46 #140)
+#138 := (= #45 #135)
+#132 := (- #129)
+#136 := (= #132 #135)
+#137 := [rewrite]: #136
+#133 := (= #45 #132)
+#130 := (= #44 #129)
+#111 := (= #35 #110)
+#112 := [rewrite]: #111
+#108 := (= #34 #107)
+#109 := [rewrite]: #108
+#131 := [monotonicity #109 #112]: #130
+#134 := [monotonicity #131]: #133
+#139 := [trans #134 #137]: #138
+#104 := (iff #32 #103)
+#101 := (iff #31 #100)
+#86 := (iff #28 #85)
+#87 := [rewrite]: #86
+#93 := (iff #30 #92)
+#97 := (iff #92 #92)
+#95 := (iff #91 #91)
 #96 := [rewrite]: #95
-#154 := [monotonicity #96 #99]: #153
-#157 := [monotonicity #154]: #156
-#162 := [trans #157 #160]: #161
-#92 := (iff #32 #91)
-#89 := (iff #31 #87)
-#90 := [rewrite]: #89
-#93 := [monotonicity #90]: #92
-#165 := [monotonicity #93 #162]: #164
-#168 := [monotonicity #165]: #167
-#171 := [monotonicity #168]: #170
-#174 := [monotonicity #171]: #173
-#177 := [quant-intro #174]: #176
-#194 := [trans #177 #192]: #193
-#151 := [asserted]: #50
-#195 := [mp #151 #194]: #190
-#198 := [mp~ #195 #202]: #190
-#246 := [mp #198 #245]: #243
-#277 := [mp #246 #276]: #274
-#761 := [mp #277 #760]: #756
-#71 := -3::Int
-#9 := 5::Int
-#10 := (f4 f5 5::Int)
-#74 := (f3 #10 -3::Int)
-#80 := (= #74 -1::Int)
-#83 := (not #80)
-#14 := 1::Int
-#15 := (- 1::Int)
+#98 := [monotonicity #96]: #97
+#94 := [rewrite]: #93
+#99 := [trans #94 #98]: #93
+#102 := [monotonicity #99 #87]: #101
+#89 := (iff #29 #88)
+#82 := (iff #27 #81)
+#83 := [rewrite]: #82
+#90 := [monotonicity #83 #87]: #89
+#105 := [monotonicity #90 #102]: #104
+#142 := [monotonicity #105 #139]: #141
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#151 := [monotonicity #148]: #150
+#154 := [quant-intro #151]: #153
+#54 := [asserted]: #50
+#155 := [mp #54 #154]: #152
+#216 := [mp #155 #215]: #213
+#224 := [mp~ #216 #223]: #213
+#264 := [mp #224 #263]: #261
+#295 := [mp #264 #294]: #292
+#723 := [mp #295 #722]: #718
+#70 := -2::Int
+#64 := -3::Int
+#58 := -5::Int
+#61 := (f4 f5 -5::Int)
+#67 := (f3 #61 -3::Int)
+#73 := (= #67 -2::Int)
+#76 := (not #73)
+#14 := 2::Int
+#15 := (- 2::Int)
 #11 := 3::Int
 #12 := (- 3::Int)
+#8 := 5::Int
+#9 := (- 5::Int)
+#10 := (f4 f5 #9)
 #13 := (f3 #10 #12)
 #16 := (= #13 #15)
 #17 := (not #16)
-#84 := (iff #17 #83)
-#81 := (iff #16 #80)
-#78 := (= #15 -1::Int)
-#79 := [rewrite]: #78
-#75 := (= #13 #74)
-#72 := (= #12 -3::Int)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#82 := [monotonicity #76 #79]: #81
-#85 := [monotonicity #82]: #84
-#70 := [asserted]: #17
-#88 := [mp #70 #85]: #83
-#662 := (not #756)
-#669 := (or #662 #80)
-#335 := (* -1::Int -3::Int)
-#419 := (* -1::Int 5::Int)
-#420 := (mod #419 #335)
-#421 := (+ #74 #420)
-#412 := (= #421 0::Int)
-#423 := (mod 5::Int -3::Int)
-#424 := (* -1::Int #423)
-#425 := (+ #74 #424)
-#422 := (= #425 0::Int)
-#426 := (>= 5::Int 0::Int)
-#405 := (<= -3::Int 0::Int)
-#740 := (or #405 #426)
-#742 := (not #740)
-#399 := (<= 5::Int 0::Int)
-#529 := (or #399 #405)
-#736 := (not #529)
-#410 := (or #736 #742)
-#411 := (ite #410 #422 #412)
-#743 := (= #74 0::Int)
-#744 := (= 5::Int 0::Int)
-#745 := (ite #744 #743 #411)
-#746 := (= 5::Int #74)
-#741 := (= -3::Int 0::Int)
-#747 := (ite #741 #746 #745)
-#653 := (or #662 #747)
-#656 := (iff #653 #669)
-#658 := (iff #669 #669)
-#659 := [rewrite]: #658
-#667 := (iff #747 #80)
-#738 := (= #74 5::Int)
-#675 := (ite false #738 #80)
-#665 := (iff #675 #80)
-#666 := [rewrite]: #665
-#671 := (iff #747 #675)
-#673 := (iff #745 #80)
-#670 := (ite false #743 #80)
-#661 := (iff #670 #80)
-#663 := [rewrite]: #661
-#672 := (iff #745 #670)
-#679 := (iff #411 #80)
-#433 := 2::Int
-#695 := (= #74 2::Int)
-#586 := (ite false #695 #80)
-#589 := (iff #586 #80)
-#682 := [rewrite]: #589
-#587 := (iff #411 #586)
-#577 := (iff #412 #80)
-#532 := (+ 1::Int #74)
-#681 := (= #532 0::Int)
-#583 := (iff #681 #80)
-#584 := [rewrite]: #583
-#566 := (iff #412 #681)
-#677 := (= #421 #532)
-#571 := (+ #74 1::Int)
-#680 := (= #571 #532)
-#582 := [rewrite]: #680
-#572 := (= #421 #571)
-#686 := (= #420 1::Int)
-#698 := -5::Int
-#531 := (mod -5::Int 3::Int)
-#687 := (= #531 1::Int)
-#688 := [rewrite]: #687
-#684 := (= #420 #531)
-#528 := (= #335 3::Int)
-#530 := [rewrite]: #528
-#692 := (= #419 -5::Int)
-#699 := [rewrite]: #692
-#685 := [monotonicity #699 #530]: #684
-#689 := [trans #685 #688]: #686
-#573 := [monotonicity #689]: #572
-#678 := [trans #573 #582]: #677
-#581 := [monotonicity #678]: #566
-#585 := [trans #581 #584]: #577
-#691 := (iff #422 #695)
-#710 := -2::Int
-#707 := (+ -2::Int #74)
-#551 := (= #707 0::Int)
-#696 := (iff #551 #695)
-#690 := [rewrite]: #696
-#693 := (iff #422 #551)
-#549 := (= #425 #707)
-#700 := (+ #74 -2::Int)
-#702 := (= #700 #707)
-#708 := [rewrite]: #702
-#701 := (= #425 #700)
-#704 := (= #424 -2::Int)
-#427 := (* -1::Int 2::Int)
-#714 := (= #427 -2::Int)
-#703 := [rewrite]: #714
-#709 := (= #424 #427)
-#711 := (= #423 2::Int)
-#712 := [rewrite]: #711
-#713 := [monotonicity #712]: #709
-#705 := [trans #713 #703]: #704
-#706 := [monotonicity #705]: #701
-#550 := [trans #706 #708]: #549
-#694 := [monotonicity #550]: #693
-#697 := [trans #694 #690]: #691
-#431 := (iff #410 false)
-#715 := (or false false)
-#720 := (iff #715 false)
-#430 := [rewrite]: #720
-#719 := (iff #410 #715)
-#440 := (iff #742 false)
-#1 := true
-#730 := (not true)
-#733 := (iff #730 false)
-#373 := [rewrite]: #733
-#717 := (iff #742 #730)
-#447 := (iff #740 true)
-#721 := (or true true)
-#445 := (iff #721 true)
-#446 := [rewrite]: #445
-#722 := (iff #740 #721)
-#732 := (iff #426 true)
-#735 := [rewrite]: #732
-#387 := (iff #405 true)
-#388 := [rewrite]: #387
-#444 := [monotonicity #388 #735]: #722
-#341 := [trans #444 #446]: #447
-#718 := [monotonicity #341]: #717
-#441 := [trans #718 #373]: #440
-#374 := (iff #736 false)
-#368 := (iff #736 #730)
-#729 := (iff #529 true)
-#389 := (or false true)
-#727 := (iff #389 true)
-#728 := [rewrite]: #727
-#725 := (iff #529 #389)
-#723 := (iff #399 false)
-#386 := [rewrite]: #723
-#726 := [monotonicity #386 #388]: #725
-#724 := [trans #726 #728]: #729
-#731 := [monotonicity #724]: #368
-#734 := [trans #731 #373]: #374
-#716 := [monotonicity #734 #441]: #719
-#432 := [trans #716 #430]: #431
-#588 := [monotonicity #432 #697 #585]: #587
-#683 := [trans #588 #682]: #679
-#739 := (iff #744 false)
-#382 := [rewrite]: #739
-#664 := [monotonicity #382 #683]: #672
-#674 := [trans #664 #663]: #673
-#402 := (iff #746 #738)
-#398 := [rewrite]: #402
-#737 := (iff #741 false)
-#397 := [rewrite]: #737
-#676 := [monotonicity #397 #398 #674]: #671
-#668 := [trans #676 #666]: #667
-#657 := [monotonicity #668]: #656
-#655 := [trans #657 #659]: #656
-#654 := [quant-inst #9 #71]: #653
-#660 := [mp #654 #655]: #669
-[unit-resolution #660 #88 #761]: false
-unsat
-61bb705d2a320e5bbcedd3ebd2ddae1fc4faa170 356 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#20 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#18 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#40 := (f4 f5 #18)
-#41 := (f3 #40 #20)
-#766 := (pattern #41)
-#22 := 0::Int
-#70 := -1::Int
-#108 := (* -1::Int #20)
-#105 := (* -1::Int #18)
-#163 := (mod #105 #108)
-#278 := (+ #41 #163)
+#77 := (iff #17 #76)
+#74 := (iff #16 #73)
+#71 := (= #15 -2::Int)
+#72 := [rewrite]: #71
+#68 := (= #13 #67)
+#65 := (= #12 -3::Int)
+#66 := [rewrite]: #65
+#62 := (= #10 #61)
+#59 := (= #9 -5::Int)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#69 := [monotonicity #63 #66]: #68
+#75 := [monotonicity #69 #72]: #74
+#78 := [monotonicity #75]: #77
+#52 := [asserted]: #17
+#79 := [mp #52 #78]: #76
+#633 := (not #718)
+#638 := (or #633 #73)
+#373 := (* -1::Int -3::Int)
+#372 := (* -1::Int -5::Int)
+#705 := (mod #372 #373)
+#706 := (+ #67 #705)
+#707 := (= #706 0::Int)
+#704 := (mod -5::Int -3::Int)
+#361 := (* -1::Int #704)
+#491 := (+ #67 #361)
+#698 := (= #491 0::Int)
+#385 := (<= -3::Int 0::Int)
+#384 := (>= -5::Int 0::Int)
+#388 := (or #384 #385)
+#367 := (not #388)
+#374 := (<= -5::Int 0::Int)
+#386 := (or #374 #385)
+#387 := (not #386)
+#702 := (or #387 #367)
+#708 := (if #702 #698 #707)
+#383 := (= #67 0::Int)
+#382 := (= -5::Int 0::Int)
+#703 := (if #382 #383 #708)
+#381 := (= #67 -5::Int)
+#296 := (= -3::Int 0::Int)
+#709 := (if #296 #381 #703)
+#627 := (or #633 #709)
+#629 := (iff #627 #638)
+#624 := (iff #638 #638)
+#631 := [rewrite]: #624
+#636 := (iff #709 #73)
+#634 := (if false #381 #73)
+#625 := (iff #634 #73)
+#635 := [rewrite]: #625
+#626 := (iff #709 #634)
+#645 := (iff #703 #73)
+#549 := (if false #383 #73)
+#644 := (iff #549 #73)
+#641 := [rewrite]: #644
+#550 := (iff #703 #549)
+#547 := (iff #708 #73)
+#314 := 1::Int
+#511 := (= #67 1::Int)
+#528 := (if false #511 #73)
+#546 := (iff #528 #73)
+#539 := [rewrite]: #546
+#543 := (iff #708 #528)
+#640 := (iff #707 #73)
+#650 := (+ 2::Int #67)
+#535 := (= #650 0::Int)
+#544 := (iff #535 #73)
+#639 := [rewrite]: #544
+#494 := (iff #707 #535)
+#533 := (= #706 #650)
+#646 := (+ #67 2::Int)
+#648 := (= #646 #650)
+#651 := [rewrite]: #648
+#647 := (= #706 #646)
+#492 := (= #705 2::Int)
+#659 := (mod 5::Int 3::Int)
+#661 := (= #659 2::Int)
+#490 := [rewrite]: #661
+#660 := (= #705 #659)
+#652 := (= #373 3::Int)
+#653 := [rewrite]: #652
+#657 := (= #372 5::Int)
+#658 := [rewrite]: #657
+#654 := [monotonicity #658 #653]: #660
+#493 := [trans #654 #490]: #492
+#649 := [monotonicity #493]: #647
+#534 := [trans #649 #651]: #533
+#642 := [monotonicity #534]: #494
+#643 := [trans #642 #639]: #640
+#655 := (iff #698 #511)
+#666 := (+ -1::Int #67)
+#669 := (= #666 0::Int)
+#512 := (iff #669 #511)
+#513 := [rewrite]: #512
+#664 := (iff #698 #669)
+#663 := (= #491 #666)
+#672 := (+ #67 -1::Int)
+#667 := (= #672 #666)
+#662 := [rewrite]: #667
+#676 := (= #491 #672)
+#671 := (= #361 -1::Int)
+#394 := (* -1::Int 1::Int)
+#674 := (= #394 -1::Int)
+#389 := [rewrite]: #674
+#395 := (= #361 #394)
+#392 := (= #704 1::Int)
+#393 := [rewrite]: #392
+#673 := [monotonicity #393]: #395
+#675 := [trans #673 #389]: #671
+#665 := [monotonicity #675]: #676
+#668 := [trans #665 #662]: #663
+#670 := [monotonicity #668]: #664
+#656 := [trans #670 #513]: #655
+#678 := (iff #702 false)
+#680 := (or false false)
+#677 := (iff #680 false)
+#681 := [rewrite]: #677
+#402 := (iff #702 #680)
+#302 := (iff #367 false)
+#1 := true
+#690 := (not true)
+#692 := (iff #690 false)
+#330 := [rewrite]: #692
+#408 := (iff #367 #690)
+#406 := (iff #388 true)
+#696 := (or false true)
+#683 := (iff #696 true)
+#684 := [rewrite]: #683
+#694 := (iff #388 #696)
+#344 := (iff #385 true)
+#685 := [rewrite]: #344
+#335 := (iff #384 false)
+#336 := [rewrite]: #335
+#697 := [monotonicity #336 #685]: #694
+#407 := [trans #697 #684]: #406
+#409 := [monotonicity #407]: #408
+#679 := [trans #409 #330]: #302
+#693 := (iff #387 false)
+#691 := (iff #387 #690)
+#688 := (iff #386 true)
+#348 := (or true true)
+#351 := (iff #348 true)
+#687 := [rewrite]: #351
+#349 := (iff #386 #348)
+#360 := (iff #374 true)
+#701 := [rewrite]: #360
+#350 := [monotonicity #701 #685]: #349
+#689 := [trans #350 #687]: #688
+#686 := [monotonicity #689]: #691
+#695 := [trans #686 #330]: #693
+#403 := [monotonicity #695 #679]: #402
+#682 := [trans #403 #681]: #678
+#545 := [monotonicity #682 #656 #643]: #543
+#548 := [trans #545 #539]: #547
+#364 := (iff #382 false)
+#700 := [rewrite]: #364
+#551 := [monotonicity #700 #548]: #550
+#632 := [trans #551 #641]: #645
+#699 := (iff #296 false)
+#359 := [rewrite]: #699
+#623 := [monotonicity #359 #632]: #626
+#637 := [trans #623 #635]: #636
+#630 := [monotonicity #637]: #629
+#615 := [trans #630 #631]: #629
+#628 := [quant-inst #58 #64]: #627
+#616 := [mp #628 #615]: #638
+[unit-resolution #616 #79 #723]: false
+ef703ebceb3fa98287d10eb7ea1d68a68c17e1d3 342 0
+unsat
+#2 := false
+#19 := 0::Int
+decl f6 :: Int
+#8 := f6
+#369 := (<= f6 0::Int)
+#379 := (>= f6 0::Int)
+#690 := (not #379)
+#346 := (not #369)
+#691 := (or #346 #690)
+#653 := (not #691)
+#10 := 3::Int
+#699 := (mod f6 3::Int)
+#97 := -1::Int
+#356 := (* -1::Int #699)
+decl f3 :: (-> S2 Int Int)
+decl f4 :: (-> S3 Int S2)
+decl f5 :: S3
+#7 := f5
+#9 := (f4 f5 f6)
+#11 := (f3 #9 3::Int)
+#486 := (+ #11 #356)
+#693 := (= #486 0::Int)
+#644 := (not #693)
+#654 := (<= #486 0::Int)
+#599 := (not #654)
+#603 := (>= #699 3::Int)
+#604 := (not #603)
+#1 := true
+#164 := [true-axiom]: true
+#594 := (or false #604)
+#595 := [th-lemma arith]: #594
+#596 := [unit-resolution #595 #164]: #604
+#597 := [hypothesis]: #654
+#167 := (>= #11 3::Int)
+#54 := (<= 3::Int #11)
+#166 := (iff #54 #167)
+#168 := [rewrite]: #166
+#12 := (< #11 3::Int)
+#13 := (not #12)
+#68 := (iff #13 #54)
+#55 := (not #54)
+#63 := (not #55)
+#66 := (iff #63 #54)
+#67 := [rewrite]: #66
+#64 := (iff #13 #63)
+#56 := (iff #12 #55)
+#60 := (iff #55 #55)
+#58 := (iff #54 #54)
+#59 := [rewrite]: #58
+#61 := [monotonicity #59]: #60
+#57 := [rewrite]: #56
+#62 := [trans #57 #61]: #56
+#65 := [monotonicity #62]: #64
+#69 := [trans #65 #67]: #68
+#48 := [asserted]: #13
+#70 := [mp #48 #69]: #54
+#169 := [mp #70 #168]: #167
+#598 := [th-lemma arith farkas -1 1 1 #169 #597 #596]: false
+#600 := [lemma #598]: #599
+#632 := (or #644 #654)
+#534 := [th-lemma arith triangle-eq]: #632
+#629 := [unit-resolution #534 #600]: #644
+#592 := (or #653 #693)
+#678 := -3::Int
+#367 := (* -1::Int f6)
+#402 := (mod #367 -3::Int)
+#297 := (+ #11 #402)
+#397 := (= #297 0::Int)
+#676 := (if #691 #693 #397)
+#378 := (= #11 0::Int)
+#377 := (= f6 0::Int)
+#387 := (if #377 #378 #676)
+#17 := (:var 0 Int)
+#15 := (:var 1 Int)
+#37 := (f4 f5 #15)
+#38 := (f3 #37 #17)
+#712 := (pattern #38)
+#101 := (* -1::Int #17)
+#98 := (* -1::Int #15)
+#120 := (mod #98 #101)
+#280 := (+ #38 #120)
+#281 := (= #280 0::Int)
+#39 := (mod #15 #17)
+#277 := (* -1::Int #39)
+#278 := (+ #38 #277)
 #279 := (= #278 0::Int)
-#42 := (mod #18 #20)
-#275 := (* -1::Int #42)
-#276 := (+ #41 #275)
-#277 := (= #276 0::Int)
-#137 := (>= #18 0::Int)
-#130 := (<= #20 0::Int)
-#222 := (or #130 #137)
-#223 := (not #222)
-#126 := (<= #18 0::Int)
-#220 := (or #126 #130)
+#75 := (<= #17 0::Int)
+#171 := (>= #15 0::Int)
+#224 := (or #171 #75)
+#225 := (not #224)
+#71 := (<= #15 0::Int)
+#220 := (or #71 #75)
 #221 := (not #220)
-#226 := (or #221 #223)
-#280 := (ite #226 #277 #279)
-#274 := (= #41 0::Int)
-#23 := (= #18 0::Int)
-#281 := (ite #23 #274 #280)
-#273 := (= #18 #41)
-#24 := (= #20 0::Int)
-#282 := (ite #24 #273 #281)
-#767 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #766) #282)
-#285 := (forall (vars (?v0 Int) (?v1 Int)) #282)
-#770 := (iff #285 #767)
-#768 := (iff #282 #282)
-#769 := [refl]: #768
-#771 := [quant-intro #769]: #770
-#169 := (* -1::Int #163)
-#242 := (ite #226 #42 #169)
-#245 := (ite #23 0::Int #242)
-#248 := (ite #24 #18 #245)
-#251 := (= #41 #248)
-#254 := (forall (vars (?v0 Int) (?v1 Int)) #251)
-#286 := (iff #254 #285)
-#283 := (iff #251 #282)
-#284 := [rewrite]: #283
-#287 := [quant-intro #284]: #286
-#138 := (not #137)
-#131 := (not #130)
-#141 := (and #131 #138)
-#127 := (not #126)
-#134 := (and #127 #131)
-#144 := (or #134 #141)
-#189 := (ite #144 #42 #169)
-#192 := (ite #23 0::Int #189)
-#195 := (ite #24 #18 #192)
-#198 := (= #41 #195)
-#201 := (forall (vars (?v0 Int) (?v1 Int)) #198)
-#255 := (iff #201 #254)
-#252 := (iff #198 #251)
-#249 := (= #195 #248)
-#246 := (= #192 #245)
-#243 := (= #189 #242)
-#227 := (iff #144 #226)
-#224 := (iff #141 #223)
-#225 := [rewrite]: #224
-#214 := (iff #134 #221)
-#215 := [rewrite]: #214
-#228 := [monotonicity #215 #225]: #227
-#244 := [monotonicity #228]: #243
-#247 := [monotonicity #244]: #246
-#250 := [monotonicity #247]: #249
-#253 := [monotonicity #250]: #252
-#256 := [quant-intro #253]: #255
-#212 := (~ #201 #201)
-#211 := (~ #198 #198)
-#208 := [refl]: #211
-#213 := [nnf-pos #208]: #212
-#34 := (- #20)
-#33 := (- #18)
-#43 := (mod #33 #34)
-#44 := (- #43)
-#27 := (< 0::Int #20)
-#29 := (< #18 0::Int)
-#30 := (and #29 #27)
-#26 := (< 0::Int #18)
-#28 := (and #26 #27)
-#31 := (or #28 #30)
-#45 := (ite #31 #42 #44)
-#46 := (ite #23 0::Int #45)
-#47 := (ite #24 #18 #46)
-#48 := (= #41 #47)
-#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
-#204 := (iff #49 #201)
-#99 := (and #27 #29)
-#102 := (or #28 #99)
-#174 := (ite #102 #42 #169)
-#177 := (ite #23 0::Int #174)
-#180 := (ite #24 #18 #177)
-#183 := (= #41 #180)
-#186 := (forall (vars (?v0 Int) (?v1 Int)) #183)
-#202 := (iff #186 #201)
-#199 := (iff #183 #198)
-#196 := (= #180 #195)
-#193 := (= #177 #192)
-#190 := (= #174 #189)
-#145 := (iff #102 #144)
-#142 := (iff #99 #141)
-#139 := (iff #29 #138)
-#140 := [rewrite]: #139
-#132 := (iff #27 #131)
-#133 := [rewrite]: #132
-#143 := [monotonicity #133 #140]: #142
-#135 := (iff #28 #134)
-#128 := (iff #26 #127)
-#129 := [rewrite]: #128
-#136 := [monotonicity #129 #133]: #135
-#146 := [monotonicity #136 #143]: #145
-#191 := [monotonicity #146]: #190
-#194 := [monotonicity #191]: #193
-#197 := [monotonicity #194]: #196
-#200 := [monotonicity #197]: #199
-#203 := [quant-intro #200]: #202
-#187 := (iff #49 #186)
-#184 := (iff #48 #183)
-#181 := (= #47 #180)
-#178 := (= #46 #177)
-#175 := (= #45 #174)
-#172 := (= #44 #169)
-#166 := (- #163)
-#170 := (= #166 #169)
-#171 := [rewrite]: #170
-#167 := (= #44 #166)
-#164 := (= #43 #163)
-#109 := (= #34 #108)
-#110 := [rewrite]: #109
-#106 := (= #33 #105)
-#107 := [rewrite]: #106
-#165 := [monotonicity #107 #110]: #164
-#168 := [monotonicity #165]: #167
-#173 := [trans #168 #171]: #172
-#103 := (iff #31 #102)
-#100 := (iff #30 #99)
-#101 := [rewrite]: #100
-#104 := [monotonicity #101]: #103
-#176 := [monotonicity #104 #173]: #175
+#228 := (or #221 #225)
+#282 := (if #228 #279 #281)
+#276 := (= #38 0::Int)
+#20 := (= #15 0::Int)
+#283 := (if #20 #276 #282)
+#275 := (= #38 #15)
+#21 := (= #17 0::Int)
+#284 := (if #21 #275 #283)
+#713 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #712) #284)
+#287 := (forall (vars (?v0 Int) (?v1 Int)) #284)
+#716 := (iff #287 #713)
+#714 := (iff #284 #284)
+#715 := [refl]: #714
+#717 := [quant-intro #715]: #716
+#126 := (* -1::Int #120)
+#244 := (if #228 #39 #126)
+#247 := (if #20 0::Int #244)
+#250 := (if #21 #15 #247)
+#253 := (= #38 #250)
+#256 := (forall (vars (?v0 Int) (?v1 Int)) #253)
+#288 := (iff #256 #287)
+#285 := (iff #253 #284)
+#286 := [rewrite]: #285
+#289 := [quant-intro #286]: #288
+#76 := (not #75)
+#174 := (not #171)
+#177 := (and #174 #76)
+#72 := (not #71)
+#79 := (and #72 #76)
+#180 := (or #79 #177)
+#196 := (if #180 #39 #126)
+#199 := (if #20 0::Int #196)
+#202 := (if #21 #15 #199)
+#205 := (= #38 #202)
+#208 := (forall (vars (?v0 Int) (?v1 Int)) #205)
+#257 := (iff #208 #256)
+#254 := (iff #205 #253)
+#251 := (= #202 #250)
+#248 := (= #199 #247)
+#245 := (= #196 #244)
+#229 := (iff #180 #228)
+#226 := (iff #177 #225)
+#227 := [rewrite]: #226
+#222 := (iff #79 #221)
+#223 := [rewrite]: #222
+#230 := [monotonicity #223 #227]: #229
+#246 := [monotonicity #230]: #245
+#249 := [monotonicity #246]: #248
+#252 := [monotonicity #249]: #251
+#255 := [monotonicity #252]: #254
+#258 := [quant-intro #255]: #257
+#215 := (~ #208 #208)
+#170 := (~ #205 #205)
+#214 := [refl]: #170
+#218 := [nnf-pos #214]: #215
+#82 := (<= 0::Int #15)
+#83 := (not #82)
+#91 := (and #83 #76)
+#94 := (or #79 #91)
+#131 := (if #94 #39 #126)
+#134 := (if #20 0::Int #131)
+#137 := (if #21 #15 #134)
+#140 := (= #38 #137)
+#143 := (forall (vars (?v0 Int) (?v1 Int)) #140)
+#209 := (iff #143 #208)
+#206 := (iff #140 #205)
+#203 := (= #137 #202)
+#200 := (= #134 #199)
+#197 := (= #131 #196)
+#181 := (iff #94 #180)
+#178 := (iff #91 #177)
+#175 := (iff #83 #174)
+#172 := (iff #82 #171)
+#173 := [rewrite]: #172
+#176 := [monotonicity #173]: #175
 #179 := [monotonicity #176]: #178
 #182 := [monotonicity #179]: #181
-#185 := [monotonicity #182]: #184
-#188 := [quant-intro #185]: #187
-#205 := [trans #188 #203]: #204
-#162 := [asserted]: #49
-#206 := [mp #162 #205]: #201
-#209 := [mp~ #206 #213]: #201
-#257 := [mp #209 #256]: #254
-#288 := [mp #257 #287]: #285
-#772 := [mp #288 #771]: #767
-#14 := 2::Int
-#12 := 3::Int
-#73 := (f4 f5 -1::Int)
-#76 := (f3 #73 3::Int)
-#79 := (= #76 2::Int)
-#92 := (not #79)
-#9 := 1::Int
-#10 := (- 1::Int)
-#11 := (f4 f5 #10)
-#13 := (f3 #11 3::Int)
-#15 := (= #13 2::Int)
-#16 := (not #15)
-#95 := (iff #16 #92)
-#82 := (= 2::Int #76)
-#87 := (not #82)
-#93 := (iff #87 #92)
-#90 := (iff #82 #79)
-#91 := [rewrite]: #90
-#94 := [monotonicity #91]: #93
-#88 := (iff #16 #87)
-#85 := (iff #15 #82)
-#83 := (iff #79 #82)
-#84 := [rewrite]: #83
-#80 := (iff #15 #79)
-#77 := (= #13 #76)
-#74 := (= #11 #73)
-#71 := (= #10 -1::Int)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#81 := [monotonicity #78]: #80
-#86 := [trans #81 #84]: #85
-#89 := [monotonicity #86]: #88
-#96 := [trans #89 #94]: #95
-#69 := [asserted]: #16
-#97 := [mp #69 #96]: #92
-#680 := (not #767)
-#664 := (or #680 #79)
-#346 := (* -1::Int 3::Int)
-#430 := (* -1::Int -1::Int)
-#431 := (mod #430 #346)
-#432 := (+ #76 #431)
-#423 := (= #432 0::Int)
-#434 := (mod -1::Int 3::Int)
-#435 := (* -1::Int #434)
-#436 := (+ #76 #435)
-#433 := (= #436 0::Int)
-#437 := (>= -1::Int 0::Int)
-#416 := (<= 3::Int 0::Int)
-#751 := (or #416 #437)
-#753 := (not #751)
-#410 := (<= -1::Int 0::Int)
-#540 := (or #410 #416)
-#747 := (not #540)
-#421 := (or #747 #753)
-#422 := (ite #421 #433 #423)
-#754 := (= #76 0::Int)
-#755 := (= -1::Int 0::Int)
-#756 := (ite #755 #754 #422)
-#757 := (= -1::Int #76)
-#752 := (= 3::Int 0::Int)
-#758 := (ite #752 #757 #756)
-#665 := (or #680 #758)
-#668 := (iff #665 #664)
-#670 := (iff #664 #664)
-#666 := [rewrite]: #670
-#679 := (iff #758 #79)
-#749 := (= #76 -1::Int)
-#682 := (ite false #749 #79)
-#677 := (iff #682 #79)
-#678 := [rewrite]: #677
-#687 := (iff #758 #682)
-#685 := (iff #756 #79)
-#683 := (ite false #754 #79)
-#674 := (iff #683 #79)
-#684 := [rewrite]: #674
-#675 := (iff #756 #683)
-#694 := (iff #422 #79)
-#1 := true
-#598 := (ite true #79 #749)
-#693 := (iff #598 #79)
-#690 := [rewrite]: #693
-#599 := (iff #422 #598)
-#596 := (iff #423 #749)
-#691 := (+ 1::Int #76)
-#577 := (= #691 0::Int)
-#595 := (iff #577 #749)
-#588 := [rewrite]: #595
-#592 := (iff #423 #577)
-#689 := (= #432 #691)
-#583 := (+ #76 1::Int)
-#593 := (= #583 #691)
-#688 := [rewrite]: #593
-#584 := (= #432 #583)
-#700 := (= #431 1::Int)
-#539 := -3::Int
-#695 := (mod 1::Int -3::Int)
-#699 := (= #695 1::Int)
-#697 := [rewrite]: #699
-#696 := (= #431 #695)
-#541 := (= #346 -3::Int)
-#542 := [rewrite]: #541
-#703 := (= #430 1::Int)
-#710 := [rewrite]: #703
-#698 := [monotonicity #710 #542]: #696
-#582 := [trans #698 #697]: #700
-#543 := [monotonicity #582]: #584
-#692 := [trans #543 #688]: #689
-#594 := [monotonicity #692]: #592
-#597 := [trans #594 #588]: #596
-#708 := (iff #433 #79)
-#714 := -2::Int
-#719 := (+ -2::Int #76)
-#705 := (= #719 0::Int)
-#701 := (iff #705 #79)
-#702 := [rewrite]: #701
-#706 := (iff #433 #705)
-#562 := (= #436 #719)
-#717 := (+ #76 -2::Int)
-#560 := (= #717 #719)
-#561 := [rewrite]: #560
-#718 := (= #436 #717)
-#711 := (= #435 -2::Int)
-#724 := (* -1::Int 2::Int)
-#715 := (= #724 -2::Int)
-#716 := [rewrite]: #715
-#721 := (= #435 #724)
-#438 := (= #434 2::Int)
-#720 := [rewrite]: #438
-#725 := [monotonicity #720]: #721
-#712 := [trans #725 #716]: #711
-#713 := [monotonicity #712]: #718
-#704 := [trans #713 #561]: #562
-#707 := [monotonicity #704]: #706
-#709 := [trans #707 #702]: #708
-#722 := (iff #421 true)
-#731 := (or false true)
-#443 := (iff #731 true)
-#444 := [rewrite]: #443
-#441 := (iff #421 #731)
-#730 := (iff #753 true)
-#728 := (not false)
-#452 := (iff #728 true)
-#726 := [rewrite]: #452
-#729 := (iff #753 #728)
-#458 := (iff #751 false)
-#732 := (or false false)
-#456 := (iff #732 false)
-#457 := [rewrite]: #456
-#733 := (iff #751 #732)
-#743 := (iff #437 false)
-#746 := [rewrite]: #743
-#398 := (iff #416 false)
-#399 := [rewrite]: #398
-#455 := [monotonicity #399 #746]: #733
-#352 := [trans #455 #457]: #458
-#451 := [monotonicity #352]: #729
-#727 := [trans #451 #726]: #730
-#385 := (iff #747 false)
-#741 := (not true)
-#744 := (iff #741 false)
-#384 := [rewrite]: #744
-#379 := (iff #747 #741)
-#740 := (iff #540 true)
-#400 := (or true false)
-#738 := (iff #400 true)
-#739 := [rewrite]: #738
-#736 := (iff #540 #400)
-#734 := (iff #410 true)
-#397 := [rewrite]: #734
-#737 := [monotonicity #397 #399]: #736
-#735 := [trans #737 #739]: #740
-#742 := [monotonicity #735]: #379
-#745 := [trans #742 #384]: #385
-#442 := [monotonicity #745 #727]: #441
-#723 := [trans #442 #444]: #722
-#600 := [monotonicity #723 #709 #597]: #599
-#681 := [trans #600 #690]: #694
-#750 := (iff #755 false)
-#393 := [rewrite]: #750
-#672 := [monotonicity #393 #681]: #675
-#686 := [trans #672 #684]: #685
-#413 := (iff #757 #749)
-#409 := [rewrite]: #413
-#748 := (iff #752 false)
-#408 := [rewrite]: #748
-#676 := [monotonicity #408 #409 #686]: #687
-#673 := [trans #676 #678]: #679
-#669 := [monotonicity #673]: #668
-#671 := [trans #669 #666]: #668
-#667 := [quant-inst #70 #12]: #665
-#657 := [mp #667 #671]: #664
-[unit-resolution #657 #97 #772]: false
-unsat
-1b6da3cc7294aa933e099fc6231e1c711dbb5442 347 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
+#198 := [monotonicity #182]: #197
+#201 := [monotonicity #198]: #200
+#204 := [monotonicity #201]: #203
+#207 := [monotonicity #204]: #206
+#210 := [quant-intro #207]: #209
+#31 := (- #17)
+#30 := (- #15)
+#40 := (mod #30 #31)
+#41 := (- #40)
+#24 := (< 0::Int #17)
+#26 := (< #15 0::Int)
+#27 := (and #26 #24)
+#23 := (< 0::Int #15)
+#25 := (and #23 #24)
+#28 := (or #25 #27)
+#42 := (if #28 #39 #41)
+#43 := (if #20 0::Int #42)
+#44 := (if #21 #15 #43)
+#45 := (= #38 #44)
+#46 := (forall (vars (?v0 Int) (?v1 Int)) #45)
+#144 := (iff #46 #143)
+#141 := (iff #45 #140)
+#138 := (= #44 #137)
+#135 := (= #43 #134)
+#132 := (= #42 #131)
+#129 := (= #41 #126)
+#123 := (- #120)
+#127 := (= #123 #126)
+#128 := [rewrite]: #127
+#124 := (= #41 #123)
+#121 := (= #40 #120)
+#102 := (= #31 #101)
+#103 := [rewrite]: #102
+#99 := (= #30 #98)
+#100 := [rewrite]: #99
+#122 := [monotonicity #100 #103]: #121
+#125 := [monotonicity #122]: #124
+#130 := [trans #125 #128]: #129
+#95 := (iff #28 #94)
+#92 := (iff #27 #91)
+#77 := (iff #24 #76)
+#78 := [rewrite]: #77
+#84 := (iff #26 #83)
+#88 := (iff #83 #83)
+#86 := (iff #82 #82)
+#87 := [rewrite]: #86
+#89 := [monotonicity #87]: #88
+#85 := [rewrite]: #84
+#90 := [trans #85 #89]: #84
+#93 := [monotonicity #90 #78]: #92
+#80 := (iff #25 #79)
+#73 := (iff #23 #72)
+#74 := [rewrite]: #73
+#81 := [monotonicity #74 #78]: #80
+#96 := [monotonicity #81 #93]: #95
+#133 := [monotonicity #96 #130]: #132
+#136 := [monotonicity #133]: #135
+#139 := [monotonicity #136]: #138
+#142 := [monotonicity #139]: #141
+#145 := [quant-intro #142]: #144
+#50 := [asserted]: #46
+#146 := [mp #50 #145]: #143
+#211 := [mp #146 #210]: #208
+#219 := [mp~ #211 #218]: #208
+#259 := [mp #219 #258]: #256
+#290 := [mp #259 #289]: #287
+#718 := [mp #290 #717]: #713
+#671 := (not #713)
+#660 := (or #671 #387)
+#368 := (* -1::Int 3::Int)
+#700 := (mod #367 #368)
+#701 := (+ #11 #700)
+#702 := (= #701 0::Int)
+#380 := (<= 3::Int 0::Int)
+#383 := (or #379 #380)
+#362 := (not #383)
+#381 := (or #369 #380)
+#382 := (not #381)
+#697 := (or #382 #362)
+#703 := (if #697 #693 #702)
+#698 := (if #377 #378 #703)
+#376 := (= #11 f6)
+#291 := (= 3::Int 0::Int)
+#704 := (if #291 #376 #698)
+#661 := (or #671 #704)
+#657 := (iff #661 #660)
+#663 := (iff #660 #660)
+#664 := [rewrite]: #663
+#670 := (iff #704 #387)
+#390 := (if false #376 #387)
+#384 := (iff #390 #387)
+#666 := [rewrite]: #384
+#668 := (iff #704 #390)
+#388 := (iff #698 #387)
+#673 := (iff #703 #676)
+#398 := (iff #702 #397)
+#674 := (= #701 #297)
+#403 := (= #700 #402)
+#679 := (= #368 -3::Int)
+#401 := [rewrite]: #679
+#404 := [monotonicity #401]: #403
+#675 := [monotonicity #404]: #674
+#672 := [monotonicity #675]: #398
+#689 := (iff #697 #691)
+#330 := (iff #362 #690)
+#325 := (iff #383 #379)
+#684 := (or #379 false)
+#681 := (iff #684 #379)
+#687 := [rewrite]: #681
+#685 := (iff #383 #684)
+#359 := (iff #380 false)
+#695 := [rewrite]: #359
+#686 := [monotonicity #695]: #685
+#688 := [trans #686 #687]: #325
+#331 := [monotonicity #688]: #330
+#682 := (iff #382 #346)
+#344 := (iff #381 #369)
+#355 := (or #369 false)
+#680 := (iff #355 #369)
+#343 := [rewrite]: #680
+#696 := (iff #381 #355)
+#339 := [monotonicity #695]: #696
+#345 := [trans #339 #343]: #344
+#683 := [monotonicity #345]: #682
+#692 := [monotonicity #683 #331]: #689
+#677 := [monotonicity #692 #672]: #673
+#389 := [monotonicity #677]: #388
+#694 := (iff #291 false)
+#354 := [rewrite]: #694
+#669 := [monotonicity #354 #389]: #668
+#667 := [trans #669 #666]: #670
+#658 := [monotonicity #667]: #657
+#659 := [trans #658 #664]: #657
+#662 := [quant-inst #8 #10]: #661
+#665 := [mp #662 #659]: #660
+#621 := [unit-resolution #665 #718]: #387
+#489 := (not #377)
+#530 := (not #387)
+#633 := (or #530 #489)
+#638 := (not #378)
+#506 := (<= #11 0::Int)
+#627 := (not #506)
+#545 := (not #167)
+#546 := (or #627 #545)
+#639 := [th-lemma arith farkas 1 1]: #546
+#636 := [unit-resolution #639 #169]: #627
+#618 := (or #638 #506)
+#620 := [th-lemma arith triangle-eq]: #618
+#628 := [unit-resolution #620 #636]: #638
+#637 := (or #530 #489 #378)
+#539 := [def-axiom]: #637
+#609 := [unit-resolution #539 #628]: #633
+#589 := [unit-resolution #609 #621]: #489
+#634 := (or #530 #377 #676)
+#635 := [def-axiom]: #634
+#590 := [unit-resolution #635 #589 #621]: #676
+#485 := (not #676)
+#487 := (or #485 #653 #693)
+#488 := [def-axiom]: #487
+#593 := [unit-resolution #488 #590]: #592
+#630 := [unit-resolution #593 #629]: #653
+#508 := (or #691 #369)
+#650 := [def-axiom]: #508
+#631 := [unit-resolution #650 #630]: #369
+#651 := (or #691 #379)
+#652 := [def-axiom]: #651
+#601 := [unit-resolution #652 #630]: #379
+#591 := (or #377 #346 #690)
+#602 := [th-lemma arith triangle-eq]: #591
+#580 := [unit-resolution #602 #589]: #691
+[unit-resolution #580 #601 #631]: false
+1a816085b7feac64dcd1be391f3e9629f980d336 343 0
+unsat
+#2 := false
+#10 := 3::Int
+decl f6 :: Int
+#8 := f6
+#706 := (mod f6 3::Int)
+#625 := (>= #706 3::Int)
+#621 := (not #625)
+#1 := true
+#173 := [true-axiom]: true
+#607 := (or false #621)
+#608 := [th-lemma arith]: #607
+#609 := [unit-resolution #608 #173]: #621
+#21 := 0::Int
+decl f3 :: (-> S2 Int Int)
+decl f4 :: (-> S3 Int S2)
+decl f5 :: S3
+#7 := f5
+#9 := (f4 f5 f6)
+#11 := (f3 #9 3::Int)
+#106 := -1::Int
+#601 := (* -1::Int #11)
+#602 := (+ f6 #601)
+#603 := (<= #602 0::Int)
+#599 := (= f6 #11)
+#12 := (= #11 f6)
+#56 := (<= 3::Int f6)
+#57 := (not #56)
+#68 := (not #12)
+#69 := (or #68 #57)
+#74 := (not #69)
+#13 := (< f6 3::Int)
+#14 := (implies #12 #13)
+#15 := (not #14)
+#75 := (iff #15 #74)
+#72 := (iff #14 #69)
+#65 := (implies #12 #57)
+#70 := (iff #65 #69)
+#71 := [rewrite]: #70
+#66 := (iff #14 #65)
+#58 := (iff #13 #57)
+#62 := (iff #57 #57)
+#60 := (iff #56 #56)
+#61 := [rewrite]: #60
+#63 := [monotonicity #61]: #62
+#59 := [rewrite]: #58
+#64 := [trans #59 #63]: #58
+#67 := [monotonicity #64]: #66
+#73 := [trans #67 #71]: #72
+#76 := [monotonicity #73]: #75
+#50 := [asserted]: #15
+#77 := [mp #50 #76]: #74
+#78 := [not-or-elim #77]: #12
+#610 := [symm #78]: #599
+#600 := (not #599)
+#611 := (or #600 #603)
+#589 := [th-lemma arith triangle-eq]: #611
+#590 := [unit-resolution #589 #610]: #603
+#217 := (>= f6 3::Int)
+#175 := (iff #56 #217)
+#218 := [rewrite]: #175
+#79 := [not-or-elim #77]: #56
+#219 := [mp #79 #218]: #217
+#708 := (* -1::Int #706)
+#365 := (+ #11 #708)
+#662 := (<= #365 0::Int)
+#495 := (= #365 0::Int)
+#701 := -3::Int
+#702 := (* -1::Int f6)
+#410 := (mod #702 -3::Int)
+#413 := (+ #11 #410)
+#684 := (= #413 0::Int)
+#391 := (>= f6 0::Int)
+#697 := (not #391)
+#387 := (<= f6 0::Int)
+#354 := (not #387)
+#340 := (or #354 #697)
+#681 := (if #340 #495 #684)
+#386 := (= #11 0::Int)
+#385 := (= f6 0::Int)
+#686 := (if #385 #386 #681)
 #19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
 #17 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#38 := (f4 f5 #17)
-#39 := (f3 #38 #19)
-#781 := (pattern #39)
-#13 := 0::Int
-#112 := -1::Int
-#116 := (* -1::Int #19)
-#113 := (* -1::Int #17)
-#177 := (mod #113 #116)
-#292 := (+ #39 #177)
-#293 := (= #292 0::Int)
-#40 := (mod #17 #19)
-#289 := (* -1::Int #40)
-#290 := (+ #39 #289)
-#291 := (= #290 0::Int)
-#151 := (>= #17 0::Int)
-#144 := (<= #19 0::Int)
-#236 := (or #144 #151)
-#237 := (not #236)
-#140 := (<= #17 0::Int)
-#234 := (or #140 #144)
-#235 := (not #234)
-#240 := (or #235 #237)
-#294 := (ite #240 #291 #293)
-#288 := (= #39 0::Int)
-#21 := (= #17 0::Int)
-#295 := (ite #21 #288 #294)
-#287 := (= #17 #39)
-#22 := (= #19 0::Int)
-#296 := (ite #22 #287 #295)
-#782 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #781) #296)
-#299 := (forall (vars (?v0 Int) (?v1 Int)) #296)
-#785 := (iff #299 #782)
-#783 := (iff #296 #296)
-#784 := [refl]: #783
-#786 := [quant-intro #784]: #785
-#183 := (* -1::Int #177)
-#256 := (ite #240 #40 #183)
-#259 := (ite #21 0::Int #256)
-#262 := (ite #22 #17 #259)
-#265 := (= #39 #262)
-#268 := (forall (vars (?v0 Int) (?v1 Int)) #265)
-#300 := (iff #268 #299)
+#39 := (f4 f5 #17)
+#40 := (f3 #39 #19)
+#721 := (pattern #40)
+#110 := (* -1::Int #19)
+#107 := (* -1::Int #17)
+#129 := (mod #107 #110)
+#289 := (+ #40 #129)
+#290 := (= #289 0::Int)
+#41 := (mod #17 #19)
+#286 := (* -1::Int #41)
+#287 := (+ #40 #286)
+#288 := (= #287 0::Int)
+#84 := (<= #19 0::Int)
+#176 := (>= #17 0::Int)
+#233 := (or #176 #84)
+#234 := (not #233)
+#80 := (<= #17 0::Int)
+#231 := (or #80 #84)
+#232 := (not #231)
+#237 := (or #232 #234)
+#291 := (if #237 #288 #290)
+#285 := (= #40 0::Int)
+#22 := (= #17 0::Int)
+#292 := (if #22 #285 #291)
+#284 := (= #40 #17)
+#23 := (= #19 0::Int)
+#293 := (if #23 #284 #292)
+#722 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #721) #293)
+#296 := (forall (vars (?v0 Int) (?v1 Int)) #293)
+#725 := (iff #296 #722)
+#723 := (iff #293 #293)
+#724 := [refl]: #723
+#726 := [quant-intro #724]: #725
+#135 := (* -1::Int #129)
+#253 := (if #237 #41 #135)
+#256 := (if #22 0::Int #253)
+#259 := (if #23 #17 #256)
+#262 := (= #40 #259)
+#265 := (forall (vars (?v0 Int) (?v1 Int)) #262)
 #297 := (iff #265 #296)
-#298 := [rewrite]: #297
-#301 := [quant-intro #298]: #300
-#152 := (not #151)
-#145 := (not #144)
-#155 := (and #145 #152)
-#141 := (not #140)
-#148 := (and #141 #145)
-#158 := (or #148 #155)
-#203 := (ite #158 #40 #183)
-#206 := (ite #21 0::Int #203)
-#209 := (ite #22 #17 #206)
-#212 := (= #39 #209)
-#215 := (forall (vars (?v0 Int) (?v1 Int)) #212)
-#269 := (iff #215 #268)
-#266 := (iff #212 #265)
-#263 := (= #209 #262)
-#260 := (= #206 #259)
-#257 := (= #203 #256)
-#241 := (iff #158 #240)
-#238 := (iff #155 #237)
-#239 := [rewrite]: #238
-#228 := (iff #148 #235)
-#229 := [rewrite]: #228
-#242 := [monotonicity #229 #239]: #241
-#258 := [monotonicity #242]: #257
+#294 := (iff #262 #293)
+#295 := [rewrite]: #294
+#298 := [quant-intro #295]: #297
+#85 := (not #84)
+#179 := (not #176)
+#182 := (and #179 #85)
+#81 := (not #80)
+#88 := (and #81 #85)
+#185 := (or #88 #182)
+#201 := (if #185 #41 #135)
+#204 := (if #22 0::Int #201)
+#207 := (if #23 #17 #204)
+#210 := (= #40 #207)
+#213 := (forall (vars (?v0 Int) (?v1 Int)) #210)
+#266 := (iff #213 #265)
+#263 := (iff #210 #262)
+#260 := (= #207 #259)
+#257 := (= #204 #256)
+#254 := (= #201 #253)
+#238 := (iff #185 #237)
+#235 := (iff #182 #234)
+#236 := [rewrite]: #235
+#229 := (iff #88 #232)
+#230 := [rewrite]: #229
+#239 := [monotonicity #230 #236]: #238
+#255 := [monotonicity #239]: #254
+#258 := [monotonicity #255]: #257
 #261 := [monotonicity #258]: #260
 #264 := [monotonicity #261]: #263
-#267 := [monotonicity #264]: #266
-#270 := [quant-intro #267]: #269
-#226 := (~ #215 #215)
-#225 := (~ #212 #212)
-#222 := [refl]: #225
-#227 := [nnf-pos #222]: #226
-#32 := (- #19)
-#31 := (- #17)
-#41 := (mod #31 #32)
-#42 := (- #41)
-#25 := (< 0::Int #19)
-#27 := (< #17 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #17)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#43 := (ite #29 #40 #42)
-#44 := (ite #21 0::Int #43)
-#45 := (ite #22 #17 #44)
-#46 := (= #39 #45)
-#47 := (forall (vars (?v0 Int) (?v1 Int)) #46)
-#218 := (iff #47 #215)
-#106 := (and #25 #27)
-#109 := (or #26 #106)
-#188 := (ite #109 #40 #183)
-#97 := (= 0::Int #17)
-#191 := (ite #97 0::Int #188)
-#100 := (= 0::Int #19)
-#194 := (ite #100 #17 #191)
-#197 := (= #39 #194)
-#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
-#216 := (iff #200 #215)
-#213 := (iff #197 #212)
-#210 := (= #194 #209)
-#207 := (= #191 #206)
-#204 := (= #188 #203)
-#159 := (iff #109 #158)
-#156 := (iff #106 #155)
-#153 := (iff #27 #152)
-#154 := [rewrite]: #153
-#146 := (iff #25 #145)
-#147 := [rewrite]: #146
-#157 := [monotonicity #147 #154]: #156
-#149 := (iff #26 #148)
-#142 := (iff #24 #141)
-#143 := [rewrite]: #142
-#150 := [monotonicity #143 #147]: #149
-#160 := [monotonicity #150 #157]: #159
-#205 := [monotonicity #160]: #204
-#134 := (iff #97 #21)
-#135 := [rewrite]: #134
-#208 := [monotonicity #135 #205]: #207
-#136 := (iff #100 #22)
+#267 := [quant-intro #264]: #266
+#226 := (~ #213 #213)
+#228 := (~ #210 #210)
+#225 := [refl]: #228
+#221 := [nnf-pos #225]: #226
+#91 := (<= 0::Int #17)
+#92 := (not #91)
+#100 := (and #92 #85)
+#103 := (or #88 #100)
+#140 := (if #103 #41 #135)
+#143 := (if #22 0::Int #140)
+#146 := (if #23 #17 #143)
+#149 := (= #40 #146)
+#152 := (forall (vars (?v0 Int) (?v1 Int)) #149)
+#214 := (iff #152 #213)
+#211 := (iff #149 #210)
+#208 := (= #146 #207)
+#205 := (= #143 #204)
+#202 := (= #140 #201)
+#186 := (iff #103 #185)
+#183 := (iff #100 #182)
+#180 := (iff #92 #179)
+#177 := (iff #91 #176)
+#178 := [rewrite]: #177
+#181 := [monotonicity #178]: #180
+#184 := [monotonicity #181]: #183
+#187 := [monotonicity #184]: #186
+#203 := [monotonicity #187]: #202
+#206 := [monotonicity #203]: #205
+#209 := [monotonicity #206]: #208
+#212 := [monotonicity #209]: #211
+#215 := [quant-intro #212]: #214
+#33 := (- #19)
+#32 := (- #17)
+#42 := (mod #32 #33)
+#43 := (- #42)
+#26 := (< 0::Int #19)
+#28 := (< #17 0::Int)
+#29 := (and #28 #26)
+#25 := (< 0::Int #17)
+#27 := (and #25 #26)
+#30 := (or #27 #29)
+#44 := (if #30 #41 #43)
+#45 := (if #22 0::Int #44)
+#46 := (if #23 #17 #45)
+#47 := (= #40 #46)
+#48 := (forall (vars (?v0 Int) (?v1 Int)) #47)
+#153 := (iff #48 #152)
+#150 := (iff #47 #149)
+#147 := (= #46 #146)
+#144 := (= #45 #143)
+#141 := (= #44 #140)
+#138 := (= #43 #135)
+#132 := (- #129)
+#136 := (= #132 #135)
 #137 := [rewrite]: #136
-#211 := [monotonicity #137 #208]: #210
+#133 := (= #43 #132)
+#130 := (= #42 #129)
+#111 := (= #33 #110)
+#112 := [rewrite]: #111
+#108 := (= #32 #107)
+#109 := [rewrite]: #108
+#131 := [monotonicity #109 #112]: #130
+#134 := [monotonicity #131]: #133
+#139 := [trans #134 #137]: #138
+#104 := (iff #30 #103)
+#101 := (iff #29 #100)
+#86 := (iff #26 #85)
+#87 := [rewrite]: #86
+#93 := (iff #28 #92)
+#97 := (iff #92 #92)
+#95 := (iff #91 #91)
+#96 := [rewrite]: #95
+#98 := [monotonicity #96]: #97
+#94 := [rewrite]: #93
+#99 := [trans #94 #98]: #93
+#102 := [monotonicity #99 #87]: #101
+#89 := (iff #27 #88)
+#82 := (iff #25 #81)
+#83 := [rewrite]: #82
+#90 := [monotonicity #83 #87]: #89
+#105 := [monotonicity #90 #102]: #104
+#142 := [monotonicity #105 #139]: #141
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#151 := [monotonicity #148]: #150
+#154 := [quant-intro #151]: #153
+#52 := [asserted]: #48
+#155 := [mp #52 #154]: #152
+#216 := [mp #155 #215]: #213
+#222 := [mp~ #216 #221]: #213
+#268 := [mp #222 #267]: #265
+#299 := [mp #268 #298]: #296
+#727 := [mp #299 #726]: #722
+#676 := (not #722)
+#680 := (or #676 #686)
+#376 := (* -1::Int 3::Int)
+#377 := (mod #702 #376)
+#709 := (+ #11 #377)
+#710 := (= #709 0::Int)
+#378 := (<= 3::Int 0::Int)
+#388 := (or #391 #378)
+#392 := (not #388)
+#389 := (or #387 #378)
+#390 := (not #389)
+#371 := (or #390 #392)
+#711 := (if #371 #495 #710)
+#712 := (if #385 #386 #711)
+#300 := (= 3::Int 0::Int)
+#707 := (if #300 #12 #712)
+#669 := (or #676 #707)
+#671 := (iff #669 #680)
+#667 := (iff #680 #680)
+#672 := [rewrite]: #667
+#675 := (iff #707 #686)
+#398 := (if false #12 #686)
+#678 := (iff #398 #686)
+#393 := [rewrite]: #678
+#399 := (iff #707 #398)
+#396 := (iff #712 #686)
+#685 := (iff #711 #681)
+#406 := (iff #710 #684)
+#306 := (= #709 #413)
+#411 := (= #377 #410)
+#687 := (= #376 -3::Int)
+#688 := [rewrite]: #687
+#412 := [monotonicity #688]: #411
+#683 := [monotonicity #412]: #306
+#407 := [monotonicity #683]: #406
+#700 := (iff #371 #340)
+#699 := (iff #392 #697)
+#696 := (iff #388 #391)
+#692 := (or #391 false)
+#695 := (iff #692 #391)
+#690 := [rewrite]: #695
+#693 := (iff #388 #692)
+#363 := (iff #378 false)
+#368 := [rewrite]: #363
+#694 := [monotonicity #368]: #693
+#334 := [trans #694 #690]: #696
+#339 := [monotonicity #334]: #699
+#355 := (iff #390 #354)
+#352 := (iff #389 #387)
+#704 := (or #387 false)
+#348 := (iff #704 #387)
+#689 := [rewrite]: #348
+#364 := (iff #389 #704)
+#705 := [monotonicity #368]: #364
+#353 := [trans #705 #689]: #352
+#691 := [monotonicity #353]: #355
+#698 := [monotonicity #691 #339]: #700
+#682 := [monotonicity #698 #407]: #685
+#397 := [monotonicity #682]: #396
+#713 := (iff #300 false)
+#703 := [rewrite]: #713
+#677 := [monotonicity #703 #397]: #399
+#679 := [trans #677 #393]: #675
+#666 := [monotonicity #679]: #671
+#673 := [trans #666 #672]: #671
+#670 := [quant-inst #8 #10]: #669
+#668 := [mp #670 #673]: #680
+#592 := [unit-resolution #668 #727]: #686
+#655 := (not #686)
+#579 := (or #655 #681)
+#537 := (not #385)
+#593 := (not #217)
+#594 := (or #354 #593)
+#595 := [th-lemma arith farkas 1 1]: #594
+#596 := [unit-resolution #595 #219]: #354
+#591 := (or #537 #387)
+#597 := [th-lemma arith triangle-eq]: #591
+#583 := [unit-resolution #597 #596]: #537
+#498 := (or #655 #385 #681)
+#646 := [def-axiom]: #498
+#580 := [unit-resolution #646 #583]: #579
+#581 := [unit-resolution #580 #592]: #681
+#664 := (not #681)
+#585 := (or #664 #495)
+#674 := (or #340 #387)
+#515 := [def-axiom]: #674
+#584 := [unit-resolution #515 #596]: #340
+#659 := (not #340)
+#658 := (or #664 #659 #495)
+#665 := [def-axiom]: #658
+#586 := [unit-resolution #665 #584]: #585
+#587 := [unit-resolution #586 #581]: #495
+#497 := (not #495)
+#582 := (or #497 #662)
+#588 := [th-lemma arith triangle-eq]: #582
+#561 := [unit-resolution #588 #587]: #662
+[th-lemma arith farkas 1 -1 1 1 #561 #219 #590 #609]: false
+84faad2fa160ef59638bbef257c0b4c92bf64f96 569 0
+unsat
+#2 := false
+#23 := 0::Int
+decl f4 :: (-> S2 Int Int)
+#10 := 1::Int
+decl f5 :: (-> S3 Int S2)
+decl f3 :: Int
+#7 := f3
+decl f7 :: S3
+#13 := f7
+#14 := (f5 f7 f3)
+#15 := (f4 #14 1::Int)
+#96 := -1::Int
+#167 := (* -1::Int #15)
+decl f6 :: S3
+#8 := f6
+#9 := (f5 f6 f3)
+#11 := (f4 #9 1::Int)
+#166 := (* -1::Int #11)
+#168 := (+ f3 #166 #167)
+#380 := (>= #168 0::Int)
+#576 := (<= #15 0::Int)
+#640 := (= #15 0::Int)
+#381 := (= f3 0::Int)
+#527 := (not #381)
+#558 := (not #640)
+#499 := [hypothesis]: #558
+#535 := (or #527 #640)
+#704 := (* -1::Int f3)
+#645 := (mod #704 -1::Int)
+#612 := (+ #15 #645)
+#593 := (= #612 0::Int)
+#366 := (>= f3 0::Int)
+#406 := (not #366)
+#385 := (<= f3 0::Int)
+#692 := (not #385)
+#302 := (or #692 #406)
+#597 := (if #302 #640 #593)
+#600 := (if #381 #640 #597)
+#21 := (:var 0 Int)
+#19 := (:var 1 Int)
+#41 := (f5 f7 #19)
+#42 := (f4 #41 #21)
+#716 := (pattern #42)
+#100 := (* -1::Int #21)
+#97 := (* -1::Int #19)
+#119 := (mod #97 #100)
+#285 := (+ #42 #119)
+#286 := (= #285 0::Int)
+#43 := (mod #19 #21)
+#282 := (* -1::Int #43)
+#283 := (+ #42 #282)
+#284 := (= #283 0::Int)
+#74 := (<= #21 0::Int)
+#176 := (>= #19 0::Int)
+#229 := (or #176 #74)
+#230 := (not #229)
+#70 := (<= #19 0::Int)
+#225 := (or #70 #74)
+#226 := (not #225)
+#233 := (or #226 #230)
+#287 := (if #233 #284 #286)
+#281 := (= #42 0::Int)
+#24 := (= #19 0::Int)
+#288 := (if #24 #281 #287)
+#280 := (= #42 #19)
+#25 := (= #21 0::Int)
+#289 := (if #25 #280 #288)
+#717 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #716) #289)
+#292 := (forall (vars (?v0 Int) (?v1 Int)) #289)
+#720 := (iff #292 #717)
+#718 := (iff #289 #289)
+#719 := [refl]: #718
+#721 := [quant-intro #719]: #720
+#125 := (* -1::Int #119)
+#249 := (if #233 #43 #125)
+#252 := (if #24 0::Int #249)
+#255 := (if #25 #19 #252)
+#258 := (= #42 #255)
+#261 := (forall (vars (?v0 Int) (?v1 Int)) #258)
+#293 := (iff #261 #292)
+#290 := (iff #258 #289)
+#291 := [rewrite]: #290
+#294 := [quant-intro #291]: #293
+#75 := (not #74)
+#179 := (not #176)
+#182 := (and #179 #75)
+#71 := (not #70)
+#78 := (and #71 #75)
+#185 := (or #78 #182)
+#201 := (if #185 #43 #125)
+#204 := (if #24 0::Int #201)
+#207 := (if #25 #19 #204)
+#210 := (= #42 #207)
+#213 := (forall (vars (?v0 Int) (?v1 Int)) #210)
+#262 := (iff #213 #261)
+#259 := (iff #210 #258)
+#256 := (= #207 #255)
+#253 := (= #204 #252)
+#250 := (= #201 #249)
+#234 := (iff #185 #233)
+#231 := (iff #182 #230)
+#232 := [rewrite]: #231
+#227 := (iff #78 #226)
+#228 := [rewrite]: #227
+#235 := [monotonicity #228 #232]: #234
+#251 := [monotonicity #235]: #250
+#254 := [monotonicity #251]: #253
+#257 := [monotonicity #254]: #256
+#260 := [monotonicity #257]: #259
+#263 := [quant-intro #260]: #262
+#165 := (~ #213 #213)
+#218 := (~ #210 #210)
+#164 := [refl]: #218
+#223 := [nnf-pos #164]: #165
+#81 := (<= 0::Int #19)
+#82 := (not #81)
+#90 := (and #82 #75)
+#93 := (or #78 #90)
+#130 := (if #93 #43 #125)
+#133 := (if #24 0::Int #130)
+#136 := (if #25 #19 #133)
+#139 := (= #42 #136)
+#142 := (forall (vars (?v0 Int) (?v1 Int)) #139)
+#214 := (iff #142 #213)
+#211 := (iff #139 #210)
+#208 := (= #136 #207)
+#205 := (= #133 #204)
+#202 := (= #130 #201)
+#186 := (iff #93 #185)
+#183 := (iff #90 #182)
+#180 := (iff #82 #179)
+#177 := (iff #81 #176)
+#178 := [rewrite]: #177
+#181 := [monotonicity #178]: #180
+#184 := [monotonicity #181]: #183
+#187 := [monotonicity #184]: #186
+#203 := [monotonicity #187]: #202
+#206 := [monotonicity #203]: #205
+#209 := [monotonicity #206]: #208
+#212 := [monotonicity #209]: #211
+#215 := [quant-intro #212]: #214
+#35 := (- #21)
+#34 := (- #19)
+#44 := (mod #34 #35)
+#45 := (- #44)
+#28 := (< 0::Int #21)
+#30 := (< #19 0::Int)
+#31 := (and #30 #28)
+#27 := (< 0::Int #19)
+#29 := (and #27 #28)
+#32 := (or #29 #31)
+#46 := (if #32 #43 #45)
+#47 := (if #24 0::Int #46)
+#48 := (if #25 #19 #47)
+#49 := (= #42 #48)
+#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
+#143 := (iff #50 #142)
+#140 := (iff #49 #139)
+#137 := (= #48 #136)
+#134 := (= #47 #133)
+#131 := (= #46 #130)
+#128 := (= #45 #125)
+#122 := (- #119)
+#126 := (= #122 #125)
+#127 := [rewrite]: #126
+#123 := (= #45 #122)
+#120 := (= #44 #119)
+#101 := (= #35 #100)
+#102 := [rewrite]: #101
+#98 := (= #34 #97)
+#99 := [rewrite]: #98
+#121 := [monotonicity #99 #102]: #120
+#124 := [monotonicity #121]: #123
+#129 := [trans #124 #127]: #128
+#94 := (iff #32 #93)
+#91 := (iff #31 #90)
+#76 := (iff #28 #75)
+#77 := [rewrite]: #76
+#83 := (iff #30 #82)
+#87 := (iff #82 #82)
+#85 := (iff #81 #81)
+#86 := [rewrite]: #85
+#88 := [monotonicity #86]: #87
+#84 := [rewrite]: #83
+#89 := [trans #84 #88]: #83
+#92 := [monotonicity #89 #77]: #91
+#79 := (iff #29 #78)
+#72 := (iff #27 #71)
+#73 := [rewrite]: #72
+#80 := [monotonicity #73 #77]: #79
+#95 := [monotonicity #80 #92]: #94
+#132 := [monotonicity #95 #129]: #131
+#135 := [monotonicity #132]: #134
+#138 := [monotonicity #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [quant-intro #141]: #143
+#54 := [asserted]: #50
+#145 := [mp #54 #144]: #142
+#216 := [mp #145 #215]: #213
+#224 := [mp~ #216 #223]: #213
+#264 := [mp #224 #263]: #261
+#295 := [mp #264 #294]: #292
+#722 := [mp #295 #721]: #717
+#587 := (not #717)
+#588 := (or #587 #600)
+#705 := (* -1::Int 1::Int)
+#625 := (mod #704 #705)
+#622 := (+ #15 #625)
+#624 := (= #622 0::Int)
+#489 := (mod f3 1::Int)
+#644 := (* -1::Int #489)
+#631 := (+ #15 #644)
+#633 := (= #631 0::Int)
+#386 := (<= 1::Int 0::Int)
+#701 := (or #366 #386)
+#703 := (not #701)
+#383 := (or #385 #386)
+#387 := (not #383)
+#360 := (or #387 #703)
+#634 := (if #360 #633 #624)
+#635 := (if #381 #640 #634)
+#643 := (= #15 f3)
+#382 := (= 1::Int 0::Int)
+#636 := (if #382 #643 #635)
+#589 := (or #587 #636)
+#591 := (iff #589 #588)
+#592 := (iff #588 #588)
+#578 := [rewrite]: #592
+#584 := (iff #636 #600)
+#603 := (if false #643 #600)
+#595 := (iff #603 #600)
+#606 := [rewrite]: #595
+#604 := (iff #636 #603)
+#601 := (iff #635 #600)
+#598 := (iff #634 #597)
+#594 := (iff #624 #593)
+#609 := (= #622 #612)
+#610 := (= #625 #645)
+#401 := (= #705 -1::Int)
+#402 := [rewrite]: #401
+#611 := [monotonicity #402]: #610
+#613 := [monotonicity #611]: #609
+#596 := [monotonicity #613]: #594
+#607 := (iff #633 #640)
+#616 := (= #631 #15)
+#615 := (+ #15 0::Int)
+#619 := (= #615 #15)
+#620 := [rewrite]: #619
+#617 := (= #631 #615)
+#630 := (= #644 0::Int)
+#626 := (* -1::Int 0::Int)
+#629 := (= #626 0::Int)
+#623 := [rewrite]: #629
+#627 := (= #644 #626)
+#632 := (= #489 0::Int)
+#637 := [rewrite]: #632
+#628 := [monotonicity #637]: #627
+#614 := [trans #628 #623]: #630
+#618 := [monotonicity #614]: #617
+#621 := [trans #618 #620]: #616
+#608 := [monotonicity #621]: #607
+#678 := (iff #360 #302)
+#407 := (iff #703 #406)
+#683 := (iff #701 #366)
+#335 := (or #366 false)
+#696 := (iff #335 #366)
+#682 := [rewrite]: #696
+#695 := (iff #701 #335)
+#350 := (iff #386 false)
+#686 := [rewrite]: #350
+#693 := [monotonicity #686]: #695
+#405 := [trans #693 #682]: #683
+#408 := [monotonicity #405]: #407
+#694 := (iff #387 #692)
+#691 := (iff #383 #385)
+#687 := (or #385 false)
+#690 := (iff #687 #385)
+#685 := [rewrite]: #690
+#688 := (iff #383 #687)
+#689 := [monotonicity #686]: #688
+#329 := [trans #689 #685]: #691
+#334 := [monotonicity #329]: #694
+#679 := [monotonicity #334 #408]: #678
+#599 := [monotonicity #679 #608 #596]: #598
+#602 := [monotonicity #599]: #601
+#363 := (iff #382 false)
+#699 := [rewrite]: #363
+#605 := [monotonicity #699 #602]: #604
+#585 := [trans #605 #606]: #584
+#586 := [monotonicity #585]: #591
+#574 := [trans #586 #578]: #591
+#590 := [quant-inst #7 #10]: #589
+#575 := [mp #590 #574]: #588
+#554 := [unit-resolution #575 #722]: #600
+#565 := (not #600)
+#566 := (or #565 #527 #640)
+#567 := [def-axiom]: #566
+#559 := [unit-resolution #567 #554]: #535
+#560 := [unit-resolution #559 #499]: #527
+#659 := (not #302)
+#555 := (or #381 #597)
+#570 := (or #565 #381 #597)
+#571 := [def-axiom]: #570
+#561 := [unit-resolution #571 #554]: #555
+#529 := [unit-resolution #561 #560]: #597
+#582 := (not #597)
+#577 := (or #582 #659 #640)
+#583 := [def-axiom]: #577
+#536 := [unit-resolution #583 #529 #499]: #659
+#657 := (or #302 #385)
+#651 := [def-axiom]: #657
+#495 := [unit-resolution #651 #536]: #385
+#652 := (or #302 #366)
+#658 := [def-axiom]: #652
+#526 := [unit-resolution #658 #536]: #366
+#528 := (or #381 #692 #406)
+#530 := [th-lemma arith triangle-eq]: #528
+#537 := [unit-resolution #530 #526 #495 #560]: false
+#539 := [lemma #537]: #640
+#450 := (or #558 #576)
+#452 := [th-lemma arith triangle-eq]: #450
+#453 := [unit-resolution #452 #539]: #576
+#655 := (<= #11 0::Int)
+#384 := (= #11 0::Int)
+#508 := [hypothesis]: #527
+#490 := (div f3 1::Int)
+#697 := (* -1::Int #490)
+#371 := (+ #11 #697)
+#372 := (= #371 0::Int)
+#534 := (not #372)
+#486 := (+ f3 #697)
+#500 := (>= #486 0::Int)
+#525 := (= #486 0::Int)
+#1 := true
+#163 := [true-axiom]: true
+#463 := (or false #525)
+#466 := [th-lemma arith]: #463
+#468 := [unit-resolution #466 #163]: #525
+#469 := (not #525)
+#465 := (or #469 #500)
+#470 := [th-lemma arith triangle-eq]: #465
+#460 := [unit-resolution #470 #468]: #500
+#491 := (<= #371 0::Int)
+#456 := [hypothesis]: #372
+#457 := (or #534 #491)
+#461 := [th-lemma arith triangle-eq]: #457
+#454 := [unit-resolution #461 #456]: #491
+#458 := (not #500)
+#455 := (not #491)
+#462 := (not #576)
+#459 := (or #380 #462 #455 #458)
+#445 := [th-lemma arith assign-bounds 1 1 -1]: #459
+#447 := [unit-resolution #445 #454 #453 #460]: #380
+#296 := (<= #168 0::Int)
+#498 := (<= #486 0::Int)
+#448 := (or #469 #498)
+#446 := [th-lemma arith triangle-eq]: #448
+#449 := [unit-resolution #446 #468]: #498
+#579 := (>= #15 0::Int)
+#431 := (or #558 #579)
+#433 := [th-lemma arith triangle-eq]: #431
+#434 := [unit-resolution #433 #539]: #579
+#492 := (>= #371 0::Int)
+#435 := (or #534 #492)
+#436 := [th-lemma arith triangle-eq]: #435
+#437 := [unit-resolution #436 #456]: #492
+#440 := (not #498)
+#439 := (not #492)
+#438 := (not #579)
+#441 := (or #296 #438 #439 #440)
+#442 := [th-lemma arith assign-bounds 1 1 -1]: #441
+#443 := [unit-resolution #442 #437 #434 #449]: #296
+#444 := (not #380)
+#432 := (not #296)
+#424 := (or #432 #444)
+#169 := (= #168 0::Int)
+#172 := (not #169)
+#60 := (+ #11 #15)
+#63 := (= f3 #60)
+#66 := (not #63)
+#173 := (iff #66 #172)
+#170 := (iff #63 #169)
+#171 := [rewrite]: #170
+#174 := [monotonicity #171]: #173
+#12 := (* #11 1::Int)
+#16 := (+ #12 #15)
+#17 := (= f3 #16)
+#18 := (not #17)
+#67 := (iff #18 #66)
+#64 := (iff #17 #63)
+#61 := (= #16 #60)
+#58 := (= #12 #11)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#65 := [monotonicity #62]: #64
+#68 := [monotonicity #65]: #67
+#52 := [asserted]: #18
+#69 := [mp #52 #68]: #66
+#175 := [mp #69 #174]: #172
+#421 := (or #169 #432 #444)
+#423 := [th-lemma arith triangle-eq]: #421
+#425 := [unit-resolution #423 #175]: #424
+#426 := [unit-resolution #425 #443 #447]: false
+#427 := [lemma #426]: #534
+#676 := (div #704 -1::Int)
+#681 := (* -1::Int #676)
+#393 := (+ #11 #681)
+#673 := (= #393 0::Int)
+#674 := (if #302 #372 #673)
+#552 := (or #381 #674)
+#664 := (if #381 #384 #674)
+#20 := (f5 f6 #19)
+#22 := (f4 #20 #21)
+#709 := (pattern #22)
+#103 := (div #97 #100)
+#269 := (* -1::Int #103)
+#270 := (+ #22 #269)
+#271 := (= #270 0::Int)
+#33 := (div #19 #21)
+#266 := (* -1::Int #33)
+#267 := (+ #22 #266)
+#268 := (= #267 0::Int)
+#272 := (if #233 #268 #271)
+#265 := (= #22 0::Int)
+#26 := (or #24 #25)
+#273 := (if #26 #265 #272)
+#710 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #709) #273)
+#276 := (forall (vars (?v0 Int) (?v1 Int)) #273)
+#713 := (iff #276 #710)
+#711 := (iff #273 #273)
+#712 := [refl]: #711
+#714 := [quant-intro #712]: #713
+#236 := (if #233 #33 #103)
+#239 := (if #26 0::Int #236)
+#242 := (= #22 #239)
+#245 := (forall (vars (?v0 Int) (?v1 Int)) #242)
+#277 := (iff #245 #276)
+#274 := (iff #242 #273)
+#275 := [rewrite]: #274
+#278 := [quant-intro #275]: #277
+#188 := (if #185 #33 #103)
+#191 := (if #26 0::Int #188)
+#194 := (= #22 #191)
+#197 := (forall (vars (?v0 Int) (?v1 Int)) #194)
+#246 := (iff #197 #245)
+#243 := (iff #194 #242)
+#240 := (= #191 #239)
+#237 := (= #188 #236)
+#238 := [monotonicity #235]: #237
+#241 := [monotonicity #238]: #240
+#244 := [monotonicity #241]: #243
+#247 := [quant-intro #244]: #246
+#221 := (~ #197 #197)
+#219 := (~ #194 #194)
+#220 := [refl]: #219
+#222 := [nnf-pos #220]: #221
+#106 := (if #93 #33 #103)
+#109 := (if #26 0::Int #106)
+#112 := (= #22 #109)
+#115 := (forall (vars (?v0 Int) (?v1 Int)) #112)
+#198 := (iff #115 #197)
+#195 := (iff #112 #194)
+#192 := (= #109 #191)
+#189 := (= #106 #188)
+#190 := [monotonicity #187]: #189
+#193 := [monotonicity #190]: #192
+#196 := [monotonicity #193]: #195
+#199 := [quant-intro #196]: #198
+#36 := (div #34 #35)
+#37 := (if #32 #33 #36)
+#38 := (if #26 0::Int #37)
+#39 := (= #22 #38)
+#40 := (forall (vars (?v0 Int) (?v1 Int)) #39)
+#116 := (iff #40 #115)
+#113 := (iff #39 #112)
+#110 := (= #38 #109)
+#107 := (= #37 #106)
+#104 := (= #36 #103)
+#105 := [monotonicity #99 #102]: #104
+#108 := [monotonicity #95 #105]: #107
+#111 := [monotonicity #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [quant-intro #114]: #116
+#53 := [asserted]: #40
+#118 := [mp #53 #117]: #115
+#200 := [mp #118 #199]: #197
+#217 := [mp~ #200 #222]: #197
+#248 := [mp #217 #247]: #245
+#279 := [mp #248 #278]: #276
+#715 := [mp #279 #714]: #710
+#661 := (not #710)
+#662 := (or #661 #664)
+#706 := (div #704 #705)
+#707 := (* -1::Int #706)
+#702 := (+ #11 #707)
+#708 := (= #702 0::Int)
+#698 := (if #360 #372 #708)
+#373 := (or #381 #382)
+#358 := (if #373 #384 #698)
+#667 := (or #661 #358)
+#663 := (iff #667 #662)
+#510 := (iff #662 #662)
+#511 := [rewrite]: #510
+#665 := (iff #358 #664)
+#671 := (iff #698 #674)
+#388 := (iff #708 #673)
+#394 := (= #702 #393)
+#391 := (= #707 #681)
+#680 := (= #706 #676)
+#677 := [monotonicity #402]: #680
+#392 := [monotonicity #677]: #391
+#672 := [monotonicity #392]: #394
+#670 := [monotonicity #672]: #388
+#675 := [monotonicity #679 #670]: #671
+#348 := (iff #373 #381)
+#359 := (or #381 false)
+#684 := (iff #359 #381)
+#347 := [rewrite]: #684
+#700 := (iff #373 #359)
+#343 := [monotonicity #699]: #700
+#349 := [trans #343 #347]: #348
+#666 := [monotonicity #349 #675]: #665
+#669 := [monotonicity #666]: #663
+#512 := [trans #669 #511]: #663
+#668 := [quant-inst #7 #10]: #667
+#654 := [mp #668 #512]: #662
+#531 := [unit-resolution #654 #715]: #664
+#642 := (not #664)
+#545 := (or #642 #381 #674)
+#538 := [def-axiom]: #545
+#507 := [unit-resolution #538 #531]: #552
+#501 := [unit-resolution #507 #508]: #674
+#649 := (not #674)
+#647 := (or #649 #659 #372)
+#650 := [def-axiom]: #647
+#502 := [unit-resolution #650 #501 #427]: #659
+#503 := [unit-resolution #651 #502]: #385
+#504 := [unit-resolution #658 #502]: #366
+#505 := [unit-resolution #530 #504 #503 #508]: false
+#488 := [lemma #505]: #381
+#506 := (or #527 #384)
+#542 := (or #642 #527 #384)
+#544 := [def-axiom]: #542
+#514 := [unit-resolution #544 #531]: #506
+#515 := [unit-resolution #514 #488]: #384
+#546 := (not #384)
+#516 := (or #546 #655)
+#517 := [th-lemma arith triangle-eq]: #516
+#518 := [unit-resolution #517 #515]: #655
+#519 := (or #527 #366)
+#520 := [th-lemma arith triangle-eq]: #519
+#521 := [unit-resolution #520 #488]: #366
+#522 := (not #655)
+#523 := (or #380 #522 #462 #406)
+#524 := [th-lemma arith assign-bounds 1 1 -1]: #523
+#509 := [unit-resolution #524 #521 #518 #453]: #380
+#656 := (>= #11 0::Int)
+#487 := (or #546 #656)
+#494 := [th-lemma arith triangle-eq]: #487
+#496 := [unit-resolution #494 #515]: #656
+#497 := (or #527 #385)
+#428 := [th-lemma arith triangle-eq]: #497
+#429 := [unit-resolution #428 #488]: #385
+#422 := (not #656)
+#430 := (or #296 #422 #438 #692)
+#415 := [th-lemma arith assign-bounds 1 1 -1]: #430
+#416 := [unit-resolution #415 #429 #496 #434]: #296
+[unit-resolution #425 #416 #509]: false
+34442a78b76a0af7e551b55a4cf9e46f5680194f 558 0
+unsat
+#2 := false
+#23 := 0::Int
+decl f4 :: (-> S2 Int Int)
+#10 := 3::Int
+decl f5 :: (-> S3 Int S2)
+decl f3 :: Int
+#7 := f3
+decl f6 :: S3
+#8 := f6
+#9 := (f5 f6 f3)
+#11 := (f4 #9 3::Int)
+#659 := (>= #11 0::Int)
+#387 := (= #11 0::Int)
+#384 := (= f3 0::Int)
+#530 := (not #384)
+#566 := [hypothesis]: #530
+#388 := (<= f3 0::Int)
+#369 := (>= f3 0::Int)
+#409 := (not #369)
+#695 := (not #388)
+#304 := (or #695 #409)
+#662 := (not #304)
+#167 := -3::Int
+#97 := -1::Int
+#707 := (* -1::Int f3)
+#679 := (div #707 -3::Int)
+#684 := (* -1::Int #679)
+#396 := (+ #11 #684)
+#676 := (= #396 0::Int)
+#493 := (div f3 3::Int)
+#700 := (* -1::Int #493)
+#374 := (+ #11 #700)
+#375 := (= #374 0::Int)
+#677 := (if #304 #375 #676)
+#567 := (or #384 #677)
+#667 := (if #384 #387 #677)
+#21 := (:var 0 Int)
+#19 := (:var 1 Int)
+#20 := (f5 f6 #19)
+#22 := (f4 #20 #21)
+#712 := (pattern #22)
+#101 := (* -1::Int #21)
+#98 := (* -1::Int #19)
+#104 := (div #98 #101)
+#271 := (* -1::Int #104)
+#272 := (+ #22 #271)
+#273 := (= #272 0::Int)
+#33 := (div #19 #21)
+#268 := (* -1::Int #33)
+#269 := (+ #22 #268)
+#270 := (= #269 0::Int)
+#75 := (<= #21 0::Int)
+#178 := (>= #19 0::Int)
+#231 := (or #178 #75)
+#232 := (not #231)
+#71 := (<= #19 0::Int)
+#227 := (or #71 #75)
+#228 := (not #227)
+#235 := (or #228 #232)
+#274 := (if #235 #270 #273)
+#267 := (= #22 0::Int)
+#25 := (= #21 0::Int)
+#24 := (= #19 0::Int)
+#26 := (or #24 #25)
+#275 := (if #26 #267 #274)
+#713 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #712) #275)
+#278 := (forall (vars (?v0 Int) (?v1 Int)) #275)
+#716 := (iff #278 #713)
+#714 := (iff #275 #275)
+#715 := [refl]: #714
+#717 := [quant-intro #715]: #716
+#238 := (if #235 #33 #104)
+#241 := (if #26 0::Int #238)
+#244 := (= #22 #241)
+#247 := (forall (vars (?v0 Int) (?v1 Int)) #244)
+#279 := (iff #247 #278)
+#276 := (iff #244 #275)
+#277 := [rewrite]: #276
+#280 := [quant-intro #277]: #279
+#76 := (not #75)
+#181 := (not #178)
+#184 := (and #181 #76)
+#72 := (not #71)
+#79 := (and #72 #76)
+#187 := (or #79 #184)
+#190 := (if #187 #33 #104)
+#193 := (if #26 0::Int #190)
+#196 := (= #22 #193)
+#199 := (forall (vars (?v0 Int) (?v1 Int)) #196)
+#248 := (iff #199 #247)
+#245 := (iff #196 #244)
+#242 := (= #193 #241)
+#239 := (= #190 #238)
+#236 := (iff #187 #235)
+#233 := (iff #184 #232)
+#234 := [rewrite]: #233
+#229 := (iff #79 #228)
+#230 := [rewrite]: #229
+#237 := [monotonicity #230 #234]: #236
+#240 := [monotonicity #237]: #239
+#243 := [monotonicity #240]: #242
+#246 := [monotonicity #243]: #245
+#249 := [quant-intro #246]: #248
+#165 := (~ #199 #199)
+#221 := (~ #196 #196)
+#222 := [refl]: #221
+#166 := [nnf-pos #222]: #165
+#82 := (<= 0::Int #19)
+#83 := (not #82)
+#91 := (and #83 #76)
+#94 := (or #79 #91)
+#107 := (if #94 #33 #104)
+#110 := (if #26 0::Int #107)
+#113 := (= #22 #110)
+#116 := (forall (vars (?v0 Int) (?v1 Int)) #113)
+#200 := (iff #116 #199)
+#197 := (iff #113 #196)
+#194 := (= #110 #193)
+#191 := (= #107 #190)
+#188 := (iff #94 #187)
+#185 := (iff #91 #184)
+#182 := (iff #83 #181)
+#179 := (iff #82 #178)
+#180 := [rewrite]: #179
+#183 := [monotonicity #180]: #182
+#186 := [monotonicity #183]: #185
+#189 := [monotonicity #186]: #188
+#192 := [monotonicity #189]: #191
+#195 := [monotonicity #192]: #194
+#198 := [monotonicity #195]: #197
+#201 := [quant-intro #198]: #200
+#35 := (- #21)
+#34 := (- #19)
+#36 := (div #34 #35)
+#28 := (< 0::Int #21)
+#30 := (< #19 0::Int)
+#31 := (and #30 #28)
+#27 := (< 0::Int #19)
+#29 := (and #27 #28)
+#32 := (or #29 #31)
+#37 := (if #32 #33 #36)
+#38 := (if #26 0::Int #37)
+#39 := (= #22 #38)
+#40 := (forall (vars (?v0 Int) (?v1 Int)) #39)
+#117 := (iff #40 #116)
+#114 := (iff #39 #113)
+#111 := (= #38 #110)
+#108 := (= #37 #107)
+#105 := (= #36 #104)
+#102 := (= #35 #101)
+#103 := [rewrite]: #102
+#99 := (= #34 #98)
+#100 := [rewrite]: #99
+#106 := [monotonicity #100 #103]: #105
+#95 := (iff #32 #94)
+#92 := (iff #31 #91)
+#77 := (iff #28 #76)
+#78 := [rewrite]: #77
+#84 := (iff #30 #83)
+#88 := (iff #83 #83)
+#86 := (iff #82 #82)
+#87 := [rewrite]: #86
+#89 := [monotonicity #87]: #88
+#85 := [rewrite]: #84
+#90 := [trans #85 #89]: #84
+#93 := [monotonicity #90 #78]: #92
+#80 := (iff #29 #79)
+#73 := (iff #27 #72)
+#74 := [rewrite]: #73
+#81 := [monotonicity #74 #78]: #80
+#96 := [monotonicity #81 #93]: #95
+#109 := [monotonicity #96 #106]: #108
+#112 := [monotonicity #109]: #111
+#115 := [monotonicity #112]: #114
+#118 := [quant-intro #115]: #117
+#53 := [asserted]: #40
+#119 := [mp #53 #118]: #116
+#202 := [mp #119 #201]: #199
+#219 := [mp~ #202 #166]: #199
+#250 := [mp #219 #249]: #247
+#281 := [mp #250 #280]: #278
+#718 := [mp #281 #717]: #713
+#664 := (not #713)
+#665 := (or #664 #667)
+#708 := (* -1::Int 3::Int)
+#709 := (div #707 #708)
+#710 := (* -1::Int #709)
+#705 := (+ #11 #710)
+#711 := (= #705 0::Int)
+#389 := (<= 3::Int 0::Int)
+#704 := (or #369 #389)
+#706 := (not #704)
+#386 := (or #388 #389)
+#390 := (not #386)
+#363 := (or #390 #706)
+#701 := (if #363 #375 #711)
+#385 := (= 3::Int 0::Int)
+#376 := (or #384 #385)
+#361 := (if #376 #387 #701)
+#670 := (or #664 #361)
+#666 := (iff #670 #665)
+#513 := (iff #665 #665)
+#514 := [rewrite]: #513
+#668 := (iff #361 #667)
+#674 := (iff #701 #677)
+#391 := (iff #711 #676)
+#397 := (= #705 #396)
+#394 := (= #710 #684)
+#683 := (= #709 #679)
+#404 := (= #708 -3::Int)
+#405 := [rewrite]: #404
+#680 := [monotonicity #405]: #683
+#395 := [monotonicity #680]: #394
+#675 := [monotonicity #395]: #397
+#673 := [monotonicity #675]: #391
+#681 := (iff #363 #304)
+#410 := (iff #706 #409)
+#686 := (iff #704 #369)
+#338 := (or #369 false)
+#699 := (iff #338 #369)
+#685 := [rewrite]: #699
+#698 := (iff #704 #338)
+#353 := (iff #389 false)
+#689 := [rewrite]: #353
+#696 := [monotonicity #689]: #698
+#408 := [trans #696 #685]: #686
+#411 := [monotonicity #408]: #410
+#697 := (iff #390 #695)
+#694 := (iff #386 #388)
+#690 := (or #388 false)
+#693 := (iff #690 #388)
+#688 := [rewrite]: #693
+#691 := (iff #386 #690)
+#692 := [monotonicity #689]: #691
+#332 := [trans #692 #688]: #694
+#337 := [monotonicity #332]: #697
+#682 := [monotonicity #337 #411]: #681
+#678 := [monotonicity #682 #673]: #674
+#351 := (iff #376 #384)
+#362 := (or #384 false)
+#687 := (iff #362 #384)
+#350 := [rewrite]: #687
+#703 := (iff #376 #362)
+#366 := (iff #385 false)
+#702 := [rewrite]: #366
+#346 := [monotonicity #702]: #703
+#352 := [trans #346 #350]: #351
+#669 := [monotonicity #352 #678]: #668
+#672 := [monotonicity #669]: #666
+#515 := [trans #672 #514]: #666
+#671 := [quant-inst #7 #10]: #670
+#657 := [mp #671 #515]: #665
+#570 := [unit-resolution #657 #718]: #667
+#645 := (not #667)
+#548 := (or #645 #384 #677)
+#541 := [def-axiom]: #548
+#572 := [unit-resolution #541 #570]: #567
+#568 := [unit-resolution #572 #566]: #677
+#648 := (mod #707 -3::Int)
+decl f7 :: S3
+#13 := f7
+#14 := (f5 f7 f3)
+#15 := (f4 #14 3::Int)
+#629 := (+ #15 #648)
+#632 := (= #629 0::Int)
+#492 := (mod f3 3::Int)
+#647 := (* -1::Int #492)
+#634 := (+ #15 #647)
+#636 := (= #634 0::Int)
+#617 := (if #304 #636 #632)
+#574 := (or #384 #617)
+#643 := (= #15 0::Int)
+#621 := (if #384 #643 #617)
+#41 := (f5 f7 #19)
+#42 := (f4 #41 #21)
+#719 := (pattern #42)
+#120 := (mod #98 #101)
+#287 := (+ #42 #120)
+#288 := (= #287 0::Int)
+#43 := (mod #19 #21)
+#284 := (* -1::Int #43)
+#285 := (+ #42 #284)
+#286 := (= #285 0::Int)
+#289 := (if #235 #286 #288)
+#283 := (= #42 0::Int)
+#290 := (if #24 #283 #289)
+#282 := (= #42 #19)
+#291 := (if #25 #282 #290)
+#720 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #719) #291)
+#294 := (forall (vars (?v0 Int) (?v1 Int)) #291)
+#723 := (iff #294 #720)
+#721 := (iff #291 #291)
+#722 := [refl]: #721
+#724 := [quant-intro #722]: #723
+#126 := (* -1::Int #120)
+#251 := (if #235 #43 #126)
+#254 := (if #24 0::Int #251)
+#257 := (if #25 #19 #254)
+#260 := (= #42 #257)
+#263 := (forall (vars (?v0 Int) (?v1 Int)) #260)
+#295 := (iff #263 #294)
+#292 := (iff #260 #291)
+#293 := [rewrite]: #292
+#296 := [quant-intro #293]: #295
+#203 := (if #187 #43 #126)
+#206 := (if #24 0::Int #203)
+#209 := (if #25 #19 #206)
+#212 := (= #42 #209)
+#215 := (forall (vars (?v0 Int) (?v1 Int)) #212)
+#264 := (iff #215 #263)
+#261 := (iff #212 #260)
+#258 := (= #209 #257)
+#255 := (= #206 #254)
+#252 := (= #203 #251)
+#253 := [monotonicity #237]: #252
+#256 := [monotonicity #253]: #255
+#259 := [monotonicity #256]: #258
+#262 := [monotonicity #259]: #261
+#265 := [quant-intro #262]: #264
+#224 := (~ #215 #215)
+#220 := (~ #212 #212)
+#223 := [refl]: #220
+#225 := [nnf-pos #223]: #224
+#131 := (if #94 #43 #126)
+#134 := (if #24 0::Int #131)
+#137 := (if #25 #19 #134)
+#140 := (= #42 #137)
+#143 := (forall (vars (?v0 Int) (?v1 Int)) #140)
+#216 := (iff #143 #215)
+#213 := (iff #140 #212)
+#210 := (= #137 #209)
+#207 := (= #134 #206)
+#204 := (= #131 #203)
+#205 := [monotonicity #189]: #204
+#208 := [monotonicity #205]: #207
+#211 := [monotonicity #208]: #210
 #214 := [monotonicity #211]: #213
 #217 := [quant-intro #214]: #216
-#201 := (iff #47 #200)
-#198 := (iff #46 #197)
-#195 := (= #45 #194)
-#192 := (= #44 #191)
-#189 := (= #43 #188)
-#186 := (= #42 #183)
-#180 := (- #177)
-#184 := (= #180 #183)
-#185 := [rewrite]: #184
-#181 := (= #42 #180)
-#178 := (= #41 #177)
-#117 := (= #32 #116)
-#118 := [rewrite]: #117
-#114 := (= #31 #113)
-#115 := [rewrite]: #114
-#179 := [monotonicity #115 #118]: #178
-#182 := [monotonicity #179]: #181
-#187 := [trans #182 #185]: #186
-#110 := (iff #29 #109)
-#107 := (iff #28 #106)
-#108 := [rewrite]: #107
-#111 := [monotonicity #108]: #110
-#190 := [monotonicity #111 #187]: #189
-#98 := (iff #21 #97)
-#99 := [rewrite]: #98
-#193 := [monotonicity #99 #190]: #192
-#101 := (iff #22 #100)
-#102 := [rewrite]: #101
-#196 := [monotonicity #102 #193]: #195
-#199 := [monotonicity #196]: #198
-#202 := [quant-intro #199]: #201
-#219 := [trans #202 #217]: #218
-#176 := [asserted]: #47
-#220 := [mp #176 #219]: #215
-#223 := [mp~ #220 #227]: #215
-#271 := [mp #223 #270]: #268
-#302 := [mp #271 #301]: #299
-#787 := [mp #302 #786]: #782
-#9 := 3::Int
-#68 := -3::Int
-#71 := (f4 f5 -3::Int)
-#74 := (f3 #71 3::Int)
-#77 := (= #74 0::Int)
-#90 := (not #77)
-#10 := (- 3::Int)
-#11 := (f4 f5 #10)
-#12 := (f3 #11 3::Int)
-#14 := (= #12 0::Int)
-#15 := (not #14)
-#93 := (iff #15 #90)
-#80 := (= 0::Int #74)
-#85 := (not #80)
-#91 := (iff #85 #90)
-#88 := (iff #80 #77)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#86 := (iff #15 #85)
-#83 := (iff #14 #80)
-#81 := (iff #77 #80)
-#82 := [rewrite]: #81
-#78 := (iff #14 #77)
-#75 := (= #12 #74)
-#72 := (= #11 #71)
-#69 := (= #10 -3::Int)
-#70 := [rewrite]: #69
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73]: #75
-#79 := [monotonicity #76]: #78
-#84 := [trans #79 #82]: #83
-#87 := [monotonicity #84]: #86
-#94 := [trans #87 #92]: #93
-#67 := [asserted]: #15
-#95 := [mp #67 #94]: #90
-#615 := (not #782)
-#708 := (or #615 #77)
-#360 := (* -1::Int 3::Int)
-#445 := (* -1::Int -3::Int)
-#446 := (mod #445 #360)
-#447 := (+ #74 #446)
-#438 := (= #447 0::Int)
-#449 := (mod -3::Int 3::Int)
-#450 := (* -1::Int #449)
-#378 := (+ #74 #450)
-#451 := (= #378 0::Int)
-#448 := (>= -3::Int 0::Int)
-#452 := (<= 3::Int 0::Int)
-#431 := (or #452 #448)
-#766 := (not #431)
-#768 := (<= -3::Int 0::Int)
-#425 := (or #768 #452)
-#555 := (not #425)
-#762 := (or #555 #766)
-#436 := (ite #762 #451 #438)
-#437 := (= -3::Int 0::Int)
-#769 := (ite #437 #77 #436)
-#770 := (= -3::Int #74)
-#771 := (= 3::Int 0::Int)
-#772 := (ite #771 #770 #769)
-#705 := (or #615 #772)
-#696 := (iff #705 #708)
-#690 := (iff #708 #708)
-#687 := [rewrite]: #690
-#613 := (iff #772 #77)
-#423 := (= #74 -3::Int)
-#609 := (ite false #423 #77)
-#611 := (iff #609 #77)
-#612 := [rewrite]: #611
-#610 := (iff #772 #609)
-#592 := (iff #769 #77)
-#706 := (ite false #77 #77)
-#704 := (iff #706 #77)
-#707 := [rewrite]: #704
-#608 := (iff #769 #706)
-#599 := (iff #436 #77)
-#1 := true
-#714 := (ite true #77 #77)
-#597 := (iff #714 #77)
-#598 := [rewrite]: #597
-#712 := (iff #436 #714)
-#711 := (iff #438 #77)
-#557 := (= #447 #74)
-#731 := (+ #74 0::Int)
-#732 := (= #731 #74)
-#733 := [rewrite]: #732
-#554 := (= #447 #731)
-#718 := (= #446 0::Int)
-#722 := (mod 3::Int -3::Int)
-#723 := (= #722 0::Int)
-#724 := [rewrite]: #723
-#716 := (= #446 #722)
-#720 := (= #360 -3::Int)
-#721 := [rewrite]: #720
-#577 := (= #445 3::Int)
-#719 := [rewrite]: #577
-#717 := [monotonicity #719 #721]: #716
-#725 := [trans #717 #724]: #718
-#556 := [monotonicity #725]: #554
-#710 := [trans #556 #733]: #557
-#713 := [monotonicity #710]: #711
-#575 := (iff #451 #77)
-#728 := (= #378 #74)
-#726 := (= #378 #731)
-#729 := (= #450 0::Int)
-#453 := (* -1::Int 0::Int)
-#736 := (= #453 0::Int)
-#740 := [rewrite]: #736
-#735 := (= #450 #453)
-#737 := (= #449 0::Int)
-#738 := [rewrite]: #737
-#739 := [monotonicity #738]: #735
-#730 := [trans #739 #740]: #729
-#727 := [monotonicity #730]: #726
-#734 := [trans #727 #733]: #728
-#576 := [monotonicity #734]: #575
-#458 := (iff #762 true)
-#745 := (or false true)
-#456 := (iff #745 true)
-#457 := [rewrite]: #456
-#742 := (iff #762 #745)
-#467 := (iff #766 true)
-#473 := (not false)
-#744 := (iff #473 true)
-#466 := [rewrite]: #744
-#366 := (iff #766 #473)
-#471 := (iff #431 false)
-#758 := (or false false)
-#748 := (iff #758 false)
-#470 := [rewrite]: #748
-#761 := (iff #431 #758)
-#400 := (iff #448 false)
-#760 := [rewrite]: #400
-#749 := (iff #452 false)
-#412 := [rewrite]: #749
-#747 := [monotonicity #412 #760]: #761
-#472 := [trans #747 #470]: #471
-#743 := [monotonicity #472]: #366
-#741 := [trans #743 #466]: #467
-#759 := (iff #555 false)
-#755 := (not true)
-#394 := (iff #755 false)
-#757 := [rewrite]: #394
-#750 := (iff #555 #755)
-#753 := (iff #425 true)
-#413 := (or true false)
-#751 := (iff #413 true)
-#752 := [rewrite]: #751
-#414 := (iff #425 #413)
-#765 := (iff #768 true)
-#408 := [rewrite]: #765
-#415 := [monotonicity #408 #412]: #414
-#754 := [trans #415 #752]: #753
-#756 := [monotonicity #754]: #750
-#399 := [trans #756 #757]: #759
-#746 := [monotonicity #399 #741]: #742
-#459 := [trans #746 #457]: #458
-#715 := [monotonicity #459 #576 #713]: #712
-#558 := [trans #715 #598]: #599
-#764 := (iff #437 false)
-#424 := [rewrite]: #764
-#703 := [monotonicity #424 #558]: #608
-#607 := [trans #703 #707]: #592
-#763 := (iff #770 #423)
-#428 := [rewrite]: #763
-#767 := (iff #771 false)
-#773 := [rewrite]: #767
-#603 := [monotonicity #773 #428 #607]: #610
-#614 := [trans #603 #612]: #613
-#698 := [monotonicity #614]: #696
-#689 := [trans #698 #687]: #696
-#709 := [quant-inst #68 #9]: #705
-#699 := [mp #709 #689]: #708
-[unit-resolution #699 #95 #787]: false
-unsat
-87d1d567f09067d2cc55adc1f2aa0c235a1e5e4a 359 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#20 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#18 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#40 := (f4 f5 #18)
-#41 := (f3 #40 #20)
-#767 := (pattern #41)
-#22 := 0::Int
-#105 := -1::Int
-#109 := (* -1::Int #20)
-#106 := (* -1::Int #18)
-#164 := (mod #106 #109)
-#279 := (+ #41 #164)
-#280 := (= #279 0::Int)
-#42 := (mod #18 #20)
-#276 := (* -1::Int #42)
-#277 := (+ #41 #276)
-#278 := (= #277 0::Int)
-#138 := (>= #18 0::Int)
-#131 := (<= #20 0::Int)
-#223 := (or #131 #138)
-#224 := (not #223)
-#127 := (<= #18 0::Int)
-#221 := (or #127 #131)
-#222 := (not #221)
-#227 := (or #222 #224)
-#281 := (ite #227 #278 #280)
-#275 := (= #41 0::Int)
-#23 := (= #18 0::Int)
-#282 := (ite #23 #275 #281)
-#274 := (= #18 #41)
-#24 := (= #20 0::Int)
-#283 := (ite #24 #274 #282)
-#768 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #767) #283)
-#286 := (forall (vars (?v0 Int) (?v1 Int)) #283)
-#771 := (iff #286 #768)
-#769 := (iff #283 #283)
-#770 := [refl]: #769
-#772 := [quant-intro #770]: #771
-#170 := (* -1::Int #164)
-#243 := (ite #227 #42 #170)
-#246 := (ite #23 0::Int #243)
-#249 := (ite #24 #18 #246)
-#252 := (= #41 #249)
-#255 := (forall (vars (?v0 Int) (?v1 Int)) #252)
-#287 := (iff #255 #286)
-#284 := (iff #252 #283)
-#285 := [rewrite]: #284
-#288 := [quant-intro #285]: #287
-#139 := (not #138)
-#132 := (not #131)
-#142 := (and #132 #139)
-#128 := (not #127)
-#135 := (and #128 #132)
-#145 := (or #135 #142)
-#190 := (ite #145 #42 #170)
-#193 := (ite #23 0::Int #190)
-#196 := (ite #24 #18 #193)
-#199 := (= #41 #196)
-#202 := (forall (vars (?v0 Int) (?v1 Int)) #199)
-#256 := (iff #202 #255)
-#253 := (iff #199 #252)
-#250 := (= #196 #249)
-#247 := (= #193 #246)
-#244 := (= #190 #243)
-#228 := (iff #145 #227)
-#225 := (iff #142 #224)
-#226 := [rewrite]: #225
-#215 := (iff #135 #222)
-#216 := [rewrite]: #215
-#229 := [monotonicity #216 #226]: #228
-#245 := [monotonicity #229]: #244
-#248 := [monotonicity #245]: #247
-#251 := [monotonicity #248]: #250
-#254 := [monotonicity #251]: #253
-#257 := [quant-intro #254]: #256
-#213 := (~ #202 #202)
-#212 := (~ #199 #199)
-#209 := [refl]: #212
-#214 := [nnf-pos #209]: #213
-#34 := (- #20)
-#33 := (- #18)
-#43 := (mod #33 #34)
-#44 := (- #43)
-#27 := (< 0::Int #20)
-#29 := (< #18 0::Int)
-#30 := (and #29 #27)
-#26 := (< 0::Int #18)
-#28 := (and #26 #27)
-#31 := (or #28 #30)
-#45 := (ite #31 #42 #44)
-#46 := (ite #23 0::Int #45)
-#47 := (ite #24 #18 #46)
-#48 := (= #41 #47)
-#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
-#205 := (iff #49 #202)
-#99 := (and #27 #29)
-#102 := (or #28 #99)
-#175 := (ite #102 #42 #170)
-#178 := (ite #23 0::Int #175)
-#181 := (ite #24 #18 #178)
-#184 := (= #41 #181)
-#187 := (forall (vars (?v0 Int) (?v1 Int)) #184)
-#203 := (iff #187 #202)
-#200 := (iff #184 #199)
-#197 := (= #181 #196)
-#194 := (= #178 #193)
-#191 := (= #175 #190)
-#146 := (iff #102 #145)
-#143 := (iff #99 #142)
-#140 := (iff #29 #139)
-#141 := [rewrite]: #140
-#133 := (iff #27 #132)
-#134 := [rewrite]: #133
-#144 := [monotonicity #134 #141]: #143
-#136 := (iff #28 #135)
-#129 := (iff #26 #128)
-#130 := [rewrite]: #129
-#137 := [monotonicity #130 #134]: #136
-#147 := [monotonicity #137 #144]: #146
-#192 := [monotonicity #147]: #191
-#195 := [monotonicity #192]: #194
-#198 := [monotonicity #195]: #197
-#201 := [monotonicity #198]: #200
-#204 := [quant-intro #201]: #203
-#188 := (iff #49 #187)
-#185 := (iff #48 #184)
-#182 := (= #47 #181)
-#179 := (= #46 #178)
-#176 := (= #45 #175)
-#173 := (= #44 #170)
-#167 := (- #164)
-#171 := (= #167 #170)
-#172 := [rewrite]: #171
-#168 := (= #44 #167)
-#165 := (= #43 #164)
-#110 := (= #34 #109)
-#111 := [rewrite]: #110
-#107 := (= #33 #106)
-#108 := [rewrite]: #107
-#166 := [monotonicity #108 #111]: #165
-#169 := [monotonicity #166]: #168
-#174 := [trans #169 #172]: #173
-#103 := (iff #31 #102)
-#100 := (iff #30 #99)
-#101 := [rewrite]: #100
-#104 := [monotonicity #101]: #103
-#177 := [monotonicity #104 #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [monotonicity #180]: #182
-#186 := [monotonicity #183]: #185
-#189 := [quant-intro #186]: #188
-#206 := [trans #189 #204]: #205
-#163 := [asserted]: #49
-#207 := [mp #163 #206]: #202
-#210 := [mp~ #207 #214]: #202
-#258 := [mp #210 #257]: #255
-#289 := [mp #258 #288]: #286
-#773 := [mp #289 #772]: #768
-#14 := 1::Int
-#12 := 3::Int
-#70 := -5::Int
-#73 := (f4 f5 -5::Int)
-#76 := (f3 #73 3::Int)
-#79 := (= #76 1::Int)
-#92 := (not #79)
-#9 := 5::Int
-#10 := (- 5::Int)
-#11 := (f4 f5 #10)
-#13 := (f3 #11 3::Int)
-#15 := (= #13 1::Int)
-#16 := (not #15)
-#95 := (iff #16 #92)
-#82 := (= 1::Int #76)
-#87 := (not #82)
-#93 := (iff #87 #92)
-#90 := (iff #82 #79)
-#91 := [rewrite]: #90
-#94 := [monotonicity #91]: #93
-#88 := (iff #16 #87)
-#85 := (iff #15 #82)
-#83 := (iff #79 #82)
-#84 := [rewrite]: #83
-#80 := (iff #15 #79)
-#77 := (= #13 #76)
-#74 := (= #11 #73)
-#71 := (= #10 -5::Int)
+#44 := (mod #34 #35)
+#45 := (- #44)
+#46 := (if #32 #43 #45)
+#47 := (if #24 0::Int #46)
+#48 := (if #25 #19 #47)
+#49 := (= #42 #48)
+#50 := (forall (vars (?v0 Int) (?v1 Int)) #49)
+#144 := (iff #50 #143)
+#141 := (iff #49 #140)
+#138 := (= #48 #137)
+#135 := (= #47 #134)
+#132 := (= #46 #131)
+#129 := (= #45 #126)
+#123 := (- #120)
+#127 := (= #123 #126)
+#128 := [rewrite]: #127
+#124 := (= #45 #123)
+#121 := (= #44 #120)
+#122 := [monotonicity #100 #103]: #121
+#125 := [monotonicity #122]: #124
+#130 := [trans #125 #128]: #129
+#133 := [monotonicity #96 #130]: #132
+#136 := [monotonicity #133]: #135
+#139 := [monotonicity #136]: #138
+#142 := [monotonicity #139]: #141
+#145 := [quant-intro #142]: #144
+#54 := [asserted]: #50
+#146 := [mp #54 #145]: #143
+#218 := [mp #146 #217]: #215
+#226 := [mp~ #218 #225]: #215
+#266 := [mp #226 #265]: #263
+#297 := [mp #266 #296]: #294
+#725 := [mp #297 #724]: #720
+#612 := (not #720)
+#616 := (or #612 #621)
+#628 := (mod #707 #708)
+#625 := (+ #15 #628)
+#627 := (= #625 0::Int)
+#637 := (if #363 #636 #627)
+#638 := (if #384 #643 #637)
+#646 := (= #15 f3)
+#639 := (if #385 #646 #638)
+#596 := (or #612 #639)
+#599 := (iff #596 #616)
+#601 := (iff #616 #616)
+#602 := [rewrite]: #601
+#614 := (iff #639 #621)
+#619 := (if false #646 #621)
+#611 := (iff #619 #621)
+#613 := [rewrite]: #611
+#624 := (iff #639 #619)
+#622 := (iff #638 #621)
+#618 := (iff #637 #617)
+#626 := (iff #627 #632)
+#630 := (= #625 #629)
+#635 := (= #628 #648)
+#640 := [monotonicity #405]: #635
+#631 := [monotonicity #640]: #630
+#633 := [monotonicity #631]: #626
+#620 := [monotonicity #682 #633]: #618
+#623 := [monotonicity #620]: #622
+#610 := [monotonicity #702 #623]: #624
+#615 := [trans #610 #613]: #614
+#600 := [monotonicity #615]: #599
+#603 := [trans #600 #602]: #599
+#597 := [quant-inst #7 #10]: #596
+#604 := [mp #597 #603]: #616
+#573 := [unit-resolution #604 #725]: #621
+#578 := (not #621)
+#583 := (or #578 #384 #617)
+#584 := [def-axiom]: #583
+#575 := [unit-resolution #584 #573]: #574
+#571 := [unit-resolution #575 #566]: #617
+#652 := (not #677)
+#587 := (not #617)
+#430 := (or #662 #587 #652)
+#608 := (>= #634 0::Int)
+#489 := [hypothesis]: #617
+#490 := [hypothesis]: #304
+#588 := (or #587 #662 #636)
+#590 := [def-axiom]: #588
+#497 := [unit-resolution #590 #490 #489]: #636
+#593 := (not #636)
+#438 := (or #593 #608)
+#439 := [th-lemma arith triangle-eq]: #438
+#440 := [unit-resolution #439 #497]: #608
+#495 := (>= #374 0::Int)
+#480 := [hypothesis]: #677
+#650 := (or #652 #662 #375)
+#653 := [def-axiom]: #650
+#481 := [unit-resolution #653 #490 #480]: #375
+#537 := (not #375)
+#441 := (or #537 #495)
+#442 := [th-lemma arith triangle-eq]: #441
+#443 := [unit-resolution #442 #481]: #495
+#169 := (* -1::Int #15)
+#168 := (* -3::Int #11)
+#170 := (+ f3 #168 #169)
+#298 := (<= #170 0::Int)
+#444 := (not #298)
+#383 := (>= #170 0::Int)
+#503 := (not #383)
+#504 := [hypothesis]: #503
+#529 := (or #384 #383)
+#329 := (or #662 #383 #587 #652)
+#607 := (<= #634 0::Int)
+#499 := (or #593 #607)
+#500 := [th-lemma arith triangle-eq]: #499
+#501 := [unit-resolution #500 #497]: #607
+#502 := (* -3::Int #493)
+#557 := (+ f3 #647 #502)
+#532 := (>= #557 0::Int)
+#556 := (= #557 0::Int)
+#1 := true
+#164 := [true-axiom]: true
+#505 := (or false #556)
+#506 := [th-lemma arith]: #505
+#507 := [unit-resolution #506 #164]: #556
+#508 := (not #556)
+#491 := (or #508 #532)
+#509 := [th-lemma arith triangle-eq]: #491
+#479 := [unit-resolution #509 #507]: #532
+#494 := (<= #374 0::Int)
+#482 := (or #537 #494)
+#484 := [th-lemma arith triangle-eq]: #482
+#485 := [unit-resolution #484 #481]: #494
+#486 := [th-lemma arith farkas 3 -1 1 1 #485 #479 #504 #501]: false
+#487 := [lemma #486]: #329
+#576 := [unit-resolution #487 #571 #504 #568]: #662
+#660 := (or #304 #388)
+#654 := [def-axiom]: #660
+#538 := [unit-resolution #654 #576]: #388
+#655 := (or #304 #369)
+#661 := [def-axiom]: #655
+#562 := [unit-resolution #661 #576]: #369
+#563 := (or #384 #695 #409)
+#558 := [th-lemma arith triangle-eq]: #563
+#498 := [unit-resolution #558 #562 #538 #566]: false
+#525 := [lemma #498]: #529
+#526 := [unit-resolution #525 #504]: #384
+#527 := (or #530 #369)
+#512 := [th-lemma arith triangle-eq]: #527
+#528 := [unit-resolution #512 #526]: #369
+#605 := (<= #15 0::Int)
+#564 := (or #530 #643)
+#579 := (or #578 #530 #643)
+#582 := [def-axiom]: #579
+#483 := [unit-resolution #582 #573]: #564
+#488 := [unit-resolution #483 #526]: #643
+#585 := (not #643)
+#467 := (or #585 #605)
+#470 := [th-lemma arith triangle-eq]: #467
+#474 := [unit-resolution #470 #488]: #605
+#658 := (<= #11 0::Int)
+#476 := (or #530 #387)
+#545 := (or #645 #530 #387)
+#547 := [def-axiom]: #545
+#477 := [unit-resolution #547 #570]: #476
+#475 := [unit-resolution #477 #526]: #387
+#549 := (not #387)
+#478 := (or #549 #658)
+#466 := [th-lemma arith triangle-eq]: #478
+#469 := [unit-resolution #466 #475]: #658
+#471 := [th-lemma arith farkas -3 -1 -1 1 #469 #474 #504 #528]: false
+#472 := [lemma #471]: #383
+#435 := (or #444 #503)
+#171 := (= #170 0::Int)
+#174 := (not #171)
+#58 := (* 3::Int #11)
+#61 := (+ #58 #15)
+#64 := (= f3 #61)
+#67 := (not #64)
+#175 := (iff #67 #174)
+#172 := (iff #64 #171)
+#173 := [rewrite]: #172
+#176 := [monotonicity #173]: #175
+#12 := (* #11 3::Int)
+#16 := (+ #12 #15)
+#17 := (= f3 #16)
+#18 := (not #17)
+#68 := (iff #18 #67)
+#65 := (iff #17 #64)
+#62 := (= #16 #61)
+#59 := (= #12 #58)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#66 := [monotonicity #63]: #65
+#69 := [monotonicity #66]: #68
+#52 := [asserted]: #18
+#70 := [mp #52 #69]: #67
+#177 := [mp #70 #176]: #174
+#445 := (or #171 #444 #503)
+#446 := [th-lemma arith triangle-eq]: #445
+#447 := [unit-resolution #446 #177]: #435
+#424 := [unit-resolution #447 #472]: #444
+#511 := (<= #557 0::Int)
+#426 := (or #508 #511)
+#427 := [th-lemma arith triangle-eq]: #426
+#428 := [unit-resolution #427 #507]: #511
+#429 := [th-lemma arith farkas -1 1 3 1 #428 #424 #443 #440]: false
+#431 := [lemma #429]: #430
+#468 := [unit-resolution #431 #571 #568]: #662
+#531 := [unit-resolution #654 #468]: #388
+#473 := [unit-resolution #661 #468]: #369
+#463 := [unit-resolution #558 #473 #531 #566]: false
+#453 := [lemma #463]: #384
+#533 := [unit-resolution #477 #453]: #387
+#540 := (or #549 #659)
+#542 := [th-lemma arith triangle-eq]: #540
+#543 := [unit-resolution #542 #533]: #659
+#606 := (>= #15 0::Int)
+#544 := [unit-resolution #483 #453]: #643
+#554 := (or #585 #606)
+#534 := [th-lemma arith triangle-eq]: #554
+#555 := [unit-resolution #534 #544]: #606
+#510 := (or #530 #388)
+#516 := [th-lemma arith triangle-eq]: #510
+#517 := [unit-resolution #516 #453]: #388
+[th-lemma arith farkas -1/3 1/3 1/3 1 #517 #555 #424 #543]: false
+44e7de81026e9de87a6d1cf926d12ef2c6a20dc7 86 0
+unsat
+#2 := false
+#7 := 0::Int
+decl f3 :: Int
+#8 := f3
+#28 := -1::Int
+#29 := (* -1::Int f3)
+#70 := (>= f3 0::Int)
+#73 := (if #70 f3 #29)
+#93 := (* -1::Int #73)
+#96 := (+ #29 #93)
+#97 := (<= #96 0::Int)
+#69 := (= #29 #73)
+#88 := (not #70)
+#94 := (+ f3 #93)
+#95 := (<= #94 0::Int)
+#68 := (= f3 #73)
+#100 := [hypothesis]: #70
+#89 := (or #88 #68)
+#90 := [def-axiom]: #89
+#101 := [unit-resolution #90 #100]: #68
+#102 := (not #68)
+#103 := (or #102 #95)
+#104 := [th-lemma arith triangle-eq]: #103
+#105 := [unit-resolution #104 #101]: #95
+#80 := (>= #73 0::Int)
+#84 := (not #80)
+#19 := (<= 0::Int f3)
+#35 := (if #19 f3 #29)
+#40 := (<= 0::Int #35)
+#46 := (not #40)
+#85 := (iff #46 #84)
+#82 := (iff #40 #80)
+#76 := (<= 0::Int #73)
+#79 := (iff #76 #80)
+#81 := [rewrite]: #79
+#77 := (iff #40 #76)
+#74 := (= #35 #73)
+#71 := (iff #19 #70)
 #72 := [rewrite]: #71
 #75 := [monotonicity #72]: #74
 #78 := [monotonicity #75]: #77
-#81 := [monotonicity #78]: #80
-#86 := [trans #81 #84]: #85
-#89 := [monotonicity #86]: #88
-#96 := [trans #89 #94]: #95
-#69 := [asserted]: #16
-#97 := [mp #69 #96]: #92
-#666 := (not #768)
-#668 := (or #666 #79)
-#347 := (* -1::Int 3::Int)
-#431 := (* -1::Int -5::Int)
-#432 := (mod #431 #347)
-#433 := (+ #76 #432)
-#424 := (= #433 0::Int)
-#435 := (mod -5::Int 3::Int)
-#436 := (* -1::Int #435)
-#437 := (+ #76 #436)
-#434 := (= #437 0::Int)
-#438 := (>= -5::Int 0::Int)
-#417 := (<= 3::Int 0::Int)
-#752 := (or #417 #438)
-#754 := (not #752)
-#411 := (<= -5::Int 0::Int)
-#541 := (or #411 #417)
-#748 := (not #541)
-#422 := (or #748 #754)
-#423 := (ite #422 #434 #424)
-#755 := (= #76 0::Int)
-#756 := (= -5::Int 0::Int)
-#757 := (ite #756 #755 #423)
-#758 := (= -5::Int #76)
-#753 := (= 3::Int 0::Int)
-#759 := (ite #753 #758 #757)
-#669 := (or #666 #759)
-#671 := (iff #669 #668)
-#672 := (iff #668 #668)
-#658 := [rewrite]: #672
-#681 := (iff #759 #79)
-#750 := (= #76 -5::Int)
-#677 := (ite false #750 #79)
-#680 := (iff #677 #79)
-#674 := [rewrite]: #680
-#678 := (iff #759 #677)
-#683 := (iff #757 #79)
-#673 := (ite false #755 #79)
-#686 := (iff #673 #79)
-#687 := [rewrite]: #686
-#675 := (iff #757 #673)
-#684 := (iff #423 #79)
-#596 := -2::Int
-#589 := (= #76 -2::Int)
-#1 := true
-#601 := (ite true #79 #589)
-#695 := (iff #601 #79)
-#682 := [rewrite]: #695
-#694 := (iff #423 #601)
-#599 := (iff #424 #589)
-#699 := 2::Int
-#692 := (+ 2::Int #76)
-#578 := (= #692 0::Int)
-#597 := (iff #578 #589)
-#598 := [rewrite]: #597
-#593 := (iff #424 #578)
-#690 := (= #433 #692)
-#584 := (+ #76 2::Int)
-#594 := (= #584 #692)
-#689 := [rewrite]: #594
-#585 := (= #433 #584)
-#701 := (= #432 2::Int)
-#711 := -3::Int
-#543 := (mod 5::Int -3::Int)
-#700 := (= #543 2::Int)
-#698 := [rewrite]: #700
-#696 := (= #432 #543)
-#540 := (= #347 -3::Int)
-#542 := [rewrite]: #540
-#710 := (= #431 5::Int)
-#704 := [rewrite]: #710
-#697 := [monotonicity #704 #542]: #696
-#583 := [trans #697 #698]: #701
-#544 := [monotonicity #583]: #585
-#693 := [trans #544 #689]: #690
-#595 := [monotonicity #693]: #593
-#600 := [trans #595 #598]: #599
-#703 := (iff #434 #79)
-#714 := (+ -1::Int #76)
-#705 := (= #714 0::Int)
-#708 := (iff #705 #79)
-#702 := [rewrite]: #708
-#706 := (iff #434 #705)
-#562 := (= #437 #714)
-#713 := (+ #76 -1::Int)
-#720 := (= #713 #714)
-#561 := [rewrite]: #720
-#718 := (= #437 #713)
-#717 := (= #436 -1::Int)
-#725 := (* -1::Int 1::Int)
-#715 := (= #725 -1::Int)
-#716 := [rewrite]: #715
-#722 := (= #436 #725)
-#439 := (= #435 1::Int)
-#721 := [rewrite]: #439
-#726 := [monotonicity #721]: #722
-#712 := [trans #726 #716]: #717
-#719 := [monotonicity #712]: #718
-#563 := [trans #719 #561]: #562
-#707 := [monotonicity #563]: #706
-#709 := [trans #707 #702]: #703
-#723 := (iff #422 true)
-#732 := (or false true)
-#444 := (iff #732 true)
-#445 := [rewrite]: #444
-#442 := (iff #422 #732)
-#731 := (iff #754 true)
-#729 := (not false)
-#453 := (iff #729 true)
-#727 := [rewrite]: #453
-#730 := (iff #754 #729)
-#459 := (iff #752 false)
-#733 := (or false false)
-#457 := (iff #733 false)
-#458 := [rewrite]: #457
-#734 := (iff #752 #733)
-#744 := (iff #438 false)
-#747 := [rewrite]: #744
-#399 := (iff #417 false)
-#400 := [rewrite]: #399
-#456 := [monotonicity #400 #747]: #734
-#353 := [trans #456 #458]: #459
-#452 := [monotonicity #353]: #730
-#728 := [trans #452 #727]: #731
-#386 := (iff #748 false)
-#742 := (not true)
-#745 := (iff #742 false)
-#385 := [rewrite]: #745
-#380 := (iff #748 #742)
-#741 := (iff #541 true)
-#401 := (or true false)
-#739 := (iff #401 true)
-#740 := [rewrite]: #739
-#737 := (iff #541 #401)
-#735 := (iff #411 true)
-#398 := [rewrite]: #735
-#738 := [monotonicity #398 #400]: #737
-#736 := [trans #738 #740]: #741
-#743 := [monotonicity #736]: #380
-#746 := [trans #743 #385]: #386
-#443 := [monotonicity #746 #728]: #442
-#724 := [trans #443 #445]: #723
-#691 := [monotonicity #724 #709 #600]: #694
-#676 := [trans #691 #682]: #684
-#751 := (iff #756 false)
-#394 := [rewrite]: #751
-#685 := [monotonicity #394 #676]: #675
-#688 := [trans #685 #687]: #683
-#414 := (iff #758 #750)
-#410 := [rewrite]: #414
-#749 := (iff #753 false)
-#409 := [rewrite]: #749
-#679 := [monotonicity #409 #410 #688]: #678
-#665 := [trans #679 #674]: #681
-#667 := [monotonicity #665]: #671
-#659 := [trans #667 #658]: #671
-#670 := [quant-inst #70 #12]: #669
-#661 := [mp #670 #659]: #668
-[unit-resolution #661 #97 #773]: false
-unsat
-a9cfdba4600f8dcec381f4d9749257e8345a31c8 353 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#20 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#18 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#40 := (f4 f5 #18)
-#41 := (f3 #40 #20)
-#769 := (pattern #41)
-#22 := 0::Int
-#70 := -1::Int
-#111 := (* -1::Int #20)
-#108 := (* -1::Int #18)
-#166 := (mod #108 #111)
-#281 := (+ #41 #166)
-#282 := (= #281 0::Int)
-#42 := (mod #18 #20)
-#278 := (* -1::Int #42)
-#279 := (+ #41 #278)
-#280 := (= #279 0::Int)
-#140 := (>= #18 0::Int)
-#133 := (<= #20 0::Int)
-#225 := (or #133 #140)
-#226 := (not #225)
-#129 := (<= #18 0::Int)
-#223 := (or #129 #133)
-#224 := (not #223)
-#229 := (or #224 #226)
-#283 := (ite #229 #280 #282)
-#277 := (= #41 0::Int)
-#23 := (= #18 0::Int)
-#284 := (ite #23 #277 #283)
-#276 := (= #18 #41)
-#24 := (= #20 0::Int)
-#285 := (ite #24 #276 #284)
-#770 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #769) #285)
-#288 := (forall (vars (?v0 Int) (?v1 Int)) #285)
-#773 := (iff #288 #770)
-#771 := (iff #285 #285)
-#772 := [refl]: #771
-#774 := [quant-intro #772]: #773
-#172 := (* -1::Int #166)
-#245 := (ite #229 #42 #172)
-#248 := (ite #23 0::Int #245)
-#251 := (ite #24 #18 #248)
-#254 := (= #41 #251)
-#257 := (forall (vars (?v0 Int) (?v1 Int)) #254)
-#289 := (iff #257 #288)
-#286 := (iff #254 #285)
-#287 := [rewrite]: #286
-#290 := [quant-intro #287]: #289
-#141 := (not #140)
-#134 := (not #133)
-#144 := (and #134 #141)
-#130 := (not #129)
-#137 := (and #130 #134)
-#147 := (or #137 #144)
-#192 := (ite #147 #42 #172)
-#195 := (ite #23 0::Int #192)
-#198 := (ite #24 #18 #195)
-#201 := (= #41 #198)
-#204 := (forall (vars (?v0 Int) (?v1 Int)) #201)
-#258 := (iff #204 #257)
-#255 := (iff #201 #254)
-#252 := (= #198 #251)
-#249 := (= #195 #248)
-#246 := (= #192 #245)
-#230 := (iff #147 #229)
-#227 := (iff #144 #226)
-#228 := [rewrite]: #227
-#217 := (iff #137 #224)
-#218 := [rewrite]: #217
-#231 := [monotonicity #218 #228]: #230
-#247 := [monotonicity #231]: #246
-#250 := [monotonicity #247]: #249
-#253 := [monotonicity #250]: #252
-#256 := [monotonicity #253]: #255
-#259 := [quant-intro #256]: #258
-#215 := (~ #204 #204)
-#214 := (~ #201 #201)
-#211 := [refl]: #214
-#216 := [nnf-pos #211]: #215
-#34 := (- #20)
-#33 := (- #18)
-#43 := (mod #33 #34)
-#44 := (- #43)
-#27 := (< 0::Int #20)
-#29 := (< #18 0::Int)
-#30 := (and #29 #27)
-#26 := (< 0::Int #18)
-#28 := (and #26 #27)
-#31 := (or #28 #30)
-#45 := (ite #31 #42 #44)
-#46 := (ite #23 0::Int #45)
-#47 := (ite #24 #18 #46)
-#48 := (= #41 #47)
-#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
-#207 := (iff #49 #204)
-#102 := (and #27 #29)
-#105 := (or #28 #102)
-#177 := (ite #105 #42 #172)
-#180 := (ite #23 0::Int #177)
-#183 := (ite #24 #18 #180)
-#186 := (= #41 #183)
-#189 := (forall (vars (?v0 Int) (?v1 Int)) #186)
-#205 := (iff #189 #204)
-#202 := (iff #186 #201)
-#199 := (= #183 #198)
-#196 := (= #180 #195)
-#193 := (= #177 #192)
-#148 := (iff #105 #147)
-#145 := (iff #102 #144)
-#142 := (iff #29 #141)
-#143 := [rewrite]: #142
-#135 := (iff #27 #134)
-#136 := [rewrite]: #135
-#146 := [monotonicity #136 #143]: #145
-#138 := (iff #28 #137)
-#131 := (iff #26 #130)
-#132 := [rewrite]: #131
-#139 := [monotonicity #132 #136]: #138
-#149 := [monotonicity #139 #146]: #148
-#194 := [monotonicity #149]: #193
-#197 := [monotonicity #194]: #196
-#200 := [monotonicity #197]: #199
-#203 := [monotonicity #200]: #202
-#206 := [quant-intro #203]: #205
-#190 := (iff #49 #189)
-#187 := (iff #48 #186)
-#184 := (= #47 #183)
-#181 := (= #46 #180)
-#178 := (= #45 #177)
-#175 := (= #44 #172)
-#169 := (- #166)
-#173 := (= #169 #172)
-#174 := [rewrite]: #173
-#170 := (= #44 #169)
-#167 := (= #43 #166)
-#112 := (= #34 #111)
+#83 := [trans #78 #81]: #82
+#86 := [monotonicity #83]: #85
+#10 := (- f3)
+#9 := (< f3 0::Int)
+#11 := (if #9 #10 f3)
+#12 := (<= 0::Int #11)
+#13 := (not #12)
+#47 := (iff #13 #46)
+#41 := (iff #12 #40)
+#43 := (iff #40 #40)
+#44 := [rewrite]: #43
+#38 := (= #11 #35)
+#20 := (not #19)
+#32 := (if #20 #29 f3)
+#36 := (= #32 #35)
+#37 := [rewrite]: #36
+#33 := (= #11 #32)
+#30 := (= #10 #29)
+#31 := [rewrite]: #30
+#21 := (iff #9 #20)
+#25 := (iff #20 #20)
+#23 := (iff #19 #19)
+#24 := [rewrite]: #23
+#26 := [monotonicity #24]: #25
+#22 := [rewrite]: #21
+#27 := [trans #22 #26]: #21
+#34 := [monotonicity #27 #31]: #33
+#39 := [trans #34 #37]: #38
+#42 := [monotonicity #39]: #41
+#45 := [trans #42 #44]: #41
+#48 := [monotonicity #45]: #47
+#15 := [asserted]: #13
+#49 := [mp #15 #48]: #46
+#87 := [mp #49 #86]: #84
+#106 := [th-lemma arith farkas -1 1 1 #100 #87 #105]: false
+#107 := [lemma #106]: #88
+#91 := (or #70 #69)
+#92 := [def-axiom]: #91
+#99 := [unit-resolution #92 #107]: #69
+#108 := (not #69)
+#109 := (or #108 #97)
+#110 := [th-lemma arith triangle-eq]: #109
+#111 := [unit-resolution #110 #99]: #97
+[th-lemma arith farkas 1 1 1 #87 #107 #111]: false
+6eee9e55ae7eb673a1282f59fcbd03d15f5bb9fe 165 0
+unsat
+#2 := false
+#8 := 0::Int
+decl f3 :: Int
+#7 := f3
+#30 := -1::Int
+#31 := (* -1::Int f3)
+#78 := (>= f3 0::Int)
+#81 := (if #78 f3 #31)
+#77 := (>= #81 0::Int)
+#95 := (not #77)
+#76 := (<= #81 0::Int)
+#94 := (not #76)
+#96 := (or #94 #95)
+#145 := (* -1::Int #81)
+#148 := (+ #31 #145)
+#162 := (<= #148 0::Int)
+#119 := (= #31 #81)
+#109 := (not #78)
+#107 := (<= f3 0::Int)
+#108 := (not #107)
+#110 := (or #108 #109)
+#97 := (not #96)
+#164 := [hypothesis]: #97
+#139 := (or #96 #110)
+#111 := (not #110)
+#114 := (iff #96 #111)
+#13 := (= f3 0::Int)
+#84 := (= #81 0::Int)
+#87 := (not #84)
+#90 := (iff #87 #13)
+#115 := (iff #90 #114)
+#112 := (iff #13 #111)
 #113 := [rewrite]: #112
-#109 := (= #33 #108)
-#110 := [rewrite]: #109
-#168 := [monotonicity #110 #113]: #167
-#171 := [monotonicity #168]: #170
-#176 := [trans #171 #174]: #175
-#106 := (iff #31 #105)
-#103 := (iff #30 #102)
+#105 := (iff #87 #96)
+#100 := (not #97)
+#103 := (iff #100 #96)
 #104 := [rewrite]: #103
-#107 := [monotonicity #104]: #106
-#179 := [monotonicity #107 #176]: #178
-#182 := [monotonicity #179]: #181
-#185 := [monotonicity #182]: #184
-#188 := [monotonicity #185]: #187
-#191 := [quant-intro #188]: #190
-#208 := [trans #191 #206]: #207
-#165 := [asserted]: #49
-#209 := [mp #165 #208]: #204
-#212 := [mp~ #209 #216]: #204
-#260 := [mp #212 #259]: #257
-#291 := [mp #260 #290]: #288
-#775 := [mp #291 #774]: #770
-#76 := -3::Int
-#73 := (f4 f5 -1::Int)
-#79 := (f3 #73 -3::Int)
-#82 := (= #79 -1::Int)
-#95 := (not #82)
-#9 := 1::Int
-#10 := (- 1::Int)
-#12 := 3::Int
-#13 := (- 3::Int)
-#11 := (f4 f5 #10)
-#14 := (f3 #11 #13)
-#15 := (= #14 #10)
-#16 := (not #15)
-#98 := (iff #16 #95)
-#85 := (= -1::Int #79)
-#90 := (not #85)
-#96 := (iff #90 #95)
-#93 := (iff #85 #82)
-#94 := [rewrite]: #93
-#97 := [monotonicity #94]: #96
-#91 := (iff #16 #90)
-#88 := (iff #15 #85)
-#86 := (iff #82 #85)
-#87 := [rewrite]: #86
-#83 := (iff #15 #82)
-#71 := (= #10 -1::Int)
-#72 := [rewrite]: #71
-#80 := (= #14 #79)
-#77 := (= #13 -3::Int)
-#78 := [rewrite]: #77
-#74 := (= #11 #73)
-#75 := [monotonicity #72]: #74
-#81 := [monotonicity #75 #78]: #80
-#84 := [monotonicity #81 #72]: #83
-#89 := [trans #84 #87]: #88
-#92 := [monotonicity #89]: #91
-#99 := [trans #92 #97]: #98
-#69 := [asserted]: #16
-#100 := [mp #69 #99]: #95
-#690 := (not #770)
-#679 := (or #690 #82)
-#349 := (* -1::Int -3::Int)
-#433 := (* -1::Int -1::Int)
-#434 := (mod #433 #349)
-#435 := (+ #79 #434)
-#426 := (= #435 0::Int)
-#437 := (mod -1::Int -3::Int)
-#438 := (* -1::Int #437)
-#439 := (+ #79 #438)
-#436 := (= #439 0::Int)
-#440 := (>= -1::Int 0::Int)
-#419 := (<= -3::Int 0::Int)
-#754 := (or #419 #440)
-#756 := (not #754)
-#413 := (<= -1::Int 0::Int)
-#543 := (or #413 #419)
-#750 := (not #543)
-#424 := (or #750 #756)
-#425 := (ite #424 #436 #426)
-#757 := (= #79 0::Int)
-#758 := (= -1::Int 0::Int)
-#759 := (ite #758 #757 #425)
-#760 := (= -3::Int 0::Int)
-#755 := (ite #760 #85 #759)
-#680 := (or #690 #755)
-#682 := (iff #680 #679)
-#683 := (iff #679 #679)
-#667 := [rewrite]: #683
-#689 := (iff #755 #82)
-#678 := (ite false #82 #82)
-#687 := (iff #678 #82)
-#688 := [rewrite]: #687
-#675 := (iff #755 #678)
-#684 := (iff #759 #82)
-#602 := (ite false #757 #82)
-#693 := (iff #602 #82)
-#697 := [rewrite]: #693
-#603 := (iff #759 #602)
-#600 := (iff #425 #82)
-#734 := 2::Int
-#564 := (= #79 2::Int)
-#595 := (ite false #564 #82)
-#591 := (iff #595 #82)
-#599 := [rewrite]: #591
-#597 := (iff #425 #595)
-#695 := (iff #426 #82)
-#700 := (+ 1::Int #79)
-#546 := (= #700 0::Int)
-#691 := (iff #546 #82)
-#692 := [rewrite]: #691
-#694 := (iff #426 #546)
-#586 := (= #435 #700)
-#699 := (+ #79 1::Int)
-#703 := (= #699 #700)
-#585 := [rewrite]: #703
-#701 := (= #435 #699)
-#545 := (= #434 1::Int)
-#712 := (mod 1::Int 3::Int)
-#542 := (= #712 1::Int)
-#544 := [rewrite]: #542
-#706 := (= #434 #712)
-#705 := (= #349 3::Int)
-#711 := [rewrite]: #705
-#710 := (= #433 1::Int)
-#704 := [rewrite]: #710
-#713 := [monotonicity #704 #711]: #706
-#698 := [trans #713 #544]: #545
-#702 := [monotonicity #698]: #701
-#587 := [trans #702 #585]: #586
-#596 := [monotonicity #587]: #694
-#580 := [trans #596 #692]: #695
-#708 := (iff #436 #564)
-#726 := -2::Int
-#719 := (+ -2::Int #79)
-#716 := (= #719 0::Int)
-#565 := (iff #716 #564)
-#707 := [rewrite]: #565
-#722 := (iff #436 #716)
-#720 := (= #439 #719)
-#728 := (+ #79 -2::Int)
-#714 := (= #728 #719)
-#715 := [rewrite]: #714
-#717 := (= #439 #728)
-#727 := (= #438 -2::Int)
-#446 := (* -1::Int 2::Int)
-#441 := (= #446 -2::Int)
-#723 := [rewrite]: #441
-#447 := (= #438 #446)
-#444 := (= #437 2::Int)
-#445 := [rewrite]: #444
-#725 := [monotonicity #445]: #447
-#724 := [trans #725 #723]: #727
-#718 := [monotonicity #724]: #717
-#721 := [trans #718 #715]: #720
-#563 := [monotonicity #721]: #722
-#709 := [trans #563 #707]: #708
-#733 := (iff #424 false)
-#731 := (or false false)
-#455 := (iff #731 false)
-#729 := [rewrite]: #455
-#732 := (iff #424 #731)
-#461 := (iff #756 false)
-#1 := true
-#741 := (not true)
-#738 := (iff #741 false)
-#744 := [rewrite]: #738
-#459 := (iff #756 #741)
-#736 := (iff #754 true)
-#388 := (or true false)
-#749 := (iff #388 true)
-#735 := [rewrite]: #749
-#748 := (iff #754 #388)
-#747 := (iff #440 false)
-#387 := [rewrite]: #747
-#753 := (iff #419 true)
-#396 := [rewrite]: #753
-#746 := [monotonicity #396 #387]: #748
-#458 := [trans #746 #735]: #736
-#460 := [monotonicity #458]: #459
-#355 := [trans #460 #744]: #461
-#382 := (iff #750 false)
-#742 := (iff #750 #741)
-#739 := (iff #543 true)
-#737 := (or true true)
-#402 := (iff #737 true)
-#403 := [rewrite]: #402
-#400 := (iff #543 #737)
-#752 := (iff #413 true)
-#412 := [rewrite]: #752
-#401 := [monotonicity #412 #396]: #400
-#740 := [trans #401 #403]: #739
-#743 := [monotonicity #740]: #742
-#745 := [trans #743 #744]: #382
-#454 := [monotonicity #745 #355]: #732
-#730 := [trans #454 #729]: #733
-#598 := [monotonicity #730 #709 #580]: #597
-#601 := [trans #598 #599]: #600
-#411 := (iff #758 false)
-#416 := [rewrite]: #411
-#696 := [monotonicity #416 #601]: #603
-#686 := [trans #696 #697]: #684
-#761 := (iff #760 false)
-#751 := [rewrite]: #761
-#677 := [monotonicity #751 #94 #686]: #675
-#685 := [trans #677 #688]: #689
-#676 := [monotonicity #685]: #682
-#668 := [trans #676 #667]: #682
-#681 := [quant-inst #70 #76]: #680
-#670 := [mp #681 #668]: #679
-[unit-resolution #670 #100 #775]: false
-unsat
-e557b56f13f4c7ec4bdb16e86d786c044fb1042a 332 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#19 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#17 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#38 := (f4 f5 #17)
-#39 := (f3 #38 #19)
-#781 := (pattern #39)
-#13 := 0::Int
-#112 := -1::Int
-#116 := (* -1::Int #19)
-#113 := (* -1::Int #17)
-#177 := (mod #113 #116)
-#292 := (+ #39 #177)
-#293 := (= #292 0::Int)
-#40 := (mod #17 #19)
-#289 := (* -1::Int #40)
-#290 := (+ #39 #289)
-#291 := (= #290 0::Int)
-#151 := (>= #17 0::Int)
-#144 := (<= #19 0::Int)
-#236 := (or #144 #151)
-#237 := (not #236)
-#140 := (<= #17 0::Int)
-#234 := (or #140 #144)
-#235 := (not #234)
-#240 := (or #235 #237)
-#294 := (ite #240 #291 #293)
-#288 := (= #39 0::Int)
-#21 := (= #17 0::Int)
-#295 := (ite #21 #288 #294)
-#287 := (= #17 #39)
-#22 := (= #19 0::Int)
-#296 := (ite #22 #287 #295)
-#782 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #781) #296)
-#299 := (forall (vars (?v0 Int) (?v1 Int)) #296)
-#785 := (iff #299 #782)
-#783 := (iff #296 #296)
-#784 := [refl]: #783
-#786 := [quant-intro #784]: #785
-#183 := (* -1::Int #177)
-#256 := (ite #240 #40 #183)
-#259 := (ite #21 0::Int #256)
-#262 := (ite #22 #17 #259)
-#265 := (= #39 #262)
-#268 := (forall (vars (?v0 Int) (?v1 Int)) #265)
-#300 := (iff #268 #299)
-#297 := (iff #265 #296)
-#298 := [rewrite]: #297
-#301 := [quant-intro #298]: #300
-#152 := (not #151)
-#145 := (not #144)
-#155 := (and #145 #152)
-#141 := (not #140)
-#148 := (and #141 #145)
-#158 := (or #148 #155)
-#203 := (ite #158 #40 #183)
-#206 := (ite #21 0::Int #203)
-#209 := (ite #22 #17 #206)
-#212 := (= #39 #209)
-#215 := (forall (vars (?v0 Int) (?v1 Int)) #212)
-#269 := (iff #215 #268)
-#266 := (iff #212 #265)
-#263 := (= #209 #262)
-#260 := (= #206 #259)
-#257 := (= #203 #256)
-#241 := (iff #158 #240)
-#238 := (iff #155 #237)
-#239 := [rewrite]: #238
-#228 := (iff #148 #235)
-#229 := [rewrite]: #228
-#242 := [monotonicity #229 #239]: #241
-#258 := [monotonicity #242]: #257
-#261 := [monotonicity #258]: #260
-#264 := [monotonicity #261]: #263
-#267 := [monotonicity #264]: #266
-#270 := [quant-intro #267]: #269
-#226 := (~ #215 #215)
-#225 := (~ #212 #212)
-#222 := [refl]: #225
-#227 := [nnf-pos #222]: #226
-#32 := (- #19)
-#31 := (- #17)
-#41 := (mod #31 #32)
-#42 := (- #41)
-#25 := (< 0::Int #19)
-#27 := (< #17 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #17)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#43 := (ite #29 #40 #42)
-#44 := (ite #21 0::Int #43)
-#45 := (ite #22 #17 #44)
-#46 := (= #39 #45)
-#47 := (forall (vars (?v0 Int) (?v1 Int)) #46)
-#218 := (iff #47 #215)
-#106 := (and #25 #27)
-#109 := (or #26 #106)
-#188 := (ite #109 #40 #183)
-#97 := (= 0::Int #17)
-#191 := (ite #97 0::Int #188)
-#100 := (= 0::Int #19)
-#194 := (ite #100 #17 #191)
-#197 := (= #39 #194)
-#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
-#216 := (iff #200 #215)
-#213 := (iff #197 #212)
-#210 := (= #194 #209)
-#207 := (= #191 #206)
-#204 := (= #188 #203)
-#159 := (iff #109 #158)
-#156 := (iff #106 #155)
-#153 := (iff #27 #152)
-#154 := [rewrite]: #153
-#146 := (iff #25 #145)
-#147 := [rewrite]: #146
-#157 := [monotonicity #147 #154]: #156
-#149 := (iff #26 #148)
-#142 := (iff #24 #141)
-#143 := [rewrite]: #142
-#150 := [monotonicity #143 #147]: #149
-#160 := [monotonicity #150 #157]: #159
-#205 := [monotonicity #160]: #204
-#134 := (iff #97 #21)
-#135 := [rewrite]: #134
-#208 := [monotonicity #135 #205]: #207
-#136 := (iff #100 #22)
-#137 := [rewrite]: #136
-#211 := [monotonicity #137 #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [quant-intro #214]: #216
-#201 := (iff #47 #200)
-#198 := (iff #46 #197)
-#195 := (= #45 #194)
-#192 := (= #44 #191)
-#189 := (= #43 #188)
-#186 := (= #42 #183)
-#180 := (- #177)
-#184 := (= #180 #183)
-#185 := [rewrite]: #184
-#181 := (= #42 #180)
-#178 := (= #41 #177)
-#117 := (= #32 #116)
-#118 := [rewrite]: #117
-#114 := (= #31 #113)
-#115 := [rewrite]: #114
-#179 := [monotonicity #115 #118]: #178
-#182 := [monotonicity #179]: #181
-#187 := [trans #182 #185]: #186
-#110 := (iff #29 #109)
-#107 := (iff #28 #106)
-#108 := [rewrite]: #107
-#111 := [monotonicity #108]: #110
-#190 := [monotonicity #111 #187]: #189
-#98 := (iff #21 #97)
+#101 := (iff #87 #100)
+#98 := (iff #84 #97)
 #99 := [rewrite]: #98
-#193 := [monotonicity #99 #190]: #192
-#101 := (iff #22 #100)
-#102 := [rewrite]: #101
-#196 := [monotonicity #102 #193]: #195
-#199 := [monotonicity #196]: #198
-#202 := [quant-intro #199]: #201
-#219 := [trans #202 #217]: #218
-#176 := [asserted]: #47
-#220 := [mp #176 #219]: #215
-#223 := [mp~ #220 #227]: #215
-#271 := [mp #223 #270]: #268
-#302 := [mp #271 #301]: #299
-#787 := [mp #302 #786]: #782
-#68 := -3::Int
-#71 := (f4 f5 -3::Int)
-#74 := (f3 #71 -3::Int)
-#77 := (= #74 0::Int)
-#90 := (not #77)
-#9 := 3::Int
-#10 := (- 3::Int)
-#11 := (f4 f5 #10)
-#12 := (f3 #11 #10)
-#14 := (= #12 0::Int)
-#15 := (not #14)
-#93 := (iff #15 #90)
-#80 := (= 0::Int #74)
-#85 := (not #80)
-#91 := (iff #85 #90)
-#88 := (iff #80 #77)
-#89 := [rewrite]: #88
+#102 := [monotonicity #99]: #101
+#106 := [trans #102 #104]: #105
+#116 := [monotonicity #106 #113]: #115
+#21 := (<= 0::Int f3)
+#37 := (if #21 f3 #31)
+#42 := (= #37 0::Int)
+#51 := (not #42)
+#52 := (iff #51 #13)
+#91 := (iff #52 #90)
+#88 := (iff #51 #87)
+#85 := (iff #42 #84)
+#82 := (= #37 #81)
+#79 := (iff #21 #78)
+#80 := [rewrite]: #79
+#83 := [monotonicity #80]: #82
+#86 := [monotonicity #83]: #85
+#89 := [monotonicity #86]: #88
 #92 := [monotonicity #89]: #91
-#86 := (iff #15 #85)
-#83 := (iff #14 #80)
-#81 := (iff #77 #80)
-#82 := [rewrite]: #81
-#78 := (iff #14 #77)
-#75 := (= #12 #74)
-#69 := (= #10 -3::Int)
-#70 := [rewrite]: #69
-#72 := (= #11 #71)
-#73 := [monotonicity #70]: #72
-#76 := [monotonicity #73 #70]: #75
-#79 := [monotonicity #76]: #78
-#84 := [trans #79 #82]: #83
-#87 := [monotonicity #84]: #86
-#94 := [trans #87 #92]: #93
-#67 := [asserted]: #15
-#95 := [mp #67 #94]: #90
-#558 := (not #782)
-#706 := (or #558 #77)
-#360 := (* -1::Int -3::Int)
-#445 := (mod #360 #360)
-#446 := (+ #74 #445)
-#447 := (= #446 0::Int)
-#438 := (mod -3::Int -3::Int)
-#449 := (* -1::Int #438)
-#450 := (+ #74 #449)
-#378 := (= #450 0::Int)
-#451 := (>= -3::Int 0::Int)
-#448 := (<= -3::Int 0::Int)
-#452 := (or #448 #451)
-#431 := (not #452)
-#766 := (or #448 #448)
-#768 := (not #766)
-#425 := (or #768 #431)
-#555 := (ite #425 #378 #447)
-#762 := (= -3::Int 0::Int)
-#436 := (ite #762 #77 #555)
-#437 := (= -3::Int #74)
-#769 := (ite #762 #437 #436)
-#608 := (or #558 #769)
-#704 := (iff #608 #706)
-#592 := (iff #706 #706)
-#607 := [rewrite]: #592
-#598 := (iff #769 #77)
-#767 := (= #74 -3::Int)
-#713 := (ite false #767 #77)
-#715 := (iff #713 #77)
-#597 := [rewrite]: #715
-#714 := (iff #769 #713)
-#710 := (iff #436 #77)
-#716 := (ite false #77 #77)
-#724 := (iff #716 #77)
-#718 := [rewrite]: #724
-#556 := (iff #436 #716)
-#725 := (iff #555 #77)
-#717 := (iff #555 #716)
-#721 := (iff #447 #77)
-#719 := (= #446 #74)
-#459 := (+ #74 0::Int)
-#453 := (= #459 #74)
-#735 := [rewrite]: #453
-#576 := (= #446 #459)
-#734 := (= #445 0::Int)
-#726 := (mod 3::Int 3::Int)
-#733 := (= #726 0::Int)
-#728 := [rewrite]: #733
-#727 := (= #445 #726)
-#730 := (= #360 3::Int)
-#731 := [rewrite]: #730
-#732 := [monotonicity #731 #731]: #727
-#575 := [trans #732 #728]: #734
-#577 := [monotonicity #575]: #576
-#720 := [trans #577 #735]: #719
-#722 := [monotonicity #720]: #721
-#740 := (iff #378 #77)
-#739 := (= #450 #74)
-#737 := (= #450 #459)
-#457 := (= #449 0::Int)
-#741 := (* -1::Int 0::Int)
-#746 := (= #741 0::Int)
-#456 := [rewrite]: #746
-#745 := (= #449 #741)
-#466 := (= #438 0::Int)
-#467 := [rewrite]: #466
-#742 := [monotonicity #467]: #745
-#458 := [trans #742 #456]: #457
-#738 := [monotonicity #458]: #737
-#736 := [trans #738 #735]: #739
-#729 := [monotonicity #736]: #740
-#743 := (iff #425 false)
-#470 := (or false false)
-#473 := (iff #470 false)
-#366 := [rewrite]: #473
-#471 := (iff #425 #470)
-#747 := (iff #431 false)
-#1 := true
-#413 := (not true)
-#751 := (iff #413 false)
-#752 := [rewrite]: #751
-#758 := (iff #431 #413)
-#400 := (iff #452 true)
-#756 := (or true false)
-#759 := (iff #756 true)
-#399 := [rewrite]: #759
-#394 := (iff #452 #756)
-#755 := (iff #451 false)
-#750 := [rewrite]: #755
-#763 := (iff #448 true)
-#423 := [rewrite]: #763
-#757 := [monotonicity #423 #750]: #394
-#760 := [trans #757 #399]: #400
-#761 := [monotonicity #760]: #758
-#748 := [trans #761 #752]: #747
-#753 := (iff #768 false)
-#414 := (iff #768 #413)
-#749 := (iff #766 true)
-#428 := (or true true)
-#765 := (iff #428 true)
-#408 := [rewrite]: #765
-#764 := (iff #766 #428)
-#424 := [monotonicity #423 #423]: #764
-#412 := [trans #424 #408]: #749
-#415 := [monotonicity #412]: #414
-#754 := [trans #415 #752]: #753
-#472 := [monotonicity #754 #748]: #471
-#744 := [trans #472 #366]: #743
-#723 := [monotonicity #744 #729 #722]: #717
-#554 := [trans #723 #718]: #725
-#770 := (iff #762 false)
-#771 := [rewrite]: #770
-#557 := [monotonicity #771 #554]: #556
-#711 := [trans #557 #718]: #710
-#772 := (iff #437 #767)
-#773 := [rewrite]: #772
-#712 := [monotonicity #771 #773 #711]: #714
-#599 := [trans #712 #597]: #598
-#707 := [monotonicity #599]: #704
-#609 := [trans #707 #607]: #704
-#703 := [quant-inst #68 #68]: #608
-#610 := [mp #703 #609]: #706
-[unit-resolution #610 #95 #787]: false
-unsat
-23e66f7963331f26fca16a882456c891068f1234 350 0
-#2 := false
-decl f3 :: (-> S2 Int Int)
-#22 := (:var 0 Int)
-decl f4 :: (-> S3 Int S2)
-#20 := (:var 1 Int)
-decl f5 :: S3
-#8 := f5
-#42 := (f4 f5 #20)
-#43 := (f3 #42 #22)
-#764 := (pattern #43)
-#24 := 0::Int
-#101 := -1::Int
-#105 := (* -1::Int #22)
-#102 := (* -1::Int #20)
-#160 := (mod #102 #105)
-#275 := (+ #43 #160)
-#276 := (= #275 0::Int)
-#44 := (mod #20 #22)
-#272 := (* -1::Int #44)
-#273 := (+ #43 #272)
-#274 := (= #273 0::Int)
-#134 := (>= #20 0::Int)
-#127 := (<= #22 0::Int)
-#219 := (or #127 #134)
-#220 := (not #219)
-#123 := (<= #20 0::Int)
-#217 := (or #123 #127)
-#218 := (not #217)
-#223 := (or #218 #220)
-#277 := (ite #223 #274 #276)
-#271 := (= #43 0::Int)
-#25 := (= #20 0::Int)
-#278 := (ite #25 #271 #277)
-#270 := (= #20 #43)
-#26 := (= #22 0::Int)
-#279 := (ite #26 #270 #278)
-#765 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #764) #279)
-#282 := (forall (vars (?v0 Int) (?v1 Int)) #279)
-#768 := (iff #282 #765)
-#766 := (iff #279 #279)
-#767 := [refl]: #766
-#769 := [quant-intro #767]: #768
-#166 := (* -1::Int #160)
-#239 := (ite #223 #44 #166)
-#242 := (ite #25 0::Int #239)
-#245 := (ite #26 #20 #242)
-#248 := (= #43 #245)
-#251 := (forall (vars (?v0 Int) (?v1 Int)) #248)
-#283 := (iff #251 #282)
-#280 := (iff #248 #279)
-#281 := [rewrite]: #280
-#284 := [quant-intro #281]: #283
-#135 := (not #134)
-#128 := (not #127)
-#138 := (and #128 #135)
-#124 := (not #123)
-#131 := (and #124 #128)
-#141 := (or #131 #138)
-#186 := (ite #141 #44 #166)
-#189 := (ite #25 0::Int #186)
-#192 := (ite #26 #20 #189)
-#195 := (= #43 #192)
-#198 := (forall (vars (?v0 Int) (?v1 Int)) #195)
-#252 := (iff #198 #251)
-#249 := (iff #195 #248)
-#246 := (= #192 #245)
-#243 := (= #189 #242)
-#240 := (= #186 #239)
-#224 := (iff #141 #223)
-#221 := (iff #138 #220)
-#222 := [rewrite]: #221
-#211 := (iff #131 #218)
-#212 := [rewrite]: #211
-#225 := [monotonicity #212 #222]: #224
-#241 := [monotonicity #225]: #240
-#244 := [monotonicity #241]: #243
-#247 := [monotonicity #244]: #246
-#250 := [monotonicity #247]: #249
-#253 := [quant-intro #250]: #252
-#209 := (~ #198 #198)
-#208 := (~ #195 #195)
-#205 := [refl]: #208
-#210 := [nnf-pos #205]: #209
-#36 := (- #22)
-#35 := (- #20)
-#45 := (mod #35 #36)
-#46 := (- #45)
-#29 := (< 0::Int #22)
-#31 := (< #20 0::Int)
-#32 := (and #31 #29)
-#28 := (< 0::Int #20)
-#30 := (and #28 #29)
-#33 := (or #30 #32)
-#47 := (ite #33 #44 #46)
-#48 := (ite #25 0::Int #47)
-#49 := (ite #26 #20 #48)
-#50 := (= #43 #49)
-#51 := (forall (vars (?v0 Int) (?v1 Int)) #50)
-#201 := (iff #51 #198)
-#94 := (and #29 #31)
-#98 := (or #30 #94)
-#171 := (ite #98 #44 #166)
-#174 := (ite #25 0::Int #171)
-#177 := (ite #26 #20 #174)
-#180 := (= #43 #177)
-#183 := (forall (vars (?v0 Int) (?v1 Int)) #180)
-#199 := (iff #183 #198)
-#196 := (iff #180 #195)
-#193 := (= #177 #192)
-#190 := (= #174 #189)
-#187 := (= #171 #186)
-#142 := (iff #98 #141)
-#139 := (iff #94 #138)
-#136 := (iff #31 #135)
-#137 := [rewrite]: #136
-#129 := (iff #29 #128)
-#130 := [rewrite]: #129
-#140 := [monotonicity #130 #137]: #139
-#132 := (iff #30 #131)
-#125 := (iff #28 #124)
-#126 := [rewrite]: #125
-#133 := [monotonicity #126 #130]: #132
-#143 := [monotonicity #133 #140]: #142
-#188 := [monotonicity #143]: #187
-#191 := [monotonicity #188]: #190
-#194 := [monotonicity #191]: #193
-#197 := [monotonicity #194]: #196
-#200 := [quant-intro #197]: #199
-#184 := (iff #51 #183)
-#181 := (iff #50 #180)
-#178 := (= #49 #177)
-#175 := (= #48 #174)
-#172 := (= #47 #171)
-#169 := (= #46 #166)
-#163 := (- #160)
-#167 := (= #163 #166)
-#168 := [rewrite]: #167
-#164 := (= #46 #163)
-#161 := (= #45 #160)
-#106 := (= #36 #105)
-#107 := [rewrite]: #106
-#103 := (= #35 #102)
-#104 := [rewrite]: #103
-#162 := [monotonicity #104 #107]: #161
-#165 := [monotonicity #162]: #164
-#170 := [trans #165 #168]: #169
-#99 := (iff #33 #98)
-#96 := (iff #32 #94)
-#97 := [rewrite]: #96
-#100 := [monotonicity #97]: #99
-#173 := [monotonicity #100 #170]: #172
-#176 := [monotonicity #173]: #175
-#179 := [monotonicity #176]: #178
-#182 := [monotonicity #179]: #181
-#185 := [quant-intro #182]: #184
-#202 := [trans #185 #200]: #201
-#159 := [asserted]: #51
-#203 := [mp #159 #202]: #198
-#206 := [mp~ #203 #210]: #198
-#254 := [mp #206 #253]: #251
-#285 := [mp #254 #284]: #282
-#770 := [mp #285 #769]: #765
-#84 := -2::Int
-#78 := -3::Int
-#72 := -5::Int
-#75 := (f4 f5 -5::Int)
-#81 := (f3 #75 -3::Int)
-#87 := (= #81 -2::Int)
-#90 := (not #87)
-#15 := 2::Int
-#16 := (- 2::Int)
-#12 := 3::Int
-#13 := (- 3::Int)
-#9 := 5::Int
-#10 := (- 5::Int)
-#11 := (f4 f5 #10)
-#14 := (f3 #11 #13)
-#17 := (= #14 #16)
-#18 := (not #17)
-#91 := (iff #18 #90)
-#88 := (iff #17 #87)
-#85 := (= #16 -2::Int)
-#86 := [rewrite]: #85
-#82 := (= #14 #81)
-#79 := (= #13 -3::Int)
-#80 := [rewrite]: #79
-#76 := (= #11 #75)
-#73 := (= #10 -5::Int)
-#74 := [rewrite]: #73
-#77 := [monotonicity #74]: #76
-#83 := [monotonicity #77 #80]: #82
-#89 := [monotonicity #83 #86]: #88
-#92 := [monotonicity #89]: #91
-#71 := [asserted]: #18
-#95 := [mp #71 #92]: #90
-#675 := (not #765)
-#676 := (or #675 #87)
-#343 := (* -1::Int -3::Int)
-#428 := (* -1::Int -5::Int)
-#429 := (mod #428 #343)
-#430 := (+ #81 #429)
-#421 := (= #430 0::Int)
-#432 := (mod -5::Int -3::Int)
-#433 := (* -1::Int #432)
-#361 := (+ #81 #433)
-#434 := (= #361 0::Int)
-#431 := (>= -5::Int 0::Int)
-#435 := (<= -3::Int 0::Int)
-#414 := (or #435 #431)
-#749 := (not #414)
-#751 := (<= -5::Int 0::Int)
-#408 := (or #751 #435)
-#538 := (not #408)
-#745 := (or #538 #749)
-#419 := (ite #745 #434 #421)
-#420 := (= #81 0::Int)
-#752 := (= -5::Int 0::Int)
-#753 := (ite #752 #420 #419)
-#754 := (= -5::Int #81)
-#755 := (= -3::Int 0::Int)
-#750 := (ite #755 #754 #753)
-#677 := (or #675 #750)
-#678 := (iff #677 #676)
-#663 := (iff #676 #676)
-#665 := [rewrite]: #663
-#685 := (iff #750 #87)
-#411 := (= #81 -5::Int)
-#672 := (ite false #411 #87)
-#684 := (iff #672 #87)
-#680 := [rewrite]: #684
-#682 := (iff #750 #672)
-#673 := (iff #753 #87)
-#691 := (ite false #420 #87)
-#679 := (iff #691 #87)
-#681 := [rewrite]: #679
-#688 := (iff #753 #691)
-#597 := (iff #419 #87)
-#441 := 1::Int
-#702 := (= #81 1::Int)
-#593 := (ite false #702 #87)
-#595 := (iff #593 #87)
-#596 := [rewrite]: #595
-#586 := (iff #419 #593)
-#590 := (iff #421 #87)
-#580 := (+ 2::Int #81)
-#591 := (= #580 0::Int)
-#690 := (iff #591 #87)
-#575 := [rewrite]: #690
-#686 := (iff #421 #591)
-#541 := (= #430 #580)
-#697 := (+ #81 2::Int)
-#581 := (= #697 #580)
-#582 := [rewrite]: #581
-#695 := (= #430 #697)
-#694 := (= #429 2::Int)
-#708 := (mod 5::Int 3::Int)
-#540 := (= #708 2::Int)
-#693 := [rewrite]: #540
-#537 := (= #429 #708)
-#707 := (= #343 3::Int)
-#701 := [rewrite]: #707
-#700 := (= #428 5::Int)
-#706 := [rewrite]: #700
-#539 := [monotonicity #706 #701]: #537
-#696 := [trans #539 #693]: #694
-#698 := [monotonicity #696]: #695
-#689 := [trans #698 #582]: #541
-#687 := [monotonicity #689]: #686
-#592 := [trans #687 #575]: #590
-#705 := (iff #434 #702)
-#710 := (+ -1::Int #81)
-#558 := (= #710 0::Int)
-#703 := (iff #558 #702)
-#704 := [rewrite]: #703
-#559 := (iff #434 #558)
-#711 := (= #361 #710)
-#713 := (+ #81 -1::Int)
-#715 := (= #713 #710)
-#716 := [rewrite]: #715
-#714 := (= #361 #713)
-#723 := (= #433 -1::Int)
-#721 := (* -1::Int 1::Int)
-#722 := (= #721 -1::Int)
-#719 := [rewrite]: #722
-#436 := (= #433 #721)
-#442 := (= #432 1::Int)
-#720 := [rewrite]: #442
-#718 := [monotonicity #720]: #436
-#712 := [trans #718 #719]: #723
-#709 := [monotonicity #712]: #714
-#717 := [trans #709 #716]: #711
-#560 := [monotonicity #717]: #559
-#699 := [trans #560 #704]: #705
-#439 := (iff #745 false)
-#450 := (or false false)
-#725 := (iff #450 false)
-#729 := [rewrite]: #725
-#724 := (iff #745 #450)
-#727 := (iff #749 false)
-#1 := true
-#733 := (not true)
-#740 := (iff #733 false)
-#742 := [rewrite]: #740
-#349 := (iff #749 #733)
-#455 := (iff #414 true)
-#744 := (or true false)
-#453 := (iff #744 true)
-#454 := [rewrite]: #453
-#730 := (iff #414 #744)
-#743 := (iff #431 false)
-#741 := [rewrite]: #743
-#395 := (iff #435 true)
-#396 := [rewrite]: #395
-#731 := [monotonicity #396 #741]: #730
-#456 := [trans #731 #454]: #455
-#726 := [monotonicity #456]: #349
-#449 := [trans #726 #742]: #727
-#382 := (iff #538 false)
-#739 := (iff #538 #733)
-#737 := (iff #408 true)
-#397 := (or true true)
-#735 := (iff #397 true)
-#736 := [rewrite]: #735
-#398 := (iff #408 #397)
-#391 := (iff #751 true)
-#732 := [rewrite]: #391
-#734 := [monotonicity #732 #396]: #398
-#738 := [trans #734 #736]: #737
-#377 := [monotonicity #738]: #739
-#383 := [trans #377 #742]: #382
-#728 := [monotonicity #383 #449]: #724
-#440 := [trans #728 #729]: #439
-#594 := [monotonicity #440 #699 #592]: #586
-#598 := [trans #594 #596]: #597
-#407 := (iff #752 false)
-#748 := [rewrite]: #407
-#692 := [monotonicity #748 #598]: #688
-#670 := [trans #692 #681]: #673
-#406 := (iff #754 #411)
-#747 := [rewrite]: #406
-#756 := (iff #755 false)
-#746 := [rewrite]: #756
-#683 := [monotonicity #746 #747 #670]: #682
-#674 := [trans #683 #680]: #685
-#662 := [monotonicity #674]: #678
-#666 := [trans #662 #665]: #678
-#671 := [quant-inst #72 #78]: #677
-#667 := [mp #671 #666]: #676
-[unit-resolution #667 #95 #770]: false
-unsat
-7e8a6b37c3c101f2391dcbe7edf0f351fd77cf0f 327 0
-#2 := false
-#20 := 0::Int
-decl f6 :: Int
-#9 := f6
-#417 := (>= f6 0::Int)
-#737 := (<= f6 0::Int)
-#383 := (not #737)
-#726 := (not #417)
-#730 := (or #726 #383)
-#693 := (not #730)
-#11 := 3::Int
-#418 := (mod f6 3::Int)
-#87 := -1::Int
-#419 := (* -1::Int #418)
-decl f3 :: (-> S2 Int Int)
-decl f4 :: (-> S3 Int S2)
-decl f5 :: S3
-#8 := f5
-#10 := (f4 f5 f6)
-#12 := (f3 #10 3::Int)
-#347 := (+ #12 #419)
-#420 := (= #347 0::Int)
-#566 := (not #420)
-#523 := (<= #347 0::Int)
-#626 := (not #523)
-#634 := (>= #418 3::Int)
-#635 := (not #634)
-#1 := true
-#65 := [true-axiom]: true
-#622 := (or false #635)
-#623 := [th-lemma arith]: #622
-#624 := [unit-resolution #623 #65]: #635
-#625 := [hypothesis]: #523
-#72 := (>= #12 3::Int)
-#13 := (< #12 3::Int)
-#14 := (not #13)
-#79 := (iff #14 #72)
-#70 := (not #72)
-#74 := (not #70)
-#77 := (iff #74 #72)
-#78 := [rewrite]: #77
-#75 := (iff #14 #74)
-#71 := (iff #13 #70)
-#73 := [rewrite]: #71
-#76 := [monotonicity #73]: #75
-#80 := [trans #76 #78]: #79
-#67 := [asserted]: #14
-#81 := [mp #67 #80]: #72
-#620 := [th-lemma arith farkas -1 1 1 #81 #625 #624]: false
-#612 := [lemma #620]: #626
-#629 := (or #566 #523)
-#640 := [th-lemma arith triangle-eq]: #629
-#618 := [unit-resolution #640 #612]: #566
-#617 := (or #693 #420)
-#441 := -3::Int
-#414 := (* -1::Int f6)
-#712 := (mod #414 -3::Int)
-#436 := (+ #12 #712)
-#711 := (= #436 0::Int)
-#426 := (ite #730 #420 #711)
-#406 := (= #12 0::Int)
-#738 := (= f6 0::Int)
-#706 := (ite #738 #406 #426)
-#18 := (:var 0 Int)
-#16 := (:var 1 Int)
-#38 := (f4 f5 #16)
-#39 := (f3 #38 #18)
-#750 := (pattern #39)
-#91 := (* -1::Int #18)
-#88 := (* -1::Int #16)
-#146 := (mod #88 #91)
-#261 := (+ #39 #146)
-#262 := (= #261 0::Int)
-#40 := (mod #16 #18)
-#258 := (* -1::Int #40)
-#259 := (+ #39 #258)
-#260 := (= #259 0::Int)
-#120 := (>= #16 0::Int)
-#113 := (<= #18 0::Int)
-#205 := (or #113 #120)
-#206 := (not #205)
-#109 := (<= #16 0::Int)
-#203 := (or #109 #113)
-#204 := (not #203)
-#209 := (or #204 #206)
-#263 := (ite #209 #260 #262)
-#257 := (= #39 0::Int)
-#21 := (= #16 0::Int)
-#264 := (ite #21 #257 #263)
-#256 := (= #16 #39)
-#22 := (= #18 0::Int)
-#265 := (ite #22 #256 #264)
-#751 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #750) #265)
-#268 := (forall (vars (?v0 Int) (?v1 Int)) #265)
-#754 := (iff #268 #751)
-#752 := (iff #265 #265)
-#753 := [refl]: #752
-#755 := [quant-intro #753]: #754
-#152 := (* -1::Int #146)
-#225 := (ite #209 #40 #152)
-#228 := (ite #21 0::Int #225)
-#231 := (ite #22 #16 #228)
-#234 := (= #39 #231)
-#237 := (forall (vars (?v0 Int) (?v1 Int)) #234)
-#269 := (iff #237 #268)
-#266 := (iff #234 #265)
-#267 := [rewrite]: #266
-#270 := [quant-intro #267]: #269
-#121 := (not #120)
-#114 := (not #113)
-#124 := (and #114 #121)
-#110 := (not #109)
-#117 := (and #110 #114)
-#127 := (or #117 #124)
-#172 := (ite #127 #40 #152)
-#175 := (ite #21 0::Int #172)
-#178 := (ite #22 #16 #175)
-#181 := (= #39 #178)
-#184 := (forall (vars (?v0 Int) (?v1 Int)) #181)
-#238 := (iff #184 #237)
-#235 := (iff #181 #234)
-#232 := (= #178 #231)
-#229 := (= #175 #228)
-#226 := (= #172 #225)
-#210 := (iff #127 #209)
-#207 := (iff #124 #206)
-#208 := [rewrite]: #207
-#197 := (iff #117 #204)
-#198 := [rewrite]: #197
-#211 := [monotonicity #198 #208]: #210
-#227 := [monotonicity #211]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [monotonicity #233]: #235
-#239 := [quant-intro #236]: #238
-#195 := (~ #184 #184)
-#194 := (~ #181 #181)
-#191 := [refl]: #194
-#196 := [nnf-pos #191]: #195
-#32 := (- #18)
-#31 := (- #16)
-#41 := (mod #31 #32)
-#42 := (- #41)
-#25 := (< 0::Int #18)
-#27 := (< #16 0::Int)
-#28 := (and #27 #25)
-#24 := (< 0::Int #16)
-#26 := (and #24 #25)
-#29 := (or #26 #28)
-#43 := (ite #29 #40 #42)
-#44 := (ite #21 0::Int #43)
-#45 := (ite #22 #16 #44)
-#46 := (= #39 #45)
-#47 := (forall (vars (?v0 Int) (?v1 Int)) #46)
-#187 := (iff #47 #184)
-#69 := (and #25 #27)
-#84 := (or #26 #69)
-#157 := (ite #84 #40 #152)
-#160 := (ite #21 0::Int #157)
-#163 := (ite #22 #16 #160)
-#166 := (= #39 #163)
-#169 := (forall (vars (?v0 Int) (?v1 Int)) #166)
-#185 := (iff #169 #184)
-#182 := (iff #166 #181)
-#179 := (= #163 #178)
-#176 := (= #160 #175)
-#173 := (= #157 #172)
-#128 := (iff #84 #127)
-#125 := (iff #69 #124)
-#122 := (iff #27 #121)
-#123 := [rewrite]: #122
-#115 := (iff #25 #114)
-#116 := [rewrite]: #115
-#126 := [monotonicity #116 #123]: #125
-#118 := (iff #26 #117)
-#111 := (iff #24 #110)
-#112 := [rewrite]: #111
-#119 := [monotonicity #112 #116]: #118
-#129 := [monotonicity #119 #126]: #128
-#174 := [monotonicity #129]: #173
-#177 := [monotonicity #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [monotonicity #180]: #182
-#186 := [quant-intro #183]: #185
-#170 := (iff #47 #169)
-#167 := (iff #46 #166)
-#164 := (= #45 #163)
-#161 := (= #44 #160)
-#158 := (= #43 #157)
-#155 := (= #42 #152)
-#149 := (- #146)
-#153 := (= #149 #152)
-#154 := [rewrite]: #153
-#150 := (= #42 #149)
-#147 := (= #41 #146)
-#92 := (= #32 #91)
-#93 := [rewrite]: #92
-#89 := (= #31 #88)
-#90 := [rewrite]: #89
-#148 := [monotonicity #90 #93]: #147
-#151 := [monotonicity #148]: #150
-#156 := [trans #151 #154]: #155
-#85 := (iff #29 #84)
-#82 := (iff #28 #69)
-#83 := [rewrite]: #82
-#86 := [monotonicity #83]: #85
-#159 := [monotonicity #86 #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [monotonicity #162]: #164
-#168 := [monotonicity #165]: #167
-#171 := [quant-intro #168]: #170
-#188 := [trans #171 #186]: #187
-#145 := [asserted]: #47
-#189 := [mp #145 #188]: #184
-#192 := [mp~ #189 #196]: #184
-#240 := [mp #192 #239]: #237
-#271 := [mp #240 #270]: #268
-#756 := [mp #271 #755]: #751
-#695 := (not #751)
-#696 := (or #695 #706)
-#329 := (* -1::Int 3::Int)
-#415 := (mod #414 #329)
-#416 := (+ #12 #415)
-#407 := (= #416 0::Int)
-#421 := (<= 3::Int 0::Int)
-#400 := (or #421 #417)
-#735 := (not #400)
-#394 := (or #737 #421)
-#524 := (not #394)
-#731 := (or #524 #735)
-#405 := (ite #731 #420 #407)
-#739 := (ite #738 #406 #405)
-#740 := (= f6 #12)
-#741 := (= 3::Int 0::Int)
-#736 := (ite #741 #740 #739)
-#701 := (or #695 #736)
-#697 := (iff #701 #696)
-#544 := (iff #696 #696)
-#545 := [rewrite]: #544
-#699 := (iff #736 #706)
-#704 := (ite false #740 #706)
-#709 := (iff #704 #706)
-#698 := [rewrite]: #709
-#708 := (iff #736 #704)
-#707 := (iff #739 #706)
-#427 := (iff #405 #426)
-#715 := (iff #407 #711)
-#710 := (= #416 #436)
-#713 := (= #415 #712)
-#442 := (= #329 -3::Int)
-#335 := [rewrite]: #442
-#435 := [monotonicity #335]: #713
-#714 := [monotonicity #435]: #710
-#425 := [monotonicity #714]: #715
-#439 := (iff #731 #730)
-#369 := (or #383 #726)
-#716 := (iff #369 #730)
-#717 := [rewrite]: #716
-#729 := (iff #731 #369)
-#728 := (iff #735 #726)
-#725 := (iff #400 #417)
-#721 := (or false #417)
-#724 := (iff #721 #417)
-#719 := [rewrite]: #724
-#722 := (iff #400 #721)
-#392 := (iff #421 false)
-#397 := [rewrite]: #392
-#723 := [monotonicity #397]: #722
-#363 := [trans #723 #719]: #725
-#368 := [monotonicity #363]: #728
-#384 := (iff #524 #383)
-#381 := (iff #394 #737)
-#733 := (or #737 false)
-#377 := (iff #733 #737)
-#718 := [rewrite]: #377
-#393 := (iff #394 #733)
-#734 := [monotonicity #397]: #393
-#382 := [trans #734 #718]: #381
-#720 := [monotonicity #382]: #384
-#727 := [monotonicity #720 #368]: #729
-#440 := [trans #727 #717]: #439
-#428 := [monotonicity #440 #425]: #427
-#422 := [monotonicity #428]: #707
-#742 := (iff #741 false)
-#732 := [rewrite]: #742
-#705 := [monotonicity #732 #422]: #708
-#700 := [trans #705 #698]: #699
-#703 := [monotonicity #700]: #697
-#546 := [trans #703 #545]: #697
-#702 := [quant-inst #9 #11]: #701
-#688 := [mp #702 #546]: #696
-#619 := [unit-resolution #688 #756]: #706
-#673 := (not #738)
-#672 := (not #706)
-#614 := (or #672 #673)
-#579 := (not #406)
-#689 := (<= #12 0::Int)
-#621 := (not #689)
-#651 := (or #621 #70)
-#652 := [th-lemma arith farkas 1 1]: #651
-#608 := [unit-resolution #652 #81]: #621
-#609 := (or #579 #689)
-#610 := [th-lemma arith triangle-eq]: #609
-#613 := [unit-resolution #610 #608]: #579
-#676 := (or #672 #673 #406)
-#561 := [def-axiom]: #676
-#615 := [unit-resolution #561 #613]: #614
-#616 := [unit-resolution #615 #619]: #673
-#576 := (or #672 #738 #426)
-#578 := [def-axiom]: #576
-#611 := [unit-resolution #578 #616 #619]: #426
-#680 := (not #426)
-#682 := (or #680 #693 #420)
-#683 := [def-axiom]: #682
-#590 := [unit-resolution #683 #611]: #617
-#591 := [unit-resolution #590 #618]: #693
-#691 := (or #730 #417)
-#685 := [def-axiom]: #691
-#592 := [unit-resolution #685 #591]: #417
-#686 := (or #730 #737)
-#692 := [def-axiom]: #686
-#485 := [unit-resolution #692 #591]: #737
-#596 := (or #738 #383 #726)
-#597 := [th-lemma arith triangle-eq]: #596
-#598 := [unit-resolution #597 #616]: #369
-[unit-resolution #598 #485 #592]: false
-unsat
-c1c2bfe366703ecc21257a3d4934900d916d5721 365 0
-#2 := false
-#11 := 3::Int
-decl f3 :: (-> S2 Int Int)
-decl f4 :: (-> S3 Int S2)
-decl f6 :: Int
-#9 := f6
-decl f5 :: S3
-#8 := f5
-#10 := (f4 f5 f6)
-#12 := (f3 #10 3::Int)
-#372 := (mod #12 3::Int)
-#634 := (>= #372 3::Int)
-#635 := (not #634)
-#1 := true
-#67 := [true-axiom]: true
-#622 := (or false #635)
-#623 := [th-lemma arith]: #622
-#628 := [unit-resolution #623 #67]: #635
-#22 := 0::Int
-#112 := -1::Int
-#439 := (* -1::Int #12)
-#691 := (+ f6 #439)
-#696 := (<= #691 0::Int)
-#70 := (= f6 #12)
-#87 := (>= f6 3::Int)
-#85 := (not #87)
-#76 := (not #70)
-#92 := (or #76 #85)
-#97 := (not #92)
-#14 := (< f6 3::Int)
-#13 := (= #12 f6)
-#15 := (implies #13 #14)
-#16 := (not #15)
-#100 := (iff #16 #97)
-#77 := (or #14 #76)
-#82 := (not #77)
-#98 := (iff #82 #97)
-#95 := (iff #77 #92)
-#89 := (or #85 #76)
-#93 := (iff #89 #92)
-#94 := [rewrite]: #93
-#90 := (iff #77 #89)
-#86 := (iff #14 #85)
-#88 := [rewrite]: #86
-#91 := [monotonicity #88]: #90
-#96 := [trans #91 #94]: #95
-#99 := [monotonicity #96]: #98
-#83 := (iff #16 #82)
-#80 := (iff #15 #77)
-#73 := (implies #70 #14)
-#78 := (iff #73 #77)
-#79 := [rewrite]: #78
-#74 := (iff #15 #73)
-#71 := (iff #13 #70)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#81 := [trans #75 #79]: #80
-#84 := [monotonicity #81]: #83
-#101 := [trans #84 #99]: #100
-#69 := [asserted]: #16
-#102 := [mp #69 #101]: #97
-#103 := [not-or-elim #102]: #70
-#624 := (or #76 #696)
-#625 := [th-lemma arith triangle-eq]: #624
-#626 := [unit-resolution #625 #103]: #696
-#104 := [not-or-elim #102]: #87
-#441 := (f4 f5 #12)
-#432 := (f3 #441 3::Int)
-#739 := (* -1::Int #432)
-#686 := (+ #12 #739)
-#687 := (<= #686 0::Int)
-#761 := (= #12 #432)
-#627 := (= #432 #12)
-#630 := (= #441 #10)
-#629 := [symm #103]: #13
-#631 := [monotonicity #629]: #630
-#632 := [monotonicity #631]: #627
-#612 := [symm #632]: #761
-#558 := (not #761)
-#613 := (or #558 #687)
-#594 := [th-lemma arith triangle-eq]: #613
-#618 := [unit-resolution #594 #612]: #687
-#736 := (+ #372 #739)
-#602 := (>= #736 0::Int)
-#740 := (= #736 0::Int)
-#731 := -3::Int
-#729 := (mod #439 -3::Int)
-#734 := (+ #432 #729)
-#725 := (= #734 0::Int)
-#549 := (<= #12 0::Int)
-#745 := (not #549)
-#425 := (>= #12 0::Int)
-#393 := (not #425)
-#742 := (or #393 #745)
-#726 := (ite #742 #740 #725)
-#764 := (= #432 0::Int)
-#765 := (= #12 0::Int)
-#728 := (ite #765 #764 #726)
-#20 := (:var 0 Int)
-#18 := (:var 1 Int)
-#40 := (f4 f5 #18)
-#41 := (f3 #40 #20)
-#775 := (pattern #41)
-#116 := (* -1::Int #20)
-#113 := (* -1::Int #18)
-#171 := (mod #113 #116)
-#286 := (+ #41 #171)
-#287 := (= #286 0::Int)
-#42 := (mod #18 #20)
-#283 := (* -1::Int #42)
-#284 := (+ #41 #283)
-#285 := (= #284 0::Int)
-#145 := (>= #18 0::Int)
-#138 := (<= #20 0::Int)
-#230 := (or #138 #145)
-#231 := (not #230)
-#134 := (<= #18 0::Int)
-#216 := (or #134 #138)
-#217 := (not #216)
-#234 := (or #217 #231)
-#288 := (ite #234 #285 #287)
-#282 := (= #41 0::Int)
-#23 := (= #18 0::Int)
-#289 := (ite #23 #282 #288)
-#281 := (= #18 #41)
-#24 := (= #20 0::Int)
-#290 := (ite #24 #281 #289)
-#776 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #775) #290)
-#293 := (forall (vars (?v0 Int) (?v1 Int)) #290)
-#779 := (iff #293 #776)
-#777 := (iff #290 #290)
-#778 := [refl]: #777
-#780 := [quant-intro #778]: #779
-#177 := (* -1::Int #171)
-#250 := (ite #234 #42 #177)
-#253 := (ite #23 0::Int #250)
-#256 := (ite #24 #18 #253)
-#259 := (= #41 #256)
-#262 := (forall (vars (?v0 Int) (?v1 Int)) #259)
-#294 := (iff #262 #293)
-#291 := (iff #259 #290)
-#292 := [rewrite]: #291
-#295 := [quant-intro #292]: #294
-#146 := (not #145)
-#139 := (not #138)
-#149 := (and #139 #146)
-#135 := (not #134)
-#142 := (and #135 #139)
-#152 := (or #142 #149)
-#197 := (ite #152 #42 #177)
-#200 := (ite #23 0::Int #197)
-#203 := (ite #24 #18 #200)
-#206 := (= #41 #203)
-#209 := (forall (vars (?v0 Int) (?v1 Int)) #206)
-#263 := (iff #209 #262)
-#260 := (iff #206 #259)
-#257 := (= #203 #256)
-#254 := (= #200 #253)
-#251 := (= #197 #250)
-#235 := (iff #152 #234)
-#232 := (iff #149 #231)
-#233 := [rewrite]: #232
-#224 := (iff #142 #217)
-#225 := [rewrite]: #224
-#236 := [monotonicity #225 #233]: #235
-#252 := [monotonicity #236]: #251
-#255 := [monotonicity #252]: #254
-#258 := [monotonicity #255]: #257
-#261 := [monotonicity #258]: #260
-#264 := [quant-intro #261]: #263
-#222 := (~ #209 #209)
-#221 := (~ #206 #206)
-#218 := [refl]: #221
-#223 := [nnf-pos #218]: #222
-#34 := (- #20)
-#33 := (- #18)
-#43 := (mod #33 #34)
-#44 := (- #43)
-#27 := (< 0::Int #20)
-#29 := (< #18 0::Int)
-#30 := (and #29 #27)
-#26 := (< 0::Int #18)
-#28 := (and #26 #27)
-#31 := (or #28 #30)
-#45 := (ite #31 #42 #44)
-#46 := (ite #23 0::Int #45)
-#47 := (ite #24 #18 #46)
-#48 := (= #41 #47)
-#49 := (forall (vars (?v0 Int) (?v1 Int)) #48)
-#212 := (iff #49 #209)
-#106 := (and #27 #29)
-#109 := (or #28 #106)
-#182 := (ite #109 #42 #177)
-#185 := (ite #23 0::Int #182)
-#188 := (ite #24 #18 #185)
-#191 := (= #41 #188)
-#194 := (forall (vars (?v0 Int) (?v1 Int)) #191)
-#210 := (iff #194 #209)
-#207 := (iff #191 #206)
-#204 := (= #188 #203)
-#201 := (= #185 #200)
-#198 := (= #182 #197)
-#153 := (iff #109 #152)
-#150 := (iff #106 #149)
-#147 := (iff #29 #146)
-#148 := [rewrite]: #147
-#140 := (iff #27 #139)
-#141 := [rewrite]: #140
-#151 := [monotonicity #141 #148]: #150
-#143 := (iff #28 #142)
-#136 := (iff #26 #135)
-#137 := [rewrite]: #136
-#144 := [monotonicity #137 #141]: #143
-#154 := [monotonicity #144 #151]: #153
-#199 := [monotonicity #154]: #198
-#202 := [monotonicity #199]: #201
-#205 := [monotonicity #202]: #204
-#208 := [monotonicity #205]: #207
-#211 := [quant-intro #208]: #210
-#195 := (iff #49 #194)
-#192 := (iff #48 #191)
-#189 := (= #47 #188)
-#186 := (= #46 #185)
-#183 := (= #45 #182)
-#180 := (= #44 #177)
-#174 := (- #171)
-#178 := (= #174 #177)
-#179 := [rewrite]: #178
-#175 := (= #44 #174)
-#172 := (= #43 #171)
-#117 := (= #34 #116)
-#118 := [rewrite]: #117
-#114 := (= #33 #113)
-#115 := [rewrite]: #114
-#173 := [monotonicity #115 #118]: #172
-#176 := [monotonicity #173]: #175
-#181 := [trans #176 #179]: #180
-#110 := (iff #31 #109)
-#107 := (iff #30 #106)
-#108 := [rewrite]: #107
-#111 := [monotonicity #108]: #110
-#184 := [monotonicity #111 #181]: #183
-#187 := [monotonicity #184]: #186
-#190 := [monotonicity #187]: #189
-#193 := [monotonicity #190]: #192
-#196 := [quant-intro #193]: #195
-#213 := [trans #196 #211]: #212
-#170 := [asserted]: #49
-#214 := [mp #170 #213]: #209
-#219 := [mp~ #214 #223]: #209
-#265 := [mp #219 #264]: #262
-#296 := [mp #265 #295]: #293
-#781 := [mp #296 #780]: #776
-#717 := (not #776)
-#718 := (or #717 #728)
-#354 := (* -1::Int 3::Int)
-#440 := (mod #439 #354)
-#443 := (+ #432 #440)
-#444 := (= #443 0::Int)
-#445 := (* -1::Int #372)
-#442 := (+ #432 #445)
-#446 := (= #442 0::Int)
-#760 := (<= 3::Int 0::Int)
-#762 := (or #760 #425)
-#419 := (not #762)
-#756 := (or #549 #760)
-#430 := (not #756)
-#431 := (or #430 #419)
-#763 := (ite #431 #446 #444)
-#766 := (ite #765 #764 #763)
-#767 := (= 3::Int 0::Int)
-#757 := (ite #767 #761 #766)
-#712 := (or #717 #757)
-#548 := (iff #712 #718)
-#551 := (iff #718 #718)
-#704 := [rewrite]: #551
-#710 := (iff #757 #728)
-#571 := (ite false #761 #728)
-#715 := (iff #571 #728)
-#716 := [rewrite]: #715
-#713 := (iff #757 #571)
-#569 := (iff #766 #728)
-#727 := (iff #763 #726)
-#720 := (iff #444 #725)
-#723 := (= #443 #734)
-#733 := (= #440 #729)
-#732 := (= #354 -3::Int)
-#447 := [rewrite]: #732
-#730 := [monotonicity #447]: #733
-#724 := [monotonicity #730]: #723
-#721 := [monotonicity #724]: #720
-#452 := (iff #446 #740)
-#360 := (+ #445 #432)
-#460 := (= #360 0::Int)
-#450 := (iff #460 #740)
-#451 := [rewrite]: #450
-#461 := (iff #446 #460)
-#737 := (= #442 #360)
-#738 := [rewrite]: #737
-#735 := [monotonicity #738]: #461
-#453 := [trans #735 #451]: #452
-#466 := (iff #431 #742)
-#752 := (or #745 #393)
-#464 := (iff #752 #742)
-#465 := [rewrite]: #464
-#755 := (iff #431 #752)
-#394 := (iff #419 #393)
-#751 := (iff #762 #425)
-#748 := (or false #425)
-#750 := (iff #748 #425)
-#388 := [rewrite]: #750
-#749 := (iff #762 #748)
-#758 := (iff #760 false)
-#418 := [rewrite]: #758
-#744 := [monotonicity #418]: #749
-#753 := [trans #744 #388]: #751
-#754 := [monotonicity #753]: #394
-#746 := (iff #430 #745)
-#408 := (iff #756 #549)
-#759 := (or #549 false)
-#406 := (iff #759 #549)
-#407 := [rewrite]: #406
-#402 := (iff #756 #759)
-#743 := [monotonicity #418]: #402
-#409 := [trans #743 #407]: #408
-#747 := [monotonicity #409]: #746
-#741 := [monotonicity #747 #754]: #755
-#467 := [trans #741 #465]: #466
-#722 := [monotonicity #467 #453 #721]: #727
-#570 := [monotonicity #722]: #569
-#417 := (iff #767 false)
-#422 := [rewrite]: #417
-#714 := [monotonicity #422 #570]: #713
-#711 := [trans #714 #716]: #710
-#550 := [monotonicity #711]: #548
-#705 := [trans #550 #704]: #548
-#719 := [quant-inst #12 #11]: #712
-#707 := [mp #719 #705]: #718
-#619 := [unit-resolution #707 #781]: #728
-#699 := (not #765)
-#614 := (not #696)
-#620 := (or #745 #85 #614)
-#588 := [th-lemma arith assign-bounds 1 1]: #620
-#595 := [unit-resolution #588 #104 #626]: #745
-#554 := (or #699 #549)
-#585 := [th-lemma arith triangle-eq]: #554
-#587 := [unit-resolution #585 #595]: #699
-#702 := (not #728)
-#692 := (or #702 #765 #726)
-#684 := [def-axiom]: #692
-#589 := [unit-resolution #684 #587 #619]: #726
-#709 := (or #742 #549)
-#591 := [def-axiom]: #709
-#596 := [unit-resolution #591 #595]: #742
-#592 := (not #742)
-#701 := (not #726)
-#586 := (or #701 #592 #740)
-#601 := [def-axiom]: #586
-#598 := [unit-resolution #601 #596 #589]: #740
-#597 := (not #740)
-#599 := (or #597 #602)
-#600 := [th-lemma arith triangle-eq]: #599
-#610 := [unit-resolution #600 #598]: #602
-[th-lemma arith farkas -1 1 -1 1 1 #610 #618 #104 #626 #628]: false
-unsat
-b4c5fd98177a46b2cc0b910f32ebb8121f604602 575 0
-#2 := false
-#24 := 0::Int
-decl f4 :: (-> S2 Int Int)
-#11 := 1::Int
-decl f5 :: (-> S3 Int S2)
+#10 := (- f3)
+#9 := (< f3 0::Int)
+#11 := (if #9 #10 f3)
+#12 := (= #11 0::Int)
+#14 := (iff #12 #13)
+#15 := (not #14)
+#55 := (iff #15 #52)
+#45 := (iff #42 #13)
+#48 := (not #45)
+#53 := (iff #48 #52)
+#54 := [rewrite]: #53
+#49 := (iff #15 #48)
+#46 := (iff #14 #45)
+#43 := (iff #12 #42)
+#40 := (= #11 #37)
+#22 := (not #21)
+#34 := (if #22 #31 f3)
+#38 := (= #34 #37)
+#39 := [rewrite]: #38
+#35 := (= #11 #34)
+#32 := (= #10 #31)
+#33 := [rewrite]: #32
+#23 := (iff #9 #22)
+#27 := (iff #22 #22)
+#25 := (iff #21 #21)
+#26 := [rewrite]: #25
+#28 := [monotonicity #26]: #27
+#24 := [rewrite]: #23
+#29 := [trans #24 #28]: #23
+#36 := [monotonicity #29 #33]: #35
+#41 := [trans #36 #39]: #40
+#44 := [monotonicity #41]: #43
+#47 := [monotonicity #44]: #46
+#50 := [monotonicity #47]: #49
+#56 := [trans #50 #54]: #55
+#17 := [asserted]: #15
+#57 := [mp #17 #56]: #52
+#93 := [mp #57 #92]: #90
+#117 := [mp #93 #116]: #114
+#136 := (not #114)
+#137 := (or #96 #110 #136)
+#138 := [def-axiom]: #137
+#140 := [unit-resolution #138 #117]: #139
+#165 := [unit-resolution #140 #164]: #110
+#124 := (or #96 #76)
+#125 := [def-axiom]: #124
+#166 := [unit-resolution #125 #164]: #76
+#160 := (or #107 #94)
+#146 := (+ f3 #145)
+#147 := (<= #146 0::Int)
+#118 := (= f3 #81)
+#149 := [hypothesis]: #108
+#150 := (or #107 #78)
+#151 := [th-lemma arith farkas 1 1]: #150
+#152 := [unit-resolution #151 #149]: #78
+#120 := (or #109 #118)
+#121 := [def-axiom]: #120
+#153 := [unit-resolution #121 #152]: #118
+#154 := (not #118)
+#155 := (or #154 #147)
+#156 := [th-lemma arith triangle-eq]: #155
+#157 := [unit-resolution #156 #153]: #147
+#158 := [hypothesis]: #76
+#159 := [th-lemma arith farkas -1 1 1 #149 #158 #157]: false
+#161 := [lemma #159]: #160
+#167 := [unit-resolution #161 #166]: #107
+#134 := (or #111 #108 #109)
+#135 := [def-axiom]: #134
+#168 := [unit-resolution #135 #167 #165]: #109
+#122 := (or #78 #119)
+#123 := [def-axiom]: #122
+#169 := [unit-resolution #123 #168]: #119
+#170 := (not #119)
+#171 := (or #170 #162)
+#172 := [th-lemma arith triangle-eq]: #171
+#173 := [unit-resolution #172 #169]: #162
+#174 := [th-lemma arith farkas 1 1 1 #166 #168 #173]: false
+#175 := [lemma #174]: #96
+#143 := (or #97 #111)
+#141 := (or #97 #111 #136)
+#142 := [def-axiom]: #141
+#144 := [unit-resolution #142 #117]: #143
+#176 := [unit-resolution #144 #175]: #111
+#132 := (or #110 #78)
+#133 := [def-axiom]: #132
+#177 := [unit-resolution #133 #176]: #78
+#178 := [unit-resolution #121 #177]: #118
+#179 := [unit-resolution #156 #178]: #147
+#180 := (not #147)
+#181 := (or #77 #109 #180)
+#182 := [th-lemma arith assign-bounds -1 1]: #181
+#183 := [unit-resolution #182 #177 #179]: #77
+#163 := (>= #146 0::Int)
+#184 := (or #154 #163)
+#185 := [th-lemma arith triangle-eq]: #184
+#186 := [unit-resolution #185 #178]: #163
+#130 := (or #110 #107)
+#131 := [def-axiom]: #130
+#187 := [unit-resolution #131 #176]: #107
+#188 := (not #163)
+#189 := (or #76 #108 #188)
+#190 := [th-lemma arith assign-bounds -1 1]: #189
+#191 := [unit-resolution #190 #187 #186]: #76
+#128 := (or #97 #94 #95)
+#129 := [def-axiom]: #128
+[unit-resolution #129 #191 #183 #175]: false
+1f4bd6ea16be20cad268dc7281facb65139024ab 130 0
+unsat
+#2 := false
+#7 := 0::Int
 decl f3 :: Int
 #8 := f3
-decl f7 :: S3
-#14 := f7
-#15 := (f5 f7 f3)
-#16 := (f4 #15 1::Int)
-#83 := -1::Int
-#85 := (* -1::Int #16)
-decl f6 :: S3
-#9 := f6
-#10 := (f5 f6 f3)
-#12 := (f4 #10 1::Int)
-#84 := (* -1::Int #12)
-#86 := (+ #84 #85)
-#87 := (+ f3 #86)
-#429 := (>= #87 0::Int)
-#602 := (<= #16 0::Int)
-#673 := (= #16 0::Int)
-#757 := (= f3 0::Int)
-#752 := (>= f3 0::Int)
-#455 := (not #752)
-#420 := (<= f3 0::Int)
-#741 := (not #420)
-#641 := (or #741 #455 #757)
-#621 := (not #641)
-#588 := [hypothesis]: #621
-#615 := (or #641 #752)
-#616 := [def-axiom]: #615
-#589 := [unit-resolution #616 #588]: #752
-#618 := (or #641 #420)
-#614 := [def-axiom]: #618
-#590 := [unit-resolution #614 #588]: #420
-#576 := (not #757)
-#619 := (or #641 #576)
-#620 := [def-axiom]: #619
-#600 := [unit-resolution #620 #588]: #576
-#580 := (or #757 #741 #455)
-#601 := [th-lemma arith triangle-eq]: #580
-#556 := [unit-resolution #601 #600 #590 #589]: false
-#557 := [lemma #556]: #641
-#504 := (or #621 #673)
-#431 := (* -1::Int f3)
-#694 := (mod #431 -1::Int)
-#661 := (+ #16 #694)
-#642 := (= #661 0::Int)
-#624 := (ite #641 #673 #642)
-#22 := (:var 0 Int)
-#20 := (:var 1 Int)
-#42 := (f5 f7 #20)
-#43 := (f4 #42 #22)
-#765 := (pattern #43)
-#107 := (* -1::Int #22)
-#104 := (* -1::Int #20)
-#162 := (mod #104 #107)
-#277 := (+ #43 #162)
-#278 := (= #277 0::Int)
-#44 := (mod #20 #22)
-#274 := (* -1::Int #44)
-#275 := (+ #43 #274)
-#276 := (= #275 0::Int)
-#136 := (>= #20 0::Int)
-#129 := (<= #22 0::Int)
-#221 := (or #129 #136)
-#222 := (not #221)
-#125 := (<= #20 0::Int)
-#219 := (or #125 #129)
-#220 := (not #219)
-#225 := (or #220 #222)
-#279 := (ite #225 #276 #278)
-#273 := (= #43 0::Int)
-#25 := (= #20 0::Int)
-#280 := (ite #25 #273 #279)
-#272 := (= #20 #43)
-#26 := (= #22 0::Int)
-#281 := (ite #26 #272 #280)
-#766 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #765) #281)
-#284 := (forall (vars (?v0 Int) (?v1 Int)) #281)
-#769 := (iff #284 #766)
-#767 := (iff #281 #281)
-#768 := [refl]: #767
-#770 := [quant-intro #768]: #769
-#168 := (* -1::Int #162)
-#241 := (ite #225 #44 #168)
-#244 := (ite #25 0::Int #241)
-#247 := (ite #26 #20 #244)
-#250 := (= #43 #247)
-#253 := (forall (vars (?v0 Int) (?v1 Int)) #250)
-#285 := (iff #253 #284)
-#282 := (iff #250 #281)
-#283 := [rewrite]: #282
-#286 := [quant-intro #283]: #285
-#137 := (not #136)
-#130 := (not #129)
-#140 := (and #130 #137)
-#126 := (not #125)
-#133 := (and #126 #130)
-#143 := (or #133 #140)
-#188 := (ite #143 #44 #168)
-#191 := (ite #25 0::Int #188)
-#194 := (ite #26 #20 #191)
-#197 := (= #43 #194)
-#200 := (forall (vars (?v0 Int) (?v1 Int)) #197)
-#254 := (iff #200 #253)
-#251 := (iff #197 #250)
-#248 := (= #194 #247)
-#245 := (= #191 #244)
-#242 := (= #188 #241)
-#226 := (iff #143 #225)
-#223 := (iff #140 #222)
-#224 := [rewrite]: #223
-#213 := (iff #133 #220)
-#214 := [rewrite]: #213
-#227 := [monotonicity #214 #224]: #226
-#243 := [monotonicity #227]: #242
-#246 := [monotonicity #243]: #245
-#249 := [monotonicity #246]: #248
-#252 := [monotonicity #249]: #251
-#255 := [quant-intro #252]: #254
-#211 := (~ #200 #200)
-#210 := (~ #197 #197)
-#207 := [refl]: #210
-#212 := [nnf-pos #207]: #211
-#36 := (- #22)
-#35 := (- #20)
-#45 := (mod #35 #36)
-#46 := (- #45)
-#29 := (< 0::Int #22)
-#31 := (< #20 0::Int)
-#32 := (and #31 #29)
-#28 := (< 0::Int #20)
-#30 := (and #28 #29)
-#33 := (or #30 #32)
-#47 := (ite #33 #44 #46)
-#48 := (ite #25 0::Int #47)
-#49 := (ite #26 #20 #48)
-#50 := (= #43 #49)
-#51 := (forall (vars (?v0 Int) (?v1 Int)) #50)
-#203 := (iff #51 #200)
-#98 := (and #29 #31)
-#101 := (or #30 #98)
-#173 := (ite #101 #44 #168)
-#176 := (ite #25 0::Int #173)
-#179 := (ite #26 #20 #176)
-#182 := (= #43 #179)
-#185 := (forall (vars (?v0 Int) (?v1 Int)) #182)
-#201 := (iff #185 #200)
-#198 := (iff #182 #197)
-#195 := (= #179 #194)
-#192 := (= #176 #191)
-#189 := (= #173 #188)
-#144 := (iff #101 #143)
-#141 := (iff #98 #140)
-#138 := (iff #31 #137)
-#139 := [rewrite]: #138
-#131 := (iff #29 #130)
-#132 := [rewrite]: #131
-#142 := [monotonicity #132 #139]: #141
-#134 := (iff #30 #133)
-#127 := (iff #28 #126)
-#128 := [rewrite]: #127
-#135 := [monotonicity #128 #132]: #134
-#145 := [monotonicity #135 #142]: #144
-#190 := [monotonicity #145]: #189
-#193 := [monotonicity #190]: #192
-#196 := [monotonicity #193]: #195
-#199 := [monotonicity #196]: #198
-#202 := [quant-intro #199]: #201
-#186 := (iff #51 #185)
-#183 := (iff #50 #182)
-#180 := (= #49 #179)
-#177 := (= #48 #176)
-#174 := (= #47 #173)
-#171 := (= #46 #168)
-#165 := (- #162)
-#169 := (= #165 #168)
-#170 := [rewrite]: #169
-#166 := (= #46 #165)
-#163 := (= #45 #162)
-#108 := (= #36 #107)
-#109 := [rewrite]: #108
-#105 := (= #35 #104)
-#106 := [rewrite]: #105
-#164 := [monotonicity #106 #109]: #163
-#167 := [monotonicity #164]: #166
-#172 := [trans #167 #170]: #171
-#102 := (iff #33 #101)
-#99 := (iff #32 #98)
-#100 := [rewrite]: #99
-#103 := [monotonicity #100]: #102
-#175 := [monotonicity #103 #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [monotonicity #178]: #180
-#184 := [monotonicity #181]: #183
-#187 := [quant-intro #184]: #186
-#204 := [trans #187 #202]: #203
-#161 := [asserted]: #51
-#205 := [mp #161 #204]: #200
-#208 := [mp~ #205 #212]: #200
-#256 := [mp #208 #255]: #253
-#287 := [mp #256 #286]: #284
-#771 := [mp #287 #770]: #766
-#631 := (not #766)
-#626 := (or #631 #624)
-#430 := (* -1::Int 1::Int)
-#692 := (mod #431 #430)
-#689 := (+ #16 #692)
-#693 := (= #689 0::Int)
-#538 := (mod f3 1::Int)
-#680 := (* -1::Int #538)
-#682 := (+ #16 #680)
-#674 := (= #682 0::Int)
-#409 := (<= 1::Int 0::Int)
-#539 := (or #409 #752)
-#746 := (not #539)
-#421 := (or #420 #409)
-#753 := (not #421)
-#754 := (or #753 #746)
-#671 := (ite #754 #674 #693)
-#683 := (ite #757 #673 #671)
-#684 := (= f3 #16)
-#751 := (= 1::Int 0::Int)
-#685 := (ite #751 #684 #683)
-#632 := (or #631 #685)
-#606 := (iff #632 #626)
-#500 := (iff #626 #626)
-#611 := [rewrite]: #500
-#629 := (iff #685 #624)
-#351 := (or #741 #455)
-#652 := (or #351 #757)
-#653 := (ite #652 #673 #642)
-#625 := (iff #653 #624)
-#627 := (iff #652 #641)
-#623 := [rewrite]: #627
-#628 := [monotonicity #623]: #625
-#640 := (iff #685 #653)
-#634 := (ite false #684 #653)
-#638 := (iff #634 #653)
-#639 := [rewrite]: #638
-#636 := (iff #685 #634)
-#655 := (iff #683 #653)
-#646 := (ite #351 #673 #642)
-#649 := (ite #757 #673 #646)
-#654 := (iff #649 #653)
-#644 := [rewrite]: #654
-#650 := (iff #683 #649)
-#647 := (iff #671 #646)
-#643 := (iff #693 #642)
-#658 := (= #689 #661)
-#659 := (= #692 #694)
-#450 := (= #430 -1::Int)
-#451 := [rewrite]: #450
-#660 := [monotonicity #451]: #659
-#662 := [monotonicity #660]: #658
-#645 := [monotonicity #662]: #643
-#656 := (iff #674 #673)
-#665 := (= #682 #16)
-#664 := (+ #16 0::Int)
-#668 := (= #664 #16)
-#669 := [rewrite]: #668
-#666 := (= #682 #664)
-#679 := (= #680 0::Int)
-#675 := (* -1::Int 0::Int)
-#678 := (= #675 0::Int)
-#672 := [rewrite]: #678
-#676 := (= #680 #675)
-#681 := (= #538 0::Int)
-#686 := [rewrite]: #681
-#677 := [monotonicity #686]: #676
-#663 := [trans #677 #672]: #679
-#667 := [monotonicity #663]: #666
-#670 := [trans #667 #669]: #665
-#657 := [monotonicity #670]: #656
-#727 := (iff #754 #351)
-#456 := (iff #746 #455)
-#732 := (iff #539 #752)
-#384 := (or false #752)
-#745 := (iff #384 #752)
-#731 := [rewrite]: #745
-#744 := (iff #539 #384)
-#399 := (iff #409 false)
-#735 := [rewrite]: #399
-#742 := [monotonicity #735]: #744
-#454 := [trans #742 #731]: #732
-#457 := [monotonicity #454]: #456
-#743 := (iff #753 #741)
-#740 := (iff #421 #420)
-#736 := (or #420 false)
-#739 := (iff #736 #420)
-#734 := [rewrite]: #739
-#737 := (iff #421 #736)
-#738 := [monotonicity #735]: #737
-#378 := [trans #738 #734]: #740
-#383 := [monotonicity #378]: #743
-#728 := [monotonicity #383 #457]: #727
-#648 := [monotonicity #728 #657 #645]: #647
-#651 := [monotonicity #648]: #650
-#633 := [trans #651 #644]: #655
-#412 := (iff #751 false)
-#748 := [rewrite]: #412
-#637 := [monotonicity #748 #633]: #636
-#635 := [trans #637 #639]: #640
-#630 := [trans #635 #628]: #629
-#607 := [monotonicity #630]: #606
-#612 := [trans #607 #611]: #606
-#605 := [quant-inst #8 #11]: #632
-#613 := [mp #605 #612]: #626
-#511 := [unit-resolution #613 #771]: #624
-#608 := (not #624)
-#609 := (or #608 #621 #673)
-#604 := [def-axiom]: #609
-#507 := [unit-resolution #604 #511]: #504
-#508 := [unit-resolution #507 #557]: #673
-#585 := (not #673)
-#494 := (or #585 #602)
-#496 := [th-lemma arith triangle-eq]: #494
-#497 := [unit-resolution #496 #508]: #602
-#704 := (<= #12 0::Int)
-#756 := (= #12 0::Int)
-#459 := [hypothesis]: #576
-#708 := (not #351)
-#432 := (div f3 1::Int)
-#436 := (* -1::Int #432)
-#415 := (+ #12 #436)
-#750 := (= #415 0::Int)
-#583 := (not #750)
-#550 := (+ f3 #436)
-#555 := (>= #550 0::Int)
-#549 := (= #550 0::Int)
-#1 := true
-#69 := [true-axiom]: true
-#499 := (or false #549)
-#501 := [th-lemma arith]: #499
-#502 := [unit-resolution #501 #69]: #549
-#505 := (not #549)
-#506 := (or #505 #555)
-#510 := [th-lemma arith triangle-eq]: #506
-#503 := [unit-resolution #510 #502]: #555
-#540 := (<= #415 0::Int)
-#495 := [hypothesis]: #750
-#498 := (or #583 #540)
-#480 := [th-lemma arith triangle-eq]: #498
-#482 := [unit-resolution #480 #495]: #540
-#485 := (not #555)
-#484 := (not #540)
-#483 := (not #602)
-#486 := (or #429 #483 #484 #485)
-#487 := [th-lemma arith assign-bounds 1 1 -1]: #486
-#488 := [unit-resolution #487 #482 #497 #503]: #429
-#345 := (<= #87 0::Int)
-#537 := (<= #550 0::Int)
-#489 := (or #505 #537)
-#490 := [th-lemma arith triangle-eq]: #489
-#491 := [unit-resolution #490 #502]: #537
-#548 := (>= #16 0::Int)
-#492 := (or #585 #548)
-#481 := [th-lemma arith triangle-eq]: #492
-#493 := [unit-resolution #481 #508]: #548
-#541 := (>= #415 0::Int)
-#470 := (or #583 #541)
-#472 := [th-lemma arith triangle-eq]: #470
-#473 := [unit-resolution #472 #495]: #541
-#476 := (not #537)
-#475 := (not #541)
-#474 := (not #548)
-#477 := (or #345 #474 #475 #476)
-#478 := [th-lemma arith assign-bounds 1 1 -1]: #477
-#471 := [unit-resolution #478 #473 #493 #491]: #345
-#464 := (not #429)
-#479 := (not #345)
-#468 := (or #479 #464)
-#88 := (= #87 0::Int)
-#91 := (not #88)
-#13 := (* #12 1::Int)
-#17 := (+ #13 #16)
-#18 := (= f3 #17)
-#19 := (not #18)
-#94 := (iff #19 #91)
-#74 := (+ #12 #16)
-#77 := (= f3 #74)
-#80 := (not #77)
-#92 := (iff #80 #91)
-#89 := (iff #77 #88)
-#90 := [rewrite]: #89
-#93 := [monotonicity #90]: #92
-#81 := (iff #19 #80)
-#78 := (iff #18 #77)
-#75 := (= #17 #74)
-#72 := (= #13 #12)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#79 := [monotonicity #76]: #78
-#82 := [monotonicity #79]: #81
-#95 := [trans #82 #93]: #94
-#71 := [asserted]: #19
-#96 := [mp #71 #95]: #91
-#465 := (or #88 #479 #464)
-#466 := [th-lemma arith triangle-eq]: #465
-#467 := [unit-resolution #466 #96]: #468
-#469 := [unit-resolution #467 #471 #488]: false
-#458 := [lemma #469]: #583
-#725 := (div #431 -1::Int)
-#730 := (* -1::Int #725)
-#442 := (+ #12 #730)
-#722 := (= #442 0::Int)
-#723 := (ite #351 #750 #722)
-#452 := (or #757 #723)
-#713 := (ite #757 #756 #723)
-#21 := (f5 f6 #20)
-#23 := (f4 #21 #22)
-#758 := (pattern #23)
-#110 := (div #104 #107)
-#261 := (* -1::Int #110)
-#262 := (+ #23 #261)
-#263 := (= #262 0::Int)
-#34 := (div #20 #22)
-#258 := (* -1::Int #34)
-#259 := (+ #23 #258)
-#260 := (= #259 0::Int)
-#264 := (ite #225 #260 #263)
-#257 := (= #23 0::Int)
-#27 := (or #25 #26)
-#265 := (ite #27 #257 #264)
-#759 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #758) #265)
-#268 := (forall (vars (?v0 Int) (?v1 Int)) #265)
-#762 := (iff #268 #759)
-#760 := (iff #265 #265)
-#761 := [refl]: #760
-#763 := [quant-intro #761]: #762
-#228 := (ite #225 #34 #110)
-#231 := (ite #27 0::Int #228)
-#234 := (= #23 #231)
-#237 := (forall (vars (?v0 Int) (?v1 Int)) #234)
-#269 := (iff #237 #268)
-#266 := (iff #234 #265)
-#267 := [rewrite]: #266
-#270 := [quant-intro #267]: #269
-#146 := (ite #143 #34 #110)
-#149 := (ite #27 0::Int #146)
-#152 := (= #23 #149)
-#155 := (forall (vars (?v0 Int) (?v1 Int)) #152)
-#238 := (iff #155 #237)
-#235 := (iff #152 #234)
-#232 := (= #149 #231)
-#229 := (= #146 #228)
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [monotonicity #233]: #235
-#239 := [quant-intro #236]: #238
-#217 := (~ #155 #155)
-#215 := (~ #152 #152)
-#216 := [refl]: #215
-#218 := [nnf-pos #216]: #217
-#37 := (div #35 #36)
-#38 := (ite #33 #34 #37)
-#39 := (ite #27 0::Int #38)
-#40 := (= #23 #39)
-#41 := (forall (vars (?v0 Int) (?v1 Int)) #40)
-#158 := (iff #41 #155)
-#113 := (ite #101 #34 #110)
-#116 := (ite #27 0::Int #113)
-#119 := (= #23 #116)
-#122 := (forall (vars (?v0 Int) (?v1 Int)) #119)
-#156 := (iff #122 #155)
-#153 := (iff #119 #152)
-#150 := (= #116 #149)
-#147 := (= #113 #146)
-#148 := [monotonicity #145]: #147
-#151 := [monotonicity #148]: #150
-#154 := [monotonicity #151]: #153
-#157 := [quant-intro #154]: #156
-#123 := (iff #41 #122)
-#120 := (iff #40 #119)
-#117 := (= #39 #116)
-#114 := (= #38 #113)
-#111 := (= #37 #110)
-#112 := [monotonicity #106 #109]: #111
-#115 := [monotonicity #103 #112]: #114
-#118 := [monotonicity #115]: #117
-#121 := [monotonicity #118]: #120
-#124 := [quant-intro #121]: #123
-#159 := [trans #124 #157]: #158
-#97 := [asserted]: #41
-#160 := [mp #97 #159]: #155
-#209 := [mp~ #160 #218]: #155
-#240 := [mp #209 #239]: #237
-#271 := [mp #240 #270]: #268
-#764 := [mp #271 #763]: #759
-#710 := (not #759)
-#711 := (or #710 #713)
-#422 := (div #431 #430)
-#433 := (* -1::Int #422)
-#434 := (+ #12 #433)
-#435 := (= #434 0::Int)
-#755 := (ite #754 #750 #435)
-#747 := (or #757 #751)
-#407 := (ite #747 #756 #755)
-#716 := (or #710 #407)
-#712 := (iff #716 #711)
-#559 := (iff #711 #711)
-#560 := [rewrite]: #559
-#714 := (iff #407 #713)
-#720 := (iff #755 #723)
-#437 := (iff #435 #722)
-#443 := (= #434 #442)
-#440 := (= #433 #730)
-#729 := (= #422 #725)
-#726 := [monotonicity #451]: #729
-#441 := [monotonicity #726]: #440
-#721 := [monotonicity #441]: #443
-#719 := [monotonicity #721]: #437
-#724 := [monotonicity #728 #719]: #720
-#397 := (iff #747 #757)
-#408 := (or #757 false)
-#733 := (iff #408 #757)
-#396 := [rewrite]: #733
-#749 := (iff #747 #408)
-#392 := [monotonicity #748]: #749
-#398 := [trans #392 #396]: #397
-#715 := [monotonicity #398 #724]: #714
-#718 := [monotonicity #715]: #712
-#561 := [trans #718 #560]: #712
-#717 := [quant-inst #8 #11]: #716
-#703 := [mp #717 #561]: #711
-#460 := [unit-resolution #703 #764]: #713
-#691 := (not #713)
-#594 := (or #691 #757 #723)
-#587 := [def-axiom]: #594
-#461 := [unit-resolution #587 #460]: #452
-#462 := [unit-resolution #461 #459]: #723
-#698 := (not #723)
-#696 := (or #698 #708 #750)
-#699 := [def-axiom]: #696
-#453 := [unit-resolution #699 #462 #458]: #708
-#706 := (or #351 #420)
-#700 := [def-axiom]: #706
-#463 := [unit-resolution #700 #453]: #420
-#701 := (or #351 #752)
-#707 := [def-axiom]: #701
-#444 := [unit-resolution #707 #453]: #752
-#445 := [unit-resolution #601 #444 #463 #459]: false
-#446 := [lemma #445]: #757
-#438 := (or #576 #756)
-#591 := (or #691 #576 #756)
-#593 := [def-axiom]: #591
-#447 := [unit-resolution #593 #460]: #438
-#448 := [unit-resolution #447 #446]: #756
-#595 := (not #756)
-#439 := (or #595 #704)
-#449 := [th-lemma arith triangle-eq]: #439
-#416 := [unit-resolution #449 #448]: #704
-#418 := (or #576 #752)
-#419 := [th-lemma arith triangle-eq]: #418
-#410 := [unit-resolution #419 #446]: #752
-#423 := (not #704)
-#424 := (or #429 #423 #483 #455)
-#425 := [th-lemma arith assign-bounds 1 1 -1]: #424
-#426 := [unit-resolution #425 #410 #416 #497]: #429
-#705 := (>= #12 0::Int)
-#427 := (or #595 #705)
-#417 := [th-lemma arith triangle-eq]: #427
-#428 := [unit-resolution #417 #448]: #705
-#411 := (or #576 #420)
-#413 := [th-lemma arith triangle-eq]: #411
-#414 := [unit-resolution #413 #446]: #420
-#393 := (not #705)
-#395 := (or #345 #393 #474 #741)
-#400 := [th-lemma arith assign-bounds 1 1 -1]: #395
-#401 := [unit-resolution #400 #414 #428 #493]: #345
-[unit-resolution #467 #401 #426]: false
-unsat
-29994559a294fef222a1bfa1d73aa449b16d980f 552 0
-#2 := false
-#24 := 0::Int
-decl f4 :: (-> S2 Int Int)
-#11 := 3::Int
-decl f5 :: (-> S3 Int S2)
+#29 := -1::Int
+#30 := (* -1::Int f3)
+#76 := (>= f3 0::Int)
+#82 := (if #76 f3 #30)
+#75 := (* -1::Int #82)
+#130 := (+ #30 #75)
+#131 := (<= #130 0::Int)
+#110 := (= #30 #82)
+#79 := (not #76)
+#92 := (+ f3 #75)
+#93 := (<= #92 0::Int)
+#95 := (not #93)
+#74 := (>= #92 0::Int)
+#94 := (not #74)
+#96 := (or #94 #95)
+#97 := (not #96)
+#109 := (= f3 #82)
+#133 := (not #109)
+#134 := [hypothesis]: #133
+#111 := (or #79 #109)
+#112 := [def-axiom]: #111
+#135 := [unit-resolution #112 #134]: #79
+#124 := (or #76 #97)
+#103 := (iff #76 #96)
+#85 := (= #82 f3)
+#88 := (iff #79 #85)
+#106 := (iff #88 #103)
+#100 := (iff #79 #97)
+#104 := (iff #100 #103)
+#105 := [rewrite]: #104
+#101 := (iff #88 #100)
+#98 := (iff #85 #97)
+#99 := [rewrite]: #98
+#102 := [monotonicity #99]: #101
+#107 := [trans #102 #105]: #106
+#9 := (<= 0::Int f3)
+#36 := (if #9 f3 #30)
+#41 := (= #36 f3)
+#23 := (not #9)
+#50 := (iff #23 #41)
+#89 := (iff #50 #88)
+#86 := (iff #41 #85)
+#83 := (= #36 #82)
+#77 := (iff #9 #76)
+#78 := [rewrite]: #77
+#84 := [monotonicity #78]: #83
+#87 := [monotonicity #84]: #86
+#80 := (iff #23 #79)
+#81 := [monotonicity #78]: #80
+#90 := [monotonicity #81 #87]: #89
+#11 := (- f3)
+#10 := (< f3 0::Int)
+#12 := (if #10 #11 f3)
+#13 := (= #12 f3)
+#14 := (iff #9 #13)
+#15 := (not #14)
+#53 := (iff #15 #50)
+#44 := (iff #9 #41)
+#47 := (not #44)
+#51 := (iff #47 #50)
+#52 := [rewrite]: #51
+#48 := (iff #15 #47)
+#45 := (iff #14 #44)
+#42 := (iff #13 #41)
+#39 := (= #12 #36)
+#33 := (if #23 #30 f3)
+#37 := (= #33 #36)
+#38 := [rewrite]: #37
+#34 := (= #12 #33)
+#31 := (= #11 #30)
+#32 := [rewrite]: #31
+#24 := (iff #10 #23)
+#26 := (iff #23 #23)
+#21 := (iff #9 #9)
+#22 := [rewrite]: #21
+#27 := [monotonicity #22]: #26
+#25 := [rewrite]: #24
+#28 := [trans #25 #27]: #24
+#35 := [monotonicity #28 #32]: #34
+#40 := [trans #35 #38]: #39
+#43 := [monotonicity #40]: #42
+#46 := [monotonicity #22 #43]: #45
+#49 := [monotonicity #46]: #48
+#54 := [trans #49 #52]: #53
+#17 := [asserted]: #15
+#55 := [mp #17 #54]: #50
+#91 := [mp #55 #90]: #88
+#108 := [mp #91 #107]: #103
+#121 := (not #103)
+#122 := (or #76 #97 #121)
+#123 := [def-axiom]: #122
+#125 := [unit-resolution #123 #108]: #124
+#136 := [unit-resolution #125 #135]: #97
+#117 := (or #96 #93)
+#118 := [def-axiom]: #117
+#137 := [unit-resolution #118 #136]: #93
+#115 := (or #96 #74)
+#116 := [def-axiom]: #115
+#138 := [unit-resolution #116 #136]: #74
+#139 := (or #109 #95 #94)
+#140 := [th-lemma arith triangle-eq]: #139
+#141 := [unit-resolution #140 #134 #138 #137]: false
+#142 := [lemma #141]: #109
+#143 := (or #133 #74)
+#144 := [th-lemma arith triangle-eq]: #143
+#145 := [unit-resolution #144 #142]: #74
+#146 := (or #133 #93)
+#147 := [th-lemma arith triangle-eq]: #146
+#148 := [unit-resolution #147 #142]: #93
+#119 := (or #97 #94 #95)
+#120 := [def-axiom]: #119
+#149 := [unit-resolution #120 #148 #145]: #97
+#128 := (or #79 #96)
+#126 := (or #79 #96 #121)
+#127 := [def-axiom]: #126
+#129 := [unit-resolution #127 #108]: #128
+#150 := [unit-resolution #129 #149]: #79
+#113 := (or #76 #110)
+#114 := [def-axiom]: #113
+#151 := [unit-resolution #114 #150]: #110
+#152 := (not #110)
+#153 := (or #152 #131)
+#154 := [th-lemma arith triangle-eq]: #153
+#155 := [unit-resolution #154 #151]: #131
+[th-lemma arith farkas 2 1 1 #150 #145 #155]: false
+d4189e2ade5b8393242e31d994e5b087c3842ddf 143 0
+#2 := false
+#8 := 0::Int
 decl f3 :: Int
-#8 := f3
-decl f6 :: S3
-#9 := f6
-#10 := (f5 f6 f3)
-#12 := (f4 #10 3::Int)
-#707 := (>= #12 0::Int)
-#758 := (= #12 0::Int)
-#754 := (= f3 0::Int)
-#694 := (not #754)
-#566 := [hypothesis]: #694
-#749 := (<= f3 0::Int)
-#753 := (>= f3 0::Int)
-#457 := (not #753)
-#381 := (not #749)
-#460 := (or #381 #457)
-#710 := (not #460)
-#84 := -3::Int
-#86 := -1::Int
-#434 := (* -1::Int f3)
-#454 := (div #434 -3::Int)
-#729 := (* -1::Int #454)
-#444 := (+ #12 #729)
-#724 := (= #444 0::Int)
-#438 := (div f3 3::Int)
-#435 := (* -1::Int #438)
-#439 := (+ #12 #435)
-#418 := (= #439 0::Int)
-#722 := (ite #460 #418 #724)
-#568 := (or #754 #722)
-#727 := (ite #754 #758 #722)
-#22 := (:var 0 Int)
-#20 := (:var 1 Int)
-#21 := (f5 f6 #20)
-#23 := (f4 #21 #22)
-#761 := (pattern #23)
-#109 := (* -1::Int #22)
-#106 := (* -1::Int #20)
-#112 := (div #106 #109)
-#263 := (* -1::Int #112)
-#264 := (+ #23 #263)
-#265 := (= #264 0::Int)
-#34 := (div #20 #22)
-#260 := (* -1::Int #34)
-#261 := (+ #23 #260)
-#262 := (= #261 0::Int)
-#138 := (>= #20 0::Int)
-#131 := (<= #22 0::Int)
-#223 := (or #131 #138)
-#224 := (not #223)
-#127 := (<= #20 0::Int)
-#221 := (or #127 #131)
-#222 := (not #221)
-#227 := (or #222 #224)
-#266 := (ite #227 #262 #265)
-#259 := (= #23 0::Int)
-#26 := (= #22 0::Int)
-#25 := (= #20 0::Int)
-#27 := (or #25 #26)
-#267 := (ite #27 #259 #266)
-#762 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #761) #267)
-#270 := (forall (vars (?v0 Int) (?v1 Int)) #267)
-#765 := (iff #270 #762)
-#763 := (iff #267 #267)
-#764 := [refl]: #763
-#766 := [quant-intro #764]: #765
-#230 := (ite #227 #34 #112)
-#233 := (ite #27 0::Int #230)
-#236 := (= #23 #233)
-#239 := (forall (vars (?v0 Int) (?v1 Int)) #236)
-#271 := (iff #239 #270)
-#268 := (iff #236 #267)
-#269 := [rewrite]: #268
-#272 := [quant-intro #269]: #271
-#139 := (not #138)
-#132 := (not #131)
-#142 := (and #132 #139)
-#128 := (not #127)
-#135 := (and #128 #132)
-#145 := (or #135 #142)
-#148 := (ite #145 #34 #112)
-#151 := (ite #27 0::Int #148)
-#154 := (= #23 #151)
-#157 := (forall (vars (?v0 Int) (?v1 Int)) #154)
-#240 := (iff #157 #239)
-#237 := (iff #154 #236)
-#234 := (= #151 #233)
-#231 := (= #148 #230)
-#228 := (iff #145 #227)
-#225 := (iff #142 #224)
-#226 := [rewrite]: #225
-#215 := (iff #135 #222)
-#216 := [rewrite]: #215
-#229 := [monotonicity #216 #226]: #228
-#232 := [monotonicity #229]: #231
-#235 := [monotonicity #232]: #234
-#238 := [monotonicity #235]: #237
-#241 := [quant-intro #238]: #240
-#219 := (~ #157 #157)
-#217 := (~ #154 #154)
-#218 := [refl]: #217
-#220 := [nnf-pos #218]: #219
-#36 := (- #22)
-#35 := (- #20)
-#37 := (div #35 #36)
-#29 := (< 0::Int #22)
-#31 := (< #20 0::Int)
-#32 := (and #31 #29)
-#28 := (< 0::Int #20)
-#30 := (and #28 #29)
-#33 := (or #30 #32)
-#38 := (ite #33 #34 #37)
-#39 := (ite #27 0::Int #38)
-#40 := (= #23 #39)
-#41 := (forall (vars (?v0 Int) (?v1 Int)) #40)
-#160 := (iff #41 #157)
-#100 := (and #29 #31)
-#103 := (or #30 #100)
-#115 := (ite #103 #34 #112)
-#118 := (ite #27 0::Int #115)
-#121 := (= #23 #118)
-#124 := (forall (vars (?v0 Int) (?v1 Int)) #121)
-#158 := (iff #124 #157)
-#155 := (iff #121 #154)
-#152 := (= #118 #151)
-#149 := (= #115 #148)
-#146 := (iff #103 #145)
-#143 := (iff #100 #142)
-#140 := (iff #31 #139)
-#141 := [rewrite]: #140
-#133 := (iff #29 #132)
-#134 := [rewrite]: #133
-#144 := [monotonicity #134 #141]: #143
-#136 := (iff #30 #135)
-#129 := (iff #28 #128)
-#130 := [rewrite]: #129
-#137 := [monotonicity #130 #134]: #136
-#147 := [monotonicity #137 #144]: #146
-#150 := [monotonicity #147]: #149
-#153 := [monotonicity #150]: #152
-#156 := [monotonicity #153]: #155
-#159 := [quant-intro #156]: #158
-#125 := (iff #41 #124)
-#122 := (iff #40 #121)
-#119 := (= #39 #118)
-#116 := (= #38 #115)
-#113 := (= #37 #112)
-#110 := (= #36 #109)
-#111 := [rewrite]: #110
-#107 := (= #35 #106)
-#108 := [rewrite]: #107
-#114 := [monotonicity #108 #111]: #113
-#104 := (iff #33 #103)
-#101 := (iff #32 #100)
-#102 := [rewrite]: #101
-#105 := [monotonicity #102]: #104
-#117 := [monotonicity #105 #114]: #116
-#120 := [monotonicity #117]: #119
-#123 := [monotonicity #120]: #122
-#126 := [quant-intro #123]: #125
-#161 := [trans #126 #159]: #160
-#99 := [asserted]: #41
-#162 := [mp #99 #161]: #157
-#211 := [mp~ #162 #220]: #157
-#242 := [mp #211 #241]: #239
-#273 := [mp #242 #272]: #270
-#767 := [mp #273 #766]: #762
-#718 := (not #762)
-#713 := (or #718 #727)
-#433 := (* -1::Int 3::Int)
-#425 := (div #434 #433)
-#436 := (* -1::Int #425)
-#437 := (+ #12 #436)
-#365 := (= #437 0::Int)
-#755 := (<= 3::Int 0::Int)
-#412 := (or #755 #753)
-#542 := (not #412)
-#423 := (or #749 #755)
-#424 := (not #423)
-#756 := (or #424 #542)
-#757 := (ite #756 #418 #365)
-#759 := (= 3::Int 0::Int)
-#760 := (or #754 #759)
-#750 := (ite #760 #758 #757)
-#714 := (or #718 #750)
-#720 := (iff #714 #713)
-#721 := (iff #713 #713)
-#562 := [rewrite]: #721
-#716 := (iff #750 #727)
-#726 := (iff #757 #722)
-#725 := (iff #365 #724)
-#445 := (= #437 #444)
-#733 := (= #436 #729)
-#728 := (= #425 #454)
-#731 := (= #433 -3::Int)
-#453 := [rewrite]: #731
-#732 := [monotonicity #453]: #728
-#443 := [monotonicity #732]: #733
-#446 := [monotonicity #443]: #445
-#440 := [monotonicity #446]: #725
-#353 := (iff #756 #460)
-#458 := (iff #542 #457)
-#734 := (iff #412 #753)
-#386 := (or false #753)
-#745 := (iff #386 #753)
-#748 := [rewrite]: #745
-#387 := (iff #412 #386)
-#401 := (iff #755 false)
-#402 := [rewrite]: #401
-#747 := [monotonicity #402]: #387
-#735 := [trans #747 #748]: #734
-#459 := [monotonicity #735]: #458
-#744 := (iff #424 #381)
-#737 := (iff #423 #749)
-#738 := (or #749 false)
-#741 := (iff #738 #749)
-#742 := [rewrite]: #741
-#739 := (iff #423 #738)
-#740 := [monotonicity #402]: #739
-#743 := [trans #740 #742]: #737
-#746 := [monotonicity #743]: #744
-#730 := [monotonicity #746 #459]: #353
-#723 := [monotonicity #730 #440]: #726
-#399 := (iff #760 #754)
-#751 := (or #754 false)
-#395 := (iff #751 #754)
-#736 := [rewrite]: #395
-#411 := (iff #760 #751)
-#410 := (iff #759 false)
-#415 := [rewrite]: #410
-#752 := [monotonicity #415]: #411
-#400 := [trans #752 #736]: #399
-#717 := [monotonicity #400 #723]: #716
-#715 := [monotonicity #717]: #720
-#563 := [trans #715 #562]: #720
-#719 := [quant-inst #8 #11]: #714
-#564 := [mp #719 #563]: #713
-#567 := [unit-resolution #564 #767]: #727
-#691 := (not #727)
-#596 := (or #691 #754 #722)
-#597 := [def-axiom]: #596
-#569 := [unit-resolution #597 #567]: #568
-#570 := [unit-resolution #569 #566]: #722
-#544 := (mod #434 -3::Int)
-decl f7 :: S3
-#14 := f7
-#15 := (f5 f7 f3)
-#16 := (f4 #15 3::Int)
-#689 := (+ #16 #544)
-#680 := (= #689 0::Int)
-#712 := (mod f3 3::Int)
-#696 := (* -1::Int #712)
-#683 := (+ #16 #696)
-#685 := (= #683 0::Int)
-#682 := (ite #460 #685 #680)
-#529 := (or #754 #682)
-#674 := (= #16 0::Int)
-#669 := (ite #754 #674 #682)
-#42 := (f5 f7 #20)
-#43 := (f4 #42 #22)
-#768 := (pattern #43)
-#164 := (mod #106 #109)
-#279 := (+ #43 #164)
-#280 := (= #279 0::Int)
-#44 := (mod #20 #22)
-#276 := (* -1::Int #44)
-#277 := (+ #43 #276)
-#278 := (= #277 0::Int)
-#281 := (ite #227 #278 #280)
-#275 := (= #43 0::Int)
-#282 := (ite #25 #275 #281)
-#274 := (= #20 #43)
-#283 := (ite #26 #274 #282)
-#769 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #768) #283)
-#286 := (forall (vars (?v0 Int) (?v1 Int)) #283)
-#772 := (iff #286 #769)
-#770 := (iff #283 #283)
-#771 := [refl]: #770
-#773 := [quant-intro #771]: #772
-#170 := (* -1::Int #164)
-#243 := (ite #227 #44 #170)
-#246 := (ite #25 0::Int #243)
-#249 := (ite #26 #20 #246)
-#252 := (= #43 #249)
-#255 := (forall (vars (?v0 Int) (?v1 Int)) #252)
-#287 := (iff #255 #286)
-#284 := (iff #252 #283)
-#285 := [rewrite]: #284
-#288 := [quant-intro #285]: #287
-#190 := (ite #145 #44 #170)
-#193 := (ite #25 0::Int #190)
-#196 := (ite #26 #20 #193)
-#199 := (= #43 #196)
-#202 := (forall (vars (?v0 Int) (?v1 Int)) #199)
-#256 := (iff #202 #255)
-#253 := (iff #199 #252)
-#250 := (= #196 #249)
-#247 := (= #193 #246)
-#244 := (= #190 #243)
-#245 := [monotonicity #229]: #244
-#248 := [monotonicity #245]: #247
-#251 := [monotonicity #248]: #250
-#254 := [monotonicity #251]: #253
-#257 := [quant-intro #254]: #256
-#213 := (~ #202 #202)
-#212 := (~ #199 #199)
-#209 := [refl]: #212
-#214 := [nnf-pos #209]: #213
-#45 := (mod #35 #36)
-#46 := (- #45)
-#47 := (ite #33 #44 #46)
-#48 := (ite #25 0::Int #47)
-#49 := (ite #26 #20 #48)
-#50 := (= #43 #49)
-#51 := (forall (vars (?v0 Int) (?v1 Int)) #50)
-#205 := (iff #51 #202)
-#175 := (ite #103 #44 #170)
-#178 := (ite #25 0::Int #175)
-#181 := (ite #26 #20 #178)
-#184 := (= #43 #181)
-#187 := (forall (vars (?v0 Int) (?v1 Int)) #184)
-#203 := (iff #187 #202)
-#200 := (iff #184 #199)
-#197 := (= #181 #196)
-#194 := (= #178 #193)
-#191 := (= #175 #190)
-#192 := [monotonicity #147]: #191
-#195 := [monotonicity #192]: #194
-#198 := [monotonicity #195]: #197
-#201 := [monotonicity #198]: #200
-#204 := [quant-intro #201]: #203
-#188 := (iff #51 #187)
-#185 := (iff #50 #184)
-#182 := (= #49 #181)
-#179 := (= #48 #178)
-#176 := (= #47 #175)
-#173 := (= #46 #170)
-#167 := (- #164)
-#171 := (= #167 #170)
-#172 := [rewrite]: #171
-#168 := (= #46 #167)
-#165 := (= #45 #164)
-#166 := [monotonicity #108 #111]: #165
-#169 := [monotonicity #166]: #168
-#174 := [trans #169 #172]: #173
-#177 := [monotonicity #105 #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [monotonicity #180]: #182
-#186 := [monotonicity #183]: #185
-#189 := [quant-intro #186]: #188
-#206 := [trans #189 #204]: #205
-#163 := [asserted]: #51
-#207 := [mp #163 #206]: #202
-#210 := [mp~ #207 #214]: #202
-#258 := [mp #210 #257]: #255
-#289 := [mp #258 #288]: #286
-#774 := [mp #289 #773]: #769
-#664 := (not #769)
-#661 := (or #664 #669)
-#602 := (mod #434 #433)
-#695 := (+ #16 #602)
-#692 := (= #695 0::Int)
-#677 := (ite #756 #685 #692)
-#676 := (ite #754 #674 #677)
-#686 := (= f3 #16)
-#687 := (ite #759 #686 #676)
-#665 := (or #664 #687)
-#646 := (iff #665 #661)
-#649 := (iff #661 #661)
-#650 := [rewrite]: #649
-#662 := (iff #687 #669)
-#672 := (ite false #686 #669)
-#659 := (iff #672 #669)
-#660 := [rewrite]: #659
-#668 := (iff #687 #672)
-#670 := (iff #676 #669)
-#666 := (iff #677 #682)
-#681 := (iff #692 #680)
-#678 := (= #695 #689)
-#688 := (= #602 #544)
-#684 := [monotonicity #453]: #688
-#679 := [monotonicity #684]: #678
-#675 := [monotonicity #679]: #681
-#667 := [monotonicity #730 #675]: #666
-#671 := [monotonicity #667]: #670
-#673 := [monotonicity #415 #671]: #668
-#663 := [trans #673 #660]: #662
-#648 := [monotonicity #663]: #646
-#651 := [trans #648 #650]: #646
-#645 := [quant-inst #8 #11]: #665
-#652 := [mp #645 #651]: #661
-#625 := [unit-resolution #652 #774]: #669
-#626 := (not #669)
-#631 := (or #626 #754 #682)
-#632 := [def-axiom]: #631
-#530 := [unit-resolution #632 #625]: #529
-#531 := [unit-resolution #530 #566]: #682
-#700 := (not #722)
-#658 := (not #682)
-#495 := (or #710 #658 #700)
-#656 := (>= #683 0::Int)
-#571 := [hypothesis]: #682
-#572 := [hypothesis]: #460
-#636 := (or #658 #710 #685)
-#637 := [def-axiom]: #636
-#573 := [unit-resolution #637 #572 #571]: #685
-#641 := (not #685)
-#497 := (or #641 #656)
-#499 := [th-lemma arith triangle-eq]: #497
-#500 := [unit-resolution #499 #573]: #656
-#543 := (>= #439 0::Int)
-#553 := [hypothesis]: #722
-#701 := (or #700 #710 #418)
-#699 := [def-axiom]: #701
-#554 := [unit-resolution #699 #572 #553]: #418
-#585 := (not #418)
-#498 := (or #585 #543)
-#501 := [th-lemma arith triangle-eq]: #498
-#483 := [unit-resolution #501 #554]: #543
-#87 := (* -1::Int #16)
-#85 := (* -3::Int #12)
-#88 := (+ #85 #87)
-#89 := (+ f3 #88)
-#347 := (<= #89 0::Int)
-#485 := (not #347)
-#432 := (>= #89 0::Int)
-#561 := (not #432)
-#577 := [hypothesis]: #561
-#537 := (or #754 #432)
-#558 := (or #710 #432 #658 #700)
-#655 := (<= #683 0::Int)
-#574 := (or #641 #655)
-#575 := [th-lemma arith triangle-eq]: #574
-#576 := [unit-resolution #575 #573]: #655
-#619 := (* -3::Int #438)
-#622 := (+ #619 #696)
-#623 := (+ f3 #622)
-#605 := (>= #623 0::Int)
-#618 := (= #623 0::Int)
-#1 := true
-#69 := [true-axiom]: true
-#538 := (or false #618)
-#539 := [th-lemma arith]: #538
-#546 := [unit-resolution #539 #69]: #618
-#548 := (not #618)
-#549 := (or #548 #605)
-#550 := [th-lemma arith triangle-eq]: #549
-#552 := [unit-resolution #550 #546]: #605
-#541 := (<= #439 0::Int)
-#555 := (or #585 #541)
-#556 := [th-lemma arith triangle-eq]: #555
-#557 := [unit-resolution #556 #554]: #541
-#540 := [th-lemma arith farkas 3 -1 1 1 #557 #552 #577 #576]: false
-#528 := [lemma #540]: #558
-#533 := [unit-resolution #528 #531 #577 #570]: #710
-#708 := (or #460 #749)
-#709 := [def-axiom]: #708
-#534 := [unit-resolution #709 #533]: #749
-#703 := (or #460 #753)
-#704 := [def-axiom]: #703
-#535 := [unit-resolution #704 #533]: #753
-#378 := (or #754 #381 #457)
-#536 := [th-lemma arith triangle-eq]: #378
-#532 := [unit-resolution #536 #535 #534 #566]: false
-#516 := [lemma #532]: #537
-#519 := [unit-resolution #516 #577]: #754
-#523 := (or #694 #753)
-#525 := [th-lemma arith triangle-eq]: #523
-#526 := [unit-resolution #525 #519]: #753
-#653 := (<= #16 0::Int)
-#524 := (or #694 #674)
-#627 := (or #626 #694 #674)
-#628 := [def-axiom]: #627
-#527 := [unit-resolution #628 #625]: #524
-#515 := [unit-resolution #527 #519]: #674
-#633 := (not #674)
-#518 := (or #633 #653)
-#520 := [th-lemma arith triangle-eq]: #518
-#521 := [unit-resolution #520 #515]: #653
-#706 := (<= #12 0::Int)
-#517 := (or #694 #758)
-#579 := (or #691 #694 #758)
-#594 := [def-axiom]: #579
-#522 := [unit-resolution #594 #567]: #517
-#512 := [unit-resolution #522 #519]: #758
-#590 := (not #758)
-#502 := (or #590 #706)
-#504 := [th-lemma arith triangle-eq]: #502
-#505 := [unit-resolution #504 #512]: #706
-#508 := [th-lemma arith farkas -3 -1 -1 1 #505 #521 #577 #526]: false
-#509 := [lemma #508]: #432
-#488 := (or #485 #561)
-#90 := (= #89 0::Int)
-#93 := (not #90)
-#13 := (* #12 3::Int)
-#17 := (+ #13 #16)
-#18 := (= f3 #17)
-#19 := (not #18)
-#96 := (iff #19 #93)
-#72 := (* 3::Int #12)
-#75 := (+ #72 #16)
-#78 := (= f3 #75)
-#81 := (not #78)
-#94 := (iff #81 #93)
-#91 := (iff #78 #90)
-#92 := [rewrite]: #91
-#95 := [monotonicity #92]: #94
-#82 := (iff #19 #81)
-#79 := (iff #18 #78)
-#76 := (= #17 #75)
-#73 := (= #13 #72)
-#74 := [rewrite]: #73
-#77 := [monotonicity #74]: #76
-#80 := [monotonicity #77]: #79
-#83 := [monotonicity #80]: #82
-#97 := [trans #83 #95]: #96
-#71 := [asserted]: #19
-#98 := [mp #71 #97]: #93
-#486 := (or #90 #485 #561)
-#487 := [th-lemma arith triangle-eq]: #486
-#489 := [unit-resolution #487 #98]: #488
-#490 := [unit-resolution #489 #509]: #485
-#513 := (<= #623 0::Int)
-#491 := (or #548 #513)
-#492 := [th-lemma arith triangle-eq]: #491
-#493 := [unit-resolution #492 #546]: #513
-#494 := [th-lemma arith farkas -1 1 3 1 #493 #490 #483 #500]: false
-#484 := [lemma #494]: #495
-#506 := [unit-resolution #484 #531 #570]: #710
-#514 := [unit-resolution #709 #506]: #749
-#507 := [unit-resolution #704 #506]: #753
-#510 := [unit-resolution #536 #507 #514 #566]: false
-#511 := [lemma #510]: #754
-#496 := [unit-resolution #522 #511]: #758
-#473 := (or #590 #707)
-#475 := [th-lemma arith triangle-eq]: #473
-#476 := [unit-resolution #475 #496]: #707
-#654 := (>= #16 0::Int)
-#477 := [unit-resolution #527 #511]: #674
-#478 := (or #633 #654)
-#479 := [th-lemma arith triangle-eq]: #478
-#480 := [unit-resolution #479 #477]: #654
-#481 := (or #694 #749)
-#474 := [th-lemma arith triangle-eq]: #481
-#482 := [unit-resolution #474 #511]: #749
-[th-lemma arith farkas -1/3 1/3 1/3 1 #482 #480 #490 #476]: false
-unsat
-cacbb4776a876130daed2cf13657b41ab1c7df25 75 0
+#7 := f3
+#36 := -1::Int
+#37 := (* -1::Int f3)
+#58 := (>= f3 0::Int)
+#65 := (if #58 f3 #37)
+#104 := (* -1::Int #65)
+#154 := (+ f3 #104)
+#155 := (<= #154 0::Int)
+#90 := (= f3 #65)
+#105 := (+ #37 #104)
+#107 := (>= #105 0::Int)
+#91 := (= #37 #65)
+#59 := (not #58)
+#139 := [hypothesis]: #59
+#88 := (or #58 #91)
+#89 := [def-axiom]: #88
+#140 := [unit-resolution #89 #139]: #91
+#133 := (not #91)
+#141 := (or #133 #107)
+#142 := [th-lemma arith triangle-eq]: #141
+#143 := [unit-resolution #142 #140]: #107
+#73 := (+ f3 #65)
+#86 := (<= #73 0::Int)
+#148 := (not #86)
+#87 := (>= #73 0::Int)
+#106 := (<= #105 0::Int)
+#74 := (= #73 0::Int)
+#94 := (not #74)
+#126 := (not #87)
+#127 := [hypothesis]: #126
+#128 := (or #94 #87)
+#129 := [th-lemma arith triangle-eq]: #128
+#130 := [unit-resolution #129 #127]: #94
+#124 := (or #59 #74)
+#111 := (= f3 0::Int)
+#9 := (<= f3 0::Int)
+#108 := [hypothesis]: #94
+#102 := (or #9 #74)
+#52 := (not #9)
+#79 := (iff #52 #74)
+#11 := (- f3)
+#10 := (< f3 0::Int)
+#12 := (if #10 #11 f3)
+#13 := (= #12 #11)
+#14 := (iff #9 #13)
+#15 := (not #14)
+#82 := (iff #15 #79)
+#40 := (if #10 #37 f3)
+#43 := (= #40 #37)
+#53 := (iff #52 #43)
+#80 := (iff #53 #79)
+#77 := (iff #43 #74)
+#70 := (= #65 #37)
+#75 := (iff #70 #74)
+#76 := [rewrite]: #75
+#71 := (iff #43 #70)
+#68 := (= #40 #65)
+#62 := (if #59 #37 f3)
+#66 := (= #62 #65)
+#67 := [rewrite]: #66
+#63 := (= #40 #62)
+#60 := (iff #10 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#69 := [trans #64 #67]: #68
+#72 := [monotonicity #69]: #71
+#78 := [trans #72 #76]: #77
+#81 := [monotonicity #78]: #80
+#56 := (iff #15 #53)
+#46 := (iff #9 #43)
+#49 := (not #46)
+#54 := (iff #49 #53)
+#55 := [rewrite]: #54
+#50 := (iff #15 #49)
+#47 := (iff #14 #46)
+#44 := (iff #13 #43)
+#38 := (= #11 #37)
+#39 := [rewrite]: #38
+#41 := (= #12 #40)
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42 #39]: #44
+#48 := [monotonicity #45]: #47
+#51 := [monotonicity #48]: #50
+#57 := [trans #51 #55]: #56
+#83 := [trans #57 #81]: #82
+#35 := [asserted]: #15
+#84 := [mp #35 #83]: #79
+#95 := (not #79)
+#100 := (or #9 #74 #95)
+#101 := [def-axiom]: #100
+#103 := [unit-resolution #101 #84]: #102
+#109 := [unit-resolution #103 #108]: #9
+#110 := [hypothesis]: #58
+#112 := [th-lemma arith eq-propagate 0 0 #110 #109]: #111
+#120 := (= #73 f3)
+#118 := (= #65 f3)
+#92 := (or #59 #90)
+#93 := [def-axiom]: #92
+#113 := [unit-resolution #93 #110]: #90
+#119 := [symm #113]: #118
+#116 := (= #73 #65)
+#114 := (= #65 #73)
+#115 := [th-lemma arith eq-propagate 1 1 #110 #109]: #114
+#117 := [symm #115]: #116
+#121 := [trans #117 #119]: #120
+#122 := [trans #121 #112]: #74
+#123 := [unit-resolution #108 #122]: false
+#125 := [lemma #123]: #124
+#131 := [unit-resolution #125 #130]: #59
+#132 := [unit-resolution #89 #131]: #91
+#134 := (or #133 #106)
+#135 := [th-lemma arith triangle-eq]: #134
+#136 := [unit-resolution #135 #132]: #106
+#137 := [th-lemma arith farkas 1 1 #127 #136]: false
+#138 := [lemma #137]: #87
+#144 := (or #58 #9)
+#145 := [th-lemma arith farkas 1 1]: #144
+#146 := [unit-resolution #145 #139]: #9
+#98 := (or #52 #94)
+#96 := (or #52 #94 #95)
+#97 := [def-axiom]: #96
+#99 := [unit-resolution #97 #84]: #98
+#147 := [unit-resolution #99 #146]: #94
+#149 := (or #74 #148 #126)
+#150 := [th-lemma arith triangle-eq]: #149
+#151 := [unit-resolution #150 #147 #138]: #148
+#152 := [th-lemma arith farkas 1 1 #151 #143]: false
+#153 := [lemma #152]: #58
+#157 := [unit-resolution #93 #153]: #90
+#158 := (not #90)
+#159 := (or #158 #155)
+#160 := [th-lemma arith triangle-eq]: #159
+#161 := [unit-resolution #160 #157]: #155
+#162 := [unit-resolution #125 #153]: #74
+#163 := (or #94 #86)
+#164 := [th-lemma arith triangle-eq]: #163
+#165 := [unit-resolution #164 #162]: #86
+#166 := [unit-resolution #99 #162]: #52
+[th-lemma arith farkas 2 1 1 #166 #165 #161]: false
+unsat
+6e505bbe74d8a0cc7b4aa4675a487119e8023d46 116 0
 #2 := false
 #8 := 0::Int
 decl f3 :: Int
-#9 := f3
-#35 := -1::Int
-#36 := (* -1::Int f3)
-#48 := (>= f3 0::Int)
-#55 := (ite #48 f3 #36)
-#75 := (* -1::Int #55)
-#84 := (+ #36 #75)
-#93 := (<= #84 0::Int)
-#80 := (= #36 #55)
-#49 := (not #48)
-#76 := (+ f3 #75)
-#83 := (<= #76 0::Int)
-#79 := (= f3 #55)
-#85 := [hypothesis]: #48
-#81 := (or #49 #79)
-#82 := [def-axiom]: #81
-#86 := [unit-resolution #82 #85]: #79
-#87 := (not #79)
-#88 := (or #87 #83)
-#89 := [th-lemma arith triangle-eq]: #88
-#90 := [unit-resolution #89 #86]: #83
-#64 := (>= #55 0::Int)
-#68 := (not #64)
-#11 := (- f3)
-#10 := (< f3 0::Int)
-#12 := (ite #10 #11 f3)
-#13 := (<= 0::Int #12)
+#7 := f3
+#37 := -1::Int
+#38 := (* -1::Int f3)
+#64 := (>= f3 0::Int)
+#71 := (if #64 f3 #38)
+#85 := (* -1::Int #71)
+#125 := (+ #38 #85)
+#141 := (<= #125 0::Int)
+#113 := (= #38 #71)
+#65 := (not #64)
+#123 := (+ f3 #85)
+#124 := (<= #123 0::Int)
+#112 := (= f3 #71)
+#126 := [hypothesis]: #64
+#108 := (or #65 #112)
+#109 := [def-axiom]: #108
+#127 := [unit-resolution #109 #126]: #112
+#128 := (not #112)
+#129 := (or #128 #124)
+#130 := [th-lemma arith triangle-eq]: #129
+#131 := [unit-resolution #130 #127]: #124
+#80 := (>= #71 0::Int)
+#79 := (not #80)
+#91 := (if #80 #71 #85)
+#110 := (= #71 #91)
+#134 := (not #110)
+#96 := (= #91 #71)
+#99 := (not #96)
+#135 := (iff #99 #134)
+#132 := (iff #96 #110)
+#133 := [commutativity]: #132
+#136 := [monotonicity #133]: #135
+#10 := (- f3)
+#9 := (< f3 0::Int)
+#11 := (if #9 #10 f3)
+#13 := (- #11)
+#12 := (< #11 0::Int)
+#14 := (if #12 #13 #11)
+#15 := (= #14 #11)
+#16 := (not #15)
+#102 := (iff #16 #99)
+#41 := (if #9 #38 f3)
+#50 := (* -1::Int #41)
+#44 := (< #41 0::Int)
+#55 := (if #44 #50 #41)
+#58 := (= #55 #41)
+#61 := (not #58)
+#100 := (iff #61 #99)
+#97 := (iff #58 #96)
+#74 := (= #41 #71)
+#68 := (if #65 #38 f3)
+#72 := (= #68 #71)
+#73 := [rewrite]: #72
+#69 := (= #41 #68)
+#66 := (iff #9 #65)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#75 := [trans #70 #73]: #74
+#94 := (= #55 #91)
+#88 := (if #79 #85 #71)
+#92 := (= #88 #91)
+#93 := [rewrite]: #92
+#89 := (= #55 #88)
+#86 := (= #50 #85)
+#87 := [monotonicity #75]: #86
+#83 := (iff #44 #79)
+#76 := (< #71 0::Int)
+#81 := (iff #76 #79)
+#82 := [rewrite]: #81
+#77 := (iff #44 #76)
+#78 := [monotonicity #75]: #77
+#84 := [trans #78 #82]: #83
+#90 := [monotonicity #84 #87 #75]: #89
+#95 := [trans #90 #93]: #94
+#98 := [monotonicity #95 #75]: #97
+#101 := [monotonicity #98]: #100
+#62 := (iff #16 #61)
+#59 := (iff #15 #58)
+#42 := (= #11 #41)
+#39 := (= #10 #38)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#56 := (= #14 #55)
+#53 := (= #13 #50)
+#47 := (- #41)
+#51 := (= #47 #50)
+#52 := [rewrite]: #51
+#48 := (= #13 #47)
+#49 := [monotonicity #43]: #48
+#54 := [trans #49 #52]: #53
+#45 := (iff #12 #44)
+#46 := [monotonicity #43]: #45
+#57 := [monotonicity #46 #54 #43]: #56
+#60 := [monotonicity #57 #43]: #59
+#63 := [monotonicity #60]: #62
+#103 := [trans #63 #101]: #102
+#36 := [asserted]: #16
+#104 := [mp #36 #103]: #99
+#137 := [mp #104 #136]: #134
+#114 := (or #79 #110)
+#115 := [def-axiom]: #114
+#138 := [unit-resolution #115 #137]: #79
+#139 := [th-lemma arith farkas -1 1 1 #126 #138 #131]: false
+#140 := [lemma #139]: #65
+#106 := (or #64 #113)
+#107 := [def-axiom]: #106
+#143 := [unit-resolution #107 #140]: #113
+#144 := (not #113)
+#145 := (or #144 #141)
+#146 := [th-lemma arith triangle-eq]: #145
+#147 := [unit-resolution #146 #143]: #141
+[th-lemma arith farkas 1 1 1 #140 #138 #147]: false
+unsat
+b84cd4b4d4f113193dc5e0fed03847844f8dc058 57 0
+#2 := false
+#14 := 0::Int
+decl f4 :: Int
+#8 := f4
+decl f3 :: Int
+#7 := f3
+#36 := -1::Int
+#37 := (* -1::Int f4)
+#38 := (+ f3 #37)
+#39 := (<= #38 0::Int)
+#42 := (if #39 f3 f4)
+#50 := (* -1::Int #42)
+#59 := (+ f4 #50)
+#73 := (>= #59 0::Int)
+#63 := (= f4 #42)
+#64 := (not #39)
+#62 := (= f3 #42)
+#67 := (not #62)
+#51 := (+ f3 #50)
+#49 := (>= #51 0::Int)
+#55 := (not #49)
+#9 := (<= f3 f4)
+#10 := (if #9 f3 f4)
+#11 := (<= #10 f3)
+#12 := (not #11)
+#56 := (iff #12 #55)
+#53 := (iff #11 #49)
+#45 := (<= #42 f3)
+#48 := (iff #45 #49)
+#52 := [rewrite]: #48
+#46 := (iff #11 #45)
+#43 := (= #10 #42)
+#40 := (iff #9 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#47 := [monotonicity #44]: #46
+#54 := [trans #47 #52]: #53
+#57 := [monotonicity #54]: #56
+#33 := [asserted]: #12
+#58 := [mp #33 #57]: #55
+#66 := [hypothesis]: #62
+#68 := (or #67 #49)
+#69 := [th-lemma arith triangle-eq]: #68
+#70 := [unit-resolution #69 #66 #58]: false
+#71 := [lemma #70]: #67
+#65 := (or #64 #62)
+#60 := [def-axiom]: #65
+#74 := [unit-resolution #60 #71]: #64
+#61 := (or #39 #63)
+#35 := [def-axiom]: #61
+#75 := [unit-resolution #35 #74]: #63
+#76 := (not #63)
+#77 := (or #76 #73)
+#78 := [th-lemma arith triangle-eq]: #77
+#79 := [unit-resolution #78 #75]: #73
+[th-lemma arith farkas 1 1 1 #58 #74 #79]: false
+unsat
+57cb3c449627b0e103d175fe91d160e37eb458b9 57 0
+#2 := false
+#14 := 0::Int
+decl f4 :: Int
+#8 := f4
+decl f3 :: Int
+#7 := f3
+#36 := -1::Int
+#37 := (* -1::Int f4)
+#38 := (+ f3 #37)
+#39 := (<= #38 0::Int)
+#42 := (if #39 f3 f4)
+#49 := (* -1::Int #42)
+#50 := (+ f4 #49)
+#48 := (>= #50 0::Int)
+#55 := (not #48)
+#9 := (<= f3 f4)
+#10 := (if #9 f3 f4)
+#11 := (<= #10 f4)
+#12 := (not #11)
+#56 := (iff #12 #55)
+#53 := (iff #11 #48)
+#45 := (<= #42 f4)
+#51 := (iff #45 #48)
+#52 := [rewrite]: #51
+#46 := (iff #11 #45)
+#43 := (= #10 #42)
+#40 := (iff #9 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#47 := [monotonicity #44]: #46
+#54 := [trans #47 #52]: #53
+#57 := [monotonicity #54]: #56
+#33 := [asserted]: #12
+#58 := [mp #33 #57]: #55
+#63 := (= f4 #42)
+#64 := (not #39)
+#68 := [hypothesis]: #39
+#59 := (+ f3 #49)
+#67 := (>= #59 0::Int)
+#62 := (= f3 #42)
+#65 := (or #64 #62)
+#60 := [def-axiom]: #65
+#69 := [unit-resolution #60 #68]: #62
+#70 := (not #62)
+#71 := (or #70 #67)
+#72 := [th-lemma arith triangle-eq]: #71
+#73 := [unit-resolution #72 #69]: #67
+#74 := [th-lemma arith farkas -1 1 1 #73 #58 #68]: false
+#75 := [lemma #74]: #64
+#61 := (or #39 #63)
+#35 := [def-axiom]: #61
+#76 := [unit-resolution #35 #75]: #63
+#77 := (not #63)
+#78 := (or #77 #48)
+#79 := [th-lemma arith triangle-eq]: #78
+[unit-resolution #79 #76 #58]: false
+unsat
+ead5d10b3d302f37ae6691af9bffd34bbe254dbf 103 0
+#2 := false
+#19 := 0::Int
+decl f5 :: Int
+#10 := f5
+decl f4 :: Int
+#8 := f4
+#46 := -1::Int
+#55 := (* -1::Int f5)
+#65 := (+ f4 #55)
+#66 := (<= #65 0::Int)
+#69 := (if #66 f4 f5)
+#77 := (* -1::Int #69)
+decl f3 :: Int
+#7 := f3
+#78 := (+ f3 #77)
+#76 := (>= #78 0::Int)
+#75 := (not #76)
+#56 := (+ f3 #55)
+#54 := (>= #56 0::Int)
+#53 := (not #54)
+#49 := (* -1::Int f4)
+#50 := (+ f3 #49)
+#48 := (>= #50 0::Int)
+#47 := (not #48)
+#59 := (and #47 #53)
+#62 := (not #59)
+#83 := (or #62 #75)
+#86 := (not #83)
+#13 := (<= f4 f5)
+#14 := (if #13 f4 f5)
+#15 := (< f3 #14)
+#11 := (< f3 f5)
+#9 := (< f3 f4)
+#12 := (and #9 #11)
+#16 := (implies #12 #15)
+#17 := (not #16)
+#89 := (iff #17 #86)
+#39 := (not #12)
+#40 := (or #39 #15)
+#43 := (not #40)
+#87 := (iff #43 #86)
+#84 := (iff #40 #83)
+#81 := (iff #15 #75)
+#72 := (< f3 #69)
+#79 := (iff #72 #75)
+#80 := [rewrite]: #79
+#73 := (iff #15 #72)
+#70 := (= #14 #69)
+#67 := (iff #13 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#74 := [monotonicity #71]: #73
+#82 := [trans #74 #80]: #81
+#63 := (iff #39 #62)
+#60 := (iff #12 #59)
+#57 := (iff #11 #53)
+#58 := [rewrite]: #57
+#51 := (iff #9 #47)
+#52 := [rewrite]: #51
+#61 := [monotonicity #52 #58]: #60
+#64 := [monotonicity #61]: #63
+#85 := [monotonicity #64 #82]: #84
+#88 := [monotonicity #85]: #87
+#44 := (iff #17 #43)
+#41 := (iff #16 #40)
+#42 := [rewrite]: #41
+#45 := [monotonicity #42]: #44
+#90 := [trans #45 #88]: #89
+#38 := [asserted]: #17
+#91 := [mp #38 #90]: #86
+#95 := [not-or-elim #91]: #76
+#92 := [not-or-elim #91]: #59
+#94 := [and-elim #92]: #53
+#100 := (+ f5 #77)
+#117 := (<= #100 0::Int)
+#106 := (= f5 #69)
+#107 := (not #66)
+#105 := (= f4 #69)
+#112 := (not #105)
+#102 := (+ f4 #77)
+#99 := (<= #102 0::Int)
+#109 := (not #99)
+#93 := [and-elim #92]: #47
+#97 := [hypothesis]: #99
+#98 := [th-lemma arith farkas -1 -1 1 #97 #93 #95]: false
+#110 := [lemma #98]: #109
+#111 := [hypothesis]: #105
+#113 := (or #112 #99)
+#114 := [th-lemma arith triangle-eq]: #113
+#115 := [unit-resolution #114 #111 #110]: false
+#116 := [lemma #115]: #112
+#108 := (or #107 #105)
+#103 := [def-axiom]: #108
+#119 := [unit-resolution #103 #116]: #107
+#104 := (or #66 #106)
+#101 := [def-axiom]: #104
+#120 := [unit-resolution #101 #119]: #106
+#121 := (not #106)
+#122 := (or #121 #117)
+#123 := [th-lemma arith triangle-eq]: #122
+#124 := [unit-resolution #123 #120]: #117
+[th-lemma arith farkas -1 -1 1 #124 #94 #95]: false
+unsat
+0b3e4057c520e862b76979ea431eac352d39a39b 94 0
+#2 := false
+decl f3 :: Int
+#7 := f3
+decl f4 :: Int
+#8 := f4
+#16 := 0::Int
+#38 := -1::Int
+#39 := (* -1::Int f4)
+#40 := (+ f3 #39)
+#48 := (>= #40 0::Int)
+#50 := (if #48 f4 f3)
+#41 := (<= #40 0::Int)
+#44 := (if #41 f3 f4)
+#53 := (= #44 #50)
+#60 := (= f4 #50)
+#65 := (not #41)
+#63 := (= f3 #44)
+#105 := (not #63)
+#67 := (= f3 #50)
+#74 := (not #67)
+#75 := [hypothesis]: #74
+#71 := (or #48 #67)
+#72 := [def-axiom]: #71
+#76 := [unit-resolution #72 #75]: #48
+#68 := (not #48)
+#69 := (or #68 #60)
+#70 := [def-axiom]: #69
+#77 := [unit-resolution #70 #76]: #60
+#73 := (= f3 f4)
+#64 := (= f4 #44)
+#87 := (not #64)
+#56 := (not #53)
+#88 := (iff #56 #87)
+#85 := (iff #53 #64)
+#83 := (iff #64 #53)
+#78 := (= #50 #44)
+#81 := (iff #78 #53)
+#82 := [commutativity]: #81
+#79 := (iff #64 #78)
+#80 := [monotonicity #77]: #79
+#84 := [trans #80 #82]: #83
+#86 := [symm #84]: #85
+#89 := [monotonicity #86]: #88
+#11 := (<= f4 f3)
+#12 := (if #11 f4 f3)
+#9 := (<= f3 f4)
+#10 := (if #9 f3 f4)
+#13 := (= #10 #12)
+#14 := (not #13)
+#57 := (iff #14 #56)
+#54 := (iff #13 #53)
+#51 := (= #12 #50)
+#47 := (iff #11 #48)
+#49 := [rewrite]: #47
+#52 := [monotonicity #49]: #51
+#45 := (= #10 #44)
+#42 := (iff #9 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#55 := [monotonicity #46 #52]: #54
+#58 := [monotonicity #55]: #57
+#35 := [asserted]: #14
+#59 := [mp #35 #58]: #56
+#90 := [mp #59 #89]: #87
+#62 := (or #41 #64)
+#37 := [def-axiom]: #62
+#91 := [unit-resolution #37 #90]: #41
+#94 := (or #73 #65)
+#92 := (or #73 #65 #68)
+#93 := [th-lemma arith triangle-eq]: #92
+#95 := [unit-resolution #93 #76]: #94
+#96 := [unit-resolution #95 #91]: #73
+#97 := [trans #96 #77]: #67
+#98 := [unit-resolution #75 #97]: false
+#99 := [lemma #98]: #67
+#101 := (= #44 f3)
+#100 := [hypothesis]: #63
+#102 := [symm #100]: #101
+#103 := [trans #102 #99]: #53
+#104 := [unit-resolution #59 #103]: false
+#106 := [lemma #104]: #105
+#66 := (or #65 #63)
+#61 := [def-axiom]: #66
+#107 := [unit-resolution #61 #106]: #65
+#109 := (or #48 #41)
+#110 := [th-lemma arith farkas 1 1]: #109
+#111 := [unit-resolution #110 #107]: #48
+#112 := [unit-resolution #70 #111]: #60
+#115 := (= #44 f4)
+#108 := [unit-resolution #37 #107]: #64
+#116 := [symm #108]: #115
+#117 := [trans #116 #112]: #53
+[unit-resolution #59 #117]: false
+unsat
+c34966074811c5f7bd6d1d6b1a5efd6aba6c7ebc 53 0
+#2 := false
+#7 := 0::Int
+decl f3 :: Int
+#8 := f3
+#10 := (<= f3 0::Int)
+#11 := (if #10 f3 0::Int)
+#12 := (= #11 0::Int)
+#63 := (= f3 0::Int)
+#58 := (not #12)
+#44 := (>= f3 0::Int)
+#45 := (not #44)
+#48 := (or #45 #12)
+#51 := (not #48)
+#9 := (<= 0::Int f3)
+#13 := (implies #9 #12)
 #14 := (not #13)
-#71 := (iff #14 #68)
-#39 := (ite #10 #36 f3)
-#42 := (<= 0::Int #39)
+#54 := (iff #14 #51)
+#35 := (not #9)
+#36 := (or #35 #12)
+#39 := (not #36)
+#52 := (iff #39 #51)
+#49 := (iff #36 #48)
+#46 := (iff #35 #45)
+#42 := (iff #9 #44)
+#43 := [rewrite]: #42
+#47 := [monotonicity #43]: #46
+#50 := [monotonicity #47]: #49
+#53 := [monotonicity #50]: #52
+#40 := (iff #14 #39)
+#37 := (iff #13 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#55 := [trans #41 #53]: #54
+#34 := [asserted]: #14
+#56 := [mp #34 #55]: #51
+#59 := [not-or-elim #56]: #58
+#65 := (or #10 #12)
+#66 := [def-axiom]: #65
+#64 := [unit-resolution #66 #59]: #10
+#57 := [not-or-elim #56]: #44
+#68 := (not #10)
+#61 := (or #63 #68 #45)
+#62 := [th-lemma arith triangle-eq]: #61
+#71 := [unit-resolution #62 #57 #64]: #63
+#73 := (= #11 f3)
+#67 := (= f3 #11)
+#69 := (or #68 #67)
+#70 := [def-axiom]: #69
+#72 := [unit-resolution #70 #64]: #67
+#74 := [symm #72]: #73
+#75 := [trans #74 #71]: #12
+[unit-resolution #59 #75]: false
+unsat
+27e0298cf8da33cbbea5b9b24d6cd2a5d79bcdcc 124 0
+#2 := false
+#12 := 0::Int
+decl f4 :: Int
+#8 := f4
+decl f3 :: Int
+#7 := f3
+#38 := -1::Int
+#40 := (* -1::Int f4)
+#53 := (+ f3 #40)
+#54 := (<= #53 0::Int)
+#57 := (if #54 f3 f4)
+#105 := (* -1::Int #57)
+#106 := (+ f3 #105)
+#108 := (>= #106 0::Int)
+#93 := (= f3 #57)
+#107 := (+ f4 #105)
+#125 := (>= #107 0::Int)
+#94 := (= f4 #57)
+#95 := (not #54)
+#136 := [hypothesis]: #95
+#92 := (or #54 #94)
+#89 := [def-axiom]: #92
+#137 := [unit-resolution #89 #136]: #94
+#128 := (not #94)
+#129 := (or #128 #125)
+#130 := [th-lemma arith triangle-eq]: #129
+#138 := [unit-resolution #130 #137]: #125
+#39 := (* -1::Int f3)
+#41 := (+ #39 #40)
+#11 := (+ f3 f4)
+#60 := (>= #11 0::Int)
+#67 := (if #60 #11 #41)
+#75 := (* -1::Int #67)
+#104 := (+ #41 #75)
+#124 := (<= #104 0::Int)
+#97 := (= #41 #67)
+#61 := (not #60)
+#109 := [hypothesis]: #60
+#76 := (+ #57 #75)
+#77 := (<= #76 0::Int)
+#82 := (not #77)
+#14 := (- #11)
+#13 := (< #11 0::Int)
+#15 := (if #13 #14 #11)
+#9 := (<= f3 f4)
+#10 := (if #9 f3 f4)
+#16 := (<= #10 #15)
+#17 := (not #16)
+#85 := (iff #17 #82)
+#44 := (if #13 #41 #11)
+#47 := (<= #10 #44)
+#50 := (not #47)
+#83 := (iff #50 #82)
+#80 := (iff #47 #77)
+#72 := (<= #57 #67)
+#78 := (iff #72 #77)
+#79 := [rewrite]: #78
+#73 := (iff #47 #72)
+#70 := (= #44 #67)
+#64 := (if #61 #41 #11)
+#68 := (= #64 #67)
+#69 := [rewrite]: #68
+#65 := (= #44 #64)
+#62 := (iff #13 #61)
+#63 := [rewrite]: #62
+#66 := [monotonicity #63]: #65
+#71 := [trans #66 #69]: #70
+#58 := (= #10 #57)
+#55 := (iff #9 #54)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#74 := [monotonicity #59 #71]: #73
+#81 := [trans #74 #79]: #80
+#84 := [monotonicity #81]: #83
+#51 := (iff #17 #50)
+#48 := (iff #16 #47)
+#45 := (= #15 #44)
+#42 := (= #14 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#49 := [monotonicity #46]: #48
+#52 := [monotonicity #49]: #51
+#86 := [trans #52 #84]: #85
+#37 := [asserted]: #17
+#87 := [mp #37 #86]: #82
+#122 := (or #95 #61)
+#110 := [hypothesis]: #54
+#96 := (or #95 #93)
+#91 := [def-axiom]: #96
+#111 := [unit-resolution #91 #110]: #93
+#112 := (not #93)
+#113 := (or #112 #108)
+#114 := [th-lemma arith triangle-eq]: #113
+#115 := [unit-resolution #114 #111]: #108
+#102 := (+ #11 #75)
+#103 := (<= #102 0::Int)
+#90 := (= #11 #67)
+#98 := (or #61 #90)
+#99 := [def-axiom]: #98
+#116 := [unit-resolution #99 #109]: #90
+#117 := (not #90)
+#118 := (or #117 #103)
+#119 := [th-lemma arith triangle-eq]: #118
+#120 := [unit-resolution #119 #116]: #103
+#121 := [th-lemma arith farkas 2 2 2 1 1 #120 #115 #87 #110 #109]: false
+#123 := [lemma #121]: #122
+#126 := [unit-resolution #123 #109]: #95
+#127 := [unit-resolution #89 #126]: #94
+#131 := [unit-resolution #130 #127]: #125
+#132 := [th-lemma arith farkas 2 2 1 2 1 #120 #131 #126 #87 #109]: false
+#133 := [lemma #132]: #61
+#100 := (or #60 #97)
+#101 := [def-axiom]: #100
+#139 := [unit-resolution #101 #133]: #97
+#140 := (not #97)
+#141 := (or #140 #124)
+#142 := [th-lemma arith triangle-eq]: #141
+#143 := [unit-resolution #142 #139]: #124
+#144 := [th-lemma arith farkas 3/2 1/2 1 1 1 #133 #136 #87 #143 #138]: false
+#145 := [lemma #144]: #54
+#146 := [unit-resolution #91 #145]: #93
+#147 := [unit-resolution #114 #146]: #108
+[th-lemma arith farkas 1/2 3/2 1 1 1 #145 #133 #87 #143 #147]: false
+unsat
+6172e7a5fce8d6d8bfd1cb6db3a242b38caaaf52 57 0
+#2 := false
+#14 := 0::Int
+decl f3 :: Int
+#7 := f3
+decl f4 :: Int
+#8 := f4
+#36 := -1::Int
+#37 := (* -1::Int f4)
+#38 := (+ f3 #37)
+#39 := (<= #38 0::Int)
+#42 := (if #39 f4 f3)
+#48 := (* -1::Int #42)
+#49 := (+ f3 #48)
+#50 := (<= #49 0::Int)
+#55 := (not #50)
+#9 := (<= f3 f4)
+#10 := (if #9 f4 f3)
+#11 := (<= f3 #10)
+#12 := (not #11)
+#56 := (iff #12 #55)
+#53 := (iff #11 #50)
+#45 := (<= f3 #42)
+#51 := (iff #45 #50)
+#52 := [rewrite]: #51
+#46 := (iff #11 #45)
+#43 := (= #10 #42)
+#40 := (iff #9 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#47 := [monotonicity #44]: #46
+#54 := [trans #47 #52]: #53
+#57 := [monotonicity #54]: #56
+#33 := [asserted]: #12
+#58 := [mp #33 #57]: #55
+#63 := (= f3 #42)
+#64 := (not #39)
+#68 := [hypothesis]: #39
+#59 := (+ f4 #48)
+#66 := (<= #59 0::Int)
+#62 := (= f4 #42)
+#65 := (or #64 #62)
+#60 := [def-axiom]: #65
+#69 := [unit-resolution #60 #68]: #62
+#70 := (not #62)
+#71 := (or #70 #66)
+#72 := [th-lemma arith triangle-eq]: #71
+#73 := [unit-resolution #72 #69]: #66
+#74 := [th-lemma arith farkas 1 -1 1 #73 #58 #68]: false
+#75 := [lemma #74]: #64
+#61 := (or #39 #63)
+#35 := [def-axiom]: #61
+#76 := [unit-resolution #35 #75]: #63
+#77 := (not #63)
+#78 := (or #77 #50)
+#79 := [th-lemma arith triangle-eq]: #78
+[unit-resolution #79 #76 #58]: false
+unsat
+eb721fdcb56947acb47cbd291d0d784fc39e4176 57 0
+#2 := false
+#14 := 0::Int
+decl f4 :: Int
+#8 := f4
+decl f3 :: Int
+#7 := f3
+#36 := -1::Int
+#39 := (* -1::Int f4)
+#40 := (+ f3 #39)
+#38 := (>= #40 0::Int)
+#42 := (if #38 f3 f4)
+#48 := (* -1::Int #42)
+#59 := (+ f4 #48)
+#72 := (<= #59 0::Int)
+#63 := (= f4 #42)
+#64 := (not #38)
+#62 := (= f3 #42)
+#67 := (not #62)
+#49 := (+ f3 #48)
+#50 := (<= #49 0::Int)
+#55 := (not #50)
+#9 := (<= f4 f3)
+#10 := (if #9 f3 f4)
+#11 := (<= f3 #10)
+#12 := (not #11)
+#56 := (iff #12 #55)
+#53 := (iff #11 #50)
+#45 := (<= f3 #42)
+#51 := (iff #45 #50)
+#52 := [rewrite]: #51
+#46 := (iff #11 #45)
+#43 := (= #10 #42)
+#37 := (iff #9 #38)
+#41 := [rewrite]: #37
+#44 := [monotonicity #41]: #43
+#47 := [monotonicity #44]: #46
+#54 := [trans #47 #52]: #53
+#57 := [monotonicity #54]: #56
+#33 := [asserted]: #12
+#58 := [mp #33 #57]: #55
+#66 := [hypothesis]: #62
+#68 := (or #67 #50)
+#69 := [th-lemma arith triangle-eq]: #68
+#70 := [unit-resolution #69 #66 #58]: false
+#71 := [lemma #70]: #67
+#65 := (or #64 #62)
+#60 := [def-axiom]: #65
+#74 := [unit-resolution #60 #71]: #64
+#61 := (or #38 #63)
+#35 := [def-axiom]: #61
+#75 := [unit-resolution #35 #74]: #63
+#76 := (not #63)
+#77 := (or #76 #72)
+#78 := [th-lemma arith triangle-eq]: #77
+#79 := [unit-resolution #78 #75]: #72
+[th-lemma arith farkas 1 1 1 #58 #74 #79]: false
+unsat
+34a316044a78671ecbd5861430fe1013fee421ec 103 0
+#2 := false
+#19 := 0::Int
+decl f3 :: Int
+#7 := f3
+decl f5 :: Int
+#10 := f5
+#46 := -1::Int
+#53 := (* -1::Int f5)
+#65 := (+ f3 #53)
+#66 := (<= #65 0::Int)
+#69 := (if #66 f5 f3)
+#75 := (* -1::Int #69)
+decl f4 :: Int
+#8 := f4
+#76 := (+ f4 #75)
+#77 := (<= #76 0::Int)
+#78 := (not #77)
+#54 := (+ f4 #53)
+#55 := (<= #54 0::Int)
+#56 := (not #55)
+#49 := (* -1::Int f4)
+#50 := (+ f3 #49)
+#48 := (>= #50 0::Int)
+#47 := (not #48)
+#59 := (and #47 #56)
+#62 := (not #59)
+#83 := (or #62 #78)
+#86 := (not #83)
+#13 := (<= f3 f5)
+#14 := (if #13 f5 f3)
+#15 := (< #14 f4)
+#11 := (< f5 f4)
+#9 := (< f3 f4)
+#12 := (and #9 #11)
+#16 := (implies #12 #15)
+#17 := (not #16)
+#89 := (iff #17 #86)
+#39 := (not #12)
+#40 := (or #39 #15)
+#43 := (not #40)
+#87 := (iff #43 #86)
+#84 := (iff #40 #83)
+#81 := (iff #15 #78)
+#72 := (< #69 f4)
+#79 := (iff #72 #78)
+#80 := [rewrite]: #79
+#73 := (iff #15 #72)
+#70 := (= #14 #69)
+#67 := (iff #13 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#74 := [monotonicity #71]: #73
+#82 := [trans #74 #80]: #81
+#63 := (iff #39 #62)
+#60 := (iff #12 #59)
+#57 := (iff #11 #56)
+#58 := [rewrite]: #57
+#51 := (iff #9 #47)
+#52 := [rewrite]: #51
+#61 := [monotonicity #52 #58]: #60
+#64 := [monotonicity #61]: #63
+#85 := [monotonicity #64 #82]: #84
+#88 := [monotonicity #85]: #87
+#44 := (iff #17 #43)
+#41 := (iff #16 #40)
+#42 := [rewrite]: #41
+#45 := [monotonicity #42]: #44
+#90 := [trans #45 #88]: #89
+#38 := [asserted]: #17
+#91 := [mp #38 #90]: #86
+#95 := [not-or-elim #91]: #77
+#92 := [not-or-elim #91]: #59
+#93 := [and-elim #92]: #47
+#99 := (+ f3 #75)
+#118 := (>= #99 0::Int)
+#106 := (= f3 #69)
+#107 := (not #66)
+#105 := (= f5 #69)
+#112 := (not #105)
+#102 := (+ f5 #75)
+#100 := (>= #102 0::Int)
+#109 := (not #100)
+#94 := [and-elim #92]: #56
+#97 := [hypothesis]: #100
+#98 := [th-lemma arith farkas -1 -1 1 #97 #94 #95]: false
+#110 := [lemma #98]: #109
+#111 := [hypothesis]: #105
+#113 := (or #112 #100)
+#114 := [th-lemma arith triangle-eq]: #113
+#115 := [unit-resolution #114 #111 #110]: false
+#116 := [lemma #115]: #112
+#108 := (or #107 #105)
+#103 := [def-axiom]: #108
+#119 := [unit-resolution #103 #116]: #107
+#104 := (or #66 #106)
+#101 := [def-axiom]: #104
+#120 := [unit-resolution #101 #119]: #106
+#121 := (not #106)
+#122 := (or #121 #118)
+#123 := [th-lemma arith triangle-eq]: #122
+#124 := [unit-resolution #123 #120]: #118
+[th-lemma arith farkas -1 1 1 #124 #93 #95]: false
+unsat
+3fa37a402d59529838df2e5f73f6f77682f7982d 96 0
+#2 := false
+decl f4 :: Int
+#8 := f4
+decl f3 :: Int
+#7 := f3
+#16 := 0::Int
+#38 := -1::Int
+#39 := (* -1::Int f4)
+#40 := (+ f3 #39)
+#48 := (>= #40 0::Int)
+#50 := (if #48 f3 f4)
+#41 := (<= #40 0::Int)
+#44 := (if #41 f4 f3)
+#53 := (= #44 #50)
+#60 := (= f3 #50)
+#65 := (not #41)
+#63 := (= f4 #44)
+#107 := (not #63)
+#67 := (= f4 #50)
+#74 := (not #67)
+#75 := [hypothesis]: #74
+#71 := (or #48 #67)
+#72 := [def-axiom]: #71
+#76 := [unit-resolution #72 #75]: #48
+#68 := (not #48)
+#69 := (or #68 #60)
+#70 := [def-axiom]: #69
+#77 := [unit-resolution #70 #76]: #60
+#97 := (= f4 f3)
+#73 := (= f3 f4)
+#64 := (= f3 #44)
+#87 := (not #64)
+#56 := (not #53)
+#88 := (iff #56 #87)
+#85 := (iff #53 #64)
+#83 := (iff #64 #53)
+#78 := (= #50 #44)
+#81 := (iff #78 #53)
+#82 := [commutativity]: #81
+#79 := (iff #64 #78)
+#80 := [monotonicity #77]: #79
+#84 := [trans #80 #82]: #83
+#86 := [symm #84]: #85
+#89 := [monotonicity #86]: #88
+#11 := (<= f4 f3)
+#12 := (if #11 f3 f4)
+#9 := (<= f3 f4)
+#10 := (if #9 f4 f3)
+#13 := (= #10 #12)
+#14 := (not #13)
+#57 := (iff #14 #56)
+#54 := (iff #13 #53)
+#51 := (= #12 #50)
+#47 := (iff #11 #48)
+#49 := [rewrite]: #47
+#52 := [monotonicity #49]: #51
+#45 := (= #10 #44)
+#42 := (iff #9 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#55 := [monotonicity #46 #52]: #54
+#58 := [monotonicity #55]: #57
+#35 := [asserted]: #14
+#59 := [mp #35 #58]: #56
+#90 := [mp #59 #89]: #87
+#62 := (or #41 #64)
+#37 := [def-axiom]: #62
+#91 := [unit-resolution #37 #90]: #41
+#94 := (or #73 #65)
+#92 := (or #73 #65 #68)
+#93 := [th-lemma arith triangle-eq]: #92
+#95 := [unit-resolution #93 #76]: #94
+#96 := [unit-resolution #95 #91]: #73
+#98 := [symm #96]: #97
+#99 := [trans #98 #77]: #67
+#100 := [unit-resolution #75 #99]: false
+#101 := [lemma #100]: #67
+#103 := (= #44 f4)
+#102 := [hypothesis]: #63
+#104 := [symm #102]: #103
+#105 := [trans #104 #101]: #53
+#106 := [unit-resolution #59 #105]: false
+#108 := [lemma #106]: #107
+#66 := (or #65 #63)
+#61 := [def-axiom]: #66
+#109 := [unit-resolution #61 #108]: #65
+#111 := (or #48 #41)
+#112 := [th-lemma arith farkas 1 1]: #111
+#113 := [unit-resolution #112 #109]: #48
+#114 := [unit-resolution #70 #113]: #60
+#117 := (= #44 f3)
+#110 := [unit-resolution #37 #109]: #64
+#118 := [symm #110]: #117
+#119 := [trans #118 #114]: #53
+[unit-resolution #59 #119]: false
+unsat
+f995c21ac02db2a6cac2e38b26761e729e79b379 60 0
+#2 := false
+decl f3 :: Int
+#8 := f3
+#7 := 0::Int
+#10 := (<= f3 0::Int)
+#11 := (if #10 0::Int f3)
+#68 := (= f3 #11)
+#80 := (= 0::Int #11)
+#67 := (= #11 0::Int)
+#71 := (not #68)
+#12 := (= #11 f3)
+#58 := (not #12)
+#72 := (iff #58 #71)
+#61 := (iff #12 #68)
+#62 := [commutativity]: #61
+#73 := [monotonicity #62]: #72
+#44 := (>= f3 0::Int)
+#45 := (not #44)
+#48 := (or #45 #12)
+#51 := (not #48)
+#9 := (<= 0::Int f3)
+#13 := (implies #9 #12)
+#14 := (not #13)
+#54 := (iff #14 #51)
+#35 := (not #9)
+#36 := (or #35 #12)
+#39 := (not #36)
+#52 := (iff #39 #51)
+#49 := (iff #36 #48)
+#46 := (iff #35 #45)
+#42 := (iff #9 #44)
+#43 := [rewrite]: #42
+#47 := [monotonicity #43]: #46
+#50 := [monotonicity #47]: #49
+#53 := [monotonicity #50]: #52
+#40 := (iff #14 #39)
+#37 := (iff #13 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#55 := [trans #41 #53]: #54
+#34 := [asserted]: #14
+#56 := [mp #34 #55]: #51
+#59 := [not-or-elim #56]: #58
+#74 := [mp #59 #73]: #71
+#66 := (or #10 #68)
+#63 := [def-axiom]: #66
+#75 := [unit-resolution #63 #74]: #10
+#69 := (not #10)
+#70 := (or #69 #67)
+#65 := [def-axiom]: #70
+#76 := [unit-resolution #65 #75]: #67
+#81 := [symm #76]: #80
+#64 := (= f3 0::Int)
+#57 := [not-or-elim #56]: #44
+#77 := (or #64 #69 #45)
+#78 := [th-lemma arith triangle-eq]: #77
+#79 := [unit-resolution #78 #57 #75]: #64
+#82 := [trans #79 #81]: #68
+[unit-resolution #74 #82]: false
+unsat
+05cfbef4515b026ca06ebf58a35758847fe6425e 214 0
+#2 := false
+#8 := 0::Int
+decl f4 :: Int
+#13 := f4
+#42 := -1::Int
+#57 := (* -1::Int f4)
+#93 := (>= f4 0::Int)
+#100 := (if #93 f4 #57)
+#105 := (* -1::Int #100)
+#160 := (+ #57 #105)
+#182 := (<= #160 0::Int)
+#136 := (= #57 #100)
+#94 := (not #93)
+decl f3 :: Int
+#7 := f3
+#111 := (+ f3 #57)
+#112 := (<= #111 0::Int)
+#115 := (if #112 f4 f3)
+#154 := (* -1::Int #115)
+#155 := (+ f4 #154)
+#156 := (<= #155 0::Int)
+#157 := (+ f3 #154)
+#192 := (<= #157 0::Int)
+#148 := (= f3 #115)
+#149 := (not #112)
+#147 := (= f4 #115)
+#194 := [hypothesis]: #112
+#150 := (or #149 #147)
+#151 := [def-axiom]: #150
+#195 := [unit-resolution #151 #194]: #147
+#196 := (not #147)
+#197 := (or #196 #156)
+#198 := [th-lemma arith triangle-eq]: #197
+#199 := [unit-resolution #198 #195]: #156
+#178 := (not #156)
+#190 := (or #94 #178)
+#158 := (+ f4 #105)
+#159 := (<= #158 0::Int)
+#135 := (= f4 #100)
+#164 := [hypothesis]: #93
+#143 := (or #94 #135)
+#144 := [def-axiom]: #143
+#165 := [unit-resolution #144 #164]: #135
+#166 := (not #135)
+#167 := (or #166 #159)
+#168 := [th-lemma arith triangle-eq]: #167
+#169 := [unit-resolution #168 #165]: #159
+#78 := (>= f3 0::Int)
+#79 := (not #78)
+#176 := [hypothesis]: #156
+#179 := (or #79 #94 #178)
+#124 := (+ #100 #115)
+#43 := (* -1::Int f3)
+#85 := (if #78 f3 #43)
+#125 := (+ #85 #124)
+#122 := (>= #125 0::Int)
+#128 := (not #122)
+#18 := (<= f3 f4)
+#19 := (if #18 f4 f3)
+#15 := (- f4)
+#14 := (< f4 0::Int)
+#16 := (if #14 #15 f4)
+#10 := (- f3)
+#9 := (< f3 0::Int)
+#11 := (if #9 #10 f3)
+#12 := (- #11)
+#17 := (- #12 #16)
+#20 := (<= #17 #19)
+#21 := (not #20)
+#131 := (iff #21 #128)
+#60 := (if #14 #57 f4)
+#66 := (* -1::Int #60)
+#46 := (if #9 #43 f3)
+#52 := (* -1::Int #46)
+#67 := (+ #52 #66)
+#72 := (<= #67 #19)
+#75 := (not #72)
+#129 := (iff #75 #128)
+#126 := (iff #72 #122)
+#90 := (* -1::Int #85)
+#108 := (+ #90 #105)
+#118 := (<= #108 #115)
+#121 := (iff #118 #122)
+#123 := [rewrite]: #121
+#119 := (iff #72 #118)
+#116 := (= #19 #115)
+#113 := (iff #18 #112)
+#114 := [rewrite]: #113
+#117 := [monotonicity #114]: #116
+#109 := (= #67 #108)
+#106 := (= #66 #105)
+#103 := (= #60 #100)
+#97 := (if #94 #57 f4)
+#101 := (= #97 #100)
+#102 := [rewrite]: #101
+#98 := (= #60 #97)
+#95 := (iff #14 #94)
+#96 := [rewrite]: #95
+#99 := [monotonicity #96]: #98
+#104 := [trans #99 #102]: #103
+#107 := [monotonicity #104]: #106
+#91 := (= #52 #90)
+#88 := (= #46 #85)
+#82 := (if #79 #43 f3)
+#86 := (= #82 #85)
+#87 := [rewrite]: #86
+#83 := (= #46 #82)
+#80 := (iff #9 #79)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#89 := [trans #84 #87]: #88
+#92 := [monotonicity #89]: #91
+#110 := [monotonicity #92 #107]: #109
+#120 := [monotonicity #110 #117]: #119
+#127 := [trans #120 #123]: #126
+#130 := [monotonicity #127]: #129
+#76 := (iff #21 #75)
+#73 := (iff #20 #72)
+#70 := (= #17 #67)
+#63 := (- #52 #60)
+#68 := (= #63 #67)
+#69 := [rewrite]: #68
+#64 := (= #17 #63)
+#61 := (= #16 #60)
+#58 := (= #15 #57)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#55 := (= #12 #52)
+#49 := (- #46)
+#53 := (= #49 #52)
+#54 := [rewrite]: #53
+#50 := (= #12 #49)
+#47 := (= #11 #46)
+#44 := (= #10 #43)
+#45 := [rewrite]: #44
+#48 := [monotonicity #45]: #47
+#51 := [monotonicity #48]: #50
+#56 := [trans #51 #54]: #55
+#65 := [monotonicity #56 #62]: #64
+#71 := [trans #65 #69]: #70
+#74 := [monotonicity #71]: #73
+#77 := [monotonicity #74]: #76
+#132 := [trans #77 #130]: #131
+#41 := [asserted]: #21
+#133 := [mp #41 #132]: #128
+#161 := (+ f3 #90)
+#162 := (<= #161 0::Int)
+#139 := (= f3 #85)
+#170 := [hypothesis]: #78
+#141 := (or #79 #139)
+#142 := [def-axiom]: #141
+#171 := [unit-resolution #142 #170]: #139
+#172 := (not #139)
+#173 := (or #172 #162)
+#174 := [th-lemma arith triangle-eq]: #173
+#175 := [unit-resolution #174 #171]: #162
+#177 := [th-lemma arith farkas -2 1 -1 1 1 1 #164 #176 #170 #175 #133 #169]: false
+#180 := [lemma #177]: #179
+#183 := [unit-resolution #180 #164 #176]: #79
+#163 := (+ #43 #90)
+#181 := (<= #163 0::Int)
+#140 := (= #43 #85)
+#137 := (or #78 #140)
+#138 := [def-axiom]: #137
+#184 := [unit-resolution #138 #183]: #140
+#185 := (not #140)
+#186 := (or #185 #181)
+#187 := [th-lemma arith triangle-eq]: #186
+#188 := [unit-resolution #187 #184]: #181
+#189 := [th-lemma arith farkas 2 1 1 1 1 1 #164 #176 #133 #188 #183 #169]: false
+#191 := [lemma #189]: #190
+#200 := [unit-resolution #191 #199]: #94
+#145 := (or #93 #136)
+#146 := [def-axiom]: #145
+#201 := [unit-resolution #146 #200]: #136
+#202 := (not #136)
+#203 := (or #202 #182)
+#204 := [th-lemma arith triangle-eq]: #203
+#205 := [unit-resolution #204 #201]: #182
+#206 := (or #79 #149 #93)
+#207 := [th-lemma arith assign-bounds 1 1]: #206
+#208 := [unit-resolution #207 #200 #194]: #79
+#209 := [unit-resolution #138 #208]: #140
+#210 := [unit-resolution #187 #209]: #181
+#211 := [th-lemma arith farkas 1 1 1 1 1 #199 #133 #210 #208 #205]: false
+#212 := [lemma #211]: #149
+#152 := (or #112 #148)
+#153 := [def-axiom]: #152
+#223 := [unit-resolution #153 #212]: #148
+#224 := (not #148)
+#225 := (or #224 #192)
+#226 := [th-lemma arith triangle-eq]: #225
+#227 := [unit-resolution #226 #223]: #192
+#230 := (not #192)
+#231 := (or #156 #112 #230)
+#232 := [th-lemma arith assign-bounds 1 1]: #231
+#233 := [unit-resolution #232 #212 #227]: #156
+#234 := [unit-resolution #191 #233]: #94
+#235 := [unit-resolution #146 #234]: #136
+#236 := [unit-resolution #204 #235]: #182
+#215 := [hypothesis]: #79
+#216 := (or #94 #78 #112)
+#217 := [th-lemma arith assign-bounds 1 1]: #216
+#218 := [unit-resolution #217 #215 #212]: #94
+#219 := [unit-resolution #146 #218]: #136
+#220 := [unit-resolution #204 #219]: #182
+#221 := [unit-resolution #138 #215]: #140
+#222 := [unit-resolution #187 #221]: #181
+#228 := [th-lemma arith farkas 1 1 1 1 1 1 #215 #212 #227 #133 #222 #220]: false
+#229 := [lemma #228]: #78
+#237 := [unit-resolution #142 #229]: #139
+#238 := [unit-resolution #174 #237]: #162
+[th-lemma arith farkas 1 1 1 1 1 1 #212 #227 #133 #229 #238 #236]: false
+unsat
+a4bea54c174a812dc90d41994d00a1b62e09324a 53 0
+#2 := false
+#10 := 1::Int
+decl f3 :: Int
+#8 := f3
+#76 := (>= f3 1::Int)
+#78 := (not #76)
+#13 := (= f3 1::Int)
+#65 := (not #13)
+#11 := (<= f3 1::Int)
+#7 := 0::Int
+#43 := (<= f3 0::Int)
+#44 := (not #43)
+#47 := (and #44 #11)
+#50 := (not #47)
+#53 := (or #50 #13)
+#56 := (not #53)
+#9 := (< 0::Int f3)
+#12 := (and #9 #11)
+#14 := (implies #12 #13)
+#15 := (not #14)
+#59 := (iff #15 #56)
+#36 := (not #12)
+#37 := (or #36 #13)
+#40 := (not #37)
+#57 := (iff #40 #56)
+#54 := (iff #37 #53)
+#51 := (iff #36 #50)
+#48 := (iff #12 #47)
+#45 := (iff #9 #44)
+#46 := [rewrite]: #45
+#49 := [monotonicity #46]: #48
+#52 := [monotonicity #49]: #51
+#55 := [monotonicity #52]: #54
+#58 := [monotonicity #55]: #57
+#41 := (iff #15 #40)
+#38 := (iff #14 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#60 := [trans #42 #58]: #59
+#35 := [asserted]: #15
+#61 := [mp #35 #60]: #56
+#66 := [not-or-elim #61]: #65
+#75 := (or #13 #78)
+#62 := [not-or-elim #61]: #47
+#64 := [and-elim #62]: #11
+#77 := (not #11)
+#79 := (or #13 #77 #78)
+#74 := [th-lemma arith triangle-eq]: #79
+#72 := [unit-resolution #74 #64]: #75
+#73 := [unit-resolution #72 #66]: #78
+#63 := [and-elim #62]: #44
+[th-lemma arith farkas 1 1 #63 #73]: false
+unsat
+6b1fd4164c9a3bc3b6f6a1779970e5f9a212ac94 18 0
+#2 := false
+decl f3 :: Int
+#7 := f3
+#8 := (<= f3 f3)
+#9 := (not #8)
+#40 := (iff #9 false)
+#1 := true
+#35 := (not true)
+#38 := (iff #35 false)
+#39 := [rewrite]: #38
+#36 := (iff #9 #35)
+#33 := (iff #8 true)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#41 := [trans #37 #39]: #40
+#30 := [asserted]: #9
+[mp #30 #41]: false
+unsat
+d32e1c3a9584812c7d4ef0093047f73880b01a2e 51 0
+#2 := false
+decl f4 :: Int
+#8 := f4
+#10 := 3::Int
+#12 := (* 3::Int f4)
+decl f3 :: Int
+#7 := f3
+#11 := (* 3::Int f3)
+#13 := (<= #11 #12)
+#9 := (<= f3 f4)
+#14 := (implies #9 #13)
+#15 := (not #14)
+#69 := (iff #15 false)
+#37 := (not #9)
+#38 := (or #37 #13)
+#41 := (not #38)
+#67 := (iff #41 false)
+#1 := true
+#62 := (not true)
+#65 := (iff #62 false)
+#66 := [rewrite]: #65
+#63 := (iff #41 #62)
+#60 := (iff #38 true)
+#17 := 0::Int
+#44 := -1::Int
+#45 := (* -1::Int f4)
+#46 := (+ f3 #45)
+#47 := (<= #46 0::Int)
+#50 := (not #47)
+#55 := (or #50 #47)
+#58 := (iff #55 true)
+#59 := [rewrite]: #58
+#56 := (iff #38 #55)
+#53 := (iff #13 #47)
+#54 := [rewrite]: #53
+#51 := (iff #37 #50)
+#48 := (iff #9 #47)
+#49 := [rewrite]: #48
+#52 := [monotonicity #49]: #51
+#57 := [monotonicity #52 #54]: #56
+#61 := [trans #57 #59]: #60
+#64 := [monotonicity #61]: #63
+#68 := [trans #64 #66]: #67
+#42 := (iff #15 #41)
+#39 := (iff #14 #38)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#70 := [trans #43 #68]: #69
+#36 := [asserted]: #15
+[mp #36 #70]: false
+unsat
+3ad7098d25ffe898fa92bcf6a3b1bf60731ed829 56 0
+#2 := false
+decl f4 :: Int
+#8 := f4
+#10 := 3::Int
+#12 := (* 3::Int f4)
+decl f3 :: Int
+#7 := f3
+#11 := (* 3::Int f3)
+#13 := (< #11 #12)
+#9 := (< f3 f4)
+#14 := (implies #9 #13)
+#15 := (not #14)
+#74 := (iff #15 false)
+#37 := (not #9)
+#38 := (or #37 #13)
+#41 := (not #38)
+#72 := (iff #41 false)
+#1 := true
+#67 := (not true)
+#70 := (iff #67 false)
+#71 := [rewrite]: #70
+#68 := (iff #41 #67)
+#65 := (iff #38 true)
+#17 := 0::Int
+#44 := -1::Int
+#47 := (* -1::Int f4)
+#48 := (+ f3 #47)
+#46 := (>= #48 0::Int)
+#45 := (not #46)
+#59 := (or #46 #45)
+#63 := (iff #59 true)
+#64 := [rewrite]: #63
+#61 := (iff #38 #59)
+#60 := (iff #13 #45)
+#58 := [rewrite]: #60
+#56 := (iff #37 #46)
+#51 := (not #45)
+#54 := (iff #51 #46)
+#55 := [rewrite]: #54
+#52 := (iff #37 #51)
+#49 := (iff #9 #45)
+#50 := [rewrite]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#62 := [monotonicity #57 #58]: #61
+#66 := [trans #62 #64]: #65
+#69 := [monotonicity #66]: #68
+#73 := [trans #69 #71]: #72
+#42 := (iff #15 #41)
+#39 := (iff #14 #38)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#75 := [trans #43 #73]: #74
+#36 := [asserted]: #15
+[mp #36 #75]: false
+unsat
+021a2ccfe2f169916c13de90c0a65b798955c7c4 52 0
+#2 := false
+#14 := 0::Int
+decl f4 :: Int
+#8 := f4
+#41 := -1::Int
+#44 := (* -1::Int f4)
+decl f3 :: Int
+#7 := f3
+#45 := (+ f3 #44)
+#55 := (<= #45 0::Int)
+#68 := (not #55)
+#43 := (>= #45 0::Int)
+#58 := (or #43 #55)
+#61 := (not #58)
+#10 := (<= f3 f4)
+#9 := (< f3 f4)
+#11 := (implies #9 #10)
+#12 := (not #11)
+#64 := (iff #12 #61)
+#34 := (not #9)
+#35 := (or #34 #10)
+#38 := (not #35)
+#62 := (iff #38 #61)
+#59 := (iff #35 #58)
+#56 := (iff #10 #55)
+#57 := [rewrite]: #56
+#53 := (iff #34 #43)
+#42 := (not #43)
+#48 := (not #42)
+#51 := (iff #48 #43)
+#52 := [rewrite]: #51
+#49 := (iff #34 #48)
+#46 := (iff #9 #42)
+#47 := [rewrite]: #46
+#50 := [monotonicity #47]: #49
+#54 := [trans #50 #52]: #53
+#60 := [monotonicity #54 #57]: #59
+#63 := [monotonicity #60]: #62
+#39 := (iff #12 #38)
+#36 := (iff #11 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#65 := [trans #40 #63]: #64
+#33 := [asserted]: #12
+#66 := [mp #33 #65]: #61
+#69 := [not-or-elim #66]: #68
+#67 := [not-or-elim #66]: #42
+#77 := (or #55 #43)
+#78 := [th-lemma arith farkas 1 1]: #77
+#79 := [unit-resolution #78 #67]: #55
+[unit-resolution #79 #69]: false
+unsat
+cd494a327086bb14c2815a5bf50e8d8ef62f947f 73 0
+#2 := false
+#54 := -1::Int
+decl f4 :: Int
+#8 := f4
+#57 := (* -1::Int f4)
+decl f3 :: Int
+#7 := f3
+#58 := (+ f3 #57)
+#68 := (<= #58 -1::Int)
+#16 := 0::Int
+#56 := (>= #58 0::Int)
+#55 := (not #56)
+#82 := (not #68)
+#88 := [hypothesis]: #82
+#86 := (or #55 #68)
+#71 := (iff #56 #68)
+#10 := 1::Int
+#11 := (+ f3 1::Int)
+#12 := (<= #11 f4)
+#9 := (< f3 f4)
+#13 := (iff #9 #12)
+#14 := (not #13)
+#74 := (iff #14 #71)
+#36 := (+ 1::Int f3)
+#39 := (<= #36 f4)
+#48 := (not #9)
+#49 := (iff #48 #39)
+#72 := (iff #49 #71)
+#69 := (iff #39 #68)
+#70 := [rewrite]: #69
+#66 := (iff #48 #56)
+#61 := (not #55)
+#64 := (iff #61 #56)
+#65 := [rewrite]: #64
+#62 := (iff #48 #61)
+#59 := (iff #9 #55)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#67 := [trans #63 #65]: #66
+#73 := [monotonicity #67 #70]: #72
+#52 := (iff #14 #49)
+#42 := (iff #9 #39)
 #45 := (not #42)
-#69 := (iff #45 #68)
-#66 := (iff #42 #64)
-#60 := (<= 0::Int #55)
-#63 := (iff #60 #64)
-#65 := [rewrite]: #63
-#61 := (iff #42 #60)
-#58 := (= #39 #55)
-#52 := (ite #49 #36 f3)
-#56 := (= #52 #55)
-#57 := [rewrite]: #56
-#53 := (= #39 #52)
-#50 := (iff #10 #49)
+#50 := (iff #45 #49)
 #51 := [rewrite]: #50
-#54 := [monotonicity #51]: #53
-#59 := [trans #54 #57]: #58
-#62 := [monotonicity #59]: #61
-#67 := [trans #62 #65]: #66
-#70 := [monotonicity #67]: #69
 #46 := (iff #14 #45)
 #43 := (iff #13 #42)
-#40 := (= #12 #39)
+#40 := (iff #12 #39)
 #37 := (= #11 #36)
 #38 := [rewrite]: #37
 #41 := [monotonicity #38]: #40
 #44 := [monotonicity #41]: #43
 #47 := [monotonicity #44]: #46
-#72 := [trans #47 #70]: #71
-#34 := [asserted]: #14
-#73 := [mp #34 #72]: #68
-#91 := [th-lemma arith farkas -1 1 1 #85 #73 #90]: false
-#92 := [lemma #91]: #49
-#77 := (or #48 #80)
-#78 := [def-axiom]: #77
-#95 := [unit-resolution #78 #92]: #80
-#96 := (not #80)
-#97 := (or #96 #93)
-#98 := [th-lemma arith triangle-eq]: #97
-#99 := [unit-resolution #98 #95]: #93
-[th-lemma arith farkas 1 1 1 #92 #73 #99]: false
-unsat
-72eab31a3a69b2d560f65ab53e94b5e0f28ca228 128 0
-#2 := false
-#9 := 0::Int
-decl f3 :: Int
-#8 := f3
-#37 := -1::Int
-#38 := (* -1::Int f3)
-#137 := (<= #38 0::Int)
-#136 := (= #38 0::Int)
-#69 := (>= f3 0::Int)
-#76 := (ite #69 f3 #38)
-#85 := (= #76 0::Int)
-#105 := (= f3 #76)
-#127 := (not #105)
-#101 := (not #85)
-#128 := (iff #101 #127)
-#125 := (iff #85 #105)
-#123 := (iff #105 #85)
-#81 := (= 0::Int #76)
-#84 := (iff #81 #85)
-#122 := [commutativity]: #84
-#120 := (iff #105 #81)
-#14 := (= f3 0::Int)
-#118 := [hypothesis]: #101
-#115 := (or #14 #85)
-#63 := (not #14)
-#92 := (iff #63 #85)
-#11 := (- f3)
-#10 := (< f3 0::Int)
-#12 := (ite #10 #11 f3)
-#13 := (= #12 0::Int)
-#15 := (iff #13 #14)
-#16 := (not #15)
-#97 := (iff #16 #92)
-#41 := (ite #10 #38 f3)
-#47 := (= 0::Int #41)
-#64 := (iff #47 #63)
-#95 := (iff #64 #92)
-#89 := (iff #85 #63)
-#93 := (iff #89 #92)
-#94 := [rewrite]: #93
-#90 := (iff #64 #89)
-#87 := (iff #47 #85)
-#86 := [rewrite]: #84
-#82 := (iff #47 #81)
-#79 := (= #41 #76)
-#70 := (not #69)
-#73 := (ite #70 #38 f3)
-#77 := (= #73 #76)
-#78 := [rewrite]: #77
-#74 := (= #41 #73)
-#71 := (iff #10 #70)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#80 := [trans #75 #78]: #79
-#83 := [monotonicity #80]: #82
-#88 := [trans #83 #86]: #87
-#91 := [monotonicity #88]: #90
-#96 := [trans #91 #94]: #95
-#67 := (iff #16 #64)
-#55 := (iff #14 #47)
-#60 := (not #55)
-#65 := (iff #60 #64)
-#66 := [rewrite]: #65
-#61 := (iff #16 #60)
-#58 := (iff #15 #55)
-#52 := (iff #47 #14)
-#56 := (iff #52 #55)
-#57 := [rewrite]: #56
-#53 := (iff #15 #52)
-#50 := (iff #13 #47)
-#44 := (= #41 0::Int)
-#48 := (iff #44 #47)
-#49 := [rewrite]: #48
-#45 := (iff #13 #44)
-#42 := (= #12 #41)
-#39 := (= #11 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#51 := [trans #46 #49]: #50
-#54 := [monotonicity #51]: #53
-#59 := [trans #54 #57]: #58
-#62 := [monotonicity #59]: #61
-#68 := [trans #62 #66]: #67
-#98 := [trans #68 #96]: #97
-#36 := [asserted]: #16
-#99 := [mp #36 #98]: #92
-#102 := (not #92)
-#113 := (or #14 #85 #102)
-#114 := [def-axiom]: #113
-#116 := [unit-resolution #114 #99]: #115
-#119 := [unit-resolution #116 #118]: #14
-#121 := [monotonicity #119]: #120
-#124 := [trans #121 #122]: #123
-#126 := [symm #124]: #125
-#129 := [monotonicity #126]: #128
-#130 := [mp #118 #129]: #127
-#131 := (or #63 #69)
-#132 := [th-lemma arith triangle-eq]: #131
-#133 := [unit-resolution #132 #119]: #69
-#107 := (or #70 #105)
-#108 := [def-axiom]: #107
-#134 := [unit-resolution #108 #133 #130]: false
-#135 := [lemma #134]: #85
-#106 := (= #38 #76)
-#144 := (iff #63 #127)
-#142 := (iff #14 #105)
-#140 := (iff #105 #14)
-#141 := [monotonicity #135]: #140
-#143 := [symm #141]: #142
-#145 := [monotonicity #143]: #144
-#111 := (or #63 #101)
-#109 := (or #63 #101 #102)
-#110 := [def-axiom]: #109
-#112 := [unit-resolution #110 #99]: #111
-#139 := [unit-resolution #112 #135]: #63
-#146 := [mp #139 #145]: #127
-#147 := [unit-resolution #108 #146]: #70
-#103 := (or #69 #106)
-#104 := [def-axiom]: #103
-#148 := [unit-resolution #104 #147]: #106
-#149 := [trans #148 #135]: #136
-#150 := (not #136)
-#151 := (or #150 #137)
-#152 := [th-lemma arith triangle-eq]: #151
-#153 := [unit-resolution #152 #149]: #137
-[th-lemma arith farkas 1 1 #147 #153]: false
-unsat
-65683f244c3b3437d2ff4b46228877d5d6db1b1c 103 0
-#2 := false
-#8 := 0::Int
-decl f3 :: Int
-#9 := f3
-#64 := (>= f3 0::Int)
-#37 := -1::Int
-#38 := (* -1::Int f3)
-#111 := (* -1::Int #38)
-#112 := (+ f3 #111)
-#114 := (>= #112 0::Int)
-#110 := (= f3 #38)
-#71 := (ite #64 f3 #38)
-#118 := (= #71 #38)
-#99 := (= #38 #71)
-#65 := (not #64)
-#115 := [hypothesis]: #65
-#102 := (or #64 #99)
-#97 := [def-axiom]: #102
-#116 := [unit-resolution #97 #115]: #99
-#119 := [symm #116]: #118
-#76 := (= f3 #71)
-#108 := (or #64 #76)
-#86 := (iff #65 #76)
-#12 := (- f3)
-#11 := (< f3 0::Int)
-#13 := (ite #11 #12 f3)
-#14 := (= #13 f3)
-#10 := (<= 0::Int f3)
-#15 := (iff #10 #14)
-#16 := (not #15)
-#91 := (iff #16 #86)
-#58 := (not #10)
-#41 := (ite #11 #38 f3)
-#47 := (= f3 #41)
-#59 := (iff #47 #58)
-#89 := (iff #59 #86)
-#83 := (iff #76 #65)
-#87 := (iff #83 #86)
-#88 := [rewrite]: #87
-#84 := (iff #59 #83)
-#81 := (iff #58 #65)
-#79 := (iff #10 #64)
-#80 := [rewrite]: #79
-#82 := [monotonicity #80]: #81
-#77 := (iff #47 #76)
-#74 := (= #41 #71)
-#68 := (ite #65 #38 f3)
-#72 := (= #68 #71)
-#73 := [rewrite]: #72
-#69 := (= #41 #68)
-#66 := (iff #11 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#75 := [trans #70 #73]: #74
-#78 := [monotonicity #75]: #77
-#85 := [monotonicity #78 #82]: #84
-#90 := [trans #85 #88]: #89
-#62 := (iff #16 #59)
-#52 := (iff #10 #47)
-#55 := (not #52)
-#60 := (iff #55 #59)
-#61 := [rewrite]: #60
-#56 := (iff #16 #55)
-#53 := (iff #15 #52)
-#50 := (iff #14 #47)
-#44 := (= #41 f3)
-#48 := (iff #44 #47)
-#49 := [rewrite]: #48
-#45 := (iff #14 #44)
-#42 := (= #13 #41)
-#39 := (= #12 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#51 := [trans #46 #49]: #50
-#54 := [monotonicity #51]: #53
-#57 := [monotonicity #54]: #56
-#63 := [trans #57 #61]: #62
-#92 := [trans #63 #90]: #91
-#36 := [asserted]: #16
-#93 := [mp #36 #92]: #86
-#95 := (not #86)
-#106 := (or #64 #76 #95)
-#107 := [def-axiom]: #106
-#109 := [unit-resolution #107 #93]: #108
-#117 := [unit-resolution #109 #115]: #76
-#120 := [trans #117 #119]: #110
-#121 := (not #110)
-#122 := (or #121 #114)
-#123 := [th-lemma arith triangle-eq]: #122
-#124 := [unit-resolution #123 #120]: #114
-#125 := [th-lemma arith farkas 2 1 #115 #124]: false
-#126 := [lemma #125]: #64
-#100 := (or #65 #76)
-#101 := [def-axiom]: #100
-#113 := [unit-resolution #101 #126]: #76
-#98 := (not #76)
-#104 := (or #65 #98)
-#96 := (or #65 #98 #95)
-#103 := [def-axiom]: #96
-#105 := [unit-resolution #103 #93]: #104
-[unit-resolution #105 #113 #126]: false
-unsat
-6706cda989499422594f4bdacb2cec77f1d7ef2e 152 0
-#2 := false
-#9 := 0::Int
-decl f3 :: Int
-#8 := f3
-#37 := -1::Int
-#38 := (* -1::Int f3)
-#64 := (>= f3 0::Int)
-#71 := (ite #64 f3 #38)
-#114 := (* -1::Int #71)
-#164 := (+ f3 #114)
-#165 := (<= #164 0::Int)
-#101 := (= f3 #71)
-#115 := (+ #38 #114)
-#117 := (>= #115 0::Int)
-#76 := (= #38 #71)
-#65 := (not #64)
-#149 := [hypothesis]: #65
-#104 := (or #64 #76)
-#99 := [def-axiom]: #104
-#150 := [unit-resolution #99 #149]: #76
-#143 := (not #76)
-#151 := (or #143 #117)
-#152 := [th-lemma arith triangle-eq]: #151
-#153 := [unit-resolution #152 #150]: #117
-#81 := (+ f3 #71)
-#100 := (<= #81 0::Int)
-#158 := (not #100)
-#97 := (>= #81 0::Int)
-#116 := (<= #115 0::Int)
-#80 := (= #81 0::Int)
-#98 := (not #80)
-#136 := (not #97)
-#137 := [hypothesis]: #136
-#138 := (or #98 #97)
-#139 := [th-lemma arith triangle-eq]: #138
-#140 := [unit-resolution #139 #137]: #98
-#134 := (or #65 #80)
-#121 := (= f3 0::Int)
-#10 := (<= f3 0::Int)
-#118 := [hypothesis]: #98
-#112 := (or #10 #80)
-#58 := (not #10)
-#88 := (iff #58 #80)
-#12 := (- f3)
-#11 := (< f3 0::Int)
-#13 := (ite #11 #12 f3)
-#14 := (= #13 #12)
-#15 := (iff #10 #14)
-#16 := (not #15)
-#93 := (iff #16 #88)
-#41 := (ite #11 #38 f3)
-#47 := (= #38 #41)
-#59 := (iff #47 #58)
-#91 := (iff #59 #88)
-#85 := (iff #80 #58)
-#89 := (iff #85 #88)
-#90 := [rewrite]: #89
-#86 := (iff #59 #85)
-#83 := (iff #47 #80)
-#79 := (iff #76 #80)
-#82 := [rewrite]: #79
-#77 := (iff #47 #76)
-#74 := (= #41 #71)
-#68 := (ite #65 #38 f3)
-#72 := (= #68 #71)
-#73 := [rewrite]: #72
-#69 := (= #41 #68)
-#66 := (iff #11 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#75 := [trans #70 #73]: #74
-#78 := [monotonicity #75]: #77
-#84 := [trans #78 #82]: #83
-#87 := [monotonicity #84]: #86
-#92 := [trans #87 #90]: #91
-#62 := (iff #16 #59)
-#52 := (iff #10 #47)
-#55 := (not #52)
-#60 := (iff #55 #59)
-#61 := [rewrite]: #60
-#56 := (iff #16 #55)
-#53 := (iff #15 #52)
-#50 := (iff #14 #47)
-#44 := (= #41 #38)
-#48 := (iff #44 #47)
-#49 := [rewrite]: #48
-#45 := (iff #14 #44)
-#39 := (= #12 #38)
-#40 := [rewrite]: #39
-#42 := (= #13 #41)
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43 #40]: #45
-#51 := [trans #46 #49]: #50
-#54 := [monotonicity #51]: #53
-#57 := [monotonicity #54]: #56
-#63 := [trans #57 #61]: #62
-#94 := [trans #63 #92]: #93
-#36 := [asserted]: #16
-#95 := [mp #36 #94]: #88
-#105 := (not #88)
-#110 := (or #10 #80 #105)
-#111 := [def-axiom]: #110
-#113 := [unit-resolution #111 #95]: #112
-#119 := [unit-resolution #113 #118]: #10
-#120 := [hypothesis]: #64
-#122 := [th-lemma arith eq-propagate 0 0 #120 #119]: #121
-#130 := (= #81 f3)
-#128 := (= #71 f3)
-#102 := (or #65 #101)
-#103 := [def-axiom]: #102
-#123 := [unit-resolution #103 #120]: #101
-#129 := [symm #123]: #128
-#126 := (= #81 #71)
-#124 := (= #71 #81)
-#125 := [th-lemma arith eq-propagate 1 1 #120 #119]: #124
-#127 := [symm #125]: #126
-#131 := [trans #127 #129]: #130
-#132 := [trans #131 #122]: #80
-#133 := [unit-resolution #118 #132]: false
-#135 := [lemma #133]: #134
-#141 := [unit-resolution #135 #140]: #65
-#142 := [unit-resolution #99 #141]: #76
-#144 := (or #143 #116)
-#145 := [th-lemma arith triangle-eq]: #144
-#146 := [unit-resolution #145 #142]: #116
-#147 := [th-lemma arith farkas 1 1 #137 #146]: false
-#148 := [lemma #147]: #97
-#154 := (or #64 #10)
-#155 := [th-lemma arith farkas 1 1]: #154
-#156 := [unit-resolution #155 #149]: #10
-#108 := (or #58 #98)
-#106 := (or #58 #98 #105)
-#107 := [def-axiom]: #106
-#109 := [unit-resolution #107 #95]: #108
-#157 := [unit-resolution #109 #156]: #98
-#159 := (or #80 #158 #136)
-#160 := [th-lemma arith triangle-eq]: #159
-#161 := [unit-resolution #160 #157 #148]: #158
-#162 := [th-lemma arith farkas 1 1 #161 #153]: false
-#163 := [lemma #162]: #64
-#167 := [unit-resolution #103 #163]: #101
-#168 := (not #101)
-#169 := (or #168 #165)
-#170 := [th-lemma arith triangle-eq]: #169
-#171 := [unit-resolution #170 #167]: #165
-#172 := [unit-resolution #135 #163]: #80
-#173 := (or #98 #100)
-#174 := [th-lemma arith triangle-eq]: #173
-#175 := [unit-resolution #174 #172]: #100
-#176 := [unit-resolution #109 #172]: #58
-[th-lemma arith farkas 2 1 1 #176 #175 #171]: false
-unsat
-7937f47574f63ba7fda8d181035eac5a04f1804b 114 0
-#2 := false
-#9 := 0::Int
-decl f3 :: Int
-#8 := f3
-#38 := -1::Int
-#39 := (* -1::Int f3)
-#70 := (>= f3 0::Int)
-#77 := (ite #70 f3 #39)
-#91 := (* -1::Int #77)
-#130 := (+ #39 #91)
-#140 := (<= #130 0::Int)
-#117 := (= #39 #77)
-#71 := (not #70)
-#128 := (+ f3 #91)
-#129 := (<= #128 0::Int)
-#116 := (= f3 #77)
-#131 := [hypothesis]: #70
-#118 := (or #71 #116)
-#119 := [def-axiom]: #118
-#132 := [unit-resolution #119 #131]: #116
-#133 := (not #116)
-#134 := (or #133 #129)
-#135 := [th-lemma arith triangle-eq]: #134
-#136 := [unit-resolution #135 #132]: #129
-#86 := (>= #77 0::Int)
-#85 := (not #86)
-#97 := (ite #86 #77 #91)
-#102 := (= #77 #97)
-#105 := (not #102)
-#11 := (- f3)
-#10 := (< f3 0::Int)
-#12 := (ite #10 #11 f3)
-#14 := (- #12)
-#13 := (< #12 0::Int)
-#15 := (ite #13 #14 #12)
-#16 := (= #15 #12)
-#17 := (not #16)
-#108 := (iff #17 #105)
-#42 := (ite #10 #39 f3)
-#51 := (* -1::Int #42)
-#45 := (< #42 0::Int)
-#56 := (ite #45 #51 #42)
-#62 := (= #42 #56)
-#67 := (not #62)
-#106 := (iff #67 #105)
-#103 := (iff #62 #102)
-#100 := (= #56 #97)
-#94 := (ite #85 #91 #77)
-#98 := (= #94 #97)
-#99 := [rewrite]: #98
-#95 := (= #56 #94)
-#80 := (= #42 #77)
-#74 := (ite #71 #39 f3)
-#78 := (= #74 #77)
-#79 := [rewrite]: #78
-#75 := (= #42 #74)
-#72 := (iff #10 #71)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#81 := [trans #76 #79]: #80
-#92 := (= #51 #91)
-#93 := [monotonicity #81]: #92
-#89 := (iff #45 #85)
-#82 := (< #77 0::Int)
-#87 := (iff #82 #85)
-#88 := [rewrite]: #87
-#83 := (iff #45 #82)
-#84 := [monotonicity #81]: #83
-#90 := [trans #84 #88]: #89
-#96 := [monotonicity #90 #93 #81]: #95
-#101 := [trans #96 #99]: #100
-#104 := [monotonicity #81 #101]: #103
-#107 := [monotonicity #104]: #106
-#68 := (iff #17 #67)
-#65 := (iff #16 #62)
-#59 := (= #56 #42)
-#63 := (iff #59 #62)
-#64 := [rewrite]: #63
-#60 := (iff #16 #59)
-#43 := (= #12 #42)
-#40 := (= #11 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#57 := (= #15 #56)
-#54 := (= #14 #51)
-#48 := (- #42)
-#52 := (= #48 #51)
-#53 := [rewrite]: #52
-#49 := (= #14 #48)
-#50 := [monotonicity #44]: #49
-#55 := [trans #50 #53]: #54
-#46 := (iff #13 #45)
-#47 := [monotonicity #44]: #46
-#58 := [monotonicity #47 #55 #44]: #57
-#61 := [monotonicity #58 #44]: #60
-#66 := [trans #61 #64]: #65
-#69 := [monotonicity #66]: #68
-#109 := [trans #69 #107]: #108
-#37 := [asserted]: #17
-#110 := [mp #37 #109]: #105
-#113 := (or #85 #102)
-#120 := [def-axiom]: #113
-#137 := [unit-resolution #120 #110]: #85
-#138 := [th-lemma arith farkas -1 1 1 #131 #137 #136]: false
-#139 := [lemma #138]: #71
-#114 := (or #70 #117)
-#115 := [def-axiom]: #114
-#142 := [unit-resolution #115 #139]: #117
-#143 := (not #117)
-#144 := (or #143 #140)
-#145 := [th-lemma arith triangle-eq]: #144
-#146 := [unit-resolution #145 #142]: #140
-[th-lemma arith farkas 1 1 1 #139 #137 #146]: false
-unsat
-a868efa9f7901f51a029173b2123a5ae296196e1 57 0
-#2 := false
-#39 := 0::Int
-decl f4 :: Int
-#9 := f4
-decl f3 :: Int
-#8 := f3
-#36 := -1::Int
-#37 := (* -1::Int f4)
-#38 := (+ f3 #37)
-#40 := (<= #38 0::Int)
-#43 := (ite #40 f3 f4)
-#51 := (* -1::Int #43)
-#60 := (+ f4 #51)
-#74 := (>= #60 0::Int)
-#64 := (= f4 #43)
-#65 := (not #40)
-#63 := (= f3 #43)
-#68 := (not #63)
-#52 := (+ f3 #51)
-#50 := (>= #52 0::Int)
-#56 := (not #50)
-#10 := (<= f3 f4)
-#11 := (ite #10 f3 f4)
-#12 := (<= #11 f3)
-#13 := (not #12)
-#57 := (iff #13 #56)
-#54 := (iff #12 #50)
-#46 := (<= #43 f3)
-#49 := (iff #46 #50)
-#53 := [rewrite]: #49
-#47 := (iff #12 #46)
-#44 := (= #11 #43)
-#41 := (iff #10 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#55 := [trans #48 #53]: #54
-#58 := [monotonicity #55]: #57
-#33 := [asserted]: #13
-#59 := [mp #33 #58]: #56
-#67 := [hypothesis]: #63
-#69 := (or #68 #50)
-#70 := [th-lemma arith triangle-eq]: #69
-#71 := [unit-resolution #70 #67 #59]: false
-#72 := [lemma #71]: #68
-#66 := (or #65 #63)
-#61 := [def-axiom]: #66
-#75 := [unit-resolution #61 #72]: #65
-#62 := (or #40 #64)
-#35 := [def-axiom]: #62
-#76 := [unit-resolution #35 #75]: #64
-#77 := (not #64)
-#78 := (or #77 #74)
-#79 := [th-lemma arith triangle-eq]: #78
-#80 := [unit-resolution #79 #76]: #74
-[th-lemma arith farkas 1 1 1 #59 #75 #80]: false
-unsat
-82b647da9fab0aa64c094a4662b5883d9bc7b999 57 0
-#2 := false
-#39 := 0::Int
-decl f4 :: Int
-#9 := f4
-decl f3 :: Int
-#8 := f3
-#36 := -1::Int
-#37 := (* -1::Int f4)
-#38 := (+ f3 #37)
-#40 := (<= #38 0::Int)
-#43 := (ite #40 f3 f4)
-#50 := (* -1::Int #43)
-#51 := (+ f4 #50)
-#49 := (>= #51 0::Int)
-#56 := (not #49)
-#10 := (<= f3 f4)
-#11 := (ite #10 f3 f4)
-#12 := (<= #11 f4)
-#13 := (not #12)
-#57 := (iff #13 #56)
-#54 := (iff #12 #49)
-#46 := (<= #43 f4)
-#52 := (iff #46 #49)
-#53 := [rewrite]: #52
-#47 := (iff #12 #46)
-#44 := (= #11 #43)
-#41 := (iff #10 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#55 := [trans #48 #53]: #54
-#58 := [monotonicity #55]: #57
-#33 := [asserted]: #13
-#59 := [mp #33 #58]: #56
-#64 := (= f4 #43)
-#65 := (not #40)
-#69 := [hypothesis]: #40
-#60 := (+ f3 #50)
-#68 := (>= #60 0::Int)
-#63 := (= f3 #43)
-#66 := (or #65 #63)
-#61 := [def-axiom]: #66
-#70 := [unit-resolution #61 #69]: #63
-#71 := (not #63)
-#72 := (or #71 #68)
-#73 := [th-lemma arith triangle-eq]: #72
-#74 := [unit-resolution #73 #70]: #68
-#75 := [th-lemma arith farkas -1 1 1 #74 #59 #69]: false
-#76 := [lemma #75]: #65
-#62 := (or #40 #64)
-#35 := [def-axiom]: #62
-#77 := [unit-resolution #35 #76]: #64
-#78 := (not #64)
-#79 := (or #78 #49)
-#80 := [th-lemma arith triangle-eq]: #79
-[unit-resolution #80 #77 #59]: false
-unsat
-9b46d108c41d783ae69f553dfb50c9b551e3e4dc 103 0
-#2 := false
-#48 := 0::Int
-decl f5 :: Int
-#11 := f5
-decl f4 :: Int
-#9 := f4
-#46 := -1::Int
-#56 := (* -1::Int f5)
-#66 := (+ f4 #56)
-#67 := (<= #66 0::Int)
-#70 := (ite #67 f4 f5)
-#78 := (* -1::Int #70)
-decl f3 :: Int
-#8 := f3
-#79 := (+ f3 #78)
-#77 := (>= #79 0::Int)
-#76 := (not #77)
-#57 := (+ f3 #56)
-#55 := (>= #57 0::Int)
-#54 := (not #55)
-#50 := (* -1::Int f4)
-#51 := (+ f3 #50)
-#49 := (>= #51 0::Int)
-#47 := (not #49)
-#60 := (and #47 #54)
-#63 := (not #60)
-#84 := (or #63 #76)
-#87 := (not #84)
-#14 := (<= f4 f5)
-#15 := (ite #14 f4 f5)
-#16 := (< f3 #15)
-#12 := (< f3 f5)
-#10 := (< f3 f4)
-#13 := (and #10 #12)
-#17 := (implies #13 #16)
-#18 := (not #17)
-#90 := (iff #18 #87)
-#39 := (not #13)
-#40 := (or #39 #16)
-#43 := (not #40)
-#88 := (iff #43 #87)
-#85 := (iff #40 #84)
-#82 := (iff #16 #76)
-#73 := (< f3 #70)
-#80 := (iff #73 #76)
-#81 := [rewrite]: #80
-#74 := (iff #16 #73)
-#71 := (= #15 #70)
-#68 := (iff #14 #67)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#83 := [trans #75 #81]: #82
-#64 := (iff #39 #63)
-#61 := (iff #13 #60)
-#58 := (iff #12 #54)
-#59 := [rewrite]: #58
-#52 := (iff #10 #47)
-#53 := [rewrite]: #52
-#62 := [monotonicity #53 #59]: #61
-#65 := [monotonicity #62]: #64
-#86 := [monotonicity #65 #83]: #85
-#89 := [monotonicity #86]: #88
-#44 := (iff #18 #43)
-#41 := (iff #17 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#91 := [trans #45 #89]: #90
-#38 := [asserted]: #18
-#92 := [mp #38 #91]: #87
-#96 := [not-or-elim #92]: #77
-#93 := [not-or-elim #92]: #60
-#95 := [and-elim #93]: #54
-#101 := (+ f5 #78)
-#118 := (<= #101 0::Int)
-#107 := (= f5 #70)
-#108 := (not #67)
-#106 := (= f4 #70)
-#113 := (not #106)
-#103 := (+ f4 #78)
-#100 := (<= #103 0::Int)
-#110 := (not #100)
-#94 := [and-elim #93]: #47
-#98 := [hypothesis]: #100
-#99 := [th-lemma arith farkas -1 -1 1 #98 #94 #96]: false
-#111 := [lemma #99]: #110
-#112 := [hypothesis]: #106
-#114 := (or #113 #100)
-#115 := [th-lemma arith triangle-eq]: #114
-#116 := [unit-resolution #115 #112 #111]: false
-#117 := [lemma #116]: #113
-#109 := (or #108 #106)
-#104 := [def-axiom]: #109
-#120 := [unit-resolution #104 #117]: #108
-#105 := (or #67 #107)
-#102 := [def-axiom]: #105
-#121 := [unit-resolution #102 #120]: #107
-#122 := (not #107)
-#123 := (or #122 #118)
-#124 := [th-lemma arith triangle-eq]: #123
-#125 := [unit-resolution #124 #121]: #118
-[th-lemma arith farkas -1 -1 1 #125 #95 #96]: false
-unsat
-384d72c036cb4a504daa40b92a17937fc9e8eeef 94 0
+#53 := [trans #47 #51]: #52
+#75 := [trans #53 #73]: #74
+#35 := [asserted]: #14
+#76 := [mp #35 #75]: #71
+#83 := (not #71)
+#78 := (or #55 #68 #83)
+#79 := [def-axiom]: #78
+#87 := [unit-resolution #79 #76]: #86
+#89 := [unit-resolution #87 #88]: #55
+#90 := [th-lemma arith farkas 1 1 #88 #89]: false
+#91 := [lemma #90]: #68
+#92 := (or #82 #55)
+#93 := [th-lemma arith farkas 1 1]: #92
+#94 := [unit-resolution #93 #91]: #55
+#80 := (or #56 #82)
+#84 := (or #56 #82 #83)
+#85 := [def-axiom]: #84
+#81 := [unit-resolution #85 #76]: #80
+[unit-resolution #81 #94 #91]: false
+unsat
+945ffcf16061a167fde6a7075ed9332c98f7d17c 15 0
 #2 := false
 decl f3 :: Int
-#8 := f3
-decl f4 :: Int
-#9 := f4
-#41 := 0::Int
-#38 := -1::Int
-#39 := (* -1::Int f4)
-#40 := (+ f3 #39)
-#49 := (>= #40 0::Int)
-#51 := (ite #49 f4 f3)
-#42 := (<= #40 0::Int)
-#45 := (ite #42 f3 f4)
-#54 := (= #45 #51)
-#61 := (= f4 #51)
-#66 := (not #42)
-#64 := (= f3 #45)
-#106 := (not #64)
-#68 := (= f3 #51)
-#75 := (not #68)
-#76 := [hypothesis]: #75
-#72 := (or #49 #68)
-#73 := [def-axiom]: #72
-#77 := [unit-resolution #73 #76]: #49
-#69 := (not #49)
-#70 := (or #69 #61)
-#71 := [def-axiom]: #70
-#78 := [unit-resolution #71 #77]: #61
-#74 := (= f3 f4)
-#65 := (= f4 #45)
-#88 := (not #65)
-#57 := (not #54)
-#89 := (iff #57 #88)
-#86 := (iff #54 #65)
-#84 := (iff #65 #54)
-#79 := (= #51 #45)
-#82 := (iff #79 #54)
-#83 := [commutativity]: #82
-#80 := (iff #65 #79)
-#81 := [monotonicity #78]: #80
-#85 := [trans #81 #83]: #84
-#87 := [symm #85]: #86
-#90 := [monotonicity #87]: #89
-#12 := (<= f4 f3)
-#13 := (ite #12 f4 f3)
-#10 := (<= f3 f4)
-#11 := (ite #10 f3 f4)
-#14 := (= #11 #13)
-#15 := (not #14)
-#58 := (iff #15 #57)
-#55 := (iff #14 #54)
-#52 := (= #13 #51)
-#48 := (iff #12 #49)
-#50 := [rewrite]: #48
-#53 := [monotonicity #50]: #52
-#46 := (= #11 #45)
-#43 := (iff #10 #42)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#56 := [monotonicity #47 #53]: #55
-#59 := [monotonicity #56]: #58
-#35 := [asserted]: #15
-#60 := [mp #35 #59]: #57
-#91 := [mp #60 #90]: #88
-#63 := (or #42 #65)
-#37 := [def-axiom]: #63
-#92 := [unit-resolution #37 #91]: #42
-#95 := (or #74 #66)
-#93 := (or #74 #66 #69)
-#94 := [th-lemma arith triangle-eq]: #93
-#96 := [unit-resolution #94 #77]: #95
-#97 := [unit-resolution #96 #92]: #74
-#98 := [trans #97 #78]: #68
-#99 := [unit-resolution #76 #98]: false
-#100 := [lemma #99]: #68
-#102 := (= #45 f3)
-#101 := [hypothesis]: #64
-#103 := [symm #101]: #102
-#104 := [trans #103 #100]: #54
-#105 := [unit-resolution #60 #104]: false
-#107 := [lemma #105]: #106
-#67 := (or #66 #64)
-#62 := [def-axiom]: #67
-#108 := [unit-resolution #62 #107]: #66
-#110 := (or #49 #42)
-#111 := [th-lemma arith farkas 1 1]: #110
-#112 := [unit-resolution #111 #108]: #49
-#113 := [unit-resolution #71 #112]: #61
-#116 := (= #45 f4)
-#109 := [unit-resolution #37 #108]: #65
-#117 := [symm #109]: #116
-#118 := [trans #117 #113]: #54
-[unit-resolution #60 #118]: false
-unsat
-5df6354637212a118c8e9d3b4d92806fed1f414a 68 0
-#2 := false
-#8 := 0::Int
-decl f3 :: Int
-#9 := f3
-#11 := (<= f3 0::Int)
-#12 := (ite #11 f3 0::Int)
-#13 := (= #12 0::Int)
-#79 := (= f3 0::Int)
-#53 := (>= f3 0::Int)
-#54 := (not #53)
-#62 := (or #13 #54)
-#67 := (not #62)
-#10 := (<= 0::Int f3)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#70 := (iff #15 #67)
-#36 := (= 0::Int #12)
-#42 := (not #10)
-#43 := (or #42 #36)
-#48 := (not #43)
-#68 := (iff #48 #67)
-#65 := (iff #43 #62)
-#59 := (or #54 #13)
-#63 := (iff #59 #62)
-#64 := [rewrite]: #63
-#60 := (iff #43 #59)
-#57 := (iff #36 #13)
-#58 := [rewrite]: #57
-#55 := (iff #42 #54)
-#51 := (iff #10 #53)
-#52 := [rewrite]: #51
-#56 := [monotonicity #52]: #55
-#61 := [monotonicity #56 #58]: #60
-#66 := [trans #61 #64]: #65
-#69 := [monotonicity #66]: #68
-#49 := (iff #15 #48)
-#46 := (iff #14 #43)
-#39 := (implies #10 #36)
-#44 := (iff #39 #43)
-#45 := [rewrite]: #44
-#40 := (iff #14 #39)
-#37 := (iff #13 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#47 := [trans #41 #45]: #46
-#50 := [monotonicity #47]: #49
-#71 := [trans #50 #69]: #70
-#35 := [asserted]: #15
-#72 := [mp #35 #71]: #67
-#75 := [not-or-elim #72]: #53
-#73 := (not #13)
-#74 := [not-or-elim #72]: #73
-#81 := (or #11 #13)
-#82 := [def-axiom]: #81
-#80 := [unit-resolution #82 #74]: #11
-#84 := (not #11)
-#77 := (or #79 #84 #54)
-#78 := [th-lemma arith triangle-eq]: #77
-#87 := [unit-resolution #78 #80 #75]: #79
-#89 := (= #12 f3)
-#83 := (= f3 #12)
-#85 := (or #84 #83)
-#86 := [def-axiom]: #85
-#88 := [unit-resolution #86 #80]: #83
-#90 := [symm #88]: #89
-#91 := [trans #90 #87]: #13
-[unit-resolution #74 #91]: false
-unsat
-830a0546cfefe0a710f523435755e68520136af4 124 0
-#2 := false
-#13 := 0::Int
-decl f4 :: Int
-#9 := f4
-decl f3 :: Int
-#8 := f3
-#39 := -1::Int
-#41 := (* -1::Int f4)
-#54 := (+ f3 #41)
-#55 := (<= #54 0::Int)
-#58 := (ite #55 f3 f4)
-#106 := (* -1::Int #58)
-#107 := (+ f3 #106)
-#109 := (>= #107 0::Int)
-#94 := (= f3 #58)
-#108 := (+ f4 #106)
-#126 := (>= #108 0::Int)
-#95 := (= f4 #58)
-#96 := (not #55)
-#137 := [hypothesis]: #96
-#93 := (or #55 #95)
-#90 := [def-axiom]: #93
-#138 := [unit-resolution #90 #137]: #95
-#129 := (not #95)
-#130 := (or #129 #126)
-#131 := [th-lemma arith triangle-eq]: #130
-#139 := [unit-resolution #131 #138]: #126
-#40 := (* -1::Int f3)
-#42 := (+ #40 #41)
-#12 := (+ f3 f4)
-#61 := (>= #12 0::Int)
-#68 := (ite #61 #12 #42)
-#76 := (* -1::Int #68)
-#105 := (+ #42 #76)
-#125 := (<= #105 0::Int)
-#98 := (= #42 #68)
-#62 := (not #61)
-#110 := [hypothesis]: #61
-#77 := (+ #58 #76)
-#78 := (<= #77 0::Int)
-#83 := (not #78)
-#15 := (- #12)
-#14 := (< #12 0::Int)
-#16 := (ite #14 #15 #12)
-#10 := (<= f3 f4)
-#11 := (ite #10 f3 f4)
-#17 := (<= #11 #16)
-#18 := (not #17)
-#86 := (iff #18 #83)
-#45 := (ite #14 #42 #12)
-#48 := (<= #11 #45)
-#51 := (not #48)
-#84 := (iff #51 #83)
-#81 := (iff #48 #78)
-#73 := (<= #58 #68)
-#79 := (iff #73 #78)
-#80 := [rewrite]: #79
-#74 := (iff #48 #73)
-#71 := (= #45 #68)
-#65 := (ite #62 #42 #12)
-#69 := (= #65 #68)
-#70 := [rewrite]: #69
-#66 := (= #45 #65)
-#63 := (iff #14 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#72 := [trans #67 #70]: #71
-#59 := (= #11 #58)
-#56 := (iff #10 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#75 := [monotonicity #60 #72]: #74
-#82 := [trans #75 #80]: #81
-#85 := [monotonicity #82]: #84
-#52 := (iff #18 #51)
-#49 := (iff #17 #48)
-#46 := (= #16 #45)
-#43 := (= #15 #42)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#50 := [monotonicity #47]: #49
-#53 := [monotonicity #50]: #52
-#87 := [trans #53 #85]: #86
-#38 := [asserted]: #18
-#88 := [mp #38 #87]: #83
-#123 := (or #96 #62)
-#111 := [hypothesis]: #55
-#97 := (or #96 #94)
-#92 := [def-axiom]: #97
-#112 := [unit-resolution #92 #111]: #94
-#113 := (not #94)
-#114 := (or #113 #109)
-#115 := [th-lemma arith triangle-eq]: #114
-#116 := [unit-resolution #115 #112]: #109
-#103 := (+ #12 #76)
-#104 := (<= #103 0::Int)
-#91 := (= #12 #68)
-#99 := (or #62 #91)
-#100 := [def-axiom]: #99
-#117 := [unit-resolution #100 #110]: #91
-#118 := (not #91)
-#119 := (or #118 #104)
-#120 := [th-lemma arith triangle-eq]: #119
-#121 := [unit-resolution #120 #117]: #104
-#122 := [th-lemma arith farkas 2 2 2 1 1 #121 #116 #88 #111 #110]: false
-#124 := [lemma #122]: #123
-#127 := [unit-resolution #124 #110]: #96
-#128 := [unit-resolution #90 #127]: #95
-#132 := [unit-resolution #131 #128]: #126
-#133 := [th-lemma arith farkas 2 2 1 2 1 #121 #132 #127 #88 #110]: false
-#134 := [lemma #133]: #62
-#101 := (or #61 #98)
-#102 := [def-axiom]: #101
-#140 := [unit-resolution #102 #134]: #98
-#141 := (not #98)
-#142 := (or #141 #125)
-#143 := [th-lemma arith triangle-eq]: #142
-#144 := [unit-resolution #143 #140]: #125
-#145 := [th-lemma arith farkas 3/2 1/2 1 1 1 #134 #137 #88 #144 #139]: false
-#146 := [lemma #145]: #55
-#147 := [unit-resolution #92 #146]: #94
-#148 := [unit-resolution #115 #147]: #109
-[th-lemma arith farkas 1/2 3/2 1 1 1 #146 #134 #88 #144 #148]: false
-unsat
-52f99700756069f984cbcf7e031ad81024526b39 57 0
-#2 := false
-#39 := 0::Int
-decl f3 :: Int
-#8 := f3
-decl f4 :: Int
-#9 := f4
-#36 := -1::Int
-#37 := (* -1::Int f4)
-#38 := (+ f3 #37)
-#40 := (<= #38 0::Int)
-#43 := (ite #40 f4 f3)
-#49 := (* -1::Int #43)
-#50 := (+ f3 #49)
-#51 := (<= #50 0::Int)
-#56 := (not #51)
-#10 := (<= f3 f4)
-#11 := (ite #10 f4 f3)
-#12 := (<= f3 #11)
-#13 := (not #12)
-#57 := (iff #13 #56)
-#54 := (iff #12 #51)
-#46 := (<= f3 #43)
-#52 := (iff #46 #51)
-#53 := [rewrite]: #52
-#47 := (iff #12 #46)
-#44 := (= #11 #43)
-#41 := (iff #10 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#55 := [trans #48 #53]: #54
-#58 := [monotonicity #55]: #57
-#33 := [asserted]: #13
-#59 := [mp #33 #58]: #56
-#64 := (= f3 #43)
-#65 := (not #40)
-#69 := [hypothesis]: #40
-#60 := (+ f4 #49)
-#67 := (<= #60 0::Int)
-#63 := (= f4 #43)
-#66 := (or #65 #63)
-#61 := [def-axiom]: #66
-#70 := [unit-resolution #61 #69]: #63
-#71 := (not #63)
-#72 := (or #71 #67)
-#73 := [th-lemma arith triangle-eq]: #72
-#74 := [unit-resolution #73 #70]: #67
-#75 := [th-lemma arith farkas 1 -1 1 #74 #59 #69]: false
-#76 := [lemma #75]: #65
-#62 := (or #40 #64)
-#35 := [def-axiom]: #62
-#77 := [unit-resolution #35 #76]: #64
-#78 := (not #64)
-#79 := (or #78 #51)
-#80 := [th-lemma arith triangle-eq]: #79
-[unit-resolution #80 #77 #59]: false
-unsat
-f0391470173f42c2f425051fb44610cd0d3f11da 57 0
-#2 := false
-#38 := 0::Int
-decl f4 :: Int
-#9 := f4
-decl f3 :: Int
-#8 := f3
-#36 := -1::Int
-#40 := (* -1::Int f4)
-#41 := (+ f3 #40)
-#39 := (>= #41 0::Int)
-#43 := (ite #39 f3 f4)
-#49 := (* -1::Int #43)
-#60 := (+ f4 #49)
-#73 := (<= #60 0::Int)
-#64 := (= f4 #43)
-#65 := (not #39)
-#63 := (= f3 #43)
-#68 := (not #63)
-#50 := (+ f3 #49)
-#51 := (<= #50 0::Int)
-#56 := (not #51)
-#10 := (<= f4 f3)
-#11 := (ite #10 f3 f4)
-#12 := (<= f3 #11)
-#13 := (not #12)
-#57 := (iff #13 #56)
-#54 := (iff #12 #51)
-#46 := (<= f3 #43)
-#52 := (iff #46 #51)
-#53 := [rewrite]: #52
-#47 := (iff #12 #46)
-#44 := (= #11 #43)
-#37 := (iff #10 #39)
-#42 := [rewrite]: #37
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#55 := [trans #48 #53]: #54
-#58 := [monotonicity #55]: #57
-#33 := [asserted]: #13
-#59 := [mp #33 #58]: #56
-#67 := [hypothesis]: #63
-#69 := (or #68 #51)
-#70 := [th-lemma arith triangle-eq]: #69
-#71 := [unit-resolution #70 #67 #59]: false
-#72 := [lemma #71]: #68
-#66 := (or #65 #63)
-#61 := [def-axiom]: #66
-#75 := [unit-resolution #61 #72]: #65
-#62 := (or #39 #64)
-#35 := [def-axiom]: #62
-#76 := [unit-resolution #35 #75]: #64
-#77 := (not #64)
-#78 := (or #77 #73)
-#79 := [th-lemma arith triangle-eq]: #78
-#80 := [unit-resolution #79 #76]: #73
-[th-lemma arith farkas 1 1 1 #59 #75 #80]: false
-unsat
-3fca82fbf91597dcaf0c89ff56d31758ef9aa446 103 0
-#2 := false
-#48 := 0::Int
-decl f3 :: Int
-#8 := f3
-decl f5 :: Int
-#11 := f5
-#46 := -1::Int
-#54 := (* -1::Int f5)
-#66 := (+ f3 #54)
-#67 := (<= #66 0::Int)
-#70 := (ite #67 f5 f3)
-#76 := (* -1::Int #70)
-decl f4 :: Int
-#9 := f4
-#77 := (+ f4 #76)
-#78 := (<= #77 0::Int)
-#79 := (not #78)
-#55 := (+ f4 #54)
-#56 := (<= #55 0::Int)
-#57 := (not #56)
-#50 := (* -1::Int f4)
-#51 := (+ f3 #50)
-#49 := (>= #51 0::Int)
-#47 := (not #49)
-#60 := (and #47 #57)
-#63 := (not #60)
-#84 := (or #63 #79)
-#87 := (not #84)
-#14 := (<= f3 f5)
-#15 := (ite #14 f5 f3)
-#16 := (< #15 f4)
-#12 := (< f5 f4)
-#10 := (< f3 f4)
-#13 := (and #10 #12)
-#17 := (implies #13 #16)
-#18 := (not #17)
-#90 := (iff #18 #87)
-#39 := (not #13)
-#40 := (or #39 #16)
-#43 := (not #40)
-#88 := (iff #43 #87)
-#85 := (iff #40 #84)
-#82 := (iff #16 #79)
-#73 := (< #70 f4)
-#80 := (iff #73 #79)
-#81 := [rewrite]: #80
-#74 := (iff #16 #73)
-#71 := (= #15 #70)
-#68 := (iff #14 #67)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#83 := [trans #75 #81]: #82
-#64 := (iff #39 #63)
-#61 := (iff #13 #60)
-#58 := (iff #12 #57)
-#59 := [rewrite]: #58
-#52 := (iff #10 #47)
-#53 := [rewrite]: #52
-#62 := [monotonicity #53 #59]: #61
-#65 := [monotonicity #62]: #64
-#86 := [monotonicity #65 #83]: #85
-#89 := [monotonicity #86]: #88
-#44 := (iff #18 #43)
-#41 := (iff #17 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#91 := [trans #45 #89]: #90
-#38 := [asserted]: #18
-#92 := [mp #38 #91]: #87
-#96 := [not-or-elim #92]: #78
-#93 := [not-or-elim #92]: #60
-#94 := [and-elim #93]: #47
-#100 := (+ f3 #76)
-#119 := (>= #100 0::Int)
-#107 := (= f3 #70)
-#108 := (not #67)
-#106 := (= f5 #70)
-#113 := (not #106)
-#103 := (+ f5 #76)
-#101 := (>= #103 0::Int)
-#110 := (not #101)
-#95 := [and-elim #93]: #57
-#98 := [hypothesis]: #101
-#99 := [th-lemma arith farkas -1 -1 1 #98 #95 #96]: false
-#111 := [lemma #99]: #110
-#112 := [hypothesis]: #106
-#114 := (or #113 #101)
-#115 := [th-lemma arith triangle-eq]: #114
-#116 := [unit-resolution #115 #112 #111]: false
-#117 := [lemma #116]: #113
-#109 := (or #108 #106)
-#104 := [def-axiom]: #109
-#120 := [unit-resolution #104 #117]: #108
-#105 := (or #67 #107)
-#102 := [def-axiom]: #105
-#121 := [unit-resolution #102 #120]: #107
-#122 := (not #107)
-#123 := (or #122 #119)
-#124 := [th-lemma arith triangle-eq]: #123
-#125 := [unit-resolution #124 #121]: #119
-[th-lemma arith farkas -1 1 1 #125 #94 #96]: false
-unsat
-4cc8abc1cb14abf886035d59247a2facd4c8905d 96 0
-#2 := false
-decl f4 :: Int
-#9 := f4
-decl f3 :: Int
-#8 := f3
-#41 := 0::Int
-#38 := -1::Int
-#39 := (* -1::Int f4)
-#40 := (+ f3 #39)
-#49 := (>= #40 0::Int)
-#51 := (ite #49 f3 f4)
-#42 := (<= #40 0::Int)
-#45 := (ite #42 f4 f3)
-#54 := (= #45 #51)
-#61 := (= f3 #51)
-#66 := (not #42)
-#64 := (= f4 #45)
-#108 := (not #64)
-#68 := (= f4 #51)
-#75 := (not #68)
-#76 := [hypothesis]: #75
-#72 := (or #49 #68)
-#73 := [def-axiom]: #72
-#77 := [unit-resolution #73 #76]: #49
-#69 := (not #49)
-#70 := (or #69 #61)
-#71 := [def-axiom]: #70
-#78 := [unit-resolution #71 #77]: #61
-#98 := (= f4 f3)
-#74 := (= f3 f4)
-#65 := (= f3 #45)
-#88 := (not #65)
-#57 := (not #54)
-#89 := (iff #57 #88)
-#86 := (iff #54 #65)
-#84 := (iff #65 #54)
-#79 := (= #51 #45)
-#82 := (iff #79 #54)
-#83 := [commutativity]: #82
-#80 := (iff #65 #79)
-#81 := [monotonicity #78]: #80
-#85 := [trans #81 #83]: #84
-#87 := [symm #85]: #86
-#90 := [monotonicity #87]: #89
-#12 := (<= f4 f3)
-#13 := (ite #12 f3 f4)
-#10 := (<= f3 f4)
-#11 := (ite #10 f4 f3)
-#14 := (= #11 #13)
-#15 := (not #14)
-#58 := (iff #15 #57)
-#55 := (iff #14 #54)
-#52 := (= #13 #51)
-#48 := (iff #12 #49)
-#50 := [rewrite]: #48
-#53 := [monotonicity #50]: #52
-#46 := (= #11 #45)
-#43 := (iff #10 #42)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#56 := [monotonicity #47 #53]: #55
-#59 := [monotonicity #56]: #58
-#35 := [asserted]: #15
-#60 := [mp #35 #59]: #57
-#91 := [mp #60 #90]: #88
-#63 := (or #42 #65)
-#37 := [def-axiom]: #63
-#92 := [unit-resolution #37 #91]: #42
-#95 := (or #74 #66)
-#93 := (or #74 #66 #69)
-#94 := [th-lemma arith triangle-eq]: #93
-#96 := [unit-resolution #94 #77]: #95
-#97 := [unit-resolution #96 #92]: #74
-#99 := [symm #97]: #98
-#100 := [trans #99 #78]: #68
-#101 := [unit-resolution #76 #100]: false
-#102 := [lemma #101]: #68
-#104 := (= #45 f4)
-#103 := [hypothesis]: #64
-#105 := [symm #103]: #104
-#106 := [trans #105 #102]: #54
-#107 := [unit-resolution #60 #106]: false
-#109 := [lemma #107]: #108
-#67 := (or #66 #64)
-#62 := [def-axiom]: #67
-#110 := [unit-resolution #62 #109]: #66
-#112 := (or #49 #42)
-#113 := [th-lemma arith farkas 1 1]: #112
-#114 := [unit-resolution #113 #110]: #49
-#115 := [unit-resolution #71 #114]: #61
-#118 := (= #45 f3)
-#111 := [unit-resolution #37 #110]: #65
-#119 := [symm #111]: #118
-#120 := [trans #119 #115]: #54
-[unit-resolution #60 #120]: false
-unsat
-0dd105910a740ba84e327a554c15807cfbb51e90 66 0
-#2 := false
-decl f3 :: Int
-#9 := f3
-#8 := 0::Int
-#11 := (<= f3 0::Int)
-#12 := (ite #11 0::Int f3)
-#36 := (= f3 #12)
-#87 := (= 0::Int #12)
-#81 := (= #12 0::Int)
-#71 := (not #36)
-#53 := (>= f3 0::Int)
-#54 := (not #53)
-#60 := (or #36 #54)
-#65 := (not #60)
-#13 := (= #12 f3)
-#10 := (<= 0::Int f3)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#68 := (iff #15 #65)
-#42 := (not #10)
-#43 := (or #42 #36)
-#48 := (not #43)
-#66 := (iff #48 #65)
-#63 := (iff #43 #60)
-#57 := (or #54 #36)
-#61 := (iff #57 #60)
-#62 := [rewrite]: #61
-#58 := (iff #43 #57)
-#55 := (iff #42 #54)
-#51 := (iff #10 #53)
-#52 := [rewrite]: #51
-#56 := [monotonicity #52]: #55
-#59 := [monotonicity #56]: #58
-#64 := [trans #59 #62]: #63
-#67 := [monotonicity #64]: #66
-#49 := (iff #15 #48)
-#46 := (iff #14 #43)
-#39 := (implies #10 #36)
-#44 := (iff #39 #43)
-#45 := [rewrite]: #44
-#40 := (iff #14 #39)
-#37 := (iff #13 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#47 := [trans #41 #45]: #46
-#50 := [monotonicity #47]: #49
-#69 := [trans #50 #67]: #68
-#35 := [asserted]: #15
-#70 := [mp #35 #69]: #65
-#72 := [not-or-elim #70]: #71
-#79 := (or #11 #36)
-#80 := [def-axiom]: #79
-#78 := [unit-resolution #80 #72]: #11
-#82 := (not #11)
-#83 := (or #82 #81)
-#84 := [def-axiom]: #83
-#75 := [unit-resolution #84 #78]: #81
-#88 := [symm #75]: #87
-#77 := (= f3 0::Int)
-#73 := [not-or-elim #70]: #53
-#76 := (or #77 #82 #54)
-#85 := [th-lemma arith triangle-eq]: #76
-#86 := [unit-resolution #85 #78 #73]: #77
-#89 := [trans #86 #88]: #36
-[unit-resolution #72 #89]: false
-unsat
-6d096cc8e5aead61fa59d3a9e14375705bde559e 214 0
-#2 := false
-#9 := 0::Int
-decl f4 :: Int
-#14 := f4
-#43 := -1::Int
-#58 := (* -1::Int f4)
-#94 := (>= f4 0::Int)
-#101 := (ite #94 f4 #58)
-#106 := (* -1::Int #101)
-#161 := (+ #58 #106)
-#183 := (<= #161 0::Int)
-#137 := (= #58 #101)
-#95 := (not #94)
-decl f3 :: Int
-#8 := f3
-#112 := (+ f3 #58)
-#113 := (<= #112 0::Int)
-#116 := (ite #113 f4 f3)
-#155 := (* -1::Int #116)
-#156 := (+ f4 #155)
-#157 := (<= #156 0::Int)
-#158 := (+ f3 #155)
-#193 := (<= #158 0::Int)
-#149 := (= f3 #116)
-#150 := (not #113)
-#148 := (= f4 #116)
-#195 := [hypothesis]: #113
-#151 := (or #150 #148)
-#152 := [def-axiom]: #151
-#196 := [unit-resolution #152 #195]: #148
-#197 := (not #148)
-#198 := (or #197 #157)
-#199 := [th-lemma arith triangle-eq]: #198
-#200 := [unit-resolution #199 #196]: #157
-#179 := (not #157)
-#191 := (or #95 #179)
-#159 := (+ f4 #106)
-#160 := (<= #159 0::Int)
-#136 := (= f4 #101)
-#165 := [hypothesis]: #94
-#144 := (or #95 #136)
-#145 := [def-axiom]: #144
-#166 := [unit-resolution #145 #165]: #136
-#167 := (not #136)
-#168 := (or #167 #160)
-#169 := [th-lemma arith triangle-eq]: #168
-#170 := [unit-resolution #169 #166]: #160
-#44 := (* -1::Int f3)
-#79 := (>= f3 0::Int)
-#86 := (ite #79 f3 #44)
-#91 := (* -1::Int #86)
-#164 := (+ #44 #91)
-#182 := (<= #164 0::Int)
-#141 := (= #44 #86)
-#80 := (not #79)
-#177 := [hypothesis]: #157
-#180 := (or #80 #95 #179)
-#125 := (+ #101 #116)
-#126 := (+ #86 #125)
-#123 := (>= #126 0::Int)
-#129 := (not #123)
-#19 := (<= f3 f4)
-#20 := (ite #19 f4 f3)
-#16 := (- f4)
-#15 := (< f4 0::Int)
-#17 := (ite #15 #16 f4)
-#11 := (- f3)
-#10 := (< f3 0::Int)
-#12 := (ite #10 #11 f3)
-#13 := (- #12)
-#18 := (- #13 #17)
-#21 := (<= #18 #20)
-#22 := (not #21)
-#132 := (iff #22 #129)
-#61 := (ite #15 #58 f4)
-#67 := (* -1::Int #61)
-#47 := (ite #10 #44 f3)
-#53 := (* -1::Int #47)
-#68 := (+ #53 #67)
-#73 := (<= #68 #20)
-#76 := (not #73)
-#130 := (iff #76 #129)
-#127 := (iff #73 #123)
-#109 := (+ #91 #106)
-#119 := (<= #109 #116)
-#122 := (iff #119 #123)
-#124 := [rewrite]: #122
-#120 := (iff #73 #119)
-#117 := (= #20 #116)
-#114 := (iff #19 #113)
-#115 := [rewrite]: #114
-#118 := [monotonicity #115]: #117
-#110 := (= #68 #109)
-#107 := (= #67 #106)
-#104 := (= #61 #101)
-#98 := (ite #95 #58 f4)
-#102 := (= #98 #101)
-#103 := [rewrite]: #102
-#99 := (= #61 #98)
-#96 := (iff #15 #95)
-#97 := [rewrite]: #96
-#100 := [monotonicity #97]: #99
-#105 := [trans #100 #103]: #104
-#108 := [monotonicity #105]: #107
-#92 := (= #53 #91)
-#89 := (= #47 #86)
-#83 := (ite #80 #44 f3)
-#87 := (= #83 #86)
-#88 := [rewrite]: #87
-#84 := (= #47 #83)
-#81 := (iff #10 #80)
-#82 := [rewrite]: #81
-#85 := [monotonicity #82]: #84
-#90 := [trans #85 #88]: #89
-#93 := [monotonicity #90]: #92
-#111 := [monotonicity #93 #108]: #110
-#121 := [monotonicity #111 #118]: #120
-#128 := [trans #121 #124]: #127
-#131 := [monotonicity #128]: #130
-#77 := (iff #22 #76)
-#74 := (iff #21 #73)
-#71 := (= #18 #68)
-#64 := (- #53 #61)
-#69 := (= #64 #68)
-#70 := [rewrite]: #69
-#65 := (= #18 #64)
-#62 := (= #17 #61)
-#59 := (= #16 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#56 := (= #13 #53)
-#50 := (- #47)
-#54 := (= #50 #53)
-#55 := [rewrite]: #54
-#51 := (= #13 #50)
-#48 := (= #12 #47)
-#45 := (= #11 #44)
-#46 := [rewrite]: #45
-#49 := [monotonicity #46]: #48
-#52 := [monotonicity #49]: #51
-#57 := [trans #52 #55]: #56
-#66 := [monotonicity #57 #63]: #65
-#72 := [trans #66 #70]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#133 := [trans #78 #131]: #132
-#42 := [asserted]: #22
-#134 := [mp #42 #133]: #129
-#162 := (+ f3 #91)
-#163 := (<= #162 0::Int)
-#140 := (= f3 #86)
-#171 := [hypothesis]: #79
-#142 := (or #80 #140)
-#143 := [def-axiom]: #142
-#172 := [unit-resolution #143 #171]: #140
-#173 := (not #140)
-#174 := (or #173 #163)
-#175 := [th-lemma arith triangle-eq]: #174
-#176 := [unit-resolution #175 #172]: #163
-#178 := [th-lemma arith farkas -2 1 -1 1 1 1 #165 #177 #171 #176 #134 #170]: false
-#181 := [lemma #178]: #180
-#184 := [unit-resolution #181 #165 #177]: #80
-#138 := (or #79 #141)
-#139 := [def-axiom]: #138
-#185 := [unit-resolution #139 #184]: #141
-#186 := (not #141)
-#187 := (or #186 #182)
-#188 := [th-lemma arith triangle-eq]: #187
-#189 := [unit-resolution #188 #185]: #182
-#190 := [th-lemma arith farkas 2 1 1 1 1 1 #165 #177 #134 #184 #189 #170]: false
-#192 := [lemma #190]: #191
-#201 := [unit-resolution #192 #200]: #95
-#146 := (or #94 #137)
-#147 := [def-axiom]: #146
-#202 := [unit-resolution #147 #201]: #137
-#203 := (not #137)
-#204 := (or #203 #183)
-#205 := [th-lemma arith triangle-eq]: #204
-#206 := [unit-resolution #205 #202]: #183
-#207 := (or #80 #94 #150)
-#208 := [th-lemma arith assign-bounds 1 1]: #207
-#209 := [unit-resolution #208 #201 #195]: #80
-#210 := [unit-resolution #139 #209]: #141
-#211 := [unit-resolution #188 #210]: #182
-#212 := [th-lemma arith farkas 1 1 1 1 1 #200 #134 #209 #211 #206]: false
-#213 := [lemma #212]: #150
-#153 := (or #113 #149)
-#154 := [def-axiom]: #153
-#224 := [unit-resolution #154 #213]: #149
-#225 := (not #149)
-#226 := (or #225 #193)
-#227 := [th-lemma arith triangle-eq]: #226
-#228 := [unit-resolution #227 #224]: #193
-#231 := (not #193)
-#232 := (or #157 #113 #231)
-#233 := [th-lemma arith assign-bounds 1 1]: #232
-#234 := [unit-resolution #233 #213 #228]: #157
-#235 := [unit-resolution #192 #234]: #95
-#236 := [unit-resolution #147 #235]: #137
-#237 := [unit-resolution #205 #236]: #183
-#216 := [hypothesis]: #80
-#217 := (or #95 #79 #113)
-#218 := [th-lemma arith assign-bounds 1 1]: #217
-#219 := [unit-resolution #218 #216 #213]: #95
-#220 := [unit-resolution #147 #219]: #137
-#221 := [unit-resolution #205 #220]: #183
-#222 := [unit-resolution #139 #216]: #141
-#223 := [unit-resolution #188 #222]: #182
-#229 := [th-lemma arith farkas 1 1 1 1 1 1 #216 #213 #228 #134 #223 #221]: false
-#230 := [lemma #229]: #79
-#238 := [unit-resolution #143 #230]: #140
-#239 := [unit-resolution #175 #238]: #163
-[th-lemma arith farkas 1 1 1 1 1 1 #213 #228 #134 #230 #239 #237]: false
-unsat
-670f014c1852b6081232410eed442ca5e4374561 56 0
-#2 := false
-#11 := 1::Int
-decl f3 :: Int
-#9 := f3
-#14 := (= f3 1::Int)
-#12 := (<= f3 1::Int)
-#8 := 0::Int
-#44 := (<= f3 0::Int)
-#45 := (not #44)
-#51 := (and #12 #45)
-#56 := (not #51)
-#62 := (or #14 #56)
-#67 := (not #62)
-#10 := (< 0::Int f3)
-#13 := (and #10 #12)
-#15 := (implies #13 #14)
-#16 := (not #15)
-#70 := (iff #16 #67)
-#37 := (not #13)
-#38 := (or #37 #14)
-#41 := (not #38)
-#68 := (iff #41 #67)
-#65 := (iff #38 #62)
-#59 := (or #56 #14)
-#63 := (iff #59 #62)
-#64 := [rewrite]: #63
-#60 := (iff #38 #59)
-#57 := (iff #37 #56)
-#54 := (iff #13 #51)
-#48 := (and #45 #12)
-#52 := (iff #48 #51)
-#53 := [rewrite]: #52
-#49 := (iff #13 #48)
-#46 := (iff #10 #45)
-#47 := [rewrite]: #46
-#50 := [monotonicity #47]: #49
-#55 := [trans #50 #53]: #54
-#58 := [monotonicity #55]: #57
-#61 := [monotonicity #58]: #60
-#66 := [trans #61 #64]: #65
-#69 := [monotonicity #66]: #68
-#42 := (iff #16 #41)
-#39 := (iff #15 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#71 := [trans #43 #69]: #70
-#36 := [asserted]: #16
-#72 := [mp #36 #71]: #67
-#75 := [not-or-elim #72]: #51
-#76 := [and-elim #75]: #12
-#77 := [and-elim #75]: #45
-#88 := [th-lemma arith eq-propagate 0 0 #77 #76]: #14
-#73 := (not #14)
-#74 := [not-or-elim #72]: #73
-[unit-resolution #74 #88]: false
-unsat
-2c89038e9e5248b9d7775a1c2cccda0081ae4afd 18 0
-#2 := false
-decl f3 :: Int
-#8 := f3
-#9 := (<= f3 f3)
+#7 := f3
+#8 := (< f3 f3)
+#9 := (not #8)
 #10 := (not #9)
-#40 := (iff #10 false)
-#1 := true
-#35 := (not true)
-#38 := (iff #35 false)
-#39 := [rewrite]: #38
-#36 := (iff #10 #35)
-#33 := (iff #9 true)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#30 := [asserted]: #10
-[mp #30 #41]: false
-unsat
-ce89535ab1564731d3a25470ddb514abb6a5df0e 51 0
-#2 := false
-decl f4 :: Int
-#9 := f4
-#11 := 3::Int
-#13 := (* 3::Int f4)
-decl f3 :: Int
-#8 := f3
-#12 := (* 3::Int f3)
-#14 := (<= #12 #13)
-#10 := (<= f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#70 := (iff #16 false)
-#37 := (not #10)
-#38 := (or #37 #14)
-#41 := (not #38)
-#68 := (iff #41 false)
-#1 := true
-#63 := (not true)
-#66 := (iff #63 false)
-#67 := [rewrite]: #66
-#64 := (iff #41 #63)
-#61 := (iff #38 true)
-#47 := 0::Int
-#44 := -1::Int
-#45 := (* -1::Int f4)
-#46 := (+ f3 #45)
-#48 := (<= #46 0::Int)
-#51 := (not #48)
-#56 := (or #51 #48)
-#59 := (iff #56 true)
-#60 := [rewrite]: #59
-#57 := (iff #38 #56)
-#54 := (iff #14 #48)
-#55 := [rewrite]: #54
-#52 := (iff #37 #51)
-#49 := (iff #10 #48)
-#50 := [rewrite]: #49
-#53 := [monotonicity #50]: #52
-#58 := [monotonicity #53 #55]: #57
-#62 := [trans #58 #60]: #61
-#65 := [monotonicity #62]: #64
-#69 := [trans #65 #67]: #68
-#42 := (iff #16 #41)
-#39 := (iff #15 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#71 := [trans #43 #69]: #70
-#36 := [asserted]: #16
-[mp #36 #71]: false
-unsat
-6ee55a0087180d6d5b23379fd148c763bbe9469a 56 0
-#2 := false
-decl f4 :: Int
-#9 := f4
-#11 := 3::Int
-#13 := (* 3::Int f4)
-decl f3 :: Int
-#8 := f3
-#12 := (* 3::Int f3)
-#14 := (< #12 #13)
-#10 := (< f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#75 := (iff #16 false)
-#37 := (not #10)
-#38 := (or #37 #14)
-#41 := (not #38)
-#73 := (iff #41 false)
-#1 := true
-#68 := (not true)
-#71 := (iff #68 false)
-#72 := [rewrite]: #71
-#69 := (iff #41 #68)
-#66 := (iff #38 true)
-#46 := 0::Int
-#44 := -1::Int
-#48 := (* -1::Int f4)
-#49 := (+ f3 #48)
-#47 := (>= #49 0::Int)
-#45 := (not #47)
-#60 := (or #47 #45)
-#64 := (iff #60 true)
-#65 := [rewrite]: #64
-#62 := (iff #38 #60)
-#61 := (iff #14 #45)
-#59 := [rewrite]: #61
-#57 := (iff #37 #47)
-#52 := (not #45)
-#55 := (iff #52 #47)
-#56 := [rewrite]: #55
-#53 := (iff #37 #52)
-#50 := (iff #10 #45)
-#51 := [rewrite]: #50
-#54 := [monotonicity #51]: #53
-#58 := [trans #54 #56]: #57
-#63 := [monotonicity #58 #59]: #62
-#67 := [trans #63 #65]: #66
-#70 := [monotonicity #67]: #69
-#74 := [trans #70 #72]: #73
-#42 := (iff #16 #41)
-#39 := (iff #15 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#76 := [trans #43 #74]: #75
-#36 := [asserted]: #16
-[mp #36 #76]: false
-unsat
-8db8a95cca6e7fe17cb2a4cd6041ce96b6b7f6c4 52 0
-#2 := false
-#43 := 0::Int
-decl f4 :: Int
-#9 := f4
-#41 := -1::Int
-#45 := (* -1::Int f4)
-decl f3 :: Int
-#8 := f3
-#46 := (+ f3 #45)
-#56 := (<= #46 0::Int)
-#69 := (not #56)
-#44 := (>= #46 0::Int)
-#59 := (or #44 #56)
-#62 := (not #59)
-#11 := (<= f3 f4)
-#10 := (< f3 f4)
-#12 := (implies #10 #11)
-#13 := (not #12)
-#65 := (iff #13 #62)
-#34 := (not #10)
-#35 := (or #34 #11)
-#38 := (not #35)
-#63 := (iff #38 #62)
-#60 := (iff #35 #59)
-#57 := (iff #11 #56)
-#58 := [rewrite]: #57
-#54 := (iff #34 #44)
-#42 := (not #44)
-#49 := (not #42)
-#52 := (iff #49 #44)
-#53 := [rewrite]: #52
-#50 := (iff #34 #49)
-#47 := (iff #10 #42)
-#48 := [rewrite]: #47
-#51 := [monotonicity #48]: #50
-#55 := [trans #51 #53]: #54
-#61 := [monotonicity #55 #58]: #60
-#64 := [monotonicity #61]: #63
-#39 := (iff #13 #38)
-#36 := (iff #12 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#66 := [trans #40 #64]: #65
-#33 := [asserted]: #13
-#67 := [mp #33 #66]: #62
-#70 := [not-or-elim #67]: #69
-#68 := [not-or-elim #67]: #42
-#78 := (or #56 #44)
-#79 := [th-lemma arith farkas 1 1]: #78
-#80 := [unit-resolution #79 #68]: #56
-[unit-resolution #80 #70]: false
-unsat
-520cf64d6077f711a93c13c6d282b3380025b7de 73 0
-#2 := false
-#61 := 0::Int
-decl f4 :: Int
-#9 := f4
-#54 := -1::Int
-#55 := (* -1::Int f4)
-decl f3 :: Int
-#8 := f3
-#56 := (+ f3 #55)
-#62 := (>= #56 0::Int)
-#57 := (<= #56 -1::Int)
-#82 := (not #57)
-#60 := (not #62)
-#89 := [hypothesis]: #60
-#87 := (or #82 #62)
-#72 := (iff #57 #62)
-#11 := 1::Int
-#12 := (+ f3 1::Int)
-#13 := (<= #12 f4)
-#10 := (< f3 f4)
-#14 := (iff #10 #13)
-#15 := (not #14)
-#75 := (iff #15 #72)
-#48 := (not #10)
-#36 := (+ 1::Int f3)
-#39 := (<= #36 f4)
-#49 := (iff #39 #48)
-#73 := (iff #49 #72)
-#70 := (iff #48 #62)
-#65 := (not #60)
-#68 := (iff #65 #62)
-#69 := [rewrite]: #68
-#66 := (iff #48 #65)
-#63 := (iff #10 #60)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#71 := [trans #67 #69]: #70
-#58 := (iff #39 #57)
-#59 := [rewrite]: #58
-#74 := [monotonicity #59 #71]: #73
-#52 := (iff #15 #49)
-#42 := (iff #10 #39)
-#45 := (not #42)
-#50 := (iff #45 #49)
-#51 := [rewrite]: #50
-#46 := (iff #15 #45)
-#43 := (iff #14 #42)
-#40 := (iff #13 #39)
-#37 := (= #12 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#53 := [trans #47 #51]: #52
-#76 := [trans #53 #74]: #75
-#35 := [asserted]: #15
-#77 := [mp #35 #76]: #72
-#83 := (not #72)
-#79 := (or #82 #62 #83)
-#80 := [def-axiom]: #79
-#88 := [unit-resolution #80 #77]: #87
-#90 := [unit-resolution #88 #89]: #82
-#91 := [th-lemma arith farkas 1 1 #89 #90]: false
-#92 := [lemma #91]: #62
-#93 := (or #60 #82)
-#94 := [th-lemma arith farkas 1 1]: #93
-#95 := [unit-resolution #94 #92]: #82
-#86 := (or #57 #60)
-#84 := (or #57 #60 #83)
-#85 := [def-axiom]: #84
-#81 := [unit-resolution #85 #77]: #86
-[unit-resolution #81 #95 #92]: false
-unsat
-6728a1b6710185d5f5ea081e6ce67e8aed169134 15 0
-#2 := false
-decl f3 :: Int
-#8 := f3
-#9 := (< f3 f3)
-#10 := (not #9)
-#11 := (not #10)
-#36 := (iff #11 false)
-#34 := (iff #9 false)
+#36 := (iff #10 false)
+#34 := (iff #8 false)
 #35 := [rewrite]: #34
-#32 := (iff #11 #9)
+#32 := (iff #10 #8)
 #33 := [rewrite]: #32
 #37 := [trans #33 #35]: #36
-#31 := [asserted]: #11
+#31 := [asserted]: #10
 [mp #31 #37]: false
 unsat
-520ba5bbc17bf10c5d1972b6fdcb0044f080e0c0 75 0
-#2 := false
-#56 := 0::Int
+85f19ade787969483a16e4ebd4b917f9f0234f87 75 0
+#2 := false
+#17 := 0::Int
 decl f5 :: Int
-#11 := f5
+#10 := f5
 #53 := -1::Int
 #54 := (* -1::Int f5)
 decl f4 :: Int
-#9 := f4
+#8 := f4
 #55 := (+ f4 #54)
-#57 := (<= #55 0::Int)
-#67 := (* -1::Int f4)
+#56 := (<= #55 0::Int)
 decl f3 :: Int
-#8 := f3
-#68 := (+ f3 #67)
-#69 := (<= #68 0::Int)
-#72 := (not #69)
-#63 := (+ f3 #54)
-#64 := (<= #63 0::Int)
-#60 := (not #57)
-#81 := (or #60 #64 #72)
-#86 := (not #81)
-#13 := (<= f3 f5)
-#12 := (<= f4 f5)
-#14 := (implies #12 #13)
-#10 := (<= f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#89 := (iff #16 #86)
-#37 := (not #12)
-#38 := (or #37 #13)
-#44 := (not #10)
+#7 := f3
+#62 := (+ f3 #54)
+#63 := (<= #62 0::Int)
+#59 := (not #56)
+#66 := (* -1::Int f4)
+#67 := (+ f3 #66)
+#68 := (<= #67 0::Int)
+#71 := (not #68)
+#80 := (or #71 #59 #63)
+#85 := (not #80)
+#12 := (<= f3 f5)
+#11 := (<= f4 f5)
+#13 := (implies #11 #12)
+#9 := (<= f3 f4)
+#14 := (implies #9 #13)
+#15 := (not #14)
+#88 := (iff #15 #85)
+#37 := (not #11)
+#38 := (or #37 #12)
+#44 := (not #9)
 #45 := (or #44 #38)
 #50 := (not #45)
-#87 := (iff #50 #86)
-#84 := (iff #45 #81)
-#75 := (or #60 #64)
-#78 := (or #72 #75)
-#82 := (iff #78 #81)
-#83 := [rewrite]: #82
-#79 := (iff #45 #78)
-#76 := (iff #38 #75)
-#65 := (iff #13 #64)
-#66 := [rewrite]: #65
-#61 := (iff #37 #60)
-#58 := (iff #12 #57)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#77 := [monotonicity #62 #66]: #76
+#86 := (iff #50 #85)
+#83 := (iff #45 #80)
+#74 := (or #59 #63)
+#77 := (or #71 #74)
+#81 := (iff #77 #80)
+#82 := [rewrite]: #81
+#78 := (iff #45 #77)
+#75 := (iff #38 #74)
+#64 := (iff #12 #63)
+#65 := [rewrite]: #64
+#60 := (iff #37 #59)
+#57 := (iff #11 #56)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#76 := [monotonicity #61 #65]: #75
+#72 := (iff #44 #71)
+#69 := (iff #9 #68)
+#70 := [rewrite]: #69
+#73 := [monotonicity #70]: #72
+#79 := [monotonicity #73 #76]: #78
+#84 := [trans #79 #82]: #83
+#87 := [monotonicity #84]: #86
+#51 := (iff #15 #50)
+#48 := (iff #14 #45)
+#41 := (implies #9 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #14 #41)
+#39 := (iff #13 #38)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#49 := [trans #43 #47]: #48
+#52 := [monotonicity #49]: #51
+#89 := [trans #52 #87]: #88
+#36 := [asserted]: #15
+#90 := [mp #36 #89]: #85
+#92 := [not-or-elim #90]: #56
+#93 := (not #63)
+#94 := [not-or-elim #90]: #93
+#91 := [not-or-elim #90]: #68
+[th-lemma arith farkas 1 -1 1 #91 #94 #92]: false
+unsat
+931acbba508535ba7d1335a982cf7a172a535d9c 80 0
+#2 := false
+#17 := 0::Int
+decl f5 :: Int
+#10 := f5
+#53 := -1::Int
+#54 := (* -1::Int f5)
+decl f4 :: Int
+#8 := f4
+#55 := (+ f4 #54)
+#56 := (<= #55 0::Int)
+decl f3 :: Int
+#7 := f3
+#62 := (+ f3 #54)
+#63 := (<= #62 0::Int)
+#59 := (not #56)
+#68 := (* -1::Int f4)
+#69 := (+ f3 #68)
+#67 := (>= #69 0::Int)
+#85 := (or #67 #59 #63)
+#90 := (not #85)
+#12 := (<= f3 f5)
+#11 := (<= f4 f5)
+#13 := (implies #11 #12)
+#9 := (< f3 f4)
+#14 := (implies #9 #13)
+#15 := (not #14)
+#93 := (iff #15 #90)
+#37 := (not #11)
+#38 := (or #37 #12)
+#44 := (not #9)
+#45 := (or #44 #38)
+#50 := (not #45)
+#91 := (iff #50 #90)
+#88 := (iff #45 #85)
+#79 := (or #59 #63)
+#82 := (or #67 #79)
+#86 := (iff #82 #85)
+#87 := [rewrite]: #86
+#83 := (iff #45 #82)
+#80 := (iff #38 #79)
+#64 := (iff #12 #63)
+#65 := [rewrite]: #64
+#60 := (iff #37 #59)
+#57 := (iff #11 #56)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#81 := [monotonicity #61 #65]: #80
+#77 := (iff #44 #67)
+#66 := (not #67)
+#72 := (not #66)
+#75 := (iff #72 #67)
+#76 := [rewrite]: #75
 #73 := (iff #44 #72)
-#70 := (iff #10 #69)
+#70 := (iff #9 #66)
 #71 := [rewrite]: #70
 #74 := [monotonicity #71]: #73
-#80 := [monotonicity #74 #77]: #79
-#85 := [trans #80 #83]: #84
-#88 := [monotonicity #85]: #87
-#51 := (iff #16 #50)
-#48 := (iff #15 #45)
-#41 := (implies #10 #38)
+#78 := [trans #74 #76]: #77
+#84 := [monotonicity #78 #81]: #83
+#89 := [trans #84 #87]: #88
+#92 := [monotonicity #89]: #91
+#51 := (iff #15 #50)
+#48 := (iff #14 #45)
+#41 := (implies #9 #38)
 #46 := (iff #41 #45)
 #47 := [rewrite]: #46
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
+#42 := (iff #14 #41)
+#39 := (iff #13 #38)
 #40 := [rewrite]: #39
 #43 := [monotonicity #40]: #42
 #49 := [trans #43 #47]: #48
 #52 := [monotonicity #49]: #51
-#90 := [trans #52 #88]: #89
-#36 := [asserted]: #16
-#91 := [mp #36 #90]: #86
-#92 := [not-or-elim #91]: #57
-#93 := (not #64)
-#94 := [not-or-elim #91]: #93
-#95 := [not-or-elim #91]: #69
-[th-lemma arith farkas 1 -1 1 #95 #94 #92]: false
-unsat
-dcf1c788b6911dd9d0d36f4c26d7c585e6116ff5 80 0
-#2 := false
-#56 := 0::Int
+#94 := [trans #52 #92]: #93
+#36 := [asserted]: #15
+#95 := [mp #36 #94]: #90
+#97 := [not-or-elim #95]: #56
+#96 := [not-or-elim #95]: #66
+#98 := (not #63)
+#99 := [not-or-elim #95]: #98
+[th-lemma arith farkas 1 1 1 #99 #96 #97]: false
+unsat
+816d4005adca7e29ab45b1020b26b4dce5e836b4 80 0
+#2 := false
+#17 := 0::Int
 decl f5 :: Int
-#11 := f5
+#10 := f5
 #53 := -1::Int
-#54 := (* -1::Int f5)
+#56 := (* -1::Int f5)
+decl f3 :: Int
+#7 := f3
+#67 := (+ f3 #56)
+#68 := (<= #67 0::Int)
+#98 := (not #68)
 decl f4 :: Int
-#9 := f4
-#55 := (+ f4 #54)
-#57 := (<= #55 0::Int)
-#69 := (* -1::Int f4)
-decl f3 :: Int
-#8 := f3
-#70 := (+ f3 #69)
-#68 := (>= #70 0::Int)
-#63 := (+ f3 #54)
-#64 := (<= #63 0::Int)
-#60 := (not #57)
-#86 := (or #60 #64 #68)
-#91 := (not #86)
-#13 := (<= f3 f5)
-#12 := (<= f4 f5)
-#14 := (implies #12 #13)
-#10 := (< f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#94 := (iff #16 #91)
-#37 := (not #12)
-#38 := (or #37 #13)
-#44 := (not #10)
+#8 := f4
+#57 := (+ f4 #56)
+#55 := (>= #57 0::Int)
+#71 := (* -1::Int f4)
+#72 := (+ f3 #71)
+#73 := (<= #72 0::Int)
+#76 := (not #73)
+#85 := (or #76 #55 #68)
+#90 := (not #85)
+#12 := (<= f3 f5)
+#11 := (< f4 f5)
+#13 := (implies #11 #12)
+#9 := (<= f3 f4)
+#14 := (implies #9 #13)
+#15 := (not #14)
+#93 := (iff #15 #90)
+#37 := (not #11)
+#38 := (or #37 #12)
+#44 := (not #9)
 #45 := (or #44 #38)
 #50 := (not #45)
-#92 := (iff #50 #91)
-#89 := (iff #45 #86)
-#80 := (or #60 #64)
-#83 := (or #68 #80)
-#87 := (iff #83 #86)
-#88 := [rewrite]: #87
-#84 := (iff #45 #83)
-#81 := (iff #38 #80)
-#65 := (iff #13 #64)
-#66 := [rewrite]: #65
+#91 := (iff #50 #90)
+#88 := (iff #45 #85)
+#79 := (or #55 #68)
+#82 := (or #76 #79)
+#86 := (iff #82 #85)
+#87 := [rewrite]: #86
+#83 := (iff #45 #82)
+#80 := (iff #38 #79)
+#69 := (iff #12 #68)
+#70 := [rewrite]: #69
+#65 := (iff #37 #55)
+#54 := (not #55)
+#60 := (not #54)
+#63 := (iff #60 #55)
+#64 := [rewrite]: #63
 #61 := (iff #37 #60)
-#58 := (iff #12 #57)
+#58 := (iff #11 #54)
 #59 := [rewrite]: #58
 #62 := [monotonicity #59]: #61
-#82 := [monotonicity #62 #66]: #81
-#78 := (iff #44 #68)
-#67 := (not #68)
-#73 := (not #67)
-#76 := (iff #73 #68)
-#77 := [rewrite]: #76
-#74 := (iff #44 #73)
-#71 := (iff #10 #67)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#79 := [trans #75 #77]: #78
-#85 := [monotonicity #79 #82]: #84
-#90 := [trans #85 #88]: #89
-#93 := [monotonicity #90]: #92
-#51 := (iff #16 #50)
-#48 := (iff #15 #45)
-#41 := (implies #10 #38)
+#66 := [trans #62 #64]: #65
+#81 := [monotonicity #66 #70]: #80
+#77 := (iff #44 #76)
+#74 := (iff #9 #73)
+#75 := [rewrite]: #74
+#78 := [monotonicity #75]: #77
+#84 := [monotonicity #78 #81]: #83
+#89 := [trans #84 #87]: #88
+#92 := [monotonicity #89]: #91
+#51 := (iff #15 #50)
+#48 := (iff #14 #45)
+#41 := (implies #9 #38)
 #46 := (iff #41 #45)
 #47 := [rewrite]: #46
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#95 := [trans #52 #93]: #94
-#36 := [asserted]: #16
-#96 := [mp #36 #95]: #91
-#97 := [not-or-elim #96]: #57
-#98 := (not #64)
-#99 := [not-or-elim #96]: #98
-#100 := [not-or-elim #96]: #67
-[th-lemma arith farkas 1 1 1 #100 #99 #97]: false
-unsat
-c158570854bd04b541514c1e42ef7c6a80910ace 80 0
-#2 := false
-#55 := 0::Int
-decl f4 :: Int
-#9 := f4
-#53 := -1::Int
-#72 := (* -1::Int f4)
-decl f3 :: Int
-#8 := f3
-#73 := (+ f3 #72)
-#74 := (<= #73 0::Int)
-#77 := (not #74)
-decl f5 :: Int
-#11 := f5
-#57 := (* -1::Int f5)
-#68 := (+ f3 #57)
-#69 := (<= #68 0::Int)
-#58 := (+ f4 #57)
-#56 := (>= #58 0::Int)
-#86 := (or #56 #69 #77)
-#91 := (not #86)
-#13 := (<= f3 f5)
-#12 := (< f4 f5)
-#14 := (implies #12 #13)
-#10 := (<= f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#94 := (iff #16 #91)
-#37 := (not #12)
-#38 := (or #37 #13)
-#44 := (not #10)
-#45 := (or #44 #38)
-#50 := (not #45)
-#92 := (iff #50 #91)
-#89 := (iff #45 #86)
-#80 := (or #56 #69)
-#83 := (or #77 #80)
-#87 := (iff #83 #86)
-#88 := [rewrite]: #87
-#84 := (iff #45 #83)
-#81 := (iff #38 #80)
-#70 := (iff #13 #69)
-#71 := [rewrite]: #70
-#66 := (iff #37 #56)
-#54 := (not #56)
-#61 := (not #54)
-#64 := (iff #61 #56)
-#65 := [rewrite]: #64
-#62 := (iff #37 #61)
-#59 := (iff #12 #54)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#67 := [trans #63 #65]: #66
-#82 := [monotonicity #67 #71]: #81
-#78 := (iff #44 #77)
-#75 := (iff #10 #74)
-#76 := [rewrite]: #75
-#79 := [monotonicity #76]: #78
-#85 := [monotonicity #79 #82]: #84
-#90 := [trans #85 #88]: #89
-#93 := [monotonicity #90]: #92
-#51 := (iff #16 #50)
-#48 := (iff #15 #45)
-#41 := (implies #10 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
+#42 := (iff #14 #41)
+#39 := (iff #13 #38)
 #40 := [rewrite]: #39
 #43 := [monotonicity #40]: #42
 #49 := [trans #43 #47]: #48
 #52 := [monotonicity #49]: #51
-#95 := [trans #52 #93]: #94
-#36 := [asserted]: #16
-#96 := [mp #36 #95]: #91
-#100 := [not-or-elim #96]: #74
-#98 := (not #69)
-#99 := [not-or-elim #96]: #98
-#97 := [not-or-elim #96]: #54
-[th-lemma arith farkas 1 1 1 #97 #99 #100]: false
-unsat
-e80ef8fa1f5f7f731207887aafb3d73399a22a53 85 0
-#2 := false
-#55 := 0::Int
+#94 := [trans #52 #92]: #93
+#36 := [asserted]: #15
+#95 := [mp #36 #94]: #90
+#99 := [not-or-elim #95]: #98
+#97 := [not-or-elim #95]: #54
+#96 := [not-or-elim #95]: #73
+[th-lemma arith farkas 1 1 1 #96 #97 #99]: false
+unsat
+2e4e306dde5e00fefa942379810b423549afc80a 85 0
+#2 := false
+#17 := 0::Int
 decl f5 :: Int
-#11 := f5
+#10 := f5
 #53 := -1::Int
-#57 := (* -1::Int f5)
+#56 := (* -1::Int f5)
 decl f3 :: Int
-#8 := f3
-#70 := (+ f3 #57)
-#69 := (>= #70 0::Int)
+#7 := f3
+#69 := (+ f3 #56)
+#68 := (>= #69 0::Int)
+#67 := (not #68)
 decl f4 :: Int
-#9 := f4
-#75 := (* -1::Int f4)
-#76 := (+ f3 #75)
-#74 := (>= #76 0::Int)
-#68 := (not #69)
-#58 := (+ f4 #57)
-#56 := (>= #58 0::Int)
-#92 := (or #56 #68 #74)
-#97 := (not #92)
-#13 := (< f3 f5)
-#12 := (< f4 f5)
-#14 := (implies #12 #13)
-#10 := (< f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#100 := (iff #16 #97)
-#37 := (not #12)
-#38 := (or #37 #13)
-#44 := (not #10)
+#8 := f4
+#57 := (+ f4 #56)
+#55 := (>= #57 0::Int)
+#74 := (* -1::Int f4)
+#75 := (+ f3 #74)
+#73 := (>= #75 0::Int)
+#91 := (or #73 #55 #67)
+#96 := (not #91)
+#12 := (< f3 f5)
+#11 := (< f4 f5)
+#13 := (implies #11 #12)
+#9 := (< f3 f4)
+#14 := (implies #9 #13)
+#15 := (not #14)
+#99 := (iff #15 #96)
+#37 := (not #11)
+#38 := (or #37 #12)
+#44 := (not #9)
 #45 := (or #44 #38)
 #50 := (not #45)
-#98 := (iff #50 #97)
-#95 := (iff #45 #92)
-#86 := (or #56 #68)
-#89 := (or #74 #86)
-#93 := (iff #89 #92)
-#94 := [rewrite]: #93
-#90 := (iff #45 #89)
-#87 := (iff #38 #86)
-#71 := (iff #13 #68)
-#72 := [rewrite]: #71
-#66 := (iff #37 #56)
-#54 := (not #56)
-#61 := (not #54)
-#64 := (iff #61 #56)
-#65 := [rewrite]: #64
-#62 := (iff #37 #61)
-#59 := (iff #12 #54)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#67 := [trans #63 #65]: #66
-#88 := [monotonicity #67 #72]: #87
-#84 := (iff #44 #74)
-#73 := (not #74)
-#79 := (not #73)
-#82 := (iff #79 #74)
-#83 := [rewrite]: #82
-#80 := (iff #44 #79)
-#77 := (iff #10 #73)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#85 := [trans #81 #83]: #84
-#91 := [monotonicity #85 #88]: #90
-#96 := [trans #91 #94]: #95
-#99 := [monotonicity #96]: #98
-#51 := (iff #16 #50)
-#48 := (iff #15 #45)
-#41 := (implies #10 #38)
+#97 := (iff #50 #96)
+#94 := (iff #45 #91)
+#85 := (or #55 #67)
+#88 := (or #73 #85)
+#92 := (iff #88 #91)
+#93 := [rewrite]: #92
+#89 := (iff #45 #88)
+#86 := (iff #38 #85)
+#70 := (iff #12 #67)
+#71 := [rewrite]: #70
+#65 := (iff #37 #55)
+#54 := (not #55)
+#60 := (not #54)
+#63 := (iff #60 #55)
+#64 := [rewrite]: #63
+#61 := (iff #37 #60)
+#58 := (iff #11 #54)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#66 := [trans #62 #64]: #65
+#87 := [monotonicity #66 #71]: #86
+#83 := (iff #44 #73)
+#72 := (not #73)
+#78 := (not #72)
+#81 := (iff #78 #73)
+#82 := [rewrite]: #81
+#79 := (iff #44 #78)
+#76 := (iff #9 #72)
+#77 := [rewrite]: #76
+#80 := [monotonicity #77]: #79
+#84 := [trans #80 #82]: #83
+#90 := [monotonicity #84 #87]: #89
+#95 := [trans #90 #93]: #94
+#98 := [monotonicity #95]: #97
+#51 := (iff #15 #50)
+#48 := (iff #14 #45)
+#41 := (implies #9 #38)
 #46 := (iff #41 #45)
 #47 := [rewrite]: #46
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
+#42 := (iff #14 #41)
+#39 := (iff #13 #38)
 #40 := [rewrite]: #39
 #43 := [monotonicity #40]: #42
 #49 := [trans #43 #47]: #48
 #52 := [monotonicity #49]: #51
-#101 := [trans #52 #99]: #100
-#36 := [asserted]: #16
-#102 := [mp #36 #101]: #97
-#104 := [not-or-elim #102]: #69
-#103 := [not-or-elim #102]: #54
-#105 := [not-or-elim #102]: #73
-[th-lemma arith farkas 1 1 1 #105 #103 #104]: false
-unsat
-dc84c7d91507b2575d96fd3dc930644975196557 69 0
-#2 := false
-#47 := 0::Int
+#100 := [trans #52 #98]: #99
+#36 := [asserted]: #15
+#101 := [mp #36 #100]: #96
+#104 := [not-or-elim #101]: #68
+#103 := [not-or-elim #101]: #54
+#102 := [not-or-elim #101]: #72
+[th-lemma arith farkas 1 1 1 #102 #103 #104]: false
+unsat
+6ff3c7abc0fee4a9e14344b48daedbcf5f5fa00f 69 0
+#2 := false
+#18 := 0::Int
 decl f5 :: Int
-#11 := f5
+#10 := f5
 #45 := -1::Int
-#54 := (* -1::Int f5)
+#53 := (* -1::Int f5)
 decl f3 :: Int
-#8 := f3
-#65 := (+ f3 #54)
-#66 := (<= #65 0::Int)
-#67 := (not #66)
+#7 := f3
+#64 := (+ f3 #53)
+#65 := (<= #64 0::Int)
+#66 := (not #65)
 decl f4 :: Int
-#9 := f4
-#55 := (+ f4 #54)
-#53 := (>= #55 0::Int)
-#56 := (not #53)
-#49 := (* -1::Int f4)
-#50 := (+ f3 #49)
-#48 := (>= #50 0::Int)
-#46 := (not #48)
-#59 := (and #46 #56)
-#62 := (not #59)
-#77 := (or #62 #66)
-#80 := (not #77)
-#14 := (< f5 f3)
-#15 := (not #14)
-#12 := (< f4 f5)
-#10 := (< f3 f4)
-#13 := (and #10 #12)
-#16 := (implies #13 #15)
-#17 := (not #16)
-#83 := (iff #17 #80)
-#38 := (not #13)
-#39 := (or #38 #15)
+#8 := f4
+#54 := (+ f4 #53)
+#52 := (>= #54 0::Int)
+#55 := (not #52)
+#48 := (* -1::Int f4)
+#49 := (+ f3 #48)
+#47 := (>= #49 0::Int)
+#46 := (not #47)
+#58 := (and #46 #55)
+#61 := (not #58)
+#76 := (or #61 #65)
+#79 := (not #76)
+#13 := (< f5 f3)
+#14 := (not #13)
+#11 := (< f4 f5)
+#9 := (< f3 f4)
+#12 := (and #9 #11)
+#15 := (implies #12 #14)
+#16 := (not #15)
+#82 := (iff #16 #79)
+#38 := (not #12)
+#39 := (or #38 #14)
 #42 := (not #39)
-#81 := (iff #42 #80)
-#78 := (iff #39 #77)
-#75 := (iff #15 #66)
-#70 := (not #67)
-#73 := (iff #70 #66)
-#74 := [rewrite]: #73
-#71 := (iff #15 #70)
-#68 := (iff #14 #67)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#76 := [trans #72 #74]: #75
-#63 := (iff #38 #62)
-#60 := (iff #13 #59)
-#57 := (iff #12 #56)
-#58 := [rewrite]: #57
-#51 := (iff #10 #46)
-#52 := [rewrite]: #51
-#61 := [monotonicity #52 #58]: #60
-#64 := [monotonicity #61]: #63
-#79 := [monotonicity #64 #76]: #78
-#82 := [monotonicity #79]: #81
-#43 := (iff #17 #42)
-#40 := (iff #16 #39)
+#80 := (iff #42 #79)
+#77 := (iff #39 #76)
+#74 := (iff #14 #65)
+#69 := (not #66)
+#72 := (iff #69 #65)
+#73 := [rewrite]: #72
+#70 := (iff #14 #69)
+#67 := (iff #13 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#75 := [trans #71 #73]: #74
+#62 := (iff #38 #61)
+#59 := (iff #12 #58)
+#56 := (iff #11 #55)
+#57 := [rewrite]: #56
+#50 := (iff #9 #46)
+#51 := [rewrite]: #50
+#60 := [monotonicity #51 #57]: #59
+#63 := [monotonicity #60]: #62
+#78 := [monotonicity #63 #75]: #77
+#81 := [monotonicity #78]: #80
+#43 := (iff #16 #42)
+#40 := (iff #15 #39)
 #41 := [rewrite]: #40
 #44 := [monotonicity #41]: #43
-#84 := [trans #44 #82]: #83
-#37 := [asserted]: #17
-#85 := [mp #37 #84]: #80
-#89 := [not-or-elim #85]: #67
-#86 := [not-or-elim #85]: #59
-#88 := [and-elim #86]: #56
-#87 := [and-elim #86]: #46
-[th-lemma arith farkas 1 1 1 #87 #88 #89]: false
-unsat
-f773d363f37e932f4532a69daff94825fd8ced7d 17 0
-#2 := false
-#8 := 0::Real
-#9 := (= 0::Real 0::Real)
+#83 := [trans #44 #81]: #82
+#37 := [asserted]: #16
+#84 := [mp #37 #83]: #79
+#88 := [not-or-elim #84]: #66
+#85 := [not-or-elim #84]: #58
+#87 := [and-elim #85]: #55
+#86 := [and-elim #85]: #46
+[th-lemma arith farkas 1 1 1 #86 #87 #88]: false
+unsat
+350ef141a75c095cba28d720b8371e2490c8bb19 17 0
+#2 := false
+#7 := 0::Real
+#8 := (= 0::Real 0::Real)
+#9 := (not #8)
+#37 := (iff #9 false)
+#1 := true
+#32 := (not true)
+#35 := (iff #32 false)
+#36 := [rewrite]: #35
+#33 := (iff #9 #32)
+#30 := (iff #8 true)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31]: #33
+#38 := [trans #34 #36]: #37
+#29 := [asserted]: #9
+[mp #29 #38]: false
+unsat
+21acd48b54433e537e09b8f6f2ffb24eacd32980 25 0
+#2 := false
+#7 := 0::Real
+#8 := (- 0::Real)
+#9 := (= 0::Real #8)
 #10 := (not #9)
-#38 := (iff #10 false)
+#45 := (iff #10 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #10 #40)
+#38 := (iff #9 true)
+#33 := (= 0::Real 0::Real)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #9 #33)
+#31 := (= #8 0::Real)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#30 := [asserted]: #10
+[mp #30 #46]: false
+unsat
+481d09c848302673296d6da57e855bb3bb5428f4 17 0
+#2 := false
+#7 := 1::Real
+#8 := (= 1::Real 1::Real)
+#9 := (not #8)
+#38 := (iff #9 false)
 #1 := true
 #33 := (not true)
 #36 := (iff #33 false)
 #37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#31 := (iff #9 true)
+#34 := (iff #9 #33)
+#31 := (iff #8 true)
 #32 := [rewrite]: #31
 #35 := [monotonicity #32]: #34
 #39 := [trans #35 #37]: #38
-#30 := [asserted]: #10
+#30 := [asserted]: #9
 [mp #30 #39]: false
 unsat
-22555a704748c0627782ea8aab11b16b25bd4dbb 25 0
-#2 := false
-#8 := 0::Real
-#9 := (- 0::Real)
-#10 := (= 0::Real #9)
+7526daf188c418735315464dcb1bae49e4d1c6a4 34 0
+#2 := false
+#7 := 1::Real
+#8 := (- 1::Real)
+#9 := (= #8 1::Real)
+#10 := (not #9)
 #11 := (not #10)
-#46 := (iff #11 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #11 #41)
-#39 := (iff #10 true)
-#34 := (= 0::Real 0::Real)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #10 #34)
-#32 := (= #9 0::Real)
-#33 := [rewrite]: #32
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#31 := [asserted]: #11
-[mp #31 #47]: false
-unsat
-0f47740e84f3a80bb9157630977b548c62848ac2 17 0
-#2 := false
-#8 := 1::Real
-#9 := (= 1::Real 1::Real)
-#10 := (not #9)
-#38 := (iff #10 false)
-#1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#31 := (iff #9 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#30 := [asserted]: #10
-[mp #30 #39]: false
-unsat
-267141fda78839fe6990cc2abf9a17976b208b6d 34 0
-#2 := false
-#8 := 1::Real
-#9 := (- 1::Real)
-#10 := (= #9 1::Real)
-#11 := (not #10)
-#12 := (not #11)
-#55 := (iff #12 false)
+#55 := (iff #11 false)
 #1 := true
 #50 := (not true)
 #53 := (iff #50 false)
 #54 := [rewrite]: #53
-#51 := (iff #12 #50)
-#48 := (iff #11 true)
+#51 := (iff #11 #50)
+#48 := (iff #10 true)
 #43 := (not false)
 #46 := (iff #43 true)
 #47 := [rewrite]: #46
-#44 := (iff #11 #43)
-#41 := (iff #10 false)
+#44 := (iff #10 #43)
+#41 := (iff #9 false)
 #33 := -1::Real
 #36 := (= -1::Real 1::Real)
 #39 := (iff #36 false)
 #40 := [rewrite]: #39
-#37 := (iff #10 #36)
-#34 := (= #9 -1::Real)
+#37 := (iff #9 #36)
+#34 := (= #8 -1::Real)
 #35 := [rewrite]: #34
 #38 := [monotonicity #35]: #37
 #42 := [trans #38 #40]: #41
@@ -46873,3242 +45609,14 @@
 #49 := [trans #45 #47]: #48
 #52 := [monotonicity #49]: #51
 #56 := [trans #52 #54]: #55
-#32 := [asserted]: #12
+#32 := [asserted]: #11
 [mp #32 #56]: false
 unsat
-1cceccf830fba7a0f6a7b417cdb35acf58e3b386 18 0
-#2 := false
-#9 := 1::Real
-#8 := 0::Real
-#10 := (< 0::Real 1::Real)
-#11 := (not #10)
-#41 := (iff #11 false)
-#1 := true
-#36 := (not true)
-#39 := (iff #36 false)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (iff #10 true)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#31 := [asserted]: #11
-[mp #31 #42]: false
-unsat
-cd5f0992fc4c2527863e91d7965d5cd43f959c45 18 0
-#2 := false
-#9 := 1::Real
-#8 := 0::Real
-#10 := (<= 0::Real 1::Real)
-#11 := (not #10)
-#41 := (iff #11 false)
-#1 := true
-#36 := (not true)
-#39 := (iff #36 false)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (iff #10 true)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#31 := [asserted]: #11
-[mp #31 #42]: false
-unsat
-d3dc3081a8407dc4d182c64981740ecde7c13dde 40 0
-#2 := false
-#12 := 567::Real
-#10 := 345::Real
-#8 := 123::Real
-#9 := (- 123::Real)
-#11 := (+ #9 345::Real)
-#13 := (< #11 567::Real)
-#14 := (not #13)
-#61 := (iff #14 false)
-#41 := 222::Real
-#46 := (< 222::Real 567::Real)
-#49 := (not #46)
-#59 := (iff #49 false)
-#1 := true
-#54 := (not true)
-#57 := (iff #54 false)
-#58 := [rewrite]: #57
-#55 := (iff #49 #54)
-#52 := (iff #46 true)
-#53 := [rewrite]: #52
-#56 := [monotonicity #53]: #55
-#60 := [trans #56 #58]: #59
-#50 := (iff #14 #49)
-#47 := (iff #13 #46)
-#44 := (= #11 222::Real)
-#35 := -123::Real
-#38 := (+ -123::Real 345::Real)
-#42 := (= #38 222::Real)
-#43 := [rewrite]: #42
-#39 := (= #11 #38)
-#36 := (= #9 -123::Real)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#45 := [trans #40 #43]: #44
-#48 := [monotonicity #45]: #47
-#51 := [monotonicity #48]: #50
-#62 := [trans #51 #60]: #61
-#34 := [asserted]: #14
-[mp #34 #62]: false
-unsat
-a9f49d44404eb27b3a936d2ae021bcf936255755 18 0
-#2 := false
-#9 := 2345678901::Real
-#8 := 123456789::Real
-#10 := (< 123456789::Real 2345678901::Real)
-#11 := (not #10)
-#41 := (iff #11 false)
-#1 := true
-#36 := (not true)
-#39 := (iff #36 false)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (iff #10 true)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#31 := [asserted]: #11
-[mp #31 #42]: false
-unsat
-a5a30c12b002b073c6704cbd0e9c0bff0c2be9ce 30 0
-#2 := false
-#10 := 2345678901::Real
-#8 := 123456789::Real
-#9 := (- 123456789::Real)
-#11 := (< #9 2345678901::Real)
-#12 := (not #11)
-#51 := (iff #12 false)
-#33 := -123456789::Real
-#36 := (< -123456789::Real 2345678901::Real)
-#39 := (not #36)
-#49 := (iff #39 false)
-#1 := true
-#44 := (not true)
-#47 := (iff #44 false)
-#48 := [rewrite]: #47
-#45 := (iff #39 #44)
-#42 := (iff #36 true)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#40 := (iff #12 #39)
-#37 := (iff #11 #36)
-#34 := (= #9 -123456789::Real)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#41 := [monotonicity #38]: #40
-#52 := [trans #41 #50]: #51
-#32 := [asserted]: #12
-[mp #32 #52]: false
-unsat
-503a960ec2242e052830c7ef31b928dcfd2a74cf 26 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-#9 := 0::Real
-#10 := (+ f3 0::Real)
-#11 := (= #10 f3)
-#12 := (not #11)
-#46 := (iff #12 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #11 #34)
-#33 := [rewrite]: #11
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #12
-[mp #32 #47]: false
-unsat
-770f240de3310b0d6a8016479beff839eb224176 26 0
-#2 := false
-decl f3 :: Real
-#9 := f3
-#8 := 0::Real
-#10 := (+ 0::Real f3)
-#11 := (= #10 f3)
-#12 := (not #11)
-#46 := (iff #12 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #11 #34)
-#33 := [rewrite]: #11
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #12
-[mp #32 #47]: false
-unsat
-5d138ec76d5878a62b190baf9223adf9c458ea69 29 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-decl f4 :: Real
-#9 := f4
-#11 := (+ f4 f3)
-#10 := (+ f3 f4)
-#12 := (= #10 #11)
-#13 := (not #12)
-#48 := (iff #13 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #13 #43)
-#41 := (iff #12 true)
-#36 := (= #10 #10)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #12 #36)
-#34 := (= #11 #10)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#33 := [asserted]: #13
-[mp #33 #49]: false
-unsat
-9e4deb91672100910bd4e78f0dd93df4413e0265 33 0
-#2 := false
-decl f5 :: Real
-#10 := f5
-decl f4 :: Real
-#9 := f4
-decl f3 :: Real
-#8 := f3
-#13 := (+ f3 f4)
-#14 := (+ #13 f5)
-#11 := (+ f4 f5)
-#12 := (+ f3 #11)
-#15 := (= #12 #14)
-#16 := (not #15)
-#51 := (iff #16 false)
-#1 := true
-#46 := (not true)
-#49 := (iff #46 false)
-#50 := [rewrite]: #49
-#47 := (iff #16 #46)
-#44 := (iff #15 true)
-#39 := (= #12 #12)
-#42 := (iff #39 true)
-#43 := [rewrite]: #42
-#40 := (iff #15 #39)
-#37 := (= #14 #12)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#45 := [trans #41 #43]: #44
-#48 := [monotonicity #45]: #47
-#52 := [trans #48 #50]: #51
-#36 := [asserted]: #16
-[mp #36 #52]: false
-unsat
-fa5df4da5927766ac24749e94b2f4590c5f1f525 45 0
-#2 := false
-decl f4 :: Real
-#9 := f4
-#13 := (- f4)
-decl f3 :: Real
-#8 := f3
-#14 := (= f3 #13)
-#11 := 0::Real
-#10 := (+ f3 f4)
-#12 := (= #10 0::Real)
-#15 := (iff #12 #14)
-#16 := (not #15)
-#65 := (iff #16 false)
-#50 := (not #12)
-#37 := -1::Real
-#38 := (* -1::Real f4)
-#41 := (= f3 #38)
-#51 := (iff #41 #50)
-#63 := (iff #51 false)
-#58 := (iff #12 #50)
-#61 := (iff #58 false)
-#62 := [rewrite]: #61
-#59 := (iff #51 #58)
-#56 := (iff #41 #12)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#54 := (iff #16 #51)
-#44 := (iff #12 #41)
-#47 := (not #44)
-#52 := (iff #47 #51)
-#53 := [rewrite]: #52
-#48 := (iff #16 #47)
-#45 := (iff #15 #44)
-#42 := (iff #14 #41)
-#39 := (= #13 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#49 := [monotonicity #46]: #48
-#55 := [trans #49 #53]: #54
-#66 := [trans #55 #64]: #65
-#36 := [asserted]: #16
-[mp #36 #66]: false
-unsat
-780bbf25f5cec016b113005169e826e8a8b1ab35 26 0
-#2 := false
-#8 := 1::Real
-#9 := (- 1::Real)
-#10 := (= #9 #9)
-#11 := (not #10)
-#47 := (iff #11 false)
-#1 := true
-#42 := (not true)
-#45 := (iff #42 false)
-#46 := [rewrite]: #45
-#43 := (iff #11 #42)
-#40 := (iff #10 true)
-#32 := -1::Real
-#35 := (= -1::Real -1::Real)
-#38 := (iff #35 true)
-#39 := [rewrite]: #38
-#36 := (iff #10 #35)
-#33 := (= #9 -1::Real)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34 #34]: #36
-#41 := [trans #37 #39]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#31 := [asserted]: #11
-[mp #31 #48]: false
-unsat
-605574d3c38169fc6d9055703879e99ec228f28e 26 0
-#2 := false
-#8 := 3::Real
-#9 := (- 3::Real)
-#10 := (= #9 #9)
-#11 := (not #10)
-#47 := (iff #11 false)
-#1 := true
-#42 := (not true)
-#45 := (iff #42 false)
-#46 := [rewrite]: #45
-#43 := (iff #11 #42)
-#40 := (iff #10 true)
-#32 := -3::Real
-#35 := (= -3::Real -3::Real)
-#38 := (iff #35 true)
-#39 := [rewrite]: #38
-#36 := (iff #10 #35)
-#33 := (= #9 -3::Real)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34 #34]: #36
-#41 := [trans #37 #39]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#31 := [asserted]: #11
-[mp #31 #48]: false
-unsat
-3decedf8f758750dd070188834780bf7cdda6699 58 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-#10 := 0::Real
-#12 := (< 0::Real f3)
-#9 := (- f3)
-#11 := (< #9 0::Real)
-#13 := (iff #11 #12)
-#14 := (not #13)
-#79 := (iff #14 false)
-#53 := (not #12)
-#35 := -1::Real
-#36 := (* -1::Real f3)
-#39 := (< #36 0::Real)
-#54 := (iff #39 #53)
-#77 := (iff #54 false)
-#59 := (<= f3 0::Real)
-#60 := (not #59)
-#72 := (iff #60 #59)
-#75 := (iff #72 false)
-#76 := [rewrite]: #75
-#73 := (iff #54 #72)
-#70 := (iff #53 #59)
-#65 := (not #60)
-#68 := (iff #65 #59)
-#69 := [rewrite]: #68
-#66 := (iff #53 #65)
-#63 := (iff #12 #60)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#71 := [trans #67 #69]: #70
-#61 := (iff #39 #60)
-#62 := [rewrite]: #61
-#74 := [monotonicity #62 #71]: #73
-#78 := [trans #74 #76]: #77
-#57 := (iff #14 #54)
-#45 := (iff #12 #39)
-#50 := (not #45)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #14 #50)
-#48 := (iff #13 #45)
-#42 := (iff #39 #12)
-#46 := (iff #42 #45)
-#47 := [rewrite]: #46
-#43 := (iff #13 #42)
-#40 := (iff #11 #39)
-#37 := (= #9 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#44 := [monotonicity #41]: #43
-#49 := [trans #44 #47]: #48
-#52 := [monotonicity #49]: #51
-#58 := [trans #52 #56]: #57
-#80 := [trans #58 #78]: #79
-#34 := [asserted]: #14
-[mp #34 #80]: false
-unsat
-48e8235cc2ab6c0c7ee0a64720a7854069344306 61 0
-#2 := false
-#8 := 0::Real
-decl f3 :: Real
-#9 := f3
-#11 := (- f3)
-#12 := (< #11 0::Real)
-#10 := (< 0::Real f3)
-#13 := (implies #10 #12)
-#14 := (not #13)
-#81 := (iff #14 false)
-#35 := -1::Real
-#36 := (* -1::Real f3)
-#39 := (< #36 0::Real)
-#45 := (not #10)
-#46 := (or #45 #39)
-#51 := (not #46)
-#79 := (iff #51 false)
-#1 := true
-#74 := (not true)
-#77 := (iff #74 false)
-#78 := [rewrite]: #77
-#75 := (iff #51 #74)
-#72 := (iff #46 true)
-#54 := (<= f3 0::Real)
-#55 := (not #54)
-#67 := (or #54 #55)
-#70 := (iff #67 true)
-#71 := [rewrite]: #70
-#68 := (iff #46 #67)
-#65 := (iff #39 #55)
-#66 := [rewrite]: #65
-#63 := (iff #45 #54)
-#58 := (not #55)
-#61 := (iff #58 #54)
-#62 := [rewrite]: #61
-#59 := (iff #45 #58)
-#56 := (iff #10 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#69 := [monotonicity #64 #66]: #68
-#73 := [trans #69 #71]: #72
-#76 := [monotonicity #73]: #75
-#80 := [trans #76 #78]: #79
-#52 := (iff #14 #51)
-#49 := (iff #13 #46)
-#42 := (implies #10 #39)
-#47 := (iff #42 #46)
-#48 := [rewrite]: #47
-#43 := (iff #13 #42)
-#40 := (iff #12 #39)
-#37 := (= #11 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#44 := [monotonicity #41]: #43
-#50 := [trans #44 #48]: #49
-#53 := [monotonicity #50]: #52
-#82 := [trans #53 #80]: #81
-#34 := [asserted]: #14
-[mp #34 #82]: false
-unsat
-101fc723faf759de5c8555614c6008d7a3b2f51c 61 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-#11 := (- f3)
-#9 := 0::Real
-#12 := (< 0::Real #11)
-#10 := (< f3 0::Real)
-#13 := (implies #10 #12)
-#14 := (not #13)
-#81 := (iff #14 false)
-#35 := -1::Real
-#36 := (* -1::Real f3)
-#39 := (< 0::Real #36)
-#45 := (not #10)
-#46 := (or #45 #39)
-#51 := (not #46)
-#79 := (iff #51 false)
-#1 := true
-#74 := (not true)
-#77 := (iff #74 false)
-#78 := [rewrite]: #77
-#75 := (iff #51 #74)
-#72 := (iff #46 true)
-#54 := (>= f3 0::Real)
-#55 := (not #54)
-#67 := (or #54 #55)
-#70 := (iff #67 true)
-#71 := [rewrite]: #70
-#68 := (iff #46 #67)
-#65 := (iff #39 #55)
-#66 := [rewrite]: #65
-#63 := (iff #45 #54)
-#58 := (not #55)
-#61 := (iff #58 #54)
-#62 := [rewrite]: #61
-#59 := (iff #45 #58)
-#56 := (iff #10 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#69 := [monotonicity #64 #66]: #68
-#73 := [trans #69 #71]: #72
-#76 := [monotonicity #73]: #75
-#80 := [trans #76 #78]: #79
-#52 := (iff #14 #51)
-#49 := (iff #13 #46)
-#42 := (implies #10 #39)
-#47 := (iff #42 #46)
-#48 := [rewrite]: #47
-#43 := (iff #13 #42)
-#40 := (iff #12 #39)
-#37 := (= #11 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#44 := [monotonicity #41]: #43
-#50 := [trans #44 #48]: #49
-#53 := [monotonicity #50]: #52
-#82 := [trans #53 #80]: #81
-#34 := [asserted]: #14
-[mp #34 #82]: false
-unsat
-283d9e9fd5ac4371653f698859bf2cc218d93907 26 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-#9 := 0::Real
-#10 := (- f3 0::Real)
-#11 := (= #10 f3)
-#12 := (not #11)
-#46 := (iff #12 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #11 #34)
-#33 := [rewrite]: #11
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #12
-[mp #32 #47]: false
-unsat
-377a985423ac0b4a4878b6539f76e0f6387ebc74 32 0
-#2 := false
-decl f3 :: Real
-#9 := f3
-#11 := (- f3)
-#8 := 0::Real
-#10 := (- 0::Real f3)
-#12 := (= #10 #11)
-#13 := (not #12)
-#52 := (iff #13 false)
-#1 := true
-#47 := (not true)
-#50 := (iff #47 false)
-#51 := [rewrite]: #50
-#48 := (iff #13 #47)
-#45 := (iff #12 true)
-#34 := -1::Real
-#35 := (* -1::Real f3)
-#40 := (= #35 #35)
-#43 := (iff #40 true)
-#44 := [rewrite]: #43
-#41 := (iff #12 #40)
-#38 := (= #11 #35)
-#39 := [rewrite]: #38
-#36 := (= #10 #35)
-#37 := [rewrite]: #36
-#42 := [monotonicity #37 #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#33 := [asserted]: #13
-[mp #33 #53]: false
-unsat
-17b8ad92fed9af085980d2ab3e2bbe7070317afb 64 0
-#2 := false
-#12 := 0::Real
-decl f4 :: Real
-#9 := f4
-decl f3 :: Real
-#8 := f3
-#11 := (- f3 f4)
-#13 := (< #11 0::Real)
-#10 := (< f3 f4)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#83 := (iff #15 false)
-#36 := -1::Real
-#37 := (* -1::Real f4)
-#38 := (+ f3 #37)
-#41 := (< #38 0::Real)
-#47 := (not #10)
-#48 := (or #47 #41)
-#53 := (not #48)
-#81 := (iff #53 false)
-#1 := true
-#76 := (not true)
-#79 := (iff #76 false)
-#80 := [rewrite]: #79
-#77 := (iff #53 #76)
-#74 := (iff #48 true)
-#57 := (>= #38 0::Real)
-#56 := (not #57)
-#69 := (or #57 #56)
-#72 := (iff #69 true)
-#73 := [rewrite]: #72
-#70 := (iff #48 #69)
-#67 := (iff #41 #56)
-#68 := [rewrite]: #67
-#65 := (iff #47 #57)
-#60 := (not #56)
-#63 := (iff #60 #57)
-#64 := [rewrite]: #63
-#61 := (iff #47 #60)
-#58 := (iff #10 #56)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#66 := [trans #62 #64]: #65
-#71 := [monotonicity #66 #68]: #70
-#75 := [trans #71 #73]: #74
-#78 := [monotonicity #75]: #77
-#82 := [trans #78 #80]: #81
-#54 := (iff #15 #53)
-#51 := (iff #14 #48)
-#44 := (implies #10 #41)
-#49 := (iff #44 #48)
-#50 := [rewrite]: #49
-#45 := (iff #14 #44)
-#42 := (iff #13 #41)
-#39 := (= #11 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#52 := [trans #46 #50]: #51
-#55 := [monotonicity #52]: #54
-#84 := [trans #55 #82]: #83
-#35 := [asserted]: #15
-[mp #35 #84]: false
-unsat
-f9d032808f895312ecd1abf7bac4681d8af02f4c 44 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-decl f4 :: Real
-#9 := f4
-#11 := (- f4 f3)
-#12 := (- #11)
-#10 := (- f3 f4)
-#13 := (= #10 #12)
-#14 := (not #13)
-#63 := (iff #14 false)
-#1 := true
-#58 := (not true)
-#61 := (iff #58 false)
-#62 := [rewrite]: #61
-#59 := (iff #14 #58)
-#56 := (iff #13 true)
-#35 := -1::Real
-#36 := (* -1::Real f4)
-#37 := (+ f3 #36)
-#51 := (= #37 #37)
-#54 := (iff #51 true)
-#55 := [rewrite]: #54
-#52 := (iff #13 #51)
-#49 := (= #12 #37)
-#40 := (* -1::Real f3)
-#41 := (+ #40 f4)
-#44 := (- #41)
-#47 := (= #44 #37)
-#48 := [rewrite]: #47
-#45 := (= #12 #44)
-#42 := (= #11 #41)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#38 := (= #10 #37)
-#39 := [rewrite]: #38
-#53 := [monotonicity #39 #50]: #52
-#57 := [trans #53 #55]: #56
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#34 := [asserted]: #14
-[mp #34 #64]: false
-unsat
-f5fd5763c194a7060b7d3c31354e945c4bbe4814 42 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-decl f4 :: Real
-#9 := f4
-#11 := (- f4)
-#12 := (+ #11 f3)
-#10 := (- f3 f4)
-#13 := (= #10 #12)
-#14 := (not #13)
-#61 := (iff #14 false)
-#1 := true
-#56 := (not true)
-#59 := (iff #56 false)
-#60 := [rewrite]: #59
-#57 := (iff #14 #56)
-#54 := (iff #13 true)
-#35 := -1::Real
-#36 := (* -1::Real f4)
-#37 := (+ f3 #36)
-#49 := (= #37 #37)
-#52 := (iff #49 true)
-#53 := [rewrite]: #52
-#50 := (iff #13 #49)
-#47 := (= #12 #37)
-#42 := (+ #36 f3)
-#45 := (= #42 #37)
-#46 := [rewrite]: #45
-#43 := (= #12 #42)
-#40 := (= #11 #36)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#38 := (= #10 #37)
-#39 := [rewrite]: #38
-#51 := [monotonicity #39 #48]: #50
-#55 := [trans #51 #53]: #54
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#34 := [asserted]: #14
-[mp #34 #62]: false
-unsat
-95caa8e9312490ba9ace8256d848ea1af589c930 48 0
-#2 := false
-decl f5 :: Real
-#11 := f5
-decl f4 :: Real
-#9 := f4
-#13 := (+ f4 f5)
-decl f3 :: Real
-#8 := f3
-#14 := (- f3 #13)
-#10 := (- f3 f4)
-#12 := (- #10 f5)
-#15 := (= #12 #14)
-#16 := (not #15)
-#66 := (iff #16 false)
-#1 := true
-#61 := (not true)
-#64 := (iff #61 false)
-#65 := [rewrite]: #64
-#62 := (iff #16 #61)
-#59 := (iff #15 true)
-#37 := -1::Real
-#45 := (* -1::Real f5)
-#38 := (* -1::Real f4)
-#46 := (+ #38 #45)
-#47 := (+ f3 #46)
-#54 := (= #47 #47)
-#57 := (iff #54 true)
-#58 := [rewrite]: #57
-#55 := (iff #15 #54)
-#52 := (= #14 #47)
-#53 := [rewrite]: #52
-#50 := (= #12 #47)
-#39 := (+ f3 #38)
-#42 := (- #39 f5)
-#48 := (= #42 #47)
-#49 := [rewrite]: #48
-#43 := (= #12 #42)
-#40 := (= #10 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#51 := [trans #44 #49]: #50
-#56 := [monotonicity #51 #53]: #55
-#60 := [trans #56 #58]: #59
-#63 := [monotonicity #60]: #62
-#67 := [trans #63 #65]: #66
-#36 := [asserted]: #16
-[mp #36 #67]: false
-unsat
-9268db787809f0a583b8abe2865d617f6de5f8b3 26 0
-#2 := false
-#9 := 0::Real
-decl f3 :: Real
-#8 := f3
-#10 := (* f3 0::Real)
-#11 := (= #10 0::Real)
-#12 := (not #11)
-#46 := (iff #12 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 true)
-#34 := (= 0::Real 0::Real)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #11 #34)
-#33 := [rewrite]: #11
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #12
-[mp #32 #47]: false
-unsat
-cfd2d609b4c2acdff8e2c92b7abeb35796f42074 26 0
-#2 := false
-#8 := 0::Real
-decl f3 :: Real
-#9 := f3
-#10 := (* 0::Real f3)
-#11 := (= #10 0::Real)
-#12 := (not #11)
-#46 := (iff #12 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 true)
-#34 := (= 0::Real 0::Real)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #11 #34)
-#33 := [rewrite]: #11
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #12
-[mp #32 #47]: false
-unsat
-47353b900bc68ce2e886059dcd04ac50fb7094fa 26 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-#9 := 1::Real
-#10 := (* f3 1::Real)
-#11 := (= #10 f3)
-#12 := (not #11)
-#46 := (iff #12 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #11 #34)
-#33 := [rewrite]: #11
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #12
-[mp #32 #47]: false
-unsat
-8040bc6506c5d4dcc023aa72dae05d2d6e32e35f 26 0
-#2 := false
-decl f3 :: Real
-#9 := f3
-#8 := 1::Real
-#10 := (* 1::Real f3)
-#11 := (= #10 f3)
-#12 := (not #11)
-#46 := (iff #12 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #11 #34)
-#33 := [rewrite]: #11
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #12
-[mp #32 #47]: false
-unsat
-4677e87ab7e0b998d5363f7ebb364e3f3c6ab1e8 40 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-#12 := (- f3)
-#9 := 1::Real
-#10 := (- 1::Real)
-#11 := (* f3 #10)
-#13 := (= #11 #12)
-#14 := (not #13)
-#60 := (iff #14 false)
-#1 := true
-#55 := (not true)
-#58 := (iff #55 false)
-#59 := [rewrite]: #58
-#56 := (iff #14 #55)
-#53 := (iff #13 true)
-#35 := -1::Real
-#41 := (* -1::Real f3)
-#48 := (= #41 #41)
-#51 := (iff #48 true)
-#52 := [rewrite]: #51
-#49 := (iff #13 #48)
-#46 := (= #12 #41)
-#47 := [rewrite]: #46
-#44 := (= #11 #41)
-#38 := (* f3 -1::Real)
-#42 := (= #38 #41)
-#43 := [rewrite]: #42
-#39 := (= #11 #38)
-#36 := (= #10 -1::Real)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#45 := [trans #40 #43]: #44
-#50 := [monotonicity #45 #47]: #49
-#54 := [trans #50 #52]: #53
-#57 := [monotonicity #54]: #56
-#61 := [trans #57 #59]: #60
-#34 := [asserted]: #14
-[mp #34 #61]: false
-unsat
-492e40909f53004b845757b180e8cdede75e5952 35 0
-#2 := false
-decl f3 :: Real
-#10 := f3
-#12 := (- f3)
-#8 := 1::Real
-#9 := (- 1::Real)
-#11 := (* #9 f3)
-#13 := (= #11 #12)
-#14 := (not #13)
-#55 := (iff #14 false)
-#1 := true
-#50 := (not true)
-#53 := (iff #50 false)
-#54 := [rewrite]: #53
-#51 := (iff #14 #50)
-#48 := (iff #13 true)
-#35 := -1::Real
-#38 := (* -1::Real f3)
-#43 := (= #38 #38)
-#46 := (iff #43 true)
-#47 := [rewrite]: #46
-#44 := (iff #13 #43)
-#41 := (= #12 #38)
-#42 := [rewrite]: #41
-#39 := (= #11 #38)
-#36 := (= #9 -1::Real)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#45 := [monotonicity #40 #42]: #44
-#49 := [trans #45 #47]: #48
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#34 := [asserted]: #14
-[mp #34 #56]: false
-unsat
-b2af4404d7b254702c70ed75613252bd5ca4ca66 28 0
-#2 := false
-#8 := 3::Real
-decl f3 :: Real
-#9 := f3
-#11 := (* f3 3::Real)
-#10 := (* 3::Real f3)
-#12 := (= #10 #11)
-#13 := (not #12)
-#48 := (iff #13 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #13 #43)
-#41 := (iff #12 true)
-#36 := (= #10 #10)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #12 #36)
-#34 := (= #11 #10)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#33 := [asserted]: #13
-[mp #33 #49]: false
-unsat
-7f36309c810a189f03d30657a767073413e0a633 30 0
+f989bf5d645754958077a25b45a102186a2c8468 18 0
 #2 := false
 #8 := 1::Real
-#9 := 2::Real
-#10 := (/ 1::Real 2::Real)
-#11 := (< #10 1::Real)
-#12 := (not #11)
-#51 := (iff #12 false)
-#33 := 1/2::Real
-#36 := (< 1/2::Real 1::Real)
-#39 := (not #36)
-#49 := (iff #39 false)
-#1 := true
-#44 := (not true)
-#47 := (iff #44 false)
-#48 := [rewrite]: #47
-#45 := (iff #39 #44)
-#42 := (iff #36 true)
-#43 := [rewrite]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#40 := (iff #12 #39)
-#37 := (iff #11 #36)
-#34 := (= #10 1/2::Real)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#41 := [monotonicity #38]: #40
-#52 := [trans #41 #50]: #51
-#32 := [asserted]: #12
-[mp #32 #52]: false
-unsat
-ccf056a1d000a2f5db9acd154a1e12ae03fe47c3 27 0
-#2 := false
-#9 := 3::Real
-#8 := 1::Real
-#10 := (/ 1::Real 3::Real)
-#11 := (= #10 #10)
-#12 := (not #11)
-#48 := (iff #12 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (iff #11 true)
-#33 := 1/3::Real
-#36 := (= 1/3::Real 1/3::Real)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (= #10 1/3::Real)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35 #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#32 := [asserted]: #12
-[mp #32 #49]: false
-unsat
-0561d9f0efd34ebe23cfd267e2f9c9ab1b730a91 48 0
-#2 := false
-#9 := 3::Real
-#8 := 1::Real
-#12 := (- 1::Real)
-#13 := (/ #12 3::Real)
-#10 := (- 3::Real)
-#11 := (/ 1::Real #10)
-#14 := (= #11 #13)
-#15 := (not #14)
-#69 := (iff #15 false)
-#1 := true
-#64 := (not true)
-#67 := (iff #64 false)
-#68 := [rewrite]: #67
-#65 := (iff #15 #64)
-#62 := (iff #14 true)
-#42 := -1/3::Real
-#57 := (= -1/3::Real -1/3::Real)
-#60 := (iff #57 true)
-#61 := [rewrite]: #60
-#58 := (iff #14 #57)
-#55 := (= #13 -1/3::Real)
-#47 := -1::Real
-#50 := (/ -1::Real 3::Real)
-#53 := (= #50 -1/3::Real)
-#54 := [rewrite]: #53
-#51 := (= #13 #50)
-#48 := (= #12 -1::Real)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#45 := (= #11 -1/3::Real)
-#36 := -3::Real
-#39 := (/ 1::Real -3::Real)
-#43 := (= #39 -1/3::Real)
-#44 := [rewrite]: #43
-#40 := (= #11 #39)
-#37 := (= #10 -3::Real)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#46 := [trans #41 #44]: #45
-#59 := [monotonicity #46 #56]: #58
-#63 := [trans #59 #61]: #62
-#66 := [monotonicity #63]: #65
-#70 := [trans #66 #68]: #69
-#35 := [asserted]: #15
-[mp #35 #70]: false
-unsat
-36baa91bad72cdcdeb69c09cae275d7dd51d0ec0 36 0
-#2 := false
-#10 := 3::Real
-#8 := 1::Real
-#9 := (- 1::Real)
-#11 := (/ #9 3::Real)
-#12 := (= #11 #11)
-#13 := (not #12)
-#57 := (iff #13 false)
-#1 := true
-#52 := (not true)
-#55 := (iff #52 false)
-#56 := [rewrite]: #55
-#53 := (iff #13 #52)
-#50 := (iff #12 true)
-#40 := -1/3::Real
-#45 := (= -1/3::Real -1/3::Real)
-#48 := (iff #45 true)
-#49 := [rewrite]: #48
-#46 := (iff #12 #45)
-#43 := (= #11 -1/3::Real)
-#34 := -1::Real
-#37 := (/ -1::Real 3::Real)
-#41 := (= #37 -1/3::Real)
-#42 := [rewrite]: #41
-#38 := (= #11 #37)
-#35 := (= #9 -1::Real)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#44 := [trans #39 #42]: #43
-#47 := [monotonicity #44 #44]: #46
-#51 := [trans #47 #49]: #50
-#54 := [monotonicity #51]: #53
-#58 := [trans #54 #56]: #57
-#33 := [asserted]: #13
-[mp #33 #58]: false
-unsat
-27179242be2af6441aee8a632ff4f9f46f4559e7 43 0
-#2 := false
-#10 := 3::Real
-#8 := 1::Real
-#13 := (/ 1::Real 3::Real)
-#11 := (- 3::Real)
-#9 := (- 1::Real)
-#12 := (/ #9 #11)
-#14 := (= #12 #13)
-#15 := (not #14)
-#64 := (iff #15 false)
-#1 := true
-#59 := (not true)
-#62 := (iff #59 false)
-#63 := [rewrite]: #62
-#60 := (iff #15 #59)
-#57 := (iff #14 true)
-#45 := 1/3::Real
-#52 := (= 1/3::Real 1/3::Real)
-#55 := (iff #52 true)
-#56 := [rewrite]: #55
-#53 := (iff #14 #52)
-#50 := (= #13 1/3::Real)
-#51 := [rewrite]: #50
-#48 := (= #12 1/3::Real)
-#39 := -3::Real
-#36 := -1::Real
-#42 := (/ -1::Real -3::Real)
-#46 := (= #42 1/3::Real)
-#47 := [rewrite]: #46
-#43 := (= #12 #42)
-#40 := (= #11 -3::Real)
-#41 := [rewrite]: #40
-#37 := (= #9 -1::Real)
-#38 := [rewrite]: #37
-#44 := [monotonicity #38 #41]: #43
-#49 := [trans #44 #47]: #48
-#54 := [monotonicity #49 #51]: #53
-#58 := [trans #54 #56]: #57
-#61 := [monotonicity #58]: #60
-#65 := [trans #61 #63]: #64
-#35 := [asserted]: #15
-[mp #35 #65]: false
-unsat
-f8feec24442a22841814d6bc2bb6f89a1a5ccdca 26 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-#9 := 1::Real
-#10 := (/ f3 1::Real)
-#11 := (= #10 f3)
-#12 := (not #11)
-#46 := (iff #12 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#39 := (iff #11 true)
-#34 := (= f3 f3)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #11 #34)
-#33 := [rewrite]: #11
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#32 := [asserted]: #12
-[mp #32 #47]: false
-unsat
-c05f02963ca1f0c7b2cf36a8d547885cab5aa79a 60 0
-#2 := false
-#8 := 0::Real
-decl f3 :: Real
-#9 := f3
-#68 := 2/3::Real
-#69 := (* 2/3::Real f3)
-#70 := (<= #69 0::Real)
-#66 := (not #70)
-#55 := (<= f3 0::Real)
-#72 := (or #55 #66)
-#75 := (not #72)
-#11 := 3::Real
-#12 := (/ f3 3::Real)
-#13 := (< #12 f3)
-#10 := (< 0::Real f3)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#78 := (iff #15 #75)
-#36 := 1/3::Real
-#37 := (* 1/3::Real f3)
-#40 := (< #37 f3)
-#46 := (not #10)
-#47 := (or #46 #40)
-#52 := (not #47)
-#76 := (iff #52 #75)
-#73 := (iff #47 #72)
-#67 := (iff #40 #66)
-#71 := [rewrite]: #67
-#64 := (iff #46 #55)
-#56 := (not #55)
-#59 := (not #56)
-#62 := (iff #59 #55)
-#63 := [rewrite]: #62
-#60 := (iff #46 #59)
-#57 := (iff #10 #56)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#65 := [trans #61 #63]: #64
-#74 := [monotonicity #65 #71]: #73
-#77 := [monotonicity #74]: #76
-#53 := (iff #15 #52)
-#50 := (iff #14 #47)
-#43 := (implies #10 #40)
-#48 := (iff #43 #47)
-#49 := [rewrite]: #48
-#44 := (iff #14 #43)
-#41 := (iff #13 #40)
-#38 := (= #12 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#51 := [trans #45 #49]: #50
-#54 := [monotonicity #51]: #53
-#79 := [trans #54 #77]: #78
-#35 := [asserted]: #15
-#80 := [mp #35 #79]: #75
-#82 := [not-or-elim #80]: #70
-#81 := [not-or-elim #80]: #56
-[th-lemma arith farkas -2/3 1 #81 #82]: false
-unsat
-9b3f58b1809134cb88eb2695df7f6a346a6afe80 60 0
-#2 := false
-#9 := 0::Real
-decl f3 :: Real
-#8 := f3
-#70 := 2/3::Real
-#71 := (* 2/3::Real f3)
-#68 := (>= #71 0::Real)
-#66 := (not #68)
-#57 := (>= f3 0::Real)
-#72 := (or #57 #66)
-#75 := (not #72)
-#11 := 3::Real
-#12 := (/ f3 3::Real)
-#13 := (< f3 #12)
-#10 := (< f3 0::Real)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#78 := (iff #15 #75)
-#36 := 1/3::Real
-#37 := (* 1/3::Real f3)
-#40 := (< f3 #37)
-#46 := (not #10)
-#47 := (or #46 #40)
-#52 := (not #47)
-#76 := (iff #52 #75)
-#73 := (iff #47 #72)
-#67 := (iff #40 #66)
-#69 := [rewrite]: #67
-#64 := (iff #46 #57)
-#55 := (not #57)
-#59 := (not #55)
-#62 := (iff #59 #57)
-#63 := [rewrite]: #62
-#60 := (iff #46 #59)
-#56 := (iff #10 #55)
-#58 := [rewrite]: #56
-#61 := [monotonicity #58]: #60
-#65 := [trans #61 #63]: #64
-#74 := [monotonicity #65 #69]: #73
-#77 := [monotonicity #74]: #76
-#53 := (iff #15 #52)
-#50 := (iff #14 #47)
-#43 := (implies #10 #40)
-#48 := (iff #43 #47)
-#49 := [rewrite]: #48
-#44 := (iff #14 #43)
-#41 := (iff #13 #40)
-#38 := (= #12 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#51 := [trans #45 #49]: #50
-#54 := [monotonicity #51]: #53
-#79 := [trans #54 #77]: #78
-#35 := [asserted]: #15
-#80 := [mp #35 #79]: #75
-#82 := [not-or-elim #80]: #68
-#81 := [not-or-elim #80]: #55
-[th-lemma arith farkas -2/3 1 #81 #82]: false
-unsat
-445e35b9311219b2f5634562f77afc853349ceea 36 0
-#2 := false
-decl f3 :: Real
-#9 := f3
-#8 := 3::Real
-#10 := (/ f3 3::Real)
-#11 := (* 3::Real #10)
-#12 := (= #11 f3)
-#13 := (not #12)
-#56 := (iff #13 false)
-#1 := true
-#51 := (not true)
-#54 := (iff #51 false)
-#55 := [rewrite]: #54
-#52 := (iff #13 #51)
-#49 := (iff #12 true)
-#44 := (= f3 f3)
-#47 := (iff #44 true)
-#48 := [rewrite]: #47
-#45 := (iff #12 #44)
-#34 := 1/3::Real
-#35 := (* 1/3::Real f3)
-#38 := (* 3::Real #35)
-#41 := (= #38 f3)
-#42 := [rewrite]: #41
-#39 := (= #11 #38)
-#36 := (= #10 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#43 := [trans #40 #42]: #12
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#33 := [asserted]: #13
-[mp #33 #57]: false
-unsat
-c9d4409876d543b534cb12358001a3188eb10d21 35 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-#9 := 3::Real
-#10 := (* f3 3::Real)
-#11 := (/ #10 3::Real)
-#12 := (= #11 f3)
-#13 := (not #12)
-#55 := (iff #13 false)
-#1 := true
-#50 := (not true)
-#53 := (iff #50 false)
-#54 := [rewrite]: #53
-#51 := (iff #13 #50)
-#48 := (iff #12 true)
-#43 := (= f3 f3)
-#46 := (iff #43 true)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#34 := (* 3::Real f3)
-#37 := (/ #34 3::Real)
-#40 := (= #37 f3)
-#41 := [rewrite]: #40
-#38 := (= #11 #37)
-#35 := (= #10 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#42 := [trans #39 #41]: #12
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#52 := [monotonicity #49]: #51
-#56 := [trans #52 #54]: #55
-#33 := [asserted]: #13
-[mp #33 #56]: false
-unsat
-b7467d5d6041c1b17f2b5e32374743df439ee2c2 62 0
-#2 := false
-#8 := 0::Real
-decl f3 :: Real
-#9 := f3
-#70 := 1/3::Real
-#71 := (* 1/3::Real f3)
-#72 := (<= #71 0::Real)
-#68 := (not #72)
-#57 := (<= f3 0::Real)
-#74 := (or #57 #68)
-#77 := (not #74)
-#13 := 3::Real
-#11 := 2::Real
-#12 := (* 2::Real f3)
-#14 := (/ #12 3::Real)
-#15 := (< #14 f3)
-#10 := (< 0::Real f3)
-#16 := (implies #10 #15)
-#17 := (not #16)
-#80 := (iff #17 #77)
-#39 := 2/3::Real
-#40 := (* 2/3::Real f3)
-#42 := (< #40 f3)
-#48 := (not #10)
-#49 := (or #48 #42)
-#54 := (not #49)
-#78 := (iff #54 #77)
-#75 := (iff #49 #74)
-#69 := (iff #42 #68)
-#73 := [rewrite]: #69
-#66 := (iff #48 #57)
-#58 := (not #57)
-#61 := (not #58)
-#64 := (iff #61 #57)
-#65 := [rewrite]: #64
-#62 := (iff #48 #61)
-#59 := (iff #10 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#67 := [trans #63 #65]: #66
-#76 := [monotonicity #67 #73]: #75
-#79 := [monotonicity #76]: #78
-#55 := (iff #17 #54)
-#52 := (iff #16 #49)
-#45 := (implies #10 #42)
-#50 := (iff #45 #49)
-#51 := [rewrite]: #50
-#46 := (iff #16 #45)
-#43 := (iff #15 #42)
-#38 := (= #14 #40)
-#41 := [rewrite]: #38
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#53 := [trans #47 #51]: #52
-#56 := [monotonicity #53]: #55
-#81 := [trans #56 #79]: #80
-#37 := [asserted]: #17
-#82 := [mp #37 #81]: #77
-#84 := [not-or-elim #82]: #72
-#83 := [not-or-elim #82]: #58
-[th-lemma arith farkas -1/3 1 #83 #84]: false
-unsat
-3b59732be5ac2fe610c9e2843a63e7a1830b9838 62 0
-#2 := false
-#9 := 0::Real
-decl f3 :: Real
-#8 := f3
-#72 := 1/3::Real
-#73 := (* 1/3::Real f3)
-#70 := (>= #73 0::Real)
-#68 := (not #70)
-#59 := (>= f3 0::Real)
-#74 := (or #59 #68)
-#77 := (not #74)
-#13 := 3::Real
-#11 := 2::Real
-#12 := (* 2::Real f3)
-#14 := (/ #12 3::Real)
-#15 := (< f3 #14)
-#10 := (< f3 0::Real)
-#16 := (implies #10 #15)
-#17 := (not #16)
-#80 := (iff #17 #77)
-#39 := 2/3::Real
-#40 := (* 2/3::Real f3)
-#42 := (< f3 #40)
-#48 := (not #10)
-#49 := (or #48 #42)
-#54 := (not #49)
-#78 := (iff #54 #77)
-#75 := (iff #49 #74)
-#69 := (iff #42 #68)
-#71 := [rewrite]: #69
-#66 := (iff #48 #59)
-#57 := (not #59)
-#61 := (not #57)
-#64 := (iff #61 #59)
-#65 := [rewrite]: #64
-#62 := (iff #48 #61)
-#58 := (iff #10 #57)
-#60 := [rewrite]: #58
-#63 := [monotonicity #60]: #62
-#67 := [trans #63 #65]: #66
-#76 := [monotonicity #67 #71]: #75
-#79 := [monotonicity #76]: #78
-#55 := (iff #17 #54)
-#52 := (iff #16 #49)
-#45 := (implies #10 #42)
-#50 := (iff #45 #49)
-#51 := [rewrite]: #50
-#46 := (iff #16 #45)
-#43 := (iff #15 #42)
-#38 := (= #14 #40)
-#41 := [rewrite]: #38
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#53 := [trans #47 #51]: #52
-#56 := [monotonicity #53]: #55
-#81 := [trans #56 #79]: #80
-#37 := [asserted]: #17
-#82 := [mp #37 #81]: #77
-#84 := [not-or-elim #82]: #70
-#83 := [not-or-elim #82]: #57
-[th-lemma arith farkas -1/3 1 #83 #84]: false
-unsat
-78ae7121e195bacc5f4b6db83b123df8490f9dac 75 0
-#2 := false
-#8 := 0::Real
-decl f3 :: Real
-#9 := f3
-#35 := -1::Real
-#36 := (* -1::Real f3)
-#48 := (>= f3 0::Real)
-#55 := (ite #48 f3 #36)
-#75 := (* -1::Real #55)
-#84 := (+ #36 #75)
-#93 := (<= #84 0::Real)
-#80 := (= #36 #55)
-#49 := (not #48)
-#76 := (+ f3 #75)
-#83 := (<= #76 0::Real)
-#79 := (= f3 #55)
-#85 := [hypothesis]: #48
-#81 := (or #49 #79)
-#82 := [def-axiom]: #81
-#86 := [unit-resolution #82 #85]: #79
-#87 := (not #79)
-#88 := (or #87 #83)
-#89 := [th-lemma arith triangle-eq]: #88
-#90 := [unit-resolution #89 #86]: #83
-#64 := (>= #55 0::Real)
-#68 := (not #64)
-#11 := (- f3)
-#10 := (< f3 0::Real)
-#12 := (ite #10 #11 f3)
-#13 := (<= 0::Real #12)
-#14 := (not #13)
-#71 := (iff #14 #68)
-#39 := (ite #10 #36 f3)
-#42 := (<= 0::Real #39)
-#45 := (not #42)
-#69 := (iff #45 #68)
-#66 := (iff #42 #64)
-#60 := (<= 0::Real #55)
-#63 := (iff #60 #64)
-#65 := [rewrite]: #63
-#61 := (iff #42 #60)
-#58 := (= #39 #55)
-#52 := (ite #49 #36 f3)
-#56 := (= #52 #55)
-#57 := [rewrite]: #56
-#53 := (= #39 #52)
-#50 := (iff #10 #49)
-#51 := [rewrite]: #50
-#54 := [monotonicity #51]: #53
-#59 := [trans #54 #57]: #58
-#62 := [monotonicity #59]: #61
-#67 := [trans #62 #65]: #66
-#70 := [monotonicity #67]: #69
-#46 := (iff #14 #45)
-#43 := (iff #13 #42)
-#40 := (= #12 #39)
-#37 := (= #11 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#44 := [monotonicity #41]: #43
-#47 := [monotonicity #44]: #46
-#72 := [trans #47 #70]: #71
-#34 := [asserted]: #14
-#73 := [mp #34 #72]: #68
-#91 := [th-lemma arith farkas -1 1 1 #85 #73 #90]: false
-#92 := [lemma #91]: #49
-#77 := (or #48 #80)
-#78 := [def-axiom]: #77
-#95 := [unit-resolution #78 #92]: #80
-#96 := (not #80)
-#97 := (or #96 #93)
-#98 := [th-lemma arith triangle-eq]: #97
-#99 := [unit-resolution #98 #95]: #93
-[th-lemma arith farkas 1 1 1 #92 #73 #99]: false
-unsat
-ff789d0b06f4e86f73b38d800d6fea471c529be0 128 0
-#2 := false
-#9 := 0::Real
-decl f3 :: Real
-#8 := f3
-#37 := -1::Real
-#38 := (* -1::Real f3)
-#137 := (<= #38 0::Real)
-#136 := (= #38 0::Real)
-#69 := (>= f3 0::Real)
-#76 := (ite #69 f3 #38)
-#85 := (= #76 0::Real)
-#105 := (= f3 #76)
-#127 := (not #105)
-#101 := (not #85)
-#128 := (iff #101 #127)
-#125 := (iff #85 #105)
-#123 := (iff #105 #85)
-#81 := (= 0::Real #76)
-#84 := (iff #81 #85)
-#122 := [commutativity]: #84
-#120 := (iff #105 #81)
-#14 := (= f3 0::Real)
-#118 := [hypothesis]: #101
-#115 := (or #14 #85)
-#63 := (not #14)
-#92 := (iff #63 #85)
-#11 := (- f3)
-#10 := (< f3 0::Real)
-#12 := (ite #10 #11 f3)
-#13 := (= #12 0::Real)
-#15 := (iff #13 #14)
-#16 := (not #15)
-#97 := (iff #16 #92)
-#41 := (ite #10 #38 f3)
-#47 := (= 0::Real #41)
-#64 := (iff #47 #63)
-#95 := (iff #64 #92)
-#89 := (iff #85 #63)
-#93 := (iff #89 #92)
-#94 := [rewrite]: #93
-#90 := (iff #64 #89)
-#87 := (iff #47 #85)
-#86 := [rewrite]: #84
-#82 := (iff #47 #81)
-#79 := (= #41 #76)
-#70 := (not #69)
-#73 := (ite #70 #38 f3)
-#77 := (= #73 #76)
-#78 := [rewrite]: #77
-#74 := (= #41 #73)
-#71 := (iff #10 #70)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#80 := [trans #75 #78]: #79
-#83 := [monotonicity #80]: #82
-#88 := [trans #83 #86]: #87
-#91 := [monotonicity #88]: #90
-#96 := [trans #91 #94]: #95
-#67 := (iff #16 #64)
-#55 := (iff #14 #47)
-#60 := (not #55)
-#65 := (iff #60 #64)
-#66 := [rewrite]: #65
-#61 := (iff #16 #60)
-#58 := (iff #15 #55)
-#52 := (iff #47 #14)
-#56 := (iff #52 #55)
-#57 := [rewrite]: #56
-#53 := (iff #15 #52)
-#50 := (iff #13 #47)
-#44 := (= #41 0::Real)
-#48 := (iff #44 #47)
-#49 := [rewrite]: #48
-#45 := (iff #13 #44)
-#42 := (= #12 #41)
-#39 := (= #11 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#51 := [trans #46 #49]: #50
-#54 := [monotonicity #51]: #53
-#59 := [trans #54 #57]: #58
-#62 := [monotonicity #59]: #61
-#68 := [trans #62 #66]: #67
-#98 := [trans #68 #96]: #97
-#36 := [asserted]: #16
-#99 := [mp #36 #98]: #92
-#102 := (not #92)
-#113 := (or #14 #85 #102)
-#114 := [def-axiom]: #113
-#116 := [unit-resolution #114 #99]: #115
-#119 := [unit-resolution #116 #118]: #14
-#121 := [monotonicity #119]: #120
-#124 := [trans #121 #122]: #123
-#126 := [symm #124]: #125
-#129 := [monotonicity #126]: #128
-#130 := [mp #118 #129]: #127
-#131 := (or #63 #69)
-#132 := [th-lemma arith triangle-eq]: #131
-#133 := [unit-resolution #132 #119]: #69
-#107 := (or #70 #105)
-#108 := [def-axiom]: #107
-#134 := [unit-resolution #108 #133 #130]: false
-#135 := [lemma #134]: #85
-#106 := (= #38 #76)
-#144 := (iff #63 #127)
-#142 := (iff #14 #105)
-#140 := (iff #105 #14)
-#141 := [monotonicity #135]: #140
-#143 := [symm #141]: #142
-#145 := [monotonicity #143]: #144
-#111 := (or #63 #101)
-#109 := (or #63 #101 #102)
-#110 := [def-axiom]: #109
-#112 := [unit-resolution #110 #99]: #111
-#139 := [unit-resolution #112 #135]: #63
-#146 := [mp #139 #145]: #127
-#147 := [unit-resolution #108 #146]: #70
-#103 := (or #69 #106)
-#104 := [def-axiom]: #103
-#148 := [unit-resolution #104 #147]: #106
-#149 := [trans #148 #135]: #136
-#150 := (not #136)
-#151 := (or #150 #137)
-#152 := [th-lemma arith triangle-eq]: #151
-#153 := [unit-resolution #152 #149]: #137
-[th-lemma arith farkas 1 1 #147 #153]: false
-unsat
-a4051d759a69912da335fbbe489e426099dc4c5c 103 0
-#2 := false
-#8 := 0::Real
-decl f3 :: Real
-#9 := f3
-#64 := (>= f3 0::Real)
-#37 := -1::Real
-#38 := (* -1::Real f3)
-#111 := (* -1::Real #38)
-#112 := (+ f3 #111)
-#114 := (>= #112 0::Real)
-#110 := (= f3 #38)
-#71 := (ite #64 f3 #38)
-#118 := (= #71 #38)
-#99 := (= #38 #71)
-#65 := (not #64)
-#115 := [hypothesis]: #65
-#102 := (or #64 #99)
-#97 := [def-axiom]: #102
-#116 := [unit-resolution #97 #115]: #99
-#119 := [symm #116]: #118
-#76 := (= f3 #71)
-#108 := (or #64 #76)
-#86 := (iff #65 #76)
-#12 := (- f3)
-#11 := (< f3 0::Real)
-#13 := (ite #11 #12 f3)
-#14 := (= #13 f3)
-#10 := (<= 0::Real f3)
-#15 := (iff #10 #14)
-#16 := (not #15)
-#91 := (iff #16 #86)
-#58 := (not #10)
-#41 := (ite #11 #38 f3)
-#47 := (= f3 #41)
-#59 := (iff #47 #58)
-#89 := (iff #59 #86)
-#83 := (iff #76 #65)
-#87 := (iff #83 #86)
-#88 := [rewrite]: #87
-#84 := (iff #59 #83)
-#81 := (iff #58 #65)
-#79 := (iff #10 #64)
-#80 := [rewrite]: #79
-#82 := [monotonicity #80]: #81
-#77 := (iff #47 #76)
-#74 := (= #41 #71)
-#68 := (ite #65 #38 f3)
-#72 := (= #68 #71)
-#73 := [rewrite]: #72
-#69 := (= #41 #68)
-#66 := (iff #11 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#75 := [trans #70 #73]: #74
-#78 := [monotonicity #75]: #77
-#85 := [monotonicity #78 #82]: #84
-#90 := [trans #85 #88]: #89
-#62 := (iff #16 #59)
-#52 := (iff #10 #47)
-#55 := (not #52)
-#60 := (iff #55 #59)
-#61 := [rewrite]: #60
-#56 := (iff #16 #55)
-#53 := (iff #15 #52)
-#50 := (iff #14 #47)
-#44 := (= #41 f3)
-#48 := (iff #44 #47)
-#49 := [rewrite]: #48
-#45 := (iff #14 #44)
-#42 := (= #13 #41)
-#39 := (= #12 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#51 := [trans #46 #49]: #50
-#54 := [monotonicity #51]: #53
-#57 := [monotonicity #54]: #56
-#63 := [trans #57 #61]: #62
-#92 := [trans #63 #90]: #91
-#36 := [asserted]: #16
-#93 := [mp #36 #92]: #86
-#95 := (not #86)
-#106 := (or #64 #76 #95)
-#107 := [def-axiom]: #106
-#109 := [unit-resolution #107 #93]: #108
-#117 := [unit-resolution #109 #115]: #76
-#120 := [trans #117 #119]: #110
-#121 := (not #110)
-#122 := (or #121 #114)
-#123 := [th-lemma arith triangle-eq]: #122
-#124 := [unit-resolution #123 #120]: #114
-#125 := [th-lemma arith farkas 2 1 #115 #124]: false
-#126 := [lemma #125]: #64
-#100 := (or #65 #76)
-#101 := [def-axiom]: #100
-#113 := [unit-resolution #101 #126]: #76
-#98 := (not #76)
-#104 := (or #65 #98)
-#96 := (or #65 #98 #95)
-#103 := [def-axiom]: #96
-#105 := [unit-resolution #103 #93]: #104
-[unit-resolution #105 #113 #126]: false
-unsat
-571ce5e288c8e7c603db7dc5836a06cad2fe7128 152 0
-#2 := false
-#9 := 0::Real
-decl f3 :: Real
-#8 := f3
-#37 := -1::Real
-#38 := (* -1::Real f3)
-#64 := (>= f3 0::Real)
-#71 := (ite #64 f3 #38)
-#114 := (* -1::Real #71)
-#164 := (+ f3 #114)
-#165 := (<= #164 0::Real)
-#101 := (= f3 #71)
-#115 := (+ #38 #114)
-#117 := (>= #115 0::Real)
-#76 := (= #38 #71)
-#65 := (not #64)
-#149 := [hypothesis]: #65
-#104 := (or #64 #76)
-#99 := [def-axiom]: #104
-#150 := [unit-resolution #99 #149]: #76
-#143 := (not #76)
-#151 := (or #143 #117)
-#152 := [th-lemma arith triangle-eq]: #151
-#153 := [unit-resolution #152 #150]: #117
-#81 := (+ f3 #71)
-#100 := (<= #81 0::Real)
-#158 := (not #100)
-#97 := (>= #81 0::Real)
-#116 := (<= #115 0::Real)
-#80 := (= #81 0::Real)
-#98 := (not #80)
-#136 := (not #97)
-#137 := [hypothesis]: #136
-#138 := (or #98 #97)
-#139 := [th-lemma arith triangle-eq]: #138
-#140 := [unit-resolution #139 #137]: #98
-#134 := (or #65 #80)
-#121 := (= f3 0::Real)
-#10 := (<= f3 0::Real)
-#118 := [hypothesis]: #98
-#112 := (or #10 #80)
-#58 := (not #10)
-#88 := (iff #58 #80)
-#12 := (- f3)
-#11 := (< f3 0::Real)
-#13 := (ite #11 #12 f3)
-#14 := (= #13 #12)
-#15 := (iff #10 #14)
-#16 := (not #15)
-#93 := (iff #16 #88)
-#41 := (ite #11 #38 f3)
-#47 := (= #38 #41)
-#59 := (iff #47 #58)
-#91 := (iff #59 #88)
-#85 := (iff #80 #58)
-#89 := (iff #85 #88)
-#90 := [rewrite]: #89
-#86 := (iff #59 #85)
-#83 := (iff #47 #80)
-#79 := (iff #76 #80)
-#82 := [rewrite]: #79
-#77 := (iff #47 #76)
-#74 := (= #41 #71)
-#68 := (ite #65 #38 f3)
-#72 := (= #68 #71)
-#73 := [rewrite]: #72
-#69 := (= #41 #68)
-#66 := (iff #11 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#75 := [trans #70 #73]: #74
-#78 := [monotonicity #75]: #77
-#84 := [trans #78 #82]: #83
-#87 := [monotonicity #84]: #86
-#92 := [trans #87 #90]: #91
-#62 := (iff #16 #59)
-#52 := (iff #10 #47)
-#55 := (not #52)
-#60 := (iff #55 #59)
-#61 := [rewrite]: #60
-#56 := (iff #16 #55)
-#53 := (iff #15 #52)
-#50 := (iff #14 #47)
-#44 := (= #41 #38)
-#48 := (iff #44 #47)
-#49 := [rewrite]: #48
-#45 := (iff #14 #44)
-#39 := (= #12 #38)
-#40 := [rewrite]: #39
-#42 := (= #13 #41)
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43 #40]: #45
-#51 := [trans #46 #49]: #50
-#54 := [monotonicity #51]: #53
-#57 := [monotonicity #54]: #56
-#63 := [trans #57 #61]: #62
-#94 := [trans #63 #92]: #93
-#36 := [asserted]: #16
-#95 := [mp #36 #94]: #88
-#105 := (not #88)
-#110 := (or #10 #80 #105)
-#111 := [def-axiom]: #110
-#113 := [unit-resolution #111 #95]: #112
-#119 := [unit-resolution #113 #118]: #10
-#120 := [hypothesis]: #64
-#122 := [th-lemma arith eq-propagate 0 0 #120 #119]: #121
-#130 := (= #81 f3)
-#128 := (= #71 f3)
-#102 := (or #65 #101)
-#103 := [def-axiom]: #102
-#123 := [unit-resolution #103 #120]: #101
-#129 := [symm #123]: #128
-#126 := (= #81 #71)
-#124 := (= #71 #81)
-#125 := [th-lemma arith eq-propagate 1 1 #120 #119]: #124
-#127 := [symm #125]: #126
-#131 := [trans #127 #129]: #130
-#132 := [trans #131 #122]: #80
-#133 := [unit-resolution #118 #132]: false
-#135 := [lemma #133]: #134
-#141 := [unit-resolution #135 #140]: #65
-#142 := [unit-resolution #99 #141]: #76
-#144 := (or #143 #116)
-#145 := [th-lemma arith triangle-eq]: #144
-#146 := [unit-resolution #145 #142]: #116
-#147 := [th-lemma arith farkas 1 1 #137 #146]: false
-#148 := [lemma #147]: #97
-#154 := (or #64 #10)
-#155 := [th-lemma arith farkas 1 1]: #154
-#156 := [unit-resolution #155 #149]: #10
-#108 := (or #58 #98)
-#106 := (or #58 #98 #105)
-#107 := [def-axiom]: #106
-#109 := [unit-resolution #107 #95]: #108
-#157 := [unit-resolution #109 #156]: #98
-#159 := (or #80 #158 #136)
-#160 := [th-lemma arith triangle-eq]: #159
-#161 := [unit-resolution #160 #157 #148]: #158
-#162 := [th-lemma arith farkas 1 1 #161 #153]: false
-#163 := [lemma #162]: #64
-#167 := [unit-resolution #103 #163]: #101
-#168 := (not #101)
-#169 := (or #168 #165)
-#170 := [th-lemma arith triangle-eq]: #169
-#171 := [unit-resolution #170 #167]: #165
-#172 := [unit-resolution #135 #163]: #80
-#173 := (or #98 #100)
-#174 := [th-lemma arith triangle-eq]: #173
-#175 := [unit-resolution #174 #172]: #100
-#176 := [unit-resolution #109 #172]: #58
-[th-lemma arith farkas 2 1 1 #176 #175 #171]: false
-unsat
-f4a9c9097a96542eacf222bbd562a802c9ede1c1 114 0
-#2 := false
-#9 := 0::Real
-decl f3 :: Real
-#8 := f3
-#38 := -1::Real
-#39 := (* -1::Real f3)
-#70 := (>= f3 0::Real)
-#77 := (ite #70 f3 #39)
-#91 := (* -1::Real #77)
-#130 := (+ #39 #91)
-#140 := (<= #130 0::Real)
-#117 := (= #39 #77)
-#71 := (not #70)
-#128 := (+ f3 #91)
-#129 := (<= #128 0::Real)
-#116 := (= f3 #77)
-#131 := [hypothesis]: #70
-#118 := (or #71 #116)
-#119 := [def-axiom]: #118
-#132 := [unit-resolution #119 #131]: #116
-#133 := (not #116)
-#134 := (or #133 #129)
-#135 := [th-lemma arith triangle-eq]: #134
-#136 := [unit-resolution #135 #132]: #129
-#86 := (>= #77 0::Real)
-#85 := (not #86)
-#97 := (ite #86 #77 #91)
-#102 := (= #77 #97)
-#105 := (not #102)
-#11 := (- f3)
-#10 := (< f3 0::Real)
-#12 := (ite #10 #11 f3)
-#14 := (- #12)
-#13 := (< #12 0::Real)
-#15 := (ite #13 #14 #12)
-#16 := (= #15 #12)
-#17 := (not #16)
-#108 := (iff #17 #105)
-#42 := (ite #10 #39 f3)
-#51 := (* -1::Real #42)
-#45 := (< #42 0::Real)
-#56 := (ite #45 #51 #42)
-#62 := (= #42 #56)
-#67 := (not #62)
-#106 := (iff #67 #105)
-#103 := (iff #62 #102)
-#100 := (= #56 #97)
-#94 := (ite #85 #91 #77)
-#98 := (= #94 #97)
-#99 := [rewrite]: #98
-#95 := (= #56 #94)
-#80 := (= #42 #77)
-#74 := (ite #71 #39 f3)
-#78 := (= #74 #77)
-#79 := [rewrite]: #78
-#75 := (= #42 #74)
-#72 := (iff #10 #71)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#81 := [trans #76 #79]: #80
-#92 := (= #51 #91)
-#93 := [monotonicity #81]: #92
-#89 := (iff #45 #85)
-#82 := (< #77 0::Real)
-#87 := (iff #82 #85)
-#88 := [rewrite]: #87
-#83 := (iff #45 #82)
-#84 := [monotonicity #81]: #83
-#90 := [trans #84 #88]: #89
-#96 := [monotonicity #90 #93 #81]: #95
-#101 := [trans #96 #99]: #100
-#104 := [monotonicity #81 #101]: #103
-#107 := [monotonicity #104]: #106
-#68 := (iff #17 #67)
-#65 := (iff #16 #62)
-#59 := (= #56 #42)
-#63 := (iff #59 #62)
-#64 := [rewrite]: #63
-#60 := (iff #16 #59)
-#43 := (= #12 #42)
-#40 := (= #11 #39)
-#41 := [rewrite]: #40
-#44 := [monotonicity #41]: #43
-#57 := (= #15 #56)
-#54 := (= #14 #51)
-#48 := (- #42)
-#52 := (= #48 #51)
-#53 := [rewrite]: #52
-#49 := (= #14 #48)
-#50 := [monotonicity #44]: #49
-#55 := [trans #50 #53]: #54
-#46 := (iff #13 #45)
-#47 := [monotonicity #44]: #46
-#58 := [monotonicity #47 #55 #44]: #57
-#61 := [monotonicity #58 #44]: #60
-#66 := [trans #61 #64]: #65
-#69 := [monotonicity #66]: #68
-#109 := [trans #69 #107]: #108
-#37 := [asserted]: #17
-#110 := [mp #37 #109]: #105
-#113 := (or #85 #102)
-#120 := [def-axiom]: #113
-#137 := [unit-resolution #120 #110]: #85
-#138 := [th-lemma arith farkas -1 1 1 #131 #137 #136]: false
-#139 := [lemma #138]: #71
-#114 := (or #70 #117)
-#115 := [def-axiom]: #114
-#142 := [unit-resolution #115 #139]: #117
-#143 := (not #117)
-#144 := (or #143 #140)
-#145 := [th-lemma arith triangle-eq]: #144
-#146 := [unit-resolution #145 #142]: #140
-[th-lemma arith farkas 1 1 1 #139 #137 #146]: false
-unsat
-d767bb2fd46823ea99ed2a2f48afd14fa043b714 57 0
-#2 := false
-#39 := 0::Real
-decl f4 :: Real
-#9 := f4
-decl f3 :: Real
-#8 := f3
-#36 := -1::Real
-#37 := (* -1::Real f4)
-#38 := (+ f3 #37)
-#40 := (<= #38 0::Real)
-#43 := (ite #40 f3 f4)
-#51 := (* -1::Real #43)
-#60 := (+ f4 #51)
-#74 := (>= #60 0::Real)
-#64 := (= f4 #43)
-#65 := (not #40)
-#63 := (= f3 #43)
-#68 := (not #63)
-#52 := (+ f3 #51)
-#50 := (>= #52 0::Real)
-#56 := (not #50)
-#10 := (<= f3 f4)
-#11 := (ite #10 f3 f4)
-#12 := (<= #11 f3)
-#13 := (not #12)
-#57 := (iff #13 #56)
-#54 := (iff #12 #50)
-#46 := (<= #43 f3)
-#49 := (iff #46 #50)
-#53 := [rewrite]: #49
-#47 := (iff #12 #46)
-#44 := (= #11 #43)
-#41 := (iff #10 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#55 := [trans #48 #53]: #54
-#58 := [monotonicity #55]: #57
-#33 := [asserted]: #13
-#59 := [mp #33 #58]: #56
-#67 := [hypothesis]: #63
-#69 := (or #68 #50)
-#70 := [th-lemma arith triangle-eq]: #69
-#71 := [unit-resolution #70 #67 #59]: false
-#72 := [lemma #71]: #68
-#66 := (or #65 #63)
-#61 := [def-axiom]: #66
-#75 := [unit-resolution #61 #72]: #65
-#62 := (or #40 #64)
-#35 := [def-axiom]: #62
-#76 := [unit-resolution #35 #75]: #64
-#77 := (not #64)
-#78 := (or #77 #74)
-#79 := [th-lemma arith triangle-eq]: #78
-#80 := [unit-resolution #79 #76]: #74
-[th-lemma arith farkas 1 1 1 #59 #75 #80]: false
-unsat
-a0d049d55a4b6d63a7a4486a6dd0f26ecaa6ada7 57 0
-#2 := false
-#39 := 0::Real
-decl f4 :: Real
-#9 := f4
-decl f3 :: Real
-#8 := f3
-#36 := -1::Real
-#37 := (* -1::Real f4)
-#38 := (+ f3 #37)
-#40 := (<= #38 0::Real)
-#43 := (ite #40 f3 f4)
-#50 := (* -1::Real #43)
-#51 := (+ f4 #50)
-#49 := (>= #51 0::Real)
-#56 := (not #49)
-#10 := (<= f3 f4)
-#11 := (ite #10 f3 f4)
-#12 := (<= #11 f4)
-#13 := (not #12)
-#57 := (iff #13 #56)
-#54 := (iff #12 #49)
-#46 := (<= #43 f4)
-#52 := (iff #46 #49)
-#53 := [rewrite]: #52
-#47 := (iff #12 #46)
-#44 := (= #11 #43)
-#41 := (iff #10 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#55 := [trans #48 #53]: #54
-#58 := [monotonicity #55]: #57
-#33 := [asserted]: #13
-#59 := [mp #33 #58]: #56
-#64 := (= f4 #43)
-#65 := (not #40)
-#69 := [hypothesis]: #40
-#60 := (+ f3 #50)
-#68 := (>= #60 0::Real)
-#63 := (= f3 #43)
-#66 := (or #65 #63)
-#61 := [def-axiom]: #66
-#70 := [unit-resolution #61 #69]: #63
-#71 := (not #63)
-#72 := (or #71 #68)
-#73 := [th-lemma arith triangle-eq]: #72
-#74 := [unit-resolution #73 #70]: #68
-#75 := [th-lemma arith farkas -1 1 1 #74 #59 #69]: false
-#76 := [lemma #75]: #65
-#62 := (or #40 #64)
-#35 := [def-axiom]: #62
-#77 := [unit-resolution #35 #76]: #64
-#78 := (not #64)
-#79 := (or #78 #49)
-#80 := [th-lemma arith triangle-eq]: #79
-[unit-resolution #80 #77 #59]: false
-unsat
-9c0695856bacfb99d21d573df84afab5e5b181f4 103 0
-#2 := false
-#48 := 0::Real
-decl f5 :: Real
-#11 := f5
-decl f4 :: Real
-#9 := f4
-#46 := -1::Real
-#56 := (* -1::Real f5)
-#66 := (+ f4 #56)
-#67 := (<= #66 0::Real)
-#70 := (ite #67 f4 f5)
-#78 := (* -1::Real #70)
-decl f3 :: Real
-#8 := f3
-#79 := (+ f3 #78)
-#77 := (>= #79 0::Real)
-#76 := (not #77)
-#57 := (+ f3 #56)
-#55 := (>= #57 0::Real)
-#54 := (not #55)
-#50 := (* -1::Real f4)
-#51 := (+ f3 #50)
-#49 := (>= #51 0::Real)
-#47 := (not #49)
-#60 := (and #47 #54)
-#63 := (not #60)
-#84 := (or #63 #76)
-#87 := (not #84)
-#14 := (<= f4 f5)
-#15 := (ite #14 f4 f5)
-#16 := (< f3 #15)
-#12 := (< f3 f5)
-#10 := (< f3 f4)
-#13 := (and #10 #12)
-#17 := (implies #13 #16)
-#18 := (not #17)
-#90 := (iff #18 #87)
-#39 := (not #13)
-#40 := (or #39 #16)
-#43 := (not #40)
-#88 := (iff #43 #87)
-#85 := (iff #40 #84)
-#82 := (iff #16 #76)
-#73 := (< f3 #70)
-#80 := (iff #73 #76)
-#81 := [rewrite]: #80
-#74 := (iff #16 #73)
-#71 := (= #15 #70)
-#68 := (iff #14 #67)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#83 := [trans #75 #81]: #82
-#64 := (iff #39 #63)
-#61 := (iff #13 #60)
-#58 := (iff #12 #54)
-#59 := [rewrite]: #58
-#52 := (iff #10 #47)
-#53 := [rewrite]: #52
-#62 := [monotonicity #53 #59]: #61
-#65 := [monotonicity #62]: #64
-#86 := [monotonicity #65 #83]: #85
-#89 := [monotonicity #86]: #88
-#44 := (iff #18 #43)
-#41 := (iff #17 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#91 := [trans #45 #89]: #90
-#38 := [asserted]: #18
-#92 := [mp #38 #91]: #87
-#96 := [not-or-elim #92]: #77
-#93 := [not-or-elim #92]: #60
-#95 := [and-elim #93]: #54
-#101 := (+ f5 #78)
-#118 := (<= #101 0::Real)
-#107 := (= f5 #70)
-#108 := (not #67)
-#106 := (= f4 #70)
-#113 := (not #106)
-#103 := (+ f4 #78)
-#100 := (<= #103 0::Real)
-#110 := (not #100)
-#94 := [and-elim #93]: #47
-#98 := [hypothesis]: #100
-#99 := [th-lemma arith farkas -1 -1 1 #98 #94 #96]: false
-#111 := [lemma #99]: #110
-#112 := [hypothesis]: #106
-#114 := (or #113 #100)
-#115 := [th-lemma arith triangle-eq]: #114
-#116 := [unit-resolution #115 #112 #111]: false
-#117 := [lemma #116]: #113
-#109 := (or #108 #106)
-#104 := [def-axiom]: #109
-#120 := [unit-resolution #104 #117]: #108
-#105 := (or #67 #107)
-#102 := [def-axiom]: #105
-#121 := [unit-resolution #102 #120]: #107
-#122 := (not #107)
-#123 := (or #122 #118)
-#124 := [th-lemma arith triangle-eq]: #123
-#125 := [unit-resolution #124 #121]: #118
-[th-lemma arith farkas -1 -1 1 #125 #95 #96]: false
-unsat
-b696c36b14d9aa5d8537f0123bf4636c0a97e771 94 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-decl f4 :: Real
-#9 := f4
-#41 := 0::Real
-#38 := -1::Real
-#39 := (* -1::Real f4)
-#40 := (+ f3 #39)
-#49 := (>= #40 0::Real)
-#51 := (ite #49 f4 f3)
-#42 := (<= #40 0::Real)
-#45 := (ite #42 f3 f4)
-#54 := (= #45 #51)
-#61 := (= f4 #51)
-#66 := (not #42)
-#64 := (= f3 #45)
-#106 := (not #64)
-#68 := (= f3 #51)
-#75 := (not #68)
-#76 := [hypothesis]: #75
-#72 := (or #49 #68)
-#73 := [def-axiom]: #72
-#77 := [unit-resolution #73 #76]: #49
-#69 := (not #49)
-#70 := (or #69 #61)
-#71 := [def-axiom]: #70
-#78 := [unit-resolution #71 #77]: #61
-#74 := (= f3 f4)
-#65 := (= f4 #45)
-#88 := (not #65)
-#57 := (not #54)
-#89 := (iff #57 #88)
-#86 := (iff #54 #65)
-#84 := (iff #65 #54)
-#79 := (= #51 #45)
-#82 := (iff #79 #54)
-#83 := [commutativity]: #82
-#80 := (iff #65 #79)
-#81 := [monotonicity #78]: #80
-#85 := [trans #81 #83]: #84
-#87 := [symm #85]: #86
-#90 := [monotonicity #87]: #89
-#12 := (<= f4 f3)
-#13 := (ite #12 f4 f3)
-#10 := (<= f3 f4)
-#11 := (ite #10 f3 f4)
-#14 := (= #11 #13)
-#15 := (not #14)
-#58 := (iff #15 #57)
-#55 := (iff #14 #54)
-#52 := (= #13 #51)
-#48 := (iff #12 #49)
-#50 := [rewrite]: #48
-#53 := [monotonicity #50]: #52
-#46 := (= #11 #45)
-#43 := (iff #10 #42)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#56 := [monotonicity #47 #53]: #55
-#59 := [monotonicity #56]: #58
-#35 := [asserted]: #15
-#60 := [mp #35 #59]: #57
-#91 := [mp #60 #90]: #88
-#63 := (or #42 #65)
-#37 := [def-axiom]: #63
-#92 := [unit-resolution #37 #91]: #42
-#95 := (or #74 #66)
-#93 := (or #74 #66 #69)
-#94 := [th-lemma arith triangle-eq]: #93
-#96 := [unit-resolution #94 #77]: #95
-#97 := [unit-resolution #96 #92]: #74
-#98 := [trans #97 #78]: #68
-#99 := [unit-resolution #76 #98]: false
-#100 := [lemma #99]: #68
-#102 := (= #45 f3)
-#101 := [hypothesis]: #64
-#103 := [symm #101]: #102
-#104 := [trans #103 #100]: #54
-#105 := [unit-resolution #60 #104]: false
-#107 := [lemma #105]: #106
-#67 := (or #66 #64)
-#62 := [def-axiom]: #67
-#108 := [unit-resolution #62 #107]: #66
-#110 := (or #49 #42)
-#111 := [th-lemma arith farkas 1 1]: #110
-#112 := [unit-resolution #111 #108]: #49
-#113 := [unit-resolution #71 #112]: #61
-#116 := (= #45 f4)
-#109 := [unit-resolution #37 #108]: #65
-#117 := [symm #109]: #116
-#118 := [trans #117 #113]: #54
-[unit-resolution #60 #118]: false
-unsat
-71758f92000b4f0bd1ce8b23e790788bff528cd0 68 0
-#2 := false
-#8 := 0::Real
-decl f3 :: Real
-#9 := f3
-#11 := (<= f3 0::Real)
-#12 := (ite #11 f3 0::Real)
-#13 := (= #12 0::Real)
-#79 := (= f3 0::Real)
-#53 := (>= f3 0::Real)
-#54 := (not #53)
-#62 := (or #13 #54)
-#67 := (not #62)
-#10 := (<= 0::Real f3)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#70 := (iff #15 #67)
-#36 := (= 0::Real #12)
-#42 := (not #10)
-#43 := (or #42 #36)
-#48 := (not #43)
-#68 := (iff #48 #67)
-#65 := (iff #43 #62)
-#59 := (or #54 #13)
-#63 := (iff #59 #62)
-#64 := [rewrite]: #63
-#60 := (iff #43 #59)
-#57 := (iff #36 #13)
-#58 := [rewrite]: #57
-#55 := (iff #42 #54)
-#51 := (iff #10 #53)
-#52 := [rewrite]: #51
-#56 := [monotonicity #52]: #55
-#61 := [monotonicity #56 #58]: #60
-#66 := [trans #61 #64]: #65
-#69 := [monotonicity #66]: #68
-#49 := (iff #15 #48)
-#46 := (iff #14 #43)
-#39 := (implies #10 #36)
-#44 := (iff #39 #43)
-#45 := [rewrite]: #44
-#40 := (iff #14 #39)
-#37 := (iff #13 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#47 := [trans #41 #45]: #46
-#50 := [monotonicity #47]: #49
-#71 := [trans #50 #69]: #70
-#35 := [asserted]: #15
-#72 := [mp #35 #71]: #67
-#75 := [not-or-elim #72]: #53
-#73 := (not #13)
-#74 := [not-or-elim #72]: #73
-#81 := (or #11 #13)
-#82 := [def-axiom]: #81
-#80 := [unit-resolution #82 #74]: #11
-#84 := (not #11)
-#77 := (or #79 #84 #54)
-#78 := [th-lemma arith triangle-eq]: #77
-#87 := [unit-resolution #78 #80 #75]: #79
-#89 := (= #12 f3)
-#83 := (= f3 #12)
-#85 := (or #84 #83)
-#86 := [def-axiom]: #85
-#88 := [unit-resolution #86 #80]: #83
-#90 := [symm #88]: #89
-#91 := [trans #90 #87]: #13
-[unit-resolution #74 #91]: false
-unsat
-944eddc125ab4f02dc35653f414c25fd1dfc289a 124 0
-#2 := false
-#13 := 0::Real
-decl f4 :: Real
-#9 := f4
-decl f3 :: Real
-#8 := f3
-#39 := -1::Real
-#41 := (* -1::Real f4)
-#54 := (+ f3 #41)
-#55 := (<= #54 0::Real)
-#58 := (ite #55 f3 f4)
-#106 := (* -1::Real #58)
-#107 := (+ f3 #106)
-#109 := (>= #107 0::Real)
-#94 := (= f3 #58)
-#108 := (+ f4 #106)
-#126 := (>= #108 0::Real)
-#95 := (= f4 #58)
-#96 := (not #55)
-#137 := [hypothesis]: #96
-#93 := (or #55 #95)
-#90 := [def-axiom]: #93
-#138 := [unit-resolution #90 #137]: #95
-#129 := (not #95)
-#130 := (or #129 #126)
-#131 := [th-lemma arith triangle-eq]: #130
-#139 := [unit-resolution #131 #138]: #126
-#40 := (* -1::Real f3)
-#42 := (+ #40 #41)
-#12 := (+ f3 f4)
-#61 := (>= #12 0::Real)
-#68 := (ite #61 #12 #42)
-#76 := (* -1::Real #68)
-#105 := (+ #42 #76)
-#125 := (<= #105 0::Real)
-#98 := (= #42 #68)
-#62 := (not #61)
-#110 := [hypothesis]: #61
-#77 := (+ #58 #76)
-#78 := (<= #77 0::Real)
-#83 := (not #78)
-#15 := (- #12)
-#14 := (< #12 0::Real)
-#16 := (ite #14 #15 #12)
-#10 := (<= f3 f4)
-#11 := (ite #10 f3 f4)
-#17 := (<= #11 #16)
-#18 := (not #17)
-#86 := (iff #18 #83)
-#45 := (ite #14 #42 #12)
-#48 := (<= #11 #45)
-#51 := (not #48)
-#84 := (iff #51 #83)
-#81 := (iff #48 #78)
-#73 := (<= #58 #68)
-#79 := (iff #73 #78)
-#80 := [rewrite]: #79
-#74 := (iff #48 #73)
-#71 := (= #45 #68)
-#65 := (ite #62 #42 #12)
-#69 := (= #65 #68)
-#70 := [rewrite]: #69
-#66 := (= #45 #65)
-#63 := (iff #14 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#72 := [trans #67 #70]: #71
-#59 := (= #11 #58)
-#56 := (iff #10 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#75 := [monotonicity #60 #72]: #74
-#82 := [trans #75 #80]: #81
-#85 := [monotonicity #82]: #84
-#52 := (iff #18 #51)
-#49 := (iff #17 #48)
-#46 := (= #16 #45)
-#43 := (= #15 #42)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#50 := [monotonicity #47]: #49
-#53 := [monotonicity #50]: #52
-#87 := [trans #53 #85]: #86
-#38 := [asserted]: #18
-#88 := [mp #38 #87]: #83
-#123 := (or #96 #62)
-#111 := [hypothesis]: #55
-#97 := (or #96 #94)
-#92 := [def-axiom]: #97
-#112 := [unit-resolution #92 #111]: #94
-#113 := (not #94)
-#114 := (or #113 #109)
-#115 := [th-lemma arith triangle-eq]: #114
-#116 := [unit-resolution #115 #112]: #109
-#103 := (+ #12 #76)
-#104 := (<= #103 0::Real)
-#91 := (= #12 #68)
-#99 := (or #62 #91)
-#100 := [def-axiom]: #99
-#117 := [unit-resolution #100 #110]: #91
-#118 := (not #91)
-#119 := (or #118 #104)
-#120 := [th-lemma arith triangle-eq]: #119
-#121 := [unit-resolution #120 #117]: #104
-#122 := [th-lemma arith farkas 2 2 2 1 1 #121 #116 #88 #111 #110]: false
-#124 := [lemma #122]: #123
-#127 := [unit-resolution #124 #110]: #96
-#128 := [unit-resolution #90 #127]: #95
-#132 := [unit-resolution #131 #128]: #126
-#133 := [th-lemma arith farkas 2 2 1 2 1 #121 #132 #127 #88 #110]: false
-#134 := [lemma #133]: #62
-#101 := (or #61 #98)
-#102 := [def-axiom]: #101
-#140 := [unit-resolution #102 #134]: #98
-#141 := (not #98)
-#142 := (or #141 #125)
-#143 := [th-lemma arith triangle-eq]: #142
-#144 := [unit-resolution #143 #140]: #125
-#145 := [th-lemma arith farkas 3/2 1/2 1 1 1 #134 #137 #88 #144 #139]: false
-#146 := [lemma #145]: #55
-#147 := [unit-resolution #92 #146]: #94
-#148 := [unit-resolution #115 #147]: #109
-[th-lemma arith farkas 1/2 3/2 1 1 1 #146 #134 #88 #144 #148]: false
-unsat
-c6a40e55705377f4a18787e86ca1381bc32f9048 57 0
-#2 := false
-#39 := 0::Real
-decl f3 :: Real
-#8 := f3
-decl f4 :: Real
-#9 := f4
-#36 := -1::Real
-#37 := (* -1::Real f4)
-#38 := (+ f3 #37)
-#40 := (<= #38 0::Real)
-#43 := (ite #40 f4 f3)
-#49 := (* -1::Real #43)
-#50 := (+ f3 #49)
-#51 := (<= #50 0::Real)
-#56 := (not #51)
-#10 := (<= f3 f4)
-#11 := (ite #10 f4 f3)
-#12 := (<= f3 #11)
-#13 := (not #12)
-#57 := (iff #13 #56)
-#54 := (iff #12 #51)
-#46 := (<= f3 #43)
-#52 := (iff #46 #51)
-#53 := [rewrite]: #52
-#47 := (iff #12 #46)
-#44 := (= #11 #43)
-#41 := (iff #10 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#55 := [trans #48 #53]: #54
-#58 := [monotonicity #55]: #57
-#33 := [asserted]: #13
-#59 := [mp #33 #58]: #56
-#64 := (= f3 #43)
-#65 := (not #40)
-#69 := [hypothesis]: #40
-#60 := (+ f4 #49)
-#67 := (<= #60 0::Real)
-#63 := (= f4 #43)
-#66 := (or #65 #63)
-#61 := [def-axiom]: #66
-#70 := [unit-resolution #61 #69]: #63
-#71 := (not #63)
-#72 := (or #71 #67)
-#73 := [th-lemma arith triangle-eq]: #72
-#74 := [unit-resolution #73 #70]: #67
-#75 := [th-lemma arith farkas 1 -1 1 #74 #59 #69]: false
-#76 := [lemma #75]: #65
-#62 := (or #40 #64)
-#35 := [def-axiom]: #62
-#77 := [unit-resolution #35 #76]: #64
-#78 := (not #64)
-#79 := (or #78 #51)
-#80 := [th-lemma arith triangle-eq]: #79
-[unit-resolution #80 #77 #59]: false
-unsat
-08f86b81fe9ac7c3b38ce6a48d6dd15649d787f7 57 0
-#2 := false
-#38 := 0::Real
-decl f4 :: Real
-#9 := f4
-decl f3 :: Real
-#8 := f3
-#36 := -1::Real
-#40 := (* -1::Real f4)
-#41 := (+ f3 #40)
-#39 := (>= #41 0::Real)
-#43 := (ite #39 f3 f4)
-#49 := (* -1::Real #43)
-#60 := (+ f4 #49)
-#73 := (<= #60 0::Real)
-#64 := (= f4 #43)
-#65 := (not #39)
-#63 := (= f3 #43)
-#68 := (not #63)
-#50 := (+ f3 #49)
-#51 := (<= #50 0::Real)
-#56 := (not #51)
-#10 := (<= f4 f3)
-#11 := (ite #10 f3 f4)
-#12 := (<= f3 #11)
-#13 := (not #12)
-#57 := (iff #13 #56)
-#54 := (iff #12 #51)
-#46 := (<= f3 #43)
-#52 := (iff #46 #51)
-#53 := [rewrite]: #52
-#47 := (iff #12 #46)
-#44 := (= #11 #43)
-#37 := (iff #10 #39)
-#42 := [rewrite]: #37
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#55 := [trans #48 #53]: #54
-#58 := [monotonicity #55]: #57
-#33 := [asserted]: #13
-#59 := [mp #33 #58]: #56
-#67 := [hypothesis]: #63
-#69 := (or #68 #51)
-#70 := [th-lemma arith triangle-eq]: #69
-#71 := [unit-resolution #70 #67 #59]: false
-#72 := [lemma #71]: #68
-#66 := (or #65 #63)
-#61 := [def-axiom]: #66
-#75 := [unit-resolution #61 #72]: #65
-#62 := (or #39 #64)
-#35 := [def-axiom]: #62
-#76 := [unit-resolution #35 #75]: #64
-#77 := (not #64)
-#78 := (or #77 #73)
-#79 := [th-lemma arith triangle-eq]: #78
-#80 := [unit-resolution #79 #76]: #73
-[th-lemma arith farkas 1 1 1 #59 #75 #80]: false
-unsat
-a8742c9687e5f318c69c4d286746cf373c1fed40 103 0
-#2 := false
-#48 := 0::Real
-decl f3 :: Real
-#8 := f3
-decl f5 :: Real
-#11 := f5
-#46 := -1::Real
-#54 := (* -1::Real f5)
-#66 := (+ f3 #54)
-#67 := (<= #66 0::Real)
-#70 := (ite #67 f5 f3)
-#76 := (* -1::Real #70)
-decl f4 :: Real
-#9 := f4
-#77 := (+ f4 #76)
-#78 := (<= #77 0::Real)
-#79 := (not #78)
-#55 := (+ f4 #54)
-#56 := (<= #55 0::Real)
-#57 := (not #56)
-#50 := (* -1::Real f4)
-#51 := (+ f3 #50)
-#49 := (>= #51 0::Real)
-#47 := (not #49)
-#60 := (and #47 #57)
-#63 := (not #60)
-#84 := (or #63 #79)
-#87 := (not #84)
-#14 := (<= f3 f5)
-#15 := (ite #14 f5 f3)
-#16 := (< #15 f4)
-#12 := (< f5 f4)
-#10 := (< f3 f4)
-#13 := (and #10 #12)
-#17 := (implies #13 #16)
-#18 := (not #17)
-#90 := (iff #18 #87)
-#39 := (not #13)
-#40 := (or #39 #16)
-#43 := (not #40)
-#88 := (iff #43 #87)
-#85 := (iff #40 #84)
-#82 := (iff #16 #79)
-#73 := (< #70 f4)
-#80 := (iff #73 #79)
-#81 := [rewrite]: #80
-#74 := (iff #16 #73)
-#71 := (= #15 #70)
-#68 := (iff #14 #67)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#75 := [monotonicity #72]: #74
-#83 := [trans #75 #81]: #82
-#64 := (iff #39 #63)
-#61 := (iff #13 #60)
-#58 := (iff #12 #57)
-#59 := [rewrite]: #58
-#52 := (iff #10 #47)
-#53 := [rewrite]: #52
-#62 := [monotonicity #53 #59]: #61
-#65 := [monotonicity #62]: #64
-#86 := [monotonicity #65 #83]: #85
-#89 := [monotonicity #86]: #88
-#44 := (iff #18 #43)
-#41 := (iff #17 #40)
-#42 := [rewrite]: #41
-#45 := [monotonicity #42]: #44
-#91 := [trans #45 #89]: #90
-#38 := [asserted]: #18
-#92 := [mp #38 #91]: #87
-#96 := [not-or-elim #92]: #78
-#93 := [not-or-elim #92]: #60
-#94 := [and-elim #93]: #47
-#100 := (+ f3 #76)
-#119 := (>= #100 0::Real)
-#107 := (= f3 #70)
-#108 := (not #67)
-#106 := (= f5 #70)
-#113 := (not #106)
-#103 := (+ f5 #76)
-#101 := (>= #103 0::Real)
-#110 := (not #101)
-#95 := [and-elim #93]: #57
-#98 := [hypothesis]: #101
-#99 := [th-lemma arith farkas -1 -1 1 #98 #95 #96]: false
-#111 := [lemma #99]: #110
-#112 := [hypothesis]: #106
-#114 := (or #113 #101)
-#115 := [th-lemma arith triangle-eq]: #114
-#116 := [unit-resolution #115 #112 #111]: false
-#117 := [lemma #116]: #113
-#109 := (or #108 #106)
-#104 := [def-axiom]: #109
-#120 := [unit-resolution #104 #117]: #108
-#105 := (or #67 #107)
-#102 := [def-axiom]: #105
-#121 := [unit-resolution #102 #120]: #107
-#122 := (not #107)
-#123 := (or #122 #119)
-#124 := [th-lemma arith triangle-eq]: #123
-#125 := [unit-resolution #124 #121]: #119
-[th-lemma arith farkas -1 1 1 #125 #94 #96]: false
-unsat
-cf9d7301e2783e3a9529677f7376e191e2553752 96 0
-#2 := false
-decl f4 :: Real
-#9 := f4
-decl f3 :: Real
-#8 := f3
-#41 := 0::Real
-#38 := -1::Real
-#39 := (* -1::Real f4)
-#40 := (+ f3 #39)
-#49 := (>= #40 0::Real)
-#51 := (ite #49 f3 f4)
-#42 := (<= #40 0::Real)
-#45 := (ite #42 f4 f3)
-#54 := (= #45 #51)
-#61 := (= f3 #51)
-#66 := (not #42)
-#64 := (= f4 #45)
-#108 := (not #64)
-#68 := (= f4 #51)
-#75 := (not #68)
-#76 := [hypothesis]: #75
-#72 := (or #49 #68)
-#73 := [def-axiom]: #72
-#77 := [unit-resolution #73 #76]: #49
-#69 := (not #49)
-#70 := (or #69 #61)
-#71 := [def-axiom]: #70
-#78 := [unit-resolution #71 #77]: #61
-#98 := (= f4 f3)
-#74 := (= f3 f4)
-#65 := (= f3 #45)
-#88 := (not #65)
-#57 := (not #54)
-#89 := (iff #57 #88)
-#86 := (iff #54 #65)
-#84 := (iff #65 #54)
-#79 := (= #51 #45)
-#82 := (iff #79 #54)
-#83 := [commutativity]: #82
-#80 := (iff #65 #79)
-#81 := [monotonicity #78]: #80
-#85 := [trans #81 #83]: #84
-#87 := [symm #85]: #86
-#90 := [monotonicity #87]: #89
-#12 := (<= f4 f3)
-#13 := (ite #12 f3 f4)
-#10 := (<= f3 f4)
-#11 := (ite #10 f4 f3)
-#14 := (= #11 #13)
-#15 := (not #14)
-#58 := (iff #15 #57)
-#55 := (iff #14 #54)
-#52 := (= #13 #51)
-#48 := (iff #12 #49)
-#50 := [rewrite]: #48
-#53 := [monotonicity #50]: #52
-#46 := (= #11 #45)
-#43 := (iff #10 #42)
-#44 := [rewrite]: #43
-#47 := [monotonicity #44]: #46
-#56 := [monotonicity #47 #53]: #55
-#59 := [monotonicity #56]: #58
-#35 := [asserted]: #15
-#60 := [mp #35 #59]: #57
-#91 := [mp #60 #90]: #88
-#63 := (or #42 #65)
-#37 := [def-axiom]: #63
-#92 := [unit-resolution #37 #91]: #42
-#95 := (or #74 #66)
-#93 := (or #74 #66 #69)
-#94 := [th-lemma arith triangle-eq]: #93
-#96 := [unit-resolution #94 #77]: #95
-#97 := [unit-resolution #96 #92]: #74
-#99 := [symm #97]: #98
-#100 := [trans #99 #78]: #68
-#101 := [unit-resolution #76 #100]: false
-#102 := [lemma #101]: #68
-#104 := (= #45 f4)
-#103 := [hypothesis]: #64
-#105 := [symm #103]: #104
-#106 := [trans #105 #102]: #54
-#107 := [unit-resolution #60 #106]: false
-#109 := [lemma #107]: #108
-#67 := (or #66 #64)
-#62 := [def-axiom]: #67
-#110 := [unit-resolution #62 #109]: #66
-#112 := (or #49 #42)
-#113 := [th-lemma arith farkas 1 1]: #112
-#114 := [unit-resolution #113 #110]: #49
-#115 := [unit-resolution #71 #114]: #61
-#118 := (= #45 f3)
-#111 := [unit-resolution #37 #110]: #65
-#119 := [symm #111]: #118
-#120 := [trans #119 #115]: #54
-[unit-resolution #60 #120]: false
-unsat
-d5aa9479bc1880b81fc3a8f2f0ffecc7788dfa18 66 0
-#2 := false
-decl f3 :: Real
-#9 := f3
-#8 := 0::Real
-#11 := (<= f3 0::Real)
-#12 := (ite #11 0::Real f3)
-#36 := (= f3 #12)
-#87 := (= 0::Real #12)
-#81 := (= #12 0::Real)
-#71 := (not #36)
-#53 := (>= f3 0::Real)
-#54 := (not #53)
-#60 := (or #36 #54)
-#65 := (not #60)
-#13 := (= #12 f3)
-#10 := (<= 0::Real f3)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#68 := (iff #15 #65)
-#42 := (not #10)
-#43 := (or #42 #36)
-#48 := (not #43)
-#66 := (iff #48 #65)
-#63 := (iff #43 #60)
-#57 := (or #54 #36)
-#61 := (iff #57 #60)
-#62 := [rewrite]: #61
-#58 := (iff #43 #57)
-#55 := (iff #42 #54)
-#51 := (iff #10 #53)
-#52 := [rewrite]: #51
-#56 := [monotonicity #52]: #55
-#59 := [monotonicity #56]: #58
-#64 := [trans #59 #62]: #63
-#67 := [monotonicity #64]: #66
-#49 := (iff #15 #48)
-#46 := (iff #14 #43)
-#39 := (implies #10 #36)
-#44 := (iff #39 #43)
-#45 := [rewrite]: #44
-#40 := (iff #14 #39)
-#37 := (iff #13 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#47 := [trans #41 #45]: #46
-#50 := [monotonicity #47]: #49
-#69 := [trans #50 #67]: #68
-#35 := [asserted]: #15
-#70 := [mp #35 #69]: #65
-#72 := [not-or-elim #70]: #71
-#79 := (or #11 #36)
-#80 := [def-axiom]: #79
-#78 := [unit-resolution #80 #72]: #11
-#82 := (not #11)
-#83 := (or #82 #81)
-#84 := [def-axiom]: #83
-#75 := [unit-resolution #84 #78]: #81
-#88 := [symm #75]: #87
-#77 := (= f3 0::Real)
-#73 := [not-or-elim #70]: #53
-#76 := (or #77 #82 #54)
-#85 := [th-lemma arith triangle-eq]: #76
-#86 := [unit-resolution #85 #78 #73]: #77
-#89 := [trans #86 #88]: #36
-[unit-resolution #72 #89]: false
-unsat
-7f8cef3bf22a3ab0ad21a7a5668eaf6fccce9da2 214 0
-#2 := false
-#9 := 0::Real
-decl f4 :: Real
-#14 := f4
-#43 := -1::Real
-#58 := (* -1::Real f4)
-#94 := (>= f4 0::Real)
-#101 := (ite #94 f4 #58)
-#106 := (* -1::Real #101)
-#161 := (+ #58 #106)
-#183 := (<= #161 0::Real)
-#137 := (= #58 #101)
-#95 := (not #94)
-decl f3 :: Real
-#8 := f3
-#112 := (+ f3 #58)
-#113 := (<= #112 0::Real)
-#116 := (ite #113 f4 f3)
-#155 := (* -1::Real #116)
-#156 := (+ f4 #155)
-#157 := (<= #156 0::Real)
-#158 := (+ f3 #155)
-#193 := (<= #158 0::Real)
-#149 := (= f3 #116)
-#150 := (not #113)
-#148 := (= f4 #116)
-#195 := [hypothesis]: #113
-#151 := (or #150 #148)
-#152 := [def-axiom]: #151
-#196 := [unit-resolution #152 #195]: #148
-#197 := (not #148)
-#198 := (or #197 #157)
-#199 := [th-lemma arith triangle-eq]: #198
-#200 := [unit-resolution #199 #196]: #157
-#179 := (not #157)
-#191 := (or #95 #179)
-#159 := (+ f4 #106)
-#160 := (<= #159 0::Real)
-#136 := (= f4 #101)
-#165 := [hypothesis]: #94
-#144 := (or #95 #136)
-#145 := [def-axiom]: #144
-#166 := [unit-resolution #145 #165]: #136
-#167 := (not #136)
-#168 := (or #167 #160)
-#169 := [th-lemma arith triangle-eq]: #168
-#170 := [unit-resolution #169 #166]: #160
-#44 := (* -1::Real f3)
-#79 := (>= f3 0::Real)
-#86 := (ite #79 f3 #44)
-#91 := (* -1::Real #86)
-#164 := (+ #44 #91)
-#182 := (<= #164 0::Real)
-#141 := (= #44 #86)
-#80 := (not #79)
-#177 := [hypothesis]: #157
-#180 := (or #80 #95 #179)
-#125 := (+ #101 #116)
-#126 := (+ #86 #125)
-#123 := (>= #126 0::Real)
-#129 := (not #123)
-#19 := (<= f3 f4)
-#20 := (ite #19 f4 f3)
-#16 := (- f4)
-#15 := (< f4 0::Real)
-#17 := (ite #15 #16 f4)
-#11 := (- f3)
-#10 := (< f3 0::Real)
-#12 := (ite #10 #11 f3)
-#13 := (- #12)
-#18 := (- #13 #17)
-#21 := (<= #18 #20)
-#22 := (not #21)
-#132 := (iff #22 #129)
-#61 := (ite #15 #58 f4)
-#67 := (* -1::Real #61)
-#47 := (ite #10 #44 f3)
-#53 := (* -1::Real #47)
-#68 := (+ #53 #67)
-#73 := (<= #68 #20)
-#76 := (not #73)
-#130 := (iff #76 #129)
-#127 := (iff #73 #123)
-#109 := (+ #91 #106)
-#119 := (<= #109 #116)
-#122 := (iff #119 #123)
-#124 := [rewrite]: #122
-#120 := (iff #73 #119)
-#117 := (= #20 #116)
-#114 := (iff #19 #113)
-#115 := [rewrite]: #114
-#118 := [monotonicity #115]: #117
-#110 := (= #68 #109)
-#107 := (= #67 #106)
-#104 := (= #61 #101)
-#98 := (ite #95 #58 f4)
-#102 := (= #98 #101)
-#103 := [rewrite]: #102
-#99 := (= #61 #98)
-#96 := (iff #15 #95)
-#97 := [rewrite]: #96
-#100 := [monotonicity #97]: #99
-#105 := [trans #100 #103]: #104
-#108 := [monotonicity #105]: #107
-#92 := (= #53 #91)
-#89 := (= #47 #86)
-#83 := (ite #80 #44 f3)
-#87 := (= #83 #86)
-#88 := [rewrite]: #87
-#84 := (= #47 #83)
-#81 := (iff #10 #80)
-#82 := [rewrite]: #81
-#85 := [monotonicity #82]: #84
-#90 := [trans #85 #88]: #89
-#93 := [monotonicity #90]: #92
-#111 := [monotonicity #93 #108]: #110
-#121 := [monotonicity #111 #118]: #120
-#128 := [trans #121 #124]: #127
-#131 := [monotonicity #128]: #130
-#77 := (iff #22 #76)
-#74 := (iff #21 #73)
-#71 := (= #18 #68)
-#64 := (- #53 #61)
-#69 := (= #64 #68)
-#70 := [rewrite]: #69
-#65 := (= #18 #64)
-#62 := (= #17 #61)
-#59 := (= #16 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#56 := (= #13 #53)
-#50 := (- #47)
-#54 := (= #50 #53)
-#55 := [rewrite]: #54
-#51 := (= #13 #50)
-#48 := (= #12 #47)
-#45 := (= #11 #44)
-#46 := [rewrite]: #45
-#49 := [monotonicity #46]: #48
-#52 := [monotonicity #49]: #51
-#57 := [trans #52 #55]: #56
-#66 := [monotonicity #57 #63]: #65
-#72 := [trans #66 #70]: #71
-#75 := [monotonicity #72]: #74
-#78 := [monotonicity #75]: #77
-#133 := [trans #78 #131]: #132
-#42 := [asserted]: #22
-#134 := [mp #42 #133]: #129
-#162 := (+ f3 #91)
-#163 := (<= #162 0::Real)
-#140 := (= f3 #86)
-#171 := [hypothesis]: #79
-#142 := (or #80 #140)
-#143 := [def-axiom]: #142
-#172 := [unit-resolution #143 #171]: #140
-#173 := (not #140)
-#174 := (or #173 #163)
-#175 := [th-lemma arith triangle-eq]: #174
-#176 := [unit-resolution #175 #172]: #163
-#178 := [th-lemma arith farkas -2 1 -1 1 1 1 #165 #177 #171 #176 #134 #170]: false
-#181 := [lemma #178]: #180
-#184 := [unit-resolution #181 #165 #177]: #80
-#138 := (or #79 #141)
-#139 := [def-axiom]: #138
-#185 := [unit-resolution #139 #184]: #141
-#186 := (not #141)
-#187 := (or #186 #182)
-#188 := [th-lemma arith triangle-eq]: #187
-#189 := [unit-resolution #188 #185]: #182
-#190 := [th-lemma arith farkas 2 1 1 1 1 1 #165 #177 #134 #184 #189 #170]: false
-#192 := [lemma #190]: #191
-#201 := [unit-resolution #192 #200]: #95
-#146 := (or #94 #137)
-#147 := [def-axiom]: #146
-#202 := [unit-resolution #147 #201]: #137
-#203 := (not #137)
-#204 := (or #203 #183)
-#205 := [th-lemma arith triangle-eq]: #204
-#206 := [unit-resolution #205 #202]: #183
-#207 := (or #80 #94 #150)
-#208 := [th-lemma arith assign-bounds 1 1]: #207
-#209 := [unit-resolution #208 #201 #195]: #80
-#210 := [unit-resolution #139 #209]: #141
-#211 := [unit-resolution #188 #210]: #182
-#212 := [th-lemma arith farkas 1 1 1 1 1 #200 #134 #209 #211 #206]: false
-#213 := [lemma #212]: #150
-#153 := (or #113 #149)
-#154 := [def-axiom]: #153
-#224 := [unit-resolution #154 #213]: #149
-#225 := (not #149)
-#226 := (or #225 #193)
-#227 := [th-lemma arith triangle-eq]: #226
-#228 := [unit-resolution #227 #224]: #193
-#231 := (not #193)
-#232 := (or #157 #113 #231)
-#233 := [th-lemma arith assign-bounds 1 1]: #232
-#234 := [unit-resolution #233 #213 #228]: #157
-#235 := [unit-resolution #192 #234]: #95
-#236 := [unit-resolution #147 #235]: #137
-#237 := [unit-resolution #205 #236]: #183
-#216 := [hypothesis]: #80
-#217 := (or #95 #79 #113)
-#218 := [th-lemma arith assign-bounds 1 1]: #217
-#219 := [unit-resolution #218 #216 #213]: #95
-#220 := [unit-resolution #147 #219]: #137
-#221 := [unit-resolution #205 #220]: #183
-#222 := [unit-resolution #139 #216]: #141
-#223 := [unit-resolution #188 #222]: #182
-#229 := [th-lemma arith farkas 1 1 1 1 1 1 #216 #213 #228 #134 #223 #221]: false
-#230 := [lemma #229]: #79
-#238 := [unit-resolution #143 #230]: #140
-#239 := [unit-resolution #175 #238]: #163
-[th-lemma arith farkas 1 1 1 1 1 1 #213 #228 #134 #230 #239 #237]: false
-unsat
-aa55c98f65865ce1fb459036f5d6d595375e9913 18 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-#9 := (<= f3 f3)
+#7 := 0::Real
+#9 := (< 0::Real 1::Real)
 #10 := (not #9)
 #40 := (iff #10 false)
 #1 := true
@@ -50123,7480 +45631,8885 @@
 #30 := [asserted]: #10
 [mp #30 #41]: false
 unsat
-881af9588484ddb06449bbce47773b99bf77b5e8 50 0
-#2 := false
-#47 := 0::Real
+71711cc01c8c80c87657e4ad599846d287b28e35 18 0
+#2 := false
+#8 := 1::Real
+#7 := 0::Real
+#9 := (<= 0::Real 1::Real)
+#10 := (not #9)
+#40 := (iff #10 false)
+#1 := true
+#35 := (not true)
+#38 := (iff #35 false)
+#39 := [rewrite]: #38
+#36 := (iff #10 #35)
+#33 := (iff #9 true)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#41 := [trans #37 #39]: #40
+#30 := [asserted]: #10
+[mp #30 #41]: false
+unsat
+ea4d13d40e3f40148fe15c5ac2bbd56a3256548a 40 0
+#2 := false
+#11 := 567::Real
+#9 := 345::Real
+#7 := 123::Real
+#8 := (- 123::Real)
+#10 := (+ #8 345::Real)
+#12 := (< #10 567::Real)
+#13 := (not #12)
+#61 := (iff #13 false)
+#41 := 222::Real
+#46 := (< 222::Real 567::Real)
+#49 := (not #46)
+#59 := (iff #49 false)
+#1 := true
+#54 := (not true)
+#57 := (iff #54 false)
+#58 := [rewrite]: #57
+#55 := (iff #49 #54)
+#52 := (iff #46 true)
+#53 := [rewrite]: #52
+#56 := [monotonicity #53]: #55
+#60 := [trans #56 #58]: #59
+#50 := (iff #13 #49)
+#47 := (iff #12 #46)
+#44 := (= #10 222::Real)
+#35 := -123::Real
+#38 := (+ -123::Real 345::Real)
+#42 := (= #38 222::Real)
+#43 := [rewrite]: #42
+#39 := (= #10 #38)
+#36 := (= #8 -123::Real)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#45 := [trans #40 #43]: #44
+#48 := [monotonicity #45]: #47
+#51 := [monotonicity #48]: #50
+#62 := [trans #51 #60]: #61
+#34 := [asserted]: #13
+[mp #34 #62]: false
+unsat
+f37864df8bd3862357cec2b2b3e0079ce8f89a8d 18 0
+#2 := false
+#8 := 2345678901::Real
+#7 := 123456789::Real
+#9 := (< 123456789::Real 2345678901::Real)
+#10 := (not #9)
+#41 := (iff #10 false)
+#1 := true
+#36 := (not true)
+#39 := (iff #36 false)
+#40 := [rewrite]: #39
+#37 := (iff #10 #36)
+#34 := (iff #9 true)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#42 := [trans #38 #40]: #41
+#31 := [asserted]: #10
+[mp #31 #42]: false
+unsat
+848068d33a75fce3ca7ec5b7cc3564150c9afd1d 30 0
+#2 := false
+#9 := 2345678901::Real
+#7 := 123456789::Real
+#8 := (- 123456789::Real)
+#10 := (< #8 2345678901::Real)
+#11 := (not #10)
+#51 := (iff #11 false)
+#33 := -123456789::Real
+#36 := (< -123456789::Real 2345678901::Real)
+#39 := (not #36)
+#49 := (iff #39 false)
+#1 := true
+#44 := (not true)
+#47 := (iff #44 false)
+#48 := [rewrite]: #47
+#45 := (iff #39 #44)
+#42 := (iff #36 true)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#40 := (iff #11 #39)
+#37 := (iff #10 #36)
+#34 := (= #8 -123456789::Real)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#52 := [trans #41 #50]: #51
+#32 := [asserted]: #11
+[mp #32 #52]: false
+unsat
[phone]dfd970c057cb8150c9652aec59e07704 26 0
+#2 := false
+decl f3 :: Real
+#7 := f3
+#8 := 0::Real
+#9 := (+ f3 0::Real)
+#10 := (= #9 f3)
+#11 := (not #10)
+#45 := (iff #11 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #11 #40)
+#38 := (iff #10 true)
+#33 := (= f3 f3)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #10 #33)
+#32 := [rewrite]: #10
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#31 := [asserted]: #11
+[mp #31 #46]: false
+unsat
+6757cdf387098ea19b45fbcbcb515eeb487bf8f8 26 0
+#2 := false
+decl f3 :: Real
+#8 := f3
+#7 := 0::Real
+#9 := (+ 0::Real f3)
+#10 := (= #9 f3)
+#11 := (not #10)
+#45 := (iff #11 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #11 #40)
+#38 := (iff #10 true)
+#33 := (= f3 f3)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #10 #33)
+#32 := [rewrite]: #10
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#31 := [asserted]: #11
+[mp #31 #46]: false
+unsat
+3f2d195dd68cf890f1ca7d83a830eeccc0d57255 29 0
+#2 := false
+decl f3 :: Real
+#7 := f3
+decl f4 :: Real
+#8 := f4
+#10 := (+ f4 f3)
+#9 := (+ f3 f4)
+#11 := (= #9 #10)
+#12 := (not #11)
+#48 := (iff #12 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (iff #11 true)
+#36 := (= #9 #9)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #11 #36)
+#34 := (= #10 #9)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#33 := [asserted]: #12
+[mp #33 #49]: false
+unsat
+e8a6e64d56abb2bc442b2a42c9dd8c760a528cdb 33 0
+#2 := false
+decl f5 :: Real
+#9 := f5
+decl f4 :: Real
+#8 := f4
+decl f3 :: Real
+#7 := f3
+#12 := (+ f3 f4)
+#13 := (+ #12 f5)
+#10 := (+ f4 f5)
+#11 := (+ f3 #10)
+#14 := (= #11 #13)
+#15 := (not #14)
+#51 := (iff #15 false)
+#1 := true
+#46 := (not true)
+#49 := (iff #46 false)
+#50 := [rewrite]: #49
+#47 := (iff #15 #46)
+#44 := (iff #14 true)
+#39 := (= #11 #11)
+#42 := (iff #39 true)
+#43 := [rewrite]: #42
+#40 := (iff #14 #39)
+#37 := (= #13 #11)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#48 := [monotonicity #45]: #47
+#52 := [trans #48 #50]: #51
+#36 := [asserted]: #15
+[mp #36 #52]: false
+unsat
+da67a8554477e4765556fd0a3f279034168c96a4 45 0
+#2 := false
+decl f4 :: Real
+#8 := f4
+#12 := (- f4)
+decl f3 :: Real
+#7 := f3
+#13 := (= f3 #12)
+#10 := 0::Real
+#9 := (+ f3 f4)
+#11 := (= #9 0::Real)
+#14 := (iff #11 #13)
+#15 := (not #14)
+#64 := (iff #15 false)
+#36 := -1::Real
+#37 := (* -1::Real f4)
+#40 := (= f3 #37)
+#49 := (not #11)
+#50 := (iff #49 #40)
+#62 := (iff #50 false)
+#57 := (iff #49 #11)
+#60 := (iff #57 false)
+#61 := [rewrite]: #60
+#58 := (iff #50 #57)
+#55 := (iff #40 #11)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#63 := [trans #59 #61]: #62
+#53 := (iff #15 #50)
+#43 := (iff #11 #40)
+#46 := (not #43)
+#51 := (iff #46 #50)
+#52 := [rewrite]: #51
+#47 := (iff #15 #46)
+#44 := (iff #14 #43)
+#41 := (iff #13 #40)
+#38 := (= #12 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#54 := [trans #48 #52]: #53
+#65 := [trans #54 #63]: #64
+#35 := [asserted]: #15
+[mp #35 #65]: false
+unsat
+6811cc1a4bfad536ab1a6a586c61daecfd29788f 26 0
+#2 := false
+#7 := 1::Real
+#8 := (- 1::Real)
+#9 := (= #8 #8)
+#10 := (not #9)
+#47 := (iff #10 false)
+#1 := true
+#42 := (not true)
+#45 := (iff #42 false)
+#46 := [rewrite]: #45
+#43 := (iff #10 #42)
+#40 := (iff #9 true)
+#32 := -1::Real
+#35 := (= -1::Real -1::Real)
+#38 := (iff #35 true)
+#39 := [rewrite]: #38
+#36 := (iff #9 #35)
+#33 := (= #8 -1::Real)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34 #34]: #36
+#41 := [trans #37 #39]: #40
+#44 := [monotonicity #41]: #43
+#48 := [trans #44 #46]: #47
+#31 := [asserted]: #10
+[mp #31 #48]: false
+unsat
+aa2cb1d7717b9c49c4e48402428e4ddb7de5523b 26 0
+#2 := false
+#7 := 3::Real
+#8 := (- 3::Real)
+#9 := (= #8 #8)
+#10 := (not #9)
+#47 := (iff #10 false)
+#1 := true
+#42 := (not true)
+#45 := (iff #42 false)
+#46 := [rewrite]: #45
+#43 := (iff #10 #42)
+#40 := (iff #9 true)
+#32 := -3::Real
+#35 := (= -3::Real -3::Real)
+#38 := (iff #35 true)
+#39 := [rewrite]: #38
+#36 := (iff #9 #35)
+#33 := (= #8 -3::Real)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34 #34]: #36
+#41 := [trans #37 #39]: #40
+#44 := [monotonicity #41]: #43
+#48 := [trans #44 #46]: #47
+#31 := [asserted]: #10
+[mp #31 #48]: false
+unsat
+b82f2c57c3991807ae36eb3352dd673d6ee809c4 53 0
+#2 := false
+decl f3 :: Real
+#7 := f3
+#9 := 0::Real
+#11 := (< 0::Real f3)
+#8 := (- f3)
+#10 := (< #8 0::Real)
+#12 := (iff #10 #11)
+#13 := (not #12)
+#73 := (iff #13 false)
+#34 := -1::Real
+#35 := (* -1::Real f3)
+#38 := (< #35 0::Real)
+#47 := (not #38)
+#48 := (iff #47 #11)
+#71 := (iff #48 false)
+#53 := (<= f3 0::Real)
+#54 := (not #53)
+#66 := (iff #53 #54)
+#69 := (iff #66 false)
+#70 := [rewrite]: #69
+#67 := (iff #48 #66)
+#64 := (iff #11 #54)
+#65 := [rewrite]: #64
+#62 := (iff #47 #53)
+#57 := (not #54)
+#60 := (iff #57 #53)
+#61 := [rewrite]: #60
+#58 := (iff #47 #57)
+#55 := (iff #38 #54)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#63 := [trans #59 #61]: #62
+#68 := [monotonicity #63 #65]: #67
+#72 := [trans #68 #70]: #71
+#51 := (iff #13 #48)
+#41 := (iff #38 #11)
+#44 := (not #41)
+#49 := (iff #44 #48)
+#50 := [rewrite]: #49
+#45 := (iff #13 #44)
+#42 := (iff #12 #41)
+#39 := (iff #10 #38)
+#36 := (= #8 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#46 := [monotonicity #43]: #45
+#52 := [trans #46 #50]: #51
+#74 := [trans #52 #72]: #73
+#33 := [asserted]: #13
+[mp #33 #74]: false
+unsat
+49601c2ee192c05037ae2ddde04a749818f5a75e 61 0
+#2 := false
+#7 := 0::Real
+decl f3 :: Real
+#8 := f3
+#10 := (- f3)
+#11 := (< #10 0::Real)
+#9 := (< 0::Real f3)
+#12 := (implies #9 #11)
+#13 := (not #12)
+#80 := (iff #13 false)
+#34 := -1::Real
+#35 := (* -1::Real f3)
+#38 := (< #35 0::Real)
+#44 := (not #9)
+#45 := (or #44 #38)
+#50 := (not #45)
+#78 := (iff #50 false)
+#1 := true
+#73 := (not true)
+#76 := (iff #73 false)
+#77 := [rewrite]: #76
+#74 := (iff #50 #73)
+#71 := (iff #45 true)
+#53 := (<= f3 0::Real)
+#54 := (not #53)
+#66 := (or #53 #54)
+#69 := (iff #66 true)
+#70 := [rewrite]: #69
+#67 := (iff #45 #66)
+#64 := (iff #38 #54)
+#65 := [rewrite]: #64
+#62 := (iff #44 #53)
+#57 := (not #54)
+#60 := (iff #57 #53)
+#61 := [rewrite]: #60
+#58 := (iff #44 #57)
+#55 := (iff #9 #54)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#63 := [trans #59 #61]: #62
+#68 := [monotonicity #63 #65]: #67
+#72 := [trans #68 #70]: #71
+#75 := [monotonicity #72]: #74
+#79 := [trans #75 #77]: #78
+#51 := (iff #13 #50)
+#48 := (iff #12 #45)
+#41 := (implies #9 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #12 #41)
+#39 := (iff #11 #38)
+#36 := (= #10 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#49 := [trans #43 #47]: #48
+#52 := [monotonicity #49]: #51
+#81 := [trans #52 #79]: #80
+#33 := [asserted]: #13
+[mp #33 #81]: false
+unsat
+51f38431acaaabbe473cf949af6afab6ca1aafcf 61 0
+#2 := false
+decl f3 :: Real
+#7 := f3
+#10 := (- f3)
+#8 := 0::Real
+#11 := (< 0::Real #10)
+#9 := (< f3 0::Real)
+#12 := (implies #9 #11)
+#13 := (not #12)
+#80 := (iff #13 false)
+#34 := -1::Real
+#35 := (* -1::Real f3)
+#38 := (< 0::Real #35)
+#44 := (not #9)
+#45 := (or #44 #38)
+#50 := (not #45)
+#78 := (iff #50 false)
+#1 := true
+#73 := (not true)
+#76 := (iff #73 false)
+#77 := [rewrite]: #76
+#74 := (iff #50 #73)
+#71 := (iff #45 true)
+#53 := (>= f3 0::Real)
+#54 := (not #53)
+#66 := (or #53 #54)
+#69 := (iff #66 true)
+#70 := [rewrite]: #69
+#67 := (iff #45 #66)
+#64 := (iff #38 #54)
+#65 := [rewrite]: #64
+#62 := (iff #44 #53)
+#57 := (not #54)
+#60 := (iff #57 #53)
+#61 := [rewrite]: #60
+#58 := (iff #44 #57)
+#55 := (iff #9 #54)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#63 := [trans #59 #61]: #62
+#68 := [monotonicity #63 #65]: #67
+#72 := [trans #68 #70]: #71
+#75 := [monotonicity #72]: #74
+#79 := [trans #75 #77]: #78
+#51 := (iff #13 #50)
+#48 := (iff #12 #45)
+#41 := (implies #9 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #12 #41)
+#39 := (iff #11 #38)
+#36 := (= #10 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#49 := [trans #43 #47]: #48
+#52 := [monotonicity #49]: #51
+#81 := [trans #52 #79]: #80
+#33 := [asserted]: #13
+[mp #33 #81]: false
+unsat
+0b167657d89597cff4ad497a1e580da4d6c11e72 26 0
+#2 := false
+decl f3 :: Real
+#7 := f3
+#8 := 0::Real
+#9 := (- f3 0::Real)
+#10 := (= #9 f3)
+#11 := (not #10)
+#45 := (iff #11 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #11 #40)
+#38 := (iff #10 true)
+#33 := (= f3 f3)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #10 #33)
+#32 := [rewrite]: #10
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#31 := [asserted]: #11
+[mp #31 #46]: false
+unsat
+ccfbfd13a5b76b3c59e23f1d5b1857adca54db23 32 0
+#2 := false
+decl f3 :: Real
+#8 := f3
+#10 := (- f3)
+#7 := 0::Real
+#9 := (- 0::Real f3)
+#11 := (= #9 #10)
+#12 := (not #11)
+#51 := (iff #12 false)
+#1 := true
+#46 := (not true)
+#49 := (iff #46 false)
+#50 := [rewrite]: #49
+#47 := (iff #12 #46)
+#44 := (iff #11 true)
+#33 := -1::Real
+#34 := (* -1::Real f3)
+#39 := (= #34 #34)
+#42 := (iff #39 true)
+#43 := [rewrite]: #42
+#40 := (iff #11 #39)
+#37 := (= #10 #34)
+#38 := [rewrite]: #37
+#35 := (= #9 #34)
+#36 := [rewrite]: #35
+#41 := [monotonicity #36 #38]: #40
+#45 := [trans #41 #43]: #44
+#48 := [monotonicity #45]: #47
+#52 := [trans #48 #50]: #51
+#32 := [asserted]: #12
+[mp #32 #52]: false
+unsat
+a5fc90b4c796e1c2116bff64e4df36775c337a04 64 0
+#2 := false
+#11 := 0::Real
+decl f4 :: Real
+#8 := f4
+decl f3 :: Real
+#7 := f3
+#10 := (- f3 f4)
+#12 := (< #10 0::Real)
+#9 := (< f3 f4)
+#13 := (implies #9 #12)
+#14 := (not #13)
+#82 := (iff #14 false)
+#35 := -1::Real
+#36 := (* -1::Real f4)
+#37 := (+ f3 #36)
+#40 := (< #37 0::Real)
+#46 := (not #9)
+#47 := (or #46 #40)
+#52 := (not #47)
+#80 := (iff #52 false)
+#1 := true
+#75 := (not true)
+#78 := (iff #75 false)
+#79 := [rewrite]: #78
+#76 := (iff #52 #75)
+#73 := (iff #47 true)
+#56 := (>= #37 0::Real)
+#55 := (not #56)
+#68 := (or #56 #55)
+#71 := (iff #68 true)
+#72 := [rewrite]: #71
+#69 := (iff #47 #68)
+#66 := (iff #40 #55)
+#67 := [rewrite]: #66
+#64 := (iff #46 #56)
+#59 := (not #55)
+#62 := (iff #59 #56)
+#63 := [rewrite]: #62
+#60 := (iff #46 #59)
+#57 := (iff #9 #55)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#65 := [trans #61 #63]: #64
+#70 := [monotonicity #65 #67]: #69
+#74 := [trans #70 #72]: #73
+#77 := [monotonicity #74]: #76
+#81 := [trans #77 #79]: #80
+#53 := (iff #14 #52)
+#50 := (iff #13 #47)
+#43 := (implies #9 #40)
+#48 := (iff #43 #47)
+#49 := [rewrite]: #48
+#44 := (iff #13 #43)
+#41 := (iff #12 #40)
+#38 := (= #10 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#51 := [trans #45 #49]: #50
+#54 := [monotonicity #51]: #53
+#83 := [trans #54 #81]: #82
+#34 := [asserted]: #14
+[mp #34 #83]: false
+unsat
+7ed72828350129130a88941dee3cc368dd21cb65 44 0
+#2 := false
+decl f3 :: Real
+#7 := f3
+decl f4 :: Real
+#8 := f4
+#10 := (- f4 f3)
+#11 := (- #10)
+#9 := (- f3 f4)
+#12 := (= #9 #11)
+#13 := (not #12)
+#63 := (iff #13 false)
+#1 := true
+#58 := (not true)
+#61 := (iff #58 false)
+#62 := [rewrite]: #61
+#59 := (iff #13 #58)
+#56 := (iff #12 true)
+#35 := -1::Real
+#36 := (* -1::Real f4)
+#37 := (+ f3 #36)
+#51 := (= #37 #37)
+#54 := (iff #51 true)
+#55 := [rewrite]: #54
+#52 := (iff #12 #51)
+#49 := (= #11 #37)
+#40 := (* -1::Real f3)
+#41 := (+ #40 f4)
+#44 := (- #41)
+#47 := (= #44 #37)
+#48 := [rewrite]: #47
+#45 := (= #11 #44)
+#42 := (= #10 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#38 := (= #9 #37)
+#39 := [rewrite]: #38
+#53 := [monotonicity #39 #50]: #52
+#57 := [trans #53 #55]: #56
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#34 := [asserted]: #13
+[mp #34 #64]: false
+unsat
+c431a50fe81f19bdf1df51651ad04729ae603478 42 0
+#2 := false
+decl f3 :: Real
+#7 := f3
+decl f4 :: Real
+#8 := f4
+#10 := (- f4)
+#11 := (+ #10 f3)
+#9 := (- f3 f4)
+#12 := (= #9 #11)
+#13 := (not #12)
+#61 := (iff #13 false)
+#1 := true
+#56 := (not true)
+#59 := (iff #56 false)
+#60 := [rewrite]: #59
+#57 := (iff #13 #56)
+#54 := (iff #12 true)
+#35 := -1::Real
+#36 := (* -1::Real f4)
+#37 := (+ f3 #36)
+#49 := (= #37 #37)
+#52 := (iff #49 true)
+#53 := [rewrite]: #52
+#50 := (iff #12 #49)
+#47 := (= #11 #37)
+#42 := (+ #36 f3)
+#45 := (= #42 #37)
+#46 := [rewrite]: #45
+#43 := (= #11 #42)
+#40 := (= #10 #36)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#48 := [trans #44 #46]: #47
+#38 := (= #9 #37)
+#39 := [rewrite]: #38
+#51 := [monotonicity #39 #48]: #50
+#55 := [trans #51 #53]: #54
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#34 := [asserted]: #13
+[mp #34 #62]: false
+unsat
+65271dc3ab073ac04b3246ac44e6c8414e091882 48 0
+#2 := false
+decl f5 :: Real
+#10 := f5
 decl f4 :: Real
-#9 := f4
+#8 := f4
+#12 := (+ f4 f5)
+decl f3 :: Real
+#7 := f3
+#13 := (- f3 #12)
+#9 := (- f3 f4)
+#11 := (- #9 f5)
+#14 := (= #11 #13)
+#15 := (not #14)
+#66 := (iff #15 false)
+#1 := true
+#61 := (not true)
+#64 := (iff #61 false)
+#65 := [rewrite]: #64
+#62 := (iff #15 #61)
+#59 := (iff #14 true)
+#37 := -1::Real
+#45 := (* -1::Real f5)
+#38 := (* -1::Real f4)
+#46 := (+ #38 #45)
+#47 := (+ f3 #46)
+#54 := (= #47 #47)
+#57 := (iff #54 true)
+#58 := [rewrite]: #57
+#55 := (iff #14 #54)
+#52 := (= #13 #47)
+#53 := [rewrite]: #52
+#50 := (= #11 #47)
+#39 := (+ f3 #38)
+#42 := (- #39 f5)
+#48 := (= #42 #47)
+#49 := [rewrite]: #48
+#43 := (= #11 #42)
+#40 := (= #9 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#51 := [trans #44 #49]: #50
+#56 := [monotonicity #51 #53]: #55
+#60 := [trans #56 #58]: #59
+#63 := [monotonicity #60]: #62
+#67 := [trans #63 #65]: #66
+#36 := [asserted]: #15
+[mp #36 #67]: false
+unsat
[phone]c50ce7830d84e557641bcca3c4812dd5 26 0
+#2 := false
+#8 := 0::Real
+decl f3 :: Real
+#7 := f3
+#9 := (* f3 0::Real)
+#10 := (= #9 0::Real)
+#11 := (not #10)
+#45 := (iff #11 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #11 #40)
+#38 := (iff #10 true)
+#33 := (= 0::Real 0::Real)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #10 #33)
+#32 := [rewrite]: #10
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#31 := [asserted]: #11
+[mp #31 #46]: false
+unsat
+856e04187cdbc2035a45396cc77f893736b91735 26 0
+#2 := false
+#7 := 0::Real
+decl f3 :: Real
+#8 := f3
+#9 := (* 0::Real f3)
+#10 := (= #9 0::Real)
+#11 := (not #10)
+#45 := (iff #11 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #11 #40)
+#38 := (iff #10 true)
+#33 := (= 0::Real 0::Real)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #10 #33)
+#32 := [rewrite]: #10
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#31 := [asserted]: #11
+[mp #31 #46]: false
+unsat
+851b09d524dddf4dc26796a2641c88c095c084d1 26 0
+#2 := false
+decl f3 :: Real
+#7 := f3
+#8 := 1::Real
+#9 := (* f3 1::Real)
+#10 := (= #9 f3)
+#11 := (not #10)
+#46 := (iff #11 false)
+#1 := true
+#41 := (not true)
+#44 := (iff #41 false)
+#45 := [rewrite]: #44
+#42 := (iff #11 #41)
+#39 := (iff #10 true)
+#34 := (= f3 f3)
+#37 := (iff #34 true)
+#38 := [rewrite]: #37
+#35 := (iff #10 #34)
+#33 := [rewrite]: #10
+#36 := [monotonicity #33]: #35
+#40 := [trans #36 #38]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#32 := [asserted]: #11
+[mp #32 #47]: false
+unsat
+e644fd725742c5947a76808fa8508e0afd656cd8 26 0
+#2 := false
+decl f3 :: Real
+#8 := f3
+#7 := 1::Real
+#9 := (* 1::Real f3)
+#10 := (= #9 f3)
+#11 := (not #10)
+#46 := (iff #11 false)
+#1 := true
+#41 := (not true)
+#44 := (iff #41 false)
+#45 := [rewrite]: #44
+#42 := (iff #11 #41)
+#39 := (iff #10 true)
+#34 := (= f3 f3)
+#37 := (iff #34 true)
+#38 := [rewrite]: #37
+#35 := (iff #10 #34)
+#33 := [rewrite]: #10
+#36 := [monotonicity #33]: #35
+#40 := [trans #36 #38]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#32 := [asserted]: #11
+[mp #32 #47]: false
+unsat
+0ddad1522f46ecc70264e9eb7e7c8e72b14a1fe7 40 0
+#2 := false
+decl f3 :: Real
+#7 := f3
+#11 := (- f3)
+#8 := 1::Real
+#9 := (- 1::Real)
+#10 := (* f3 #9)
+#12 := (= #10 #11)
+#13 := (not #12)
+#60 := (iff #13 false)
+#1 := true
+#55 := (not true)
+#58 := (iff #55 false)
+#59 := [rewrite]: #58
+#56 := (iff #13 #55)
+#53 := (iff #12 true)
+#35 := -1::Real
+#41 := (* -1::Real f3)
+#48 := (= #41 #41)
+#51 := (iff #48 true)
+#52 := [rewrite]: #51
+#49 := (iff #12 #48)
+#46 := (= #11 #41)
+#47 := [rewrite]: #46
+#44 := (= #10 #41)
+#38 := (* f3 -1::Real)
+#42 := (= #38 #41)
+#43 := [rewrite]: #42
+#39 := (= #10 #38)
+#36 := (= #9 -1::Real)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#45 := [trans #40 #43]: #44
+#50 := [monotonicity #45 #47]: #49
+#54 := [trans #50 #52]: #53
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#34 := [asserted]: #13
+[mp #34 #61]: false
+unsat
+f5c5be999a961dbeb7007aacb486ddf3fbcad948 35 0
+#2 := false
+decl f3 :: Real
+#9 := f3
+#11 := (- f3)
+#7 := 1::Real
+#8 := (- 1::Real)
+#10 := (* #8 f3)
+#12 := (= #10 #11)
+#13 := (not #12)
+#55 := (iff #13 false)
+#1 := true
+#50 := (not true)
+#53 := (iff #50 false)
+#54 := [rewrite]: #53
+#51 := (iff #13 #50)
+#48 := (iff #12 true)
+#35 := -1::Real
+#38 := (* -1::Real f3)
+#43 := (= #38 #38)
+#46 := (iff #43 true)
+#47 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (= #11 #38)
+#42 := [rewrite]: #41
+#39 := (= #10 #38)
+#36 := (= #8 -1::Real)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#45 := [monotonicity #40 #42]: #44
+#49 := [trans #45 #47]: #48
+#52 := [monotonicity #49]: #51
+#56 := [trans #52 #54]: #55
+#34 := [asserted]: #13
+[mp #34 #56]: false
+unsat
+fa62ab1f8f4c43363df0c20a0e78ae4b3d0bf5f6 28 0
+#2 := false
+#7 := 3::Real
+decl f3 :: Real
+#8 := f3
+#10 := (* f3 3::Real)
+#9 := (* 3::Real f3)
+#11 := (= #9 #10)
+#12 := (not #11)
+#48 := (iff #12 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (iff #11 true)
+#36 := (= #9 #9)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #11 #36)
+#34 := (= #10 #9)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#33 := [asserted]: #12
+[mp #33 #49]: false
+unsat
+ca0e54020823cad060f3d1ba1d831227210c5d87 30 0
+#2 := false
+#7 := 1::Real
+#8 := 2::Real
+#9 := (/ 1::Real 2::Real)
+#10 := (< #9 1::Real)
+#11 := (not #10)
+#51 := (iff #11 false)
+#33 := 1/2::Real
+#36 := (< 1/2::Real 1::Real)
+#39 := (not #36)
+#49 := (iff #39 false)
+#1 := true
+#44 := (not true)
+#47 := (iff #44 false)
+#48 := [rewrite]: #47
+#45 := (iff #39 #44)
+#42 := (iff #36 true)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#40 := (iff #11 #39)
+#37 := (iff #10 #36)
+#34 := (= #9 1/2::Real)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#52 := [trans #41 #50]: #51
+#32 := [asserted]: #11
+[mp #32 #52]: false
+unsat
+ad7a6067815e419f4adff50cf7e013cfa4e44591 27 0
+#2 := false
+#8 := 3::Real
+#7 := 1::Real
+#9 := (/ 1::Real 3::Real)
+#10 := (= #9 #9)
+#11 := (not #10)
+#48 := (iff #11 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #11 #43)
+#41 := (iff #10 true)
+#33 := 1/3::Real
+#36 := (= 1/3::Real 1/3::Real)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #10 #36)
+#34 := (= #9 1/3::Real)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35 #35]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#32 := [asserted]: #11
+[mp #32 #49]: false
+unsat
+a99a6f9f59161e07ca4bb424da1dda7f3599b9d0 48 0
+#2 := false
+#8 := 3::Real
+#7 := 1::Real
+#11 := (- 1::Real)
+#12 := (/ #11 3::Real)
+#9 := (- 3::Real)
+#10 := (/ 1::Real #9)
+#13 := (= #10 #12)
+#14 := (not #13)
+#69 := (iff #14 false)
+#1 := true
+#64 := (not true)
+#67 := (iff #64 false)
+#68 := [rewrite]: #67
+#65 := (iff #14 #64)
+#62 := (iff #13 true)
+#42 := -1/3::Real
+#57 := (= -1/3::Real -1/3::Real)
+#60 := (iff #57 true)
+#61 := [rewrite]: #60
+#58 := (iff #13 #57)
+#55 := (= #12 -1/3::Real)
+#47 := -1::Real
+#50 := (/ -1::Real 3::Real)
+#53 := (= #50 -1/3::Real)
+#54 := [rewrite]: #53
+#51 := (= #12 #50)
+#48 := (= #11 -1::Real)
+#49 := [rewrite]: #48
+#52 := [monotonicity #49]: #51
+#56 := [trans #52 #54]: #55
+#45 := (= #10 -1/3::Real)
+#36 := -3::Real
+#39 := (/ 1::Real -3::Real)
+#43 := (= #39 -1/3::Real)
+#44 := [rewrite]: #43
+#40 := (= #10 #39)
+#37 := (= #9 -3::Real)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#46 := [trans #41 #44]: #45
+#59 := [monotonicity #46 #56]: #58
+#63 := [trans #59 #61]: #62
+#66 := [monotonicity #63]: #65
+#70 := [trans #66 #68]: #69
+#35 := [asserted]: #14
+[mp #35 #70]: false
+unsat
+73a0b3a2d069b59c661aa11bdb9686097aacba84 36 0
+#2 := false
+#9 := 3::Real
+#7 := 1::Real
+#8 := (- 1::Real)
+#10 := (/ #8 3::Real)
+#11 := (= #10 #10)
+#12 := (not #11)
+#57 := (iff #12 false)
+#1 := true
+#52 := (not true)
+#55 := (iff #52 false)
+#56 := [rewrite]: #55
+#53 := (iff #12 #52)
+#50 := (iff #11 true)
+#40 := -1/3::Real
+#45 := (= -1/3::Real -1/3::Real)
+#48 := (iff #45 true)
+#49 := [rewrite]: #48
+#46 := (iff #11 #45)
+#43 := (= #10 -1/3::Real)
+#34 := -1::Real
+#37 := (/ -1::Real 3::Real)
+#41 := (= #37 -1/3::Real)
+#42 := [rewrite]: #41
+#38 := (= #10 #37)
+#35 := (= #8 -1::Real)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#44 := [trans #39 #42]: #43
+#47 := [monotonicity #44 #44]: #46
+#51 := [trans #47 #49]: #50
+#54 := [monotonicity #51]: #53
+#58 := [trans #54 #56]: #57
+#33 := [asserted]: #12
+[mp #33 #58]: false
+unsat
+e455683e14454659c86babd4206469f19c262efb 43 0
+#2 := false
+#9 := 3::Real
+#7 := 1::Real
+#12 := (/ 1::Real 3::Real)
+#10 := (- 3::Real)
+#8 := (- 1::Real)
+#11 := (/ #8 #10)
+#13 := (= #11 #12)
+#14 := (not #13)
+#64 := (iff #14 false)
+#1 := true
+#59 := (not true)
+#62 := (iff #59 false)
+#63 := [rewrite]: #62
+#60 := (iff #14 #59)
+#57 := (iff #13 true)
+#45 := 1/3::Real
+#52 := (= 1/3::Real 1/3::Real)
+#55 := (iff #52 true)
+#56 := [rewrite]: #55
+#53 := (iff #13 #52)
+#50 := (= #12 1/3::Real)
+#51 := [rewrite]: #50
+#48 := (= #11 1/3::Real)
+#39 := -3::Real
+#36 := -1::Real
+#42 := (/ -1::Real -3::Real)
+#46 := (= #42 1/3::Real)
+#47 := [rewrite]: #46
+#43 := (= #11 #42)
+#40 := (= #10 -3::Real)
+#41 := [rewrite]: #40
+#37 := (= #8 -1::Real)
+#38 := [rewrite]: #37
+#44 := [monotonicity #38 #41]: #43
+#49 := [trans #44 #47]: #48
+#54 := [monotonicity #49 #51]: #53
+#58 := [trans #54 #56]: #57
+#61 := [monotonicity #58]: #60
+#65 := [trans #61 #63]: #64
+#35 := [asserted]: #14
+[mp #35 #65]: false
+unsat
+4e89ec99c186f4d0cc4950beb34277bc35815fff 26 0
+#2 := false
+decl f3 :: Real
+#7 := f3
+#8 := 1::Real
+#9 := (/ f3 1::Real)
+#10 := (= #9 f3)
+#11 := (not #10)
+#46 := (iff #11 false)
+#1 := true
+#41 := (not true)
+#44 := (iff #41 false)
+#45 := [rewrite]: #44
+#42 := (iff #11 #41)
+#39 := (iff #10 true)
+#34 := (= f3 f3)
+#37 := (iff #34 true)
+#38 := [rewrite]: #37
+#35 := (iff #10 #34)
+#33 := [rewrite]: #10
+#36 := [monotonicity #33]: #35
+#40 := [trans #36 #38]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#32 := [asserted]: #11
+[mp #32 #47]: false
+unsat
+ba8acb319606519055ab94494c9ac613c5c038a0 60 0
+#2 := false
+#7 := 0::Real
+decl f3 :: Real
+#8 := f3
+#67 := 2/3::Real
+#68 := (* 2/3::Real f3)
+#69 := (<= #68 0::Real)
+#65 := (not #69)
+#54 := (<= f3 0::Real)
+#71 := (or #54 #65)
+#74 := (not #71)
+#10 := 3::Real
+#11 := (/ f3 3::Real)
+#12 := (< #11 f3)
+#9 := (< 0::Real f3)
+#13 := (implies #9 #12)
+#14 := (not #13)
+#77 := (iff #14 #74)
+#35 := 1/3::Real
+#36 := (* 1/3::Real f3)
+#39 := (< #36 f3)
+#45 := (not #9)
+#46 := (or #45 #39)
+#51 := (not #46)
+#75 := (iff #51 #74)
+#72 := (iff #46 #71)
+#66 := (iff #39 #65)
+#70 := [rewrite]: #66
+#63 := (iff #45 #54)
+#55 := (not #54)
+#58 := (not #55)
+#61 := (iff #58 #54)
+#62 := [rewrite]: #61
+#59 := (iff #45 #58)
+#56 := (iff #9 #55)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#73 := [monotonicity #64 #70]: #72
+#76 := [monotonicity #73]: #75
+#52 := (iff #14 #51)
+#49 := (iff #13 #46)
+#42 := (implies #9 #39)
+#47 := (iff #42 #46)
+#48 := [rewrite]: #47
+#43 := (iff #13 #42)
+#40 := (iff #12 #39)
+#37 := (= #11 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#44 := [monotonicity #41]: #43
+#50 := [trans #44 #48]: #49
+#53 := [monotonicity #50]: #52
+#78 := [trans #53 #76]: #77
+#34 := [asserted]: #14
+#79 := [mp #34 #78]: #74
+#81 := [not-or-elim #79]: #69
+#80 := [not-or-elim #79]: #55
+[th-lemma arith farkas -2/3 1 #80 #81]: false
+unsat
+c254f7743432efb3168908069776d39b954adceb 60 0
+#2 := false
+#8 := 0::Real
+decl f3 :: Real
+#7 := f3
+#69 := 2/3::Real
+#70 := (* 2/3::Real f3)
+#67 := (>= #70 0::Real)
+#65 := (not #67)
+#56 := (>= f3 0::Real)
+#71 := (or #56 #65)
+#74 := (not #71)
+#10 := 3::Real
+#11 := (/ f3 3::Real)
+#12 := (< f3 #11)
+#9 := (< f3 0::Real)
+#13 := (implies #9 #12)
+#14 := (not #13)
+#77 := (iff #14 #74)
+#35 := 1/3::Real
+#36 := (* 1/3::Real f3)
+#39 := (< f3 #36)
+#45 := (not #9)
+#46 := (or #45 #39)
+#51 := (not #46)
+#75 := (iff #51 #74)
+#72 := (iff #46 #71)
+#66 := (iff #39 #65)
+#68 := [rewrite]: #66
+#63 := (iff #45 #56)
+#54 := (not #56)
+#58 := (not #54)
+#61 := (iff #58 #56)
+#62 := [rewrite]: #61
+#59 := (iff #45 #58)
+#55 := (iff #9 #54)
+#57 := [rewrite]: #55
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#73 := [monotonicity #64 #68]: #72
+#76 := [monotonicity #73]: #75
+#52 := (iff #14 #51)
+#49 := (iff #13 #46)
+#42 := (implies #9 #39)
+#47 := (iff #42 #46)
+#48 := [rewrite]: #47
+#43 := (iff #13 #42)
+#40 := (iff #12 #39)
+#37 := (= #11 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#44 := [monotonicity #41]: #43
+#50 := [trans #44 #48]: #49
+#53 := [monotonicity #50]: #52
+#78 := [trans #53 #76]: #77
+#34 := [asserted]: #14
+#79 := [mp #34 #78]: #74
+#81 := [not-or-elim #79]: #67
+#80 := [not-or-elim #79]: #54
+[th-lemma arith farkas -2/3 1 #80 #81]: false
+unsat
+52f1e86ce55eba5021ed07ab92d87cf35261926b 36 0
+#2 := false
+decl f3 :: Real
+#8 := f3
+#7 := 3::Real
+#9 := (/ f3 3::Real)
+#10 := (* 3::Real #9)
+#11 := (= #10 f3)
+#12 := (not #11)
+#56 := (iff #12 false)
+#1 := true
+#51 := (not true)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #12 #51)
+#49 := (iff #11 true)
+#44 := (= f3 f3)
+#47 := (iff #44 true)
+#48 := [rewrite]: #47
+#45 := (iff #11 #44)
+#34 := 1/3::Real
+#35 := (* 1/3::Real f3)
+#38 := (* 3::Real #35)
+#41 := (= #38 f3)
+#42 := [rewrite]: #41
+#39 := (= #10 #38)
+#36 := (= #9 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [trans #40 #42]: #11
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#33 := [asserted]: #12
+[mp #33 #57]: false
+unsat
+d1e89f661ec44eae20b1e53978b42ef04f82af17 35 0
+#2 := false
+decl f3 :: Real
+#7 := f3
+#8 := 3::Real
+#9 := (* f3 3::Real)
+#10 := (/ #9 3::Real)
+#11 := (= #10 f3)
+#12 := (not #11)
+#55 := (iff #12 false)
+#1 := true
+#50 := (not true)
+#53 := (iff #50 false)
+#54 := [rewrite]: #53
+#51 := (iff #12 #50)
+#48 := (iff #11 true)
+#43 := (= f3 f3)
+#46 := (iff #43 true)
+#47 := [rewrite]: #46
+#44 := (iff #11 #43)
+#34 := (* 3::Real f3)
+#37 := (/ #34 3::Real)
+#40 := (= #37 f3)
+#41 := [rewrite]: #40
+#38 := (= #10 #37)
+#35 := (= #9 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#42 := [trans #39 #41]: #11
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#52 := [monotonicity #49]: #51
+#56 := [trans #52 #54]: #55
+#33 := [asserted]: #12
+[mp #33 #56]: false
+unsat
+0fdc33b7cc1348a0833bcf7f4b4149307e635b6c 62 0
+#2 := false
+#7 := 0::Real
+decl f3 :: Real
+#8 := f3
+#69 := 1/3::Real
+#70 := (* 1/3::Real f3)
+#71 := (<= #70 0::Real)
+#67 := (not #71)
+#56 := (<= f3 0::Real)
+#73 := (or #56 #67)
+#76 := (not #73)
+#12 := 3::Real
+#10 := 2::Real
+#11 := (* 2::Real f3)
+#13 := (/ #11 3::Real)
+#14 := (< #13 f3)
+#9 := (< 0::Real f3)
+#15 := (implies #9 #14)
+#16 := (not #15)
+#79 := (iff #16 #76)
+#38 := 2/3::Real
+#39 := (* 2/3::Real f3)
+#41 := (< #39 f3)
+#47 := (not #9)
+#48 := (or #47 #41)
+#53 := (not #48)
+#77 := (iff #53 #76)
+#74 := (iff #48 #73)
+#68 := (iff #41 #67)
+#72 := [rewrite]: #68
+#65 := (iff #47 #56)
+#57 := (not #56)
+#60 := (not #57)
+#63 := (iff #60 #56)
+#64 := [rewrite]: #63
+#61 := (iff #47 #60)
+#58 := (iff #9 #57)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#66 := [trans #62 #64]: #65
+#75 := [monotonicity #66 #72]: #74
+#78 := [monotonicity #75]: #77
+#54 := (iff #16 #53)
+#51 := (iff #15 #48)
+#44 := (implies #9 #41)
+#49 := (iff #44 #48)
+#50 := [rewrite]: #49
+#45 := (iff #15 #44)
+#42 := (iff #14 #41)
+#37 := (= #13 #39)
+#40 := [rewrite]: #37
+#43 := [monotonicity #40]: #42
+#46 := [monotonicity #43]: #45
+#52 := [trans #46 #50]: #51
+#55 := [monotonicity #52]: #54
+#80 := [trans #55 #78]: #79
+#36 := [asserted]: #16
+#81 := [mp #36 #80]: #76
+#83 := [not-or-elim #81]: #71
+#82 := [not-or-elim #81]: #57
+[th-lemma arith farkas -1/3 1 #82 #83]: false
+unsat
+f09f517e7e4cbc63db43c6d99d036f9d3a4315bf 62 0
+#2 := false
+#8 := 0::Real
+decl f3 :: Real
+#7 := f3
+#71 := 1/3::Real
+#72 := (* 1/3::Real f3)
+#69 := (>= #72 0::Real)
+#67 := (not #69)
+#58 := (>= f3 0::Real)
+#73 := (or #58 #67)
+#76 := (not #73)
+#12 := 3::Real
+#10 := 2::Real
+#11 := (* 2::Real f3)
+#13 := (/ #11 3::Real)
+#14 := (< f3 #13)
+#9 := (< f3 0::Real)
+#15 := (implies #9 #14)
+#16 := (not #15)
+#79 := (iff #16 #76)
+#38 := 2/3::Real
+#39 := (* 2/3::Real f3)
+#41 := (< f3 #39)
+#47 := (not #9)
+#48 := (or #47 #41)
+#53 := (not #48)
+#77 := (iff #53 #76)
+#74 := (iff #48 #73)
+#68 := (iff #41 #67)
+#70 := [rewrite]: #68
+#65 := (iff #47 #58)
+#56 := (not #58)
+#60 := (not #56)
+#63 := (iff #60 #58)
+#64 := [rewrite]: #63
+#61 := (iff #47 #60)
+#57 := (iff #9 #56)
+#59 := [rewrite]: #57
+#62 := [monotonicity #59]: #61
+#66 := [trans #62 #64]: #65
+#75 := [monotonicity #66 #70]: #74
+#78 := [monotonicity #75]: #77
+#54 := (iff #16 #53)
+#51 := (iff #15 #48)
+#44 := (implies #9 #41)
+#49 := (iff #44 #48)
+#50 := [rewrite]: #49
+#45 := (iff #15 #44)
+#42 := (iff #14 #41)
+#37 := (= #13 #39)
+#40 := [rewrite]: #37
+#43 := [monotonicity #40]: #42
+#46 := [monotonicity #43]: #45
+#52 := [trans #46 #50]: #51
+#55 := [monotonicity #52]: #54
+#80 := [trans #55 #78]: #79
+#36 := [asserted]: #16
+#81 := [mp #36 #80]: #76
+#83 := [not-or-elim #81]: #69
+#82 := [not-or-elim #81]: #56
+[th-lemma arith farkas -1/3 1 #82 #83]: false
+unsat
+89b345e26e51ed464cc683659a5ae8f2c05647b0 75 0
+#2 := false
+#7 := 0::Real
+decl f3 :: Real
+#8 := f3
+#34 := -1::Real
+#35 := (* -1::Real f3)
+#47 := (>= f3 0::Real)
+#54 := (if #47 f3 #35)
+#74 := (* -1::Real #54)
+#83 := (+ #35 #74)
+#92 := (<= #83 0::Real)
+#79 := (= #35 #54)
+#48 := (not #47)
+#75 := (+ f3 #74)
+#82 := (<= #75 0::Real)
+#78 := (= f3 #54)
+#84 := [hypothesis]: #47
+#80 := (or #48 #78)
+#81 := [def-axiom]: #80
+#85 := [unit-resolution #81 #84]: #78
+#86 := (not #78)
+#87 := (or #86 #82)
+#88 := [th-lemma arith triangle-eq]: #87
+#89 := [unit-resolution #88 #85]: #82
+#63 := (>= #54 0::Real)
+#67 := (not #63)
+#10 := (- f3)
+#9 := (< f3 0::Real)
+#11 := (if #9 #10 f3)
+#12 := (<= 0::Real #11)
+#13 := (not #12)
+#70 := (iff #13 #67)
+#38 := (if #9 #35 f3)
+#41 := (<= 0::Real #38)
+#44 := (not #41)
+#68 := (iff #44 #67)
+#65 := (iff #41 #63)
+#59 := (<= 0::Real #54)
+#62 := (iff #59 #63)
+#64 := [rewrite]: #62
+#60 := (iff #41 #59)
+#57 := (= #38 #54)
+#51 := (if #48 #35 f3)
+#55 := (= #51 #54)
+#56 := [rewrite]: #55
+#52 := (= #38 #51)
+#49 := (iff #9 #48)
+#50 := [rewrite]: #49
+#53 := [monotonicity #50]: #52
+#58 := [trans #53 #56]: #57
+#61 := [monotonicity #58]: #60
+#66 := [trans #61 #64]: #65
+#69 := [monotonicity #66]: #68
+#45 := (iff #13 #44)
+#42 := (iff #12 #41)
+#39 := (= #11 #38)
+#36 := (= #10 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#46 := [monotonicity #43]: #45
+#71 := [trans #46 #69]: #70
+#33 := [asserted]: #13
+#72 := [mp #33 #71]: #67
+#90 := [th-lemma arith farkas -1 1 1 #84 #72 #89]: false
+#91 := [lemma #90]: #48
+#76 := (or #47 #79)
+#77 := [def-axiom]: #76
+#94 := [unit-resolution #77 #91]: #79
+#95 := (not #79)
+#96 := (or #95 #92)
+#97 := [th-lemma arith triangle-eq]: #96
+#98 := [unit-resolution #97 #94]: #92
+[th-lemma arith farkas 1 1 1 #72 #91 #98]: false
+unsat
+985bcf7e8f8c4a491bb0e856a8f7804095f5404a 103 0
+#2 := false
+#8 := 0::Real
+decl f3 :: Real
+#7 := f3
+#36 := -1::Real
+#37 := (* -1::Real f3)
+#58 := (>= f3 0::Real)
+#65 := (if #58 f3 #37)
+#70 := (= #65 0::Real)
+#13 := (= f3 0::Real)
+#118 := (iff #13 #70)
+#87 := (= f3 #65)
+#101 := (<= #37 0::Real)
+#100 := (= #37 0::Real)
+#84 := (not #13)
+#59 := (not #58)
+#103 := [hypothesis]: #59
+#104 := (or #84 #58)
+#105 := [th-lemma arith triangle-eq]: #104
+#106 := [unit-resolution #105 #103]: #84
+#98 := (or #70 #13)
+#73 := (not #70)
+#76 := (iff #73 #13)
+#10 := (- f3)
+#9 := (< f3 0::Real)
+#11 := (if #9 #10 f3)
+#12 := (= #11 0::Real)
+#14 := (iff #12 #13)
+#15 := (not #14)
+#79 := (iff #15 #76)
+#40 := (if #9 #37 f3)
+#43 := (= #40 0::Real)
+#52 := (not #43)
+#53 := (iff #52 #13)
+#77 := (iff #53 #76)
+#74 := (iff #52 #73)
+#71 := (iff #43 #70)
+#68 := (= #40 #65)
+#62 := (if #59 #37 f3)
+#66 := (= #62 #65)
+#67 := [rewrite]: #66
+#63 := (= #40 #62)
+#60 := (iff #9 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#69 := [trans #64 #67]: #68
+#72 := [monotonicity #69]: #71
+#75 := [monotonicity #72]: #74
+#78 := [monotonicity #75]: #77
+#56 := (iff #15 #53)
+#46 := (iff #43 #13)
+#49 := (not #46)
+#54 := (iff #49 #53)
+#55 := [rewrite]: #54
+#50 := (iff #15 #49)
+#47 := (iff #14 #46)
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#38 := (= #10 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#51 := [monotonicity #48]: #50
+#57 := [trans #51 #55]: #56
+#80 := [trans #57 #78]: #79
+#35 := [asserted]: #15
+#81 := [mp #35 #80]: #76
+#91 := (not #76)
+#96 := (or #70 #13 #91)
+#97 := [def-axiom]: #96
+#99 := [unit-resolution #97 #81]: #98
+#107 := [unit-resolution #99 #106]: #70
+#88 := (= #37 #65)
+#85 := (or #58 #88)
+#86 := [def-axiom]: #85
+#108 := [unit-resolution #86 #103]: #88
+#109 := [trans #108 #107]: #100
+#110 := (not #100)
+#111 := (or #110 #101)
+#112 := [th-lemma arith triangle-eq]: #111
+#113 := [unit-resolution #112 #109]: #101
+#114 := [th-lemma arith farkas 1 1 #103 #113]: false
+#115 := [lemma #114]: #58
+#89 := (or #59 #87)
+#90 := [def-axiom]: #89
+#117 := [unit-resolution #90 #115]: #87
+#119 := [monotonicity #117]: #118
+#120 := (iff #84 #73)
+#121 := [monotonicity #119]: #120
+#102 := [hypothesis]: #84
+#122 := [mp #102 #121]: #73
+#116 := [unit-resolution #99 #102]: #70
+#123 := [unit-resolution #116 #122]: false
+#124 := [lemma #123]: #13
+#126 := [mp #124 #119]: #70
+#94 := (or #73 #84)
+#92 := (or #73 #84 #91)
+#93 := [def-axiom]: #92
+#95 := [unit-resolution #93 #81]: #94
+#125 := [unit-resolution #95 #124]: #73
+[unit-resolution #125 #126]: false
+unsat
+54d70864c8e13c2ab5f71e5ded8863232101a991 102 0
+#2 := false
+#7 := 0::Real
+decl f3 :: Real
+#8 := f3
+#36 := -1::Real
+#37 := (* -1::Real f3)
+#112 := (* -1::Real #37)
+#113 := (+ f3 #112)
+#115 := (>= #113 0::Real)
+#111 := (= f3 #37)
+#58 := (>= f3 0::Real)
+#69 := (if #58 f3 #37)
+#119 := (= #69 #37)
+#89 := (= #37 #69)
+#61 := (not #58)
+#74 := (= #69 f3)
+#88 := (= f3 #69)
+#105 := (not #88)
+#84 := (not #74)
+#106 := (iff #84 #105)
+#103 := (iff #74 #88)
+#104 := [commutativity]: #103
+#107 := [monotonicity #104]: #106
+#100 := [hypothesis]: #84
+#108 := [mp #100 #107]: #105
+#98 := (or #58 #74)
+#77 := (iff #61 #74)
+#11 := (- f3)
+#10 := (< f3 0::Real)
+#12 := (if #10 #11 f3)
+#13 := (= #12 f3)
+#9 := (<= 0::Real f3)
+#14 := (iff #9 #13)
+#15 := (not #14)
+#80 := (iff #15 #77)
+#40 := (if #10 #37 f3)
+#43 := (= #40 f3)
+#52 := (not #9)
+#53 := (iff #52 #43)
+#78 := (iff #53 #77)
+#75 := (iff #43 #74)
+#72 := (= #40 #69)
+#66 := (if #61 #37 f3)
+#70 := (= #66 #69)
+#71 := [rewrite]: #70
+#67 := (= #40 #66)
+#64 := (iff #10 #61)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#73 := [trans #68 #71]: #72
+#76 := [monotonicity #73]: #75
+#62 := (iff #52 #61)
+#59 := (iff #9 #58)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#79 := [monotonicity #63 #76]: #78
+#56 := (iff #15 #53)
+#46 := (iff #9 #43)
+#49 := (not #46)
+#54 := (iff #49 #53)
+#55 := [rewrite]: #54
+#50 := (iff #15 #49)
+#47 := (iff #14 #46)
+#44 := (iff #13 #43)
+#41 := (= #12 #40)
+#38 := (= #11 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#51 := [monotonicity #48]: #50
+#57 := [trans #51 #55]: #56
+#81 := [trans #57 #79]: #80
+#35 := [asserted]: #15
+#82 := [mp #35 #81]: #77
+#85 := (not #77)
+#96 := (or #58 #74 #85)
+#97 := [def-axiom]: #96
+#99 := [unit-resolution #97 #82]: #98
+#101 := [unit-resolution #99 #100]: #58
+#90 := (or #61 #88)
+#91 := [def-axiom]: #90
+#102 := [unit-resolution #91 #101]: #88
+#109 := [unit-resolution #102 #108]: false
+#110 := [lemma #109]: #74
+#94 := (or #61 #84)
+#92 := (or #61 #84 #85)
+#93 := [def-axiom]: #92
+#95 := [unit-resolution #93 #82]: #94
+#116 := [unit-resolution #95 #110]: #61
+#86 := (or #58 #89)
+#87 := [def-axiom]: #86
+#117 := [unit-resolution #87 #116]: #89
+#120 := [symm #117]: #119
+#118 := [symm #110]: #88
+#121 := [trans #118 #120]: #111
+#122 := (not #111)
+#123 := (or #122 #115)
+#124 := [th-lemma arith triangle-eq]: #123
+#125 := [unit-resolution #124 #121]: #115
+[th-lemma arith farkas 2 1 #116 #125]: false
+unsat
+75f83357dfd0e95b567e5e16d1b564f2aacd5f8b 143 0
+#2 := false
+#8 := 0::Real
+decl f3 :: Real
+#7 := f3
+#36 := -1::Real
+#37 := (* -1::Real f3)
+#58 := (>= f3 0::Real)
+#65 := (if #58 f3 #37)
+#104 := (* -1::Real #65)
+#154 := (+ f3 #104)
+#155 := (<= #154 0::Real)
+#90 := (= f3 #65)
+#105 := (+ #37 #104)
+#107 := (>= #105 0::Real)
+#91 := (= #37 #65)
+#59 := (not #58)
+#139 := [hypothesis]: #59
+#88 := (or #58 #91)
+#89 := [def-axiom]: #88
+#140 := [unit-resolution #89 #139]: #91
+#133 := (not #91)
+#141 := (or #133 #107)
+#142 := [th-lemma arith triangle-eq]: #141
+#143 := [unit-resolution #142 #140]: #107
+#73 := (+ f3 #65)
+#86 := (<= #73 0::Real)
+#148 := (not #86)
+#87 := (>= #73 0::Real)
+#106 := (<= #105 0::Real)
+#74 := (= #73 0::Real)
+#94 := (not #74)
+#126 := (not #87)
+#127 := [hypothesis]: #126
+#128 := (or #94 #87)
+#129 := [th-lemma arith triangle-eq]: #128
+#130 := [unit-resolution #129 #127]: #94
+#124 := (or #59 #74)
+#111 := (= f3 0::Real)
+#9 := (<= f3 0::Real)
+#108 := [hypothesis]: #94
+#102 := (or #9 #74)
+#52 := (not #9)
+#79 := (iff #52 #74)
+#11 := (- f3)
+#10 := (< f3 0::Real)
+#12 := (if #10 #11 f3)
+#13 := (= #12 #11)
+#14 := (iff #9 #13)
+#15 := (not #14)
+#82 := (iff #15 #79)
+#40 := (if #10 #37 f3)
+#43 := (= #40 #37)
+#53 := (iff #52 #43)
+#80 := (iff #53 #79)
+#77 := (iff #43 #74)
+#70 := (= #65 #37)
+#75 := (iff #70 #74)
+#76 := [rewrite]: #75
+#71 := (iff #43 #70)
+#68 := (= #40 #65)
+#62 := (if #59 #37 f3)
+#66 := (= #62 #65)
+#67 := [rewrite]: #66
+#63 := (= #40 #62)
+#60 := (iff #10 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#69 := [trans #64 #67]: #68
+#72 := [monotonicity #69]: #71
+#78 := [trans #72 #76]: #77
+#81 := [monotonicity #78]: #80
+#56 := (iff #15 #53)
+#46 := (iff #9 #43)
+#49 := (not #46)
+#54 := (iff #49 #53)
+#55 := [rewrite]: #54
+#50 := (iff #15 #49)
+#47 := (iff #14 #46)
+#44 := (iff #13 #43)
+#38 := (= #11 #37)
+#39 := [rewrite]: #38
+#41 := (= #12 #40)
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42 #39]: #44
+#48 := [monotonicity #45]: #47
+#51 := [monotonicity #48]: #50
+#57 := [trans #51 #55]: #56
+#83 := [trans #57 #81]: #82
+#35 := [asserted]: #15
+#84 := [mp #35 #83]: #79
+#95 := (not #79)
+#100 := (or #9 #74 #95)
+#101 := [def-axiom]: #100
+#103 := [unit-resolution #101 #84]: #102
+#109 := [unit-resolution #103 #108]: #9
+#110 := [hypothesis]: #58
+#112 := [th-lemma arith eq-propagate 0 0 #110 #109]: #111
+#120 := (= #73 f3)
+#118 := (= #65 f3)
+#92 := (or #59 #90)
+#93 := [def-axiom]: #92
+#113 := [unit-resolution #93 #110]: #90
+#119 := [symm #113]: #118
+#116 := (= #73 #65)
+#114 := (= #65 #73)
+#115 := [th-lemma arith eq-propagate 1 1 #110 #109]: #114
+#117 := [symm #115]: #116
+#121 := [trans #117 #119]: #120
+#122 := [trans #121 #112]: #74
+#123 := [unit-resolution #108 #122]: false
+#125 := [lemma #123]: #124
+#131 := [unit-resolution #125 #130]: #59
+#132 := [unit-resolution #89 #131]: #91
+#134 := (or #133 #106)
+#135 := [th-lemma arith triangle-eq]: #134
+#136 := [unit-resolution #135 #132]: #106
+#137 := [th-lemma arith farkas 1 1 #127 #136]: false
+#138 := [lemma #137]: #87
+#144 := (or #58 #9)
+#145 := [th-lemma arith farkas 1 1]: #144
+#146 := [unit-resolution #145 #139]: #9
+#98 := (or #52 #94)
+#96 := (or #52 #94 #95)
+#97 := [def-axiom]: #96
+#99 := [unit-resolution #97 #84]: #98
+#147 := [unit-resolution #99 #146]: #94
+#149 := (or #74 #148 #126)
+#150 := [th-lemma arith triangle-eq]: #149
+#151 := [unit-resolution #150 #147 #138]: #148
+#152 := [th-lemma arith farkas 1 1 #151 #143]: false
+#153 := [lemma #152]: #58
+#157 := [unit-resolution #93 #153]: #90
+#158 := (not #90)
+#159 := (or #158 #155)
+#160 := [th-lemma arith triangle-eq]: #159
+#161 := [unit-resolution #160 #157]: #155
+#162 := [unit-resolution #125 #153]: #74
+#163 := (or #94 #86)
+#164 := [th-lemma arith triangle-eq]: #163
+#165 := [unit-resolution #164 #162]: #86
+#166 := [unit-resolution #99 #162]: #52
+[th-lemma arith farkas 2 1 1 #166 #165 #161]: false
+unsat
+170a46884b0c93a265ba9103f7b32d3822f6590a 116 0
+#2 := false
+#8 := 0::Real
+decl f3 :: Real
+#7 := f3
+#37 := -1::Real
+#38 := (* -1::Real f3)
+#64 := (>= f3 0::Real)
+#71 := (if #64 f3 #38)
+#85 := (* -1::Real #71)
+#125 := (+ #38 #85)
+#141 := (<= #125 0::Real)
+#113 := (= #38 #71)
+#65 := (not #64)
+#123 := (+ f3 #85)
+#124 := (<= #123 0::Real)
+#112 := (= f3 #71)
+#126 := [hypothesis]: #64
+#108 := (or #65 #112)
+#109 := [def-axiom]: #108
+#127 := [unit-resolution #109 #126]: #112
+#128 := (not #112)
+#129 := (or #128 #124)
+#130 := [th-lemma arith triangle-eq]: #129
+#131 := [unit-resolution #130 #127]: #124
+#80 := (>= #71 0::Real)
+#79 := (not #80)
+#91 := (if #80 #71 #85)
+#110 := (= #71 #91)
+#134 := (not #110)
+#96 := (= #91 #71)
+#99 := (not #96)
+#135 := (iff #99 #134)
+#132 := (iff #96 #110)
+#133 := [commutativity]: #132
+#136 := [monotonicity #133]: #135
+#10 := (- f3)
+#9 := (< f3 0::Real)
+#11 := (if #9 #10 f3)
+#13 := (- #11)
+#12 := (< #11 0::Real)
+#14 := (if #12 #13 #11)
+#15 := (= #14 #11)
+#16 := (not #15)
+#102 := (iff #16 #99)
+#41 := (if #9 #38 f3)
+#50 := (* -1::Real #41)
+#44 := (< #41 0::Real)
+#55 := (if #44 #50 #41)
+#58 := (= #55 #41)
+#61 := (not #58)
+#100 := (iff #61 #99)
+#97 := (iff #58 #96)
+#74 := (= #41 #71)
+#68 := (if #65 #38 f3)
+#72 := (= #68 #71)
+#73 := [rewrite]: #72
+#69 := (= #41 #68)
+#66 := (iff #9 #65)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#75 := [trans #70 #73]: #74
+#94 := (= #55 #91)
+#88 := (if #79 #85 #71)
+#92 := (= #88 #91)
+#93 := [rewrite]: #92
+#89 := (= #55 #88)
+#86 := (= #50 #85)
+#87 := [monotonicity #75]: #86
+#83 := (iff #44 #79)
+#76 := (< #71 0::Real)
+#81 := (iff #76 #79)
+#82 := [rewrite]: #81
+#77 := (iff #44 #76)
+#78 := [monotonicity #75]: #77
+#84 := [trans #78 #82]: #83
+#90 := [monotonicity #84 #87 #75]: #89
+#95 := [trans #90 #93]: #94
+#98 := [monotonicity #95 #75]: #97
+#101 := [monotonicity #98]: #100
+#62 := (iff #16 #61)
+#59 := (iff #15 #58)
+#42 := (= #11 #41)
+#39 := (= #10 #38)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#56 := (= #14 #55)
+#53 := (= #13 #50)
+#47 := (- #41)
+#51 := (= #47 #50)
+#52 := [rewrite]: #51
+#48 := (= #13 #47)
+#49 := [monotonicity #43]: #48
+#54 := [trans #49 #52]: #53
+#45 := (iff #12 #44)
+#46 := [monotonicity #43]: #45
+#57 := [monotonicity #46 #54 #43]: #56
+#60 := [monotonicity #57 #43]: #59
+#63 := [monotonicity #60]: #62
+#103 := [trans #63 #101]: #102
+#36 := [asserted]: #16
+#104 := [mp #36 #103]: #99
+#137 := [mp #104 #136]: #134
+#114 := (or #79 #110)
+#115 := [def-axiom]: #114
+#138 := [unit-resolution #115 #137]: #79
+#139 := [th-lemma arith farkas -1 1 1 #126 #138 #131]: false
+#140 := [lemma #139]: #65
+#106 := (or #64 #113)
+#107 := [def-axiom]: #106
+#143 := [unit-resolution #107 #140]: #113
+#144 := (not #113)
+#145 := (or #144 #141)
+#146 := [th-lemma arith triangle-eq]: #145
+#147 := [unit-resolution #146 #143]: #141
+[th-lemma arith farkas 1 1 1 #140 #138 #147]: false
+unsat
+343b8694d01ceec9aadefda1d9bec8e7b858a0bc 57 0
+#2 := false
+#15 := 0::Real
+decl f4 :: Real
+#8 := f4
+decl f3 :: Real
+#7 := f3
+#36 := -1::Real
+#37 := (* -1::Real f4)
+#38 := (+ f3 #37)
+#39 := (<= #38 0::Real)
+#42 := (if #39 f3 f4)
+#50 := (* -1::Real #42)
+#59 := (+ f4 #50)
+#73 := (>= #59 0::Real)
+#63 := (= f4 #42)
+#64 := (not #39)
+#62 := (= f3 #42)
+#67 := (not #62)
+#51 := (+ f3 #50)
+#49 := (>= #51 0::Real)
+#55 := (not #49)
+#9 := (<= f3 f4)
+#10 := (if #9 f3 f4)
+#11 := (<= #10 f3)
+#12 := (not #11)
+#56 := (iff #12 #55)
+#53 := (iff #11 #49)
+#45 := (<= #42 f3)
+#48 := (iff #45 #49)
+#52 := [rewrite]: #48
+#46 := (iff #11 #45)
+#43 := (= #10 #42)
+#40 := (iff #9 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#47 := [monotonicity #44]: #46
+#54 := [trans #47 #52]: #53
+#57 := [monotonicity #54]: #56
+#33 := [asserted]: #12
+#58 := [mp #33 #57]: #55
+#66 := [hypothesis]: #62
+#68 := (or #67 #49)
+#69 := [th-lemma arith triangle-eq]: #68
+#70 := [unit-resolution #69 #66 #58]: false
+#71 := [lemma #70]: #67
+#65 := (or #64 #62)
+#60 := [def-axiom]: #65
+#74 := [unit-resolution #60 #71]: #64
+#61 := (or #39 #63)
+#35 := [def-axiom]: #61
+#75 := [unit-resolution #35 #74]: #63
+#76 := (not #63)
+#77 := (or #76 #73)
+#78 := [th-lemma arith triangle-eq]: #77
+#79 := [unit-resolution #78 #75]: #73
+[th-lemma arith farkas 1 1 1 #58 #74 #79]: false
+unsat
+488e735c5af613e8d7cafc6137d916a7f9ebe0e4 57 0
+#2 := false
+#15 := 0::Real
+decl f4 :: Real
+#8 := f4
+decl f3 :: Real
+#7 := f3
+#36 := -1::Real
+#37 := (* -1::Real f4)
+#38 := (+ f3 #37)
+#39 := (<= #38 0::Real)
+#42 := (if #39 f3 f4)
+#49 := (* -1::Real #42)
+#50 := (+ f4 #49)
+#48 := (>= #50 0::Real)
+#55 := (not #48)
+#9 := (<= f3 f4)
+#10 := (if #9 f3 f4)
+#11 := (<= #10 f4)
+#12 := (not #11)
+#56 := (iff #12 #55)
+#53 := (iff #11 #48)
+#45 := (<= #42 f4)
+#51 := (iff #45 #48)
+#52 := [rewrite]: #51
+#46 := (iff #11 #45)
+#43 := (= #10 #42)
+#40 := (iff #9 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#47 := [monotonicity #44]: #46
+#54 := [trans #47 #52]: #53
+#57 := [monotonicity #54]: #56
+#33 := [asserted]: #12
+#58 := [mp #33 #57]: #55
+#63 := (= f4 #42)
+#64 := (not #39)
+#68 := [hypothesis]: #39
+#59 := (+ f3 #49)
+#67 := (>= #59 0::Real)
+#62 := (= f3 #42)
+#65 := (or #64 #62)
+#60 := [def-axiom]: #65
+#69 := [unit-resolution #60 #68]: #62
+#70 := (not #62)
+#71 := (or #70 #67)
+#72 := [th-lemma arith triangle-eq]: #71
+#73 := [unit-resolution #72 #69]: #67
+#74 := [th-lemma arith farkas -1 1 1 #73 #58 #68]: false
+#75 := [lemma #74]: #64
+#61 := (or #39 #63)
+#35 := [def-axiom]: #61
+#76 := [unit-resolution #35 #75]: #63
+#77 := (not #63)
+#78 := (or #77 #48)
+#79 := [th-lemma arith triangle-eq]: #78
+[unit-resolution #79 #76 #58]: false
+unsat
+be2bc9d6a85f1d0753b3453c53165fb3cf75d021 103 0
+#2 := false
+#20 := 0::Real
+decl f5 :: Real
+#10 := f5
+decl f4 :: Real
+#8 := f4
+#46 := -1::Real
+#55 := (* -1::Real f5)
+#65 := (+ f4 #55)
+#66 := (<= #65 0::Real)
+#69 := (if #66 f4 f5)
+#77 := (* -1::Real #69)
+decl f3 :: Real
+#7 := f3
+#78 := (+ f3 #77)
+#76 := (>= #78 0::Real)
+#75 := (not #76)
+#56 := (+ f3 #55)
+#54 := (>= #56 0::Real)
+#53 := (not #54)
+#49 := (* -1::Real f4)
+#50 := (+ f3 #49)
+#48 := (>= #50 0::Real)
+#47 := (not #48)
+#59 := (and #47 #53)
+#62 := (not #59)
+#83 := (or #62 #75)
+#86 := (not #83)
+#13 := (<= f4 f5)
+#14 := (if #13 f4 f5)
+#15 := (< f3 #14)
+#11 := (< f3 f5)
+#9 := (< f3 f4)
+#12 := (and #9 #11)
+#16 := (implies #12 #15)
+#17 := (not #16)
+#89 := (iff #17 #86)
+#39 := (not #12)
+#40 := (or #39 #15)
+#43 := (not #40)
+#87 := (iff #43 #86)
+#84 := (iff #40 #83)
+#81 := (iff #15 #75)
+#72 := (< f3 #69)
+#79 := (iff #72 #75)
+#80 := [rewrite]: #79
+#73 := (iff #15 #72)
+#70 := (= #14 #69)
+#67 := (iff #13 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#74 := [monotonicity #71]: #73
+#82 := [trans #74 #80]: #81
+#63 := (iff #39 #62)
+#60 := (iff #12 #59)
+#57 := (iff #11 #53)
+#58 := [rewrite]: #57
+#51 := (iff #9 #47)
+#52 := [rewrite]: #51
+#61 := [monotonicity #52 #58]: #60
+#64 := [monotonicity #61]: #63
+#85 := [monotonicity #64 #82]: #84
+#88 := [monotonicity #85]: #87
+#44 := (iff #17 #43)
+#41 := (iff #16 #40)
+#42 := [rewrite]: #41
+#45 := [monotonicity #42]: #44
+#90 := [trans #45 #88]: #89
+#38 := [asserted]: #17
+#91 := [mp #38 #90]: #86
+#95 := [not-or-elim #91]: #76
+#92 := [not-or-elim #91]: #59
+#94 := [and-elim #92]: #53
+#100 := (+ f5 #77)
+#117 := (<= #100 0::Real)
+#106 := (= f5 #69)
+#107 := (not #66)
+#105 := (= f4 #69)
+#112 := (not #105)
+#102 := (+ f4 #77)
+#99 := (<= #102 0::Real)
+#109 := (not #99)
+#93 := [and-elim #92]: #47
+#97 := [hypothesis]: #99
+#98 := [th-lemma arith farkas -1 -1 1 #97 #93 #95]: false
+#110 := [lemma #98]: #109
+#111 := [hypothesis]: #105
+#113 := (or #112 #99)
+#114 := [th-lemma arith triangle-eq]: #113
+#115 := [unit-resolution #114 #111 #110]: false
+#116 := [lemma #115]: #112
+#108 := (or #107 #105)
+#103 := [def-axiom]: #108
+#119 := [unit-resolution #103 #116]: #107
+#104 := (or #66 #106)
+#101 := [def-axiom]: #104
+#120 := [unit-resolution #101 #119]: #106
+#121 := (not #106)
+#122 := (or #121 #117)
+#123 := [th-lemma arith triangle-eq]: #122
+#124 := [unit-resolution #123 #120]: #117
+[th-lemma arith farkas -1 -1 1 #124 #94 #95]: false
+unsat
+8a834764014f7a0fc98f83812b7df5e9e71d3228 94 0
+#2 := false
+decl f3 :: Real
+#7 := f3
+decl f4 :: Real
+#8 := f4
+#17 := 0::Real
+#38 := -1::Real
+#39 := (* -1::Real f4)
+#40 := (+ f3 #39)
+#48 := (>= #40 0::Real)
+#50 := (if #48 f4 f3)
+#41 := (<= #40 0::Real)
+#44 := (if #41 f3 f4)
+#53 := (= #44 #50)
+#60 := (= f4 #50)
+#65 := (not #41)
+#63 := (= f3 #44)
+#105 := (not #63)
+#67 := (= f3 #50)
+#74 := (not #67)
+#75 := [hypothesis]: #74
+#71 := (or #48 #67)
+#72 := [def-axiom]: #71
+#76 := [unit-resolution #72 #75]: #48
+#68 := (not #48)
+#69 := (or #68 #60)
+#70 := [def-axiom]: #69
+#77 := [unit-resolution #70 #76]: #60
+#73 := (= f3 f4)
+#64 := (= f4 #44)
+#87 := (not #64)
+#56 := (not #53)
+#88 := (iff #56 #87)
+#85 := (iff #53 #64)
+#83 := (iff #64 #53)
+#78 := (= #50 #44)
+#81 := (iff #78 #53)
+#82 := [commutativity]: #81
+#79 := (iff #64 #78)
+#80 := [monotonicity #77]: #79
+#84 := [trans #80 #82]: #83
+#86 := [symm #84]: #85
+#89 := [monotonicity #86]: #88
+#11 := (<= f4 f3)
+#12 := (if #11 f4 f3)
+#9 := (<= f3 f4)
+#10 := (if #9 f3 f4)
+#13 := (= #10 #12)
+#14 := (not #13)
+#57 := (iff #14 #56)
+#54 := (iff #13 #53)
+#51 := (= #12 #50)
+#47 := (iff #11 #48)
+#49 := [rewrite]: #47
+#52 := [monotonicity #49]: #51
+#45 := (= #10 #44)
+#42 := (iff #9 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#55 := [monotonicity #46 #52]: #54
+#58 := [monotonicity #55]: #57
+#35 := [asserted]: #14
+#59 := [mp #35 #58]: #56
+#90 := [mp #59 #89]: #87
+#62 := (or #41 #64)
+#37 := [def-axiom]: #62
+#91 := [unit-resolution #37 #90]: #41
+#94 := (or #73 #65)
+#92 := (or #73 #65 #68)
+#93 := [th-lemma arith triangle-eq]: #92
+#95 := [unit-resolution #93 #76]: #94
+#96 := [unit-resolution #95 #91]: #73
+#97 := [trans #96 #77]: #67
+#98 := [unit-resolution #75 #97]: false
+#99 := [lemma #98]: #67
+#101 := (= #44 f3)
+#100 := [hypothesis]: #63
+#102 := [symm #100]: #101
+#103 := [trans #102 #99]: #53
+#104 := [unit-resolution #59 #103]: false
+#106 := [lemma #104]: #105
+#66 := (or #65 #63)
+#61 := [def-axiom]: #66
+#107 := [unit-resolution #61 #106]: #65
+#109 := (or #48 #41)
+#110 := [th-lemma arith farkas 1 1]: #109
+#111 := [unit-resolution #110 #107]: #48
+#112 := [unit-resolution #70 #111]: #60
+#115 := (= #44 f4)
+#108 := [unit-resolution #37 #107]: #64
+#116 := [symm #108]: #115
+#117 := [trans #116 #112]: #53
+[unit-resolution #59 #117]: false
+unsat
+565ea5cad625ceae443c2aa9665a6caa8c4432ef 53 0
+#2 := false
+#7 := 0::Real
+decl f3 :: Real
+#8 := f3
+#10 := (<= f3 0::Real)
+#11 := (if #10 f3 0::Real)
+#12 := (= #11 0::Real)
+#63 := (= f3 0::Real)
+#58 := (not #12)
+#44 := (>= f3 0::Real)
+#45 := (not #44)
+#48 := (or #45 #12)
+#51 := (not #48)
+#9 := (<= 0::Real f3)
+#13 := (implies #9 #12)
+#14 := (not #13)
+#54 := (iff #14 #51)
+#35 := (not #9)
+#36 := (or #35 #12)
+#39 := (not #36)
+#52 := (iff #39 #51)
+#49 := (iff #36 #48)
+#46 := (iff #35 #45)
+#42 := (iff #9 #44)
+#43 := [rewrite]: #42
+#47 := [monotonicity #43]: #46
+#50 := [monotonicity #47]: #49
+#53 := [monotonicity #50]: #52
+#40 := (iff #14 #39)
+#37 := (iff #13 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#55 := [trans #41 #53]: #54
+#34 := [asserted]: #14
+#56 := [mp #34 #55]: #51
+#59 := [not-or-elim #56]: #58
+#65 := (or #10 #12)
+#66 := [def-axiom]: #65
+#64 := [unit-resolution #66 #59]: #10
+#57 := [not-or-elim #56]: #44
+#68 := (not #10)
+#61 := (or #63 #68 #45)
+#62 := [th-lemma arith triangle-eq]: #61
+#71 := [unit-resolution #62 #57 #64]: #63
+#73 := (= #11 f3)
+#67 := (= f3 #11)
+#69 := (or #68 #67)
+#70 := [def-axiom]: #69
+#72 := [unit-resolution #70 #64]: #67
+#74 := [symm #72]: #73
+#75 := [trans #74 #71]: #12
+[unit-resolution #59 #75]: false
+unsat
+6b8315813f4cc23842e26ce083c1ccaeb3b9f4ea 124 0
+#2 := false
+#12 := 0::Real
+decl f4 :: Real
+#8 := f4
+decl f3 :: Real
+#7 := f3
+#38 := -1::Real
+#40 := (* -1::Real f4)
+#53 := (+ f3 #40)
+#54 := (<= #53 0::Real)
+#57 := (if #54 f3 f4)
+#105 := (* -1::Real #57)
+#106 := (+ f3 #105)
+#108 := (>= #106 0::Real)
+#93 := (= f3 #57)
+#107 := (+ f4 #105)
+#125 := (>= #107 0::Real)
+#94 := (= f4 #57)
+#95 := (not #54)
+#136 := [hypothesis]: #95
+#92 := (or #54 #94)
+#89 := [def-axiom]: #92
+#137 := [unit-resolution #89 #136]: #94
+#128 := (not #94)
+#129 := (or #128 #125)
+#130 := [th-lemma arith triangle-eq]: #129
+#138 := [unit-resolution #130 #137]: #125
+#39 := (* -1::Real f3)
+#41 := (+ #39 #40)
+#11 := (+ f3 f4)
+#60 := (>= #11 0::Real)
+#67 := (if #60 #11 #41)
+#75 := (* -1::Real #67)
+#104 := (+ #41 #75)
+#124 := (<= #104 0::Real)
+#97 := (= #41 #67)
+#61 := (not #60)
+#109 := [hypothesis]: #60
+#76 := (+ #57 #75)
+#77 := (<= #76 0::Real)
+#82 := (not #77)
+#14 := (- #11)
+#13 := (< #11 0::Real)
+#15 := (if #13 #14 #11)
+#9 := (<= f3 f4)
+#10 := (if #9 f3 f4)
+#16 := (<= #10 #15)
+#17 := (not #16)
+#85 := (iff #17 #82)
+#44 := (if #13 #41 #11)
+#47 := (<= #10 #44)
+#50 := (not #47)
+#83 := (iff #50 #82)
+#80 := (iff #47 #77)
+#72 := (<= #57 #67)
+#78 := (iff #72 #77)
+#79 := [rewrite]: #78
+#73 := (iff #47 #72)
+#70 := (= #44 #67)
+#64 := (if #61 #41 #11)
+#68 := (= #64 #67)
+#69 := [rewrite]: #68
+#65 := (= #44 #64)
+#62 := (iff #13 #61)
+#63 := [rewrite]: #62
+#66 := [monotonicity #63]: #65
+#71 := [trans #66 #69]: #70
+#58 := (= #10 #57)
+#55 := (iff #9 #54)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#74 := [monotonicity #59 #71]: #73
+#81 := [trans #74 #79]: #80
+#84 := [monotonicity #81]: #83
+#51 := (iff #17 #50)
+#48 := (iff #16 #47)
+#45 := (= #15 #44)
+#42 := (= #14 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#49 := [monotonicity #46]: #48
+#52 := [monotonicity #49]: #51
+#86 := [trans #52 #84]: #85
+#37 := [asserted]: #17
+#87 := [mp #37 #86]: #82
+#122 := (or #95 #61)
+#110 := [hypothesis]: #54
+#96 := (or #95 #93)
+#91 := [def-axiom]: #96
+#111 := [unit-resolution #91 #110]: #93
+#112 := (not #93)
+#113 := (or #112 #108)
+#114 := [th-lemma arith triangle-eq]: #113
+#115 := [unit-resolution #114 #111]: #108
+#102 := (+ #11 #75)
+#103 := (<= #102 0::Real)
+#90 := (= #11 #67)
+#98 := (or #61 #90)
+#99 := [def-axiom]: #98
+#116 := [unit-resolution #99 #109]: #90
+#117 := (not #90)
+#118 := (or #117 #103)
+#119 := [th-lemma arith triangle-eq]: #118
+#120 := [unit-resolution #119 #116]: #103
+#121 := [th-lemma arith farkas 2 2 2 1 1 #120 #115 #87 #110 #109]: false
+#123 := [lemma #121]: #122
+#126 := [unit-resolution #123 #109]: #95
+#127 := [unit-resolution #89 #126]: #94
+#131 := [unit-resolution #130 #127]: #125
+#132 := [th-lemma arith farkas 2 2 1 2 1 #120 #131 #126 #87 #109]: false
+#133 := [lemma #132]: #61
+#100 := (or #60 #97)
+#101 := [def-axiom]: #100
+#139 := [unit-resolution #101 #133]: #97
+#140 := (not #97)
+#141 := (or #140 #124)
+#142 := [th-lemma arith triangle-eq]: #141
+#143 := [unit-resolution #142 #139]: #124
+#144 := [th-lemma arith farkas 3/2 1/2 1 1 1 #133 #136 #87 #143 #138]: false
+#145 := [lemma #144]: #54
+#146 := [unit-resolution #91 #145]: #93
+#147 := [unit-resolution #114 #146]: #108
+[th-lemma arith farkas 1/2 3/2 1 1 1 #145 #133 #87 #143 #147]: false
+unsat
+af561b282d1827f310ac70556912361f746c755e 57 0
+#2 := false
+#15 := 0::Real
+decl f3 :: Real
+#7 := f3
+decl f4 :: Real
+#8 := f4
+#36 := -1::Real
+#37 := (* -1::Real f4)
+#38 := (+ f3 #37)
+#39 := (<= #38 0::Real)
+#42 := (if #39 f4 f3)
+#48 := (* -1::Real #42)
+#49 := (+ f3 #48)
+#50 := (<= #49 0::Real)
+#55 := (not #50)
+#9 := (<= f3 f4)
+#10 := (if #9 f4 f3)
+#11 := (<= f3 #10)
+#12 := (not #11)
+#56 := (iff #12 #55)
+#53 := (iff #11 #50)
+#45 := (<= f3 #42)
+#51 := (iff #45 #50)
+#52 := [rewrite]: #51
+#46 := (iff #11 #45)
+#43 := (= #10 #42)
+#40 := (iff #9 #39)
+#41 := [rewrite]: #40
+#44 := [monotonicity #41]: #43
+#47 := [monotonicity #44]: #46
+#54 := [trans #47 #52]: #53
+#57 := [monotonicity #54]: #56
+#33 := [asserted]: #12
+#58 := [mp #33 #57]: #55
+#63 := (= f3 #42)
+#64 := (not #39)
+#68 := [hypothesis]: #39
+#59 := (+ f4 #48)
+#66 := (<= #59 0::Real)
+#62 := (= f4 #42)
+#65 := (or #64 #62)
+#60 := [def-axiom]: #65
+#69 := [unit-resolution #60 #68]: #62
+#70 := (not #62)
+#71 := (or #70 #66)
+#72 := [th-lemma arith triangle-eq]: #71
+#73 := [unit-resolution #72 #69]: #66
+#74 := [th-lemma arith farkas 1 -1 1 #73 #58 #68]: false
+#75 := [lemma #74]: #64
+#61 := (or #39 #63)
+#35 := [def-axiom]: #61
+#76 := [unit-resolution #35 #75]: #63
+#77 := (not #63)
+#78 := (or #77 #50)
+#79 := [th-lemma arith triangle-eq]: #78
+[unit-resolution #79 #76 #58]: false
+unsat
+c76d8e5e48d2562cff8ec7cba9425b7fcddfd09a 57 0
+#2 := false
+#15 := 0::Real
+decl f4 :: Real
+#8 := f4
+decl f3 :: Real
+#7 := f3
+#36 := -1::Real
+#39 := (* -1::Real f4)
+#40 := (+ f3 #39)
+#38 := (>= #40 0::Real)
+#42 := (if #38 f3 f4)
+#48 := (* -1::Real #42)
+#59 := (+ f4 #48)
+#72 := (<= #59 0::Real)
+#63 := (= f4 #42)
+#64 := (not #38)
+#62 := (= f3 #42)
+#67 := (not #62)
+#49 := (+ f3 #48)
+#50 := (<= #49 0::Real)
+#55 := (not #50)
+#9 := (<= f4 f3)
+#10 := (if #9 f3 f4)
+#11 := (<= f3 #10)
+#12 := (not #11)
+#56 := (iff #12 #55)
+#53 := (iff #11 #50)
+#45 := (<= f3 #42)
+#51 := (iff #45 #50)
+#52 := [rewrite]: #51
+#46 := (iff #11 #45)
+#43 := (= #10 #42)
+#37 := (iff #9 #38)
+#41 := [rewrite]: #37
+#44 := [monotonicity #41]: #43
+#47 := [monotonicity #44]: #46
+#54 := [trans #47 #52]: #53
+#57 := [monotonicity #54]: #56
+#33 := [asserted]: #12
+#58 := [mp #33 #57]: #55
+#66 := [hypothesis]: #62
+#68 := (or #67 #50)
+#69 := [th-lemma arith triangle-eq]: #68
+#70 := [unit-resolution #69 #66 #58]: false
+#71 := [lemma #70]: #67
+#65 := (or #64 #62)
+#60 := [def-axiom]: #65
+#74 := [unit-resolution #60 #71]: #64
+#61 := (or #38 #63)
+#35 := [def-axiom]: #61
+#75 := [unit-resolution #35 #74]: #63
+#76 := (not #63)
+#77 := (or #76 #72)
+#78 := [th-lemma arith triangle-eq]: #77
+#79 := [unit-resolution #78 #75]: #72
+[th-lemma arith farkas 1 1 1 #58 #74 #79]: false
+unsat
+309c80c26e888c63759e9988268f1cdcc26ef28b 103 0
+#2 := false
+#20 := 0::Real
+decl f3 :: Real
+#7 := f3
+decl f5 :: Real
+#10 := f5
+#46 := -1::Real
+#53 := (* -1::Real f5)
+#65 := (+ f3 #53)
+#66 := (<= #65 0::Real)
+#69 := (if #66 f5 f3)
+#75 := (* -1::Real #69)
+decl f4 :: Real
+#8 := f4
+#76 := (+ f4 #75)
+#77 := (<= #76 0::Real)
+#78 := (not #77)
+#54 := (+ f4 #53)
+#55 := (<= #54 0::Real)
+#56 := (not #55)
+#49 := (* -1::Real f4)
+#50 := (+ f3 #49)
+#48 := (>= #50 0::Real)
+#47 := (not #48)
+#59 := (and #47 #56)
+#62 := (not #59)
+#83 := (or #62 #78)
+#86 := (not #83)
+#13 := (<= f3 f5)
+#14 := (if #13 f5 f3)
+#15 := (< #14 f4)
+#11 := (< f5 f4)
+#9 := (< f3 f4)
+#12 := (and #9 #11)
+#16 := (implies #12 #15)
+#17 := (not #16)
+#89 := (iff #17 #86)
+#39 := (not #12)
+#40 := (or #39 #15)
+#43 := (not #40)
+#87 := (iff #43 #86)
+#84 := (iff #40 #83)
+#81 := (iff #15 #78)
+#72 := (< #69 f4)
+#79 := (iff #72 #78)
+#80 := [rewrite]: #79
+#73 := (iff #15 #72)
+#70 := (= #14 #69)
+#67 := (iff #13 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#74 := [monotonicity #71]: #73
+#82 := [trans #74 #80]: #81
+#63 := (iff #39 #62)
+#60 := (iff #12 #59)
+#57 := (iff #11 #56)
+#58 := [rewrite]: #57
+#51 := (iff #9 #47)
+#52 := [rewrite]: #51
+#61 := [monotonicity #52 #58]: #60
+#64 := [monotonicity #61]: #63
+#85 := [monotonicity #64 #82]: #84
+#88 := [monotonicity #85]: #87
+#44 := (iff #17 #43)
+#41 := (iff #16 #40)
+#42 := [rewrite]: #41
+#45 := [monotonicity #42]: #44
+#90 := [trans #45 #88]: #89
+#38 := [asserted]: #17
+#91 := [mp #38 #90]: #86
+#95 := [not-or-elim #91]: #77
+#92 := [not-or-elim #91]: #59
+#93 := [and-elim #92]: #47
+#99 := (+ f3 #75)
+#118 := (>= #99 0::Real)
+#106 := (= f3 #69)
+#107 := (not #66)
+#105 := (= f5 #69)
+#112 := (not #105)
+#102 := (+ f5 #75)
+#100 := (>= #102 0::Real)
+#109 := (not #100)
+#94 := [and-elim #92]: #56
+#97 := [hypothesis]: #100
+#98 := [th-lemma arith farkas -1 -1 1 #97 #94 #95]: false
+#110 := [lemma #98]: #109
+#111 := [hypothesis]: #105
+#113 := (or #112 #100)
+#114 := [th-lemma arith triangle-eq]: #113
+#115 := [unit-resolution #114 #111 #110]: false
+#116 := [lemma #115]: #112
+#108 := (or #107 #105)
+#103 := [def-axiom]: #108
+#119 := [unit-resolution #103 #116]: #107
+#104 := (or #66 #106)
+#101 := [def-axiom]: #104
+#120 := [unit-resolution #101 #119]: #106
+#121 := (not #106)
+#122 := (or #121 #118)
+#123 := [th-lemma arith triangle-eq]: #122
+#124 := [unit-resolution #123 #120]: #118
+[th-lemma arith farkas -1 1 1 #124 #93 #95]: false
+unsat
+23c443b999f944a6345020be737a4a7b628ff638 96 0
+#2 := false
+decl f4 :: Real
+#8 := f4
+decl f3 :: Real
+#7 := f3
+#17 := 0::Real
+#38 := -1::Real
+#39 := (* -1::Real f4)
+#40 := (+ f3 #39)
+#48 := (>= #40 0::Real)
+#50 := (if #48 f3 f4)
+#41 := (<= #40 0::Real)
+#44 := (if #41 f4 f3)
+#53 := (= #44 #50)
+#60 := (= f3 #50)
+#65 := (not #41)
+#63 := (= f4 #44)
+#107 := (not #63)
+#67 := (= f4 #50)
+#74 := (not #67)
+#75 := [hypothesis]: #74
+#71 := (or #48 #67)
+#72 := [def-axiom]: #71
+#76 := [unit-resolution #72 #75]: #48
+#68 := (not #48)
+#69 := (or #68 #60)
+#70 := [def-axiom]: #69
+#77 := [unit-resolution #70 #76]: #60
+#97 := (= f4 f3)
+#73 := (= f3 f4)
+#64 := (= f3 #44)
+#87 := (not #64)
+#56 := (not #53)
+#88 := (iff #56 #87)
+#85 := (iff #53 #64)
+#83 := (iff #64 #53)
+#78 := (= #50 #44)
+#81 := (iff #78 #53)
+#82 := [commutativity]: #81
+#79 := (iff #64 #78)
+#80 := [monotonicity #77]: #79
+#84 := [trans #80 #82]: #83
+#86 := [symm #84]: #85
+#89 := [monotonicity #86]: #88
+#11 := (<= f4 f3)
+#12 := (if #11 f3 f4)
+#9 := (<= f3 f4)
+#10 := (if #9 f4 f3)
+#13 := (= #10 #12)
+#14 := (not #13)
+#57 := (iff #14 #56)
+#54 := (iff #13 #53)
+#51 := (= #12 #50)
+#47 := (iff #11 #48)
+#49 := [rewrite]: #47
+#52 := [monotonicity #49]: #51
+#45 := (= #10 #44)
+#42 := (iff #9 #41)
+#43 := [rewrite]: #42
+#46 := [monotonicity #43]: #45
+#55 := [monotonicity #46 #52]: #54
+#58 := [monotonicity #55]: #57
+#35 := [asserted]: #14
+#59 := [mp #35 #58]: #56
+#90 := [mp #59 #89]: #87
+#62 := (or #41 #64)
+#37 := [def-axiom]: #62
+#91 := [unit-resolution #37 #90]: #41
+#94 := (or #73 #65)
+#92 := (or #73 #65 #68)
+#93 := [th-lemma arith triangle-eq]: #92
+#95 := [unit-resolution #93 #76]: #94
+#96 := [unit-resolution #95 #91]: #73
+#98 := [symm #96]: #97
+#99 := [trans #98 #77]: #67
+#100 := [unit-resolution #75 #99]: false
+#101 := [lemma #100]: #67
+#103 := (= #44 f4)
+#102 := [hypothesis]: #63
+#104 := [symm #102]: #103
+#105 := [trans #104 #101]: #53
+#106 := [unit-resolution #59 #105]: false
+#108 := [lemma #106]: #107
+#66 := (or #65 #63)
+#61 := [def-axiom]: #66
+#109 := [unit-resolution #61 #108]: #65
+#111 := (or #48 #41)
+#112 := [th-lemma arith farkas 1 1]: #111
+#113 := [unit-resolution #112 #109]: #48
+#114 := [unit-resolution #70 #113]: #60
+#117 := (= #44 f3)
+#110 := [unit-resolution #37 #109]: #64
+#118 := [symm #110]: #117
+#119 := [trans #118 #114]: #53
+[unit-resolution #59 #119]: false
+unsat
+8fad80a1b745334993da3fb8733536800cca704f 60 0
+#2 := false
+decl f3 :: Real
+#8 := f3
+#7 := 0::Real
+#10 := (<= f3 0::Real)
+#11 := (if #10 0::Real f3)
+#68 := (= f3 #11)
+#80 := (= 0::Real #11)
+#67 := (= #11 0::Real)
+#71 := (not #68)
+#12 := (= #11 f3)
+#58 := (not #12)
+#72 := (iff #58 #71)
+#61 := (iff #12 #68)
+#62 := [commutativity]: #61
+#73 := [monotonicity #62]: #72
+#44 := (>= f3 0::Real)
+#45 := (not #44)
+#48 := (or #45 #12)
+#51 := (not #48)
+#9 := (<= 0::Real f3)
+#13 := (implies #9 #12)
+#14 := (not #13)
+#54 := (iff #14 #51)
+#35 := (not #9)
+#36 := (or #35 #12)
+#39 := (not #36)
+#52 := (iff #39 #51)
+#49 := (iff #36 #48)
+#46 := (iff #35 #45)
+#42 := (iff #9 #44)
+#43 := [rewrite]: #42
+#47 := [monotonicity #43]: #46
+#50 := [monotonicity #47]: #49
+#53 := [monotonicity #50]: #52
+#40 := (iff #14 #39)
+#37 := (iff #13 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#55 := [trans #41 #53]: #54
+#34 := [asserted]: #14
+#56 := [mp #34 #55]: #51
+#59 := [not-or-elim #56]: #58
+#74 := [mp #59 #73]: #71
+#66 := (or #10 #68)
+#63 := [def-axiom]: #66
+#75 := [unit-resolution #63 #74]: #10
+#69 := (not #10)
+#70 := (or #69 #67)
+#65 := [def-axiom]: #70
+#76 := [unit-resolution #65 #75]: #67
+#81 := [symm #76]: #80
+#64 := (= f3 0::Real)
+#57 := [not-or-elim #56]: #44
+#77 := (or #64 #69 #45)
+#78 := [th-lemma arith triangle-eq]: #77
+#79 := [unit-resolution #78 #57 #75]: #64
+#82 := [trans #79 #81]: #68
+[unit-resolution #74 #82]: false
+unsat
+11277aae59b3fc835742651d4832ca0de4c045ff 214 0
+#2 := false
+#8 := 0::Real
+decl f4 :: Real
+#13 := f4
+#42 := -1::Real
+#57 := (* -1::Real f4)
+#93 := (>= f4 0::Real)
+#100 := (if #93 f4 #57)
+#105 := (* -1::Real #100)
+#160 := (+ #57 #105)
+#182 := (<= #160 0::Real)
+#136 := (= #57 #100)
+#94 := (not #93)
+decl f3 :: Real
+#7 := f3
+#111 := (+ f3 #57)
+#112 := (<= #111 0::Real)
+#115 := (if #112 f4 f3)
+#154 := (* -1::Real #115)
+#155 := (+ f4 #154)
+#156 := (<= #155 0::Real)
+#157 := (+ f3 #154)
+#192 := (<= #157 0::Real)
+#148 := (= f3 #115)
+#149 := (not #112)
+#147 := (= f4 #115)
+#194 := [hypothesis]: #112
+#150 := (or #149 #147)
+#151 := [def-axiom]: #150
+#195 := [unit-resolution #151 #194]: #147
+#196 := (not #147)
+#197 := (or #196 #156)
+#198 := [th-lemma arith triangle-eq]: #197
+#199 := [unit-resolution #198 #195]: #156
+#178 := (not #156)
+#190 := (or #94 #178)
+#158 := (+ f4 #105)
+#159 := (<= #158 0::Real)
+#135 := (= f4 #100)
+#164 := [hypothesis]: #93
+#143 := (or #94 #135)
+#144 := [def-axiom]: #143
+#165 := [unit-resolution #144 #164]: #135
+#166 := (not #135)
+#167 := (or #166 #159)
+#168 := [th-lemma arith triangle-eq]: #167
+#169 := [unit-resolution #168 #165]: #159
+#78 := (>= f3 0::Real)
+#79 := (not #78)
+#176 := [hypothesis]: #156
+#179 := (or #79 #94 #178)
+#124 := (+ #100 #115)
+#43 := (* -1::Real f3)
+#85 := (if #78 f3 #43)
+#125 := (+ #85 #124)
+#122 := (>= #125 0::Real)
+#128 := (not #122)
+#18 := (<= f3 f4)
+#19 := (if #18 f4 f3)
+#15 := (- f4)
+#14 := (< f4 0::Real)
+#16 := (if #14 #15 f4)
+#10 := (- f3)
+#9 := (< f3 0::Real)
+#11 := (if #9 #10 f3)
+#12 := (- #11)
+#17 := (- #12 #16)
+#20 := (<= #17 #19)
+#21 := (not #20)
+#131 := (iff #21 #128)
+#60 := (if #14 #57 f4)
+#66 := (* -1::Real #60)
+#46 := (if #9 #43 f3)
+#52 := (* -1::Real #46)
+#67 := (+ #52 #66)
+#72 := (<= #67 #19)
+#75 := (not #72)
+#129 := (iff #75 #128)
+#126 := (iff #72 #122)
+#90 := (* -1::Real #85)
+#108 := (+ #90 #105)
+#118 := (<= #108 #115)
+#121 := (iff #118 #122)
+#123 := [rewrite]: #121
+#119 := (iff #72 #118)
+#116 := (= #19 #115)
+#113 := (iff #18 #112)
+#114 := [rewrite]: #113
+#117 := [monotonicity #114]: #116
+#109 := (= #67 #108)
+#106 := (= #66 #105)
+#103 := (= #60 #100)
+#97 := (if #94 #57 f4)
+#101 := (= #97 #100)
+#102 := [rewrite]: #101
+#98 := (= #60 #97)
+#95 := (iff #14 #94)
+#96 := [rewrite]: #95
+#99 := [monotonicity #96]: #98
+#104 := [trans #99 #102]: #103
+#107 := [monotonicity #104]: #106
+#91 := (= #52 #90)
+#88 := (= #46 #85)
+#82 := (if #79 #43 f3)
+#86 := (= #82 #85)
+#87 := [rewrite]: #86
+#83 := (= #46 #82)
+#80 := (iff #9 #79)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#89 := [trans #84 #87]: #88
+#92 := [monotonicity #89]: #91
+#110 := [monotonicity #92 #107]: #109
+#120 := [monotonicity #110 #117]: #119
+#127 := [trans #120 #123]: #126
+#130 := [monotonicity #127]: #129
+#76 := (iff #21 #75)
+#73 := (iff #20 #72)
+#70 := (= #17 #67)
+#63 := (- #52 #60)
+#68 := (= #63 #67)
+#69 := [rewrite]: #68
+#64 := (= #17 #63)
+#61 := (= #16 #60)
+#58 := (= #15 #57)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#55 := (= #12 #52)
+#49 := (- #46)
+#53 := (= #49 #52)
+#54 := [rewrite]: #53
+#50 := (= #12 #49)
+#47 := (= #11 #46)
+#44 := (= #10 #43)
+#45 := [rewrite]: #44
+#48 := [monotonicity #45]: #47
+#51 := [monotonicity #48]: #50
+#56 := [trans #51 #54]: #55
+#65 := [monotonicity #56 #62]: #64
+#71 := [trans #65 #69]: #70
+#74 := [monotonicity #71]: #73
+#77 := [monotonicity #74]: #76
+#132 := [trans #77 #130]: #131
+#41 := [asserted]: #21
+#133 := [mp #41 #132]: #128
+#161 := (+ f3 #90)
+#162 := (<= #161 0::Real)
+#139 := (= f3 #85)
+#170 := [hypothesis]: #78
+#141 := (or #79 #139)
+#142 := [def-axiom]: #141
+#171 := [unit-resolution #142 #170]: #139
+#172 := (not #139)
+#173 := (or #172 #162)
+#174 := [th-lemma arith triangle-eq]: #173
+#175 := [unit-resolution #174 #171]: #162
+#177 := [th-lemma arith farkas -2 1 -1 1 1 1 #164 #176 #170 #175 #133 #169]: false
+#180 := [lemma #177]: #179
+#183 := [unit-resolution #180 #164 #176]: #79
+#163 := (+ #43 #90)
+#181 := (<= #163 0::Real)
+#140 := (= #43 #85)
+#137 := (or #78 #140)
+#138 := [def-axiom]: #137
+#184 := [unit-resolution #138 #183]: #140
+#185 := (not #140)
+#186 := (or #185 #181)
+#187 := [th-lemma arith triangle-eq]: #186
+#188 := [unit-resolution #187 #184]: #181
+#189 := [th-lemma arith farkas 2 1 1 1 1 1 #164 #176 #133 #188 #183 #169]: false
+#191 := [lemma #189]: #190
+#200 := [unit-resolution #191 #199]: #94
+#145 := (or #93 #136)
+#146 := [def-axiom]: #145
+#201 := [unit-resolution #146 #200]: #136
+#202 := (not #136)
+#203 := (or #202 #182)
+#204 := [th-lemma arith triangle-eq]: #203
+#205 := [unit-resolution #204 #201]: #182
+#206 := (or #79 #149 #93)
+#207 := [th-lemma arith assign-bounds 1 1]: #206
+#208 := [unit-resolution #207 #200 #194]: #79
+#209 := [unit-resolution #138 #208]: #140
+#210 := [unit-resolution #187 #209]: #181
+#211 := [th-lemma arith farkas 1 1 1 1 1 #199 #133 #210 #208 #205]: false
+#212 := [lemma #211]: #149
+#152 := (or #112 #148)
+#153 := [def-axiom]: #152
+#223 := [unit-resolution #153 #212]: #148
+#224 := (not #148)
+#225 := (or #224 #192)
+#226 := [th-lemma arith triangle-eq]: #225
+#227 := [unit-resolution #226 #223]: #192
+#230 := (not #192)
+#231 := (or #156 #112 #230)
+#232 := [th-lemma arith assign-bounds 1 1]: #231
+#233 := [unit-resolution #232 #212 #227]: #156
+#234 := [unit-resolution #191 #233]: #94
+#235 := [unit-resolution #146 #234]: #136
+#236 := [unit-resolution #204 #235]: #182
+#215 := [hypothesis]: #79
+#216 := (or #94 #78 #112)
+#217 := [th-lemma arith assign-bounds 1 1]: #216
+#218 := [unit-resolution #217 #215 #212]: #94
+#219 := [unit-resolution #146 #218]: #136
+#220 := [unit-resolution #204 #219]: #182
+#221 := [unit-resolution #138 #215]: #140
+#222 := [unit-resolution #187 #221]: #181
+#228 := [th-lemma arith farkas 1 1 1 1 1 1 #215 #212 #227 #133 #222 #220]: false
+#229 := [lemma #228]: #78
+#237 := [unit-resolution #142 #229]: #139
+#238 := [unit-resolution #174 #237]: #162
+[th-lemma arith farkas 1 1 1 1 1 1 #212 #227 #133 #229 #238 #236]: false
+unsat
+2becd4c16c00f4a8b711aba96699b51eb714fa29 18 0
+#2 := false
+decl f3 :: Real
+#7 := f3
+#8 := (<= f3 f3)
+#9 := (not #8)
+#40 := (iff #9 false)
+#1 := true
+#35 := (not true)
+#38 := (iff #35 false)
+#39 := [rewrite]: #38
+#36 := (iff #9 #35)
+#33 := (iff #8 true)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#41 := [trans #37 #39]: #40
+#30 := [asserted]: #9
+[mp #30 #41]: false
+unsat
+ee2f03e2614b76303135a935f1f2b05f83a4efce 50 0
+#2 := false
+#18 := 0::Real
+decl f4 :: Real
+#8 := f4
 #44 := -1::Real
 #45 := (* -1::Real f4)
 decl f3 :: Real
-#8 := f3
+#7 := f3
 #46 := (+ f3 #45)
-#48 := (<= #46 0::Real)
-#54 := -3::Real
-#55 := (* -3::Real f4)
-#11 := 3::Real
-#12 := (* 3::Real f3)
-#56 := (+ #12 #55)
-#57 := (<= #56 0::Real)
-#51 := (not #48)
-#60 := (or #51 #57)
-#63 := (not #60)
-#13 := (* 3::Real f4)
-#14 := (<= #12 #13)
-#10 := (<= f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#66 := (iff #16 #63)
-#37 := (not #10)
-#38 := (or #37 #14)
-#41 := (not #38)
-#64 := (iff #41 #63)
-#61 := (iff #38 #60)
-#58 := (iff #14 #57)
-#59 := [rewrite]: #58
-#52 := (iff #37 #51)
-#49 := (iff #10 #48)
-#50 := [rewrite]: #49
-#53 := [monotonicity #50]: #52
-#62 := [monotonicity #53 #59]: #61
-#65 := [monotonicity #62]: #64
-#42 := (iff #16 #41)
-#39 := (iff #15 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#67 := [trans #43 #65]: #66
-#36 := [asserted]: #16
-#68 := [mp #36 #67]: #63
-#69 := [not-or-elim #68]: #48
-#70 := (not #57)
-#71 := [not-or-elim #68]: #70
-[th-lemma arith farkas -1/3 1 #71 #69]: false
-unsat
-afc3a7275e2a12cddf1eb01b0e78b5320cfe3bbf 55 0
-#2 := false
-#46 := 0::Real
-decl f4 :: Real
-#9 := f4
-#59 := -3::Real
-#62 := (* -3::Real f4)
-decl f3 :: Real
-#8 := f3
-#11 := 3::Real
-#12 := (* 3::Real f3)
-#63 := (+ #12 #62)
-#61 := (>= #63 0::Real)
-#60 := (not #61)
-#44 := -1::Real
-#48 := (* -1::Real f4)
-#49 := (+ f3 #48)
-#47 := (>= #49 0::Real)
-#66 := (or #47 #60)
-#69 := (not #66)
-#13 := (* 3::Real f4)
-#14 := (< #12 #13)
-#10 := (< f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#72 := (iff #16 #69)
-#37 := (not #10)
-#38 := (or #37 #14)
-#41 := (not #38)
-#70 := (iff #41 #69)
-#67 := (iff #38 #66)
-#64 := (iff #14 #60)
-#65 := [rewrite]: #64
-#57 := (iff #37 #47)
-#45 := (not #47)
-#52 := (not #45)
-#55 := (iff #52 #47)
-#56 := [rewrite]: #55
-#53 := (iff #37 #52)
-#50 := (iff #10 #45)
-#51 := [rewrite]: #50
-#54 := [monotonicity #51]: #53
-#58 := [trans #54 #56]: #57
-#68 := [monotonicity #58 #65]: #67
-#71 := [monotonicity #68]: #70
-#42 := (iff #16 #41)
-#39 := (iff #15 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#73 := [trans #43 #71]: #72
-#36 := [asserted]: #16
-#74 := [mp #36 #73]: #69
-#76 := [not-or-elim #74]: #61
-#75 := [not-or-elim #74]: #45
-[th-lemma arith farkas 3 1 #75 #76]: false
-unsat
-a47b8f528836ea6757883cbcf031d400004e56c0 52 0
-#2 := false
-#43 := 0::Real
-decl f4 :: Real
-#9 := f4
-#41 := -1::Real
-#45 := (* -1::Real f4)
-decl f3 :: Real
-#8 := f3
-#46 := (+ f3 #45)
-#56 := (<= #46 0::Real)
-#69 := (not #56)
-#44 := (>= #46 0::Real)
-#59 := (or #44 #56)
+#47 := (<= #46 0::Real)
+#53 := -3::Real
+#54 := (* -3::Real f4)
+#10 := 3::Real
+#11 := (* 3::Real f3)
+#55 := (+ #11 #54)
+#56 := (<= #55 0::Real)
+#50 := (not #47)
+#59 := (or #50 #56)
 #62 := (not #59)
-#11 := (<= f3 f4)
-#10 := (< f3 f4)
-#12 := (implies #10 #11)
-#13 := (not #12)
-#65 := (iff #13 #62)
-#34 := (not #10)
-#35 := (or #34 #11)
-#38 := (not #35)
-#63 := (iff #38 #62)
-#60 := (iff #35 #59)
-#57 := (iff #11 #56)
+#12 := (* 3::Real f4)
+#13 := (<= #11 #12)
+#9 := (<= f3 f4)
+#14 := (implies #9 #13)
+#15 := (not #14)
+#65 := (iff #15 #62)
+#37 := (not #9)
+#38 := (or #37 #13)
+#41 := (not #38)
+#63 := (iff #41 #62)
+#60 := (iff #38 #59)
+#57 := (iff #13 #56)
 #58 := [rewrite]: #57
-#54 := (iff #34 #44)
-#42 := (not #44)
-#49 := (not #42)
-#52 := (iff #49 #44)
-#53 := [rewrite]: #52
-#50 := (iff #34 #49)
-#47 := (iff #10 #42)
-#48 := [rewrite]: #47
-#51 := [monotonicity #48]: #50
-#55 := [trans #51 #53]: #54
-#61 := [monotonicity #55 #58]: #60
+#51 := (iff #37 #50)
+#48 := (iff #9 #47)
+#49 := [rewrite]: #48
+#52 := [monotonicity #49]: #51
+#61 := [monotonicity #52 #58]: #60
 #64 := [monotonicity #61]: #63
-#39 := (iff #13 #38)
-#36 := (iff #12 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#66 := [trans #40 #64]: #65
-#33 := [asserted]: #13
-#67 := [mp #33 #66]: #62
-#70 := [not-or-elim #67]: #69
-#68 := [not-or-elim #67]: #42
-#78 := (or #56 #44)
-#79 := [th-lemma arith farkas 1 1]: #78
-#80 := [unit-resolution #79 #68]: #56
-[unit-resolution #80 #70]: false
-unsat
-1c7cd0067170dad35b430a2211d9d52ff14ffc78 15 0
-#2 := false
-decl f3 :: Real
-#8 := f3
-#9 := (< f3 f3)
-#10 := (not #9)
-#11 := (not #10)
-#36 := (iff #11 false)
-#34 := (iff #9 false)
-#35 := [rewrite]: #34
-#32 := (iff #11 #9)
-#33 := [rewrite]: #32
-#37 := [trans #33 #35]: #36
-#31 := [asserted]: #11
-[mp #31 #37]: false
-unsat
-ae8743955951475c05ecf14ad6f216d2f85844fd 75 0
-#2 := false
-#56 := 0::Real
-decl f5 :: Real
-#11 := f5
-#53 := -1::Real
-#54 := (* -1::Real f5)
-decl f4 :: Real
-#9 := f4
-#55 := (+ f4 #54)
-#57 := (<= #55 0::Real)
-#67 := (* -1::Real f4)
-decl f3 :: Real
-#8 := f3
-#68 := (+ f3 #67)
-#69 := (<= #68 0::Real)
-#72 := (not #69)
-#63 := (+ f3 #54)
-#64 := (<= #63 0::Real)
-#60 := (not #57)
-#81 := (or #60 #64 #72)
-#86 := (not #81)
-#13 := (<= f3 f5)
-#12 := (<= f4 f5)
-#14 := (implies #12 #13)
-#10 := (<= f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#89 := (iff #16 #86)
-#37 := (not #12)
-#38 := (or #37 #13)
-#44 := (not #10)
-#45 := (or #44 #38)
-#50 := (not #45)
-#87 := (iff #50 #86)
-#84 := (iff #45 #81)
-#75 := (or #60 #64)
-#78 := (or #72 #75)
-#82 := (iff #78 #81)
-#83 := [rewrite]: #82
-#79 := (iff #45 #78)
-#76 := (iff #38 #75)
-#65 := (iff #13 #64)
-#66 := [rewrite]: #65
-#61 := (iff #37 #60)
-#58 := (iff #12 #57)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#77 := [monotonicity #62 #66]: #76
-#73 := (iff #44 #72)
-#70 := (iff #10 #69)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#80 := [monotonicity #74 #77]: #79
-#85 := [trans #80 #83]: #84
-#88 := [monotonicity #85]: #87
-#51 := (iff #16 #50)
-#48 := (iff #15 #45)
-#41 := (implies #10 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
 #42 := (iff #15 #41)
 #39 := (iff #14 #38)
 #40 := [rewrite]: #39
 #43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#90 := [trans #52 #88]: #89
-#36 := [asserted]: #16
-#91 := [mp #36 #90]: #86
-#92 := [not-or-elim #91]: #57
-#93 := (not #64)
-#94 := [not-or-elim #91]: #93
-#95 := [not-or-elim #91]: #69
-[th-lemma arith farkas 1 -1 1 #95 #94 #92]: false
-unsat
-787bdcef7a733082f1b18886b52fc521c0ed8560 80 0
-#2 := false
-#56 := 0::Real
-decl f5 :: Real
-#11 := f5
-#53 := -1::Real
-#54 := (* -1::Real f5)
+#66 := [trans #43 #64]: #65
+#36 := [asserted]: #15
+#67 := [mp #36 #66]: #62
+#68 := [not-or-elim #67]: #47
+#69 := (not #56)
+#70 := [not-or-elim #67]: #69
+[th-lemma arith farkas -1/3 1 #70 #68]: false
+unsat
+3d2fe72db9db1a875a3d783608c94c040b9afc1b 55 0
+#2 := false
+#18 := 0::Real
 decl f4 :: Real
-#9 := f4
-#55 := (+ f4 #54)
-#57 := (<= #55 0::Real)
-#69 := (* -1::Real f4)
+#8 := f4
+#58 := -3::Real
+#61 := (* -3::Real f4)
 decl f3 :: Real
-#8 := f3
-#70 := (+ f3 #69)
-#68 := (>= #70 0::Real)
-#63 := (+ f3 #54)
-#64 := (<= #63 0::Real)
-#60 := (not #57)
-#86 := (or #60 #64 #68)
-#91 := (not #86)
-#13 := (<= f3 f5)
-#12 := (<= f4 f5)
-#14 := (implies #12 #13)
-#10 := (< f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#94 := (iff #16 #91)
-#37 := (not #12)
+#7 := f3
+#10 := 3::Real
+#11 := (* 3::Real f3)
+#62 := (+ #11 #61)
+#60 := (>= #62 0::Real)
+#59 := (not #60)
+#44 := -1::Real
+#47 := (* -1::Real f4)
+#48 := (+ f3 #47)
+#46 := (>= #48 0::Real)
+#65 := (or #46 #59)
+#68 := (not #65)
+#12 := (* 3::Real f4)
+#13 := (< #11 #12)
+#9 := (< f3 f4)
+#14 := (implies #9 #13)
+#15 := (not #14)
+#71 := (iff #15 #68)
+#37 := (not #9)
 #38 := (or #37 #13)
-#44 := (not #10)
-#45 := (or #44 #38)
-#50 := (not #45)
-#92 := (iff #50 #91)
-#89 := (iff #45 #86)
-#80 := (or #60 #64)
-#83 := (or #68 #80)
-#87 := (iff #83 #86)
-#88 := [rewrite]: #87
-#84 := (iff #45 #83)
-#81 := (iff #38 #80)
-#65 := (iff #13 #64)
-#66 := [rewrite]: #65
-#61 := (iff #37 #60)
-#58 := (iff #12 #57)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#82 := [monotonicity #62 #66]: #81
-#78 := (iff #44 #68)
-#67 := (not #68)
-#73 := (not #67)
-#76 := (iff #73 #68)
-#77 := [rewrite]: #76
-#74 := (iff #44 #73)
-#71 := (iff #10 #67)
-#72 := [rewrite]: #71
-#75 := [monotonicity #72]: #74
-#79 := [trans #75 #77]: #78
-#85 := [monotonicity #79 #82]: #84
-#90 := [trans #85 #88]: #89
-#93 := [monotonicity #90]: #92
-#51 := (iff #16 #50)
-#48 := (iff #15 #45)
-#41 := (implies #10 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
+#41 := (not #38)
+#69 := (iff #41 #68)
+#66 := (iff #38 #65)
+#63 := (iff #13 #59)
+#64 := [rewrite]: #63
+#56 := (iff #37 #46)
+#45 := (not #46)
+#51 := (not #45)
+#54 := (iff #51 #46)
+#55 := [rewrite]: #54
+#52 := (iff #37 #51)
+#49 := (iff #9 #45)
+#50 := [rewrite]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#67 := [monotonicity #57 #64]: #66
+#70 := [monotonicity #67]: #69
 #42 := (iff #15 #41)
 #39 := (iff #14 #38)
 #40 := [rewrite]: #39
 #43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#95 := [trans #52 #93]: #94
-#36 := [asserted]: #16
-#96 := [mp #36 #95]: #91
-#97 := [not-or-elim #96]: #57
-#98 := (not #64)
-#99 := [not-or-elim #96]: #98
-#100 := [not-or-elim #96]: #67
-[th-lemma arith farkas 1 1 1 #100 #99 #97]: false
-unsat
-b3f48d3d4ae5df26c230c46ec0af407248139694 80 0
-#2 := false
-#55 := 0::Real
+#72 := [trans #43 #70]: #71
+#36 := [asserted]: #15
+#73 := [mp #36 #72]: #68
+#75 := [not-or-elim #73]: #60
+#74 := [not-or-elim #73]: #45
+[th-lemma arith farkas 3 1 #74 #75]: false
+unsat
+165755fec51f7e6c4b1e62511cb967090732b747 52 0
+#2 := false
+#15 := 0::Real
 decl f4 :: Real
-#9 := f4
-#53 := -1::Real
-#72 := (* -1::Real f4)
+#8 := f4
+#41 := -1::Real
+#44 := (* -1::Real f4)
 decl f3 :: Real
-#8 := f3
-#73 := (+ f3 #72)
-#74 := (<= #73 0::Real)
-#77 := (not #74)
+#7 := f3
+#45 := (+ f3 #44)
+#55 := (<= #45 0::Real)
+#68 := (not #55)
+#43 := (>= #45 0::Real)
+#58 := (or #43 #55)
+#61 := (not #58)
+#10 := (<= f3 f4)
+#9 := (< f3 f4)
+#11 := (implies #9 #10)
+#12 := (not #11)
+#64 := (iff #12 #61)
+#34 := (not #9)
+#35 := (or #34 #10)
+#38 := (not #35)
+#62 := (iff #38 #61)
+#59 := (iff #35 #58)
+#56 := (iff #10 #55)
+#57 := [rewrite]: #56
+#53 := (iff #34 #43)
+#42 := (not #43)
+#48 := (not #42)
+#51 := (iff #48 #43)
+#52 := [rewrite]: #51
+#49 := (iff #34 #48)
+#46 := (iff #9 #42)
+#47 := [rewrite]: #46
+#50 := [monotonicity #47]: #49
+#54 := [trans #50 #52]: #53
+#60 := [monotonicity #54 #57]: #59
+#63 := [monotonicity #60]: #62
+#39 := (iff #12 #38)
+#36 := (iff #11 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#65 := [trans #40 #63]: #64
+#33 := [asserted]: #12
+#66 := [mp #33 #65]: #61
+#69 := [not-or-elim #66]: #68
+#67 := [not-or-elim #66]: #42
+#77 := (or #55 #43)
+#78 := [th-lemma arith farkas 1 1]: #77
+#79 := [unit-resolution #78 #67]: #55
+[unit-resolution #79 #69]: false
+unsat
+33e0b153e51916a2167061300cc75c8e67ab4fda 15 0
+#2 := false
+decl f3 :: Real
+#7 := f3
+#8 := (< f3 f3)
+#9 := (not #8)
+#10 := (not #9)
+#36 := (iff #10 false)
+#34 := (iff #8 false)
+#35 := [rewrite]: #34
+#32 := (iff #10 #8)
+#33 := [rewrite]: #32
+#37 := [trans #33 #35]: #36
+#31 := [asserted]: #10
+[mp #31 #37]: false
+unsat
+2340fd8d860bd4e1165d0c23c1f96e5421c798e2 75 0
+#2 := false
+#18 := 0::Real
 decl f5 :: Real
-#11 := f5
-#57 := (* -1::Real f5)
-#68 := (+ f3 #57)
-#69 := (<= #68 0::Real)
-#58 := (+ f4 #57)
-#56 := (>= #58 0::Real)
-#86 := (or #56 #69 #77)
-#91 := (not #86)
-#13 := (<= f3 f5)
-#12 := (< f4 f5)
-#14 := (implies #12 #13)
-#10 := (<= f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#94 := (iff #16 #91)
-#37 := (not #12)
-#38 := (or #37 #13)
-#44 := (not #10)
+#10 := f5
+#53 := -1::Real
+#54 := (* -1::Real f5)
+decl f4 :: Real
+#8 := f4
+#55 := (+ f4 #54)
+#56 := (<= #55 0::Real)
+decl f3 :: Real
+#7 := f3
+#62 := (+ f3 #54)
+#63 := (<= #62 0::Real)
+#59 := (not #56)
+#66 := (* -1::Real f4)
+#67 := (+ f3 #66)
+#68 := (<= #67 0::Real)
+#71 := (not #68)
+#80 := (or #71 #59 #63)
+#85 := (not #80)
+#12 := (<= f3 f5)
+#11 := (<= f4 f5)
+#13 := (implies #11 #12)
+#9 := (<= f3 f4)
+#14 := (implies #9 #13)
+#15 := (not #14)
+#88 := (iff #15 #85)
+#37 := (not #11)
+#38 := (or #37 #12)
+#44 := (not #9)
 #45 := (or #44 #38)
 #50 := (not #45)
-#92 := (iff #50 #91)
-#89 := (iff #45 #86)
-#80 := (or #56 #69)
-#83 := (or #77 #80)
-#87 := (iff #83 #86)
-#88 := [rewrite]: #87
-#84 := (iff #45 #83)
-#81 := (iff #38 #80)
-#70 := (iff #13 #69)
-#71 := [rewrite]: #70
-#66 := (iff #37 #56)
-#54 := (not #56)
-#61 := (not #54)
-#64 := (iff #61 #56)
+#86 := (iff #50 #85)
+#83 := (iff #45 #80)
+#74 := (or #59 #63)
+#77 := (or #71 #74)
+#81 := (iff #77 #80)
+#82 := [rewrite]: #81
+#78 := (iff #45 #77)
+#75 := (iff #38 #74)
+#64 := (iff #12 #63)
 #65 := [rewrite]: #64
-#62 := (iff #37 #61)
-#59 := (iff #12 #54)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#67 := [trans #63 #65]: #66
-#82 := [monotonicity #67 #71]: #81
-#78 := (iff #44 #77)
-#75 := (iff #10 #74)
-#76 := [rewrite]: #75
-#79 := [monotonicity #76]: #78
-#85 := [monotonicity #79 #82]: #84
-#90 := [trans #85 #88]: #89
-#93 := [monotonicity #90]: #92
-#51 := (iff #16 #50)
-#48 := (iff #15 #45)
-#41 := (implies #10 #38)
+#60 := (iff #37 #59)
+#57 := (iff #11 #56)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#76 := [monotonicity #61 #65]: #75
+#72 := (iff #44 #71)
+#69 := (iff #9 #68)
+#70 := [rewrite]: #69
+#73 := [monotonicity #70]: #72
+#79 := [monotonicity #73 #76]: #78
+#84 := [trans #79 #82]: #83
+#87 := [monotonicity #84]: #86
+#51 := (iff #15 #50)
+#48 := (iff #14 #45)
+#41 := (implies #9 #38)
 #46 := (iff #41 #45)
 #47 := [rewrite]: #46
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#49 := [trans #43 #47]: #48
-#52 := [monotonicity #49]: #51
-#95 := [trans #52 #93]: #94
-#36 := [asserted]: #16
-#96 := [mp #36 #95]: #91
-#100 := [not-or-elim #96]: #74
-#98 := (not #69)
-#99 := [not-or-elim #96]: #98
-#97 := [not-or-elim #96]: #54
-[th-lemma arith farkas 1 1 1 #97 #99 #100]: false
-unsat
-ca2cf358a9693d3f8c3ab7c0c2862ca77ccd856e 85 0
-#2 := false
-#55 := 0::Real
-decl f5 :: Real
-#11 := f5
-#53 := -1::Real
-#57 := (* -1::Real f5)
-decl f3 :: Real
-#8 := f3
-#70 := (+ f3 #57)
-#69 := (>= #70 0::Real)
-decl f4 :: Real
-#9 := f4
-#75 := (* -1::Real f4)
-#76 := (+ f3 #75)
-#74 := (>= #76 0::Real)
-#68 := (not #69)
-#58 := (+ f4 #57)
-#56 := (>= #58 0::Real)
-#92 := (or #56 #68 #74)
-#97 := (not #92)
-#13 := (< f3 f5)
-#12 := (< f4 f5)
-#14 := (implies #12 #13)
-#10 := (< f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#100 := (iff #16 #97)
-#37 := (not #12)
-#38 := (or #37 #13)
-#44 := (not #10)
-#45 := (or #44 #38)
-#50 := (not #45)
-#98 := (iff #50 #97)
-#95 := (iff #45 #92)
-#86 := (or #56 #68)
-#89 := (or #74 #86)
-#93 := (iff #89 #92)
-#94 := [rewrite]: #93
-#90 := (iff #45 #89)
-#87 := (iff #38 #86)
-#71 := (iff #13 #68)
-#72 := [rewrite]: #71
-#66 := (iff #37 #56)
-#54 := (not #56)
-#61 := (not #54)
-#64 := (iff #61 #56)
-#65 := [rewrite]: #64
-#62 := (iff #37 #61)
-#59 := (iff #12 #54)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#67 := [trans #63 #65]: #66
-#88 := [monotonicity #67 #72]: #87
-#84 := (iff #44 #74)
-#73 := (not #74)
-#79 := (not #73)
-#82 := (iff #79 #74)
-#83 := [rewrite]: #82
-#80 := (iff #44 #79)
-#77 := (iff #10 #73)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#85 := [trans #81 #83]: #84
-#91 := [monotonicity #85 #88]: #90
-#96 := [trans #91 #94]: #95
-#99 := [monotonicity #96]: #98
-#51 := (iff #16 #50)
-#48 := (iff #15 #45)
-#41 := (implies #10 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
+#42 := (iff #14 #41)
+#39 := (iff #13 #38)
 #40 := [rewrite]: #39
 #43 := [monotonicity #40]: #42
 #49 := [trans #43 #47]: #48
 #52 := [monotonicity #49]: #51
-#101 := [trans #52 #99]: #100
-#36 := [asserted]: #16
-#102 := [mp #36 #101]: #97
-#104 := [not-or-elim #102]: #69
-#103 := [not-or-elim #102]: #54
-#105 := [not-or-elim #102]: #73
-[th-lemma arith farkas 1 1 1 #105 #103 #104]: false
-unsat
-f171037adc5d16b4f868a5116f823085196df83e 69 0
-#2 := false
-#47 := 0::Real
+#89 := [trans #52 #87]: #88
+#36 := [asserted]: #15
+#90 := [mp #36 #89]: #85
+#92 := [not-or-elim #90]: #56
+#93 := (not #63)
+#94 := [not-or-elim #90]: #93
+#91 := [not-or-elim #90]: #68
+[th-lemma arith farkas 1 -1 1 #91 #94 #92]: false
+unsat
+8716c7aaa7f48c44ab9ce5531737a3b55fdf1e37 80 0
+#2 := false
+#18 := 0::Real
 decl f5 :: Real
-#11 := f5
-#45 := -1::Real
+#10 := f5
+#53 := -1::Real
 #54 := (* -1::Real f5)
-decl f3 :: Real
-#8 := f3
-#65 := (+ f3 #54)
-#66 := (<= #65 0::Real)
-#67 := (not #66)
 decl f4 :: Real
-#9 := f4
+#8 := f4
 #55 := (+ f4 #54)
-#53 := (>= #55 0::Real)
-#56 := (not #53)
-#49 := (* -1::Real f4)
-#50 := (+ f3 #49)
-#48 := (>= #50 0::Real)
-#46 := (not #48)
-#59 := (and #46 #56)
-#62 := (not #59)
-#77 := (or #62 #66)
-#80 := (not #77)
-#14 := (< f5 f3)
-#15 := (not #14)
-#12 := (< f4 f5)
-#10 := (< f3 f4)
-#13 := (and #10 #12)
-#16 := (implies #13 #15)
-#17 := (not #16)
-#83 := (iff #17 #80)
-#38 := (not #13)
-#39 := (or #38 #15)
+#56 := (<= #55 0::Real)
+decl f3 :: Real
+#7 := f3
+#62 := (+ f3 #54)
+#63 := (<= #62 0::Real)
+#59 := (not #56)
+#68 := (* -1::Real f4)
+#69 := (+ f3 #68)
+#67 := (>= #69 0::Real)
+#85 := (or #67 #59 #63)
+#90 := (not #85)
+#12 := (<= f3 f5)
+#11 := (<= f4 f5)
+#13 := (implies #11 #12)
+#9 := (< f3 f4)
+#14 := (implies #9 #13)
+#15 := (not #14)
+#93 := (iff #15 #90)
+#37 := (not #11)
+#38 := (or #37 #12)
+#44 := (not #9)
+#45 := (or #44 #38)
+#50 := (not #45)
+#91 := (iff #50 #90)
+#88 := (iff #45 #85)
+#79 := (or #59 #63)
+#82 := (or #67 #79)
+#86 := (iff #82 #85)
+#87 := [rewrite]: #86
+#83 := (iff #45 #82)
+#80 := (iff #38 #79)
+#64 := (iff #12 #63)
+#65 := [rewrite]: #64
+#60 := (iff #37 #59)
+#57 := (iff #11 #56)
+#58 := [rewrite]: #57
+#61 := [monotonicity #58]: #60
+#81 := [monotonicity #61 #65]: #80
+#77 := (iff #44 #67)
+#66 := (not #67)
+#72 := (not #66)
+#75 := (iff #72 #67)
+#76 := [rewrite]: #75
+#73 := (iff #44 #72)
+#70 := (iff #9 #66)
+#71 := [rewrite]: #70
+#74 := [monotonicity #71]: #73
+#78 := [trans #74 #76]: #77
+#84 := [monotonicity #78 #81]: #83
+#89 := [trans #84 #87]: #88
+#92 := [monotonicity #89]: #91
+#51 := (iff #15 #50)
+#48 := (iff #14 #45)
+#41 := (implies #9 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #14 #41)
+#39 := (iff #13 #38)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#49 := [trans #43 #47]: #48
+#52 := [monotonicity #49]: #51
+#94 := [trans #52 #92]: #93
+#36 := [asserted]: #15
+#95 := [mp #36 #94]: #90
+#97 := [not-or-elim #95]: #56
+#96 := [not-or-elim #95]: #66
+#98 := (not #63)
+#99 := [not-or-elim #95]: #98
+[th-lemma arith farkas 1 1 1 #99 #96 #97]: false
+unsat
+82e5c8e2d49baa3249133d0cc70e4f9710ed01cc 80 0
+#2 := false
+#18 := 0::Real
+decl f5 :: Real
+#10 := f5
+#53 := -1::Real
+#56 := (* -1::Real f5)
+decl f3 :: Real
+#7 := f3
+#67 := (+ f3 #56)
+#68 := (<= #67 0::Real)
+#98 := (not #68)
+decl f4 :: Real
+#8 := f4
+#57 := (+ f4 #56)
+#55 := (>= #57 0::Real)
+#71 := (* -1::Real f4)
+#72 := (+ f3 #71)
+#73 := (<= #72 0::Real)
+#76 := (not #73)
+#85 := (or #76 #55 #68)
+#90 := (not #85)
+#12 := (<= f3 f5)
+#11 := (< f4 f5)
+#13 := (implies #11 #12)
+#9 := (<= f3 f4)
+#14 := (implies #9 #13)
+#15 := (not #14)
+#93 := (iff #15 #90)
+#37 := (not #11)
+#38 := (or #37 #12)
+#44 := (not #9)
+#45 := (or #44 #38)
+#50 := (not #45)
+#91 := (iff #50 #90)
+#88 := (iff #45 #85)
+#79 := (or #55 #68)
+#82 := (or #76 #79)
+#86 := (iff #82 #85)
+#87 := [rewrite]: #86
+#83 := (iff #45 #82)
+#80 := (iff #38 #79)
+#69 := (iff #12 #68)
+#70 := [rewrite]: #69
+#65 := (iff #37 #55)
+#54 := (not #55)
+#60 := (not #54)
+#63 := (iff #60 #55)
+#64 := [rewrite]: #63
+#61 := (iff #37 #60)
+#58 := (iff #11 #54)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#66 := [trans #62 #64]: #65
+#81 := [monotonicity #66 #70]: #80
+#77 := (iff #44 #76)
+#74 := (iff #9 #73)
+#75 := [rewrite]: #74
+#78 := [monotonicity #75]: #77
+#84 := [monotonicity #78 #81]: #83
+#89 := [trans #84 #87]: #88
+#92 := [monotonicity #89]: #91
+#51 := (iff #15 #50)
+#48 := (iff #14 #45)
+#41 := (implies #9 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #14 #41)
+#39 := (iff #13 #38)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#49 := [trans #43 #47]: #48
+#52 := [monotonicity #49]: #51
+#94 := [trans #52 #92]: #93
+#36 := [asserted]: #15
+#95 := [mp #36 #94]: #90
+#99 := [not-or-elim #95]: #98
+#97 := [not-or-elim #95]: #54
+#96 := [not-or-elim #95]: #73
+[th-lemma arith farkas 1 1 1 #96 #97 #99]: false
+unsat
+54f206f7168f092b568f3c4ba80a32ed01dca4e9 85 0
+#2 := false
+#18 := 0::Real
+decl f5 :: Real
+#10 := f5
+#53 := -1::Real
+#56 := (* -1::Real f5)
+decl f3 :: Real
+#7 := f3
+#69 := (+ f3 #56)
+#68 := (>= #69 0::Real)
+#67 := (not #68)
+decl f4 :: Real
+#8 := f4
+#57 := (+ f4 #56)
+#55 := (>= #57 0::Real)
+#74 := (* -1::Real f4)
+#75 := (+ f3 #74)
+#73 := (>= #75 0::Real)
+#91 := (or #73 #55 #67)
+#96 := (not #91)
+#12 := (< f3 f5)
+#11 := (< f4 f5)
+#13 := (implies #11 #12)
+#9 := (< f3 f4)
+#14 := (implies #9 #13)
+#15 := (not #14)
+#99 := (iff #15 #96)
+#37 := (not #11)
+#38 := (or #37 #12)
+#44 := (not #9)
+#45 := (or #44 #38)
+#50 := (not #45)
+#97 := (iff #50 #96)
+#94 := (iff #45 #91)
+#85 := (or #55 #67)
+#88 := (or #73 #85)
+#92 := (iff #88 #91)
+#93 := [rewrite]: #92
+#89 := (iff #45 #88)
+#86 := (iff #38 #85)
+#70 := (iff #12 #67)
+#71 := [rewrite]: #70
+#65 := (iff #37 #55)
+#54 := (not #55)
+#60 := (not #54)
+#63 := (iff #60 #55)
+#64 := [rewrite]: #63
+#61 := (iff #37 #60)
+#58 := (iff #11 #54)
+#59 := [rewrite]: #58
+#62 := [monotonicity #59]: #61
+#66 := [trans #62 #64]: #65
+#87 := [monotonicity #66 #71]: #86
+#83 := (iff #44 #73)
+#72 := (not #73)
+#78 := (not #72)
+#81 := (iff #78 #73)
+#82 := [rewrite]: #81
+#79 := (iff #44 #78)
+#76 := (iff #9 #72)
+#77 := [rewrite]: #76
+#80 := [monotonicity #77]: #79
+#84 := [trans #80 #82]: #83
+#90 := [monotonicity #84 #87]: #89
+#95 := [trans #90 #93]: #94
+#98 := [monotonicity #95]: #97
+#51 := (iff #15 #50)
+#48 := (iff #14 #45)
+#41 := (implies #9 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #14 #41)
+#39 := (iff #13 #38)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#49 := [trans #43 #47]: #48
+#52 := [monotonicity #49]: #51
+#100 := [trans #52 #98]: #99
+#36 := [asserted]: #15
+#101 := [mp #36 #100]: #96
+#104 := [not-or-elim #101]: #68
+#103 := [not-or-elim #101]: #54
+#102 := [not-or-elim #101]: #72
+[th-lemma arith farkas 1 1 1 #102 #103 #104]: false
+unsat
+8921a5763dbd9b6bdd641b747fbac9ee9c2dd42d 69 0
+#2 := false
+#19 := 0::Real
+decl f5 :: Real
+#10 := f5
+#45 := -1::Real
+#53 := (* -1::Real f5)
+decl f3 :: Real
+#7 := f3
+#64 := (+ f3 #53)
+#65 := (<= #64 0::Real)
+#66 := (not #65)
+decl f4 :: Real
+#8 := f4
+#54 := (+ f4 #53)
+#52 := (>= #54 0::Real)
+#55 := (not #52)
+#48 := (* -1::Real f4)
+#49 := (+ f3 #48)
+#47 := (>= #49 0::Real)
+#46 := (not #47)
+#58 := (and #46 #55)
+#61 := (not #58)
+#76 := (or #61 #65)
+#79 := (not #76)
+#13 := (< f5 f3)
+#14 := (not #13)
+#11 := (< f4 f5)
+#9 := (< f3 f4)
+#12 := (and #9 #11)
+#15 := (implies #12 #14)
+#16 := (not #15)
+#82 := (iff #16 #79)
+#38 := (not #12)
+#39 := (or #38 #14)
 #42 := (not #39)
-#81 := (iff #42 #80)
-#78 := (iff #39 #77)
-#75 := (iff #15 #66)
-#70 := (not #67)
-#73 := (iff #70 #66)
-#74 := [rewrite]: #73
-#71 := (iff #15 #70)
-#68 := (iff #14 #67)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#76 := [trans #72 #74]: #75
-#63 := (iff #38 #62)
-#60 := (iff #13 #59)
-#57 := (iff #12 #56)
-#58 := [rewrite]: #57
-#51 := (iff #10 #46)
-#52 := [rewrite]: #51
-#61 := [monotonicity #52 #58]: #60
-#64 := [monotonicity #61]: #63
-#79 := [monotonicity #64 #76]: #78
-#82 := [monotonicity #79]: #81
-#43 := (iff #17 #42)
-#40 := (iff #16 #39)
+#80 := (iff #42 #79)
+#77 := (iff #39 #76)
+#74 := (iff #14 #65)
+#69 := (not #66)
+#72 := (iff #69 #65)
+#73 := [rewrite]: #72
+#70 := (iff #14 #69)
+#67 := (iff #13 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#75 := [trans #71 #73]: #74
+#62 := (iff #38 #61)
+#59 := (iff #12 #58)
+#56 := (iff #11 #55)
+#57 := [rewrite]: #56
+#50 := (iff #9 #46)
+#51 := [rewrite]: #50
+#60 := [monotonicity #51 #57]: #59
+#63 := [monotonicity #60]: #62
+#78 := [monotonicity #63 #75]: #77
+#81 := [monotonicity #78]: #80
+#43 := (iff #16 #42)
+#40 := (iff #15 #39)
 #41 := [rewrite]: #40
 #44 := [monotonicity #41]: #43
-#84 := [trans #44 #82]: #83
-#37 := [asserted]: #17
-#85 := [mp #37 #84]: #80
-#89 := [not-or-elim #85]: #67
-#86 := [not-or-elim #85]: #59
-#88 := [and-elim #86]: #56
-#87 := [and-elim #86]: #46
-[th-lemma arith farkas 1 1 1 #87 #88 #89]: false
-unsat
-78fe7fd2fee546c83d198c598a1a57a1faebea4e 50 0
+#83 := [trans #44 #81]: #82
+#37 := [asserted]: #16
+#84 := [mp #37 #83]: #79
+#88 := [not-or-elim #84]: #66
+#85 := [not-or-elim #84]: #58
+#87 := [and-elim #85]: #55
+#86 := [and-elim #85]: #46
+[th-lemma arith farkas 1 1 1 #86 #87 #88]: false
+unsat
+ba3cc9798e91eb2c981ec527a914f13a432e9973 46 0
 #2 := false
 decl f3 :: (-> S3 S4 S2)
 decl f5 :: (-> S5 S2 S4)
 decl f10 :: S2
-#30 := f10
+#29 := f10
 decl f6 :: (-> S6 S2 S5)
 decl f9 :: S2
-#28 := f9
+#27 := f9
 decl f7 :: S6
-#9 := f7
-#29 := (f6 f7 f9)
-#31 := (f5 #29 f10)
+#8 := f7
+#28 := (f6 f7 f9)
+#30 := (f5 #28 f10)
 decl f4 :: S3
-#8 := f4
-#32 := (f3 f4 #31)
-#33 := (= f9 #32)
-#34 := (not #33)
-#77 := [asserted]: #34
-#12 := (:var 0 S2)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#570 := (pattern #13)
-#14 := (f3 f4 #13)
-#55 := (= #10 #14)
-#571 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #570) #55)
-#58 := (forall (vars (?v0 S2) (?v1 S2)) #55)
-#574 := (iff #58 #571)
-#572 := (iff #55 #55)
-#573 := [refl]: #572
-#575 := [quant-intro #573]: #574
-#92 := (~ #58 #58)
-#90 := (~ #55 #55)
-#91 := [refl]: #90
-#93 := [nnf-pos #91]: #92
-#15 := (= #14 #10)
-#16 := (forall (vars (?v0 S2) (?v1 S2)) #15)
-#59 := (iff #16 #58)
-#56 := (iff #15 #55)
-#57 := [rewrite]: #56
-#60 := [quant-intro #57]: #59
-#54 := [asserted]: #16
-#63 := [mp #54 #60]: #58
-#80 := [mp~ #63 #93]: #58
-#576 := [mp #80 #575]: #571
-#153 := (not #571)
-#240 := (or #153 #33)
-#154 := [quant-inst #28 #30]: #240
-[unit-resolution #154 #576 #77]: false
-unsat
-571b672b8bd2cf605e4360f1b7c3d8abab0072cd 50 0
+#7 := f4
+#31 := (f3 f4 #30)
+#32 := (= f9 #31)
+#136 := (= #31 f9)
+#11 := (:var 0 S2)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#552 := (pattern #12)
+#13 := (f3 f4 #12)
+#14 := (= #13 #9)
+#553 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #552) #14)
+#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
+#556 := (iff #15 #553)
+#554 := (iff #14 #14)
+#555 := [refl]: #554
+#557 := [quant-intro #555]: #556
+#71 := (~ #15 #15)
+#69 := (~ #14 #14)
+#70 := [refl]: #69
+#72 := [nnf-pos #70]: #71
+#54 := [asserted]: #15
+#59 := [mp~ #54 #72]: #15
+#558 := [mp #59 #557]: #553
+#223 := (not #553)
+#138 := (or #223 #136)
+#224 := [quant-inst #27 #29]: #138
+#208 := [unit-resolution #224 #558]: #136
+#544 := [symm #208]: #32
+#33 := (not #32)
+#57 := [asserted]: #33
+[unit-resolution #57 #544]: false
+unsat
+a080cdd5a7725df3669f655e4a1ddc1f94e11bc0 46 0
 #2 := false
 decl f3 :: (-> S3 S4 S2)
 decl f5 :: (-> S5 S2 S4)
 decl f9 :: S2
-#28 := f9
+#27 := f9
+decl f6 :: (-> S6 S2 S5)
+decl f10 :: S2
+#28 := f10
+decl f7 :: S6
+#8 := f7
+#29 := (f6 f7 f10)
+#30 := (f5 #29 f9)
+decl f8 :: S3
+#16 := f8
+#31 := (f3 f8 #30)
+#32 := (= f9 #31)
+#137 := (= #31 f9)
+#11 := (:var 0 S2)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#552 := (pattern #12)
+#17 := (f3 f8 #12)
+#18 := (= #17 #11)
+#559 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #552) #18)
+#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
+#562 := (iff #19 #559)
+#560 := (iff #18 #18)
+#561 := [refl]: #560
+#563 := [quant-intro #561]: #562
+#61 := (~ #19 #19)
+#60 := (~ #18 #18)
+#73 := [refl]: #60
+#62 := [nnf-pos #73]: #61
+#55 := [asserted]: #19
+#74 := [mp~ #55 #62]: #19
+#564 := [mp #74 #563]: #559
+#227 := (not #559)
+#228 := (or #227 #137)
+#225 := [quant-inst #28 #27]: #228
+#208 := [unit-resolution #225 #564]: #137
+#544 := [symm #208]: #32
+#33 := (not #32)
+#57 := [asserted]: #33
+[unit-resolution #57 #544]: false
+unsat
+1b9aec38c55c28fabd079dac192f971ebc6b0be8 86 0
+#2 := false
+decl f5 :: (-> S5 S2 S4)
+decl f9 :: S2
+#27 := f9
 decl f6 :: (-> S6 S2 S5)
 decl f10 :: S2
 #29 := f10
 decl f7 :: S6
-#9 := f7
-#30 := (f6 f7 f10)
-#31 := (f5 #30 f9)
-decl f8 :: S3
-#17 := f8
-#32 := (f3 f8 #31)
-#33 := (= f9 #32)
-#34 := (not #33)
-#77 := [asserted]: #34
-#12 := (:var 0 S2)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#570 := (pattern #13)
-#18 := (f3 f8 #13)
-#62 := (= #12 #18)
-#577 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #570) #62)
-#66 := (forall (vars (?v0 S2) (?v1 S2)) #62)
-#580 := (iff #66 #577)
-#578 := (iff #62 #62)
-#579 := [refl]: #578
-#581 := [quant-intro #579]: #580
-#82 := (~ #66 #66)
-#81 := (~ #62 #62)
-#94 := [refl]: #81
-#83 := [nnf-pos #94]: #82
-#19 := (= #18 #12)
-#20 := (forall (vars (?v0 S2) (?v1 S2)) #19)
-#67 := (iff #20 #66)
-#64 := (iff #19 #62)
-#65 := [rewrite]: #64
-#68 := [quant-intro #65]: #67
-#61 := [asserted]: #20
-#71 := [mp #61 #68]: #66
-#95 := [mp~ #71 #83]: #66
-#582 := [mp #95 #581]: #577
-#243 := (not #577)
-#244 := (or #243 #33)
-#172 := [quant-inst #29 #28]: #244
-[unit-resolution #172 #582 #77]: false
-unsat
-4fa63c3a3a92ef48f08b4203601002014284fd9e 93 0
-#2 := false
-decl f10 :: S2
-#30 := f10
-decl f9 :: S2
-#28 := f9
-#35 := (= f9 f10)
+#8 := f7
+#31 := (f6 f7 f10)
+#32 := (f5 #31 f9)
+#28 := (f6 f7 f9)
+#30 := (f5 #28 f10)
+#33 := (= #30 #32)
+#541 := (= f10 f9)
+#34 := (= f9 f10)
 decl f3 :: (-> S3 S4 S2)
-decl f5 :: (-> S5 S2 S4)
-decl f6 :: (-> S6 S2 S5)
-decl f7 :: S6
-#9 := f7
-#32 := (f6 f7 f10)
-#33 := (f5 #32 f9)
 decl f4 :: S3
-#8 := f4
-#359 := (f3 f4 #33)
-#558 := (= #359 f10)
-#566 := (= f10 #359)
-#12 := (:var 0 S2)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#578 := (pattern #13)
-#14 := (f3 f4 #13)
-#58 := (= #10 #14)
-#579 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #578) #58)
-#61 := (forall (vars (?v0 S2) (?v1 S2)) #58)
-#582 := (iff #61 #579)
-#580 := (iff #58 #58)
-#581 := [refl]: #580
-#583 := [quant-intro #581]: #582
-#100 := (~ #61 #61)
-#98 := (~ #58 #58)
-#99 := [refl]: #98
-#101 := [nnf-pos #99]: #100
-#15 := (= #14 #10)
-#16 := (forall (vars (?v0 S2) (?v1 S2)) #15)
-#62 := (iff #16 #61)
-#59 := (iff #15 #58)
-#60 := [rewrite]: #59
-#63 := [quant-intro #60]: #62
-#57 := [asserted]: #16
-#66 := [mp #57 #63]: #61
-#87 := [mp~ #66 #101]: #61
-#584 := [mp #87 #583]: #579
-#570 := (not #579)
-#576 := (or #570 #566)
-#571 := [quant-inst #30 #28]: #576
-#217 := [unit-resolution #571 #584]: #566
-#559 := [symm #217]: #558
-#554 := (= f9 #359)
-#29 := (f6 f7 f9)
-#31 := (f5 #29 f10)
-#253 := (f3 f4 #31)
-#556 := (= #253 #359)
-#34 := (= #31 #33)
-#568 := (= f10 f9)
-#81 := (not #34)
-#577 := [hypothesis]: #81
-#248 := (or #35 #34)
-#83 := (iff #35 #81)
-#36 := (iff #34 #35)
-#37 := (not #36)
-#84 := (iff #37 #83)
-#85 := [rewrite]: #84
-#80 := [asserted]: #37
-#88 := [mp #80 #85]: #83
-#160 := (not #83)
-#247 := (or #35 #34 #160)
-#161 := [def-axiom]: #247
-#162 := [unit-resolution #161 #88]: #248
-#567 := [unit-resolution #162 #577]: #35
-#226 := [symm #567]: #568
-#569 := (= #29 #32)
-#210 := [monotonicity #567]: #569
-#553 := [monotonicity #210 #226]: #34
-#214 := [unit-resolution #577 #553]: false
-#215 := [lemma #214]: #34
-#557 := [monotonicity #215]: #556
-#250 := (= f9 #253)
-#572 := (or #570 #250)
-#227 := [quant-inst #28 #30]: #572
-#555 := [unit-resolution #227 #584]: #250
-#560 := [trans #555 #557]: #554
-#196 := [trans #560 #559]: #35
-#249 := (not #35)
-#252 := (or #249 #81)
-#240 := (or #249 #81 #160)
-#251 := [def-axiom]: #240
-#180 := [unit-resolution #251 #88]: #252
-#216 := [unit-resolution #180 #215]: #249
-[unit-resolution #216 #196]: false
-unsat
-79f78e71a587ae1c5f4af108f19f9ffab740b9f4 166 0
+#7 := f4
+#548 := (f3 f4 #32)
+#221 := (= #548 f10)
+#11 := (:var 0 S2)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#560 := (pattern #12)
+#13 := (f3 f4 #12)
+#14 := (= #13 #9)
+#561 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #560) #14)
+#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
+#564 := (iff #15 #561)
+#562 := (iff #14 #14)
+#563 := [refl]: #562
+#565 := [quant-intro #563]: #564
+#79 := (~ #15 #15)
+#77 := (~ #14 #14)
+#78 := [refl]: #77
+#80 := [nnf-pos #78]: #79
+#57 := [asserted]: #15
+#66 := [mp~ #57 #80]: #15
+#566 := [mp #66 #565]: #561
+#554 := (not #561)
+#553 := (or #554 #221)
+#559 := [quant-inst #29 #27]: #553
+#208 := [unit-resolution #559 #566]: #221
+#199 := (= f9 #548)
+#233 := (f3 f4 #30)
+#197 := (= #233 #548)
+#144 := (not #34)
+#549 := [hypothesis]: #144
+#235 := (or #33 #34)
+#61 := (not #33)
+#62 := (iff #61 #34)
+#35 := (iff #33 #34)
+#36 := (not #35)
+#63 := (iff #36 #62)
+#64 := [rewrite]: #63
+#60 := [asserted]: #36
+#67 := [mp #60 #64]: #62
+#230 := (not #62)
+#223 := (or #33 #34 #230)
+#234 := [def-axiom]: #223
+#236 := [unit-resolution #234 #67]: #235
+#209 := [unit-resolution #236 #549]: #33
+#198 := [monotonicity #209]: #197
+#193 := (= f9 #233)
+#237 := (= #233 f9)
+#210 := (or #554 #237)
+#341 := [quant-inst #27 #29]: #210
+#551 := [unit-resolution #341 #566]: #237
+#535 := [symm #551]: #193
+#200 := [trans #535 #198]: #199
+#537 := [trans #200 #208]: #34
+#538 := [unit-resolution #549 #537]: false
+#539 := [lemma #538]: #34
+#536 := [symm #539]: #541
+#542 := (= #28 #31)
+#179 := [monotonicity #539]: #542
+#543 := [monotonicity #179 #536]: #33
+#146 := (or #61 #144)
+#145 := (or #61 #144 #230)
+#231 := [def-axiom]: #145
+#232 := [unit-resolution #231 #67]: #146
+#540 := [unit-resolution #232 #539]: #61
+[unit-resolution #540 #543]: false
+unsat
+ff46e648b8433631f11b66136c88e13e20652d28 147 0
 #2 := false
 decl f12 :: S2
-#34 := f12
+#33 := f12
 decl f10 :: S2
-#30 := f10
-#38 := (= f10 f12)
-#112 := (not #38)
+#29 := f10
+#37 := (= f10 f12)
+#91 := (not #37)
 decl f11 :: S2
-#32 := f11
+#31 := f11
 decl f9 :: S2
-#28 := f9
-#37 := (= f9 f11)
-#111 := (not #37)
-#98 := (or #111 #112)
+#27 := f9
+#36 := (= f9 f11)
+#90 := (not #36)
+#77 := (or #90 #91)
 decl f5 :: (-> S5 S2 S4)
 decl f6 :: (-> S6 S2 S5)
 decl f7 :: S6
-#9 := f7
-#33 := (f6 f7 f11)
-#35 := (f5 #33 f12)
-#29 := (f6 f7 f9)
-#31 := (f5 #29 f10)
-#36 := (= #31 #35)
-#99 := (not #98)
-#250 := [hypothesis]: #99
-#185 := (or #98 #38)
-#272 := [def-axiom]: #185
-#238 := [unit-resolution #272 #250]: #38
-#240 := (= #29 #33)
-#184 := (or #98 #37)
-#271 := [def-axiom]: #184
-#239 := [unit-resolution #271 #250]: #37
-#241 := [monotonicity #239]: #240
-#579 := [monotonicity #241 #238]: #36
-#85 := (not #36)
-#257 := (or #85 #98)
-#121 := (iff #36 #98)
-#39 := (and #37 #38)
-#87 := (iff #39 #85)
-#124 := (iff #87 #121)
-#116 := (iff #98 #36)
-#122 := (iff #116 #121)
-#123 := [rewrite]: #122
-#119 := (iff #87 #116)
-#113 := (iff #99 #85)
-#117 := (iff #113 #116)
-#118 := [rewrite]: #117
-#114 := (iff #87 #113)
-#100 := (iff #39 #99)
-#101 := [rewrite]: #100
-#115 := [monotonicity #101]: #114
-#120 := [trans #115 #118]: #119
-#125 := [trans #120 #123]: #124
-#40 := (iff #36 #39)
-#41 := (not #40)
-#88 := (iff #41 #87)
-#89 := [rewrite]: #88
-#84 := [asserted]: #41
-#92 := [mp #84 #89]: #87
-#126 := [mp #92 #125]: #121
-#264 := (not #121)
-#274 := (or #85 #98 #264)
-#278 := [def-axiom]: #274
-#594 := [unit-resolution #278 #126]: #257
-#593 := [unit-resolution #594 #250]: #85
-#580 := [unit-resolution #593 #579]: false
-#581 := [lemma #580]: #98
+#8 := f7
+#32 := (f6 f7 f11)
+#34 := (f5 #32 f12)
+#28 := (f6 f7 f9)
+#30 := (f5 #28 f10)
+#35 := (= #30 #34)
+#78 := (not #77)
+#570 := [hypothesis]: #78
+#164 := (or #77 #37)
+#250 := [def-axiom]: #164
+#217 := [unit-resolution #250 #570]: #37
+#219 := (= #28 #32)
+#163 := (or #77 #36)
+#249 := [def-axiom]: #163
+#218 := [unit-resolution #249 #570]: #36
+#556 := [monotonicity #218]: #219
+#557 := [monotonicity #556 #217]: #35
+#65 := (not #35)
+#571 := (or #65 #77)
+#95 := (iff #35 #77)
+#38 := (and #36 #37)
+#66 := (iff #65 #38)
+#98 := (iff #66 #95)
+#92 := (iff #65 #78)
+#96 := (iff #92 #95)
+#97 := [rewrite]: #96
+#93 := (iff #66 #92)
+#79 := (iff #38 #78)
+#80 := [rewrite]: #79
+#94 := [monotonicity #80]: #93
+#99 := [trans #94 #97]: #98
+#39 := (iff #35 #38)
+#40 := (not #39)
+#67 := (iff #40 #66)
+#68 := [rewrite]: #67
+#64 := [asserted]: #40
+#71 := [mp #64 #68]: #66
+#100 := [mp #71 #99]: #95
+#242 := (not #95)
+#256 := (or #65 #77 #242)
+#235 := [def-axiom]: #256
+#573 := [unit-resolution #235 #100]: #571
+#212 := [unit-resolution #573 #570]: #65
+#558 := [unit-resolution #212 #557]: false
+#559 := [lemma #558]: #77
 decl f3 :: (-> S3 S4 S2)
 decl f4 :: S3
-#8 := f4
-#598 := (f3 f4 #35)
-#585 := (= #598 f11)
-#599 := (= f11 #598)
-#12 := (:var 0 S2)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#602 := (pattern #13)
-#14 := (f3 f4 #13)
-#62 := (= #10 #14)
-#603 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #602) #62)
-#65 := (forall (vars (?v0 S2) (?v1 S2)) #62)
-#606 := (iff #65 #603)
-#604 := (iff #62 #62)
-#605 := [refl]: #604
-#607 := [quant-intro #605]: #606
-#104 := (~ #65 #65)
-#102 := (~ #62 #62)
-#103 := [refl]: #102
-#105 := [nnf-pos #103]: #104
-#15 := (= #14 #10)
-#16 := (forall (vars (?v0 S2) (?v1 S2)) #15)
-#66 := (iff #16 #65)
-#63 := (iff #15 #62)
-#64 := [rewrite]: #63
-#67 := [quant-intro #64]: #66
-#61 := [asserted]: #16
-#70 := [mp #61 #67]: #65
-#91 := [mp~ #70 #105]: #65
-#608 := [mp #91 #607]: #603
-#262 := (not #603)
-#254 := (or #262 #599)
-#592 := [quant-inst #32 #34]: #254
-#582 := [unit-resolution #592 #608]: #599
-#587 := [symm #582]: #585
-#225 := (= f9 #598)
-#596 := (f3 f4 #31)
-#584 := (= #596 #598)
-#204 := (or #36 #99)
-#275 := (or #36 #99 #264)
-#276 := [def-axiom]: #275
-#277 := [unit-resolution #276 #126]: #204
-#583 := [unit-resolution #277 #581]: #36
-#220 := [monotonicity #583]: #584
-#251 := (= f9 #596)
-#263 := (or #262 #251)
-#597 := [quant-inst #28 #30]: #263
-#578 := [unit-resolution #597 #608]: #251
-#226 := [trans #578 #220]: #225
-#588 := [trans #226 #587]: #37
+#7 := f4
+#576 := (f3 f4 #34)
+#577 := (= #576 f11)
+#11 := (:var 0 S2)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#579 := (pattern #12)
+#13 := (f3 f4 #12)
+#14 := (= #13 #9)
+#580 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #579) #14)
+#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
+#583 := (iff #15 #580)
+#581 := (iff #14 #14)
+#582 := [refl]: #581
+#584 := [quant-intro #582]: #583
+#83 := (~ #15 #15)
+#81 := (~ #14 #14)
+#82 := [refl]: #81
+#84 := [nnf-pos #82]: #83
+#61 := [asserted]: #15
+#70 := [mp~ #61 #84]: #15
+#585 := [mp #70 #584]: #580
+#241 := (not #580)
+#569 := (or #241 #577)
+#228 := [quant-inst #31 #33]: #569
+#560 := [unit-resolution #228 #585]: #577
+#204 := (= f9 #576)
+#229 := (f3 f4 #30)
+#564 := (= #229 #576)
+#255 := (or #35 #78)
+#253 := (or #35 #78 #242)
+#254 := [def-axiom]: #253
+#252 := [unit-resolution #254 #100]: #255
+#555 := [unit-resolution #252 #559]: #35
+#203 := [monotonicity #555]: #564
+#198 := (= f9 #229)
+#360 := (= #229 f9)
+#574 := (or #241 #360)
+#575 := [quant-inst #27 #29]: #574
+#561 := [unit-resolution #575 #585]: #360
+#562 := [symm #561]: #198
+#565 := [trans #562 #203]: #204
+#563 := [trans #565 #560]: #36
 decl f8 :: S3
-#17 := f8
-#591 := (f3 f8 #35)
-#282 := (= #591 f12)
-#249 := (= f12 #591)
-#18 := (f3 f8 #13)
-#69 := (= #12 #18)
-#609 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #602) #69)
-#73 := (forall (vars (?v0 S2) (?v1 S2)) #69)
-#612 := (iff #73 #609)
-#610 := (iff #69 #69)
-#611 := [refl]: #610
-#613 := [quant-intro #611]: #612
-#94 := (~ #73 #73)
-#93 := (~ #69 #69)
-#106 := [refl]: #93
-#95 := [nnf-pos #106]: #94
-#19 := (= #18 #12)
-#20 := (forall (vars (?v0 S2) (?v1 S2)) #19)
-#74 := (iff #20 #73)
-#71 := (iff #19 #69)
-#72 := [rewrite]: #71
-#75 := [quant-intro #72]: #74
-#68 := [asserted]: #20
-#78 := [mp #68 #75]: #73
-#107 := [mp~ #78 #95]: #73
-#614 := [mp #107 #613]: #609
-#600 := (not #609)
-#234 := (or #600 #249)
-#577 := [quant-inst #32 #34]: #234
-#586 := [unit-resolution #577 #614]: #249
-#298 := [symm #586]: #282
-#299 := (= f10 #591)
-#383 := (f3 f8 #31)
-#575 := (= #383 #591)
-#576 := [monotonicity #583]: #575
-#590 := (= f10 #383)
-#595 := (or #600 #590)
-#601 := [quant-inst #28 #30]: #595
-#589 := [unit-resolution #601 #614]: #590
-#300 := [trans #589 #576]: #299
-#286 := [trans #300 #298]: #38
-#186 := (or #99 #111 #112)
-#273 := [def-axiom]: #186
-[unit-resolution #273 #286 #588 #581]: false
-unsat
-baaa782cc86dd181f5b22942ed5c1e9b1d9ea37c 104 0
-#2 := false
-decl f20 :: S2
-#54 := f20
-decl f17 :: S2
-#46 := f17
-#63 := (= f17 f20)
+#16 := f8
+#227 := (f3 f8 #34)
+#232 := (= #227 f12)
+#17 := (f3 f8 #12)
+#18 := (= #17 #11)
+#586 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #579) #18)
+#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
+#589 := (iff #19 #586)
+#587 := (iff #18 #18)
+#588 := [refl]: #587
+#590 := [quant-intro #588]: #589
+#73 := (~ #19 #19)
+#72 := (~ #18 #18)
+#85 := [refl]: #72
+#74 := [nnf-pos #85]: #73
+#62 := [asserted]: #19
+#86 := [mp~ #62 #74]: #19
+#591 := [mp #86 #590]: #586
+#572 := (not #586)
+#554 := (or #572 #232)
+#216 := [quant-inst #31 #33]: #554
+#566 := [unit-resolution #216 #591]: #232
+#277 := (= f10 #227)
+#567 := (f3 f8 #30)
+#275 := (= #567 #227)
+#276 := [monotonicity #555]: #275
+#553 := (= f10 #567)
+#240 := (= #567 f10)
+#578 := (or #572 #240)
+#568 := [quant-inst #27 #29]: #578
+#552 := [unit-resolution #568 #591]: #240
+#260 := [symm #552]: #553
+#278 := [trans #260 #276]: #277
+#171 := [trans #278 #566]: #37
+#165 := (or #78 #90 #91)
+#251 := [def-axiom]: #165
+[unit-resolution #251 #171 #563 #559]: false
+unsat
+f567b3ec65cba96a359862b5638f10a1c478c9a5 97 0
+#2 := false
 decl f8 :: (-> S8 S9 S2)
 decl f10 :: (-> S10 S5 S9)
 decl f5 :: (-> S6 S3 S5)
 decl f22 :: S3
-#58 := f22
+#57 := f22
 decl f6 :: (-> S7 S2 S6)
 decl f21 :: S2
-#56 := f21
+#55 := f21
 decl f7 :: S7
-#9 := f7
-#57 := (f6 f7 f21)
-#59 := (f5 #57 f22)
+#8 := f7
+#56 := (f6 f7 f21)
+#58 := (f5 #56 f22)
 decl f11 :: (-> S11 S2 S10)
+decl f20 :: S2
+#53 := f20
 decl f12 :: S11
-#18 := f12
-#55 := (f11 f12 f20)
-#60 := (f10 #55 #59)
+#17 := f12
+#54 := (f11 f12 f20)
+#59 := (f10 #54 #58)
 decl f9 :: S8
-#17 := f9
-#61 := (f8 f9 #60)
+#16 := f9
+#60 := (f8 f9 #59)
 decl f19 :: S3
-#50 := f19
+#49 := f19
 decl f18 :: S2
-#48 := f18
-#49 := (f6 f7 f18)
-#51 := (f5 #49 f19)
-#47 := (f11 f12 f17)
-#52 := (f10 #47 #51)
-#53 := (f8 f9 #52)
-#62 := (= #53 #61)
-#64 := (iff #62 #63)
-#343 := (iff #63 #62)
-#620 := (= f20 #61)
-#20 := (:var 0 S5)
-#10 := (:var 1 S2)
-#19 := (f11 f12 #10)
-#21 := (f10 #19 #20)
-#652 := (pattern #21)
-#22 := (f8 f9 #21)
-#93 := (= #10 #22)
-#653 := (forall (vars (?v0 S2) (?v1 S5)) (:pat #652) #93)
-#97 := (forall (vars (?v0 S2) (?v1 S5)) #93)
-#656 := (iff #97 #653)
-#654 := (iff #93 #93)
-#655 := [refl]: #654
-#657 := [quant-intro #655]: #656
-#142 := (~ #97 #97)
-#141 := (~ #93 #93)
-#160 := [refl]: #141
-#143 := [nnf-pos #160]: #142
-#23 := (= #22 #10)
-#24 := (forall (vars (?v0 S2) (?v1 S5)) #23)
-#98 := (iff #24 #97)
-#95 := (iff #23 #93)
-#96 := [rewrite]: #95
-#99 := [quant-intro #96]: #98
-#92 := [asserted]: #24
-#102 := [mp #92 #99]: #97
-#161 := [mp~ #102 #143]: #97
-#658 := [mp #161 #657]: #653
-#293 := (not #653)
-#623 := (or #293 #620)
-#624 := [quant-inst #54 #59]: #623
-#341 := [unit-resolution #624 #658]: #620
-#644 := (= f17 #53)
-#636 := (or #293 #644)
-#277 := [quant-inst #46 #51]: #636
-#342 := [unit-resolution #277 #658]: #644
-#329 := [monotonicity #342 #341]: #343
-#344 := [symm #329]: #64
-#316 := (not #63)
-#133 := (not #62)
-#235 := (iff #133 #316)
-#614 := [monotonicity #344]: #235
-#632 := [hypothesis]: #133
-#615 := [mp #632 #614]: #316
-#315 := (or #63 #62)
-#135 := (iff #63 #133)
-#65 := (not #64)
-#136 := (iff #65 #135)
-#137 := [rewrite]: #136
-#132 := [asserted]: #65
-#140 := [mp #132 #137]: #135
-#227 := (not #135)
-#314 := (or #63 #62 #227)
-#228 := [def-axiom]: #314
-#229 := [unit-resolution #228 #140]: #315
-#618 := [unit-resolution #229 #632]: #63
-#337 := [unit-resolution #618 #615]: false
-#338 := [lemma #337]: #62
-#616 := [mp #338 #344]: #63
-#319 := (or #316 #133)
-#307 := (or #316 #133 #227)
-#318 := [def-axiom]: #307
-#247 := [unit-resolution #318 #140]: #319
-#612 := [unit-resolution #247 #338]: #316
-[unit-resolution #612 #616]: false
-unsat
-de215825bb06594ceb5b3aa8ef2ee6d8c084788e 230 0
+#47 := f18
+#48 := (f6 f7 f18)
+#50 := (f5 #48 f19)
+decl f17 :: S2
+#45 := f17
+#46 := (f11 f12 f17)
+#51 := (f10 #46 #50)
+#52 := (f8 f9 #51)
+#61 := (= #52 #60)
+#62 := (= f17 f20)
+#198 := (iff #62 #61)
+#63 := (iff #61 #62)
+#243 := (= #60 f20)
+#19 := (:var 0 S5)
+#9 := (:var 1 S2)
+#18 := (f11 f12 #9)
+#20 := (f10 #18 #19)
+#613 := (pattern #20)
+#21 := (f8 f9 #20)
+#22 := (= #21 #9)
+#614 := (forall (vars (?v0 S2) (?v1 S5)) (:pat #613) #22)
+#23 := (forall (vars (?v0 S2) (?v1 S5)) #22)
+#617 := (iff #23 #614)
+#615 := (iff #22 #22)
+#616 := [refl]: #615
+#618 := [quant-intro #616]: #617
+#100 := (~ #23 #23)
+#99 := (~ #22 #22)
+#118 := [refl]: #99
+#101 := [nnf-pos #118]: #100
+#86 := [asserted]: #23
+#119 := [mp~ #86 #101]: #23
+#619 := [mp #119 #618]: #614
+#597 := (not #614)
+#585 := (or #597 #243)
+#586 := [quant-inst #53 #58]: #585
+#303 := [unit-resolution #586 #619]: #243
+#595 := (= #52 f17)
+#239 := (or #597 #595)
+#581 := [quant-inst #45 #50]: #239
+#304 := [unit-resolution #581 #619]: #595
+#305 := [monotonicity #304 #303]: #63
+#575 := [symm #305]: #198
+#92 := (not #61)
+#190 := (not #62)
+#576 := (iff #190 #92)
+#298 := [monotonicity #575]: #576
+#579 := [hypothesis]: #190
+#299 := [mp #579 #298]: #92
+#281 := (or #61 #62)
+#93 := (iff #92 #62)
+#64 := (not #63)
+#94 := (iff #64 #93)
+#95 := [rewrite]: #94
+#91 := [asserted]: #64
+#98 := [mp #91 #95]: #93
+#276 := (not #93)
+#269 := (or #61 #62 #276)
+#280 := [def-axiom]: #269
+#282 := [unit-resolution #280 #98]: #281
+#580 := [unit-resolution #282 #579]: #61
+#573 := [unit-resolution #580 #299]: false
+#577 := [lemma #573]: #62
+#578 := [mp #577 #575]: #61
+#192 := (or #92 #190)
+#191 := (or #92 #190 #276)
+#277 := [def-axiom]: #191
+#278 := [unit-resolution #277 #98]: #192
+#574 := [unit-resolution #278 #577]: #92
+[unit-resolution #574 #578]: false
+unsat
+3899473eab3901c51712a93b78ff218465cc80a5 204 0
 #2 := false
 decl f22 :: S8
-#58 := f22
+#57 := f22
 decl f19 :: S8
-#50 := f19
-#64 := (= f19 f22)
-#177 := (not #64)
+#49 := f19
+#63 := (= f19 f22)
+#135 := (not #63)
 decl f21 :: S2
-#56 := f21
+#55 := f21
 decl f18 :: S2
-#48 := f18
-#63 := (= f18 f21)
-#176 := (not #63)
-#154 := (or #176 #177)
+#47 := f18
+#62 := (= f18 f21)
+#134 := (not #62)
+#112 := (or #134 #135)
 decl f15 :: (-> S13 S5 S3)
 decl f5 :: (-> S6 S3 S5)
 decl f10 :: (-> S10 S8 S3)
 decl f11 :: (-> S11 S2 S10)
 decl f12 :: S11
-#18 := f12
+#17 := f12
+#56 := (f11 f12 f21)
+#58 := (f10 #56 f22)
+decl f6 :: (-> S7 S2 S6)
+decl f20 :: S2
+#53 := f20
+decl f7 :: S7
+#8 := f7
+#54 := (f6 f7 f20)
+#59 := (f5 #54 #58)
+decl f16 :: S13
+#28 := f16
+#60 := (f15 f16 #59)
+#48 := (f11 f12 f18)
+#50 := (f10 #48 f19)
+decl f17 :: S2
+#45 := f17
+#46 := (f6 f7 f17)
+#51 := (f5 #46 #50)
+#52 := (f15 f16 #51)
+#61 := (= #52 #60)
+#306 := (= #58 #60)
+#612 := (= #60 #58)
+#11 := (:var 0 S3)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#623 := (pattern #12)
+#29 := (f15 f16 #12)
+#30 := (= #29 #11)
+#643 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #623) #30)
+#31 := (forall (vars (?v0 S2) (?v1 S3)) #30)
+#646 := (iff #31 #643)
+#644 := (iff #30 #30)
+#645 := [refl]: #644
+#647 := [quant-intro #645]: #646
+#106 := (~ #31 #31)
+#125 := (~ #30 #30)
+#126 := [refl]: #125
+#107 := [nnf-pos #126]: #106
+#90 := [asserted]: #31
+#127 := [mp~ #90 #107]: #31
+#648 := [mp #127 #647]: #643
+#621 := (not #643)
+#614 := (or #621 #612)
+#256 := [quant-inst #53 #58]: #614
+#593 := [unit-resolution #256 #648]: #612
+#307 := [symm #593]: #306
+#308 := (= #52 #58)
+#595 := (= #50 #58)
+#113 := (not #112)
+#321 := [hypothesis]: #113
+#208 := (or #112 #63)
+#294 := [def-axiom]: #208
+#315 := [unit-resolution #294 #321]: #63
+#590 := (= #48 #56)
+#207 := (or #112 #62)
+#293 := [def-axiom]: #207
+#316 := [unit-resolution #293 #321]: #62
+#594 := [monotonicity #316]: #590
+#305 := [monotonicity #594 #315]: #595
+#611 := (= #52 #50)
+#616 := (or #621 #611)
+#622 := [quant-inst #45 #50]: #616
+#591 := [unit-resolution #622 #648]: #611
+#586 := [trans #591 #305]: #308
+#587 := [trans #586 #307]: #61
+#94 := (not #61)
+#615 := (or #94 #112)
+#139 := (iff #61 #112)
+#64 := (and #62 #63)
+#95 := (iff #94 #64)
+#142 := (iff #95 #139)
+#136 := (iff #94 #113)
+#140 := (iff #136 #139)
+#141 := [rewrite]: #140
+#137 := (iff #95 #136)
+#114 := (iff #64 #113)
+#115 := [rewrite]: #114
+#138 := [monotonicity #115]: #137
+#143 := [trans #138 #141]: #142
+#65 := (iff #61 #64)
+#66 := (not #65)
+#96 := (iff #66 #95)
+#97 := [rewrite]: #96
+#93 := [asserted]: #66
+#100 := [mp #93 #97]: #95
+#144 := [mp #100 #143]: #139
+#286 := (not #139)
+#300 := (or #94 #112 #286)
+#279 := [def-axiom]: #300
+#617 := [unit-resolution #279 #144]: #615
+#322 := [unit-resolution #617 #321]: #94
+#301 := [unit-resolution #322 #587]: false
+#584 := [lemma #301]: #112
+decl f8 :: (-> S9 S3 S2)
+decl f9 :: S9
+#16 := f9
+#600 := (f8 f9 #58)
+#601 := (= #600 f21)
+#19 := (:var 0 S8)
+#18 := (f11 f12 #9)
+#20 := (f10 #18 #19)
+#630 := (pattern #20)
+#21 := (f8 f9 #20)
+#22 := (= #21 #9)
+#631 := (forall (vars (?v0 S2) (?v1 S8)) (:pat #630) #22)
+#23 := (forall (vars (?v0 S2) (?v1 S8)) #22)
+#634 := (iff #23 #631)
+#632 := (iff #22 #22)
+#633 := [refl]: #632
+#635 := [quant-intro #633]: #634
+#102 := (~ #23 #23)
+#101 := (~ #22 #22)
+#120 := [refl]: #101
+#103 := [nnf-pos #120]: #102
+#88 := [asserted]: #23
+#121 := [mp~ #88 #103]: #23
+#636 := [mp #121 #635]: #631
+#261 := (not #631)
+#242 := (or #261 #601)
+#606 := [quant-inst #55 #57]: #242
+#588 := [unit-resolution #606 #636]: #601
+#424 := (= f18 #600)
+#271 := (f8 f9 #50)
+#577 := (= #271 #600)
+#579 := (= #50 #60)
+#299 := (or #61 #113)
+#297 := (or #61 #113 #286)
+#298 := [def-axiom]: #297
+#296 := [unit-resolution #298 #144]: #299
+#585 := [unit-resolution #296 #584]: #61
+#589 := (= #50 #52)
+#578 := [symm #591]: #589
+#580 := [trans #578 #585]: #579
+#575 := [trans #580 #593]: #595
+#583 := [monotonicity #575]: #577
+#581 := (= f18 #271)
+#272 := (= #271 f18)
+#262 := (or #261 #272)
+#263 := [quant-inst #47 #49]: #262
+#576 := [unit-resolution #263 #636]: #272
+#582 := [symm #576]: #581
+#425 := [trans #582 #583]: #424
+#426 := [trans #425 #588]: #62
+decl f13 :: (-> S12 S3 S8)
+decl f14 :: S12
+#24 := f14
+#599 := (f13 f14 #58)
+#605 := (= #599 f22)
+#25 := (f13 f14 #20)
+#26 := (= #25 #19)
+#637 := (forall (vars (?v0 S2) (?v1 S8)) (:pat #630) #26)
+#27 := (forall (vars (?v0 S2) (?v1 S8)) #26)
+#640 := (iff #27 #637)
+#638 := (iff #26 #26)
+#639 := [refl]: #638
+#641 := [quant-intro #639]: #640
+#104 := (~ #27 #27)
+#122 := (~ #26 #26)
+#123 := [refl]: #122
+#105 := [nnf-pos #123]: #104
+#89 := [asserted]: #27
+#124 := [mp~ #89 #105]: #27
+#642 := [mp #124 #641]: #637
+#602 := (not #637)
+#248 := (or #602 #605)
+#609 := [quant-inst #55 #57]: #248
+#568 := [unit-resolution #609 #642]: #605
+#572 := (= f19 #599)
+#598 := (f13 f14 #50)
+#565 := (= #598 #599)
+#566 := [monotonicity #575]: #565
+#570 := (= f19 #598)
+#260 := (= #598 f19)
+#603 := (or #602 #260)
+#604 := [quant-inst #47 #49]: #603
+#569 := [unit-resolution #604 #642]: #260
+#571 := [symm #569]: #570
+#573 := [trans #571 #566]: #572
+#567 := [trans #573 #568]: #63
+#209 := (or #113 #134 #135)
+#295 := [def-axiom]: #209
+[unit-resolution #295 #567 #426 #584]: false
+unsat
+66f8caa017bcd510092693efddec3be735f82480 140 0
+#2 := false
+decl f8 :: (-> S9 S3 S2)
+decl f15 :: (-> S13 S5 S3)
+decl f5 :: (-> S6 S3 S5)
+decl f10 :: (-> S10 S8 S3)
+decl f22 :: S8
+#58 := f22
+decl f11 :: (-> S11 S2 S10)
+decl f21 :: S2
+#56 := f21
+decl f12 :: S11
+#17 := f12
 #57 := (f11 f12 f21)
 #59 := (f10 #57 f22)
 decl f6 :: (-> S7 S2 S6)
 decl f20 :: S2
 #54 := f20
 decl f7 :: S7
-#9 := f7
+#8 := f7
 #55 := (f6 f7 f20)
 #60 := (f5 #55 #59)
 decl f16 :: S13
-#29 := f16
+#28 := f16
 #61 := (f15 f16 #60)
-#49 := (f11 f12 f18)
-#51 := (f10 #49 f19)
-decl f17 :: S2
-#46 := f17
-#47 := (f6 f7 f17)
-#52 := (f5 #47 #51)
-#53 := (f15 f16 #52)
-#62 := (= #53 #61)
-#666 := (= #59 #61)
-#12 := (:var 0 S3)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#667 := (pattern #13)
-#30 := (f15 f16 #13)
-#111 := (= #12 #30)
-#687 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #667) #111)
-#115 := (forall (vars (?v0 S2) (?v1 S3)) #111)
-#690 := (iff #115 #687)
-#688 := (iff #111 #111)
-#689 := [refl]: #688
-#691 := [quant-intro #689]: #690
-#148 := (~ #115 #115)
-#167 := (~ #111 #111)
-#168 := [refl]: #167
-#149 := [nnf-pos #168]: #148
-#31 := (= #30 #12)
-#32 := (forall (vars (?v0 S2) (?v1 S3)) #31)
-#116 := (iff #32 #115)
-#113 := (iff #31 #111)
-#114 := [rewrite]: #113
-#117 := [quant-intro #114]: #116
-#110 := [asserted]: #32
-#120 := [mp #110 #117]: #115
-#169 := [mp~ #120 #149]: #115
-#692 := [mp #169 #691]: #687
-#664 := (not #687)
-#315 := (or #664 #666)
-#658 := [quant-inst #54 #59]: #315
-#257 := [unit-resolution #658 #692]: #666
-#349 := (= #53 #59)
-#639 := (= #51 #59)
-#155 := (not #154)
-#364 := [hypothesis]: #155
-#250 := (or #154 #64)
-#337 := [def-axiom]: #250
-#636 := [unit-resolution #337 #364]: #64
-#359 := (= #49 #57)
-#249 := (or #154 #63)
-#336 := [def-axiom]: #249
-#637 := [unit-resolution #336 #364]: #63
-#360 := [monotonicity #637]: #359
-#348 := [monotonicity #360 #636]: #639
-#638 := (= #53 #51)
-#448 := (= #51 #53)
-#665 := (or #664 #448)
-#660 := [quant-inst #46 #51]: #665
-#634 := [unit-resolution #660 #692]: #448
-#635 := [symm #634]: #638
-#350 := [trans #635 #348]: #349
-#352 := [trans #350 #257]: #62
-#135 := (not #62)
-#322 := (or #135 #154)
-#186 := (iff #62 #154)
-#65 := (and #63 #64)
-#137 := (iff #65 #135)
-#189 := (iff #137 #186)
-#181 := (iff #154 #62)
-#187 := (iff #181 #186)
-#188 := [rewrite]: #187
-#184 := (iff #137 #181)
-#178 := (iff #155 #135)
-#182 := (iff #178 #181)
-#183 := [rewrite]: #182
-#179 := (iff #137 #178)
-#156 := (iff #65 #155)
-#157 := [rewrite]: #156
-#180 := [monotonicity #157]: #179
-#185 := [trans #180 #183]: #184
-#190 := [trans #185 #188]: #189
-#66 := (iff #62 #65)
-#67 := (not #66)
-#138 := (iff #67 #137)
-#139 := [rewrite]: #138
-#134 := [asserted]: #67
-#142 := [mp #134 #139]: #137
-#191 := [mp #142 #190]: #186
-#329 := (not #186)
-#339 := (or #135 #154 #329)
-#343 := [def-axiom]: #339
-#659 := [unit-resolution #343 #191]: #322
-#365 := [unit-resolution #659 #364]: #135
-#630 := [unit-resolution #365 #352]: false
-#631 := [lemma #630]: #154
-decl f8 :: (-> S9 S3 S2)
 decl f9 :: S9
-#17 := f9
-#306 := (f8 f9 #59)
-#625 := (= #306 f21)
-#644 := (= f21 #306)
-#20 := (:var 0 S8)
-#19 := (f11 f12 #10)
-#21 := (f10 #19 #20)
-#674 := (pattern #21)
-#22 := (f8 f9 #21)
-#95 := (= #10 #22)
-#675 := (forall (vars (?v0 S2) (?v1 S8)) (:pat #674) #95)
-#99 := (forall (vars (?v0 S2) (?v1 S8)) #95)
-#678 := (iff #99 #675)
-#676 := (iff #95 #95)
-#677 := [refl]: #676
-#679 := [quant-intro #677]: #678
-#144 := (~ #99 #99)
-#143 := (~ #95 #95)
-#162 := [refl]: #143
-#145 := [nnf-pos #162]: #144
-#23 := (= #22 #10)
-#24 := (forall (vars (?v0 S2) (?v1 S8)) #23)
-#100 := (iff #24 #99)
-#97 := (iff #23 #95)
-#98 := [rewrite]: #97
-#101 := [quant-intro #98]: #100
-#94 := [asserted]: #24
-#104 := [mp #94 #101]: #99
-#163 := [mp~ #104 #145]: #99
-#680 := [mp #163 #679]: #675
-#303 := (not #675)
-#649 := (or #303 #644)
-#285 := [quant-inst #56 #58]: #649
-#344 := [unit-resolution #285 #680]: #644
-#626 := [symm #344]: #625
-#621 := (= f18 #306)
-#656 := (f8 f9 #51)
-#619 := (= #656 #306)
-#632 := (= #61 #59)
-#629 := [symm #257]: #632
-#633 := (= #51 #61)
-#269 := (or #62 #155)
-#340 := (or #62 #155 #329)
-#341 := [def-axiom]: #340
-#342 := [unit-resolution #341 #191]: #269
-#628 := [unit-resolution #342 #631]: #62
-#622 := [trans #634 #628]: #633
-#623 := [trans #622 #629]: #639
-#620 := [monotonicity #623]: #619
-#657 := (= f18 #656)
-#304 := (or #303 #657)
-#305 := [quant-inst #48 #50]: #304
-#624 := [unit-resolution #305 #680]: #657
-#627 := [trans #624 #620]: #621
-#468 := [trans #627 #626]: #63
+#16 := f9
+#62 := (f8 f9 #61)
+decl f19 :: S8
+#49 := f19
+decl f18 :: S2
+#47 := f18
+#48 := (f11 f12 f18)
+#50 := (f10 #48 f19)
+decl f17 :: S2
+#45 := f17
+#46 := (f6 f7 f17)
+#51 := (f5 #46 #50)
+#52 := (f15 f16 #51)
+#53 := (f8 f9 #52)
+#63 := (= #53 #62)
+#64 := (= f18 f21)
+#560 := (iff #64 #63)
+#65 := (iff #63 #64)
+#572 := (= #62 f21)
+#583 := (f8 f9 #59)
+#245 := (= #583 f21)
+#19 := (:var 0 S8)
+#9 := (:var 1 S2)
+#18 := (f11 f12 #9)
+#20 := (f10 #18 #19)
+#615 := (pattern #20)
+#21 := (f8 f9 #20)
+#22 := (= #21 #9)
+#616 := (forall (vars (?v0 S2) (?v1 S8)) (:pat #615) #22)
+#23 := (forall (vars (?v0 S2) (?v1 S8)) #22)
+#619 := (iff #23 #616)
+#617 := (iff #22 #22)
+#618 := [refl]: #617
+#620 := [quant-intro #618]: #619
+#102 := (~ #23 #23)
+#101 := (~ #22 #22)
+#120 := [refl]: #101
+#103 := [nnf-pos #120]: #102
+#88 := [asserted]: #23
+#121 := [mp~ #88 #103]: #23
+#621 := [mp #121 #620]: #616
+#257 := (not #616)
+#587 := (or #257 #245)
+#588 := [quant-inst #56 #58]: #587
+#291 := [unit-resolution #588 #621]: #245
+#293 := (= #62 #583)
+#604 := (= #61 #59)
+#11 := (:var 0 S3)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#608 := (pattern #12)
+#29 := (f15 f16 #12)
+#30 := (= #29 #11)
+#628 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #608) #30)
+#31 := (forall (vars (?v0 S2) (?v1 S3)) #30)
+#631 := (iff #31 #628)
+#629 := (iff #30 #30)
+#630 := [refl]: #629
+#632 := [quant-intro #630]: #631
+#106 := (~ #31 #31)
+#125 := (~ #30 #30)
+#126 := [refl]: #125
+#107 := [nnf-pos #126]: #106
+#90 := [asserted]: #31
+#127 := [mp~ #90 #107]: #31
+#633 := [mp #127 #632]: #628
+#269 := (not #628)
+#597 := (or #269 #604)
+#256 := [quant-inst #54 #59]: #597
+#292 := [unit-resolution #256 #633]: #604
+#571 := [monotonicity #292]: #293
+#286 := [trans #571 #291]: #572
+#563 := (= #53 f18)
+#605 := (f8 f9 #50)
+#607 := (= #605 f18)
+#599 := (or #257 #607)
+#241 := [quant-inst #47 #49]: #599
+#569 := [unit-resolution #241 #621]: #607
+#570 := (= #53 #605)
+#264 := (= #52 #50)
+#270 := (or #269 #264)
+#603 := [quant-inst #45 #50]: #270
+#573 := [unit-resolution #603 #633]: #264
+#574 := [monotonicity #573]: #570
+#564 := [trans #574 #569]: #563
+#565 := [monotonicity #564 #286]: #65
+#561 := [symm #565]: #560
+#94 := (not #63)
+#192 := (not #64)
+#566 := (iff #192 #94)
+#567 := [monotonicity #561]: #566
+#579 := [hypothesis]: #192
+#562 := [mp #579 #567]: #94
+#283 := (or #63 #64)
+#95 := (iff #94 #64)
+#66 := (not #65)
+#96 := (iff #66 #95)
+#97 := [rewrite]: #96
+#93 := [asserted]: #66
+#100 := [mp #93 #97]: #95
+#278 := (not #95)
+#271 := (or #63 #64 #278)
+#282 := [def-axiom]: #271
+#284 := [unit-resolution #282 #100]: #283
+#576 := [unit-resolution #284 #579]: #63
+#568 := [unit-resolution #576 #562]: false
+#409 := [lemma #568]: #64
+#411 := [mp #409 #561]: #63
+#194 := (or #94 #192)
+#193 := (or #94 #192 #278)
+#279 := [def-axiom]: #193
+#280 := [unit-resolution #279 #100]: #194
+#410 := [unit-resolution #280 #409]: #94
+[unit-resolution #410 #411]: false
+unsat
+ff6228ca7ad84c97bcf0916e5ffe8db03d1bc6d0 140 0
+#2 := false
 decl f13 :: (-> S12 S3 S8)
-decl f14 :: S12
-#25 := f14
-#648 := (f13 f14 #59)
-#614 := (= #648 f22)
-#643 := (= f22 #648)
-#26 := (f13 f14 #21)
-#103 := (= #20 #26)
-#681 := (forall (vars (?v0 S2) (?v1 S8)) (:pat #674) #103)
-#107 := (forall (vars (?v0 S2) (?v1 S8)) #103)
-#684 := (iff #107 #681)
-#682 := (iff #103 #103)
-#683 := [refl]: #682
-#685 := [quant-intro #683]: #684
-#146 := (~ #107 #107)
-#164 := (~ #103 #103)
-#165 := [refl]: #164
-#147 := [nnf-pos #165]: #146
-#27 := (= #26 #20)
-#28 := (forall (vars (?v0 S2) (?v1 S8)) #27)
-#108 := (iff #28 #107)
-#105 := (iff #27 #103)
-#106 := [rewrite]: #105
-#109 := [quant-intro #106]: #108
-#102 := [asserted]: #28
-#112 := [mp #102 #109]: #107
-#166 := [mp~ #112 #147]: #107
-#686 := [mp #166 #685]: #681
-#645 := (not #681)
-#290 := (or #645 #643)
-#291 := [quant-inst #56 #58]: #290
-#469 := [unit-resolution #291 #686]: #643
-#615 := [symm #469]: #614
-#609 := (= f19 #648)
-#299 := (f13 f14 #51)
-#612 := (= #299 #648)
-#613 := [monotonicity #623]: #612
-#642 := (= f19 #299)
-#646 := (or #645 #642)
-#647 := [quant-inst #48 #50]: #646
-#470 := [unit-resolution #647 #686]: #642
-#610 := [trans #470 #613]: #609
-#616 := [trans #610 #615]: #64
-#251 := (or #155 #176 #177)
-#338 := [def-axiom]: #251
-[unit-resolution #338 #616 #468 #631]: false
-unsat
-c95153d6b8f8057a992abaf6c88b4938f23f1514 160 0
-#2 := false
-decl f21 :: S2
-#57 := f21
-decl f18 :: S2
-#48 := f18
-#65 := (= f18 f21)
-decl f8 :: (-> S9 S3 S2)
 decl f15 :: (-> S13 S5 S3)
 decl f5 :: (-> S6 S3 S5)
 decl f10 :: (-> S10 S8 S3)
 decl f22 :: S8
-#59 := f22
-decl f11 :: (-> S11 S2 S10)
-decl f12 :: S11
-#18 := f12
-#58 := (f11 f12 f21)
-#60 := (f10 #58 f22)
-decl f6 :: (-> S7 S2 S6)
-decl f20 :: S2
-#55 := f20
-decl f7 :: S7
-#9 := f7
-#56 := (f6 f7 f20)
-#61 := (f5 #56 #60)
-decl f16 :: S13
-#29 := f16
-#62 := (f15 f16 #61)
-decl f9 :: S9
-#17 := f9
-#63 := (f8 f9 #62)
-decl f19 :: S8
-#50 := f19
-#49 := (f11 f12 f18)
-#51 := (f10 #49 f19)
-decl f17 :: S2
-#46 := f17
-#47 := (f6 f7 f17)
-#52 := (f5 #47 #51)
-#53 := (f15 f16 #52)
-#54 := (f8 f9 #53)
-#64 := (= #54 #63)
-#66 := (iff #64 #65)
-#608 := (= #63 f21)
-#279 := (f8 f9 #60)
-#611 := (= #279 f21)
-#622 := (= f21 #279)
-#20 := (:var 0 S8)
-#10 := (:var 1 S2)
-#19 := (f11 f12 #10)
-#21 := (f10 #19 #20)
-#654 := (pattern #21)
-#22 := (f8 f9 #21)
-#95 := (= #10 #22)
-#655 := (forall (vars (?v0 S2) (?v1 S8)) (:pat #654) #95)
-#99 := (forall (vars (?v0 S2) (?v1 S8)) #95)
-#658 := (iff #99 #655)
-#656 := (iff #95 #95)
-#657 := [refl]: #656
-#659 := [quant-intro #657]: #658
-#144 := (~ #99 #99)
-#143 := (~ #95 #95)
-#162 := [refl]: #143
-#145 := [nnf-pos #162]: #144
-#23 := (= #22 #10)
-#24 := (forall (vars (?v0 S2) (?v1 S8)) #23)
-#100 := (iff #24 #99)
-#97 := (iff #23 #95)
-#98 := [rewrite]: #97
-#101 := [quant-intro #98]: #100
-#94 := [asserted]: #24
-#104 := [mp #94 #101]: #99
-#163 := [mp~ #104 #145]: #99
-#660 := [mp #163 #659]: #655
-#637 := (not #655)
-#625 := (or #637 #622)
-#626 := [quant-inst #57 #59]: #625
-#619 := [unit-resolution #626 #660]: #622
-#324 := [symm #619]: #611
-#332 := (= #63 #279)
-#329 := (= #62 #60)
-#642 := (= #60 #62)
-#12 := (:var 0 S3)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#647 := (pattern #13)
-#30 := (f15 f16 #13)
-#111 := (= #12 #30)
-#667 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #647) #111)
-#115 := (forall (vars (?v0 S2) (?v1 S3)) #111)
-#670 := (iff #115 #667)
-#668 := (iff #111 #111)
-#669 := [refl]: #668
-#671 := [quant-intro #669]: #670
-#148 := (~ #115 #115)
-#167 := (~ #111 #111)
-#168 := [refl]: #167
-#149 := [nnf-pos #168]: #148
-#31 := (= #30 #12)
-#32 := (forall (vars (?v0 S2) (?v1 S3)) #31)
-#116 := (iff #32 #115)
-#113 := (iff #31 #111)
-#114 := [rewrite]: #113
-#117 := [quant-intro #114]: #116
-#110 := [asserted]: #32
-#120 := [mp #110 #117]: #115
-#169 := [mp~ #120 #149]: #115
-#672 := [mp #169 #671]: #667
-#635 := (not #667)
-#646 := (or #635 #642)
-#636 := [quant-inst #55 #60]: #646
-#328 := [unit-resolution #636 #672]: #642
-#330 := [symm #328]: #329
-#610 := [monotonicity #330]: #332
-#612 := [trans #610 #324]: #608
-#606 := (= #54 f18)
-#643 := (f8 f9 #51)
-#600 := (= #643 f18)
-#640 := (= f18 #643)
-#295 := (or #637 #640)
-#638 := [quant-inst #48 #50]: #295
-#609 := [unit-resolution #638 #660]: #640
-#605 := [symm #609]: #600
-#604 := (= #54 #643)
-#602 := (= #53 #51)
-#323 := (= #51 #53)
-#307 := (or #635 #323)
-#308 := [quant-inst #46 #51]: #307
-#613 := [unit-resolution #308 #672]: #323
-#603 := [symm #613]: #602
-#599 := [monotonicity #603]: #604
-#601 := [trans #599 #605]: #606
-#607 := [monotonicity #601 #612]: #66
-#318 := (not #65)
-#135 := (not #64)
-#448 := (iff #135 #318)
-#449 := [monotonicity #607]: #448
-#340 := [hypothesis]: #135
-#450 := [mp #340 #449]: #318
-#317 := (or #65 #64)
-#137 := (iff #65 #135)
-#67 := (not #66)
-#138 := (iff #67 #137)
-#139 := [rewrite]: #138
-#134 := [asserted]: #67
-#142 := [mp #134 #139]: #137
-#229 := (not #137)
-#316 := (or #65 #64 #229)
-#230 := [def-axiom]: #316
-#231 := [unit-resolution #230 #142]: #317
-#614 := [unit-resolution #231 #340]: #65
-#592 := [unit-resolution #614 #450]: false
-#593 := [lemma #592]: #64
-#595 := [mp #593 #607]: #65
-#321 := (or #318 #135)
-#309 := (or #318 #135 #229)
-#320 := [def-axiom]: #309
-#249 := [unit-resolution #320 #142]: #321
-#594 := [unit-resolution #249 #593]: #318
-[unit-resolution #594 #595]: false
-unsat
-5862efd1fb6eec78f1577addba461fdbf04f374f 160 0
-#2 := false
-decl f22 :: S8
-#59 := f22
-decl f19 :: S8
-#50 := f19
-#65 := (= f19 f22)
-decl f13 :: (-> S12 S3 S8)
-decl f15 :: (-> S13 S5 S3)
-decl f5 :: (-> S6 S3 S5)
-decl f10 :: (-> S10 S8 S3)
+#58 := f22
 decl f11 :: (-> S11 S2 S10)
 decl f21 :: S2
-#57 := f21
+#56 := f21
 decl f12 :: S11
-#18 := f12
-#58 := (f11 f12 f21)
-#60 := (f10 #58 f22)
+#17 := f12
+#57 := (f11 f12 f21)
+#59 := (f10 #57 f22)
 decl f6 :: (-> S7 S2 S6)
 decl f20 :: S2
-#55 := f20
+#54 := f20
 decl f7 :: S7
-#9 := f7
-#56 := (f6 f7 f20)
-#61 := (f5 #56 #60)
+#8 := f7
+#55 := (f6 f7 f20)
+#60 := (f5 #55 #59)
 decl f16 :: S13
-#29 := f16
-#62 := (f15 f16 #61)
+#28 := f16
+#61 := (f15 f16 #60)
 decl f14 :: S12
-#25 := f14
-#63 := (f13 f14 #62)
+#24 := f14
+#62 := (f13 f14 #61)
+decl f19 :: S8
+#49 := f19
 decl f18 :: S2
-#48 := f18
-#49 := (f11 f12 f18)
-#51 := (f10 #49 f19)
+#47 := f18
+#48 := (f11 f12 f18)
+#50 := (f10 #48 f19)
 decl f17 :: S2
-#46 := f17
-#47 := (f6 f7 f17)
-#52 := (f5 #47 #51)
-#53 := (f15 f16 #52)
-#54 := (f13 f14 #53)
-#64 := (= #54 #63)
-#66 := (iff #64 #65)
-#608 := (= #63 f22)
-#286 := (f13 f14 #60)
-#611 := (= #286 f22)
-#624 := (= f22 #286)
-#20 := (:var 0 S8)
-#10 := (:var 1 S2)
-#19 := (f11 f12 #10)
-#21 := (f10 #19 #20)
-#654 := (pattern #21)
-#26 := (f13 f14 #21)
-#103 := (= #20 #26)
-#661 := (forall (vars (?v0 S2) (?v1 S8)) (:pat #654) #103)
-#107 := (forall (vars (?v0 S2) (?v1 S8)) #103)
-#664 := (iff #107 #661)
-#662 := (iff #103 #103)
-#663 := [refl]: #662
-#665 := [quant-intro #663]: #664
-#146 := (~ #107 #107)
-#164 := (~ #103 #103)
-#165 := [refl]: #164
-#147 := [nnf-pos #165]: #146
-#27 := (= #26 #20)
-#28 := (forall (vars (?v0 S2) (?v1 S8)) #27)
-#108 := (iff #28 #107)
-#105 := (iff #27 #103)
-#106 := [rewrite]: #105
-#109 := [quant-intro #106]: #108
-#102 := [asserted]: #28
-#112 := [mp #102 #109]: #107
-#166 := [mp~ #112 #147]: #107
-#666 := [mp #166 #665]: #661
-#283 := (not #661)
-#623 := (or #283 #624)
-#629 := [quant-inst #57 #59]: #623
-#619 := [unit-resolution #629 #666]: #624
-#324 := [symm #619]: #611
-#332 := (= #63 #286)
-#329 := (= #62 #60)
-#642 := (= #60 #62)
-#12 := (:var 0 S3)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#647 := (pattern #13)
-#30 := (f15 f16 #13)
-#111 := (= #12 #30)
-#667 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #647) #111)
-#115 := (forall (vars (?v0 S2) (?v1 S3)) #111)
-#670 := (iff #115 #667)
-#668 := (iff #111 #111)
-#669 := [refl]: #668
-#671 := [quant-intro #669]: #670
-#148 := (~ #115 #115)
-#167 := (~ #111 #111)
-#168 := [refl]: #167
-#149 := [nnf-pos #168]: #148
-#31 := (= #30 #12)
-#32 := (forall (vars (?v0 S2) (?v1 S3)) #31)
-#116 := (iff #32 #115)
-#113 := (iff #31 #111)
-#114 := [rewrite]: #113
-#117 := [quant-intro #114]: #116
-#110 := [asserted]: #32
-#120 := [mp #110 #117]: #115
-#169 := [mp~ #120 #149]: #115
-#672 := [mp #169 #671]: #667
-#635 := (not #667)
-#646 := (or #635 #642)
-#636 := [quant-inst #55 #60]: #646
-#328 := [unit-resolution #636 #672]: #642
-#330 := [symm #328]: #329
-#610 := [monotonicity #330]: #332
-#612 := [trans #610 #324]: #608
-#606 := (= #54 f19)
-#294 := (f13 f14 #51)
-#600 := (= #294 f19)
-#299 := (= f19 #294)
-#284 := (or #283 #299)
-#285 := [quant-inst #48 #50]: #284
-#609 := [unit-resolution #285 #666]: #299
-#605 := [symm #609]: #600
-#604 := (= #54 #294)
-#602 := (= #53 #51)
-#323 := (= #51 #53)
-#307 := (or #635 #323)
-#308 := [quant-inst #46 #51]: #307
-#613 := [unit-resolution #308 #672]: #323
-#603 := [symm #613]: #602
-#599 := [monotonicity #603]: #604
-#601 := [trans #599 #605]: #606
-#607 := [monotonicity #601 #612]: #66
-#318 := (not #65)
-#135 := (not #64)
-#448 := (iff #135 #318)
-#449 := [monotonicity #607]: #448
-#340 := [hypothesis]: #135
-#450 := [mp #340 #449]: #318
-#317 := (or #65 #64)
-#137 := (iff #65 #135)
-#67 := (not #66)
-#138 := (iff #67 #137)
-#139 := [rewrite]: #138
-#134 := [asserted]: #67
-#142 := [mp #134 #139]: #137
-#229 := (not #137)
-#316 := (or #65 #64 #229)
-#230 := [def-axiom]: #316
-#231 := [unit-resolution #230 #142]: #317
-#614 := [unit-resolution #231 #340]: #65
-#592 := [unit-resolution #614 #450]: false
-#593 := [lemma #592]: #64
-#595 := [mp #593 #607]: #65
-#321 := (or #318 #135)
-#309 := (or #318 #135 #229)
-#320 := [def-axiom]: #309
-#249 := [unit-resolution #320 #142]: #321
-#594 := [unit-resolution #249 #593]: #318
-[unit-resolution #594 #595]: false
-unsat
-b12ef5502eccbe94c4fc7851ace776d6a343e5a2 111 0
-#2 := false
-decl f10 :: S2
-#30 := f10
-decl f9 :: S2
-#28 := f9
-#35 := (= f9 f10)
-decl f3 :: (-> S3 S4 S2)
-decl f5 :: (-> S5 S2 S4)
-decl f6 :: (-> S6 S2 S5)
-decl f7 :: S6
-#9 := f7
-#29 := (f6 f7 f9)
-#31 := (f5 #29 f10)
-decl f8 :: S3
-#17 := f8
-#33 := (f3 f8 #31)
-decl f4 :: S3
-#8 := f4
-#32 := (f3 f4 #31)
-#34 := (= #32 #33)
-#36 := (iff #34 #35)
-#225 := (iff #35 #34)
-#250 := (= f10 #33)
-#12 := (:var 0 S2)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#578 := (pattern #13)
-#18 := (f3 f8 #13)
-#65 := (= #12 #18)
-#585 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #578) #65)
-#69 := (forall (vars (?v0 S2) (?v1 S2)) #65)
-#588 := (iff #69 #585)
-#586 := (iff #65 #65)
-#587 := [refl]: #586
-#589 := [quant-intro #587]: #588
-#90 := (~ #69 #69)
-#89 := (~ #65 #65)
-#102 := [refl]: #89
-#91 := [nnf-pos #102]: #90
-#19 := (= #18 #12)
-#20 := (forall (vars (?v0 S2) (?v1 S2)) #19)
-#70 := (iff #20 #69)
-#67 := (iff #19 #65)
-#68 := [rewrite]: #67
-#71 := [quant-intro #68]: #70
-#64 := [asserted]: #20
-#74 := [mp #64 #71]: #69
-#103 := [mp~ #74 #91]: #69
-#590 := [mp #103 #589]: #585
-#359 := (not #585)
-#566 := (or #359 #250)
-#238 := [quant-inst #28 #30]: #566
-#577 := [unit-resolution #238 #590]: #250
-#253 := (= f9 #32)
-#14 := (f3 f4 #13)
-#58 := (= #10 #14)
-#579 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #578) #58)
-#61 := (forall (vars (?v0 S2) (?v1 S2)) #58)
-#582 := (iff #61 #579)
-#580 := (iff #58 #58)
-#581 := [refl]: #580
-#583 := [quant-intro #581]: #582
-#100 := (~ #61 #61)
-#98 := (~ #58 #58)
-#99 := [refl]: #98
-#101 := [nnf-pos #99]: #100
-#15 := (= #14 #10)
-#16 := (forall (vars (?v0 S2) (?v1 S2)) #15)
-#62 := (iff #16 #61)
-#59 := (iff #15 #58)
-#60 := [rewrite]: #59
-#63 := [quant-intro #60]: #62
-#57 := [asserted]: #16
-#66 := [mp #57 #63]: #61
-#87 := [mp~ #66 #101]: #61
-#584 := [mp #87 #583]: #579
-#233 := (not #579)
-#570 := (or #233 #253)
-#572 := [quant-inst #28 #30]: #570
-#567 := [unit-resolution #572 #584]: #253
-#230 := [monotonicity #567 #577]: #225
-#568 := [symm #230]: #36
-#249 := (not #35)
-#81 := (not #34)
-#226 := (iff #81 #249)
-#569 := [monotonicity #568]: #226
-#573 := [hypothesis]: #81
-#210 := [mp #573 #569]: #249
-#248 := (or #35 #34)
-#83 := (iff #35 #81)
-#37 := (not #36)
-#84 := (iff #37 #83)
-#85 := [rewrite]: #84
-#80 := [asserted]: #37
-#88 := [mp #80 #85]: #83
-#160 := (not #83)
-#247 := (or #35 #34 #160)
-#161 := [def-axiom]: #247
-#162 := [unit-resolution #161 #88]: #248
-#574 := [unit-resolution #162 #573]: #35
-#553 := [unit-resolution #574 #210]: false
-#214 := [lemma #553]: #34
-#216 := [mp #214 #568]: #35
-#252 := (or #249 #81)
-#240 := (or #249 #81 #160)
-#251 := [def-axiom]: #240
-#180 := [unit-resolution #251 #88]: #252
-#215 := [unit-resolution #180 #214]: #249
-[unit-resolution #215 #216]: false
-unsat
-9c1ac3bb26089e3bd3123b5d9934588d509a0ded 120 0
+#45 := f17
+#46 := (f6 f7 f17)
+#51 := (f5 #46 #50)
+#52 := (f15 f16 #51)
+#53 := (f13 f14 #52)
+#63 := (= #53 #62)
+#64 := (= f19 f22)
+#560 := (iff #64 #63)
+#65 := (iff #63 #64)
+#572 := (= #62 f22)
+#585 := (f13 f14 #59)
+#586 := (= #585 f22)
+#19 := (:var 0 S8)
+#9 := (:var 1 S2)
+#18 := (f11 f12 #9)
+#20 := (f10 #18 #19)
+#615 := (pattern #20)
+#25 := (f13 f14 #20)
+#26 := (= #25 #19)
+#622 := (forall (vars (?v0 S2) (?v1 S8)) (:pat #615) #26)
+#27 := (forall (vars (?v0 S2) (?v1 S8)) #26)
+#625 := (iff #27 #622)
+#623 := (iff #26 #26)
+#624 := [refl]: #623
+#626 := [quant-intro #624]: #625
+#104 := (~ #27 #27)
+#122 := (~ #26 #26)
+#123 := [refl]: #122
+#105 := [nnf-pos #123]: #104
+#89 := [asserted]: #27
+#124 := [mp~ #89 #105]: #27
+#627 := [mp #124 #626]: #622
+#246 := (not #622)
+#590 := (or #246 #586)
+#227 := [quant-inst #56 #58]: #590
+#291 := [unit-resolution #227 #627]: #586
+#293 := (= #62 #585)
+#604 := (= #61 #59)
+#11 := (:var 0 S3)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#608 := (pattern #12)
+#29 := (f15 f16 #12)
+#30 := (= #29 #11)
+#628 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #608) #30)
+#31 := (forall (vars (?v0 S2) (?v1 S3)) #30)
+#631 := (iff #31 #628)
+#629 := (iff #30 #30)
+#630 := [refl]: #629
+#632 := [quant-intro #630]: #631
+#106 := (~ #31 #31)
+#125 := (~ #30 #30)
+#126 := [refl]: #125
+#107 := [nnf-pos #126]: #106
+#90 := [asserted]: #31
+#127 := [mp~ #90 #107]: #31
+#633 := [mp #127 #632]: #628
+#269 := (not #628)
+#597 := (or #269 #604)
+#256 := [quant-inst #54 #59]: #597
+#292 := [unit-resolution #256 #633]: #604
+#571 := [monotonicity #292]: #293
+#286 := [trans #571 #291]: #572
+#563 := (= #53 f19)
+#261 := (f13 f14 #50)
+#598 := (= #261 f19)
+#247 := (or #246 #598)
+#248 := [quant-inst #47 #49]: #247
+#569 := [unit-resolution #248 #627]: #598
+#570 := (= #53 #261)
+#264 := (= #52 #50)
+#270 := (or #269 #264)
+#603 := [quant-inst #45 #50]: #270
+#573 := [unit-resolution #603 #633]: #264
+#574 := [monotonicity #573]: #570
+#564 := [trans #574 #569]: #563
+#565 := [monotonicity #564 #286]: #65
+#561 := [symm #565]: #560
+#94 := (not #63)
+#192 := (not #64)
+#566 := (iff #192 #94)
+#567 := [monotonicity #561]: #566
+#579 := [hypothesis]: #192
+#562 := [mp #579 #567]: #94
+#283 := (or #63 #64)
+#95 := (iff #94 #64)
+#66 := (not #65)
+#96 := (iff #66 #95)
+#97 := [rewrite]: #96
+#93 := [asserted]: #66
+#100 := [mp #93 #97]: #95
+#278 := (not #95)
+#271 := (or #63 #64 #278)
+#282 := [def-axiom]: #271
+#284 := [unit-resolution #282 #100]: #283
+#576 := [unit-resolution #284 #579]: #63
+#568 := [unit-resolution #576 #562]: false
+#409 := [lemma #568]: #64
+#411 := [mp #409 #561]: #63
+#194 := (or #94 #192)
+#193 := (or #94 #192 #278)
+#279 := [def-axiom]: #193
+#280 := [unit-resolution #279 #100]: #194
+#410 := [unit-resolution #280 #409]: #94
+[unit-resolution #410 #411]: false
+unsat
+c96488cbaa7f2ec1db1698b5028335098b71d55f 97 0
 #2 := false
 decl f3 :: (-> S3 S4 S2)
-decl f12 :: S4
-#34 := f12
-decl f8 :: S3
-#17 := f8
-#40 := (f3 f8 f12)
-decl f9 :: S4
-#28 := f9
-decl f4 :: S3
-#8 := f4
-#39 := (f3 f4 f9)
-#41 := (= #39 #40)
 decl f5 :: (-> S5 S2 S4)
 decl f10 :: S2
 #29 := f10
 decl f6 :: (-> S6 S2 S5)
-decl f11 :: S2
-#31 := f11
+decl f9 :: S2
+#27 := f9
 decl f7 :: S6
-#9 := f7
-#35 := (f6 f7 f11)
-#36 := (f5 #35 f10)
-#268 := (f3 f8 #36)
-#569 := (= #268 #40)
-#224 := (= #40 #268)
-#37 := (= f12 #36)
-#30 := (f6 f7 f10)
-#32 := (f5 #30 f11)
-#33 := (= f9 #32)
-#38 := (and #33 #37)
-#87 := (not #38)
-#89 := (or #87 #41)
-#92 := (not #89)
-#42 := (implies #38 #41)
-#43 := (not #42)
-#93 := (iff #43 #92)
-#90 := (iff #42 #89)
-#91 := [rewrite]: #90
-#94 := [monotonicity #91]: #93
-#86 := [asserted]: #43
-#97 := [mp #86 #94]: #92
-#95 := [not-or-elim #97]: #38
-#98 := [and-elim #95]: #37
-#567 := [monotonicity #98]: #224
-#570 := [symm #567]: #569
-#573 := (= #39 #268)
-#247 := (= f10 #268)
-#12 := (:var 0 S2)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#592 := (pattern #13)
-#18 := (f3 f8 #13)
-#71 := (= #12 #18)
-#599 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #592) #71)
-#75 := (forall (vars (?v0 S2) (?v1 S2)) #71)
-#602 := (iff #75 #599)
-#600 := (iff #71 #71)
-#601 := [refl]: #600
-#603 := [quant-intro #601]: #602
-#104 := (~ #75 #75)
-#103 := (~ #71 #71)
-#120 := [refl]: #103
-#105 := [nnf-pos #120]: #104
-#19 := (= #18 #12)
-#20 := (forall (vars (?v0 S2) (?v1 S2)) #19)
-#76 := (iff #20 #75)
-#73 := (iff #19 #71)
-#74 := [rewrite]: #73
-#77 := [quant-intro #74]: #76
-#70 := [asserted]: #20
-#80 := [mp #70 #77]: #75
-#121 := [mp~ #80 #105]: #75
-#604 := [mp #121 #603]: #599
-#194 := (not #599)
-#580 := (or #194 #247)
-#252 := [quant-inst #31 #29]: #580
-#239 := [unit-resolution #252 #604]: #247
-#571 := (= #39 f10)
-#174 := (f3 f4 #32)
-#230 := (= #174 f10)
-#261 := (= f10 #174)
-#14 := (f3 f4 #13)
-#64 := (= #10 #14)
-#593 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #592) #64)
-#67 := (forall (vars (?v0 S2) (?v1 S2)) #64)
-#596 := (iff #67 #593)
-#594 := (iff #64 #64)
-#595 := [refl]: #594
-#597 := [quant-intro #595]: #596
-#118 := (~ #67 #67)
-#116 := (~ #64 #64)
-#117 := [refl]: #116
-#119 := [nnf-pos #117]: #118
-#15 := (= #14 #10)
-#16 := (forall (vars (?v0 S2) (?v1 S2)) #15)
-#68 := (iff #16 #67)
-#65 := (iff #15 #64)
-#66 := [rewrite]: #65
-#69 := [quant-intro #66]: #68
-#63 := [asserted]: #16
-#72 := [mp #63 #69]: #67
-#102 := [mp~ #72 #119]: #67
-#598 := [mp #102 #597]: #593
-#176 := (not #593)
-#263 := (or #176 #261)
-#254 := [quant-inst #29 #31]: #263
-#581 := [unit-resolution #254 #598]: #261
-#231 := [symm #581]: #230
-#240 := (= #39 #174)
-#96 := [and-elim #95]: #33
-#583 := [monotonicity #96]: #240
-#572 := [trans #583 #231]: #571
-#568 := [trans #572 #239]: #573
-#574 := [trans #568 #570]: #41
-#99 := (not #41)
-#100 := [not-or-elim #97]: #99
-[unit-resolution #100 #574]: false
-unsat
-d42e973f7064561465558d14fa97bf977736bb4c 129 0
-#2 := false
+#8 := f7
+#28 := (f6 f7 f9)
+#30 := (f5 #28 f10)
+decl f8 :: S3
+#16 := f8
+#32 := (f3 f8 #30)
+decl f4 :: S3
+#7 := f4
+#31 := (f3 f4 #30)
+#33 := (= #31 #32)
+#34 := (= f9 f10)
+#550 := (iff #34 #33)
+#35 := (iff #33 #34)
+#237 := (= #32 f10)
+#11 := (:var 0 S2)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#560 := (pattern #12)
+#17 := (f3 f8 #12)
+#18 := (= #17 #11)
+#567 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #560) #18)
+#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
+#570 := (iff #19 #567)
+#568 := (iff #18 #18)
+#569 := [refl]: #568
+#571 := [quant-intro #569]: #570
+#69 := (~ #19 #19)
+#68 := (~ #18 #18)
+#81 := [refl]: #68
+#70 := [nnf-pos #81]: #69
+#58 := [asserted]: #19
+#82 := [mp~ #58 #70]: #19
+#572 := [mp #82 #571]: #567
+#548 := (not #567)
+#221 := (or #548 #237)
+#222 := [quant-inst #27 #29]: #221
+#549 := [unit-resolution #222 #572]: #237
+#233 := (= #31 f9)
+#13 := (f3 f4 #12)
+#14 := (= #13 #9)
+#561 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #560) #14)
+#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
+#564 := (iff #15 #561)
+#562 := (iff #14 #14)
+#563 := [refl]: #562
+#565 := [quant-intro #563]: #564
+#79 := (~ #15 #15)
+#77 := (~ #14 #14)
+#78 := [refl]: #77
+#80 := [nnf-pos #78]: #79
+#57 := [asserted]: #15
+#66 := [mp~ #57 #80]: #15
+#566 := [mp #66 #565]: #561
+#552 := (not #561)
+#554 := (or #552 #233)
+#210 := [quant-inst #27 #29]: #554
+#208 := [unit-resolution #210 #566]: #233
+#213 := [monotonicity #208 #549]: #35
+#209 := [symm #213]: #550
+#61 := (not #33)
+#144 := (not #34)
+#551 := (iff #144 #61)
+#193 := [monotonicity #209]: #551
+#556 := [hypothesis]: #144
+#535 := [mp #556 #193]: #61
+#235 := (or #33 #34)
+#62 := (iff #61 #34)
+#36 := (not #35)
+#63 := (iff #36 #62)
+#64 := [rewrite]: #63
+#60 := [asserted]: #36
+#67 := [mp #60 #64]: #62
+#230 := (not #62)
+#223 := (or #33 #34 #230)
+#234 := [def-axiom]: #223
+#236 := [unit-resolution #234 #67]: #235
+#557 := [unit-resolution #236 #556]: #33
+#197 := [unit-resolution #557 #535]: false
+#198 := [lemma #197]: #34
+#200 := [mp #198 #209]: #33
+#146 := (or #61 #144)
+#145 := (or #61 #144 #230)
+#231 := [def-axiom]: #145
+#232 := [unit-resolution #231 #67]: #146
+#199 := [unit-resolution #232 #198]: #61
+[unit-resolution #199 #200]: false
+unsat
+09a45677774b7c719ba58910500f00ef56ae315c 106 0
+#2 := false
+decl f3 :: (-> S3 S4 S2)
+decl f12 :: S4
+#33 := f12
+decl f8 :: S3
+#16 := f8
+#39 := (f3 f8 f12)
+decl f9 :: S4
+#27 := f9
+decl f4 :: S3
+#7 := f4
+#38 := (f3 f4 f9)
+#40 := (= #38 #39)
 decl f5 :: (-> S5 S2 S4)
+decl f10 :: S2
+#28 := f10
+decl f6 :: (-> S6 S2 S5)
+decl f11 :: S2
+#30 := f11
+decl f7 :: S6
+#8 := f7
+#34 := (f6 f7 f11)
+#35 := (f5 #34 f10)
+#230 := (f3 f8 #35)
+#214 := (= #230 #39)
+#549 := (= #39 #230)
+#36 := (= f12 #35)
+#29 := (f6 f7 f10)
+#31 := (f5 #29 f11)
+#32 := (= f9 #31)
+#37 := (and #32 #36)
+#67 := (not #37)
+#68 := (or #67 #40)
+#71 := (not #68)
+#41 := (implies #37 #40)
+#42 := (not #41)
+#72 := (iff #42 #71)
+#69 := (iff #41 #68)
+#70 := [rewrite]: #69
+#73 := [monotonicity #70]: #72
+#66 := [asserted]: #42
+#76 := [mp #66 #73]: #71
+#74 := [not-or-elim #76]: #37
+#77 := [and-elim #74]: #36
+#211 := [monotonicity #77]: #549
+#551 := [symm #211]: #214
+#554 := (= #38 #230)
+#212 := (= f10 #230)
+#566 := (= #230 f10)
+#11 := (:var 0 S2)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#574 := (pattern #12)
+#17 := (f3 f8 #12)
+#18 := (= #17 #11)
+#581 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #574) #18)
+#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
+#584 := (iff #19 #581)
+#582 := (iff #18 #18)
+#583 := [refl]: #582
+#585 := [quant-intro #583]: #584
+#83 := (~ #19 #19)
+#82 := (~ #18 #18)
+#99 := [refl]: #82
+#84 := [nnf-pos #99]: #83
+#64 := [asserted]: #19
+#100 := [mp~ #64 #84]: #19
+#586 := [mp #100 #585]: #581
+#250 := (not #581)
+#235 := (or #250 #566)
+#236 := [quant-inst #30 #28]: #235
+#222 := [unit-resolution #236 #586]: #566
+#213 := [symm #222]: #212
+#552 := (= #38 f10)
+#158 := (f3 f4 #31)
+#244 := (= #158 f10)
+#13 := (f3 f4 #12)
+#14 := (= #13 #9)
+#575 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #574) #14)
+#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
+#578 := (iff #15 #575)
+#576 := (iff #14 #14)
+#577 := [refl]: #576
+#579 := [quant-intro #577]: #578
+#97 := (~ #15 #15)
+#95 := (~ #14 #14)
+#96 := [refl]: #95
+#98 := [nnf-pos #96]: #97
+#63 := [asserted]: #15
+#81 := [mp~ #63 #98]: #15
+#580 := [mp #81 #579]: #575
+#160 := (not #575)
+#246 := (or #160 #244)
+#237 := [quant-inst #28 #30]: #246
+#227 := [unit-resolution #237 #580]: #244
+#565 := (= #38 #158)
+#75 := [and-elim #74]: #32
+#207 := [monotonicity #75]: #565
+#553 := [trans #207 #227]: #552
+#555 := [trans #553 #213]: #554
+#550 := [trans #555 #551]: #40
+#78 := (not #40)
+#79 := [not-or-elim #76]: #78
+[unit-resolution #79 #550]: false
+unsat
+618d08b43560c1458410e7b2d3758883c80902bb 115 0
+#2 := false
 decl f3 :: (-> S3 S4 S2)
 decl f9 :: S4
-#28 := f9
+#27 := f9
+decl f8 :: S3
+#16 := f8
+#29 := (f3 f8 f9)
 decl f4 :: S3
-#8 := f4
-#29 := (f3 f4 f9)
+#7 := f4
+#28 := (f3 f4 f9)
+#30 := (= #28 #29)
+decl f5 :: (-> S5 S2 S4)
 decl f6 :: (-> S6 S2 S5)
-decl f8 :: S3
-#17 := f8
-#30 := (f3 f8 f9)
 decl f7 :: S6
-#9 := f7
-#32 := (f6 f7 #30)
-#33 := (f5 #32 #29)
-#34 := (= f9 #33)
-#358 := (f6 f7 #29)
-#565 := (f5 #358 #30)
-#562 := (= #565 #33)
-#195 := (= #33 #565)
-#31 := (= #29 #30)
-#252 := (f3 f4 #33)
-#213 := (= #252 #30)
-#249 := (= #30 #252)
-#12 := (:var 0 S2)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#577 := (pattern #13)
-#14 := (f3 f4 #13)
-#57 := (= #10 #14)
-#578 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #577) #57)
-#60 := (forall (vars (?v0 S2) (?v1 S2)) #57)
-#581 := (iff #60 #578)
-#579 := (iff #57 #57)
-#580 := [refl]: #579
-#582 := [quant-intro #580]: #581
-#99 := (~ #60 #60)
-#97 := (~ #57 #57)
-#98 := [refl]: #97
-#100 := [nnf-pos #98]: #99
-#15 := (= #14 #10)
-#16 := (forall (vars (?v0 S2) (?v1 S2)) #15)
-#61 := (iff #16 #60)
-#58 := (iff #15 #57)
-#59 := [rewrite]: #58
-#62 := [quant-intro #59]: #61
-#56 := [asserted]: #16
-#65 := [mp #56 #62]: #60
-#86 := [mp~ #65 #100]: #60
-#583 := [mp #86 #582]: #578
-#569 := (not #578)
-#571 := (or #569 #249)
-#226 := [quant-inst #30 #29]: #571
-#567 := [unit-resolution #226 #583]: #249
-#214 := [symm #567]: #213
-#209 := (= #29 #252)
-#225 := (= #252 #29)
-#224 := (= #33 f9)
-#80 := (not #31)
-#574 := [hypothesis]: #80
-#247 := (or #34 #31)
-#82 := (iff #34 #80)
-#35 := (iff #31 #34)
-#36 := (not #35)
-#83 := (iff #36 #82)
-#84 := [rewrite]: #83
-#79 := [asserted]: #36
-#87 := [mp #79 #84]: #82
-#159 := (not #82)
-#246 := (or #34 #31 #159)
-#160 := [def-axiom]: #246
-#161 := [unit-resolution #160 #87]: #247
-#575 := [unit-resolution #161 #574]: #34
-#229 := [symm #575]: #224
-#568 := [monotonicity #229]: #225
-#552 := [symm #568]: #209
-#215 := [trans #552 #214]: #31
-#216 := [unit-resolution #574 #215]: false
-#554 := [lemma #216]: #31
-#558 := (= #32 #358)
-#556 := (= #358 #32)
-#557 := [monotonicity #554]: #556
-#553 := [symm #557]: #558
-#560 := [monotonicity #553 #554]: #195
-#200 := [symm #560]: #562
-#573 := (= f9 #565)
-#21 := (:var 0 S4)
-#24 := (f3 f8 #21)
-#591 := (pattern #24)
-#22 := (f3 f4 #21)
-#590 := (pattern #22)
-#23 := (f6 f7 #22)
-#25 := (f5 #23 #24)
-#72 := (= #21 #25)
-#592 := (forall (vars (?v0 S4)) (:pat #590 #591) #72)
-#76 := (forall (vars (?v0 S4)) #72)
-#595 := (iff #76 #592)
-#593 := (iff #72 #72)
-#594 := [refl]: #593
-#596 := [quant-intro #594]: #595
-#91 := (~ #76 #76)
-#103 := (~ #72 #72)
-#104 := [refl]: #103
-#92 := [nnf-pos #104]: #91
-#26 := (= #25 #21)
-#27 := (forall (vars (?v0 S4)) #26)
-#77 := (iff #27 #76)
-#74 := (iff #26 #72)
-#75 := [rewrite]: #74
-#78 := [quant-intro #75]: #77
-#71 := [asserted]: #27
-#81 := [mp #71 #78]: #76
-#105 := [mp~ #81 #92]: #76
-#597 := [mp #105 #596]: #592
-#570 := (not #592)
-#576 := (or #570 #573)
-#566 := [quant-inst #28]: #576
-#559 := [unit-resolution #566 #597]: #573
-#201 := [trans #559 #200]: #34
-#248 := (not #34)
-#251 := (or #248 #80)
-#239 := (or #248 #80 #159)
-#250 := [def-axiom]: #239
-#179 := [unit-resolution #250 #87]: #251
-#555 := [unit-resolution #179 #554]: #248
-[unit-resolution #555 #201]: false
-unsat
-81cd04913ffd0969a52f6b4cd2c3f918ffdcebfd 87 0
-#2 := false
+#8 := f7
+#31 := (f6 f7 #29)
+#32 := (f5 #31 #28)
+#232 := (f3 f4 #32)
+#236 := (= #232 #29)
+#11 := (:var 0 S2)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#559 := (pattern #12)
+#13 := (f3 f4 #12)
+#14 := (= #13 #9)
+#560 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #559) #14)
+#15 := (forall (vars (?v0 S2) (?v1 S2)) #14)
+#563 := (iff #15 #560)
+#561 := (iff #14 #14)
+#562 := [refl]: #561
+#564 := [quant-intro #562]: #563
+#78 := (~ #15 #15)
+#76 := (~ #14 #14)
+#77 := [refl]: #76
+#79 := [nnf-pos #77]: #78
+#56 := [asserted]: #15
+#65 := [mp~ #56 #79]: #15
+#565 := [mp #65 #564]: #560
+#553 := (not #560)
+#209 := (or #553 #236)
+#340 := [quant-inst #29 #28]: #209
+#178 := [unit-resolution #340 #565]: #236
+#545 := (= #28 #232)
+#183 := (= #232 #28)
+#535 := (= #32 f9)
+#33 := (= f9 #32)
+#547 := (f6 f7 #28)
+#220 := (f5 #547 #29)
+#199 := (= #220 #32)
+#534 := (= #32 #220)
+#143 := (not #33)
+#557 := [hypothesis]: #143
+#234 := (or #30 #33)
+#60 := (not #30)
+#61 := (iff #60 #33)
+#34 := (iff #30 #33)
+#35 := (not #34)
+#62 := (iff #35 #61)
+#63 := [rewrite]: #62
+#59 := [asserted]: #35
+#66 := [mp #59 #63]: #61
+#229 := (not #61)
+#222 := (or #30 #33 #229)
+#233 := [def-axiom]: #222
+#235 := [unit-resolution #233 #66]: #234
+#212 := [unit-resolution #235 #557]: #30
+#550 := (= #31 #547)
+#549 := (= #547 #31)
+#208 := [monotonicity #212]: #549
+#192 := [symm #208]: #550
+#196 := [monotonicity #192 #212]: #534
+#536 := [symm #196]: #199
+#197 := (= f9 #220)
+#556 := (= #220 f9)
+#20 := (:var 0 S4)
+#23 := (f3 f8 #20)
+#573 := (pattern #23)
+#21 := (f3 f4 #20)
+#572 := (pattern #21)
+#22 := (f6 f7 #21)
+#24 := (f5 #22 #23)
+#25 := (= #24 #20)
+#574 := (forall (vars (?v0 S4)) (:pat #572 #573) #25)
+#26 := (forall (vars (?v0 S4)) #25)
+#577 := (iff #26 #574)
+#575 := (iff #25 #25)
+#576 := [refl]: #575
+#578 := [quant-intro #576]: #577
+#70 := (~ #26 #26)
+#82 := (~ #25 #25)
+#83 := [refl]: #82
+#71 := [nnf-pos #83]: #70
+#58 := [asserted]: #26
+#84 := [mp~ #58 #71]: #26
+#579 := [mp #84 #578]: #574
+#558 := (not #574)
+#548 := (or #558 #556)
+#207 := [quant-inst #27]: #548
+#552 := [unit-resolution #207 #579]: #556
+#198 := [symm #552]: #197
+#537 := [trans #198 #536]: #33
+#538 := [unit-resolution #557 #537]: false
+#539 := [lemma #538]: #33
+#541 := [symm #539]: #535
+#184 := [monotonicity #541]: #183
+#543 := [symm #184]: #545
+#546 := [trans #543 #178]: #30
+#145 := (or #60 #143)
+#144 := (or #60 #143 #229)
+#230 := [def-axiom]: #144
+#231 := [unit-resolution #230 #66]: #145
+#540 := [unit-resolution #231 #539]: #60
+[unit-resolution #540 #546]: false
+unsat
+6c74b15206a530ed139b99673954ade36be4efcc 43 0
+#2 := false
+decl f9 :: S3
+#30 := f9
 decl f5 :: (-> S5 S3 S3)
-decl f9 :: S3
-#31 := f9
 decl f6 :: (-> S6 S2 S5)
 decl f21 :: S2
-#72 := f21
+#71 := f21
 decl f7 :: S6
-#9 := f7
-#73 := (f6 f7 f21)
-#74 := (f5 #73 f9)
-#285 := (f5 #73 #74)
-#373 := (= f9 #285)
-#335 := (= #74 #285)
-#351 := (= #285 #74)
-#75 := (= #74 f9)
-#161 := (= f9 #74)
+#8 := f7
+#72 := (f6 f7 f21)
+#73 := (f5 #72 f9)
+#74 := (= #73 f9)
+#75 := (not #74)
 #76 := (not #75)
-#77 := (not #76)
-#172 := (iff #77 #161)
-#164 := (not #161)
-#167 := (not #164)
-#170 := (iff #167 #161)
-#171 := [rewrite]: #170
-#168 := (iff #77 #167)
-#165 := (iff #76 #164)
-#162 := (iff #75 #161)
-#163 := [rewrite]: #162
-#166 := [monotonicity #163]: #165
-#169 := [monotonicity #166]: #168
-#173 := [trans #169 #171]: #172
-#159 := [asserted]: #77
-#176 := [mp #159 #173]: #161
-#692 := [symm #176]: #75
-#694 := [monotonicity #692]: #351
-#678 := [symm #694]: #335
-#339 := [trans #176 #678]: #373
-#365 := (not #373)
-#12 := (:var 0 S3)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#703 := (pattern #13)
-#35 := (= #13 f9)
-#36 := (not #35)
-#723 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #703) #36)
-#37 := (forall (vars (?v0 S2) (?v1 S3)) #36)
-#726 := (iff #37 #723)
-#724 := (iff #36 #36)
-#725 := [refl]: #724
-#727 := [quant-intro #725]: #726
-#183 := (~ #37 #37)
-#188 := (~ #36 #36)
-#182 := [refl]: #188
-#180 := [nnf-pos #182]: #183
-#32 := (= f9 #13)
-#33 := (not #32)
-#34 := (forall (vars (?v0 S2) (?v1 S3)) #33)
-#138 := (iff #34 #37)
-#136 := (iff #33 #36)
-#133 := (iff #32 #35)
-#135 := [rewrite]: #133
-#137 := [monotonicity #135]: #136
-#139 := [quant-intro #137]: #138
-#132 := [asserted]: #34
-#142 := [mp #132 #139]: #37
-#181 := [mp~ #142 #180]: #37
-#728 := [mp #181 #727]: #723
-#305 := (not #723)
-#378 := (or #305 #365)
-#372 := (= #285 f9)
-#286 := (not #372)
-#375 := (or #305 #286)
-#358 := (iff #375 #378)
-#697 := (iff #378 #378)
-#352 := [rewrite]: #697
-#376 := (iff #286 #365)
-#287 := (iff #372 #373)
-#374 := [rewrite]: #287
-#377 := [monotonicity #374]: #376
-#695 := [monotonicity #377]: #358
-#484 := [trans #695 #352]: #358
-#379 := [quant-inst #72 #74]: #375
-#691 := [mp #379 #484]: #378
-#702 := [unit-resolution #691 #728]: #365
-[unit-resolution #702 #339]: false
-unsat
-8067e17c7713c93c8443525a9ed56157626a11b9 75 0
-#2 := false
-decl f5 :: (-> S5 S3 S3)
+#107 := (iff #76 #74)
+#108 := [rewrite]: #107
+#106 := [asserted]: #76
+#111 := [mp #106 #108]: #74
+#11 := (:var 0 S3)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#647 := (pattern #12)
+#34 := (= #12 f9)
+#35 := (not #34)
+#673 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #647) #35)
+#36 := (forall (vars (?v0 S2) (?v1 S3)) #35)
+#676 := (iff #36 #673)
+#674 := (iff #35 #35)
+#675 := [refl]: #674
+#677 := [quant-intro #675]: #676
+#119 := (~ #36 #36)
+#145 := (~ #35 #35)
+#146 := [refl]: #145
+#120 := [nnf-pos #146]: #119
+#101 := [asserted]: #36
+#147 := [mp~ #101 #120]: #36
+#678 := [mp #147 #677]: #673
+#232 := (not #673)
+#318 := (or #232 #75)
+#233 := [quant-inst #71 #30]: #318
+[unit-resolution #233 #678 #111]: false
+unsat
+3782db2306cc866f72f70a01d2f0b8de7f1467ff 47 0
+#2 := false
 decl f9 :: S3
-#31 := f9
-decl f6 :: (-> S6 S2 S5)
-decl f22 :: S2
-#74 := f22
-decl f7 :: S6
-#9 := f7
-#75 := (f6 f7 f22)
-#76 := (f5 #75 f9)
-decl f21 :: S2
-#72 := f21
-#73 := (f6 f7 f21)
-#77 := (f5 #73 #76)
-#164 := (= f9 #77)
-#78 := (= #77 f9)
-#79 := (not #78)
-#80 := (not #79)
-#175 := (iff #80 #164)
-#167 := (not #164)
-#170 := (not #167)
-#173 := (iff #170 #164)
-#174 := [rewrite]: #173
-#171 := (iff #80 #170)
-#168 := (iff #79 #167)
-#165 := (iff #78 #164)
-#166 := [rewrite]: #165
-#169 := [monotonicity #166]: #168
-#172 := [monotonicity #169]: #171
-#176 := [trans #172 #174]: #175
-#162 := [asserted]: #80
-#179 := [mp #162 #176]: #164
-#12 := (:var 0 S3)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#706 := (pattern #13)
-#35 := (= #13 f9)
-#36 := (not #35)
-#726 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #706) #36)
-#37 := (forall (vars (?v0 S2) (?v1 S3)) #36)
-#729 := (iff #37 #726)
-#727 := (iff #36 #36)
-#728 := [refl]: #727
-#730 := [quant-intro #728]: #729
-#186 := (~ #37 #37)
-#191 := (~ #36 #36)
-#185 := [refl]: #191
-#183 := [nnf-pos #185]: #186
-#32 := (= f9 #13)
-#33 := (not #32)
-#34 := (forall (vars (?v0 S2) (?v1 S3)) #33)
-#141 := (iff #34 #37)
-#139 := (iff #33 #36)
-#136 := (iff #32 #35)
-#138 := [rewrite]: #136
-#140 := [monotonicity #138]: #139
-#142 := [quant-intro #140]: #141
-#135 := [asserted]: #34
-#145 := [mp #135 #142]: #37
-#184 := [mp~ #145 #183]: #37
-#731 := [mp #184 #730]: #726
-#381 := (not #726)
-#666 := (or #381 #167)
-#507 := (or #381 #79)
-#653 := (iff #507 #666)
-#648 := (iff #666 #666)
-#649 := [rewrite]: #648
-#654 := [monotonicity #169]: #653
-#655 := [trans #654 #649]: #653
-#652 := [quant-inst #72 #76]: #507
-#656 := [mp #652 #655]: #666
-[unit-resolution #656 #731 #179]: false
-unsat
-9adb0bde1688618887919e54f247a873d227a1e8 143 0
-#2 := false
+#30 := f9
 decl f5 :: (-> S5 S3 S3)
-decl f9 :: S3
-#31 := f9
 decl f6 :: (-> S6 S2 S5)
 decl f22 :: S2
 #73 := f22
 decl f7 :: S6
-#9 := f7
-#78 := (f6 f7 f22)
-#79 := (f5 #78 f9)
+#8 := f7
+#74 := (f6 f7 f22)
+#75 := (f5 #74 f9)
+decl f21 :: S2
+#71 := f21
+#72 := (f6 f7 f21)
+#76 := (f5 #72 #75)
+#77 := (= #76 f9)
+#78 := (not #77)
+#79 := (not #78)
+#110 := (iff #79 #77)
+#111 := [rewrite]: #110
+#109 := [asserted]: #79
+#114 := [mp #109 #111]: #77
+#11 := (:var 0 S3)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#650 := (pattern #12)
+#34 := (= #12 f9)
+#35 := (not #34)
+#676 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #650) #35)
+#36 := (forall (vars (?v0 S2) (?v1 S3)) #35)
+#679 := (iff #36 #676)
+#677 := (iff #35 #35)
+#678 := [refl]: #677
+#680 := [quant-intro #678]: #679
+#122 := (~ #36 #36)
+#148 := (~ #35 #35)
+#149 := [refl]: #148
+#123 := [nnf-pos #149]: #122
+#104 := [asserted]: #36
+#150 := [mp~ #104 #123]: #36
+#681 := [mp #150 #680]: #676
+#236 := (not #676)
+#311 := (or #236 #78)
+#312 := [quant-inst #71 #75]: #311
+[unit-resolution #312 #681 #114]: false
+unsat
+f728211cb1982632db7d0508cbcfd18907e87e3f 119 0
+#2 := false
+decl f22 :: S2
+#72 := f22
 decl f21 :: S2
-#72 := f21
-#76 := (f6 f7 f21)
-#77 := (f5 #76 f9)
-#80 := (= #77 #79)
-#74 := (= f21 f22)
-#327 := (iff #74 #80)
-#674 := (not #327)
-#81 := (not #80)
-#167 := (or #74 #81)
-#170 := (not #167)
-#75 := (not #74)
-#82 := (implies #75 #81)
-#83 := (not #82)
-#171 := (iff #83 #170)
-#168 := (iff #82 #167)
-#169 := [rewrite]: #168
-#172 := [monotonicity #169]: #171
-#165 := [asserted]: #83
-#175 := [mp #165 #172]: #170
-#174 := [not-or-elim #175]: #80
-#173 := [not-or-elim #175]: #75
-#396 := (or #674 #74 #81)
-#397 := [def-axiom]: #396
-#633 := [unit-resolution #397 #173 #174]: #674
-#23 := (:var 2 S3)
-#21 := (:var 3 S2)
-#22 := (f6 f7 #21)
-#24 := (f5 #22 #23)
-#12 := (:var 0 S3)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#717 := (pattern #13 #24)
-#126 := (= #12 #23)
-#217 := (not #126)
-#123 := (= #10 #21)
-#216 := (not #123)
-#218 := (or #216 #217)
-#219 := (not #218)
-#119 := (= #13 #24)
-#222 := (iff #119 #219)
-#718 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2) (?v3 S3)) (:pat #717) #222)
-#225 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2) (?v3 S3)) #222)
-#721 := (iff #225 #718)
-#719 := (iff #222 #222)
-#720 := [refl]: #719
-#722 := [quant-intro #720]: #721
-#129 := (and #123 #126)
-#132 := (iff #119 #129)
-#135 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2) (?v3 S3)) #132)
-#226 := (iff #135 #225)
-#223 := (iff #132 #222)
-#220 := (iff #129 #219)
-#221 := [rewrite]: #220
-#224 := [monotonicity #221]: #223
-#227 := [quant-intro #224]: #226
-#192 := (~ #135 #135)
-#194 := (~ #132 #132)
-#195 := [refl]: #194
-#193 := [nnf-pos #195]: #192
-#27 := (= #23 #12)
-#26 := (= #21 #10)
-#28 := (and #26 #27)
-#25 := (= #24 #13)
-#29 := (iff #25 #28)
-#30 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2) (?v3 S3)) #29)
-#136 := (iff #30 #135)
-#133 := (iff #29 #132)
-#130 := (iff #28 #129)
-#127 := (iff #27 #126)
-#128 := [rewrite]: #127
-#124 := (iff #26 #123)
-#125 := [rewrite]: #124
-#131 := [monotonicity #125 #128]: #130
-#121 := (iff #25 #119)
-#122 := [rewrite]: #121
-#134 := [monotonicity #122 #131]: #133
-#137 := [quant-intro #134]: #136
-#118 := [asserted]: #30
-#140 := [mp #118 #137]: #135
-#190 := [mp~ #140 #193]: #135
-#228 := [mp #190 #227]: #225
-#723 := [mp #228 #722]: #718
-#677 := (not #718)
-#678 := (or #677 #327)
-#692 := (= f9 f9)
-#364 := (not #692)
-#365 := (or #75 #364)
-#699 := (not #365)
-#700 := (iff #80 #699)
-#384 := (or #677 #700)
-#401 := (iff #384 #678)
-#388 := (iff #678 #678)
-#403 := [rewrite]: #388
-#688 := (iff #700 #327)
-#322 := (iff #80 #74)
-#328 := (iff #322 #327)
-#690 := [rewrite]: #328
-#687 := (iff #700 #322)
-#680 := (iff #699 #74)
-#681 := (not #75)
-#684 := (iff #681 #74)
-#685 := [rewrite]: #684
-#682 := (iff #699 #681)
-#342 := (iff #365 #75)
-#695 := (or #75 false)
-#340 := (iff #695 #75)
-#341 := [rewrite]: #340
-#336 := (iff #365 #695)
-#694 := (iff #364 false)
-#1 := true
-#697 := (not true)
-#351 := (iff #697 false)
-#356 := [rewrite]: #351
-#703 := (iff #364 #697)
-#701 := (iff #692 true)
-#702 := [rewrite]: #701
-#693 := [monotonicity #702]: #703
-#352 := [trans #693 #356]: #694
-#679 := [monotonicity #352]: #336
-#343 := [trans #679 #341]: #342
-#683 := [monotonicity #343]: #682
-#686 := [trans #683 #685]: #680
-#689 := [monotonicity #686]: #687
-#691 := [trans #689 #690]: #688
-#402 := [monotonicity #691]: #401
-#294 := [trans #402 #403]: #401
-#400 := [quant-inst #73 #31 #72 #31]: #384
-#673 := [mp #400 #294]: #678
-[unit-resolution #673 #723 #633]: false
-unsat
-5b137be8557b99b379f0a2d0b87dab1773ab0e37 57 0
-#2 := false
+#71 := f21
+#73 := (= f21 f22)
+decl f5 :: (-> S5 S3 S3)
+decl f9 :: S3
+#30 := f9
+decl f6 :: (-> S6 S2 S5)
+decl f7 :: S6
+#8 := f7
+#77 := (f6 f7 f22)
+#78 := (f5 #77 f9)
+#75 := (f6 f7 f21)
+#76 := (f5 #75 f9)
+#79 := (= #76 #78)
+#634 := (iff #79 #73)
+#642 := (not #634)
+#80 := (not #79)
+#113 := (or #73 #80)
+#116 := (not #113)
+#74 := (not #73)
+#81 := (implies #74 #80)
+#82 := (not #81)
+#117 := (iff #82 #116)
+#114 := (iff #81 #113)
+#115 := [rewrite]: #114
+#118 := [monotonicity #115]: #117
+#112 := [asserted]: #82
+#121 := [mp #112 #118]: #116
+#120 := [not-or-elim #121]: #79
+#119 := [not-or-elim #121]: #74
+#284 := (or #642 #80 #73)
+#645 := [def-axiom]: #284
+#484 := [unit-resolution #645 #119 #120]: #642
+#11 := (:var 0 S3)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#22 := (:var 2 S3)
+#20 := (:var 3 S2)
+#21 := (f6 f7 #20)
+#23 := (f5 #21 #22)
+#672 := (pattern #23 #12)
+#26 := (= #22 #11)
+#175 := (not #26)
+#25 := (= #20 #9)
+#174 := (not #25)
+#141 := (or #174 #175)
+#142 := (not #141)
+#24 := (= #23 #12)
+#143 := (iff #24 #142)
+#673 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2) (?v3 S3)) (:pat #672) #143)
+#177 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2) (?v3 S3)) #143)
+#676 := (iff #177 #673)
+#674 := (iff #143 #143)
+#675 := [refl]: #674
+#677 := [quant-intro #675]: #676
+#27 := (and #25 #26)
+#28 := (iff #24 #27)
+#29 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2) (?v3 S3)) #28)
+#178 := (iff #29 #177)
+#144 := (iff #28 #143)
+#145 := (iff #27 #142)
+#146 := [rewrite]: #145
+#176 := [monotonicity #146]: #144
+#179 := [quant-intro #176]: #178
+#127 := (~ #29 #29)
+#153 := (~ #28 #28)
+#154 := [refl]: #153
+#128 := [nnf-pos #154]: #127
+#105 := [asserted]: #29
+#155 := [mp~ #105 #128]: #29
+#180 := [mp #155 #179]: #177
+#678 := [mp #180 #677]: #673
+#298 := (not #673)
+#299 := (or #298 #634)
+#244 := (= f9 f9)
+#330 := (not #244)
+#333 := (or #74 #330)
+#334 := (not #333)
+#335 := (iff #79 #334)
+#636 := (or #298 #335)
+#638 := (iff #636 #299)
+#640 := (iff #299 #299)
+#635 := [rewrite]: #640
+#296 := (iff #335 #634)
+#650 := (iff #334 #73)
+#648 := (not #74)
+#649 := (iff #648 #73)
+#308 := [rewrite]: #649
+#307 := (iff #334 #648)
+#652 := (iff #333 #74)
+#321 := (or #74 false)
+#656 := (iff #321 #74)
+#657 := [rewrite]: #656
+#654 := (iff #333 #321)
+#647 := (iff #330 false)
+#1 := true
+#315 := (not true)
+#309 := (iff #315 false)
+#440 := [rewrite]: #309
+#651 := (iff #330 #315)
+#332 := (iff #244 true)
+#336 := [rewrite]: #332
+#653 := [monotonicity #336]: #651
+#320 := [trans #653 #440]: #647
+#655 := [monotonicity #320]: #654
+#658 := [trans #655 #657]: #652
+#312 := [monotonicity #658]: #307
+#292 := [trans #312 #308]: #650
+#297 := [monotonicity #292]: #296
+#639 := [monotonicity #297]: #638
+#641 := [trans #639 #635]: #638
+#637 := [quant-inst #71 #30 #72 #30]: #636
+#278 := [mp #637 #641]: #299
+[unit-resolution #278 #678 #484]: false
+unsat
+bbfd4143740fa5fa37bb46aa96df37053b73380b 43 0
+#2 := false
+decl f21 :: S2
+#71 := f21
 decl f3 :: (-> S4 S3 S2)
 decl f5 :: (-> S5 S3 S3)
 decl f22 :: S3
-#74 := f22
+#73 := f22
+decl f6 :: (-> S6 S2 S5)
+decl f7 :: S6
+#8 := f7
+#72 := (f6 f7 f21)
+#74 := (f5 #72 f22)
+decl f4 :: S4
+#7 := f4
+#75 := (f3 f4 #74)
+#76 := (= #75 f21)
+#77 := (not #76)
+#107 := [asserted]: #77
+#11 := (:var 0 S3)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#645 := (pattern #12)
+#13 := (f3 f4 #12)
+#14 := (= #13 #9)
+#646 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #645) #14)
+#15 := (forall (vars (?v0 S2) (?v1 S3)) #14)
+#649 := (iff #15 #646)
+#647 := (iff #14 #14)
+#648 := [refl]: #647
+#650 := [quant-intro #648]: #649
+#133 := (~ #15 #15)
+#131 := (~ #14 #14)
+#132 := [refl]: #131
+#134 := [nnf-pos #132]: #133
+#98 := [asserted]: #15
+#109 := [mp~ #98 #134]: #15
+#651 := [mp #109 #650]: #646
+#320 := (not #646)
+#321 := (or #320 #76)
+#318 := [quant-inst #71 #73]: #321
+[unit-resolution #318 #651 #107]: false
+unsat
+faf27be81c50266d2944b770ad1790cac070c271 42 0
+#2 := false
+decl f22 :: S3
+#73 := f22
+decl f5 :: (-> S5 S3 S3)
 decl f6 :: (-> S6 S2 S5)
 decl f21 :: S2
-#72 := f21
+#71 := f21
 decl f7 :: S6
-#9 := f7
-#73 := (f6 f7 f21)
-#75 := (f5 #73 f22)
-decl f4 :: S4
-#8 := f4
-#76 := (f3 f4 #75)
-#162 := (= f21 #76)
-#165 := (not #162)
-#77 := (= #76 f21)
-#78 := (not #77)
-#166 := (iff #78 #165)
-#163 := (iff #77 #162)
-#164 := [rewrite]: #163
-#167 := [monotonicity #164]: #166
-#160 := [asserted]: #78
-#170 := [mp #160 #167]: #165
-#12 := (:var 0 S3)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#697 := (pattern #13)
-#14 := (f3 f4 #13)
-#99 := (= #10 #14)
-#698 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #697) #99)
-#102 := (forall (vars (?v0 S2) (?v1 S3)) #99)
-#701 := (iff #102 #698)
-#699 := (iff #99 #99)
-#700 := [refl]: #699
-#702 := [quant-intro #700]: #701
-#179 := (~ #102 #102)
-#141 := (~ #99 #99)
-#178 := [refl]: #141
-#180 := [nnf-pos #178]: #179
-#15 := (= #14 #10)
-#16 := (forall (vars (?v0 S2) (?v1 S3)) #15)
-#103 := (iff #16 #102)
-#100 := (iff #15 #99)
-#101 := [rewrite]: #100
-#104 := [quant-intro #101]: #103
-#98 := [asserted]: #16
-#107 := [mp #98 #104]: #102
-#191 := [mp~ #107 #180]: #102
-#703 := [mp #191 #702]: #698
-#358 := (not #698)
-#692 := (or #358 #162)
-#693 := [quant-inst #72 #74]: #692
-[unit-resolution #693 #703 #170]: false
-unsat
-2cd08a95f4b0ad041d78f56e3299019533d2e5bc 56 0
-#2 := false
-decl f5 :: (-> S5 S3 S3)
-decl f22 :: S3
-#74 := f22
-decl f6 :: (-> S6 S2 S5)
+#8 := f7
+#72 := (f6 f7 f21)
+#74 := (f5 #72 f22)
+decl f8 :: S5
+#16 := f8
+#75 := (f5 f8 #74)
+#76 := (= #75 f22)
+#77 := (not #76)
+#107 := [asserted]: #77
+#11 := (:var 0 S3)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#645 := (pattern #12)
+#17 := (f5 f8 #12)
+#18 := (= #17 #11)
+#652 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #645) #18)
+#19 := (forall (vars (?v0 S2) (?v1 S3)) #18)
+#655 := (iff #19 #652)
+#653 := (iff #18 #18)
+#654 := [refl]: #653
+#656 := [quant-intro #654]: #655
+#111 := (~ #19 #19)
+#110 := (~ #18 #18)
+#135 := [refl]: #110
+#112 := [nnf-pos #135]: #111
+#99 := [asserted]: #19
+#136 := [mp~ #99 #112]: #19
+#657 := [mp #136 #656]: #652
+#637 := (not #652)
+#639 := (or #637 #76)
+#295 := [quant-inst #71 #73]: #639
+[unit-resolution #295 #657 #107]: false
+unsat
+ab24eb2440f220778ada1d51b0fa5d566ee21c5f 51 0
+#2 := false
 decl f21 :: S2
-#72 := f21
-decl f7 :: S6
-#9 := f7
-#73 := (f6 f7 f21)
-#75 := (f5 #73 f22)
-decl f8 :: S5
-#17 := f8
-#76 := (f5 f8 #75)
-#162 := (= f22 #76)
-#165 := (not #162)
-#77 := (= #76 f22)
-#78 := (not #77)
-#166 := (iff #78 #165)
-#163 := (iff #77 #162)
-#164 := [rewrite]: #163
-#167 := [monotonicity #164]: #166
-#160 := [asserted]: #78
-#170 := [mp #160 #167]: #165
-#12 := (:var 0 S3)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#697 := (pattern #13)
-#18 := (f5 f8 #13)
-#106 := (= #12 #18)
-#704 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #697) #106)
-#110 := (forall (vars (?v0 S2) (?v1 S3)) #106)
-#707 := (iff #110 #704)
-#705 := (iff #106 #106)
-#706 := [refl]: #705
-#708 := [quant-intro #706]: #707
-#190 := (~ #110 #110)
-#192 := (~ #106 #106)
-#189 := [refl]: #192
-#187 := [nnf-pos #189]: #190
-#19 := (= #18 #12)
-#20 := (forall (vars (?v0 S2) (?v1 S3)) #19)
-#111 := (iff #20 #110)
-#108 := (iff #19 #106)
-#109 := [rewrite]: #108
-#112 := [quant-intro #109]: #111
-#105 := [asserted]: #20
-#115 := [mp #105 #112]: #110
-#188 := [mp~ #115 #187]: #110
-#709 := [mp #188 #708]: #704
-#690 := (not #704)
-#696 := (or #690 #162)
-#686 := [quant-inst #72 #74]: #696
-[unit-resolution #686 #709 #170]: false
-unsat
-ed752090f6b3ab4e4bf6223daba34abf1b4191b6 65 0
-#2 := false
+#71 := f21
 decl f3 :: (-> S4 S3 S2)
 decl f5 :: (-> S5 S3 S3)
 decl f9 :: S3
-#31 := f9
+#30 := f9
 decl f6 :: (-> S6 S2 S5)
 decl f23 :: S2
-#76 := f23
+#75 := f23
 decl f7 :: S6
-#9 := f7
-#77 := (f6 f7 f23)
-#78 := (f5 #77 f9)
+#8 := f7
+#76 := (f6 f7 f23)
+#77 := (f5 #76 f9)
 decl f22 :: S2
-#74 := f22
-#75 := (f6 f7 f22)
-#79 := (f5 #75 #78)
-decl f21 :: S2
-#72 := f21
-#73 := (f6 f7 f21)
-#80 := (f5 #73 #79)
+#73 := f22
+#74 := (f6 f7 f22)
+#78 := (f5 #74 #77)
+#72 := (f6 f7 f21)
+#79 := (f5 #72 #78)
 decl f4 :: S4
-#8 := f4
-#81 := (f3 f4 #80)
-#167 := (= f21 #81)
-#170 := (not #167)
-#82 := (= #81 f21)
-#83 := (not #82)
-#171 := (iff #83 #170)
-#168 := (iff #82 #167)
-#169 := [rewrite]: #168
-#172 := [monotonicity #169]: #171
-#165 := [asserted]: #83
-#175 := [mp #165 #172]: #170
-#12 := (:var 0 S3)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#702 := (pattern #13)
-#14 := (f3 f4 #13)
-#104 := (= #10 #14)
-#703 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #702) #104)
-#107 := (forall (vars (?v0 S2) (?v1 S3)) #104)
-#706 := (iff #107 #703)
-#704 := (iff #104 #104)
-#705 := [refl]: #704
-#707 := [quant-intro #705]: #706
-#184 := (~ #107 #107)
-#146 := (~ #104 #104)
-#183 := [refl]: #146
-#185 := [nnf-pos #183]: #184
-#15 := (= #14 #10)
-#16 := (forall (vars (?v0 S2) (?v1 S3)) #15)
-#108 := (iff #16 #107)
-#105 := (iff #15 #104)
-#106 := [rewrite]: #105
-#109 := [quant-intro #106]: #108
-#103 := [asserted]: #16
-#112 := [mp #103 #109]: #107
-#196 := [mp~ #112 #185]: #107
-#708 := [mp #196 #707]: #703
-#636 := (not #703)
-#454 := (or #636 #167)
-#447 := [quant-inst #72 #79]: #454
-[unit-resolution #447 #708 #175]: false
-unsat
-a33518f8d625fd7259cb32bc04694351c289afa8 64 0
+#7 := f4
+#80 := (f3 f4 #79)
+#81 := (= #80 f21)
+#82 := (not #81)
+#112 := [asserted]: #82
+#11 := (:var 0 S3)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#650 := (pattern #12)
+#13 := (f3 f4 #12)
+#14 := (= #13 #9)
+#651 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #650) #14)
+#15 := (forall (vars (?v0 S2) (?v1 S3)) #14)
+#654 := (iff #15 #651)
+#652 := (iff #14 #14)
+#653 := [refl]: #652
+#655 := [quant-intro #653]: #654
+#138 := (~ #15 #15)
+#136 := (~ #14 #14)
+#137 := [refl]: #136
+#139 := [nnf-pos #137]: #138
+#103 := [asserted]: #15
+#114 := [mp~ #103 #139]: #15
+#656 := [mp #114 #655]: #651
+#620 := (not #651)
+#527 := (or #620 #81)
+#533 := [quant-inst #71 #78]: #527
+[unit-resolution #533 #656 #112]: false
+unsat
+d46d7a2ca405083ed110fa917182c9b64d529ecc 50 0
 #2 := false
 decl f5 :: (-> S5 S3 S3)
 decl f9 :: S3
-#31 := f9
+#30 := f9
 decl f6 :: (-> S6 S2 S5)
 decl f23 :: S2
-#76 := f23
+#75 := f23
 decl f7 :: S6
-#9 := f7
-#77 := (f6 f7 f23)
-#78 := (f5 #77 f9)
+#8 := f7
+#76 := (f6 f7 f23)
+#77 := (f5 #76 f9)
 decl f22 :: S2
-#74 := f22
-#75 := (f6 f7 f22)
-#79 := (f5 #75 #78)
+#73 := f22
+#74 := (f6 f7 f22)
+#78 := (f5 #74 #77)
 decl f21 :: S2
-#72 := f21
-#73 := (f6 f7 f21)
-#80 := (f5 #73 #79)
+#71 := f21
+#72 := (f6 f7 f21)
+#79 := (f5 #72 #78)
 decl f8 :: S5
-#17 := f8
-#81 := (f5 f8 #80)
-#167 := (= #79 #81)
-#170 := (not #167)
-#82 := (= #81 #79)
-#83 := (not #82)
-#171 := (iff #83 #170)
-#168 := (iff #82 #167)
-#169 := [rewrite]: #168
-#172 := [monotonicity #169]: #171
-#165 := [asserted]: #83
-#175 := [mp #165 #172]: #170
-#12 := (:var 0 S3)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#702 := (pattern #13)
-#18 := (f5 f8 #13)
-#111 := (= #12 #18)
-#709 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #702) #111)
-#115 := (forall (vars (?v0 S2) (?v1 S3)) #111)
-#712 := (iff #115 #709)
-#710 := (iff #111 #111)
-#711 := [refl]: #710
-#713 := [quant-intro #711]: #712
-#195 := (~ #115 #115)
-#197 := (~ #111 #111)
-#194 := [refl]: #197
-#192 := [nnf-pos #194]: #195
-#19 := (= #18 #12)
-#20 := (forall (vars (?v0 S2) (?v1 S3)) #19)
-#116 := (iff #20 #115)
-#113 := (iff #19 #111)
-#114 := [rewrite]: #113
-#117 := [quant-intro #114]: #116
-#110 := [asserted]: #20
-#120 := [mp #110 #117]: #115
-#193 := [mp~ #120 #192]: #115
-#714 := [mp #193 #713]: #709
-#618 := (not #709)
-#451 := (or #618 #167)
-#452 := [quant-inst #72 #79]: #451
-[unit-resolution #452 #714 #175]: false
-unsat
-1f9a3665b01fd9498f7eee032bae22316a527489 105 0
-#2 := false
+#16 := f8
+#80 := (f5 f8 #79)
+#81 := (= #80 #78)
+#82 := (not #81)
+#112 := [asserted]: #82
+#11 := (:var 0 S3)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#650 := (pattern #12)
+#17 := (f5 f8 #12)
+#18 := (= #17 #11)
+#657 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #650) #18)
+#19 := (forall (vars (?v0 S2) (?v1 S3)) #18)
+#660 := (iff #19 #657)
+#658 := (iff #18 #18)
+#659 := [refl]: #658
+#661 := [quant-intro #659]: #660
+#116 := (~ #19 #19)
+#115 := (~ #18 #18)
+#140 := [refl]: #115
+#117 := [nnf-pos #140]: #116
+#104 := [asserted]: #19
+#141 := [mp~ #104 #117]: #19
+#662 := [mp #141 #661]: #657
+#618 := (not #657)
+#516 := (or #618 #81)
+#517 := [quant-inst #71 #78]: #516
+[unit-resolution #517 #662 #112]: false
+unsat
+00d45a2105c65a05afe6de3a3f44dd3d02e667e9 80 0
+#2 := false
+decl f22 :: S2
+#73 := f22
 decl f3 :: (-> S4 S3 S2)
 decl f5 :: (-> S5 S3 S3)
 decl f9 :: S3
-#31 := f9
+#30 := f9
 decl f6 :: (-> S6 S2 S5)
 decl f23 :: S2
-#76 := f23
+#75 := f23
 decl f7 :: S6
-#9 := f7
-#77 := (f6 f7 f23)
-#78 := (f5 #77 f9)
-decl f22 :: S2
-#74 := f22
-#75 := (f6 f7 f22)
-#79 := (f5 #75 #78)
+#8 := f7
+#76 := (f6 f7 f23)
+#77 := (f5 #76 f9)
+#74 := (f6 f7 f22)
+#78 := (f5 #74 #77)
 decl f21 :: S2
-#72 := f21
-#73 := (f6 f7 f21)
-#80 := (f5 #73 #79)
+#71 := f21
+#72 := (f6 f7 f21)
+#79 := (f5 #72 #78)
 decl f8 :: S5
-#17 := f8
-#81 := (f5 f8 #80)
+#16 := f8
+#80 := (f5 f8 #79)
 decl f4 :: S4
-#8 := f4
-#82 := (f3 f4 #81)
-#168 := (= f22 #82)
-#520 := (f3 f4 #79)
-#425 := (= #520 #82)
-#440 := (= #82 #520)
-#452 := (= #81 #79)
-#455 := (= #79 #81)
-#12 := (:var 0 S3)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#703 := (pattern #13)
-#18 := (f5 f8 #13)
-#112 := (= #12 #18)
-#710 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #703) #112)
-#116 := (forall (vars (?v0 S2) (?v1 S3)) #112)
-#713 := (iff #116 #710)
-#711 := (iff #112 #112)
-#712 := [refl]: #711
-#714 := [quant-intro #712]: #713
-#196 := (~ #116 #116)
-#198 := (~ #112 #112)
-#195 := [refl]: #198
-#193 := [nnf-pos #195]: #196
-#19 := (= #18 #12)
-#20 := (forall (vars (?v0 S2) (?v1 S3)) #19)
-#117 := (iff #20 #116)
-#114 := (iff #19 #112)
-#115 := [rewrite]: #114
-#118 := [quant-intro #115]: #117
-#111 := [asserted]: #20
-#121 := [mp #111 #118]: #116
-#194 := [mp~ #121 #193]: #116
-#715 := [mp #194 #714]: #710
-#619 := (not #710)
-#453 := (or #619 #455)
-#439 := [quant-inst #72 #79]: #453
-#448 := [unit-resolution #439 #715]: #455
-#441 := [symm #448]: #452
-#443 := [monotonicity #441]: #440
-#427 := [symm #443]: #425
-#522 := (= f22 #520)
-#14 := (f3 f4 #13)
-#105 := (= #10 #14)
-#704 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #703) #105)
-#108 := (forall (vars (?v0 S2) (?v1 S3)) #105)
-#707 := (iff #108 #704)
-#705 := (iff #105 #105)
-#706 := [refl]: #705
-#708 := [quant-intro #706]: #707
-#185 := (~ #108 #108)
-#147 := (~ #105 #105)
-#184 := [refl]: #147
-#186 := [nnf-pos #184]: #185
-#15 := (= #14 #10)
-#16 := (forall (vars (?v0 S2) (?v1 S3)) #15)
-#109 := (iff #16 #108)
-#106 := (iff #15 #105)
-#107 := [rewrite]: #106
-#110 := [quant-intro #107]: #109
-#104 := [asserted]: #16
-#113 := [mp #104 #110]: #108
-#197 := [mp~ #113 #186]: #108
-#709 := [mp #197 #708]: #704
-#637 := (not #704)
-#533 := (or #637 #522)
-#534 := [quant-inst #74 #78]: #533
-#442 := [unit-resolution #534 #709]: #522
-#428 := [trans #442 #427]: #168
-#171 := (not #168)
-#83 := (= #82 f22)
-#84 := (not #83)
-#172 := (iff #84 #171)
-#169 := (iff #83 #168)
-#170 := [rewrite]: #169
-#173 := [monotonicity #170]: #172
-#166 := [asserted]: #84
-#176 := [mp #166 #173]: #171
-[unit-resolution #176 #428]: false
-unsat
-b298b421234bddee158e1132134ea7aa5bde443b 79 0
+#7 := f4
+#81 := (f3 f4 #80)
+#82 := (= #81 f22)
+#587 := (f3 f4 #78)
+#588 := (= #587 f22)
+#11 := (:var 0 S3)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#651 := (pattern #12)
+#13 := (f3 f4 #12)
+#14 := (= #13 #9)
+#652 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #651) #14)
+#15 := (forall (vars (?v0 S2) (?v1 S3)) #14)
+#655 := (iff #15 #652)
+#653 := (iff #14 #14)
+#654 := [refl]: #653
+#656 := [quant-intro #654]: #655
+#139 := (~ #15 #15)
+#137 := (~ #14 #14)
+#138 := [refl]: #137
+#140 := [nnf-pos #138]: #139
+#104 := [asserted]: #15
+#115 := [mp~ #104 #140]: #15
+#657 := [mp #115 #656]: #652
+#621 := (not #652)
+#490 := (or #621 #588)
+#491 := [quant-inst #73 #77]: #490
+#534 := [unit-resolution #491 #657]: #588
+#522 := (= #81 #587)
+#528 := (= #80 #78)
+#17 := (f5 f8 #12)
+#18 := (= #17 #11)
+#658 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #651) #18)
+#19 := (forall (vars (?v0 S2) (?v1 S3)) #18)
+#661 := (iff #19 #658)
+#659 := (iff #18 #18)
+#660 := [refl]: #659
+#662 := [quant-intro #660]: #661
+#117 := (~ #19 #19)
+#116 := (~ #18 #18)
+#141 := [refl]: #116
+#118 := [nnf-pos #141]: #117
+#105 := [asserted]: #19
+#142 := [mp~ #105 #118]: #19
+#663 := [mp #142 #662]: #658
+#619 := (not #658)
+#518 := (or #619 #528)
+#521 := [quant-inst #71 #78]: #518
+#517 := [unit-resolution #521 #663]: #528
+#523 := [monotonicity #517]: #522
+#524 := [trans #523 #534]: #82
+#83 := (not #82)
+#113 := [asserted]: #83
+[unit-resolution #113 #524]: false
+unsat
+4d55755ce8670444560059a4a2c5e8c60b925e12 61 0
 #2 := false
 decl f5 :: (-> S5 S3 S3)
 decl f9 :: S3
-#31 := f9
+#30 := f9
 decl f6 :: (-> S6 S2 S5)
 decl f23 :: S2
-#76 := f23
+#75 := f23
 decl f7 :: S6
-#9 := f7
-#77 := (f6 f7 f23)
-#78 := (f5 #77 f9)
+#8 := f7
+#76 := (f6 f7 f23)
+#77 := (f5 #76 f9)
 decl f22 :: S2
-#74 := f22
-#75 := (f6 f7 f22)
-#79 := (f5 #75 #78)
+#73 := f22
+#74 := (f6 f7 f22)
+#78 := (f5 #74 #77)
 decl f21 :: S2
-#72 := f21
-#73 := (f6 f7 f21)
-#80 := (f5 #73 #79)
+#71 := f21
+#72 := (f6 f7 f21)
+#79 := (f5 #72 #78)
 decl f8 :: S5
-#17 := f8
+#16 := f8
+#80 := (f5 f8 #79)
 #81 := (f5 f8 #80)
-#82 := (f5 f8 #81)
-#168 := (= #78 #82)
-#524 := (f5 f8 #79)
-#425 := (= #524 #82)
-#440 := (= #82 #524)
-#452 := (= #81 #79)
-#455 := (= #79 #81)
-#12 := (:var 0 S3)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#703 := (pattern #13)
-#18 := (f5 f8 #13)
-#112 := (= #12 #18)
-#710 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #703) #112)
-#116 := (forall (vars (?v0 S2) (?v1 S3)) #112)
-#713 := (iff #116 #710)
-#711 := (iff #112 #112)
-#712 := [refl]: #711
-#714 := [quant-intro #712]: #713
-#196 := (~ #116 #116)
-#198 := (~ #112 #112)
-#195 := [refl]: #198
-#193 := [nnf-pos #195]: #196
-#19 := (= #18 #12)
-#20 := (forall (vars (?v0 S2) (?v1 S3)) #19)
-#117 := (iff #20 #116)
-#114 := (iff #19 #112)
-#115 := [rewrite]: #114
-#118 := [quant-intro #115]: #117
-#111 := [asserted]: #20
-#121 := [mp #111 #118]: #116
-#194 := [mp~ #121 #193]: #116
-#715 := [mp #194 #714]: #710
-#619 := (not #710)
-#453 := (or #619 #455)
-#439 := [quant-inst #72 #79]: #453
-#448 := [unit-resolution #439 #715]: #455
-#441 := [symm #448]: #452
-#443 := [monotonicity #441]: #440
-#427 := [symm #443]: #425
-#531 := (= #78 #524)
-#525 := (or #619 #531)
-#546 := [quant-inst #74 #78]: #525
-#442 := [unit-resolution #546 #715]: #531
-#428 := [trans #442 #427]: #168
-#171 := (not #168)
-#83 := (= #82 #78)
-#84 := (not #83)
-#172 := (iff #84 #171)
-#169 := (iff #83 #168)
-#170 := [rewrite]: #169
-#173 := [monotonicity #170]: #172
-#166 := [asserted]: #84
-#176 := [mp #166 #173]: #171
-[unit-resolution #176 #428]: false
-unsat
-dbbcd10dbc84c086674cc842f20de49305282406 111 0
-#2 := false
+#82 := (= #81 #77)
+#488 := (f5 f8 #78)
+#489 := (= #488 #77)
+#11 := (:var 0 S3)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#651 := (pattern #12)
+#17 := (f5 f8 #12)
+#18 := (= #17 #11)
+#658 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #651) #18)
+#19 := (forall (vars (?v0 S2) (?v1 S3)) #18)
+#661 := (iff #19 #658)
+#659 := (iff #18 #18)
+#660 := [refl]: #659
+#662 := [quant-intro #660]: #661
+#117 := (~ #19 #19)
+#116 := (~ #18 #18)
+#141 := [refl]: #116
+#118 := [nnf-pos #141]: #117
+#105 := [asserted]: #19
+#142 := [mp~ #105 #118]: #19
+#663 := [mp #142 #662]: #658
+#619 := (not #658)
+#582 := (or #619 #489)
+#586 := [quant-inst #73 #77]: #582
+#534 := [unit-resolution #586 #663]: #489
+#522 := (= #81 #488)
+#528 := (= #80 #78)
+#518 := (or #619 #528)
+#521 := [quant-inst #71 #78]: #518
+#517 := [unit-resolution #521 #663]: #528
+#523 := [monotonicity #517]: #522
+#524 := [trans #523 #534]: #82
+#83 := (not #82)
+#113 := [asserted]: #83
+[unit-resolution #113 #524]: false
+unsat
+1e49cb75a4b4736654a002c06e5405d5c3517634 86 0
+#2 := false
+decl f28 :: S2
+#91 := f28
 decl f3 :: (-> S4 S5 S2)
 decl f10 :: (-> S10 S9 S5)
 decl f12 :: (-> S11 S9 S9)
 decl f16 :: S9
-#51 := f16
+#50 := f16
 decl f13 :: (-> S12 S5 S11)
 decl f5 :: (-> S6 S3 S5)
 decl f29 :: S3
-#94 := f29
+#93 := f29
 decl f6 :: (-> S7 S2 S6)
-decl f28 :: S2
-#92 := f28
 decl f7 :: S7
-#9 := f7
-#93 := (f6 f7 f28)
-#95 := (f5 #93 f29)
+#8 := f7
+#92 := (f6 f7 f28)
+#94 := (f5 #92 f29)
 decl f14 :: S12
-#29 := f14
-#96 := (f13 f14 #95)
-#97 := (f12 #96 f16)
+#28 := f14
+#95 := (f13 f14 #94)
+#96 := (f12 #95 f16)
 decl f11 :: S10
-#28 := f11
-#98 := (f10 f11 #97)
+#27 := f11
+#97 := (f10 f11 #96)
 decl f4 :: S4
-#8 := f4
-#99 := (f3 f4 #98)
-#209 := (= f28 #99)
-#341 := (f3 f4 #95)
-#383 := (= #341 #99)
-#744 := (= #99 #341)
-#739 := (= #98 #95)
-#395 := (= #95 #98)
-#32 := (:var 0 S9)
-#30 := (:var 1 S5)
-#31 := (f13 f14 #30)
-#33 := (f12 #31 #32)
-#780 := (pattern #33)
-#34 := (f10 f11 #33)
-#145 := (= #30 #34)
-#781 := (forall (vars (?v0 S5) (?v1 S9)) (:pat #780) #145)
-#149 := (forall (vars (?v0 S5) (?v1 S9)) #145)
-#784 := (iff #149 #781)
-#782 := (iff #145 #145)
-#783 := [refl]: #782
-#785 := [quant-intro #783]: #784
-#230 := (~ #149 #149)
-#235 := (~ #145 #145)
-#229 := [refl]: #235
-#227 := [nnf-pos #229]: #230
-#35 := (= #34 #30)
-#36 := (forall (vars (?v0 S5) (?v1 S9)) #35)
-#150 := (iff #36 #149)
-#147 := (iff #35 #145)
-#148 := [rewrite]: #147
-#151 := [quant-intro #148]: #150
-#144 := [asserted]: #36
-#154 := [mp #144 #151]: #149
-#228 := [mp~ #154 #227]: #149
-#786 := [mp #228 #785]: #781
-#398 := (not #781)
-#736 := (or #398 #395)
-#737 := [quant-inst #95 #51]: #736
-#738 := [unit-resolution #737 #786]: #395
-#377 := [symm #738]: #739
-#382 := [monotonicity #377]: #744
-#745 := [symm #382]: #383
-#428 := (= f28 #341)
-#12 := (:var 0 S3)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#759 := (pattern #13)
-#14 := (f3 f4 #13)
-#122 := (= #10 #14)
-#760 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #759) #122)
-#125 := (forall (vars (?v0 S2) (?v1 S3)) #122)
-#763 := (iff #125 #760)
-#761 := (iff #122 #122)
-#762 := [refl]: #761
-#764 := [quant-intro #762]: #763
-#232 := (~ #125 #125)
-#188 := (~ #122 #122)
-#231 := [refl]: #188
-#233 := [nnf-pos #231]: #232
-#15 := (= #14 #10)
-#16 := (forall (vars (?v0 S2) (?v1 S3)) #15)
-#126 := (iff #16 #125)
-#123 := (iff #15 #122)
-#124 := [rewrite]: #123
-#127 := [quant-intro #124]: #126
-#121 := [asserted]: #16
-#130 := [mp #121 #127]: #125
-#244 := [mp~ #130 #233]: #125
-#765 := [mp #244 #764]: #760
-#343 := (not #760)
-#430 := (or #343 #428)
-#421 := [quant-inst #92 #94]: #430
-#742 := [unit-resolution #421 #765]: #428
-#743 := [trans #742 #745]: #209
-#212 := (not #209)
-#100 := (= #99 f28)
-#101 := (not #100)
-#213 := (iff #101 #212)
-#210 := (iff #100 #209)
-#211 := [rewrite]: #210
-#214 := [monotonicity #211]: #213
-#207 := [asserted]: #101
-#217 := [mp #207 #214]: #212
-[unit-resolution #217 #743]: false
-unsat
-2e9d2577f0ec2fea58a5da10f4c502e6348db013 111 0
-#2 := false
+#7 := f4
+#98 := (f3 f4 #97)
+#99 := (= #98 f28)
+#270 := (f3 f4 #94)
+#356 := (= #270 f28)
+#11 := (:var 0 S3)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#686 := (pattern #12)
+#13 := (f3 f4 #12)
+#14 := (= #13 #9)
+#687 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #686) #14)
+#15 := (forall (vars (?v0 S2) (?v1 S3)) #14)
+#690 := (iff #15 #687)
+#688 := (iff #14 #14)
+#689 := [refl]: #688
+#691 := [quant-intro #689]: #690
+#165 := (~ #15 #15)
+#163 := (~ #14 #14)
+#164 := [refl]: #163
+#166 := [nnf-pos #164]: #165
+#121 := [asserted]: #15
+#135 := [mp~ #121 #166]: #15
+#692 := [mp #135 #691]: #687
+#272 := (not #687)
+#358 := (or #272 #356)
+#349 := [quant-inst #91 #93]: #358
+#339 := [unit-resolution #349 #692]: #356
+#324 := (= #98 #270)
+#348 := (= #97 #94)
+#31 := (:var 0 S9)
+#29 := (:var 1 S5)
+#30 := (f13 f14 #29)
+#32 := (f12 #30 #31)
+#707 := (pattern #32)
+#33 := (f10 f11 #32)
+#34 := (= #33 #29)
+#708 := (forall (vars (?v0 S5) (?v1 S9)) (:pat #707) #34)
+#35 := (forall (vars (?v0 S5) (?v1 S9)) #34)
+#711 := (iff #35 #708)
+#709 := (iff #34 #34)
+#710 := [refl]: #709
+#712 := [quant-intro #710]: #711
+#141 := (~ #35 #35)
+#172 := (~ #34 #34)
+#173 := [refl]: #172
+#142 := [nnf-pos #173]: #141
+#124 := [asserted]: #35
+#174 := [mp~ #124 #142]: #35
+#713 := [mp #174 #712]: #708
+#685 := (not #708)
+#675 := (or #685 #348)
+#334 := [quant-inst #94 #50]: #675
+#676 := [unit-resolution #334 #713]: #348
+#325 := [monotonicity #676]: #324
+#326 := [trans #325 #339]: #99
+#100 := (not #99)
+#133 := [asserted]: #100
+[unit-resolution #133 #326]: false
+unsat
+4ee836bc63884d52d61c6983c35e39ed91d8e078 86 0
+#2 := false
+decl f29 :: S3
+#93 := f29
 decl f8 :: (-> S8 S5 S3)
 decl f10 :: (-> S10 S9 S5)
 decl f12 :: (-> S11 S9 S9)
 decl f16 :: S9
-#51 := f16
+#50 := f16
 decl f13 :: (-> S12 S5 S11)
 decl f5 :: (-> S6 S3 S5)
-decl f29 :: S3
-#94 := f29
 decl f6 :: (-> S7 S2 S6)
 decl f28 :: S2
-#92 := f28
+#91 := f28
 decl f7 :: S7
-#9 := f7
-#93 := (f6 f7 f28)
-#95 := (f5 #93 f29)
+#8 := f7
+#92 := (f6 f7 f28)
+#94 := (f5 #92 f29)
 decl f14 :: S12
-#29 := f14
-#96 := (f13 f14 #95)
-#97 := (f12 #96 f16)
+#28 := f14
+#95 := (f13 f14 #94)
+#96 := (f12 #95 f16)
 decl f11 :: S10
-#28 := f11
-#98 := (f10 f11 #97)
+#27 := f11
+#97 := (f10 f11 #96)
 decl f9 :: S8
-#17 := f9
-#99 := (f8 f9 #98)
-#209 := (= f29 #99)
-#342 := (f8 f9 #95)
-#383 := (= #342 #99)
-#744 := (= #99 #342)
-#739 := (= #98 #95)
-#395 := (= #95 #98)
-#32 := (:var 0 S9)
-#30 := (:var 1 S5)
-#31 := (f13 f14 #30)
-#33 := (f12 #31 #32)
-#780 := (pattern #33)
-#34 := (f10 f11 #33)
-#145 := (= #30 #34)
-#781 := (forall (vars (?v0 S5) (?v1 S9)) (:pat #780) #145)
-#149 := (forall (vars (?v0 S5) (?v1 S9)) #145)
-#784 := (iff #149 #781)
-#782 := (iff #145 #145)
-#783 := [refl]: #782
-#785 := [quant-intro #783]: #784
-#230 := (~ #149 #149)
-#235 := (~ #145 #145)
-#229 := [refl]: #235
-#227 := [nnf-pos #229]: #230
-#35 := (= #34 #30)
-#36 := (forall (vars (?v0 S5) (?v1 S9)) #35)
-#150 := (iff #36 #149)
-#147 := (iff #35 #145)
-#148 := [rewrite]: #147
-#151 := [quant-intro #148]: #150
-#144 := [asserted]: #36
-#154 := [mp #144 #151]: #149
-#228 := [mp~ #154 #227]: #149
-#786 := [mp #228 #785]: #781
-#398 := (not #781)
-#736 := (or #398 #395)
-#737 := [quant-inst #95 #51]: #736
-#738 := [unit-resolution #737 #786]: #395
-#377 := [symm #738]: #739
-#382 := [monotonicity #377]: #744
-#745 := [symm #382]: #383
-#429 := (= f29 #342)
-#12 := (:var 0 S3)
-#10 := (:var 1 S2)
-#11 := (f6 f7 #10)
-#13 := (f5 #11 #12)
-#759 := (pattern #13)
-#18 := (f8 f9 #13)
-#129 := (= #12 #18)
-#766 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #759) #129)
-#133 := (forall (vars (?v0 S2) (?v1 S3)) #129)
-#769 := (iff #133 #766)
-#767 := (iff #129 #129)
-#768 := [refl]: #767
-#770 := [quant-intro #768]: #769
-#243 := (~ #133 #133)
-#245 := (~ #129 #129)
-#242 := [refl]: #245
-#240 := [nnf-pos #242]: #243
-#19 := (= #18 #12)
-#20 := (forall (vars (?v0 S2) (?v1 S3)) #19)
-#134 := (iff #20 #133)
-#131 := (iff #19 #129)
-#132 := [rewrite]: #131
-#135 := [quant-intro #132]: #134
-#128 := [asserted]: #20
-#138 := [mp #128 #135]: #133
-#241 := [mp~ #138 #240]: #133
-#771 := [mp #241 #770]: #766
-#361 := (not #766)
-#434 := (or #361 #429)
-#431 := [quant-inst #92 #94]: #434
-#742 := [unit-resolution #431 #771]: #429
-#743 := [trans #742 #745]: #209
-#212 := (not #209)
-#100 := (= #99 f29)
-#101 := (not #100)
-#213 := (iff #101 #212)
-#210 := (iff #100 #209)
-#211 := [rewrite]: #210
-#214 := [monotonicity #211]: #213
-#207 := [asserted]: #101
-#217 := [mp #207 #214]: #212
-[unit-resolution #217 #743]: false
-unsat
-4896dc3d983fa1db6692f7158c809398573225ab 29 0
+#16 := f9
+#98 := (f8 f9 #97)
+#99 := (= #98 f29)
+#271 := (f8 f9 #94)
+#357 := (= #271 f29)
+#11 := (:var 0 S3)
+#9 := (:var 1 S2)
+#10 := (f6 f7 #9)
+#12 := (f5 #10 #11)
+#686 := (pattern #12)
+#17 := (f8 f9 #12)
+#18 := (= #17 #11)
+#693 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #686) #18)
+#19 := (forall (vars (?v0 S2) (?v1 S3)) #18)
+#696 := (iff #19 #693)
+#694 := (iff #18 #18)
+#695 := [refl]: #694
+#697 := [quant-intro #695]: #696
+#137 := (~ #19 #19)
+#136 := (~ #18 #18)
+#167 := [refl]: #136
+#138 := [nnf-pos #167]: #137
+#122 := [asserted]: #19
+#168 := [mp~ #122 #138]: #19
+#698 := [mp #168 #697]: #693
+#362 := (not #693)
+#359 := (or #362 #357)
+#363 := [quant-inst #91 #93]: #359
+#339 := [unit-resolution #363 #698]: #357
+#324 := (= #98 #271)
+#348 := (= #97 #94)
+#31 := (:var 0 S9)
+#29 := (:var 1 S5)
+#30 := (f13 f14 #29)
+#32 := (f12 #30 #31)
+#707 := (pattern #32)
+#33 := (f10 f11 #32)
+#34 := (= #33 #29)
+#708 := (forall (vars (?v0 S5) (?v1 S9)) (:pat #707) #34)
+#35 := (forall (vars (?v0 S5) (?v1 S9)) #34)
+#711 := (iff #35 #708)
+#709 := (iff #34 #34)
+#710 := [refl]: #709
+#712 := [quant-intro #710]: #711
+#141 := (~ #35 #35)
+#172 := (~ #34 #34)
+#173 := [refl]: #172
+#142 := [nnf-pos #173]: #141
+#124 := [asserted]: #35
+#174 := [mp~ #124 #142]: #35
+#713 := [mp #174 #712]: #708
+#685 := (not #708)
+#675 := (or #685 #348)
+#334 := [quant-inst #94 #50]: #675
+#676 := [unit-resolution #334 #713]: #348
+#325 := [monotonicity #676]: #324
+#326 := [trans #325 #339]: #99
+#100 := (not #99)
+#133 := [asserted]: #100
+[unit-resolution #133 #326]: false
+unsat
+86f6f739d6e836607f1d98b07ede63d2576d444d 29 0
+#2 := false
+decl f3 :: (-> S3 S4 Int)
+decl f15 :: S4
+#41 := f15
+decl f4 :: S3
+#7 := f4
+#44 := (f3 f4 f15)
+decl f14 :: S4
+#40 := f14
+#43 := (f3 f4 f14)
+#45 := (= #43 #44)
+#42 := (= f14 f15)
+#75 := (not #42)
+#76 := (or #75 #45)
+#79 := (not #76)
+#46 := (implies #42 #45)
+#47 := (not #46)
+#80 := (iff #47 #79)
+#77 := (iff #46 #76)
+#78 := [rewrite]: #77
+#81 := [monotonicity #78]: #80
+#74 := [asserted]: #47
+#84 := [mp #74 #81]: #79
+#82 := [not-or-elim #84]: #42
+#263 := [monotonicity #82]: #45
+#83 := (not #45)
+#85 := [not-or-elim #84]: #83
+[unit-resolution #85 #263]: false
+unsat
+226b5b35f9edf656c0cea4dba57d64e428e7d1be 29 0
+#2 := false
+decl f3 :: (-> S3 S4 Int)
+decl f15 :: S4
+#41 := f15
+decl f6 :: S3
+#15 := f6
+#44 := (f3 f6 f15)
+decl f14 :: S4
+#40 := f14
+#43 := (f3 f6 f14)
+#45 := (= #43 #44)
+#42 := (= f14 f15)
+#75 := (not #42)
+#76 := (or #75 #45)
+#79 := (not #76)
+#46 := (implies #42 #45)
+#47 := (not #46)
+#80 := (iff #47 #79)
+#77 := (iff #46 #76)
+#78 := [rewrite]: #77
+#81 := [monotonicity #78]: #80
+#74 := [asserted]: #47
+#84 := [mp #74 #81]: #79
+#82 := [not-or-elim #84]: #42
+#263 := [monotonicity #82]: #45
+#83 := (not #45)
+#85 := [not-or-elim #84]: #83
+[unit-resolution #85 #263]: false
+unsat
+7e1ce21ff788fbffd8dbff9dda94f87b4ae232e3 29 0
 #2 := false
 decl f3 :: (-> S3 S4 Int)
 decl f15 :: S4
 #42 := f15
 decl f4 :: S3
-#8 := f4
-#45 := (f3 f4 f15)
+#7 := f4
+#43 := (f3 f4 f15)
 decl f14 :: S4
-#41 := f14
-#44 := (f3 f4 f14)
-#46 := (= #44 #45)
-#43 := (= f14 f15)
-#96 := (not #43)
-#97 := (or #96 #46)
-#100 := (not #97)
-#47 := (implies #43 #46)
-#48 := (not #47)
-#101 := (iff #48 #100)
-#98 := (iff #47 #97)
-#99 := [rewrite]: #98
-#102 := [monotonicity #99]: #101
-#95 := [asserted]: #48
-#105 := [mp #95 #102]: #100
-#103 := [not-or-elim #105]: #43
-#280 := [monotonicity #103]: #46
-#104 := (not #46)
-#106 := [not-or-elim #105]: #104
-[unit-resolution #106 #280]: false
-unsat
-1538231e595cc73ecc292a67c8bee9abfaf9197c 29 0
+#40 := f14
+#41 := (f3 f4 f14)
+#44 := (= #41 #43)
+#46 := (= f14 f15)
+#47 := (not #46)
+#77 := (or #44 #47)
+#80 := (not #77)
+#45 := (not #44)
+#48 := (implies #45 #47)
+#49 := (not #48)
+#81 := (iff #49 #80)
+#78 := (iff #48 #77)
+#79 := [rewrite]: #78
+#82 := [monotonicity #79]: #81
+#76 := [asserted]: #49
+#85 := [mp #76 #82]: #80
+#84 := [not-or-elim #85]: #46
+#263 := [monotonicity #84]: #44
+#83 := [not-or-elim #85]: #45
+[unit-resolution #83 #263]: false
+unsat
+ef77170e76e2077f1a99823990059fedc25a5572 29 0
 #2 := false
 decl f3 :: (-> S3 S4 Int)
 decl f15 :: S4
 #42 := f15
 decl f6 :: S3
-#16 := f6
-#45 := (f3 f6 f15)
-decl f14 :: S4
-#41 := f14
-#44 := (f3 f6 f14)
-#46 := (= #44 #45)
-#43 := (= f14 f15)
-#96 := (not #43)
-#97 := (or #96 #46)
-#100 := (not #97)
-#47 := (implies #43 #46)
-#48 := (not #47)
-#101 := (iff #48 #100)
-#98 := (iff #47 #97)
-#99 := [rewrite]: #98
-#102 := [monotonicity #99]: #101
-#95 := [asserted]: #48
-#105 := [mp #95 #102]: #100
-#103 := [not-or-elim #105]: #43
-#280 := [monotonicity #103]: #46
-#104 := (not #46)
-#106 := [not-or-elim #105]: #104
-[unit-resolution #106 #280]: false
-unsat
-392e090edba462e926403dbc1a566c88432801c7 29 0
-#2 := false
-decl f3 :: (-> S3 S4 Int)
-decl f15 :: S4
-#43 := f15
-decl f4 :: S3
-#8 := f4
-#44 := (f3 f4 f15)
+#15 := f6
+#43 := (f3 f6 f15)
 decl f14 :: S4
-#41 := f14
-#42 := (f3 f4 f14)
-#45 := (= #42 #44)
-#47 := (= f14 f15)
-#48 := (not #47)
-#98 := (or #45 #48)
-#101 := (not #98)
-#46 := (not #45)
-#49 := (implies #46 #48)
-#50 := (not #49)
-#102 := (iff #50 #101)
-#99 := (iff #49 #98)
-#100 := [rewrite]: #99
-#103 := [monotonicity #100]: #102
-#97 := [asserted]: #50
-#106 := [mp #97 #103]: #101
-#105 := [not-or-elim #106]: #47
-#280 := [monotonicity #105]: #45
-#104 := [not-or-elim #106]: #46
-[unit-resolution #104 #280]: false
-unsat
-82669adb791d3b09fa07a30d5fe3017ae8c18dc0 29 0
-#2 := false
-decl f3 :: (-> S3 S4 Int)
-decl f15 :: S4
-#43 := f15
-decl f6 :: S3
-#16 := f6
-#44 := (f3 f6 f15)
-decl f14 :: S4
-#41 := f14
-#42 := (f3 f6 f14)
-#45 := (= #42 #44)
-#47 := (= f14 f15)
-#48 := (not #47)
-#98 := (or #45 #48)
-#101 := (not #98)
-#46 := (not #45)
-#49 := (implies #46 #48)
-#50 := (not #49)
-#102 := (iff #50 #101)
-#99 := (iff #49 #98)
-#100 := [rewrite]: #99
-#103 := [monotonicity #100]: #102
-#97 := [asserted]: #50
-#106 := [mp #97 #103]: #101
-#105 := [not-or-elim #106]: #47
-#280 := [monotonicity #105]: #45
-#104 := [not-or-elim #106]: #46
-[unit-resolution #104 #280]: false
-unsat
-79da0fe967a112ed891c9268e71afaca102dd576 56 0
-#2 := false
-#41 := 3::Int
+#40 := f14
+#41 := (f3 f6 f14)
+#44 := (= #41 #43)
+#46 := (= f14 f15)
+#47 := (not #46)
+#77 := (or #44 #47)
+#80 := (not #77)
+#45 := (not #44)
+#48 := (implies #45 #47)
+#49 := (not #48)
+#81 := (iff #49 #80)
+#78 := (iff #48 #77)
+#79 := [rewrite]: #78
+#82 := [monotonicity #79]: #81
+#76 := [asserted]: #49
+#85 := [mp #76 #82]: #80
+#84 := [not-or-elim #85]: #46
+#263 := [monotonicity #84]: #44
+#83 := [not-or-elim #85]: #45
+[unit-resolution #83 #263]: false
+unsat
+05fabc68a1647a6c0b540f035499c1b64021300b 39 0
+#2 := false
+#40 := 3::Int
 decl f3 :: (-> S3 S4 Int)
 decl f5 :: (-> Int Int S2 S4)
 decl f14 :: S2
-#43 := f14
-#42 := 4::Int
-#44 := (f5 3::Int 4::Int f14)
+#42 := f14
+#41 := 4::Int
+#43 := (f5 3::Int 4::Int f14)
 decl f4 :: S3
-#8 := f4
-#45 := (f3 f4 #44)
-#46 := (= #45 3::Int)
-#47 := (not #46)
-#94 := [asserted]: #47
-#11 := (:var 0 S2)
-#10 := (:var 1 Int)
-#9 := (:var 2 Int)
-#12 := (f5 #9 #10 #11)
-#193 := (pattern #12)
-#13 := (f3 f4 #12)
-#68 := (= #9 #13)
-#194 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #193) #68)
-#71 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #68)
-#197 := (iff #71 #194)
-#195 := (iff #68 #68)
-#196 := [refl]: #195
-#198 := [quant-intro #196]: #197
-#108 := (~ #71 #71)
-#106 := (~ #68 #68)
-#107 := [refl]: #106
-#109 := [nnf-pos #107]: #108
-#14 := (= #13 #9)
-#15 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #14)
-#72 := (iff #15 #71)
-#69 := (iff #14 #68)
-#70 := [rewrite]: #69
-#73 := [quant-intro #70]: #72
-#67 := [asserted]: #15
-#76 := [mp #67 #73]: #71
-#110 := [mp~ #76 #109]: #71
-#199 := [mp #110 #198]: #194
-#238 := (not #194)
-#239 := (or #238 #46)
-#95 := (= 3::Int #45)
-#243 := (or #238 #95)
-#245 := (iff #243 #239)
-#247 := (iff #239 #239)
-#248 := [rewrite]: #247
-#101 := (iff #95 #46)
-#102 := [rewrite]: #101
-#246 := [monotonicity #102]: #245
-#249 := [trans #246 #248]: #245
-#244 := [quant-inst #41 #42 #43]: #243
-#250 := [mp #244 #249]: #239
-[unit-resolution #250 #199 #94]: false
-unsat
-218a5265d7c54eacac218a21e52867527c94dd10 56 0
-#2 := false
-#42 := 4::Int
+#7 := f4
+#44 := (f3 f4 #43)
+#45 := (= #44 3::Int)
+#46 := (not #45)
+#73 := [asserted]: #46
+#10 := (:var 0 S2)
+#9 := (:var 1 Int)
+#8 := (:var 2 Int)
+#11 := (f5 #8 #9 #10)
+#165 := (pattern #11)
+#12 := (f3 f4 #11)
+#13 := (= #12 #8)
+#166 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #165) #13)
+#14 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #13)
+#169 := (iff #14 #166)
+#167 := (iff #13 #13)
+#168 := [refl]: #167
+#170 := [quant-intro #168]: #169
+#77 := (~ #14 #14)
+#75 := (~ #13 #13)
+#76 := [refl]: #75
+#78 := [nnf-pos #76]: #77
+#67 := [asserted]: #14
+#79 := [mp~ #67 #78]: #14
+#171 := [mp #79 #170]: #166
+#215 := (not #166)
+#216 := (or #215 #45)
+#217 := [quant-inst #40 #41 #42]: #216
+[unit-resolution #217 #171 #73]: false
+unsat
+8c97cf80a4fd3efed9db6fad38cd7df3e7f9b9e4 39 0
+#2 := false
+#41 := 4::Int
+decl f3 :: (-> S3 S4 Int)
+decl f5 :: (-> Int Int S2 S4)
+decl f14 :: S2
+#42 := f14
+#40 := 3::Int
+#43 := (f5 3::Int 4::Int f14)
+decl f6 :: S3
+#15 := f6
+#44 := (f3 f6 #43)
+#45 := (= #44 4::Int)
+#46 := (not #45)
+#73 := [asserted]: #46
+#10 := (:var 0 S2)
+#9 := (:var 1 Int)
+#8 := (:var 2 Int)
+#11 := (f5 #8 #9 #10)
+#165 := (pattern #11)
+#16 := (f3 f6 #11)
+#17 := (= #16 #9)
+#172 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #165) #17)
+#18 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #17)
+#175 := (iff #18 #172)
+#173 := (iff #17 #17)
+#174 := [refl]: #173
+#176 := [quant-intro #174]: #175
+#82 := (~ #18 #18)
+#80 := (~ #17 #17)
+#81 := [refl]: #80
+#83 := [nnf-pos #81]: #82
+#68 := [asserted]: #18
+#84 := [mp~ #68 #83]: #18
+#177 := [mp #84 #176]: #172
+#220 := (not #172)
+#221 := (or #220 #45)
+#222 := [quant-inst #40 #41 #42]: #221
+[unit-resolution #222 #177 #73]: false
+unsat
+5637fa1d095ac7b67e6203665a505b9e7150a9ea 78 0
+#2 := false
+#41 := 4::Int
+#40 := 3::Int
+#234 := (= 3::Int 4::Int)
+#236 := (iff #234 false)
+#237 := [rewrite]: #236
 decl f3 :: (-> S3 S4 Int)
 decl f5 :: (-> Int Int S2 S4)
 decl f14 :: S2
-#43 := f14
-#41 := 3::Int
-#44 := (f5 3::Int 4::Int f14)
-decl f6 :: S3
-#16 := f6
-#45 := (f3 f6 #44)
-#46 := (= #45 4::Int)
-#47 := (not #46)
-#94 := [asserted]: #47
-#11 := (:var 0 S2)
-#10 := (:var 1 Int)
-#9 := (:var 2 Int)
-#12 := (f5 #9 #10 #11)
-#193 := (pattern #12)
-#17 := (f3 f6 #12)
-#75 := (= #10 #17)
-#200 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #193) #75)
-#79 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #75)
-#203 := (iff #79 #200)
-#201 := (iff #75 #75)
-#202 := [refl]: #201
-#204 := [quant-intro #202]: #203
-#113 := (~ #79 #79)
-#111 := (~ #75 #75)
-#112 := [refl]: #111
-#114 := [nnf-pos #112]: #113
-#18 := (= #17 #10)
-#19 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #18)
-#80 := (iff #19 #79)
-#77 := (iff #18 #75)
-#78 := [rewrite]: #77
-#81 := [quant-intro #78]: #80
-#74 := [asserted]: #19
-#84 := [mp #74 #81]: #79
-#115 := [mp~ #84 #114]: #79
-#205 := [mp #115 #204]: #200
-#256 := (not #200)
-#257 := (or #256 #46)
-#95 := (= 4::Int #45)
-#258 := (or #256 #95)
-#260 := (iff #258 #257)
-#262 := (iff #257 #257)
-#263 := [rewrite]: #262
-#101 := (iff #95 #46)
-#102 := [rewrite]: #101
-#261 := [monotonicity #102]: #260
-#264 := [trans #261 #263]: #260
-#259 := [quant-inst #41 #42 #43]: #258
-#265 := [mp #259 #264]: #257
-[unit-resolution #265 #205 #94]: false
-unsat
-e7133c0fe44808f56fc955cc97df0776a4963d3e 112 0
-#2 := false
-#42 := 4::Int
-#41 := 3::Int
-#272 := (= 3::Int 4::Int)
-#274 := (iff #272 false)
-#275 := [rewrite]: #274
-decl f3 :: (-> S3 S4 Int)
-decl f5 :: (-> Int Int S2 S4)
-decl f14 :: S2
-#43 := f14
-#44 := (f5 3::Int 4::Int f14)
+#42 := f14
+#43 := (f5 3::Int 4::Int f14)
 decl f6 :: S3
-#16 := f6
-#46 := (f3 f6 #44)
-#253 := (= #46 4::Int)
-#11 := (:var 0 S2)
-#10 := (:var 1 Int)
-#9 := (:var 2 Int)
-#12 := (f5 #9 #10 #11)
-#188 := (pattern #12)
-#17 := (f3 f6 #12)
-#77 := (= #10 #17)
-#195 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #188) #77)
-#81 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #77)
-#198 := (iff #81 #195)
-#196 := (iff #77 #77)
-#197 := [refl]: #196
-#199 := [quant-intro #197]: #198
-#108 := (~ #81 #81)
-#106 := (~ #77 #77)
-#107 := [refl]: #106
-#109 := [nnf-pos #107]: #108
-#18 := (= #17 #10)
-#19 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #18)
-#82 := (iff #19 #81)
-#79 := (iff #18 #77)
-#80 := [rewrite]: #79
-#83 := [quant-intro #80]: #82
-#76 := [asserted]: #19
-#86 := [mp #76 #83]: #81
-#110 := [mp~ #86 #109]: #81
-#200 := [mp #110 #199]: #195
-#254 := (not #195)
-#255 := (or #254 #253)
-#250 := (= 4::Int #46)
-#256 := (or #254 #250)
-#258 := (iff #256 #255)
-#260 := (iff #255 #255)
-#261 := [rewrite]: #260
-#251 := (iff #250 #253)
-#252 := [rewrite]: #251
-#259 := [monotonicity #252]: #258
-#262 := [trans #259 #261]: #258
-#257 := [quant-inst #41 #42 #43]: #256
-#263 := [mp #257 #262]: #255
-#264 := [unit-resolution #263 #200]: #253
-#270 := (= 3::Int #46)
-#268 := (= #46 3::Int)
+#15 := f6
+#45 := (f3 f6 #43)
+#216 := (= #45 4::Int)
+#10 := (:var 0 S2)
+#9 := (:var 1 Int)
+#8 := (:var 2 Int)
+#11 := (f5 #8 #9 #10)
+#170 := (pattern #11)
+#16 := (f3 f6 #11)
+#17 := (= #16 #9)
+#177 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #170) #17)
+#18 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #17)
+#180 := (iff #18 #177)
+#178 := (iff #17 #17)
+#179 := [refl]: #178
+#181 := [quant-intro #179]: #180
+#87 := (~ #18 #18)
+#85 := (~ #17 #17)
+#86 := [refl]: #85
+#88 := [nnf-pos #86]: #87
+#70 := [asserted]: #18
+#89 := [mp~ #70 #88]: #18
+#182 := [mp #89 #181]: #177
+#225 := (not #177)
+#226 := (or #225 #216)
+#227 := [quant-inst #40 #41 #42]: #226
+#220 := [unit-resolution #227 #182]: #216
+#232 := (= 3::Int #45)
+#230 := (= #45 3::Int)
 decl f4 :: S3
-#8 := f4
-#45 := (f3 f4 #44)
-#239 := (= #45 3::Int)
-#13 := (f3 f4 #12)
-#70 := (= #9 #13)
-#189 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #188) #70)
-#73 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #70)
-#192 := (iff #73 #189)
-#190 := (iff #70 #70)
-#191 := [refl]: #190
-#193 := [quant-intro #191]: #192
-#103 := (~ #73 #73)
-#100 := (~ #70 #70)
-#102 := [refl]: #100
-#104 := [nnf-pos #102]: #103
-#14 := (= #13 #9)
-#15 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #14)
-#74 := (iff #15 #73)
-#71 := (iff #14 #70)
-#72 := [rewrite]: #71
-#75 := [quant-intro #72]: #74
-#69 := [asserted]: #15
-#78 := [mp #69 #75]: #73
-#105 := [mp~ #78 #104]: #73
-#194 := [mp #105 #193]: #189
-#240 := (not #189)
-#241 := (or #240 #239)
-#233 := (= 3::Int #45)
-#242 := (or #240 #233)
-#244 := (iff #242 #241)
-#246 := (iff #241 #241)
-#247 := [rewrite]: #246
-#234 := (iff #233 #239)
-#238 := [rewrite]: #234
-#245 := [monotonicity #238]: #244
-#248 := [trans #245 #247]: #244
-#243 := [quant-inst #41 #42 #43]: #242
-#249 := [mp #243 #248]: #241
-#265 := [unit-resolution #249 #194]: #239
-#266 := (= #46 #45)
-#47 := (= #45 #46)
+#7 := f4
+#44 := (f3 f4 #43)
+#215 := (= #44 3::Int)
+#12 := (f3 f4 #11)
+#13 := (= #12 #8)
+#171 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #170) #13)
+#14 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #13)
+#174 := (iff #14 #171)
+#172 := (iff #13 #13)
+#173 := [refl]: #172
+#175 := [quant-intro #173]: #174
+#82 := (~ #14 #14)
+#79 := (~ #13 #13)
+#81 := [refl]: #79
+#83 := [nnf-pos #81]: #82
+#69 := [asserted]: #14
+#84 := [mp~ #69 #83]: #14
+#176 := [mp #84 #175]: #171
+#221 := (not #171)
+#222 := (or #221 #215)
+#223 := [quant-inst #40 #41 #42]: #222
+#224 := [unit-resolution #223 #176]: #215
+#228 := (= #45 #44)
+#46 := (= #44 #45)
+#47 := (not #46)
 #48 := (not #47)
-#49 := (not #48)
-#97 := (iff #49 #47)
-#98 := [rewrite]: #97
-#96 := [asserted]: #49
-#101 := [mp #96 #98]: #47
-#267 := [symm #101]: #266
-#269 := [trans #267 #265]: #268
-#271 := [symm #269]: #270
-#273 := [trans #271 #264]: #272
-[mp #273 #275]: false
-unsat
-15c9277532b8568c83e5c995d560820e0bd7af1d 73 0
+#76 := (iff #48 #46)
+#77 := [rewrite]: #76
+#75 := [asserted]: #48
+#80 := [mp #75 #77]: #46
+#229 := [symm #80]: #228
+#231 := [trans #229 #224]: #230
+#233 := [symm #231]: #232
+#235 := [trans #233 #220]: #234
+[mp #235 #237]: false
+unsat
+d9a22c09a63e8097c5f432c6c4b67fcedd7364dd 73 0
 #2 := false
 decl f7 :: (-> Int Int S3 S5)
 decl f15 :: S3
-#50 := f15
-#49 := 4::Int
-#12 := 5::Int
-#53 := (f7 5::Int 4::Int f15)
+#49 := f15
+#48 := 4::Int
+#11 := 5::Int
+#52 := (f7 5::Int 4::Int f15)
 decl f11 :: (-> S2 S5 S5)
-#48 := 3::Int
-#51 := (f7 3::Int 4::Int f15)
-decl f4 :: S2
-#8 := f4
-#52 := (f11 f4 #51)
-#54 := (= #52 #53)
-decl f3 :: (-> S2 Int Int)
-#307 := (f3 f4 3::Int)
-#308 := (f7 #307 4::Int f15)
-#346 := (= #308 #53)
-#344 := (= #53 #308)
-#338 := (= 5::Int #307)
-#336 := (= #307 5::Int)
-#9 := (:var 0 Int)
-#10 := (f3 f4 #9)
-#11 := (pattern #10)
-#13 := (= #10 5::Int)
-#14 := (forall (vars (?v0 Int)) (:pat #11) #13)
-#107 := (~ #14 #14)
-#105 := (~ #13 #13)
-#106 := [refl]: #105
-#108 := [nnf-pos #106]: #107
-#75 := [asserted]: #14
-#109 := [mp~ #75 #108]: #14
-#339 := (not #14)
-#340 := (or #339 #336)
-#341 := [quant-inst #48]: #340
-#337 := [unit-resolution #341 #109]: #336
-#342 := [symm #337]: #338
-#345 := [monotonicity #342]: #344
-#347 := [symm #345]: #346
-#309 := (= #52 #308)
-#18 := (:var 0 S3)
-#17 := (:var 1 Int)
-#16 := (:var 2 Int)
-#31 := (:var 3 S2)
-#33 := (f3 #31 #16)
-#34 := (f7 #33 #17 #18)
-#217 := (pattern #34)
-#19 := (f7 #16 #17 #18)
-#32 := (f11 #31 #19)
-#216 := (pattern #32)
-#35 := (= #32 #34)
-#218 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #216 #217) #35)
-#36 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #35)
-#221 := (iff #36 #218)
-#219 := (iff #35 #35)
-#220 := [refl]: #219
-#222 := [quant-intro #220]: #221
-#127 := (~ #36 #36)
-#125 := (~ #35 #35)
-#126 := [refl]: #125
-#128 := [nnf-pos #126]: #127
-#99 := [asserted]: #36
-#129 := [mp~ #99 #128]: #36
-#223 := [mp #129 #222]: #218
-#312 := (not #218)
-#313 := (or #312 #309)
-#314 := [quant-inst #8 #48 #49 #50]: #313
-#343 := [unit-resolution #314 #223]: #309
-#348 := [trans #343 #347]: #54
-#55 := (not #54)
-#103 := [asserted]: #55
-[unit-resolution #103 #348]: false
-unsat
-bb9eadf9d93fa155523290e9092e7b607f0bce77 73 0
+#47 := 3::Int
+#50 := (f7 3::Int 4::Int f15)
+decl f4 :: S2
+#7 := f4
+#51 := (f11 f4 #50)
+#53 := (= #51 #52)
+decl f3 :: (-> S2 Int Int)
+#248 := (f3 f4 3::Int)
+#249 := (f7 #248 4::Int f15)
+#278 := (= #249 #52)
+#276 := (= #52 #249)
+#270 := (= 5::Int #248)
+#266 := (= #248 5::Int)
+#8 := (:var 0 Int)
+#9 := (f3 f4 #8)
+#10 := (pattern #9)
+#12 := (= #9 5::Int)
+#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
+#86 := (~ #13 #13)
+#84 := (~ #12 #12)
+#85 := [refl]: #84
+#87 := [nnf-pos #85]: #86
+#75 := [asserted]: #13
+#88 := [mp~ #75 #87]: #13
+#271 := (not #13)
+#272 := (or #271 #266)
+#273 := [quant-inst #47]: #272
+#267 := [unit-resolution #273 #88]: #266
+#274 := [symm #267]: #270
+#277 := [monotonicity #274]: #276
+#279 := [symm #277]: #278
+#252 := (= #51 #249)
+#17 := (:var 0 S3)
+#16 := (:var 1 Int)
+#15 := (:var 2 Int)
+#30 := (:var 3 S2)
+#32 := (f3 #30 #15)
+#33 := (f7 #32 #16 #17)
+#198 := (pattern #33)
+#18 := (f7 #15 #16 #17)
+#31 := (f11 #30 #18)
+#197 := (pattern #31)
+#34 := (= #31 #33)
+#199 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #197 #198) #34)
+#35 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #34)
+#202 := (iff #35 #199)
+#200 := (iff #34 #34)
+#201 := [refl]: #200
+#203 := [quant-intro #201]: #202
+#106 := (~ #35 #35)
+#104 := (~ #34 #34)
+#105 := [refl]: #104
+#107 := [nnf-pos #105]: #106
+#79 := [asserted]: #35
+#108 := [mp~ #79 #107]: #35
+#204 := [mp #108 #203]: #199
+#255 := (not #199)
+#256 := (or #255 #252)
+#257 := [quant-inst #7 #47 #48 #49]: #256
+#275 := [unit-resolution #257 #204]: #252
+#280 := [trans #275 #279]: #53
+#54 := (not #53)
+#82 := [asserted]: #54
+[unit-resolution #82 #280]: false
+unsat
+e70e3b07d4ab1c8f521998d618c1a33076aeafc7 73 0
 #2 := false
 decl f7 :: (-> Int Int S3 S5)
 decl f15 :: S3
-#50 := f15
-#12 := 6::Int
-#48 := 3::Int
-#53 := (f7 3::Int 6::Int f15)
+#49 := f15
+#11 := 6::Int
+#47 := 3::Int
+#52 := (f7 3::Int 6::Int f15)
 decl f12 :: (-> S2 S5 S5)
-#49 := 4::Int
-#51 := (f7 3::Int 4::Int f15)
-decl f4 :: S2
-#8 := f4
-#52 := (f12 f4 #51)
-#54 := (= #52 #53)
-decl f3 :: (-> S2 Int Int)
-#307 := (f3 f4 4::Int)
-#308 := (f7 3::Int #307 f15)
-#346 := (= #308 #53)
-#344 := (= #53 #308)
-#338 := (= 6::Int #307)
-#334 := (= #307 6::Int)
-#9 := (:var 0 Int)
-#10 := (f3 f4 #9)
-#11 := (pattern #10)
-#13 := (= #10 6::Int)
-#14 := (forall (vars (?v0 Int)) (:pat #11) #13)
-#107 := (~ #14 #14)
-#105 := (~ #13 #13)
-#106 := [refl]: #105
-#108 := [nnf-pos #106]: #107
-#75 := [asserted]: #14
-#109 := [mp~ #75 #108]: #14
-#339 := (not #14)
-#340 := (or #339 #334)
-#341 := [quant-inst #49]: #340
-#335 := [unit-resolution #341 #109]: #334
-#342 := [symm #335]: #338
-#345 := [monotonicity #342]: #344
-#347 := [symm #345]: #346
-#309 := (= #52 #308)
-#18 := (:var 0 S3)
-#17 := (:var 1 Int)
-#31 := (:var 3 S2)
-#38 := (f3 #31 #17)
-#16 := (:var 2 Int)
-#39 := (f7 #16 #38 #18)
-#225 := (pattern #39)
-#19 := (f7 #16 #17 #18)
-#37 := (f12 #31 #19)
-#224 := (pattern #37)
-#40 := (= #37 #39)
-#226 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #224 #225) #40)
-#41 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #40)
-#229 := (iff #41 #226)
-#227 := (iff #40 #40)
-#228 := [refl]: #227
-#230 := [quant-intro #228]: #229
-#132 := (~ #41 #41)
-#130 := (~ #40 #40)
-#131 := [refl]: #130
-#133 := [nnf-pos #131]: #132
-#100 := [asserted]: #41
-#134 := [mp~ #100 #133]: #41
-#231 := [mp #134 #230]: #226
-#312 := (not #226)
-#313 := (or #312 #309)
-#314 := [quant-inst #8 #48 #49 #50]: #313
-#343 := [unit-resolution #314 #231]: #309
-#348 := [trans #343 #347]: #54
-#55 := (not #54)
-#103 := [asserted]: #55
-[unit-resolution #103 #348]: false
-unsat
-0e39c98938b4c0b9a0624f3b129bbe0a5c7f3e88 213 0
-#2 := false
+#48 := 4::Int
+#50 := (f7 3::Int 4::Int f15)
+decl f4 :: S2
+#7 := f4
+#51 := (f12 f4 #50)
+#53 := (= #51 #52)
+decl f3 :: (-> S2 Int Int)
+#249 := (f3 f4 4::Int)
+#250 := (f7 3::Int #249 f15)
+#279 := (= #250 #52)
+#277 := (= #52 #250)
+#271 := (= 6::Int #249)
+#267 := (= #249 6::Int)
+#8 := (:var 0 Int)
+#9 := (f3 f4 #8)
+#10 := (pattern #9)
+#12 := (= #9 6::Int)
+#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
+#86 := (~ #13 #13)
+#84 := (~ #12 #12)
+#85 := [refl]: #84
+#87 := [nnf-pos #85]: #86
+#75 := [asserted]: #13
+#88 := [mp~ #75 #87]: #13
+#272 := (not #13)
+#273 := (or #272 #267)
+#274 := [quant-inst #48]: #273
+#268 := [unit-resolution #274 #88]: #267
+#275 := [symm #268]: #271
+#278 := [monotonicity #275]: #277
+#280 := [symm #278]: #279
+#253 := (= #51 #250)
+#17 := (:var 0 S3)
+#16 := (:var 1 Int)
+#30 := (:var 3 S2)
+#37 := (f3 #30 #16)
+#15 := (:var 2 Int)
+#38 := (f7 #15 #37 #17)
+#207 := (pattern #38)
+#18 := (f7 #15 #16 #17)
+#36 := (f12 #30 #18)
+#206 := (pattern #36)
+#39 := (= #36 #38)
+#208 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #206 #207) #39)
+#40 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #39)
+#211 := (iff #40 #208)
+#209 := (iff #39 #39)
+#210 := [refl]: #209
+#212 := [quant-intro #210]: #211
+#111 := (~ #40 #40)
+#109 := (~ #39 #39)
+#110 := [refl]: #109
+#112 := [nnf-pos #110]: #111
+#80 := [asserted]: #40
+#113 := [mp~ #80 #112]: #40
+#213 := [mp #113 #212]: #208
+#256 := (not #208)
+#257 := (or #256 #253)
+#258 := [quant-inst #7 #47 #48 #49]: #257
+#276 := [unit-resolution #258 #213]: #253
+#281 := [trans #276 #280]: #53
+#54 := (not #53)
+#82 := [asserted]: #54
+[unit-resolution #82 #281]: false
+unsat
+3f33aa966a616642cb71cfd28f64104ffe222a76 141 0
+#2 := false
+decl f16 :: S5
+#53 := f16
 decl f13 :: (-> S2 S5 S5)
 decl f12 :: (-> S2 S5 S5)
-decl f16 :: S5
-#54 := f16
 decl f5 :: S2
-#15 := f5
-#58 := (f12 f5 f16)
-decl f4 :: S2
-#8 := f4
-#59 := (f13 f4 #58)
-#112 := (= f16 #59)
+#14 := f5
+#57 := (f12 f5 f16)
+decl f4 :: S2
+#7 := f4
+#58 := (f13 f4 #57)
+#59 := (= #58 f16)
 decl f8 :: (-> Int Int S3 S5)
-decl f10 :: (-> S6 S5 S3)
 decl f17 :: S3
-#55 := f17
-#12 := 4::Int
-#18 := 3::Int
-#56 := (f8 3::Int 4::Int f17)
-decl f11 :: S6
-#33 := f11
-#289 := (f10 f11 #56)
-decl f3 :: (-> S2 Int Int)
-#272 := (f3 f5 3::Int)
-#324 := (f8 #272 4::Int #289)
-#353 := (f13 f4 #324)
-#434 := (= #353 #59)
-#427 := (= #59 #353)
-#425 := (= #58 #324)
-#273 := (f8 #272 4::Int f17)
-#421 := (= #273 #324)
-#418 := (= #324 #273)
-#407 := (= #289 f17)
-#290 := (= f17 #289)
-#24 := (:var 0 S3)
-#23 := (:var 1 Int)
-#22 := (:var 2 Int)
-#25 := (f8 #22 #23 #24)
-#229 := (pattern #25)
-#34 := (f10 f11 #25)
-#100 := (= #24 #34)
-#242 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) (:pat #229) #100)
-#104 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #100)
-#245 := (iff #104 #242)
-#243 := (iff #100 #100)
-#244 := [refl]: #243
-#246 := [quant-intro #244]: #245
-#154 := (~ #104 #104)
-#152 := (~ #100 #100)
-#153 := [refl]: #152
-#155 := [nnf-pos #153]: #154
-#35 := (= #34 #24)
-#36 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #35)
-#105 := (iff #36 #104)
-#102 := (iff #35 #100)
-#103 := [rewrite]: #102
-#106 := [quant-intro #103]: #105
-#99 := [asserted]: #36
-#109 := [mp #99 #106]: #104
-#156 := [mp~ #109 #155]: #104
-#247 := [mp #156 #246]: #242
-#293 := (not #242)
+#54 := f17
+#11 := 4::Int
+#17 := 3::Int
+#55 := (f8 3::Int 4::Int f17)
+#327 := (= #55 f16)
+#56 := (= f16 #55)
+#91 := (not #56)
+#92 := (or #91 #59)
+#95 := (not #92)
+#60 := (implies #56 #59)
+#61 := (not #60)
+#96 := (iff #61 #95)
+#93 := (iff #60 #92)
+#94 := [rewrite]: #93
+#97 := [monotonicity #94]: #96
+#90 := [asserted]: #61
+#100 := [mp #90 #97]: #95
+#98 := [not-or-elim #100]: #56
+#328 := [symm #98]: #327
+#331 := (= #58 #55)
+decl f3 :: (-> S2 Int Int)
+#285 := (f3 f4 4::Int)
+#247 := (f3 f5 3::Int)
+#289 := (f8 #247 #285 f17)
+#325 := (= #289 #55)
+#309 := (= #285 4::Int)
+#8 := (:var 0 Int)
+#9 := (f3 f4 #8)
+#10 := (pattern #9)
+#12 := (= #9 4::Int)
+#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
+#105 := (~ #13 #13)
+#103 := (~ #12 #12)
+#104 := [refl]: #103
+#106 := [nnf-pos #104]: #105
+#82 := [asserted]: #13
+#107 := [mp~ #82 #106]: #13
+#314 := (not #13)
+#315 := (or #314 #309)
+#316 := [quant-inst #11]: #315
+#310 := [unit-resolution #316 #107]: #309
+#281 := (= #247 3::Int)
+#15 := (f3 f5 #8)
+#16 := (pattern #15)
+#18 := (= #15 3::Int)
+#19 := (forall (vars (?v0 Int)) (:pat #16) #18)
+#110 := (~ #19 #19)
+#108 := (~ #18 #18)
+#109 := [refl]: #108
+#111 := [nnf-pos #109]: #110
+#83 := [asserted]: #19
+#112 := [mp~ #83 #111]: #19
+#286 := (not #19)
+#287 := (or #286 #281)
+#288 := [quant-inst #17]: #287
+#313 := [unit-resolution #288 #112]: #281
+#326 := [monotonicity #313 #310]: #325
+#329 := (= #58 #289)
+#248 := (f8 #247 4::Int f17)
+#282 := (f13 f4 #248)
+#290 := (= #282 #289)
+#23 := (:var 0 S3)
+#22 := (:var 1 Int)
+#36 := (:var 3 S2)
+#43 := (f3 #36 #22)
+#21 := (:var 2 Int)
+#44 := (f8 #21 #43 #23)
+#231 := (pattern #44)
+#24 := (f8 #21 #22 #23)
+#42 := (f13 #36 #24)
+#230 := (pattern #42)
+#45 := (= #42 #44)
+#232 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #230 #231) #45)
+#46 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #45)
+#235 := (iff #46 #232)
+#233 := (iff #45 #45)
+#234 := [refl]: #233
+#236 := [quant-intro #234]: #235
+#135 := (~ #46 #46)
+#133 := (~ #45 #45)
+#134 := [refl]: #133
+#136 := [nnf-pos #134]: #135
+#88 := [asserted]: #46
+#137 := [mp~ #88 #136]: #46
+#237 := [mp #137 #236]: #232
+#293 := (not #232)
 #294 := (or #293 #290)
-#295 := [quant-inst #18 #12 #55]: #294
-#404 := [unit-resolution #295 #247]: #290
-#411 := [symm #404]: #407
-#419 := [monotonicity #411]: #418
-#422 := [symm #419]: #421
-#423 := (= #58 #273)
-#274 := (f12 f5 #56)
-#275 := (= #274 #273)
-#276 := (= #273 #274)
-#37 := (:var 3 S2)
-#39 := (f3 #37 #22)
-#40 := (f8 #39 #23 #24)
-#249 := (pattern #40)
-#38 := (f12 #37 #25)
-#248 := (pattern #38)
-#41 := (= #38 #40)
-#250 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #248 #249) #41)
-#42 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #41)
-#253 := (iff #42 #250)
-#251 := (iff #41 #41)
-#252 := [refl]: #251
-#254 := [quant-intro #252]: #253
-#159 := (~ #42 #42)
-#157 := (~ #41 #41)
-#158 := [refl]: #157
-#160 := [nnf-pos #158]: #159
-#107 := [asserted]: #42
-#161 := [mp~ #107 #160]: #42
-#255 := [mp #161 #254]: #250
-#279 := (not #250)
-#280 := (or #279 #276)
-#281 := (or #279 #275)
-#283 := (iff #281 #280)
-#285 := (iff #280 #280)
-#286 := [rewrite]: #285
-#277 := (iff #275 #276)
-#278 := [rewrite]: #277
-#284 := [monotonicity #278]: #283
-#287 := [trans #284 #286]: #283
-#282 := [quant-inst #15 #18 #12 #55]: #281
-#288 := [mp #282 #287]: #280
-#415 := [unit-resolution #288 #255]: #276
-#420 := [symm #415]: #275
-#416 := (= #58 #274)
-#57 := (= f16 #56)
-#118 := (not #57)
-#119 := (or #118 #112)
-#124 := (not #119)
-#60 := (= #59 f16)
-#61 := (implies #57 #60)
-#62 := (not #61)
-#125 := (iff #62 #124)
-#122 := (iff #61 #119)
-#115 := (implies #57 #112)
-#120 := (iff #115 #119)
-#121 := [rewrite]: #120
-#116 := (iff #61 #115)
-#113 := (iff #60 #112)
+#295 := [quant-inst #7 #247 #11 #54]: #294
+#317 := [unit-resolution #295 #237]: #290
+#323 := (= #58 #282)
+#321 := (= #57 #248)
+#246 := (f12 f5 #55)
+#252 := (= #246 #248)
+#38 := (f3 #36 #21)
+#39 := (f8 #38 #22 #23)
+#223 := (pattern #39)
+#37 := (f12 #36 #24)
+#222 := (pattern #37)
+#40 := (= #37 #39)
+#224 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #222 #223) #40)
+#41 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #40)
+#227 := (iff #41 #224)
+#225 := (iff #40 #40)
+#226 := [refl]: #225
+#228 := [quant-intro #226]: #227
+#130 := (~ #41 #41)
+#128 := (~ #40 #40)
+#129 := [refl]: #128
+#131 := [nnf-pos #129]: #130
+#87 := [asserted]: #41
+#132 := [mp~ #87 #131]: #41
+#229 := [mp #132 #228]: #224
+#255 := (not #224)
+#256 := (or #255 #252)
+#257 := [quant-inst #14 #17 #11 #54]: #256
+#318 := [unit-resolution #257 #229]: #252
+#319 := (= #57 #246)
+#320 := [monotonicity #98]: #319
+#322 := [trans #320 #318]: #321
+#324 := [monotonicity #322]: #323
+#330 := [trans #324 #317]: #329
+#332 := [trans #330 #326]: #331
+#333 := [trans #332 #328]: #59
+#99 := (not #59)
+#101 := [not-or-elim #100]: #99
+[unit-resolution #101 #333]: false
+unsat
+a3dcd98b917fc07cd53b4a7609efe76d08dc0731 141 0
+#2 := false
+decl f16 :: S5
+#53 := f16
+decl f12 :: (-> S2 S5 S5)
+decl f13 :: (-> S2 S5 S5)
+decl f4 :: S2
+#7 := f4
+#57 := (f13 f4 f16)
+decl f5 :: S2
+#14 := f5
+#58 := (f12 f5 #57)
+#59 := (= #58 f16)
+decl f8 :: (-> Int Int S3 S5)
+decl f17 :: S3
+#54 := f17
+#11 := 4::Int
+#17 := 3::Int
+#55 := (f8 3::Int 4::Int f17)
+#327 := (= #55 f16)
+#56 := (= f16 #55)
+#91 := (not #56)
+#92 := (or #91 #59)
+#95 := (not #92)
+#60 := (implies #56 #59)
+#61 := (not #60)
+#96 := (iff #61 #95)
+#93 := (iff #60 #92)
+#94 := [rewrite]: #93
+#97 := [monotonicity #94]: #96
+#90 := [asserted]: #61
+#100 := [mp #90 #97]: #95
+#98 := [not-or-elim #100]: #56
+#328 := [symm #98]: #327
+#331 := (= #58 #55)
+decl f3 :: (-> S2 Int Int)
+#247 := (f3 f4 4::Int)
+#285 := (f3 f5 3::Int)
+#289 := (f8 #285 #247 f17)
+#325 := (= #289 #55)
+#281 := (= #247 4::Int)
+#8 := (:var 0 Int)
+#9 := (f3 f4 #8)
+#10 := (pattern #9)
+#12 := (= #9 4::Int)
+#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
+#105 := (~ #13 #13)
+#103 := (~ #12 #12)
+#104 := [refl]: #103
+#106 := [nnf-pos #104]: #105
+#82 := [asserted]: #13
+#107 := [mp~ #82 #106]: #13
+#286 := (not #13)
+#287 := (or #286 #281)
+#288 := [quant-inst #11]: #287
+#310 := [unit-resolution #288 #107]: #281
+#309 := (= #285 3::Int)
+#15 := (f3 f5 #8)
+#16 := (pattern #15)
+#18 := (= #15 3::Int)
+#19 := (forall (vars (?v0 Int)) (:pat #16) #18)
+#110 := (~ #19 #19)
+#108 := (~ #18 #18)
+#109 := [refl]: #108
+#111 := [nnf-pos #109]: #110
+#83 := [asserted]: #19
+#112 := [mp~ #83 #111]: #19
+#314 := (not #19)
+#315 := (or #314 #309)
+#316 := [quant-inst #17]: #315
+#313 := [unit-resolution #316 #112]: #309
+#326 := [monotonicity #313 #310]: #325
+#329 := (= #58 #289)
+#248 := (f8 3::Int #247 f17)
+#282 := (f12 f5 #248)
+#290 := (= #282 #289)
+#23 := (:var 0 S3)
+#22 := (:var 1 Int)
+#21 := (:var 2 Int)
+#36 := (:var 3 S2)
+#38 := (f3 #36 #21)
+#39 := (f8 #38 #22 #23)
+#223 := (pattern #39)
+#24 := (f8 #21 #22 #23)
+#37 := (f12 #36 #24)
+#222 := (pattern #37)
+#40 := (= #37 #39)
+#224 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #222 #223) #40)
+#41 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #40)
+#227 := (iff #41 #224)
+#225 := (iff #40 #40)
+#226 := [refl]: #225
+#228 := [quant-intro #226]: #227
+#130 := (~ #41 #41)
+#128 := (~ #40 #40)
+#129 := [refl]: #128
+#131 := [nnf-pos #129]: #130
+#87 := [asserted]: #41
+#132 := [mp~ #87 #131]: #41
+#229 := [mp #132 #228]: #224
+#293 := (not #224)
+#294 := (or #293 #290)
+#295 := [quant-inst #14 #17 #247 #54]: #294
+#317 := [unit-resolution #295 #229]: #290
+#323 := (= #58 #282)
+#321 := (= #57 #248)
+#246 := (f13 f4 #55)
+#252 := (= #246 #248)
+#43 := (f3 #36 #22)
+#44 := (f8 #21 #43 #23)
+#231 := (pattern #44)
+#42 := (f13 #36 #24)
+#230 := (pattern #42)
+#45 := (= #42 #44)
+#232 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #230 #231) #45)
+#46 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #45)
+#235 := (iff #46 #232)
+#233 := (iff #45 #45)
+#234 := [refl]: #233
+#236 := [quant-intro #234]: #235
+#135 := (~ #46 #46)
+#133 := (~ #45 #45)
+#134 := [refl]: #133
+#136 := [nnf-pos #134]: #135
+#88 := [asserted]: #46
+#137 := [mp~ #88 #136]: #46
+#237 := [mp #137 #236]: #232
+#255 := (not #232)
+#256 := (or #255 #252)
+#257 := [quant-inst #7 #17 #11 #54]: #256
+#318 := [unit-resolution #257 #237]: #252
+#319 := (= #57 #246)
+#320 := [monotonicity #98]: #319
+#322 := [trans #320 #318]: #321
+#324 := [monotonicity #322]: #323
+#330 := [trans #324 #317]: #329
+#332 := [trans #330 #326]: #331
+#333 := [trans #332 #328]: #59
+#99 := (not #59)
+#101 := [not-or-elim #100]: #99
+[unit-resolution #101 #333]: false
+unsat
+37255a122064839766be2ce2cd0dc79437aeda41 29 0
+#2 := false
+decl f3 :: (-> S3 S4 Int)
+decl f26 :: S4
+#73 := f26
+decl f4 :: S3
+#7 := f4
+#76 := (f3 f4 f26)
+decl f25 :: S4
+#72 := f25
+#75 := (f3 f4 f25)
+#77 := (= #75 #76)
+#74 := (= f25 f26)
+#111 := (not #74)
+#112 := (or #111 #77)
+#115 := (not #112)
+#78 := (implies #74 #77)
+#79 := (not #78)
+#116 := (iff #79 #115)
+#113 := (iff #78 #112)
 #114 := [rewrite]: #113
 #117 := [monotonicity #114]: #116
-#123 := [trans #117 #121]: #122
-#126 := [monotonicity #123]: #125
-#111 := [asserted]: #62
-#129 := [mp #111 #126]: #124
-#127 := [not-or-elim #129]: #57
-#417 := [monotonicity #127]: #416
-#424 := [trans #417 #420]: #423
-#426 := [trans #424 #422]: #425
-#428 := [monotonicity #426]: #427
-#435 := [symm #428]: #434
-#438 := (= f16 #353)
-#348 := (f3 f4 4::Int)
-#349 := (f8 #272 #348 #289)
-#355 := (= #349 #353)
-#44 := (f3 #37 #23)
-#45 := (f8 #22 #44 #24)
-#257 := (pattern #45)
-#43 := (f13 #37 #25)
-#256 := (pattern #43)
-#46 := (= #43 #45)
-#258 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #256 #257) #46)
-#47 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #46)
-#261 := (iff #47 #258)
-#259 := (iff #46 #46)
-#260 := [refl]: #259
-#262 := [quant-intro #260]: #261
-#164 := (~ #47 #47)
-#162 := (~ #46 #46)
-#163 := [refl]: #162
-#165 := [nnf-pos #163]: #164
-#108 := [asserted]: #47
-#166 := [mp~ #108 #165]: #47
-#263 := [mp #166 #262]: #258
-#358 := (not #258)
-#359 := (or #358 #355)
-#354 := (= #353 #349)
-#360 := (or #358 #354)
-#362 := (iff #360 #359)
-#364 := (iff #359 #359)
-#365 := [rewrite]: #364
-#356 := (iff #354 #355)
-#357 := [rewrite]: #356
-#363 := [monotonicity #357]: #362
-#366 := [trans #363 #365]: #362
-#361 := [quant-inst #8 #272 #12 #289]: #360
-#367 := [mp #361 #366]: #359
-#414 := [unit-resolution #367 #263]: #355
-#436 := (= f16 #349)
-#432 := (= #56 #349)
-#430 := (= #349 #56)
-#403 := (= #348 4::Int)
-#9 := (:var 0 Int)
-#10 := (f3 f4 #9)
-#11 := (pattern #10)
-#13 := (= #10 4::Int)
-#14 := (forall (vars (?v0 Int)) (:pat #11) #13)
-#134 := (~ #14 #14)
-#132 := (~ #13 #13)
-#133 := [refl]: #132
-#135 := [nnf-pos #133]: #134
-#82 := [asserted]: #14
-#136 := [mp~ #82 #135]: #14
-#408 := (not #14)
-#409 := (or #408 #403)
-#410 := [quant-inst #12]: #409
-#412 := [unit-resolution #410 #136]: #403
-#347 := (= #272 3::Int)
-#16 := (f3 f5 #9)
-#17 := (pattern #16)
-#19 := (= #16 3::Int)
-#20 := (forall (vars (?v0 Int)) (:pat #17) #19)
-#139 := (~ #20 #20)
-#137 := (~ #19 #19)
-#138 := [refl]: #137
-#140 := [nnf-pos #138]: #139
-#83 := [asserted]: #20
-#141 := [mp~ #83 #140]: #20
-#350 := (not #20)
-#351 := (or #350 #347)
-#352 := [quant-inst #18]: #351
-#413 := [unit-resolution #352 #141]: #347
-#431 := [monotonicity #413 #412 #411]: #430
-#433 := [symm #431]: #432
-#437 := [trans #127 #433]: #436
-#439 := [trans #437 #414]: #438
-#440 := [trans #439 #435]: #112
-#128 := (not #112)
-#130 := [not-or-elim #129]: #128
-[unit-resolution #130 #440]: false
-unsat
-17df18da62b62fdb663a9f6fa37f20487dad9832 213 0
-#2 := false
-decl f12 :: (-> S2 S5 S5)
-decl f13 :: (-> S2 S5 S5)
-decl f16 :: S5
-#54 := f16
-decl f4 :: S2
-#8 := f4
-#58 := (f13 f4 f16)
-decl f5 :: S2
-#15 := f5
-#59 := (f12 f5 #58)
-#112 := (= f16 #59)
-decl f8 :: (-> Int Int S3 S5)
-decl f10 :: (-> S6 S5 S3)
-decl f17 :: S3
-#55 := f17
-#12 := 4::Int
-#18 := 3::Int
-#56 := (f8 3::Int 4::Int f17)
-decl f11 :: S6
-#33 := f11
-#289 := (f10 f11 #56)
-decl f3 :: (-> S2 Int Int)
-#272 := (f3 f4 4::Int)
-#324 := (f8 3::Int #272 #289)
-#353 := (f12 f5 #324)
-#434 := (= #353 #59)
-#427 := (= #59 #353)
-#425 := (= #58 #324)
-#273 := (f8 3::Int #272 f17)
-#421 := (= #273 #324)
-#418 := (= #324 #273)
-#407 := (= #289 f17)
-#290 := (= f17 #289)
-#24 := (:var 0 S3)
-#23 := (:var 1 Int)
-#22 := (:var 2 Int)
-#25 := (f8 #22 #23 #24)
-#229 := (pattern #25)
-#34 := (f10 f11 #25)
-#100 := (= #24 #34)
-#242 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) (:pat #229) #100)
-#104 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #100)
-#245 := (iff #104 #242)
-#243 := (iff #100 #100)
-#244 := [refl]: #243
-#246 := [quant-intro #244]: #245
-#154 := (~ #104 #104)
-#152 := (~ #100 #100)
-#153 := [refl]: #152
-#155 := [nnf-pos #153]: #154
-#35 := (= #34 #24)
-#36 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #35)
-#105 := (iff #36 #104)
-#102 := (iff #35 #100)
-#103 := [rewrite]: #102
-#106 := [quant-intro #103]: #105
-#99 := [asserted]: #36
-#109 := [mp #99 #106]: #104
-#156 := [mp~ #109 #155]: #104
-#247 := [mp #156 #246]: #242
-#293 := (not #242)
-#294 := (or #293 #290)
-#295 := [quant-inst #18 #12 #55]: #294
-#406 := [unit-resolution #295 #247]: #290
-#411 := [symm #406]: #407
-#419 := [monotonicity #411]: #418
-#422 := [symm #419]: #421
-#423 := (= #58 #273)
-#274 := (f13 f4 #56)
-#275 := (= #274 #273)
-#276 := (= #273 #274)
-#37 := (:var 3 S2)
-#44 := (f3 #37 #23)
-#45 := (f8 #22 #44 #24)
-#257 := (pattern #45)
-#43 := (f13 #37 #25)
-#256 := (pattern #43)
-#46 := (= #43 #45)
-#258 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #256 #257) #46)
-#47 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #46)
-#261 := (iff #47 #258)
-#259 := (iff #46 #46)
-#260 := [refl]: #259
-#262 := [quant-intro #260]: #261
-#164 := (~ #47 #47)
-#162 := (~ #46 #46)
-#163 := [refl]: #162
-#165 := [nnf-pos #163]: #164
-#108 := [asserted]: #47
-#166 := [mp~ #108 #165]: #47
-#263 := [mp #166 #262]: #258
-#279 := (not #258)
-#280 := (or #279 #276)
-#281 := (or #279 #275)
-#283 := (iff #281 #280)
-#285 := (iff #280 #280)
-#286 := [rewrite]: #285
-#277 := (iff #275 #276)
-#278 := [rewrite]: #277
-#284 := [monotonicity #278]: #283
-#287 := [trans #284 #286]: #283
-#282 := [quant-inst #8 #18 #12 #55]: #281
-#288 := [mp #282 #287]: #280
-#415 := [unit-resolution #288 #263]: #276
-#420 := [symm #415]: #275
-#416 := (= #58 #274)
-#57 := (= f16 #56)
-#118 := (not #57)
-#119 := (or #118 #112)
-#124 := (not #119)
-#60 := (= #59 f16)
-#61 := (implies #57 #60)
-#62 := (not #61)
-#125 := (iff #62 #124)
-#122 := (iff #61 #119)
-#115 := (implies #57 #112)
-#120 := (iff #115 #119)
-#121 := [rewrite]: #120
-#116 := (iff #61 #115)
-#113 := (iff #60 #112)
+#110 := [asserted]: #79
+#120 := [mp #110 #117]: #115
+#118 := [not-or-elim #120]: #74
+#318 := [monotonicity #118]: #77
+#119 := (not #77)
+#121 := [not-or-elim #120]: #119
+[unit-resolution #121 #318]: false
+unsat
+f90472be23afe3d7903dfeef3cf374fc3fbde35e 29 0
+#2 := false
+decl f3 :: (-> S3 S4 Int)
+decl f26 :: S4
+#73 := f26
+decl f6 :: S3
+#15 := f6
+#76 := (f3 f6 f26)
+decl f25 :: S4
+#72 := f25
+#75 := (f3 f6 f25)
+#77 := (= #75 #76)
+#74 := (= f25 f26)
+#111 := (not #74)
+#112 := (or #111 #77)
+#115 := (not #112)
+#78 := (implies #74 #77)
+#79 := (not #78)
+#116 := (iff #79 #115)
+#113 := (iff #78 #112)
 #114 := [rewrite]: #113
 #117 := [monotonicity #114]: #116
-#123 := [trans #117 #121]: #122
-#126 := [monotonicity #123]: #125
-#111 := [asserted]: #62
-#129 := [mp #111 #126]: #124
-#127 := [not-or-elim #129]: #57
-#417 := [monotonicity #127]: #416
-#424 := [trans #417 #420]: #423
-#426 := [trans #424 #422]: #425
-#428 := [monotonicity #426]: #427
-#435 := [symm #428]: #434
-#438 := (= f16 #353)
-#346 := (f3 f5 3::Int)
-#349 := (f8 #346 #272 #289)
-#355 := (= #349 #353)
-#39 := (f3 #37 #22)
-#40 := (f8 #39 #23 #24)
-#249 := (pattern #40)
-#38 := (f12 #37 #25)
-#248 := (pattern #38)
-#41 := (= #38 #40)
-#250 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #248 #249) #41)
-#42 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #41)
-#253 := (iff #42 #250)
-#251 := (iff #41 #41)
-#252 := [refl]: #251
-#254 := [quant-intro #252]: #253
-#159 := (~ #42 #42)
-#157 := (~ #41 #41)
-#158 := [refl]: #157
-#160 := [nnf-pos #158]: #159
-#107 := [asserted]: #42
-#161 := [mp~ #107 #160]: #42
-#255 := [mp #161 #254]: #250
-#358 := (not #250)
-#359 := (or #358 #355)
-#354 := (= #353 #349)
-#360 := (or #358 #354)
-#362 := (iff #360 #359)
-#364 := (iff #359 #359)
-#365 := [rewrite]: #364
-#356 := (iff #354 #355)
-#357 := [rewrite]: #356
-#363 := [monotonicity #357]: #362
-#366 := [trans #363 #365]: #362
-#361 := [quant-inst #15 #18 #272 #289]: #360
-#367 := [mp #361 #366]: #359
-#414 := [unit-resolution #367 #255]: #355
-#436 := (= f16 #349)
-#432 := (= #56 #349)
-#430 := (= #349 #56)
-#345 := (= #272 4::Int)
-#9 := (:var 0 Int)
-#10 := (f3 f4 #9)
-#11 := (pattern #10)
-#13 := (= #10 4::Int)
-#14 := (forall (vars (?v0 Int)) (:pat #11) #13)
-#134 := (~ #14 #14)
-#132 := (~ #13 #13)
-#133 := [refl]: #132
-#135 := [nnf-pos #133]: #134
-#82 := [asserted]: #14
-#136 := [mp~ #82 #135]: #14
-#350 := (not #14)
-#351 := (or #350 #345)
-#352 := [quant-inst #12]: #351
-#412 := [unit-resolution #352 #136]: #345
-#405 := (= #346 3::Int)
-#16 := (f3 f5 #9)
-#17 := (pattern #16)
-#19 := (= #16 3::Int)
-#20 := (forall (vars (?v0 Int)) (:pat #17) #19)
-#139 := (~ #20 #20)
-#137 := (~ #19 #19)
-#138 := [refl]: #137
-#140 := [nnf-pos #138]: #139
-#83 := [asserted]: #20
-#141 := [mp~ #83 #140]: #20
-#408 := (not #20)
-#409 := (or #408 #405)
-#410 := [quant-inst #18]: #409
-#413 := [unit-resolution #410 #141]: #405
-#431 := [monotonicity #413 #412 #411]: #430
-#433 := [symm #431]: #432
-#437 := [trans #127 #433]: #436
-#439 := [trans #437 #414]: #438
-#440 := [trans #439 #435]: #112
-#128 := (not #112)
-#130 := [not-or-elim #129]: #128
-[unit-resolution #130 #440]: false
-unsat
-07757efd2a62a199d8cebcd5d86d76e6e1b9ee54 29 0
+#110 := [asserted]: #79
+#120 := [mp #110 #117]: #115
+#118 := [not-or-elim #120]: #74
+#318 := [monotonicity #118]: #77
+#119 := (not #77)
+#121 := [not-or-elim #120]: #119
+[unit-resolution #121 #318]: false
+unsat
+3e714d78b380e794ca732c6150fdf6770ae1c84c 61 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f14 :: (-> S9 S4 S1)
+decl f25 :: S4
+#72 := f25
+decl f15 :: S9
+#40 := f15
+#75 := (f14 f15 f25)
+#76 := (= #75 f1)
+decl f26 :: S4
+#73 := f26
+#77 := (f14 f15 f26)
+#78 := (= #77 f1)
+#643 := (iff #78 #76)
+#79 := (iff #76 #78)
+#649 := (= #75 #77)
+#74 := (= f25 f26)
+#113 := (not #74)
+#114 := (or #113 #79)
+#117 := (not #114)
+#80 := (implies #74 #79)
+#81 := (not #80)
+#118 := (iff #81 #117)
+#115 := (iff #80 #114)
+#116 := [rewrite]: #115
+#119 := [monotonicity #116]: #118
+#112 := [asserted]: #81
+#122 := [mp #112 #119]: #117
+#120 := [not-or-elim #122]: #74
+#305 := [monotonicity #120]: #649
+#436 := [monotonicity #305]: #79
+#316 := [symm #436]: #643
+#149 := (not #76)
+#325 := (not #78)
+#317 := (iff #325 #149)
+#650 := [monotonicity #316]: #317
+#311 := [hypothesis]: #325
+#651 := [mp #311 #650]: #149
+#328 := (or #76 #78)
+#150 := (iff #149 #78)
+#121 := (not #79)
+#151 := (iff #121 #150)
+#152 := [rewrite]: #151
+#123 := [not-or-elim #122]: #121
+#153 := [mp #123 #152]: #150
+#326 := (not #150)
+#330 := (or #76 #78 #326)
+#331 := [def-axiom]: #330
+#332 := [unit-resolution #331 #153]: #328
+#647 := [unit-resolution #332 #311]: #76
+#652 := [unit-resolution #647 #651]: false
+#653 := [lemma #652]: #78
+#654 := [mp #653 #316]: #76
+#318 := (or #149 #325)
+#242 := (or #149 #325 #326)
+#327 := [def-axiom]: #242
+#329 := [unit-resolution #327 #153]: #318
+#648 := [unit-resolution #329 #653]: #149
+[unit-resolution #648 #654]: false
+unsat
+c1732efb8247153476fddeec24d6e45ea69ce202 29 0
 #2 := false
 decl f3 :: (-> S3 S4 Int)
 decl f26 :: S4
 #74 := f26
 decl f4 :: S3
-#8 := f4
-#77 := (f3 f4 f26)
+#7 := f4
+#75 := (f3 f4 f26)
 decl f25 :: S4
-#73 := f25
-#76 := (f3 f4 f25)
-#78 := (= #76 #77)
-#75 := (= f25 f26)
-#152 := (not #75)
-#153 := (or #152 #78)
-#156 := (not #153)
-#79 := (implies #75 #78)
-#80 := (not #79)
-#157 := (iff #80 #156)
-#154 := (iff #79 #153)
-#155 := [rewrite]: #154
-#158 := [monotonicity #155]: #157
-#151 := [asserted]: #80
-#161 := [mp #151 #158]: #156
-#159 := [not-or-elim #161]: #75
-#355 := [monotonicity #159]: #78
-#160 := (not #78)
-#162 := [not-or-elim #161]: #160
-[unit-resolution #162 #355]: false
-unsat
-bf2376479b77b7e06a1f1c39e37ebc8c5a4223d8 29 0
+#72 := f25
+#73 := (f3 f4 f25)
+#76 := (= #73 #75)
+#78 := (= f25 f26)
+#79 := (not #78)
+#113 := (or #76 #79)
+#116 := (not #113)
+#77 := (not #76)
+#80 := (implies #77 #79)
+#81 := (not #80)
+#117 := (iff #81 #116)
+#114 := (iff #80 #113)
+#115 := [rewrite]: #114
+#118 := [monotonicity #115]: #117
+#112 := [asserted]: #81
+#121 := [mp #112 #118]: #116
+#120 := [not-or-elim #121]: #78
+#318 := [monotonicity #120]: #76
+#119 := [not-or-elim #121]: #77
+[unit-resolution #119 #318]: false
+unsat
+195808c9b73d3e779441cc672e062afbf5c02bef 29 0
 #2 := false
 decl f3 :: (-> S3 S4 Int)
 decl f26 :: S4
 #74 := f26
 decl f6 :: S3
-#16 := f6
-#77 := (f3 f6 f26)
-decl f25 :: S4
-#73 := f25
-#76 := (f3 f6 f25)
-#78 := (= #76 #77)
-#75 := (= f25 f26)
-#152 := (not #75)
-#153 := (or #152 #78)
-#156 := (not #153)
-#79 := (implies #75 #78)
-#80 := (not #79)
-#157 := (iff #80 #156)
-#154 := (iff #79 #153)
-#155 := [rewrite]: #154
-#158 := [monotonicity #155]: #157
-#151 := [asserted]: #80
-#161 := [mp #151 #158]: #156
-#159 := [not-or-elim #161]: #75
-#355 := [monotonicity #159]: #78
-#160 := (not #78)
-#162 := [not-or-elim #161]: #160
-[unit-resolution #162 #355]: false
-unsat
-a5a95b955c8bcf895cd52677159063c5777f5e11 73 0
-#2 := false
-decl f14 :: (-> S9 S4 S1)
-decl f26 :: S4
-#74 := f26
-decl f15 :: S9
-#41 := f15
-#78 := (f14 f15 f26)
-decl f1 :: S1
-#4 := f1
-#157 := (= f1 #78)
+#15 := f6
+#75 := (f3 f6 f26)
 decl f25 :: S4
-#73 := f25
-#76 := (f14 f15 f25)
-#154 := (= f1 #76)
-#160 := (iff #154 #157)
-#699 := (= #76 #78)
-#75 := (= f25 f26)
-#166 := (not #75)
-#167 := (or #166 #160)
-#172 := (not #167)
-#79 := (= #78 f1)
-#77 := (= #76 f1)
-#80 := (iff #77 #79)
-#81 := (implies #75 #80)
-#82 := (not #81)
-#173 := (iff #82 #172)
-#170 := (iff #81 #167)
-#163 := (implies #75 #160)
-#168 := (iff #163 #167)
-#169 := [rewrite]: #168
-#164 := (iff #81 #163)
-#161 := (iff #80 #160)
-#158 := (iff #79 #157)
-#159 := [rewrite]: #158
-#155 := (iff #77 #154)
-#156 := [rewrite]: #155
-#162 := [monotonicity #156 #159]: #161
-#165 := [monotonicity #162]: #164
-#171 := [trans #165 #169]: #170
-#174 := [monotonicity #171]: #173
-#153 := [asserted]: #82
-#177 := [mp #153 #174]: #172
-#175 := [not-or-elim #177]: #75
-#701 := [monotonicity #175]: #699
-#356 := [monotonicity #701]: #160
-#380 := (not #157)
-#204 := (not #154)
-#488 := (iff #204 #380)
-#695 := [monotonicity #356]: #488
-#383 := [hypothesis]: #204
-#367 := [mp #383 #695]: #380
-#378 := (or #157 #154)
-#205 := (iff #157 #204)
-#176 := (not #160)
-#206 := (iff #176 #205)
-#207 := [rewrite]: #206
-#178 := [not-or-elim #177]: #176
-#208 := [mp #178 #207]: #205
-#376 := (not #205)
-#377 := (or #157 #154 #376)
-#292 := [def-axiom]: #377
-#369 := [unit-resolution #292 #208]: #378
-#362 := [unit-resolution #369 #383]: #157
-#368 := [unit-resolution #362 #367]: false
-#702 := [lemma #368]: #154
-#704 := [mp #702 #356]: #157
-#382 := (or #380 #204)
-#381 := (or #380 #204 #376)
-#309 := [def-axiom]: #381
-#379 := [unit-resolution #309 #208]: #382
-#703 := [unit-resolution #379 #702]: #380
-[unit-resolution #703 #704]: false
-unsat
-58db43dcfcdbe4b1a883c7f66b902f003ab05dc4 29 0
-#2 := false
-decl f3 :: (-> S3 S4 Int)
+#72 := f25
+#73 := (f3 f6 f25)
+#76 := (= #73 #75)
+#78 := (= f25 f26)
+#79 := (not #78)
+#113 := (or #76 #79)
+#116 := (not #113)
+#77 := (not #76)
+#80 := (implies #77 #79)
+#81 := (not #80)
+#117 := (iff #81 #116)
+#114 := (iff #80 #113)
+#115 := [rewrite]: #114
+#118 := [monotonicity #115]: #117
+#112 := [asserted]: #81
+#121 := [mp #112 #118]: #116
+#120 := [not-or-elim #121]: #78
+#318 := [monotonicity #120]: #76
+#119 := [not-or-elim #121]: #77
+[unit-resolution #119 #318]: false
+unsat
+0ed7d8750f50d1bb9c926ffbefc40143380c759c 66 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f14 :: (-> S9 S4 S1)
+decl f25 :: S4
+#72 := f25
+decl f15 :: S9
+#40 := f15
+#73 := (f14 f15 f25)
+#74 := (= #73 f1)
 decl f26 :: S4
 #75 := f26
-decl f4 :: S3
-#8 := f4
-#76 := (f3 f4 f26)
-decl f25 :: S4
-#73 := f25
-#74 := (f3 f4 f25)
-#77 := (= #74 #76)
-#79 := (= f25 f26)
-#80 := (not #79)
-#154 := (or #77 #80)
-#157 := (not #154)
-#78 := (not #77)
-#81 := (implies #78 #80)
-#82 := (not #81)
-#158 := (iff #82 #157)
-#155 := (iff #81 #154)
-#156 := [rewrite]: #155
-#159 := [monotonicity #156]: #158
-#153 := [asserted]: #82
-#162 := [mp #153 #159]: #157
-#161 := [not-or-elim #162]: #79
-#355 := [monotonicity #161]: #77
-#160 := [not-or-elim #162]: #78
-[unit-resolution #160 #355]: false
-unsat
-18ead81bc971c49ec98603c790964ad3ab999231 29 0
-#2 := false
-decl f3 :: (-> S3 S4 Int)
-decl f26 :: S4
-#75 := f26
-decl f6 :: S3
-#16 := f6
-#76 := (f3 f6 f26)
-decl f25 :: S4
-#73 := f25
-#74 := (f3 f6 f25)
-#77 := (= #74 #76)
-#79 := (= f25 f26)
-#80 := (not #79)
-#154 := (or #77 #80)
-#157 := (not #154)
-#78 := (not #77)
-#81 := (implies #78 #80)
-#82 := (not #81)
-#158 := (iff #82 #157)
-#155 := (iff #81 #154)
-#156 := [rewrite]: #155
-#159 := [monotonicity #156]: #158
-#153 := [asserted]: #82
-#162 := [mp #153 #159]: #157
-#161 := [not-or-elim #162]: #79
-#355 := [monotonicity #161]: #77
-#160 := [not-or-elim #162]: #78
-[unit-resolution #160 #355]: false
-unsat
-ef4902e702aa4daff26cd3cb227d2369cef2cb24 89 0
-#2 := false
-decl f14 :: (-> S9 S4 S1)
-decl f26 :: S4
-#76 := f26
-decl f15 :: S9
-#41 := f15
-#77 := (f14 f15 f26)
-decl f1 :: S1
-#4 := f1
-#159 := (= f1 #77)
-decl f25 :: S4
-#73 := f25
-#74 := (f14 f15 f25)
-#156 := (= f1 #74)
-#162 := (iff #156 #159)
-#715 := (= #74 #77)
-#81 := (= f25 f26)
-#82 := (not #81)
-#188 := (or #82 #162)
-#191 := (not #188)
-#78 := (= #77 f1)
-#75 := (= #74 f1)
-#79 := (iff #75 #78)
-#80 := (not #79)
-#83 := (implies #80 #82)
-#84 := (not #83)
-#194 := (iff #84 #191)
-#178 := (iff #159 #156)
-#177 := (or #82 #178)
-#183 := (not #177)
-#192 := (iff #183 #191)
-#189 := (iff #177 #188)
-#186 := (iff #178 #162)
-#187 := [rewrite]: #186
-#190 := [monotonicity #187]: #189
-#193 := [monotonicity #190]: #192
-#184 := (iff #84 #183)
-#181 := (iff #83 #177)
-#168 := (not #156)
-#169 := (iff #159 #168)
-#174 := (implies #169 #82)
-#179 := (iff #174 #177)
-#180 := [rewrite]: #179
-#175 := (iff #83 #174)
-#172 := (iff #80 #169)
-#165 := (not #162)
-#170 := (iff #165 #169)
-#171 := [rewrite]: #170
-#166 := (iff #80 #165)
-#163 := (iff #79 #162)
-#160 := (iff #78 #159)
-#161 := [rewrite]: #160
-#157 := (iff #75 #156)
-#158 := [rewrite]: #157
-#164 := [monotonicity #158 #161]: #163
-#167 := [monotonicity #164]: #166
-#173 := [trans #167 #171]: #172
-#176 := [monotonicity #173]: #175
-#182 := [trans #176 #180]: #181
-#185 := [monotonicity #182]: #184
-#195 := [trans #185 #193]: #194
-#155 := [asserted]: #84
-#198 := [mp #155 #195]: #191
-#196 := [not-or-elim #198]: #81
-#717 := [monotonicity #196]: #715
-#372 := [monotonicity #717]: #162
-#396 := (not #159)
-#504 := (iff #168 #396)
-#711 := [monotonicity #372]: #504
-#399 := [hypothesis]: #168
-#383 := [mp #399 #711]: #396
-#394 := (or #159 #156)
-#197 := [not-or-elim #198]: #165
-#224 := [mp #197 #171]: #169
-#392 := (not #169)
-#393 := (or #159 #156 #392)
-#308 := [def-axiom]: #393
-#385 := [unit-resolution #308 #224]: #394
-#378 := [unit-resolution #385 #399]: #159
-#384 := [unit-resolution #378 #383]: false
-#718 := [lemma #384]: #156
-#720 := [mp #718 #372]: #159
-#398 := (or #396 #168)
-#397 := (or #396 #168 #392)
-#325 := [def-axiom]: #397
-#395 := [unit-resolution #325 #224]: #398
-#719 := [unit-resolution #395 #718]: #396
-[unit-resolution #719 #720]: false
-unsat
-1c7893600df066a2c758f1fedb1170d99e7417c3 64 0
-#2 := false
-#73 := 3::Int
+#76 := (f14 f15 f26)
+#77 := (= #76 f1)
+#648 := (iff #77 #74)
+#78 := (iff #74 #77)
+#654 := (= #73 #76)
+#80 := (= f25 f26)
+#81 := (not #80)
+#122 := (or #78 #81)
+#127 := (not #122)
+#79 := (not #78)
+#82 := (implies #79 #81)
+#83 := (not #82)
+#128 := (iff #83 #127)
+#125 := (iff #82 #122)
+#115 := (not #74)
+#116 := (iff #115 #77)
+#119 := (implies #116 #81)
+#123 := (iff #119 #122)
+#124 := [rewrite]: #123
+#120 := (iff #82 #119)
+#117 := (iff #79 #116)
+#118 := [rewrite]: #117
+#121 := [monotonicity #118]: #120
+#126 := [trans #121 #124]: #125
+#129 := [monotonicity #126]: #128
+#114 := [asserted]: #83
+#132 := [mp #114 #129]: #127
+#131 := [not-or-elim #132]: #80
+#310 := [monotonicity #131]: #654
+#441 := [monotonicity #310]: #78
+#321 := [symm #441]: #648
+#330 := (not #77)
+#322 := (iff #330 #115)
+#655 := [monotonicity #321]: #322
+#316 := [hypothesis]: #330
+#656 := [mp #316 #655]: #115
+#333 := (or #74 #77)
+#130 := [not-or-elim #132]: #79
+#156 := [mp #130 #118]: #116
+#331 := (not #116)
+#335 := (or #74 #77 #331)
+#336 := [def-axiom]: #335
+#337 := [unit-resolution #336 #156]: #333
+#652 := [unit-resolution #337 #316]: #74
+#657 := [unit-resolution #652 #656]: false
+#658 := [lemma #657]: #77
+#659 := [mp #658 #321]: #74
+#323 := (or #115 #330)
+#247 := (or #115 #330 #331)
+#332 := [def-axiom]: #247
+#334 := [unit-resolution #332 #156]: #323
+#653 := [unit-resolution #334 #658]: #115
+[unit-resolution #653 #659]: false
+unsat
+cedfd03a27d5c110cccc13a70c0f9d024f224ead 47 0
+#2 := false
+#72 := 3::Int
 decl f3 :: (-> S3 S4 Int)
 decl f5 :: (-> Int Int S2 S4)
 decl f16 :: (-> S10 S8 S2)
 decl f26 :: S8
-#77 := f26
+#76 := f26
 decl f17 :: (-> S11 S1 S10)
 decl f25 :: S1
-#75 := f25
+#74 := f25
 decl f18 :: S11
-#43 := f18
-#76 := (f17 f18 f25)
-#78 := (f16 #76 f26)
-#74 := 4::Int
-#79 := (f5 3::Int 4::Int #78)
+#42 := f18
+#75 := (f17 f18 f25)
+#77 := (f16 #75 f26)
+#73 := 4::Int
+#78 := (f5 3::Int 4::Int #77)
 decl f4 :: S3
-#8 := f4
-#80 := (f3 f4 #79)
-#81 := (= #80 3::Int)
-#82 := (not #81)
-#153 := [asserted]: #82
-#11 := (:var 0 S2)
-#10 := (:var 1 Int)
-#9 := (:var 2 Int)
-#12 := (f5 #9 #10 #11)
-#272 := (pattern #12)
-#13 := (f3 f4 #12)
-#103 := (= #9 #13)
-#273 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #272) #103)
-#106 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #103)
-#276 := (iff #106 #273)
-#274 := (iff #103 #103)
-#275 := [refl]: #274
-#277 := [quant-intro #275]: #276
-#167 := (~ #106 #106)
-#165 := (~ #103 #103)
-#166 := [refl]: #165
-#168 := [nnf-pos #166]: #167
-#14 := (= #13 #9)
-#15 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #14)
-#107 := (iff #15 #106)
-#104 := (iff #14 #103)
-#105 := [rewrite]: #104
-#108 := [quant-intro #105]: #107
-#102 := [asserted]: #15
-#111 := [mp #102 #108]: #106
-#169 := [mp~ #111 #168]: #106
-#278 := [mp #169 #277]: #273
-#379 := (not #273)
-#380 := (or #379 #81)
-#154 := (= 3::Int #80)
-#384 := (or #379 #154)
-#386 := (iff #384 #380)
-#388 := (iff #380 #380)
-#389 := [rewrite]: #388
-#160 := (iff #154 #81)
-#161 := [rewrite]: #160
-#387 := [monotonicity #161]: #386
-#390 := [trans #387 #389]: #386
-#385 := [quant-inst #73 #74 #78]: #384
-#391 := [mp #385 #390]: #380
-[unit-resolution #391 #278 #153]: false
-unsat
-4378daf31705ba44a56bde40746d68e01ac8e158 64 0
-#2 := false
-#74 := 4::Int
+#7 := f4
+#79 := (f3 f4 #78)
+#80 := (= #79 3::Int)
+#81 := (not #80)
+#112 := [asserted]: #81
+#10 := (:var 0 S2)
+#9 := (:var 1 Int)
+#8 := (:var 2 Int)
+#11 := (f5 #8 #9 #10)
+#224 := (pattern #11)
+#12 := (f3 f4 #11)
+#13 := (= #12 #8)
+#225 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #224) #13)
+#14 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #13)
+#228 := (iff #14 #225)
+#226 := (iff #13 #13)
+#227 := [refl]: #226
+#229 := [quant-intro #227]: #228
+#116 := (~ #14 #14)
+#114 := (~ #13 #13)
+#115 := [refl]: #114
+#117 := [nnf-pos #115]: #116
+#102 := [asserted]: #14
+#118 := [mp~ #102 #117]: #14
+#230 := [mp #118 #229]: #225
+#326 := (not #225)
+#327 := (or #326 #80)
+#328 := [quant-inst #72 #73 #77]: #327
+[unit-resolution #328 #230 #112]: false
+unsat
+0b6022e30e4e5ac8cb4953d3a4c8504f4a0609a0 47 0
+#2 := false
+#73 := 4::Int
 decl f3 :: (-> S3 S4 Int)
 decl f5 :: (-> Int Int S2 S4)
 decl f16 :: (-> S10 S8 S2)
 decl f26 :: S8
-#77 := f26
+#76 := f26
 decl f17 :: (-> S11 S1 S10)
 decl f25 :: S1
-#75 := f25
+#74 := f25
 decl f18 :: S11
-#43 := f18
-#76 := (f17 f18 f25)
-#78 := (f16 #76 f26)
-#73 := 3::Int
-#79 := (f5 3::Int 4::Int #78)
+#42 := f18
+#75 := (f17 f18 f25)
+#77 := (f16 #75 f26)
+#72 := 3::Int
+#78 := (f5 3::Int 4::Int #77)
 decl f6 :: S3
-#16 := f6
-#80 := (f3 f6 #79)
-#81 := (= #80 4::Int)
-#82 := (not #81)
-#153 := [asserted]: #82
-#11 := (:var 0 S2)
-#10 := (:var 1 Int)
-#9 := (:var 2 Int)
-#12 := (f5 #9 #10 #11)
-#272 := (pattern #12)
-#17 := (f3 f6 #12)
-#110 := (= #10 #17)
-#279 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #272) #110)
-#114 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #110)
-#282 := (iff #114 #279)
-#280 := (iff #110 #110)
-#281 := [refl]: #280
-#283 := [quant-intro #281]: #282
-#172 := (~ #114 #114)
-#170 := (~ #110 #110)
-#171 := [refl]: #170
-#173 := [nnf-pos #171]: #172
-#18 := (= #17 #10)
-#19 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #18)
-#115 := (iff #19 #114)
-#112 := (iff #18 #110)
-#113 := [rewrite]: #112
-#116 := [quant-intro #113]: #115
-#109 := [asserted]: #19
-#119 := [mp #109 #116]: #114
-#174 := [mp~ #119 #173]: #114
-#284 := [mp #174 #283]: #279
-#397 := (not #279)
-#398 := (or #397 #81)
-#154 := (= 4::Int #80)
-#399 := (or #397 #154)
-#401 := (iff #399 #398)
-#403 := (iff #398 #398)
-#404 := [rewrite]: #403
-#160 := (iff #154 #81)
-#161 := [rewrite]: #160
-#402 := [monotonicity #161]: #401
-#405 := [trans #402 #404]: #401
-#400 := [quant-inst #73 #74 #78]: #399
-#406 := [mp #400 #405]: #398
-[unit-resolution #406 #284 #153]: false
-unsat
-7d7da3e033e9f2b40929e39aea1e30d7a07abec9 112 0
-#2 := false
+#15 := f6
+#79 := (f3 f6 #78)
+#80 := (= #79 4::Int)
+#81 := (not #80)
+#112 := [asserted]: #81
+#10 := (:var 0 S2)
+#9 := (:var 1 Int)
+#8 := (:var 2 Int)
+#11 := (f5 #8 #9 #10)
+#224 := (pattern #11)
+#16 := (f3 f6 #11)
+#17 := (= #16 #9)
+#231 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #224) #17)
+#18 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #17)
+#234 := (iff #18 #231)
+#232 := (iff #17 #17)
+#233 := [refl]: #232
+#235 := [quant-intro #233]: #234
+#121 := (~ #18 #18)
+#119 := (~ #17 #17)
+#120 := [refl]: #119
+#122 := [nnf-pos #120]: #121
+#103 := [asserted]: #18
+#123 := [mp~ #103 #122]: #18
+#236 := [mp #123 #235]: #231
+#331 := (not #231)
+#332 := (or #331 #80)
+#333 := [quant-inst #72 #73 #77]: #332
+[unit-resolution #333 #236 #112]: false
+unsat
+2ca5cee26ef695e3928e07d0a44c659cea20c0b2 85 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f25 :: S1
+#74 := f25
+#81 := (= f25 f1)
+#303 := (not #81)
+#341 := [hypothesis]: #303
 decl f14 :: (-> S9 S4 S1)
 decl f5 :: (-> Int Int S2 S4)
 decl f16 :: (-> S10 S8 S2)
 decl f26 :: S8
-#77 := f26
+#76 := f26
 decl f17 :: (-> S11 S1 S10)
-decl f25 :: S1
-#75 := f25
 decl f18 :: S11
-#43 := f18
-#76 := (f17 f18 f25)
-#78 := (f16 #76 f26)
-#74 := 4::Int
-#73 := 3::Int
-#79 := (f5 3::Int 4::Int #78)
+#42 := f18
+#75 := (f17 f18 f25)
+#77 := (f16 #75 f26)
+#73 := 4::Int
+#72 := 3::Int
+#78 := (f5 3::Int 4::Int #77)
 decl f15 :: S9
-#41 := f15
-#80 := (f14 f15 #79)
-decl f1 :: S1
-#4 := f1
-#156 := (= f1 #80)
-#168 := (not #156)
-#416 := [hypothesis]: #168
-#159 := (= f1 f25)
-#358 := (or #159 #156)
-#169 := (iff #159 #168)
-#82 := (= f25 f1)
-#81 := (= #80 f1)
-#83 := (iff #81 #82)
-#84 := (not #83)
-#172 := (iff #84 #169)
-#162 := (iff #156 #159)
-#165 := (not #162)
-#170 := (iff #165 #169)
-#171 := [rewrite]: #170
-#166 := (iff #84 #165)
-#163 := (iff #83 #162)
-#160 := (iff #82 #159)
-#161 := [rewrite]: #160
-#157 := (iff #81 #156)
-#158 := [rewrite]: #157
-#164 := [monotonicity #158 #161]: #163
-#167 := [monotonicity #164]: #166
-#173 := [trans #167 #171]: #172
-#155 := [asserted]: #84
-#176 := [mp #155 #173]: #169
-#355 := (not #169)
-#356 := (or #159 #156 #355)
-#357 := [def-axiom]: #356
-#359 := [unit-resolution #357 #176]: #358
-#417 := [unit-resolution #359 #416]: #159
-#360 := (not #159)
-#419 := (or #156 #360)
-#46 := (:var 0 S8)
-#44 := (:var 1 S1)
-#45 := (f17 f18 #44)
-#47 := (f16 #45 #46)
-#9 := (:var 2 Int)
-#42 := (:var 3 Int)
-#48 := (f5 #42 #9 #47)
-#326 := (pattern #48)
-#135 := (= f1 #44)
-#49 := (f14 f15 #48)
-#132 := (= f1 #49)
-#138 := (iff #132 #135)
-#327 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S8)) (:pat #326) #138)
-#141 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S8)) #138)
-#330 := (iff #141 #327)
-#328 := (iff #138 #138)
-#329 := [refl]: #328
-#331 := [quant-intro #329]: #330
-#208 := (~ #141 #141)
-#206 := (~ #138 #138)
-#207 := [refl]: #206
-#209 := [nnf-pos #207]: #208
-#51 := (= #44 f1)
-#50 := (= #49 f1)
-#52 := (iff #50 #51)
-#53 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S8)) #52)
-#142 := (iff #53 #141)
-#139 := (iff #52 #138)
-#136 := (iff #51 #135)
-#137 := [rewrite]: #136
-#133 := (iff #50 #132)
-#134 := [rewrite]: #133
-#140 := [monotonicity #134 #137]: #139
-#143 := [quant-intro #140]: #142
-#131 := [asserted]: #53
-#146 := [mp #131 #143]: #141
-#210 := [mp~ #146 #209]: #141
-#332 := [mp #210 #331]: #327
-#367 := (not #327)
-#368 := (or #367 #162)
-#369 := [quant-inst #73 #74 #75 #77]: #368
-#418 := [unit-resolution #369 #332]: #162
-#370 := (or #165 #156 #360)
-#371 := [def-axiom]: #370
-#420 := [unit-resolution #371 #418]: #419
-#421 := [unit-resolution #420 #417 #416]: false
-#422 := [lemma #421]: #156
-#363 := (or #360 #168)
-#361 := (or #360 #168 #355)
-#362 := [def-axiom]: #361
-#364 := [unit-resolution #362 #176]: #363
-#423 := [unit-resolution #364 #422]: #360
-#424 := (or #168 #159)
-#372 := (or #165 #168 #159)
-#373 := [def-axiom]: #372
-#425 := [unit-resolution #373 #418]: #424
-[unit-resolution #425 #423 #422]: false
-unsat
-51712135208fd24e3dca3c8d4c0d0b8eec378de9 120 0
-#2 := false
-#74 := 4::Int
-#73 := 3::Int
-#413 := (= 3::Int 4::Int)
-#415 := (iff #413 false)
-#416 := [rewrite]: #415
+#40 := f15
+#79 := (f14 f15 #78)
+#80 := (= #79 f1)
+#311 := (or #80 #81)
+#115 := (not #80)
+#116 := (iff #115 #81)
+#82 := (iff #80 #81)
+#83 := (not #82)
+#117 := (iff #83 #116)
+#118 := [rewrite]: #117
+#114 := [asserted]: #83
+#121 := [mp #114 #118]: #116
+#304 := (not #116)
+#309 := (or #80 #81 #304)
+#310 := [def-axiom]: #309
+#312 := [unit-resolution #310 #121]: #311
+#342 := [unit-resolution #312 #341]: #80
+#347 := (or #115 #81)
+#45 := (:var 0 S8)
+#43 := (:var 1 S1)
+#44 := (f17 f18 #43)
+#46 := (f16 #44 #45)
+#8 := (:var 2 Int)
+#41 := (:var 3 Int)
+#47 := (f5 #41 #8 #46)
+#274 := (pattern #47)
+#50 := (= #43 f1)
+#48 := (f14 f15 #47)
+#49 := (= #48 f1)
+#51 := (iff #49 #50)
+#275 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S8)) (:pat #274) #51)
+#52 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S8)) #51)
+#278 := (iff #52 #275)
+#276 := (iff #51 #51)
+#277 := [refl]: #276
+#279 := [quant-intro #277]: #278
+#153 := (~ #52 #52)
+#151 := (~ #51 #51)
+#152 := [refl]: #151
+#154 := [nnf-pos #152]: #153
+#110 := [asserted]: #52
+#155 := [mp~ #110 #154]: #52
+#280 := [mp #155 #279]: #275
+#315 := (not #275)
+#316 := (or #315 #82)
+#317 := [quant-inst #72 #73 #74 #76]: #316
+#346 := [unit-resolution #317 #280]: #82
+#320 := (or #83 #115 #81)
+#321 := [def-axiom]: #320
+#348 := [unit-resolution #321 #346]: #347
+#349 := [unit-resolution #348 #342 #341]: false
+#350 := [lemma #349]: #81
+#307 := (or #115 #303)
+#305 := (or #115 #303 #304)
+#306 := [def-axiom]: #305
+#308 := [unit-resolution #306 #121]: #307
+#351 := [unit-resolution #308 #350]: #115
+#352 := (or #80 #303)
+#318 := (or #83 #80 #303)
+#319 := [def-axiom]: #318
+#353 := [unit-resolution #319 #346]: #352
+[unit-resolution #353 #351 #350]: false
+unsat
+6499be1d029719ef95b78f1d0320c11c7fb7a571 86 0
+#2 := false
+#73 := 4::Int
+#72 := 3::Int
+#345 := (= 3::Int 4::Int)
+#347 := (iff #345 false)
+#348 := [rewrite]: #347
 decl f3 :: (-> S3 S4 Int)
 decl f5 :: (-> Int Int S2 S4)
 decl f16 :: (-> S10 S8 S2)
 decl f26 :: S8
-#77 := f26
+#76 := f26
 decl f17 :: (-> S11 S1 S10)
 decl f25 :: S1
-#75 := f25
+#74 := f25
 decl f18 :: S11
-#43 := f18
-#76 := (f17 f18 f25)
-#78 := (f16 #76 f26)
-#79 := (f5 3::Int 4::Int #78)
+#42 := f18
+#75 := (f17 f18 f25)
+#77 := (f16 #75 f26)
+#78 := (f5 3::Int 4::Int #77)
 decl f6 :: S3
-#16 := f6
-#81 := (f3 f6 #79)
-#394 := (= #81 4::Int)
-#11 := (:var 0 S2)
-#10 := (:var 1 Int)
-#9 := (:var 2 Int)
-#12 := (f5 #9 #10 #11)
-#267 := (pattern #12)
-#17 := (f3 f6 #12)
-#112 := (= #10 #17)
-#274 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #267) #112)
-#116 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #112)
-#277 := (iff #116 #274)
-#275 := (iff #112 #112)
-#276 := [refl]: #275
-#278 := [quant-intro #276]: #277
-#167 := (~ #116 #116)
-#165 := (~ #112 #112)
-#166 := [refl]: #165
-#168 := [nnf-pos #166]: #167
-#18 := (= #17 #10)
-#19 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #18)
-#117 := (iff #19 #116)
-#114 := (iff #18 #112)
-#115 := [rewrite]: #114
-#118 := [quant-intro #115]: #117
-#111 := [asserted]: #19
-#121 := [mp #111 #118]: #116
-#169 := [mp~ #121 #168]: #116
-#279 := [mp #169 #278]: #274
-#395 := (not #274)
-#396 := (or #395 #394)
-#391 := (= 4::Int #81)
-#397 := (or #395 #391)
-#399 := (iff #397 #396)
-#401 := (iff #396 #396)
-#402 := [rewrite]: #401
-#392 := (iff #391 #394)
-#393 := [rewrite]: #392
-#400 := [monotonicity #393]: #399
-#403 := [trans #400 #402]: #399
-#398 := [quant-inst #73 #74 #78]: #397
-#404 := [mp #398 #403]: #396
-#405 := [unit-resolution #404 #279]: #394
-#411 := (= 3::Int #81)
-#409 := (= #81 3::Int)
+#15 := f6
+#80 := (f3 f6 #78)
+#327 := (= #80 4::Int)
+#10 := (:var 0 S2)
+#9 := (:var 1 Int)
+#8 := (:var 2 Int)
+#11 := (f5 #8 #9 #10)
+#229 := (pattern #11)
+#16 := (f3 f6 #11)
+#17 := (= #16 #9)
+#236 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #229) #17)
+#18 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #17)
+#239 := (iff #18 #236)
+#237 := (iff #17 #17)
+#238 := [refl]: #237
+#240 := [quant-intro #238]: #239
+#126 := (~ #18 #18)
+#124 := (~ #17 #17)
+#125 := [refl]: #124
+#127 := [nnf-pos #125]: #126
+#105 := [asserted]: #18
+#128 := [mp~ #105 #127]: #18
+#241 := [mp #128 #240]: #236
+#336 := (not #236)
+#337 := (or #336 #327)
+#338 := [quant-inst #72 #73 #77]: #337
+#331 := [unit-resolution #338 #241]: #327
+#343 := (= 3::Int #80)
+#341 := (= #80 3::Int)
 decl f4 :: S3
-#8 := f4
-#80 := (f3 f4 #79)
-#380 := (= #80 3::Int)
-#13 := (f3 f4 #12)
-#105 := (= #9 #13)
-#268 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #267) #105)
-#108 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #105)
-#271 := (iff #108 #268)
-#269 := (iff #105 #105)
-#270 := [refl]: #269
-#272 := [quant-intro #270]: #271
-#162 := (~ #108 #108)
-#159 := (~ #105 #105)
-#161 := [refl]: #159
-#163 := [nnf-pos #161]: #162
-#14 := (= #13 #9)
-#15 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #14)
-#109 := (iff #15 #108)
-#106 := (iff #14 #105)
-#107 := [rewrite]: #106
-#110 := [quant-intro #107]: #109
-#104 := [asserted]: #15
-#113 := [mp #104 #110]: #108
-#164 := [mp~ #113 #163]: #108
-#273 := [mp #164 #272]: #268
-#381 := (not #268)
-#382 := (or #381 #380)
-#374 := (= 3::Int #80)
-#383 := (or #381 #374)
-#385 := (iff #383 #382)
-#387 := (iff #382 #382)
-#388 := [rewrite]: #387
-#375 := (iff #374 #380)
-#379 := [rewrite]: #375
-#386 := [monotonicity #379]: #385
-#389 := [trans #386 #388]: #385
-#384 := [quant-inst #73 #74 #78]: #383
-#390 := [mp #384 #389]: #382
-#406 := [unit-resolution #390 #273]: #380
-#407 := (= #81 #80)
-#82 := (= #80 #81)
+#7 := f4
+#79 := (f3 f4 #78)
+#326 := (= #79 3::Int)
+#12 := (f3 f4 #11)
+#13 := (= #12 #8)
+#230 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #229) #13)
+#14 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #13)
+#233 := (iff #14 #230)
+#231 := (iff #13 #13)
+#232 := [refl]: #231
+#234 := [quant-intro #232]: #233
+#121 := (~ #14 #14)
+#118 := (~ #13 #13)
+#120 := [refl]: #118
+#122 := [nnf-pos #120]: #121
+#104 := [asserted]: #14
+#123 := [mp~ #104 #122]: #14
+#235 := [mp #123 #234]: #230
+#332 := (not #230)
+#333 := (or #332 #326)
+#334 := [quant-inst #72 #73 #77]: #333
+#335 := [unit-resolution #334 #235]: #326
+#339 := (= #80 #79)
+#81 := (= #79 #80)
+#82 := (not #81)
 #83 := (not #82)
-#84 := (not #83)
-#156 := (iff #84 #82)
-#157 := [rewrite]: #156
-#155 := [asserted]: #84
-#160 := [mp #155 #157]: #82
-#408 := [symm #160]: #407
-#410 := [trans #408 #406]: #409
-#412 := [symm #410]: #411
-#414 := [trans #412 #405]: #413
-[mp #414 #416]: false
-unsat
-871d48a15480169e66589f44cdfbd1d2a08781b1 81 0
+#115 := (iff #83 #81)
+#116 := [rewrite]: #115
+#114 := [asserted]: #83
+#119 := [mp #114 #116]: #81
+#340 := [symm #119]: #339
+#342 := [trans #340 #335]: #341
+#344 := [symm #342]: #343
+#346 := [trans #344 #331]: #345
+[mp #346 #348]: false
+unsat
+bcff91b655305f168f8e2a483ead6b7d06750eb4 81 0
 #2 := false
 decl f7 :: (-> Int Int S3 S5)
 decl f17 :: (-> S10 S8 S3)
 decl f27 :: S8
-#84 := f27
+#83 := f27
 decl f18 :: (-> S11 S1 S10)
 decl f26 :: S1
-#82 := f26
+#81 := f26
 decl f19 :: S11
-#50 := f19
-#83 := (f18 f19 f26)
-#85 := (f17 #83 f27)
-#81 := 4::Int
-#12 := 5::Int
-#88 := (f7 5::Int 4::Int #85)
+#49 := f19
+#82 := (f18 f19 f26)
+#84 := (f17 #82 f27)
+#80 := 4::Int
+#11 := 5::Int
+#87 := (f7 5::Int 4::Int #84)
 decl f11 :: (-> S2 S5 S5)
-#80 := 3::Int
-#86 := (f7 3::Int 4::Int #85)
-decl f4 :: S2
-#8 := f4
-#87 := (f11 f4 #86)
-#89 := (= #87 #88)
-decl f3 :: (-> S2 Int Int)
-#477 := (f3 f4 3::Int)
-#478 := (f7 #477 4::Int #85)
-#547 := (= #478 #88)
-#545 := (= #88 #478)
-#539 := (= 5::Int #477)
-#537 := (= #477 5::Int)
-#9 := (:var 0 Int)
-#10 := (f3 f4 #9)
-#11 := (pattern #10)
-#13 := (= #10 5::Int)
-#14 := (forall (vars (?v0 Int)) (:pat #11) #13)
-#166 := (~ #14 #14)
-#164 := (~ #13 #13)
-#165 := [refl]: #164
-#167 := [nnf-pos #165]: #166
-#110 := [asserted]: #14
-#168 := [mp~ #110 #167]: #14
-#540 := (not #14)
-#541 := (or #540 #537)
-#542 := [quant-inst #80]: #541
-#538 := [unit-resolution #542 #168]: #537
-#543 := [symm #538]: #539
-#546 := [monotonicity #543]: #545
-#548 := [symm #546]: #547
-#479 := (= #87 #478)
-#18 := (:var 0 S3)
-#17 := (:var 1 Int)
-#16 := (:var 2 Int)
-#31 := (:var 3 S2)
-#33 := (f3 #31 #16)
-#34 := (f7 #33 #17 #18)
-#296 := (pattern #34)
-#19 := (f7 #16 #17 #18)
-#32 := (f11 #31 #19)
-#295 := (pattern #32)
-#35 := (= #32 #34)
-#297 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #295 #296) #35)
-#36 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #35)
-#300 := (iff #36 #297)
-#298 := (iff #35 #35)
-#299 := [refl]: #298
-#301 := [quant-intro #299]: #300
-#186 := (~ #36 #36)
-#184 := (~ #35 #35)
-#185 := [refl]: #184
-#187 := [nnf-pos #185]: #186
-#134 := [asserted]: #36
-#188 := [mp~ #134 #187]: #36
-#302 := [mp #188 #301]: #297
-#482 := (not #297)
-#483 := (or #482 #479)
-#484 := [quant-inst #8 #80 #81 #85]: #483
-#544 := [unit-resolution #484 #302]: #479
-#549 := [trans #544 #548]: #89
-#90 := (not #89)
-#162 := [asserted]: #90
-[unit-resolution #162 #549]: false
-unsat
-2bf1b0efe9c627655a01fe096027d6ea1d8d0de9 81 0
+#79 := 3::Int
+#85 := (f7 3::Int 4::Int #84)
+decl f4 :: S2
+#7 := f4
+#86 := (f11 f4 #85)
+#88 := (= #86 #87)
+decl f3 :: (-> S2 Int Int)
+#378 := (f3 f4 3::Int)
+#379 := (f7 #378 4::Int #84)
+#427 := (= #379 #87)
+#425 := (= #87 #379)
+#419 := (= 5::Int #378)
+#415 := (= #378 5::Int)
+#8 := (:var 0 Int)
+#9 := (f3 f4 #8)
+#10 := (pattern #9)
+#12 := (= #9 5::Int)
+#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
+#125 := (~ #13 #13)
+#123 := (~ #12 #12)
+#124 := [refl]: #123
+#126 := [nnf-pos #124]: #125
+#110 := [asserted]: #13
+#127 := [mp~ #110 #126]: #13
+#420 := (not #13)
+#421 := (or #420 #415)
+#422 := [quant-inst #79]: #421
+#416 := [unit-resolution #422 #127]: #415
+#423 := [symm #416]: #419
+#426 := [monotonicity #423]: #425
+#428 := [symm #426]: #427
+#382 := (= #86 #379)
+#17 := (:var 0 S3)
+#16 := (:var 1 Int)
+#15 := (:var 2 Int)
+#30 := (:var 3 S2)
+#32 := (f3 #30 #15)
+#33 := (f7 #32 #16 #17)
+#257 := (pattern #33)
+#18 := (f7 #15 #16 #17)
+#31 := (f11 #30 #18)
+#256 := (pattern #31)
+#34 := (= #31 #33)
+#258 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #256 #257) #34)
+#35 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #34)
+#261 := (iff #35 #258)
+#259 := (iff #34 #34)
+#260 := [refl]: #259
+#262 := [quant-intro #260]: #261
+#145 := (~ #35 #35)
+#143 := (~ #34 #34)
+#144 := [refl]: #143
+#146 := [nnf-pos #144]: #145
+#114 := [asserted]: #35
+#147 := [mp~ #114 #146]: #35
+#263 := [mp #147 #262]: #258
+#385 := (not #258)
+#386 := (or #385 #382)
+#387 := [quant-inst #7 #79 #80 #84]: #386
+#424 := [unit-resolution #387 #263]: #382
+#429 := [trans #424 #428]: #88
+#89 := (not #88)
+#121 := [asserted]: #89
+[unit-resolution #121 #429]: false
+unsat
+7462b61994002d474ce748e537732218cde820f6 81 0
 #2 := false
 decl f7 :: (-> Int Int S3 S5)
 decl f17 :: (-> S10 S8 S3)
 decl f27 :: S8
-#84 := f27
+#83 := f27
 decl f18 :: (-> S11 S1 S10)
 decl f26 :: S1
-#82 := f26
+#81 := f26
 decl f19 :: S11
-#50 := f19
-#83 := (f18 f19 f26)
-#85 := (f17 #83 f27)
-#12 := 6::Int
-#80 := 3::Int
-#88 := (f7 3::Int 6::Int #85)
+#49 := f19
+#82 := (f18 f19 f26)
+#84 := (f17 #82 f27)
+#11 := 6::Int
+#79 := 3::Int
+#87 := (f7 3::Int 6::Int #84)
 decl f12 :: (-> S2 S5 S5)
-#81 := 4::Int
-#86 := (f7 3::Int 4::Int #85)
-decl f4 :: S2
-#8 := f4
-#87 := (f12 f4 #86)
-#89 := (= #87 #88)
-decl f3 :: (-> S2 Int Int)
-#477 := (f3 f4 4::Int)
-#478 := (f7 3::Int #477 #85)
-#547 := (= #478 #88)
-#545 := (= #88 #478)
-#539 := (= 6::Int #477)
-#535 := (= #477 6::Int)
-#9 := (:var 0 Int)
-#10 := (f3 f4 #9)
-#11 := (pattern #10)
-#13 := (= #10 6::Int)
-#14 := (forall (vars (?v0 Int)) (:pat #11) #13)
-#166 := (~ #14 #14)
-#164 := (~ #13 #13)
-#165 := [refl]: #164
-#167 := [nnf-pos #165]: #166
-#110 := [asserted]: #14
-#168 := [mp~ #110 #167]: #14
-#540 := (not #14)
-#541 := (or #540 #535)
-#542 := [quant-inst #81]: #541
-#536 := [unit-resolution #542 #168]: #535
-#543 := [symm #536]: #539
-#546 := [monotonicity #543]: #545
-#548 := [symm #546]: #547
-#479 := (= #87 #478)
-#18 := (:var 0 S3)
-#17 := (:var 1 Int)
-#31 := (:var 3 S2)
-#38 := (f3 #31 #17)
-#16 := (:var 2 Int)
-#39 := (f7 #16 #38 #18)
-#304 := (pattern #39)
-#19 := (f7 #16 #17 #18)
-#37 := (f12 #31 #19)
-#303 := (pattern #37)
-#40 := (= #37 #39)
-#305 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #303 #304) #40)
-#41 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #40)
-#308 := (iff #41 #305)
-#306 := (iff #40 #40)
-#307 := [refl]: #306
-#309 := [quant-intro #307]: #308
-#191 := (~ #41 #41)
-#189 := (~ #40 #40)
-#190 := [refl]: #189
-#192 := [nnf-pos #190]: #191
-#135 := [asserted]: #41
-#193 := [mp~ #135 #192]: #41
-#310 := [mp #193 #309]: #305
-#482 := (not #305)
-#483 := (or #482 #479)
-#484 := [quant-inst #8 #80 #81 #85]: #483
-#544 := [unit-resolution #484 #310]: #479
-#549 := [trans #544 #548]: #89
-#90 := (not #89)
-#162 := [asserted]: #90
-[unit-resolution #162 #549]: false
-unsat
-f963522612a81bf3ec5143b6f63e213abb03c7fe 427 0
-#2 := false
+#80 := 4::Int
+#85 := (f7 3::Int 4::Int #84)
+decl f4 :: S2
+#7 := f4
+#86 := (f12 f4 #85)
+#88 := (= #86 #87)
+decl f3 :: (-> S2 Int Int)
+#379 := (f3 f4 4::Int)
+#380 := (f7 3::Int #379 #84)
+#428 := (= #380 #87)
+#426 := (= #87 #380)
+#420 := (= 6::Int #379)
+#416 := (= #379 6::Int)
+#8 := (:var 0 Int)
+#9 := (f3 f4 #8)
+#10 := (pattern #9)
+#12 := (= #9 6::Int)
+#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
+#125 := (~ #13 #13)
+#123 := (~ #12 #12)
+#124 := [refl]: #123
+#126 := [nnf-pos #124]: #125
+#110 := [asserted]: #13
+#127 := [mp~ #110 #126]: #13
+#421 := (not #13)
+#422 := (or #421 #416)
+#423 := [quant-inst #80]: #422
+#417 := [unit-resolution #423 #127]: #416
+#424 := [symm #417]: #420
+#427 := [monotonicity #424]: #426
+#429 := [symm #427]: #428
+#383 := (= #86 #380)
+#17 := (:var 0 S3)
+#16 := (:var 1 Int)
+#30 := (:var 3 S2)
+#37 := (f3 #30 #16)
+#15 := (:var 2 Int)
+#38 := (f7 #15 #37 #17)
+#266 := (pattern #38)
+#18 := (f7 #15 #16 #17)
+#36 := (f12 #30 #18)
+#265 := (pattern #36)
+#39 := (= #36 #38)
+#267 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #265 #266) #39)
+#40 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #39)
+#270 := (iff #40 #267)
+#268 := (iff #39 #39)
+#269 := [refl]: #268
+#271 := [quant-intro #269]: #270
+#150 := (~ #40 #40)
+#148 := (~ #39 #39)
+#149 := [refl]: #148
+#151 := [nnf-pos #149]: #150
+#115 := [asserted]: #40
+#152 := [mp~ #115 #151]: #40
+#272 := [mp #152 #271]: #267
+#386 := (not #267)
+#387 := (or #386 #383)
+#388 := [quant-inst #7 #79 #80 #84]: #387
+#425 := [unit-resolution #388 #272]: #383
+#430 := [trans #425 #429]: #88
+#89 := (not #88)
+#121 := [asserted]: #89
+[unit-resolution #121 #430]: false
+unsat
+ffaca458bf7a853e37afab709d490432c7fad3af 233 0
+#2 := false
+decl f28 :: S6
+#92 := f28
 decl f25 :: (-> S3 S6 S6)
 decl f15 :: (-> S2 S6 S6)
 decl f14 :: (-> S2 S6 S6)
-decl f28 :: S6
-#93 := f28
 decl f5 :: S2
-#15 := f5
-#99 := (f14 f5 f28)
-decl f4 :: S2
-#8 := f4
-#100 := (f15 f4 #99)
+#14 := f5
+#98 := (f14 f5 f28)
+decl f4 :: S2
+#7 := f4
+#99 := (f15 f4 #98)
 decl f7 :: S3
-#21 := f7
-#101 := (f25 f7 #100)
-#193 := (= f28 #101)
+#20 := f7
+#100 := (f25 f7 #99)
+#101 := (= #100 f28)
 decl f10 :: (-> Int Int S4 S6)
 decl f20 :: (-> S11 S9 S4)
-decl f23 :: (-> S13 S6 S9)
 decl f29 :: S9
-#95 := f29
+#94 := f29
 decl f21 :: (-> S12 S1 S11)
 decl f1 :: S1
-#4 := f1
+#3 := f1
 decl f22 :: S12
-#63 := f22
-#94 := (f21 f22 f1)
-#96 := (f20 #94 f29)
-#12 := 4::Int
-#18 := 3::Int
-#97 := (f10 3::Int 4::Int #96)
-decl f24 :: S13
-#74 := f24
-#447 := (f23 f24 #97)
-decl f18 :: (-> S10 S6 S1)
-decl f19 :: S10
-#61 := f19
-#425 := (f18 f19 #97)
-#487 := (f21 f22 #425)
-#488 := (f20 #487 #447)
-decl f3 :: (-> S2 Int Int)
-#544 := (f3 f4 4::Int)
-#564 := (f10 3::Int #544 #488)
-#639 := (f25 f7 #564)
-#808 := (= #639 #101)
-#801 := (= #101 #639)
-#799 := (= #100 #564)
-decl f12 :: (-> S7 S6 S4)
-decl f13 :: S7
-#40 := f13
-#449 := (f12 f13 #97)
-#407 := (f3 f5 3::Int)
-#545 := (f10 #407 #544 #449)
-#795 := (= #545 #564)
-#793 := (= #564 #545)
-#770 := (= #488 #449)
-#450 := (= #96 #449)
-#31 := (:var 0 S4)
-#30 := (:var 1 Int)
-#29 := (:var 2 Int)
-#32 := (f10 #29 #30 #31)
-#335 := (pattern #32)
-#41 := (f12 f13 #32)
-#157 := (= #31 #41)
-#348 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) (:pat #335) #157)
-#161 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) #157)
-#351 := (iff #161 #348)
-#349 := (iff #157 #157)
-#350 := [refl]: #349
-#352 := [quant-intro #350]: #351
-#240 := (~ #161 #161)
-#238 := (~ #157 #157)
-#239 := [refl]: #238
-#241 := [nnf-pos #239]: #240
-#42 := (= #41 #31)
-#43 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) #42)
-#162 := (iff #43 #161)
-#159 := (iff #42 #157)
-#160 := [rewrite]: #159
-#163 := [quant-intro #160]: #162
-#156 := [asserted]: #43
-#166 := [mp #156 #163]: #161
-#242 := [mp~ #166 #241]: #161
-#353 := [mp #242 #352]: #348
-#456 := (not #348)
-#457 := (or #456 #450)
-#458 := [quant-inst #18 #12 #96]: #457
-#762 := [unit-resolution #458 #353]: #450
-#768 := (= #488 #96)
-#748 := (= #447 f29)
-#448 := (= f29 #447)
-#66 := (:var 0 S9)
-#64 := (:var 1 S1)
-#65 := (f21 f22 #64)
-#67 := (f20 #65 #66)
-#62 := (:var 3 Int)
-#68 := (f10 #62 #29 #67)
-#378 := (pattern #68)
-#75 := (f23 f24 #68)
-#182 := (= #66 #75)
-#385 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S9)) (:pat #378) #182)
-#186 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S9)) #182)
-#388 := (iff #186 #385)
-#386 := (iff #182 #182)
-#387 := [refl]: #386
-#389 := [quant-intro #387]: #388
-#265 := (~ #186 #186)
-#263 := (~ #182 #182)
-#264 := [refl]: #263
-#266 := [nnf-pos #264]: #265
-#76 := (= #75 #66)
-#77 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S9)) #76)
-#187 := (iff #77 #186)
-#184 := (iff #76 #182)
-#185 := [rewrite]: #184
-#188 := [quant-intro #185]: #187
-#181 := [asserted]: #77
-#191 := [mp #181 #188]: #186
-#267 := [mp~ #191 #266]: #186
-#390 := [mp #267 #389]: #385
-#451 := (not #385)
-#452 := (or #451 #448)
-#453 := [quant-inst #18 #12 #4 #95]: #452
-#747 := [unit-resolution #453 #390]: #448
-#752 := [symm #747]: #748
-#766 := (= #487 #94)
-#764 := (= #425 f1)
-#426 := (= f1 #425)
-#172 := (= f1 #64)
-#69 := (f18 f19 #68)
-#169 := (= f1 #69)
-#175 := (iff #169 #172)
-#379 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S9)) (:pat #378) #175)
-#178 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S9)) #175)
-#382 := (iff #178 #379)
-#380 := (iff #175 #175)
-#381 := [refl]: #380
-#383 := [quant-intro #381]: #382
-#260 := (~ #178 #178)
-#258 := (~ #175 #175)
-#259 := [refl]: #258
-#261 := [nnf-pos #259]: #260
-#71 := (= #64 f1)
-#70 := (= #69 f1)
-#72 := (iff #70 #71)
-#73 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S9)) #72)
-#179 := (iff #73 #178)
-#176 := (iff #72 #175)
-#173 := (iff #71 #172)
-#174 := [rewrite]: #173
-#170 := (iff #70 #169)
-#171 := [rewrite]: #170
-#177 := [monotonicity #171 #174]: #176
-#180 := [quant-intro #177]: #179
-#168 := [asserted]: #73
-#183 := [mp #168 #180]: #178
-#262 := [mp~ #183 #261]: #178
-#384 := [mp #262 #383]: #379
-#437 := (not #379)
-#438 := (or #437 #426)
-#424 := (= f1 f1)
-#427 := (iff #426 #424)
-#439 := (or #437 #427)
-#441 := (iff #439 #438)
-#443 := (iff #438 #438)
-#444 := [rewrite]: #443
-#435 := (iff #427 #426)
-#1 := true
-#430 := (iff #426 true)
-#433 := (iff #430 #426)
-#434 := [rewrite]: #433
-#431 := (iff #427 #430)
-#428 := (iff #424 true)
-#429 := [rewrite]: #428
-#432 := [monotonicity #429]: #431
-#436 := [trans #432 #434]: #435
-#442 := [monotonicity #436]: #441
-#445 := [trans #442 #444]: #441
-#440 := [quant-inst #18 #12 #4 #95]: #439
-#446 := [mp #440 #445]: #438
-#763 := [unit-resolution #446 #384]: #426
-#765 := [symm #763]: #764
-#767 := [monotonicity #765]: #766
-#769 := [monotonicity #767 #752]: #768
-#771 := [trans #769 #762]: #770
-#773 := (= 3::Int #407)
-#543 := (= #407 3::Int)
-#9 := (:var 0 Int)
-#16 := (f3 f5 #9)
-#17 := (pattern #16)
-#19 := (= #16 3::Int)
-#20 := (forall (vars (?v0 Int)) (:pat #17) #19)
-#220 := (~ #20 #20)
-#218 := (~ #19 #19)
-#219 := [refl]: #218
-#221 := [nnf-pos #219]: #220
-#125 := [asserted]: #20
-#222 := [mp~ #125 #221]: #20
-#546 := (not #20)
-#547 := (or #546 #543)
-#548 := [quant-inst #18]: #547
-#772 := [unit-resolution #548 #222]: #543
-#774 := [symm #772]: #773
-#794 := [monotonicity #774 #771]: #793
-#796 := [symm #794]: #795
-#797 := (= #100 #545)
-#518 := (f10 #407 4::Int #449)
-#549 := (f15 f4 #518)
-#550 := (= #549 #545)
-#551 := (= #545 #549)
-#44 := (:var 3 S2)
-#51 := (f3 #44 #30)
-#52 := (f10 #29 #51 #31)
-#363 := (pattern #52)
-#50 := (f15 #44 #32)
-#362 := (pattern #50)
-#53 := (= #50 #52)
-#364 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #362 #363) #53)
-#54 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #53)
-#367 := (iff #54 #364)
-#365 := (iff #53 #53)
-#366 := [refl]: #365
-#368 := [quant-intro #366]: #367
-#250 := (~ #54 #54)
-#248 := (~ #53 #53)
-#249 := [refl]: #248
-#251 := [nnf-pos #249]: #250
-#165 := [asserted]: #54
-#252 := [mp~ #165 #251]: #54
-#369 := [mp #252 #368]: #364
-#554 := (not #364)
-#555 := (or #554 #551)
-#556 := (or #554 #550)
-#558 := (iff #556 #555)
-#560 := (iff #555 #555)
-#561 := [rewrite]: #560
-#552 := (iff #550 #551)
-#553 := [rewrite]: #552
-#559 := [monotonicity #553]: #558
-#562 := [trans #559 #561]: #558
-#557 := [quant-inst #8 #407 #12 #449]: #556
-#563 := [mp #557 #562]: #555
-#775 := [unit-resolution #563 #369]: #551
-#792 := [symm #775]: #550
-#790 := (= #100 #549)
-#788 := (= #99 #518)
-#408 := (f10 #407 4::Int #96)
-#784 := (= #408 #518)
-#781 := (= #518 #408)
-#777 := (= #449 #96)
-#778 := [symm #762]: #777
-#782 := [monotonicity #778]: #781
-#785 := [symm #782]: #784
-#786 := (= #99 #408)
-#409 := (f14 f5 #97)
-#410 := (= #409 #408)
-#411 := (= #408 #409)
-#46 := (f3 #44 #29)
-#47 := (f10 #46 #30 #31)
-#355 := (pattern #47)
-#45 := (f14 #44 #32)
-#354 := (pattern #45)
-#48 := (= #45 #47)
-#356 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #354 #355) #48)
-#49 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #48)
-#359 := (iff #49 #356)
-#357 := (iff #48 #48)
-#358 := [refl]: #357
-#360 := [quant-intro #358]: #359
-#245 := (~ #49 #49)
-#243 := (~ #48 #48)
-#244 := [refl]: #243
-#246 := [nnf-pos #244]: #245
-#164 := [asserted]: #49
-#247 := [mp~ #164 #246]: #49
-#361 := [mp #247 #360]: #356
-#414 := (not #356)
-#415 := (or #414 #411)
-#416 := (or #414 #410)
-#418 := (iff #416 #415)
-#420 := (iff #415 #415)
-#421 := [rewrite]: #420
-#412 := (iff #410 #411)
-#413 := [rewrite]: #412
-#419 := [monotonicity #413]: #418
-#422 := [trans #419 #421]: #418
-#417 := [quant-inst #15 #18 #12 #96]: #416
-#423 := [mp #417 #422]: #415
-#776 := [unit-resolution #423 #361]: #411
-#783 := [symm #776]: #410
-#779 := (= #99 #409)
-#98 := (= f28 #97)
-#199 := (not #98)
-#200 := (or #199 #193)
-#205 := (not #200)
-#102 := (= #101 f28)
-#103 := (implies #98 #102)
-#104 := (not #103)
-#206 := (iff #104 #205)
-#203 := (iff #103 #200)
-#196 := (implies #98 #193)
-#201 := (iff #196 #200)
-#202 := [rewrite]: #201
-#197 := (iff #103 #196)
-#194 := (iff #102 #193)
-#195 := [rewrite]: #194
-#198 := [monotonicity #195]: #197
-#204 := [trans #198 #202]: #203
-#207 := [monotonicity #204]: #206
-#192 := [asserted]: #104
-#210 := [mp #192 #207]: #205
-#208 := [not-or-elim #210]: #98
-#780 := [monotonicity #208]: #779
-#787 := [trans #780 #783]: #786
-#789 := [trans #787 #785]: #788
-#791 := [monotonicity #789]: #790
-#798 := [trans #791 #792]: #797
-#800 := [trans #798 #796]: #799
-#802 := [monotonicity #800]: #801
-#809 := [symm #802]: #808
-#812 := (= f28 #639)
+#62 := f22
+#93 := (f21 f22 f1)
+#95 := (f20 #93 f29)
+#11 := 4::Int
+#17 := 3::Int
+#96 := (f10 3::Int 4::Int #95)
+#583 := (= #96 f28)
+#97 := (= f28 #96)
+#144 := (not #97)
+#145 := (or #144 #101)
+#148 := (not #145)
+#102 := (implies #97 #101)
+#103 := (not #102)
+#149 := (iff #103 #148)
+#146 := (iff #102 #145)
+#147 := [rewrite]: #146
+#150 := [monotonicity #147]: #149
+#143 := [asserted]: #103
+#153 := [mp #143 #150]: #148
+#151 := [not-or-elim #153]: #97
+#584 := [symm #151]: #583
+#587 := (= #100 #96)
 decl f6 :: (-> S3 S1 S1)
-#630 := (f6 f7 #425)
-#633 := (f21 f22 #630)
-#637 := (f20 #633 #447)
-#638 := (f10 3::Int #544 #637)
-#641 := (= #638 #639)
-#78 := (:var 4 S3)
-#80 := (f6 #78 #64)
-#81 := (f21 f22 #80)
-#82 := (f20 #81 #66)
-#83 := (f10 #62 #29 #82)
-#392 := (pattern #83)
-#79 := (f25 #78 #68)
-#391 := (pattern #79)
-#84 := (= #79 #83)
-#393 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) (:pat #391 #392) #84)
-#85 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) #84)
-#396 := (iff #85 #393)
-#394 := (iff #84 #84)
-#395 := [refl]: #394
-#397 := [quant-intro #395]: #396
-#270 := (~ #85 #85)
-#268 := (~ #84 #84)
-#269 := [refl]: #268
-#271 := [nnf-pos #269]: #270
-#189 := [asserted]: #85
-#272 := [mp~ #189 #271]: #85
-#398 := [mp #272 #397]: #393
-#644 := (not #393)
-#645 := (or #644 #641)
-#640 := (= #639 #638)
-#646 := (or #644 #640)
-#648 := (iff #646 #645)
-#650 := (iff #645 #645)
-#651 := [rewrite]: #650
-#642 := (iff #640 #641)
-#643 := [rewrite]: #642
-#649 := [monotonicity #643]: #648
-#652 := [trans #649 #651]: #648
-#647 := [quant-inst #21 #18 #544 #425 #447]: #646
-#653 := [mp #647 #652]: #645
-#761 := [unit-resolution #653 #398]: #641
-#810 := (= f28 #638)
-#806 := (= #97 #638)
-#804 := (= #638 #97)
-#758 := (= #637 #96)
-#756 := (= #633 #94)
-#754 := (= #630 f1)
-#654 := (= f1 #630)
-#22 := (:var 0 S1)
-#23 := (f6 f7 #22)
-#24 := (pattern #23)
-#127 := (= f1 #23)
-#137 := (forall (vars (?v0 S1)) (:pat #24) #127)
-#225 := (~ #137 #137)
-#223 := (~ #127 #127)
-#224 := [refl]: #223
-#226 := [nnf-pos #224]: #225
-#25 := (= #23 f1)
-#26 := (iff #25 true)
-#27 := (forall (vars (?v0 S1)) (:pat #24) #26)
-#138 := (iff #27 #137)
-#135 := (iff #26 #127)
-#130 := (iff #127 true)
-#133 := (iff #130 #127)
-#134 := [rewrite]: #133
-#131 := (iff #26 #130)
-#128 := (iff #25 #127)
-#129 := [rewrite]: #128
-#132 := [monotonicity #129]: #131
-#136 := [trans #132 #134]: #135
-#139 := [quant-intro #136]: #138
-#126 := [asserted]: #27
-#142 := [mp #126 #139]: #137
-#227 := [mp~ #142 #226]: #137
-#749 := (not #137)
-#750 := (or #749 #654)
-#751 := [quant-inst #425]: #750
-#753 := [unit-resolution #751 #227]: #654
-#755 := [symm #753]: #754
-#757 := [monotonicity #755]: #756
-#759 := [monotonicity #757 #752]: #758
-#629 := (= #544 4::Int)
-#10 := (f3 f4 #9)
-#11 := (pattern #10)
-#13 := (= #10 4::Int)
-#14 := (forall (vars (?v0 Int)) (:pat #11) #13)
-#215 := (~ #14 #14)
-#213 := (~ #13 #13)
-#214 := [refl]: #213
-#216 := [nnf-pos #214]: #215
-#124 := [asserted]: #14
-#217 := [mp~ #124 #216]: #14
-#634 := (not #14)
-#635 := (or #634 #629)
-#636 := [quant-inst #12]: #635
-#760 := [unit-resolution #636 #217]: #629
-#805 := [monotonicity #760 #759]: #804
-#807 := [symm #805]: #806
-#811 := [trans #208 #807]: #810
-#813 := [trans #811 #761]: #812
-#814 := [trans #813 #809]: #193
-#209 := (not #193)
-#211 := [not-or-elim #210]: #209
-[unit-resolution #211 #814]: false
-unsat
-1fb0b37ea5eb83d1ac7f04c0c34b20399e8cbb8e 397 0
-#2 := false
+#496 := (f6 f7 f1)
+#500 := (f21 f22 #496)
+#501 := (f20 #500 f29)
+decl f3 :: (-> S2 Int Int)
+#445 := (f3 f4 4::Int)
+#502 := (f10 3::Int #445 #501)
+#581 := (= #502 #96)
+#556 := (= #501 #95)
+#549 := (= #500 #93)
+#510 := (= #496 f1)
+#21 := (:var 0 S1)
+#22 := (f6 f7 #21)
+#23 := (pattern #22)
+#24 := (= #22 f1)
+#129 := (forall (vars (?v0 S1)) (:pat #23) #24)
+#168 := (~ #129 #129)
+#166 := (~ #24 #24)
+#167 := [refl]: #166
+#169 := [nnf-pos #167]: #168
+#1 := true
+#25 := (iff #24 true)
+#26 := (forall (vars (?v0 S1)) (:pat #23) #25)
+#130 := (iff #26 #129)
+#127 := (iff #25 #24)
+#128 := [rewrite]: #127
+#131 := [quant-intro #128]: #130
+#126 := [asserted]: #26
+#134 := [mp #126 #131]: #129
+#170 := [mp~ #134 #169]: #129
+#552 := (not #129)
+#553 := (or #552 #510)
+#554 := [quant-inst #3]: #553
+#548 := [unit-resolution #554 #170]: #510
+#555 := [monotonicity #548]: #549
+#557 := [monotonicity #555]: #556
+#492 := (= #445 4::Int)
+#8 := (:var 0 Int)
+#9 := (f3 f4 #8)
+#10 := (pattern #9)
+#12 := (= #9 4::Int)
+#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
+#158 := (~ #13 #13)
+#156 := (~ #12 #12)
+#157 := [refl]: #156
+#159 := [nnf-pos #157]: #158
+#124 := [asserted]: #13
+#160 := [mp~ #124 #159]: #13
+#497 := (not #13)
+#498 := (or #497 #492)
+#499 := [quant-inst #11]: #498
+#558 := [unit-resolution #499 #160]: #492
+#582 := [monotonicity #558 #557]: #581
+#585 := (= #100 #502)
+#451 := (f10 3::Int #445 #95)
+#493 := (f25 f7 #451)
+#503 := (= #493 #502)
+#65 := (:var 0 S9)
+#63 := (:var 1 S1)
+#77 := (:var 4 S3)
+#79 := (f6 #77 #63)
+#80 := (f21 f22 #79)
+#81 := (f20 #80 #65)
+#28 := (:var 2 Int)
+#61 := (:var 3 Int)
+#82 := (f10 #61 #28 #81)
+#338 := (pattern #82)
+#64 := (f21 f22 #63)
+#66 := (f20 #64 #65)
+#67 := (f10 #61 #28 #66)
+#78 := (f25 #77 #67)
+#337 := (pattern #78)
+#83 := (= #78 #82)
+#339 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) (:pat #337 #338) #83)
+#84 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) #83)
+#342 := (iff #84 #339)
+#340 := (iff #83 #83)
+#341 := [refl]: #340
+#343 := [quant-intro #341]: #342
+#213 := (~ #84 #84)
+#211 := (~ #83 #83)
+#212 := [refl]: #211
+#214 := [nnf-pos #212]: #213
+#141 := [asserted]: #84
+#215 := [mp~ #141 #214]: #84
+#344 := [mp #215 #343]: #339
+#506 := (not #339)
+#507 := (or #506 #503)
+#508 := [quant-inst #20 #17 #445 #3 #94]: #507
+#559 := [unit-resolution #508 #344]: #503
+#579 := (= #100 #493)
+#577 := (= #99 #451)
+#355 := (f3 f5 3::Int)
+#449 := (f10 #355 #445 #95)
+#573 := (= #449 #451)
+#571 := (= #451 #449)
+#561 := (= 3::Int #355)
+#441 := (= #355 3::Int)
+#15 := (f3 f5 #8)
+#16 := (pattern #15)
+#18 := (= #15 3::Int)
+#19 := (forall (vars (?v0 Int)) (:pat #16) #18)
+#163 := (~ #19 #19)
+#161 := (~ #18 #18)
+#162 := [refl]: #161
+#164 := [nnf-pos #162]: #163
+#125 := [asserted]: #19
+#165 := [mp~ #125 #164]: #19
+#446 := (not #19)
+#447 := (or #446 #441)
+#448 := [quant-inst #17]: #447
+#560 := [unit-resolution #448 #165]: #441
+#562 := [symm #560]: #561
+#572 := [monotonicity #562]: #571
+#574 := [symm #572]: #573
+#575 := (= #99 #449)
+#354 := (f10 #355 4::Int #95)
+#442 := (f15 f4 #354)
+#450 := (= #442 #449)
+#30 := (:var 0 S4)
+#29 := (:var 1 Int)
+#43 := (:var 3 S2)
+#50 := (f3 #43 #29)
+#51 := (f10 #28 #50 #30)
+#309 := (pattern #51)
+#31 := (f10 #28 #29 #30)
+#49 := (f15 #43 #31)
+#308 := (pattern #49)
+#52 := (= #49 #51)
+#310 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #308 #309) #52)
+#53 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #52)
+#313 := (iff #53 #310)
+#311 := (iff #52 #52)
+#312 := [refl]: #311
+#314 := [quant-intro #312]: #313
+#193 := (~ #53 #53)
+#191 := (~ #52 #52)
+#192 := [refl]: #191
+#194 := [nnf-pos #192]: #193
+#137 := [asserted]: #53
+#195 := [mp~ #137 #194]: #53
+#315 := [mp #195 #314]: #310
+#453 := (not #310)
+#454 := (or #453 #450)
+#455 := [quant-inst #7 #355 #11 #95]: #454
+#563 := [unit-resolution #455 #315]: #450
+#569 := (= #99 #442)
+#567 := (= #98 #354)
+#353 := (f14 f5 #96)
+#361 := (= #353 #354)
+#45 := (f3 #43 #28)
+#46 := (f10 #45 #29 #30)
+#301 := (pattern #46)
+#44 := (f14 #43 #31)
+#300 := (pattern #44)
+#47 := (= #44 #46)
+#302 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #300 #301) #47)
+#48 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #47)
+#305 := (iff #48 #302)
+#303 := (iff #47 #47)
+#304 := [refl]: #303
+#306 := [quant-intro #304]: #305
+#188 := (~ #48 #48)
+#186 := (~ #47 #47)
+#187 := [refl]: #186
+#189 := [nnf-pos #187]: #188
+#136 := [asserted]: #48
+#190 := [mp~ #136 #189]: #48
+#307 := [mp #190 #306]: #302
+#364 := (not #302)
+#365 := (or #364 #361)
+#366 := [quant-inst #14 #17 #11 #95]: #365
+#564 := [unit-resolution #366 #307]: #361
+#565 := (= #98 #353)
+#566 := [monotonicity #151]: #565
+#568 := [trans #566 #564]: #567
+#570 := [monotonicity #568]: #569
+#576 := [trans #570 #563]: #575
+#578 := [trans #576 #574]: #577
+#580 := [monotonicity #578]: #579
+#586 := [trans #580 #559]: #585
+#588 := [trans #586 #582]: #587
+#589 := [trans #588 #584]: #101
+#152 := (not #101)
+#154 := [not-or-elim #153]: #152
+[unit-resolution #154 #589]: false
+unsat
+9055acfd16334a78cb7c2c28508fdebc2b7c7f63 233 0
+#2 := false
+decl f28 :: S6
+#92 := f28
 decl f14 :: (-> S2 S6 S6)
 decl f25 :: (-> S3 S6 S6)
 decl f15 :: (-> S2 S6 S6)
-decl f28 :: S6
-#93 := f28
-decl f4 :: S2
-#8 := f4
-#99 := (f15 f4 f28)
+decl f4 :: S2
+#7 := f4
+#98 := (f15 f4 f28)
 decl f7 :: S3
-#21 := f7
-#100 := (f25 f7 #99)
+#20 := f7
+#99 := (f25 f7 #98)
 decl f5 :: S2
-#15 := f5
-#101 := (f14 f5 #100)
-#193 := (= f28 #101)
+#14 := f5
+#100 := (f14 f5 #99)
+#101 := (= #100 f28)
 decl f10 :: (-> Int Int S4 S6)
 decl f20 :: (-> S11 S9 S4)
-decl f23 :: (-> S13 S6 S9)
 decl f29 :: S9
-#95 := f29
+#94 := f29
 decl f21 :: (-> S12 S1 S11)
 decl f1 :: S1
-#4 := f1
+#3 := f1
 decl f22 :: S12
-#63 := f22
-#94 := (f21 f22 f1)
-#96 := (f20 #94 f29)
-#12 := 4::Int
-#18 := 3::Int
-#97 := (f10 3::Int 4::Int #96)
-decl f24 :: S13
-#74 := f24
-#447 := (f23 f24 #97)
+#62 := f22
+#93 := (f21 f22 f1)
+#95 := (f20 #93 f29)
+#11 := 4::Int
+#17 := 3::Int
+#96 := (f10 3::Int 4::Int #95)
+#583 := (= #96 f28)
+#97 := (= f28 #96)
+#144 := (not #97)
+#145 := (or #144 #101)
+#148 := (not #145)
+#102 := (implies #97 #101)
+#103 := (not #102)
+#149 := (iff #103 #148)
+#146 := (iff #102 #145)
+#147 := [rewrite]: #146
+#150 := [monotonicity #147]: #149
+#143 := [asserted]: #103
+#153 := [mp #143 #150]: #148
+#151 := [not-or-elim #153]: #97
+#584 := [symm #151]: #583
+#587 := (= #100 #96)
 decl f6 :: (-> S3 S1 S1)
-decl f18 :: (-> S10 S6 S1)
-decl f19 :: S10
-#61 := f19
-#425 := (f18 f19 #97)
-#542 := (f6 f7 #425)
-#545 := (f21 f22 #542)
-#549 := (f20 #545 #447)
-#567 := (f10 3::Int 4::Int #549)
-#649 := (f14 f5 #567)
-#809 := (= #649 #101)
-#802 := (= #101 #649)
-#800 := (= #100 #567)
-decl f3 :: (-> S2 Int Int)
-#407 := (f3 f4 4::Int)
-#550 := (f10 3::Int #407 #549)
-#796 := (= #550 #567)
-#794 := (= #567 #550)
-#763 := (= 4::Int #407)
-#541 := (= #407 4::Int)
-#9 := (:var 0 Int)
-#10 := (f3 f4 #9)
-#11 := (pattern #10)
-#13 := (= #10 4::Int)
-#14 := (forall (vars (?v0 Int)) (:pat #11) #13)
-#215 := (~ #14 #14)
-#213 := (~ #13 #13)
-#214 := [refl]: #213
-#216 := [nnf-pos #214]: #215
-#124 := [asserted]: #14
-#217 := [mp~ #124 #216]: #14
-#546 := (not #14)
-#547 := (or #546 #541)
-#548 := [quant-inst #12]: #547
-#762 := [unit-resolution #548 #217]: #541
-#764 := [symm #762]: #763
-#795 := [monotonicity #764]: #794
-#797 := [symm #795]: #796
-#798 := (= #100 #550)
-#487 := (f21 f22 #425)
-#488 := (f20 #487 #447)
-#489 := (f10 3::Int #407 #488)
-#551 := (f25 f7 #489)
-#552 := (= #551 #550)
-#553 := (= #550 #551)
-#66 := (:var 0 S9)
-#64 := (:var 1 S1)
-#78 := (:var 4 S3)
-#80 := (f6 #78 #64)
-#81 := (f21 f22 #80)
-#82 := (f20 #81 #66)
-#29 := (:var 2 Int)
-#62 := (:var 3 Int)
-#83 := (f10 #62 #29 #82)
-#392 := (pattern #83)
-#65 := (f21 f22 #64)
-#67 := (f20 #65 #66)
-#68 := (f10 #62 #29 #67)
-#79 := (f25 #78 #68)
-#391 := (pattern #79)
-#84 := (= #79 #83)
-#393 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) (:pat #391 #392) #84)
-#85 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) #84)
-#396 := (iff #85 #393)
-#394 := (iff #84 #84)
-#395 := [refl]: #394
-#397 := [quant-intro #395]: #396
-#270 := (~ #85 #85)
-#268 := (~ #84 #84)
-#269 := [refl]: #268
-#271 := [nnf-pos #269]: #270
-#189 := [asserted]: #85
-#272 := [mp~ #189 #271]: #85
-#398 := [mp #272 #397]: #393
-#556 := (not #393)
-#557 := (or #556 #553)
-#558 := (or #556 #552)
-#560 := (iff #558 #557)
-#562 := (iff #557 #557)
-#563 := [rewrite]: #562
-#554 := (iff #552 #553)
-#555 := [rewrite]: #554
-#561 := [monotonicity #555]: #560
-#564 := [trans #561 #563]: #560
-#559 := [quant-inst #21 #18 #407 #425 #447]: #558
-#565 := [mp #559 #564]: #557
-#765 := [unit-resolution #565 #398]: #553
-#793 := [symm #765]: #552
-#791 := (= #100 #551)
-#789 := (= #99 #489)
-#783 := (= #97 #489)
-#776 := (= #489 #97)
-#772 := (= #488 #96)
-#748 := (= #447 f29)
-#448 := (= f29 #447)
-#378 := (pattern #68)
-#75 := (f23 f24 #68)
-#182 := (= #66 #75)
-#385 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S9)) (:pat #378) #182)
-#186 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S9)) #182)
-#388 := (iff #186 #385)
-#386 := (iff #182 #182)
-#387 := [refl]: #386
-#389 := [quant-intro #387]: #388
-#265 := (~ #186 #186)
-#263 := (~ #182 #182)
-#264 := [refl]: #263
-#266 := [nnf-pos #264]: #265
-#76 := (= #75 #66)
-#77 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S9)) #76)
-#187 := (iff #77 #186)
-#184 := (iff #76 #182)
-#185 := [rewrite]: #184
-#188 := [quant-intro #185]: #187
-#181 := [asserted]: #77
-#191 := [mp #181 #188]: #186
-#267 := [mp~ #191 #266]: #186
-#390 := [mp #267 #389]: #385
-#451 := (not #385)
-#452 := (or #451 #448)
-#453 := [quant-inst #18 #12 #4 #95]: #452
-#747 := [unit-resolution #453 #390]: #448
-#752 := [symm #747]: #748
-#770 := (= #487 #94)
-#768 := (= #425 f1)
-#426 := (= f1 #425)
-#172 := (= f1 #64)
-#69 := (f18 f19 #68)
-#169 := (= f1 #69)
-#175 := (iff #169 #172)
-#379 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S9)) (:pat #378) #175)
-#178 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S9)) #175)
-#382 := (iff #178 #379)
-#380 := (iff #175 #175)
-#381 := [refl]: #380
-#383 := [quant-intro #381]: #382
-#260 := (~ #178 #178)
-#258 := (~ #175 #175)
-#259 := [refl]: #258
-#261 := [nnf-pos #259]: #260
-#71 := (= #64 f1)
-#70 := (= #69 f1)
-#72 := (iff #70 #71)
-#73 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S9)) #72)
-#179 := (iff #73 #178)
-#176 := (iff #72 #175)
-#173 := (iff #71 #172)
-#174 := [rewrite]: #173
-#170 := (iff #70 #169)
-#171 := [rewrite]: #170
-#177 := [monotonicity #171 #174]: #176
-#180 := [quant-intro #177]: #179
-#168 := [asserted]: #73
-#183 := [mp #168 #180]: #178
-#262 := [mp~ #183 #261]: #178
-#384 := [mp #262 #383]: #379
-#437 := (not #379)
-#438 := (or #437 #426)
-#424 := (= f1 f1)
-#427 := (iff #426 #424)
-#439 := (or #437 #427)
-#441 := (iff #439 #438)
-#443 := (iff #438 #438)
-#444 := [rewrite]: #443
-#435 := (iff #427 #426)
-#1 := true
-#430 := (iff #426 true)
-#433 := (iff #430 #426)
-#434 := [rewrite]: #433
-#431 := (iff #427 #430)
-#428 := (iff #424 true)
-#429 := [rewrite]: #428
-#432 := [monotonicity #429]: #431
-#436 := [trans #432 #434]: #435
-#442 := [monotonicity #436]: #441
-#445 := [trans #442 #444]: #441
-#440 := [quant-inst #18 #12 #4 #95]: #439
-#446 := [mp #440 #445]: #438
-#767 := [unit-resolution #446 #384]: #426
-#769 := [symm #767]: #768
-#771 := [monotonicity #769]: #770
-#773 := [monotonicity #771 #752]: #772
-#777 := [monotonicity #762 #773]: #776
-#784 := [symm #777]: #783
-#787 := (= #99 #97)
-#408 := (f10 3::Int #407 #96)
-#781 := (= #408 #97)
-#778 := (= #97 #408)
-#779 := [monotonicity #764]: #778
-#782 := [symm #779]: #781
-#785 := (= #99 #408)
-#409 := (f15 f4 #97)
-#410 := (= #409 #408)
-#411 := (= #408 #409)
-#31 := (:var 0 S4)
-#30 := (:var 1 Int)
-#44 := (:var 3 S2)
-#51 := (f3 #44 #30)
-#52 := (f10 #29 #51 #31)
-#363 := (pattern #52)
-#32 := (f10 #29 #30 #31)
-#50 := (f15 #44 #32)
-#362 := (pattern #50)
-#53 := (= #50 #52)
-#364 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #362 #363) #53)
-#54 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #53)
-#367 := (iff #54 #364)
-#365 := (iff #53 #53)
-#366 := [refl]: #365
-#368 := [quant-intro #366]: #367
-#250 := (~ #54 #54)
-#248 := (~ #53 #53)
-#249 := [refl]: #248
-#251 := [nnf-pos #249]: #250
-#165 := [asserted]: #54
-#252 := [mp~ #165 #251]: #54
-#369 := [mp #252 #368]: #364
-#414 := (not #364)
-#415 := (or #414 #411)
-#416 := (or #414 #410)
-#418 := (iff #416 #415)
-#420 := (iff #415 #415)
-#421 := [rewrite]: #420
-#412 := (iff #410 #411)
-#413 := [rewrite]: #412
-#419 := [monotonicity #413]: #418
-#422 := [trans #419 #421]: #418
-#417 := [quant-inst #8 #18 #12 #96]: #416
-#423 := [mp #417 #422]: #415
-#766 := [unit-resolution #423 #369]: #411
-#780 := [symm #766]: #410
-#774 := (= #99 #409)
-#98 := (= f28 #97)
-#199 := (not #98)
-#200 := (or #199 #193)
-#205 := (not #200)
-#102 := (= #101 f28)
-#103 := (implies #98 #102)
-#104 := (not #103)
-#206 := (iff #104 #205)
-#203 := (iff #103 #200)
-#196 := (implies #98 #193)
-#201 := (iff #196 #200)
-#202 := [rewrite]: #201
-#197 := (iff #103 #196)
-#194 := (iff #102 #193)
-#195 := [rewrite]: #194
-#198 := [monotonicity #195]: #197
-#204 := [trans #198 #202]: #203
-#207 := [monotonicity #204]: #206
-#192 := [asserted]: #104
-#210 := [mp #192 #207]: #205
-#208 := [not-or-elim #210]: #98
-#775 := [monotonicity #208]: #774
-#786 := [trans #775 #780]: #785
-#788 := [trans #786 #782]: #787
-#790 := [trans #788 #784]: #789
-#792 := [monotonicity #790]: #791
-#799 := [trans #792 #793]: #798
-#801 := [trans #799 #797]: #800
-#803 := [monotonicity #801]: #802
-#810 := [symm #803]: #809
-#813 := (= f28 #649)
-#644 := (f3 f5 3::Int)
-#645 := (f10 #644 4::Int #549)
-#651 := (= #645 #649)
-#46 := (f3 #44 #29)
-#47 := (f10 #46 #30 #31)
-#355 := (pattern #47)
-#45 := (f14 #44 #32)
-#354 := (pattern #45)
-#48 := (= #45 #47)
-#356 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #354 #355) #48)
-#49 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #48)
-#359 := (iff #49 #356)
-#357 := (iff #48 #48)
-#358 := [refl]: #357
-#360 := [quant-intro #358]: #359
-#245 := (~ #49 #49)
-#243 := (~ #48 #48)
-#244 := [refl]: #243
-#246 := [nnf-pos #244]: #245
-#164 := [asserted]: #49
-#247 := [mp~ #164 #246]: #49
-#361 := [mp #247 #360]: #356
-#654 := (not #356)
-#655 := (or #654 #651)
-#650 := (= #649 #645)
-#656 := (or #654 #650)
-#658 := (iff #656 #655)
-#660 := (iff #655 #655)
-#661 := [rewrite]: #660
-#652 := (iff #650 #651)
-#653 := [rewrite]: #652
-#659 := [monotonicity #653]: #658
-#662 := [trans #659 #661]: #658
-#657 := [quant-inst #15 #18 #12 #549]: #656
-#663 := [mp #657 #662]: #655
-#761 := [unit-resolution #663 #361]: #651
-#811 := (= f28 #645)
-#807 := (= #97 #645)
-#805 := (= #645 #97)
-#758 := (= #549 #96)
-#756 := (= #545 #94)
-#754 := (= #542 f1)
-#566 := (= f1 #542)
-#22 := (:var 0 S1)
-#23 := (f6 f7 #22)
-#24 := (pattern #23)
-#127 := (= f1 #23)
-#137 := (forall (vars (?v0 S1)) (:pat #24) #127)
-#225 := (~ #137 #137)
-#223 := (~ #127 #127)
-#224 := [refl]: #223
-#226 := [nnf-pos #224]: #225
-#25 := (= #23 f1)
-#26 := (iff #25 true)
-#27 := (forall (vars (?v0 S1)) (:pat #24) #26)
-#138 := (iff #27 #137)
-#135 := (iff #26 #127)
-#130 := (iff #127 true)
-#133 := (iff #130 #127)
-#134 := [rewrite]: #133
-#131 := (iff #26 #130)
-#128 := (iff #25 #127)
-#129 := [rewrite]: #128
-#132 := [monotonicity #129]: #131
-#136 := [trans #132 #134]: #135
-#139 := [quant-intro #136]: #138
-#126 := [asserted]: #27
-#142 := [mp #126 #139]: #137
-#227 := [mp~ #142 #226]: #137
-#646 := (not #137)
-#647 := (or #646 #566)
-#648 := [quant-inst #425]: #647
-#753 := [unit-resolution #648 #227]: #566
-#755 := [symm #753]: #754
-#757 := [monotonicity #755]: #756
-#759 := [monotonicity #757 #752]: #758
-#746 := (= #644 3::Int)
-#16 := (f3 f5 #9)
-#17 := (pattern #16)
-#19 := (= #16 3::Int)
-#20 := (forall (vars (?v0 Int)) (:pat #17) #19)
-#220 := (~ #20 #20)
-#218 := (~ #19 #19)
-#219 := [refl]: #218
-#221 := [nnf-pos #219]: #220
-#125 := [asserted]: #20
-#222 := [mp~ #125 #221]: #20
-#749 := (not #20)
-#750 := (or #749 #746)
-#751 := [quant-inst #18]: #750
-#760 := [unit-resolution #751 #222]: #746
-#806 := [monotonicity #760 #759]: #805
-#808 := [symm #806]: #807
-#812 := [trans #208 #808]: #811
-#814 := [trans #812 #761]: #813
-#815 := [trans #814 #810]: #193
-#209 := (not #193)
-#211 := [not-or-elim #210]: #209
-[unit-resolution #211 #815]: false
-unsat
-b404f46cd1ab54bbfdd274ebb50cd52e1a7816c8 386 0
-#2 := false
+#445 := (f6 f7 f1)
+#449 := (f21 f22 #445)
+#450 := (f20 #449 f29)
+decl f3 :: (-> S2 Int Int)
+#493 := (f3 f5 3::Int)
+#499 := (f10 #493 4::Int #450)
+#581 := (= #499 #96)
+#556 := (= #450 #95)
+#551 := (= #449 #93)
+#459 := (= #445 f1)
+#21 := (:var 0 S1)
+#22 := (f6 f7 #21)
+#23 := (pattern #22)
+#24 := (= #22 f1)
+#129 := (forall (vars (?v0 S1)) (:pat #23) #24)
+#168 := (~ #129 #129)
+#166 := (~ #24 #24)
+#167 := [refl]: #166
+#169 := [nnf-pos #167]: #168
+#1 := true
+#25 := (iff #24 true)
+#26 := (forall (vars (?v0 S1)) (:pat #23) #25)
+#130 := (iff #26 #129)
+#127 := (iff #25 #24)
+#128 := [rewrite]: #127
+#131 := [quant-intro #128]: #130
+#126 := [asserted]: #26
+#134 := [mp #126 #131]: #129
+#170 := [mp~ #134 #169]: #129
+#496 := (not #129)
+#497 := (or #496 #459)
+#498 := [quant-inst #3]: #497
+#548 := [unit-resolution #498 #170]: #459
+#555 := [monotonicity #548]: #551
+#557 := [monotonicity #555]: #556
+#547 := (= #493 3::Int)
+#8 := (:var 0 Int)
+#15 := (f3 f5 #8)
+#16 := (pattern #15)
+#18 := (= #15 3::Int)
+#19 := (forall (vars (?v0 Int)) (:pat #16) #18)
+#163 := (~ #19 #19)
+#161 := (~ #18 #18)
+#162 := [refl]: #161
+#164 := [nnf-pos #162]: #163
+#125 := [asserted]: #19
+#165 := [mp~ #125 #164]: #19
+#552 := (not #19)
+#553 := (or #552 #547)
+#554 := [quant-inst #17]: #553
+#558 := [unit-resolution #554 #165]: #547
+#582 := [monotonicity #558 #557]: #581
+#585 := (= #100 #499)
+#453 := (f10 3::Int 4::Int #450)
+#492 := (f14 f5 #453)
+#500 := (= #492 #499)
+#30 := (:var 0 S4)
+#29 := (:var 1 Int)
+#28 := (:var 2 Int)
+#43 := (:var 3 S2)
+#45 := (f3 #43 #28)
+#46 := (f10 #45 #29 #30)
+#301 := (pattern #46)
+#31 := (f10 #28 #29 #30)
+#44 := (f14 #43 #31)
+#300 := (pattern #44)
+#47 := (= #44 #46)
+#302 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #300 #301) #47)
+#48 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #47)
+#305 := (iff #48 #302)
+#303 := (iff #47 #47)
+#304 := [refl]: #303
+#306 := [quant-intro #304]: #305
+#188 := (~ #48 #48)
+#186 := (~ #47 #47)
+#187 := [refl]: #186
+#189 := [nnf-pos #187]: #188
+#136 := [asserted]: #48
+#190 := [mp~ #136 #189]: #48
+#307 := [mp #190 #306]: #302
+#503 := (not #302)
+#504 := (or #503 #500)
+#505 := [quant-inst #14 #17 #11 #450]: #504
+#559 := [unit-resolution #505 #307]: #500
+#579 := (= #100 #492)
+#577 := (= #99 #453)
+#355 := (f3 f4 4::Int)
+#451 := (f10 3::Int #355 #450)
+#573 := (= #451 #453)
+#571 := (= #453 #451)
+#561 := (= 4::Int #355)
+#441 := (= #355 4::Int)
+#9 := (f3 f4 #8)
+#10 := (pattern #9)
+#12 := (= #9 4::Int)
+#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
+#158 := (~ #13 #13)
+#156 := (~ #12 #12)
+#157 := [refl]: #156
+#159 := [nnf-pos #157]: #158
+#124 := [asserted]: #13
+#160 := [mp~ #124 #159]: #13
+#446 := (not #13)
+#447 := (or #446 #441)
+#448 := [quant-inst #11]: #447
+#560 := [unit-resolution #448 #160]: #441
+#562 := [symm #560]: #561
+#572 := [monotonicity #562]: #571
+#574 := [symm #572]: #573
+#575 := (= #99 #451)
+#354 := (f10 3::Int #355 #95)
+#442 := (f25 f7 #354)
+#452 := (= #442 #451)
+#65 := (:var 0 S9)
+#63 := (:var 1 S1)
+#77 := (:var 4 S3)
+#79 := (f6 #77 #63)
+#80 := (f21 f22 #79)
+#81 := (f20 #80 #65)
+#61 := (:var 3 Int)
+#82 := (f10 #61 #28 #81)
+#338 := (pattern #82)
+#64 := (f21 f22 #63)
+#66 := (f20 #64 #65)
+#67 := (f10 #61 #28 #66)
+#78 := (f25 #77 #67)
+#337 := (pattern #78)
+#83 := (= #78 #82)
+#339 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) (:pat #337 #338) #83)
+#84 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) #83)
+#342 := (iff #84 #339)
+#340 := (iff #83 #83)
+#341 := [refl]: #340
+#343 := [quant-intro #341]: #342
+#213 := (~ #84 #84)
+#211 := (~ #83 #83)
+#212 := [refl]: #211
+#214 := [nnf-pos #212]: #213
+#141 := [asserted]: #84
+#215 := [mp~ #141 #214]: #84
+#344 := [mp #215 #343]: #339
+#455 := (not #339)
+#456 := (or #455 #452)
+#457 := [quant-inst #20 #17 #355 #3 #94]: #456
+#563 := [unit-resolution #457 #344]: #452
+#569 := (= #99 #442)
+#567 := (= #98 #354)
+#353 := (f15 f4 #96)
+#361 := (= #353 #354)
+#50 := (f3 #43 #29)
+#51 := (f10 #28 #50 #30)
+#309 := (pattern #51)
+#49 := (f15 #43 #31)
+#308 := (pattern #49)
+#52 := (= #49 #51)
+#310 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #308 #309) #52)
+#53 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #52)
+#313 := (iff #53 #310)
+#311 := (iff #52 #52)
+#312 := [refl]: #311
+#314 := [quant-intro #312]: #313
+#193 := (~ #53 #53)
+#191 := (~ #52 #52)
+#192 := [refl]: #191
+#194 := [nnf-pos #192]: #193
+#137 := [asserted]: #53
+#195 := [mp~ #137 #194]: #53
+#315 := [mp #195 #314]: #310
+#364 := (not #310)
+#365 := (or #364 #361)
+#366 := [quant-inst #7 #17 #11 #95]: #365
+#564 := [unit-resolution #366 #315]: #361
+#565 := (= #98 #353)
+#566 := [monotonicity #151]: #565
+#568 := [trans #566 #564]: #567
+#570 := [monotonicity #568]: #569
+#576 := [trans #570 #563]: #575
+#578 := [trans #576 #574]: #577
+#580 := [monotonicity #578]: #579
+#586 := [trans #580 #559]: #585
+#588 := [trans #586 #582]: #587
+#589 := [trans #588 #584]: #101
+#152 := (not #101)
+#154 := [not-or-elim #153]: #152
+[unit-resolution #154 #589]: false
+unsat
+67bf97bc391b1b7e654702d4edbfac8730a51707 233 0
+#2 := false
+decl f28 :: S6
+#92 := f28
 decl f15 :: (-> S2 S6 S6)
 decl f14 :: (-> S2 S6 S6)
 decl f25 :: (-> S3 S6 S6)
-decl f28 :: S6
-#93 := f28
 decl f7 :: S3
-#21 := f7
-#99 := (f25 f7 f28)
+#20 := f7
+#98 := (f25 f7 f28)
 decl f5 :: S2
-#15 := f5
-#100 := (f14 f5 #99)
-decl f4 :: S2
-#8 := f4
-#101 := (f15 f4 #100)
-#193 := (= f28 #101)
+#14 := f5
+#99 := (f14 f5 #98)
+decl f4 :: S2
+#7 := f4
+#100 := (f15 f4 #99)
+#101 := (= #100 f28)
 decl f10 :: (-> Int Int S4 S6)
-decl f12 :: (-> S7 S6 S4)
 decl f20 :: (-> S11 S9 S4)
 decl f29 :: S9
-#95 := f29
+#94 := f29
 decl f21 :: (-> S12 S1 S11)
-decl f6 :: (-> S3 S1 S1)
-decl f1 :: S1
-#4 := f1
-#407 := (f6 f7 f1)
+decl f1 :: S1
+#3 := f1
 decl f22 :: S12
-#63 := f22
-#408 := (f21 f22 #407)
-#409 := (f20 #408 f29)
-#12 := 4::Int
-#18 := 3::Int
-#410 := (f10 3::Int 4::Int #409)
-decl f13 :: S7
-#40 := f13
-#520 := (f12 f13 #410)
-decl f3 :: (-> S2 Int Int)
-#556 := (f3 f5 3::Int)
-#624 := (f10 #556 4::Int #520)
-#655 := (f15 f4 #624)
-#803 := (= #655 #101)
-#796 := (= #101 #655)
-#778 := (= #100 #624)
-#557 := (f10 #556 4::Int #409)
-#774 := (= #557 #624)
-#772 := (= #624 #557)
-#754 := (= #520 #409)
-#521 := (= #409 #520)
-#31 := (:var 0 S4)
-#30 := (:var 1 Int)
-#29 := (:var 2 Int)
-#32 := (f10 #29 #30 #31)
-#335 := (pattern #32)
-#41 := (f12 f13 #32)
-#157 := (= #31 #41)
-#348 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) (:pat #335) #157)
-#161 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) #157)
-#351 := (iff #161 #348)
-#349 := (iff #157 #157)
-#350 := [refl]: #349
-#352 := [quant-intro #350]: #351
-#240 := (~ #161 #161)
-#238 := (~ #157 #157)
-#239 := [refl]: #238
-#241 := [nnf-pos #239]: #240
-#42 := (= #41 #31)
-#43 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) #42)
-#162 := (iff #43 #161)
-#159 := (iff #42 #157)
-#160 := [rewrite]: #159
-#163 := [quant-intro #160]: #162
-#156 := [asserted]: #43
-#166 := [mp #156 #163]: #161
-#242 := [mp~ #166 #241]: #161
-#353 := [mp #242 #352]: #348
-#458 := (not #348)
-#526 := (or #458 #521)
-#527 := [quant-inst #18 #12 #409]: #526
-#751 := [unit-resolution #527 #353]: #521
-#758 := [symm #751]: #754
-#773 := [monotonicity #758]: #772
-#775 := [symm #773]: #774
-#776 := (= #100 #557)
-#561 := (f14 f5 #410)
-#562 := (= #561 #557)
-#563 := (= #557 #561)
-#44 := (:var 3 S2)
-#46 := (f3 #44 #29)
-#47 := (f10 #46 #30 #31)
-#355 := (pattern #47)
-#45 := (f14 #44 #32)
-#354 := (pattern #45)
-#48 := (= #45 #47)
-#356 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #354 #355) #48)
-#49 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #48)
-#359 := (iff #49 #356)
-#357 := (iff #48 #48)
-#358 := [refl]: #357
-#360 := [quant-intro #358]: #359
-#245 := (~ #49 #49)
-#243 := (~ #48 #48)
-#244 := [refl]: #243
-#246 := [nnf-pos #244]: #245
-#164 := [asserted]: #49
-#247 := [mp~ #164 #246]: #49
-#361 := [mp #247 #360]: #356
-#566 := (not #356)
-#567 := (or #566 #563)
-#568 := (or #566 #562)
-#570 := (iff #568 #567)
-#572 := (iff #567 #567)
-#573 := [rewrite]: #572
-#564 := (iff #562 #563)
-#565 := [rewrite]: #564
-#571 := [monotonicity #565]: #570
-#574 := [trans #571 #573]: #570
-#569 := [quant-inst #15 #18 #12 #409]: #568
-#575 := [mp #569 #574]: #567
-#762 := [unit-resolution #575 #361]: #563
-#771 := [symm #762]: #562
-#769 := (= #100 #561)
-#767 := (= #99 #410)
-#94 := (f21 f22 f1)
-#96 := (f20 #94 f29)
-#97 := (f10 3::Int 4::Int #96)
-#411 := (f25 f7 #97)
-#412 := (= #411 #410)
-#413 := (= #410 #411)
-#66 := (:var 0 S9)
-#64 := (:var 1 S1)
-#78 := (:var 4 S3)
-#80 := (f6 #78 #64)
-#81 := (f21 f22 #80)
-#82 := (f20 #81 #66)
-#62 := (:var 3 Int)
-#83 := (f10 #62 #29 #82)
-#392 := (pattern #83)
-#65 := (f21 f22 #64)
-#67 := (f20 #65 #66)
-#68 := (f10 #62 #29 #67)
-#79 := (f25 #78 #68)
-#391 := (pattern #79)
-#84 := (= #79 #83)
-#393 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) (:pat #391 #392) #84)
-#85 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) #84)
-#396 := (iff #85 #393)
-#394 := (iff #84 #84)
-#395 := [refl]: #394
-#397 := [quant-intro #395]: #396
-#270 := (~ #85 #85)
-#268 := (~ #84 #84)
-#269 := [refl]: #268
-#271 := [nnf-pos #269]: #270
-#189 := [asserted]: #85
-#272 := [mp~ #189 #271]: #85
-#398 := [mp #272 #397]: #393
-#416 := (not #393)
-#417 := (or #416 #413)
-#418 := (or #416 #412)
-#420 := (iff #418 #417)
-#422 := (iff #417 #417)
-#423 := [rewrite]: #422
-#414 := (iff #412 #413)
-#415 := [rewrite]: #414
-#421 := [monotonicity #415]: #420
-#424 := [trans #421 #423]: #420
-#419 := [quant-inst #21 #18 #12 #4 #95]: #418
-#425 := [mp #419 #424]: #417
-#763 := [unit-resolution #425 #398]: #413
-#766 := [symm #763]: #412
-#764 := (= #99 #411)
-#98 := (= f28 #97)
-#199 := (not #98)
-#200 := (or #199 #193)
-#205 := (not #200)
-#102 := (= #101 f28)
-#103 := (implies #98 #102)
-#104 := (not #103)
-#206 := (iff #104 #205)
-#203 := (iff #103 #200)
-#196 := (implies #98 #193)
-#201 := (iff #196 #200)
-#202 := [rewrite]: #201
-#197 := (iff #103 #196)
-#194 := (iff #102 #193)
-#195 := [rewrite]: #194
-#198 := [monotonicity #195]: #197
-#204 := [trans #198 #202]: #203
-#207 := [monotonicity #204]: #206
-#192 := [asserted]: #104
-#210 := [mp #192 #207]: #205
-#208 := [not-or-elim #210]: #98
-#765 := [monotonicity #208]: #764
-#768 := [trans #765 #766]: #767
-#770 := [monotonicity #768]: #769
-#777 := [trans #770 #771]: #776
-#779 := [trans #777 #775]: #778
-#797 := [monotonicity #779]: #796
-#804 := [symm #797]: #803
-#809 := (= f28 #655)
-#650 := (f3 f4 4::Int)
-#651 := (f10 #556 #650 #520)
-#657 := (= #651 #655)
-#51 := (f3 #44 #30)
-#52 := (f10 #29 #51 #31)
-#363 := (pattern #52)
-#50 := (f15 #44 #32)
-#362 := (pattern #50)
-#53 := (= #50 #52)
-#364 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #362 #363) #53)
-#54 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #53)
-#367 := (iff #54 #364)
-#365 := (iff #53 #53)
-#366 := [refl]: #365
-#368 := [quant-intro #366]: #367
-#250 := (~ #54 #54)
-#248 := (~ #53 #53)
-#249 := [refl]: #248
-#251 := [nnf-pos #249]: #250
-#165 := [asserted]: #54
-#252 := [mp~ #165 #251]: #54
-#369 := [mp #252 #368]: #364
-#660 := (not #364)
-#661 := (or #660 #657)
-#656 := (= #655 #651)
-#662 := (or #660 #656)
-#664 := (iff #662 #661)
-#666 := (iff #661 #661)
-#667 := [rewrite]: #666
-#658 := (iff #656 #657)
-#659 := [rewrite]: #658
-#665 := [monotonicity #659]: #664
-#668 := [trans #665 #667]: #664
-#663 := [quant-inst #8 #556 #12 #520]: #662
-#669 := [mp #663 #668]: #661
-#761 := [unit-resolution #669 #369]: #657
-#807 := (= f28 #651)
-#801 := (= #410 #651)
-#799 := (= #651 #410)
-#750 := (= #650 4::Int)
-#9 := (:var 0 Int)
-#10 := (f3 f4 #9)
-#11 := (pattern #10)
-#13 := (= #10 4::Int)
-#14 := (forall (vars (?v0 Int)) (:pat #11) #13)
-#215 := (~ #14 #14)
-#213 := (~ #13 #13)
-#214 := [refl]: #213
-#216 := [nnf-pos #214]: #215
-#124 := [asserted]: #14
-#217 := [mp~ #124 #216]: #14
-#755 := (not #14)
-#756 := (or #755 #750)
-#757 := [quant-inst #12]: #756
-#759 := [unit-resolution #757 #217]: #750
-#649 := (= #556 3::Int)
-#16 := (f3 f5 #9)
-#17 := (pattern #16)
-#19 := (= #16 3::Int)
-#20 := (forall (vars (?v0 Int)) (:pat #17) #19)
-#220 := (~ #20 #20)
-#218 := (~ #19 #19)
-#219 := [refl]: #218
-#221 := [nnf-pos #219]: #220
-#125 := [asserted]: #20
-#222 := [mp~ #125 #221]: #20
-#652 := (not #20)
-#653 := (or #652 #649)
-#654 := [quant-inst #18]: #653
-#760 := [unit-resolution #654 #222]: #649
-#800 := [monotonicity #760 #759 #758]: #799
-#802 := [symm #800]: #801
-#805 := (= f28 #410)
-#794 := (= #97 #410)
-#792 := (= #96 #409)
-#790 := (= #94 #408)
-#788 := (= #408 #94)
-#786 := (= #407 f1)
-decl f18 :: (-> S10 S6 S1)
-decl f19 :: S10
-#61 := f19
-#427 := (f18 f19 #97)
-#554 := (f6 f7 #427)
-#784 := (= #554 f1)
-#555 := (= f1 #554)
-#22 := (:var 0 S1)
-#23 := (f6 f7 #22)
-#24 := (pattern #23)
-#127 := (= f1 #23)
-#137 := (forall (vars (?v0 S1)) (:pat #24) #127)
-#225 := (~ #137 #137)
-#223 := (~ #127 #127)
-#224 := [refl]: #223
-#226 := [nnf-pos #224]: #225
-#1 := true
-#25 := (= #23 f1)
-#26 := (iff #25 true)
-#27 := (forall (vars (?v0 S1)) (:pat #24) #26)
-#138 := (iff #27 #137)
-#135 := (iff #26 #127)
-#130 := (iff #127 true)
-#133 := (iff #130 #127)
-#134 := [rewrite]: #133
-#131 := (iff #26 #130)
-#128 := (iff #25 #127)
-#129 := [rewrite]: #128
-#132 := [monotonicity #129]: #131
-#136 := [trans #132 #134]: #135
-#139 := [quant-intro #136]: #138
-#126 := [asserted]: #27
-#142 := [mp #126 #139]: #137
-#227 := [mp~ #142 #226]: #137
-#558 := (not #137)
-#559 := (or #558 #555)
-#560 := [quant-inst #427]: #559
-#780 := [unit-resolution #560 #227]: #555
-#785 := [symm #780]: #784
-#782 := (= #407 #554)
-#428 := (= f1 #427)
-#378 := (pattern #68)
-#172 := (= f1 #64)
-#69 := (f18 f19 #68)
-#169 := (= f1 #69)
-#175 := (iff #169 #172)
-#379 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S9)) (:pat #378) #175)
-#178 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S9)) #175)
-#382 := (iff #178 #379)
-#380 := (iff #175 #175)
-#381 := [refl]: #380
-#383 := [quant-intro #381]: #382
-#260 := (~ #178 #178)
-#258 := (~ #175 #175)
-#259 := [refl]: #258
-#261 := [nnf-pos #259]: #260
-#71 := (= #64 f1)
-#70 := (= #69 f1)
-#72 := (iff #70 #71)
-#73 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S9)) #72)
-#179 := (iff #73 #178)
-#176 := (iff #72 #175)
-#173 := (iff #71 #172)
-#174 := [rewrite]: #173
-#170 := (iff #70 #169)
-#171 := [rewrite]: #170
-#177 := [monotonicity #171 #174]: #176
-#180 := [quant-intro #177]: #179
-#168 := [asserted]: #73
-#183 := [mp #168 #180]: #178
-#262 := [mp~ #183 #261]: #178
-#384 := [mp #262 #383]: #379
-#439 := (not #379)
-#440 := (or #439 #428)
-#426 := (= f1 f1)
-#429 := (iff #428 #426)
-#441 := (or #439 #429)
-#443 := (iff #441 #440)
-#445 := (iff #440 #440)
-#446 := [rewrite]: #445
-#437 := (iff #429 #428)
-#432 := (iff #428 true)
-#435 := (iff #432 #428)
-#436 := [rewrite]: #435
-#433 := (iff #429 #432)
-#430 := (iff #426 true)
-#431 := [rewrite]: #430
-#434 := [monotonicity #431]: #433
-#438 := [trans #434 #436]: #437
-#444 := [monotonicity #438]: #443
-#447 := [trans #444 #446]: #443
-#442 := [quant-inst #18 #12 #4 #95]: #441
-#448 := [mp #442 #447]: #440
-#781 := [unit-resolution #448 #384]: #428
-#783 := [monotonicity #781]: #782
-#787 := [trans #783 #785]: #786
-#789 := [monotonicity #787]: #788
-#791 := [symm #789]: #790
-#793 := [monotonicity #791]: #792
-#795 := [monotonicity #793]: #794
-#806 := [trans #208 #795]: #805
-#808 := [trans #806 #802]: #807
-#810 := [trans #808 #761]: #809
-#811 := [trans #810 #804]: #193
-#209 := (not #193)
-#211 := [not-or-elim #210]: #209
-[unit-resolution #211 #811]: false
-unsat
-26495cecb76c01018d433fd25b109461db4ecbc6 18 0
+#62 := f22
+#93 := (f21 f22 f1)
+#95 := (f20 #93 f29)
+#11 := 4::Int
+#17 := 3::Int
+#96 := (f10 3::Int 4::Int #95)
+#583 := (= #96 f28)
+#97 := (= f28 #96)
+#144 := (not #97)
+#145 := (or #144 #101)
+#148 := (not #145)
+#102 := (implies #97 #101)
+#103 := (not #102)
+#149 := (iff #103 #148)
+#146 := (iff #102 #145)
+#147 := [rewrite]: #146
+#150 := [monotonicity #147]: #149
+#143 := [asserted]: #103
+#153 := [mp #143 #150]: #148
+#151 := [not-or-elim #153]: #97
+#584 := [symm #151]: #583
+#587 := (= #100 #96)
+decl f3 :: (-> S2 Int Int)
+#495 := (f3 f4 4::Int)
+#442 := (f3 f5 3::Int)
+#499 := (f10 #442 #495 #95)
+#581 := (= #499 #96)
+#547 := (= #495 4::Int)
+#8 := (:var 0 Int)
+#9 := (f3 f4 #8)
+#10 := (pattern #9)
+#12 := (= #9 4::Int)
+#13 := (forall (vars (?v0 Int)) (:pat #10) #12)
+#158 := (~ #13 #13)
+#156 := (~ #12 #12)
+#157 := [refl]: #156
+#159 := [nnf-pos #157]: #158
+#124 := [asserted]: #13
+#160 := [mp~ #124 #159]: #13
+#552 := (not #13)
+#553 := (or #552 #547)
+#554 := [quant-inst #11]: #553
+#548 := [unit-resolution #554 #160]: #547
+#491 := (= #442 3::Int)
+#15 := (f3 f5 #8)
+#16 := (pattern #15)
+#18 := (= #15 3::Int)
+#19 := (forall (vars (?v0 Int)) (:pat #16) #18)
+#163 := (~ #19 #19)
+#161 := (~ #18 #18)
+#162 := [refl]: #161
+#164 := [nnf-pos #162]: #163
+#125 := [asserted]: #19
+#165 := [mp~ #125 #164]: #19
+#496 := (not #19)
+#497 := (or #496 #491)
+#498 := [quant-inst #17]: #497
+#551 := [unit-resolution #498 #165]: #491
+#582 := [monotonicity #551 #548]: #581
+#585 := (= #100 #499)
+#450 := (f10 #442 4::Int #95)
+#492 := (f15 f4 #450)
+#500 := (= #492 #499)
+#30 := (:var 0 S4)
+#29 := (:var 1 Int)
+#43 := (:var 3 S2)
+#50 := (f3 #43 #29)
+#28 := (:var 2 Int)
+#51 := (f10 #28 #50 #30)
+#309 := (pattern #51)
+#31 := (f10 #28 #29 #30)
+#49 := (f15 #43 #31)
+#308 := (pattern #49)
+#52 := (= #49 #51)
+#310 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #308 #309) #52)
+#53 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #52)
+#313 := (iff #53 #310)
+#311 := (iff #52 #52)
+#312 := [refl]: #311
+#314 := [quant-intro #312]: #313
+#193 := (~ #53 #53)
+#191 := (~ #52 #52)
+#192 := [refl]: #191
+#194 := [nnf-pos #192]: #193
+#137 := [asserted]: #53
+#195 := [mp~ #137 #194]: #53
+#315 := [mp #195 #314]: #310
+#503 := (not #310)
+#504 := (or #503 #500)
+#505 := [quant-inst #7 #442 #11 #95]: #504
+#555 := [unit-resolution #505 #315]: #500
+#579 := (= #100 #492)
+#577 := (= #99 #450)
+decl f6 :: (-> S3 S1 S1)
+#355 := (f6 f7 f1)
+#354 := (f21 f22 #355)
+#361 := (f20 #354 f29)
+#448 := (f10 #442 4::Int #361)
+#573 := (= #448 #450)
+#571 := (= #450 #448)
+#561 := (= #95 #361)
+#559 := (= #361 #95)
+#557 := (= #354 #93)
+#412 := (= #355 f1)
+#21 := (:var 0 S1)
+#22 := (f6 f7 #21)
+#23 := (pattern #22)
+#24 := (= #22 f1)
+#129 := (forall (vars (?v0 S1)) (:pat #23) #24)
+#168 := (~ #129 #129)
+#166 := (~ #24 #24)
+#167 := [refl]: #166
+#169 := [nnf-pos #167]: #168
+#1 := true
+#25 := (iff #24 true)
+#26 := (forall (vars (?v0 S1)) (:pat #23) #25)
+#130 := (iff #26 #129)
+#127 := (iff #25 #24)
+#128 := [rewrite]: #127
+#131 := [quant-intro #128]: #130
+#126 := [asserted]: #26
+#134 := [mp #126 #131]: #129
+#170 := [mp~ #134 #169]: #129
+#445 := (not #129)
+#446 := (or #445 #412)
+#447 := [quant-inst #3]: #446
+#556 := [unit-resolution #447 #170]: #412
+#558 := [monotonicity #556]: #557
+#560 := [monotonicity #558]: #559
+#562 := [symm #560]: #561
+#572 := [monotonicity #562]: #571
+#574 := [symm #572]: #573
+#575 := (= #99 #448)
+#362 := (f10 3::Int 4::Int #361)
+#441 := (f14 f5 #362)
+#449 := (= #441 #448)
+#45 := (f3 #43 #28)
+#46 := (f10 #45 #29 #30)
+#301 := (pattern #46)
+#44 := (f14 #43 #31)
+#300 := (pattern #44)
+#47 := (= #44 #46)
+#302 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #300 #301) #47)
+#48 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #47)
+#305 := (iff #48 #302)
+#303 := (iff #47 #47)
+#304 := [refl]: #303
+#306 := [quant-intro #304]: #305
+#188 := (~ #48 #48)
+#186 := (~ #47 #47)
+#187 := [refl]: #186
+#189 := [nnf-pos #187]: #188
+#136 := [asserted]: #48
+#190 := [mp~ #136 #189]: #48
+#307 := [mp #190 #306]: #302
+#452 := (not #302)
+#453 := (or #452 #449)
+#454 := [quant-inst #14 #17 #11 #361]: #453
+#563 := [unit-resolution #454 #307]: #449
+#569 := (= #99 #441)
+#567 := (= #98 #362)
+#353 := (f25 f7 #96)
+#363 := (= #353 #362)
+#65 := (:var 0 S9)
+#63 := (:var 1 S1)
+#77 := (:var 4 S3)
+#79 := (f6 #77 #63)
+#80 := (f21 f22 #79)
+#81 := (f20 #80 #65)
+#61 := (:var 3 Int)
+#82 := (f10 #61 #28 #81)
+#338 := (pattern #82)
+#64 := (f21 f22 #63)
+#66 := (f20 #64 #65)
+#67 := (f10 #61 #28 #66)
+#78 := (f25 #77 #67)
+#337 := (pattern #78)
+#83 := (= #78 #82)
+#339 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) (:pat #337 #338) #83)
+#84 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S9)) #83)
+#342 := (iff #84 #339)
+#340 := (iff #83 #83)
+#341 := [refl]: #340
+#343 := [quant-intro #341]: #342
+#213 := (~ #84 #84)
+#211 := (~ #83 #83)
+#212 := [refl]: #211
+#214 := [nnf-pos #212]: #213
+#141 := [asserted]: #84
+#215 := [mp~ #141 #214]: #84
+#344 := [mp #215 #343]: #339
+#366 := (not #339)
+#367 := (or #366 #363)
+#368 := [quant-inst #20 #17 #11 #3 #94]: #367
+#564 := [unit-resolution #368 #344]: #363
+#565 := (= #98 #353)
+#566 := [monotonicity #151]: #565
+#568 := [trans #566 #564]: #567
+#570 := [monotonicity #568]: #569
+#576 := [trans #570 #563]: #575
+#578 := [trans #576 #574]: #577
+#580 := [monotonicity #578]: #579
+#586 := [trans #580 #555]: #585
+#588 := [trans #586 #582]: #587
+#589 := [trans #588 #584]: #101
+#152 := (not #101)
+#154 := [not-or-elim #153]: #152
+[unit-resolution #154 #589]: false
+unsat
+fde09c00a7285975ac7164417c3a5481fc130775 18 0
 #2 := false
 decl f3 :: S2
-#8 := f3
-#52 := (= f3 f3)
-#53 := (not #52)
-#159 := (iff #53 false)
-#1 := true
-#154 := (not true)
-#157 := (iff #154 false)
-#158 := [rewrite]: #157
-#155 := (iff #53 #154)
-#151 := (iff #52 true)
-#153 := [rewrite]: #151
-#156 := [monotonicity #153]: #155
-#160 := [trans #156 #158]: #159
-#150 := [asserted]: #53
-[mp #150 #160]: false
-unsat
-039d88747cc3aaca789d0d44ca21e3131ffed65c 18 0
+#7 := f3
+#51 := (= f3 f3)
+#52 := (not #51)
+#106 := (iff #52 false)
+#1 := true
+#101 := (not true)
+#104 := (iff #101 false)
+#105 := [rewrite]: #104
+#102 := (iff #52 #101)
+#98 := (iff #51 true)
+#100 := [rewrite]: #98
+#103 := [monotonicity #100]: #102
+#107 := [trans #103 #105]: #106
+#97 := [asserted]: #52
+[mp #97 #107]: false
+unsat
+17ef6441e1a98a1f31e9a83ffe2622bca36b5e7b 18 0
 #2 := false
 decl f6 :: S2
-#13 := f6
-#52 := (= f6 f6)
-#53 := (not #52)
-#159 := (iff #53 false)
-#1 := true
-#154 := (not true)
-#157 := (iff #154 false)
-#158 := [rewrite]: #157
-#155 := (iff #53 #154)
-#151 := (iff #52 true)
-#153 := [rewrite]: #151
-#156 := [monotonicity #153]: #155
-#160 := [trans #156 #158]: #159
-#150 := [asserted]: #53
-[mp #150 #160]: false
-unsat
-f7ce3d8d545e91c59d80b4beef160514c745ee03 281 0
-#2 := false
-#14 := 2::Int
-#10 := 1::Int
-#334 := (= 1::Int 2::Int)
-#339 := (iff #334 false)
-#340 := [rewrite]: #339
+#12 := f6
+#51 := (= f6 f6)
+#52 := (not #51)
+#106 := (iff #52 false)
+#1 := true
+#101 := (not true)
+#104 := (iff #101 false)
+#105 := [rewrite]: #104
+#102 := (iff #52 #101)
+#98 := (iff #51 true)
+#100 := [rewrite]: #98
+#103 := [monotonicity #100]: #102
+#107 := [trans #103 #105]: #106
+#97 := [asserted]: #52
+[mp #97 #107]: false
+unsat
+463ef29b79712be72c7a08cb850a77bae02ca87d 213 0
+#2 := false
+#13 := 2::Int
+#9 := 1::Int
+#243 := (= 1::Int 2::Int)
+#255 := (iff #243 false)
+#256 := [rewrite]: #255
 decl f11 :: (-> S6 S2 Int)
 decl f4 :: (-> S3 Int S2)
 decl f5 :: S3
-#9 := f5
-#15 := (f4 f5 2::Int)
+#8 := f5
+#14 := (f4 f5 2::Int)
 decl f12 :: S6
-#26 := f12
-#286 := (f11 f12 #15)
-#294 := (= #286 2::Int)
+#25 := f12
+#227 := (f11 f12 #14)
+#228 := (= #227 2::Int)
+decl f1 :: S1
+#3 := f1
 decl f13 :: (-> Int S7 S1)
 decl f14 :: S7
-#34 := f14
-#288 := (f13 2::Int f14)
-decl f1 :: S1
-#4 := f1
-#289 := (= f1 #288)
-#290 := (not #289)
-#450 := [hypothesis]: #290
-#33 := (:var 0 Int)
-#35 := (f13 #33 f14)
-#241 := (pattern #35)
-#18 := 3::Int
-#39 := (= #33 3::Int)
-#38 := (= #33 2::Int)
-#37 := (= #33 1::Int)
-#113 := (or #37 #38 #39)
-#79 := (= f1 #35)
-#118 := (iff #79 #113)
-#242 := (forall (vars (?v0 Int)) (:pat #241) #118)
-#121 := (forall (vars (?v0 Int)) #118)
-#245 := (iff #121 #242)
-#243 := (iff #118 #118)
-#244 := [refl]: #243
-#246 := [quant-intro #244]: #245
-#164 := (~ #121 #121)
-#162 := (~ #118 #118)
-#163 := [refl]: #162
-#165 := [nnf-pos #163]: #164
-#40 := (or #38 #39)
-#41 := (or #37 #40)
-#36 := (= #35 f1)
-#42 := (iff #36 #41)
-#43 := (forall (vars (?v0 Int)) #42)
-#124 := (iff #43 #121)
-#88 := (= 3::Int #33)
-#85 := (= 2::Int #33)
-#91 := (or #85 #88)
-#82 := (= 1::Int #33)
-#94 := (or #82 #91)
-#97 := (iff #79 #94)
-#100 := (forall (vars (?v0 Int)) #97)
-#122 := (iff #100 #121)
-#119 := (iff #97 #118)
-#116 := (iff #94 #113)
-#114 := (iff #41 #113)
-#115 := [rewrite]: #114
-#111 := (iff #94 #41)
-#109 := (iff #91 #40)
-#105 := (iff #88 #39)
-#106 := [rewrite]: #105
-#103 := (iff #85 #38)
-#104 := [rewrite]: #103
-#110 := [monotonicity #104 #106]: #109
-#107 := (iff #82 #37)
-#108 := [rewrite]: #107
-#112 := [monotonicity #108 #110]: #111
-#117 := [trans #112 #115]: #116
-#120 := [monotonicity #117]: #119
-#123 := [quant-intro #120]: #122
-#101 := (iff #43 #100)
-#98 := (iff #42 #97)
-#95 := (iff #41 #94)
-#92 := (iff #40 #91)
-#89 := (iff #39 #88)
-#90 := [rewrite]: #89
-#86 := (iff #38 #85)
-#87 := [rewrite]: #86
-#93 := [monotonicity #87 #90]: #92
-#83 := (iff #37 #82)
-#84 := [rewrite]: #83
-#96 := [monotonicity #84 #93]: #95
-#80 := (iff #36 #79)
-#81 := [rewrite]: #80
-#99 := [monotonicity #81 #96]: #98
-#102 := [quant-intro #99]: #101
-#125 := [trans #102 #123]: #124
-#78 := [asserted]: #43
-#126 := [mp #78 #125]: #121
-#166 := [mp~ #126 #165]: #121
-#247 := [mp #166 #246]: #242
-#357 := (not #242)
-#441 := (or #357 #289)
-#415 := (= 2::Int 3::Int)
-#418 := (= 2::Int 2::Int)
-#414 := (= 2::Int 1::Int)
-#419 := (or #414 #418 #415)
-#420 := (iff #289 #419)
-#442 := (or #357 #420)
-#444 := (iff #442 #441)
-#446 := (iff #441 #441)
-#447 := [rewrite]: #446
-#439 := (iff #420 #289)
-#1 := true
-#434 := (iff #289 true)
-#437 := (iff #434 #289)
-#438 := [rewrite]: #437
-#435 := (iff #420 #434)
-#432 := (iff #419 true)
-#427 := (or false true false)
-#430 := (iff #427 true)
-#431 := [rewrite]: #430
-#428 := (iff #419 #427)
-#425 := (iff #415 false)
-#426 := [rewrite]: #425
-#423 := (iff #418 true)
-#424 := [rewrite]: #423
-#421 := (iff #414 false)
-#422 := [rewrite]: #421
-#429 := [monotonicity #422 #424 #426]: #428
-#433 := [trans #429 #431]: #432
-#436 := [monotonicity #433]: #435
-#440 := [trans #436 #438]: #439
-#445 := [monotonicity #440]: #444
-#448 := [trans #445 #447]: #444
-#443 := [quant-inst #14]: #442
-#449 := [mp #443 #448]: #441
-#451 := [unit-resolution #449 #247 #450]: false
-#452 := [lemma #451]: #289
-#295 := (or #290 #294)
-#47 := (f4 f5 #33)
-#255 := (pattern #47)
-#48 := (f11 f12 #47)
-#135 := (= #33 #48)
-#142 := (not #79)
-#143 := (or #142 #135)
-#256 := (forall (vars (?v0 Int)) (:pat #241 #255) #143)
-#148 := (forall (vars (?v0 Int)) #143)
-#259 := (iff #148 #256)
-#257 := (iff #143 #143)
-#258 := [refl]: #257
-#260 := [quant-intro #258]: #259
-#174 := (~ #148 #148)
-#172 := (~ #143 #143)
-#173 := [refl]: #172
-#175 := [nnf-pos #173]: #174
-#49 := (= #48 #33)
-#50 := (implies #36 #49)
-#51 := (forall (vars (?v0 Int)) #50)
-#149 := (iff #51 #148)
-#146 := (iff #50 #143)
-#139 := (implies #79 #135)
-#144 := (iff #139 #143)
-#145 := [rewrite]: #144
-#140 := (iff #50 #139)
-#137 := (iff #49 #135)
-#138 := [rewrite]: #137
-#141 := [monotonicity #81 #138]: #140
-#147 := [trans #141 #145]: #146
-#150 := [quant-intro #147]: #149
-#134 := [asserted]: #51
-#153 := [mp #134 #150]: #148
-#176 := [mp~ #153 #175]: #148
-#261 := [mp #176 #260]: #256
-#274 := (not #256)
-#298 := (or #274 #290 #294)
-#287 := (= 2::Int #286)
-#291 := (or #290 #287)
-#299 := (or #274 #291)
-#306 := (iff #299 #298)
-#301 := (or #274 #295)
-#304 := (iff #301 #298)
-#305 := [rewrite]: #304
-#302 := (iff #299 #301)
-#296 := (iff #291 #295)
-#292 := (iff #287 #294)
-#293 := [rewrite]: #292
-#297 := [monotonicity #293]: #296
-#303 := [monotonicity #297]: #302
-#307 := [trans #303 #305]: #306
-#300 := [quant-inst #14]: #299
-#308 := [mp #300 #307]: #298
-#453 := [unit-resolution #308 #261]: #295
-#454 := [unit-resolution #453 #452]: #294
-#471 := (= 1::Int #286)
-#469 := (= #286 1::Int)
-#11 := (f4 f5 1::Int)
-#262 := (f11 f12 #11)
-#270 := (= #262 1::Int)
-#264 := (f13 1::Int f14)
-#265 := (= f1 #264)
-#266 := (not #265)
-#367 := [hypothesis]: #266
-#358 := (or #357 #265)
-#333 := (= 1::Int 3::Int)
-#332 := (= 1::Int 1::Int)
-#335 := (or #332 #334 #333)
-#336 := (iff #265 #335)
-#359 := (or #357 #336)
-#361 := (iff #359 #358)
-#363 := (iff #358 #358)
-#364 := [rewrite]: #363
-#355 := (iff #336 #265)
-#350 := (iff #265 true)
-#353 := (iff #350 #265)
+#33 := f14
+#217 := (f13 2::Int f14)
+#218 := (= #217 f1)
+#226 := (not #218)
+#366 := [hypothesis]: #226
+#32 := (:var 0 Int)
+#34 := (f13 #32 f14)
+#190 := (pattern #34)
+#17 := 3::Int
+#38 := (= #32 3::Int)
+#37 := (= #32 2::Int)
+#36 := (= #32 1::Int)
+#81 := (or #36 #37 #38)
+#35 := (= #34 f1)
+#84 := (iff #35 #81)
+#191 := (forall (vars (?v0 Int)) (:pat #190) #84)
+#87 := (forall (vars (?v0 Int)) #84)
+#194 := (iff #87 #191)
+#192 := (iff #84 #84)
+#193 := [refl]: #192
+#195 := [quant-intro #193]: #194
+#111 := (~ #87 #87)
+#109 := (~ #84 #84)
+#110 := [refl]: #109
+#112 := [nnf-pos #110]: #111
+#39 := (or #37 #38)
+#40 := (or #36 #39)
+#41 := (iff #35 #40)
+#42 := (forall (vars (?v0 Int)) #41)
+#88 := (iff #42 #87)
+#85 := (iff #41 #84)
+#82 := (iff #40 #81)
+#83 := [rewrite]: #82
+#86 := [monotonicity #83]: #85
+#89 := [quant-intro #86]: #88
+#78 := [asserted]: #42
+#90 := [mp #78 #89]: #87
+#113 := [mp~ #90 #112]: #87
+#196 := [mp #113 #195]: #191
+#273 := (not #191)
+#357 := (or #273 #218)
+#334 := (= 2::Int 3::Int)
+#331 := (= 2::Int 2::Int)
+#330 := (= 2::Int 1::Int)
+#335 := (or #330 #331 #334)
+#336 := (iff #218 #335)
+#358 := (or #273 #336)
+#360 := (iff #358 #357)
+#362 := (iff #357 #357)
+#363 := [rewrite]: #362
+#355 := (iff #336 #218)
+#1 := true
+#350 := (iff #218 true)
+#353 := (iff #350 #218)
 #354 := [rewrite]: #353
 #351 := (iff #336 #350)
 #348 := (iff #335 true)
-#343 := (or true false false)
+#343 := (or false true false)
 #346 := (iff #343 true)
 #347 := [rewrite]: #346
 #344 := (iff #335 #343)
-#341 := (iff #333 false)
+#341 := (iff #334 false)
 #342 := [rewrite]: #341
-#337 := (iff #332 true)
+#339 := (iff #331 true)
+#340 := [rewrite]: #339
+#337 := (iff #330 false)
 #338 := [rewrite]: #337
 #345 := [monotonicity #338 #340 #342]: #344
 #349 := [trans #345 #347]: #348
 #352 := [monotonicity #349]: #351
 #356 := [trans #352 #354]: #355
-#362 := [monotonicity #356]: #361
-#365 := [trans #362 #364]: #361
-#360 := [quant-inst #10]: #359
-#366 := [mp #360 #365]: #358
-#368 := [unit-resolution #366 #247 #367]: false
-#369 := [lemma #368]: #265
-#271 := (or #266 #270)
-#275 := (or #274 #266 #270)
-#263 := (= 1::Int #262)
-#267 := (or #266 #263)
-#276 := (or #274 #267)
-#283 := (iff #276 #275)
-#278 := (or #274 #271)
-#281 := (iff #278 #275)
-#282 := [rewrite]: #281
-#279 := (iff #276 #278)
-#272 := (iff #267 #271)
-#268 := (iff #263 #270)
-#269 := [rewrite]: #268
-#273 := [monotonicity #269]: #272
-#280 := [monotonicity #273]: #279
-#284 := [trans #280 #282]: #283
-#277 := [quant-inst #10]: #276
-#285 := [mp #277 #284]: #275
-#455 := [unit-resolution #285 #261]: #271
-#456 := [unit-resolution #455 #369]: #270
-#467 := (= #286 #262)
-#465 := (= #15 #11)
+#361 := [monotonicity #356]: #360
+#364 := [trans #361 #363]: #360
+#359 := [quant-inst #13]: #358
+#365 := [mp #359 #364]: #357
+#367 := [unit-resolution #365 #196 #366]: false
+#368 := [lemma #367]: #218
+#229 := (or #226 #228)
+#46 := (f4 f5 #32)
+#204 := (pattern #46)
+#47 := (f11 f12 #46)
+#48 := (= #47 #32)
+#91 := (not #35)
+#92 := (or #91 #48)
+#205 := (forall (vars (?v0 Int)) (:pat #190 #204) #92)
+#95 := (forall (vars (?v0 Int)) #92)
+#208 := (iff #95 #205)
+#206 := (iff #92 #92)
+#207 := [refl]: #206
+#209 := [quant-intro #207]: #208
+#121 := (~ #95 #95)
+#119 := (~ #92 #92)
+#120 := [refl]: #119
+#122 := [nnf-pos #120]: #121
+#49 := (implies #35 #48)
+#50 := (forall (vars (?v0 Int)) #49)
+#96 := (iff #50 #95)
+#93 := (iff #49 #92)
+#94 := [rewrite]: #93
+#97 := [quant-intro #94]: #96
+#80 := [asserted]: #50
+#100 := [mp #80 #97]: #95
+#123 := [mp~ #100 #122]: #95
+#210 := [mp #123 #209]: #205
+#219 := (not #205)
+#232 := (or #219 #226 #228)
+#233 := (or #219 #229)
+#235 := (iff #233 #232)
+#236 := [rewrite]: #235
+#234 := [quant-inst #13]: #233
+#237 := [mp #234 #236]: #232
+#369 := [unit-resolution #237 #210]: #229
+#370 := [unit-resolution #369 #368]: #228
+#387 := (= 1::Int #227)
+#385 := (= #227 1::Int)
+#10 := (f4 f5 1::Int)
+#214 := (f11 f12 #10)
+#215 := (= #214 1::Int)
+#211 := (f13 1::Int f14)
+#212 := (= #211 f1)
+#213 := (not #212)
+#283 := [hypothesis]: #213
+#274 := (or #273 #212)
+#250 := (= 1::Int 3::Int)
+#242 := (= 1::Int 1::Int)
+#251 := (or #242 #243 #250)
+#252 := (iff #212 #251)
+#275 := (or #273 #252)
+#277 := (iff #275 #274)
+#279 := (iff #274 #274)
+#280 := [rewrite]: #279
+#271 := (iff #252 #212)
+#266 := (iff #212 true)
+#269 := (iff #266 #212)
+#270 := [rewrite]: #269
+#267 := (iff #252 #266)
+#264 := (iff #251 true)
+#259 := (or true false false)
+#262 := (iff #259 true)
+#263 := [rewrite]: #262
+#260 := (iff #251 #259)
+#257 := (iff #250 false)
+#258 := [rewrite]: #257
+#253 := (iff #242 true)
+#254 := [rewrite]: #253
+#261 := [monotonicity #254 #256 #258]: #260
+#265 := [trans #261 #263]: #264
+#268 := [monotonicity #265]: #267
+#272 := [trans #268 #270]: #271
+#278 := [monotonicity #272]: #277
+#281 := [trans #278 #280]: #277
+#276 := [quant-inst #9]: #275
+#282 := [mp #276 #281]: #274
+#284 := [unit-resolution #282 #196 #283]: false
+#285 := [lemma #284]: #212
+#216 := (or #213 #215)
+#220 := (or #219 #213 #215)
+#221 := (or #219 #216)
+#223 := (iff #221 #220)
+#224 := [rewrite]: #223
+#222 := [quant-inst #9]: #221
+#225 := [mp #222 #224]: #220
+#371 := [unit-resolution #225 #210]: #216
+#372 := [unit-resolution #371 #285]: #215
+#383 := (= #227 #214)
+#381 := (= #14 #10)
 decl f3 :: S2
-#8 := f3
-#12 := (= f3 #11)
-#74 := [asserted]: #12
-#463 := (= #15 f3)
+#7 := f3
+#11 := (= f3 #10)
+#74 := [asserted]: #11
+#379 := (= #14 f3)
 decl f6 :: S2
-#13 := f6
-#461 := (= f6 f3)
-#52 := (= f3 f6)
+#12 := f6
+#377 := (= f6 f3)
+#51 := (= f3 f6)
+#52 := (not #51)
 #53 := (not #52)
-#54 := (not #53)
-#152 := (iff #54 #52)
-#154 := [rewrite]: #152
-#151 := [asserted]: #54
-#157 := [mp #151 #154]: #52
-#462 := [symm #157]: #461
-#459 := (= #15 f6)
-#16 := (= f6 #15)
-#75 := [asserted]: #16
-#460 := [symm #75]: #459
-#464 := [trans #460 #462]: #463
-#466 := [trans #464 #74]: #465
-#468 := [monotonicity #466]: #467
-#470 := [trans #468 #456]: #469
-#472 := [symm #470]: #471
-#473 := [trans #472 #454]: #334
-[mp #473 #340]: false
-unsat
-0b2624e5de02979d781587640b732673b386817c 293 0
-#2 := false
+#99 := (iff #53 #51)
+#101 := [rewrite]: #99
+#98 := [asserted]: #53
+#104 := [mp #98 #101]: #51
+#378 := [symm #104]: #377
+#375 := (= #14 f6)
+#15 := (= f6 #14)
+#75 := [asserted]: #15
+#376 := [symm #75]: #375
+#380 := [trans #376 #378]: #379
+#382 := [trans #380 #74]: #381
+#384 := [monotonicity #382]: #383
+#386 := [trans #384 #372]: #385
+#388 := [symm #386]: #387
+#389 := [trans #388 #370]: #243
+[mp #389 #256]: false
+unsat
+abf24d28efcf933fd63a125c58e888cf5bd3bb43 229 0
+#2 := false
+decl f6 :: S2
+#12 := f6
 decl f8 :: (-> S4 S2 S2)
 decl f3 :: S2
-#8 := f3
+#7 := f3
 decl f9 :: (-> S5 S2 S4)
 decl f10 :: S5
-#21 := f10
-#52 := (f9 f10 f3)
-#53 := (f8 #52 f3)
-decl f6 :: S2
-#13 := f6
-#153 := (= f6 #53)
-decl f4 :: (-> S3 Int S2)
-#10 := 1::Int
-decl f5 :: S3
-#9 := f5
-#11 := (f4 f5 1::Int)
-#270 := (f9 f10 #11)
-#271 := (f8 #270 #11)
-#515 := (= #271 #53)
-#511 := (= #53 #271)
-#12 := (= f3 #11)
-#75 := [asserted]: #12
-#495 := (= #52 #270)
-#493 := (= #270 #52)
-#491 := (= #11 f3)
-#492 := [symm #75]: #491
-#494 := [monotonicity #492]: #493
-#496 := [symm #494]: #495
-#512 := [monotonicity #496 #75]: #511
-#516 := [symm #512]: #515
-#519 := (= f6 #271)
+#20 := f10
+#51 := (f9 f10 f3)
+#52 := (f8 #51 f3)
+#53 := (= #52 f6)
+decl f4 :: (-> S3 Int S2)
+#13 := 2::Int
+decl f5 :: S3
+#8 := f5
+#14 := (f4 f5 2::Int)
+#435 := (= #14 f6)
+#15 := (= f6 #14)
+#76 := [asserted]: #15
+#436 := [symm #76]: #435
+#439 := (= #52 #14)
 decl f11 :: (-> S6 S2 Int)
+#9 := 1::Int
+#10 := (f4 f5 1::Int)
 decl f12 :: S6
-#26 := f12
-#267 := (f11 f12 #11)
-#14 := 2::Int
-#273 := (* 2::Int #267)
-#276 := (f4 f5 #273)
-#513 := (= #276 #271)
-#279 := (= #271 #276)
-#24 := (:var 0 S2)
-#22 := (:var 1 S2)
-#23 := (f9 f10 #22)
-#25 := (f8 #23 #24)
-#239 := (pattern #25)
-#28 := (f11 f12 #24)
-#27 := (f11 f12 #22)
-#29 := (+ #27 #28)
-#30 := (f4 f5 #29)
-#31 := (= #25 #30)
-#240 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #239) #31)
-#32 := (forall (vars (?v0 S2) (?v1 S2)) #31)
-#243 := (iff #32 #240)
-#241 := (iff #31 #31)
-#242 := [refl]: #241
-#244 := [quant-intro #242]: #243
-#164 := (~ #32 #32)
-#161 := (~ #31 #31)
-#163 := [refl]: #161
-#165 := [nnf-pos #163]: #164
-#78 := [asserted]: #32
-#166 := [mp~ #78 #165]: #32
-#245 := [mp #166 #244]: #240
-#282 := (not #240)
-#283 := (or #282 #279)
-#268 := (+ #267 #267)
-#269 := (f4 f5 #268)
-#272 := (= #271 #269)
-#284 := (or #282 #272)
-#286 := (iff #284 #283)
-#288 := (iff #283 #283)
-#289 := [rewrite]: #288
-#280 := (iff #272 #279)
-#277 := (= #269 #276)
-#274 := (= #268 #273)
-#275 := [rewrite]: #274
-#278 := [monotonicity #275]: #277
-#281 := [monotonicity #278]: #280
-#287 := [monotonicity #281]: #286
-#290 := [trans #287 #289]: #286
-#285 := [quant-inst #11 #11]: #284
-#291 := [mp #285 #290]: #283
-#490 := [unit-resolution #291 #245]: #279
-#514 := [symm #490]: #513
-#517 := (= f6 #276)
-#15 := (f4 f5 2::Int)
-#509 := (= #15 #276)
-#507 := (= 2::Int #273)
-#505 := (= #273 2::Int)
-#315 := (<= #267 1::Int)
-#299 := (= #267 1::Int)
+#25 := f12
+#211 := (f11 f12 #10)
+#215 := (* 2::Int #211)
+#218 := (f4 f5 #215)
+#433 := (= #218 #14)
+#431 := (= #14 #218)
+#420 := (= 2::Int #215)
+#418 := (= #215 2::Int)
+#248 := (<= #211 1::Int)
+#237 := (= #211 1::Int)
+decl f1 :: S1
+#3 := f1
 decl f13 :: (-> Int S7 S1)
 decl f14 :: S7
-#34 := f14
-#293 := (f13 1::Int f14)
-decl f1 :: S1
-#4 := f1
-#294 := (= f1 #293)
-#295 := (not #294)
-#487 := [hypothesis]: #295
-#33 := (:var 0 Int)
-#35 := (f13 #33 f14)
-#246 := (pattern #35)
-#18 := 3::Int
-#39 := (= #33 3::Int)
-#38 := (= #33 2::Int)
-#37 := (= #33 1::Int)
-#114 := (or #37 #38 #39)
-#80 := (= f1 #35)
-#119 := (iff #80 #114)
-#247 := (forall (vars (?v0 Int)) (:pat #246) #119)
-#122 := (forall (vars (?v0 Int)) #119)
-#250 := (iff #122 #247)
-#248 := (iff #119 #119)
-#249 := [refl]: #248
-#251 := [quant-intro #249]: #250
-#169 := (~ #122 #122)
-#167 := (~ #119 #119)
-#168 := [refl]: #167
-#170 := [nnf-pos #168]: #169
-#40 := (or #38 #39)
-#41 := (or #37 #40)
-#36 := (= #35 f1)
-#42 := (iff #36 #41)
-#43 := (forall (vars (?v0 Int)) #42)
-#125 := (iff #43 #122)
-#89 := (= 3::Int #33)
-#86 := (= 2::Int #33)
-#92 := (or #86 #89)
-#83 := (= 1::Int #33)
-#95 := (or #83 #92)
-#98 := (iff #80 #95)
-#101 := (forall (vars (?v0 Int)) #98)
-#123 := (iff #101 #122)
-#120 := (iff #98 #119)
-#117 := (iff #95 #114)
-#115 := (iff #41 #114)
-#116 := [rewrite]: #115
-#112 := (iff #95 #41)
-#110 := (iff #92 #40)
-#106 := (iff #89 #39)
-#107 := [rewrite]: #106
-#104 := (iff #86 #38)
-#105 := [rewrite]: #104
-#111 := [monotonicity #105 #107]: #110
-#108 := (iff #83 #37)
-#109 := [rewrite]: #108
-#113 := [monotonicity #109 #111]: #112
-#118 := [trans #113 #116]: #117
-#121 := [monotonicity #118]: #120
-#124 := [quant-intro #121]: #123
-#102 := (iff #43 #101)
-#99 := (iff #42 #98)
-#96 := (iff #41 #95)
-#93 := (iff #40 #92)
-#90 := (iff #39 #89)
-#91 := [rewrite]: #90
-#87 := (iff #38 #86)
-#88 := [rewrite]: #87
-#94 := [monotonicity #88 #91]: #93
-#84 := (iff #37 #83)
-#85 := [rewrite]: #84
-#97 := [monotonicity #85 #94]: #96
-#81 := (iff #36 #80)
-#82 := [rewrite]: #81
-#100 := [monotonicity #82 #97]: #99
-#103 := [quant-intro #100]: #102
-#126 := [trans #103 #124]: #125
-#79 := [asserted]: #43
-#127 := [mp #79 #126]: #122
-#171 := [mp~ #127 #170]: #122
-#252 := [mp #171 #251]: #247
-#407 := (not #247)
-#478 := (or #407 #294)
-#448 := (= 1::Int 3::Int)
-#455 := (= 1::Int 2::Int)
-#447 := (= 1::Int 1::Int)
-#456 := (or #447 #455 #448)
-#457 := (iff #294 #456)
-#479 := (or #407 #457)
-#481 := (iff #479 #478)
-#483 := (iff #478 #478)
-#484 := [rewrite]: #483
-#476 := (iff #457 #294)
-#1 := true
-#471 := (iff #294 true)
-#474 := (iff #471 #294)
-#475 := [rewrite]: #474
-#472 := (iff #457 #471)
-#469 := (iff #456 true)
-#464 := (or true false false)
-#467 := (iff #464 true)
-#468 := [rewrite]: #467
-#465 := (iff #456 #464)
-#462 := (iff #448 false)
-#463 := [rewrite]: #462
-#460 := (iff #455 false)
-#461 := [rewrite]: #460
-#458 := (iff #447 true)
-#459 := [rewrite]: #458
-#466 := [monotonicity #459 #461 #463]: #465
-#470 := [trans #466 #468]: #469
-#473 := [monotonicity #470]: #472
-#477 := [trans #473 #475]: #476
-#482 := [monotonicity #477]: #481
-#485 := [trans #482 #484]: #481
-#480 := [quant-inst #10]: #479
-#486 := [mp #480 #485]: #478
-#488 := [unit-resolution #486 #252 #487]: false
-#489 := [lemma #488]: #294
-#300 := (or #295 #299)
-#47 := (f4 f5 #33)
-#260 := (pattern #47)
-#48 := (f11 f12 #47)
-#136 := (= #33 #48)
-#143 := (not #80)
-#144 := (or #143 #136)
-#261 := (forall (vars (?v0 Int)) (:pat #246 #260) #144)
-#149 := (forall (vars (?v0 Int)) #144)
-#264 := (iff #149 #261)
-#262 := (iff #144 #144)
-#263 := [refl]: #262
-#265 := [quant-intro #263]: #264
-#179 := (~ #149 #149)
-#177 := (~ #144 #144)
-#178 := [refl]: #177
-#180 := [nnf-pos #178]: #179
-#49 := (= #48 #33)
-#50 := (implies #36 #49)
-#51 := (forall (vars (?v0 Int)) #50)
-#150 := (iff #51 #149)
-#147 := (iff #50 #144)
-#140 := (implies #80 #136)
-#145 := (iff #140 #144)
-#146 := [rewrite]: #145
-#141 := (iff #50 #140)
-#138 := (iff #49 #136)
-#139 := [rewrite]: #138
-#142 := [monotonicity #82 #139]: #141
-#148 := [trans #142 #146]: #147
-#151 := [quant-intro #148]: #150
-#135 := [asserted]: #51
-#154 := [mp #135 #151]: #149
-#181 := [mp~ #154 #180]: #149
-#266 := [mp #181 #265]: #261
-#303 := (not #261)
-#304 := (or #303 #295 #299)
-#292 := (= 1::Int #267)
-#296 := (or #295 #292)
-#305 := (or #303 #296)
-#312 := (iff #305 #304)
-#307 := (or #303 #300)
-#310 := (iff #307 #304)
-#311 := [rewrite]: #310
-#308 := (iff #305 #307)
-#301 := (iff #296 #300)
-#297 := (iff #292 #299)
-#298 := [rewrite]: #297
-#302 := [monotonicity #298]: #301
-#309 := [monotonicity #302]: #308
-#313 := [trans #309 #311]: #312
-#306 := [quant-inst #10]: #305
-#314 := [mp #306 #313]: #304
-#497 := [unit-resolution #314 #266]: #300
-#498 := [unit-resolution #497 #489]: #299
-#421 := (not #299)
-#499 := (or #421 #315)
-#500 := [th-lemma arith triangle-eq]: #499
-#501 := [unit-resolution #500 #498]: #315
-#316 := (>= #267 1::Int)
-#502 := (or #421 #316)
-#503 := [th-lemma arith triangle-eq]: #502
-#504 := [unit-resolution #503 #498]: #316
-#506 := [th-lemma arith eq-propagate -2 -2 #504 #501]: #505
-#508 := [symm #506]: #507
-#510 := [monotonicity #508]: #509
-#16 := (= f6 #15)
-#76 := [asserted]: #16
-#518 := [trans #76 #510]: #517
-#520 := [trans #518 #514]: #519
-#521 := [trans #520 #516]: #153
-#157 := (not #153)
-#54 := (= #53 f6)
-#55 := (not #54)
-#158 := (iff #55 #157)
-#155 := (iff #54 #153)
-#156 := [rewrite]: #155
-#159 := [monotonicity #156]: #158
-#152 := [asserted]: #55
-#162 := [mp #152 #159]: #157
-[unit-resolution #162 #521]: false
-unsat
-be9536e255cd44d6957fba82b89dd647b91d4120 451 0
-#2 := false
+#33 := f14
+#234 := (f13 1::Int f14)
+#235 := (= #234 f1)
+#236 := (not #235)
+#409 := [hypothesis]: #236
+#32 := (:var 0 Int)
+#34 := (f13 #32 f14)
+#188 := (pattern #34)
+#17 := 3::Int
+#38 := (= #32 3::Int)
+#37 := (= #32 2::Int)
+#36 := (= #32 1::Int)
+#82 := (or #36 #37 #38)
+#35 := (= #34 f1)
+#85 := (iff #35 #82)
+#189 := (forall (vars (?v0 Int)) (:pat #188) #85)
+#88 := (forall (vars (?v0 Int)) #85)
+#192 := (iff #88 #189)
+#190 := (iff #85 #85)
+#191 := [refl]: #190
+#193 := [quant-intro #191]: #192
+#109 := (~ #88 #88)
+#107 := (~ #85 #85)
+#108 := [refl]: #107
+#110 := [nnf-pos #108]: #109
+#39 := (or #37 #38)
+#40 := (or #36 #39)
+#41 := (iff #35 #40)
+#42 := (forall (vars (?v0 Int)) #41)
+#89 := (iff #42 #88)
+#86 := (iff #41 #85)
+#83 := (iff #40 #82)
+#84 := [rewrite]: #83
+#87 := [monotonicity #84]: #86
+#90 := [quant-intro #87]: #89
+#79 := [asserted]: #42
+#91 := [mp #79 #90]: #88
+#111 := [mp~ #91 #110]: #88
+#194 := [mp #111 #193]: #189
+#311 := (not #189)
+#400 := (or #311 #235)
+#377 := (= 1::Int 3::Int)
+#376 := (= 1::Int 2::Int)
+#375 := (= 1::Int 1::Int)
+#378 := (or #375 #376 #377)
+#379 := (iff #235 #378)
+#401 := (or #311 #379)
+#403 := (iff #401 #400)
+#405 := (iff #400 #400)
+#406 := [rewrite]: #405
+#398 := (iff #379 #235)
+#1 := true
+#393 := (iff #235 true)
+#396 := (iff #393 #235)
+#397 := [rewrite]: #396
+#394 := (iff #379 #393)
+#391 := (iff #378 true)
+#386 := (or true false false)
+#389 := (iff #386 true)
+#390 := [rewrite]: #389
+#387 := (iff #378 #386)
+#384 := (iff #377 false)
+#385 := [rewrite]: #384
+#382 := (iff #376 false)
+#383 := [rewrite]: #382
+#380 := (iff #375 true)
+#381 := [rewrite]: #380
+#388 := [monotonicity #381 #383 #385]: #387
+#392 := [trans #388 #390]: #391
+#395 := [monotonicity #392]: #394
+#399 := [trans #395 #397]: #398
+#404 := [monotonicity #399]: #403
+#407 := [trans #404 #406]: #403
+#402 := [quant-inst #9]: #401
+#408 := [mp #402 #407]: #400
+#410 := [unit-resolution #408 #194 #409]: false
+#411 := [lemma #410]: #235
+#238 := (or #236 #237)
+#46 := (f4 f5 #32)
+#202 := (pattern #46)
+#47 := (f11 f12 #46)
+#48 := (= #47 #32)
+#92 := (not #35)
+#93 := (or #92 #48)
+#203 := (forall (vars (?v0 Int)) (:pat #188 #202) #93)
+#96 := (forall (vars (?v0 Int)) #93)
+#206 := (iff #96 #203)
+#204 := (iff #93 #93)
+#205 := [refl]: #204
+#207 := [quant-intro #205]: #206
+#119 := (~ #96 #96)
+#117 := (~ #93 #93)
+#118 := [refl]: #117
+#120 := [nnf-pos #118]: #119
+#49 := (implies #35 #48)
+#50 := (forall (vars (?v0 Int)) #49)
+#97 := (iff #50 #96)
+#94 := (iff #49 #93)
+#95 := [rewrite]: #94
+#98 := [quant-intro #95]: #97
+#81 := [asserted]: #50
+#101 := [mp #81 #98]: #96
+#121 := [mp~ #101 #120]: #96
+#208 := [mp #121 #207]: #203
+#241 := (not #203)
+#242 := (or #241 #236 #237)
+#243 := (or #241 #238)
+#245 := (iff #243 #242)
+#246 := [rewrite]: #245
+#244 := [quant-inst #9]: #243
+#247 := [mp #244 #246]: #242
+#412 := [unit-resolution #247 #208]: #238
+#413 := [unit-resolution #412 #411]: #237
+#318 := (not #237)
+#357 := (or #318 #248)
+#358 := [th-lemma arith triangle-eq]: #357
+#414 := [unit-resolution #358 #413]: #248
+#249 := (>= #211 1::Int)
+#415 := (or #318 #249)
+#416 := [th-lemma arith triangle-eq]: #415
+#417 := [unit-resolution #416 #413]: #249
+#419 := [th-lemma arith eq-propagate -2 -2 #417 #414]: #418
+#421 := [symm #419]: #420
+#432 := [monotonicity #421]: #431
+#434 := [symm #432]: #433
+#437 := (= #52 #218)
+#209 := (f9 f10 #10)
+#210 := (f8 #209 #10)
+#221 := (= #210 #218)
+#23 := (:var 0 S2)
+#21 := (:var 1 S2)
+#22 := (f9 f10 #21)
+#24 := (f8 #22 #23)
+#181 := (pattern #24)
+#27 := (f11 f12 #23)
+#26 := (f11 f12 #21)
+#28 := (+ #26 #27)
+#29 := (f4 f5 #28)
+#30 := (= #24 #29)
+#182 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #181) #30)
+#31 := (forall (vars (?v0 S2) (?v1 S2)) #30)
+#185 := (iff #31 #182)
+#183 := (iff #30 #30)
+#184 := [refl]: #183
+#186 := [quant-intro #184]: #185
+#104 := (~ #31 #31)
+#102 := (~ #30 #30)
+#103 := [refl]: #102
+#105 := [nnf-pos #103]: #104
+#78 := [asserted]: #31
+#106 := [mp~ #78 #105]: #31
+#187 := [mp #106 #186]: #182
+#224 := (not #182)
+#225 := (or #224 #221)
+#212 := (+ #211 #211)
+#213 := (f4 f5 #212)
+#214 := (= #210 #213)
+#226 := (or #224 #214)
+#228 := (iff #226 #225)
+#230 := (iff #225 #225)
+#231 := [rewrite]: #230
+#222 := (iff #214 #221)
+#219 := (= #213 #218)
+#216 := (= #212 #215)
+#217 := [rewrite]: #216
+#220 := [monotonicity #217]: #219
+#223 := [monotonicity #220]: #222
+#229 := [monotonicity #223]: #228
+#232 := [trans #229 #231]: #228
+#227 := [quant-inst #10 #10]: #226
+#233 := [mp #227 #232]: #225
+#422 := [unit-resolution #233 #187]: #221
+#429 := (= #52 #210)
+#11 := (= f3 #10)
+#75 := [asserted]: #11
+#427 := (= #51 #209)
+#425 := (= #209 #51)
+#423 := (= #10 f3)
+#424 := [symm #75]: #423
+#426 := [monotonicity #424]: #425
+#428 := [symm #426]: #427
+#430 := [monotonicity #428 #75]: #429
+#438 := [trans #430 #422]: #437
+#440 := [trans #438 #434]: #439
+#441 := [trans #440 #436]: #53
+#54 := (not #53)
+#99 := [asserted]: #54
+[unit-resolution #99 #441]: false
+unsat
+260eac824b1f01737479805af42f5db11c25917d 340 0
+#2 := false
+decl f7 :: S2
+#16 := f7
 decl f8 :: (-> S4 S2 S2)
 decl f6 :: S2
-#13 := f6
+#12 := f6
 decl f9 :: (-> S5 S2 S4)
 decl f3 :: S2
-#8 := f3
+#7 := f3
 decl f10 :: S5
-#21 := f10
-#52 := (f9 f10 f3)
-#53 := (f8 #52 f6)
-decl f7 :: S2
-#17 := f7
-#153 := (= f7 #53)
-decl f4 :: (-> S3 Int S2)
-#14 := 2::Int
-decl f5 :: S3
-#9 := f5
-#15 := (f4 f5 2::Int)
-#10 := 1::Int
-#11 := (f4 f5 1::Int)
-#271 := (f9 f10 #11)
-#272 := (f8 #271 #15)
-#598 := (= #272 #53)
-#594 := (= #53 #272)
-#16 := (= f6 #15)
-#76 := [asserted]: #16
-#610 := (= #52 #271)
-#608 := (= #271 #52)
-#606 := (= #11 f3)
-#12 := (= f3 #11)
-#75 := [asserted]: #12
-#607 := [symm #75]: #606
-#609 := [monotonicity #607]: #608
-#611 := [symm #609]: #610
-#595 := [monotonicity #611 #76]: #594
-#663 := [symm #595]: #598
-#666 := (= f7 #272)
+#20 := f10
+#51 := (f9 f10 f3)
+#52 := (f8 #51 f6)
+#53 := (= #52 f7)
+decl f4 :: (-> S3 Int S2)
+#17 := 3::Int
+decl f5 :: S3
+#8 := f5
+#18 := (f4 f5 3::Int)
+#522 := (= #18 f7)
+#19 := (= f7 #18)
+#77 := [asserted]: #19
+#523 := [symm #77]: #522
+#526 := (= #52 #18)
 decl f11 :: (-> S6 S2 Int)
+#13 := 2::Int
+#14 := (f4 f5 2::Int)
 decl f12 :: S6
-#26 := f12
-#268 := (f11 f12 #11)
-#267 := (f11 f12 #15)
-#274 := (+ #267 #268)
-#277 := (f4 f5 #274)
-#596 := (= #277 #272)
-#280 := (= #272 #277)
-#24 := (:var 0 S2)
-#22 := (:var 1 S2)
-#23 := (f9 f10 #22)
-#25 := (f8 #23 #24)
-#239 := (pattern #25)
-#28 := (f11 f12 #24)
-#27 := (f11 f12 #22)
-#29 := (+ #27 #28)
-#30 := (f4 f5 #29)
-#31 := (= #25 #30)
-#240 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #239) #31)
-#32 := (forall (vars (?v0 S2) (?v1 S2)) #31)
-#243 := (iff #32 #240)
-#241 := (iff #31 #31)
-#242 := [refl]: #241
-#244 := [quant-intro #242]: #243
-#164 := (~ #32 #32)
-#161 := (~ #31 #31)
-#163 := [refl]: #161
-#165 := [nnf-pos #163]: #164
-#78 := [asserted]: #32
-#166 := [mp~ #78 #165]: #32
-#245 := [mp #166 #244]: #240
-#283 := (not #240)
-#284 := (or #283 #280)
-#269 := (+ #268 #267)
-#270 := (f4 f5 #269)
-#273 := (= #272 #270)
-#285 := (or #283 #273)
-#287 := (iff #285 #284)
-#289 := (iff #284 #284)
-#290 := [rewrite]: #289
-#281 := (iff #273 #280)
-#278 := (= #270 #277)
-#275 := (= #269 #274)
-#276 := [rewrite]: #275
-#279 := [monotonicity #276]: #278
-#282 := [monotonicity #279]: #281
-#288 := [monotonicity #282]: #287
-#291 := [trans #288 #290]: #287
-#286 := [quant-inst #11 #15]: #285
-#292 := [mp #286 #291]: #284
-#605 := [unit-resolution #292 #245]: #280
-#597 := [symm #605]: #596
-#664 := (= f7 #277)
-#18 := 3::Int
-#19 := (f4 f5 3::Int)
-#590 := (= #19 #277)
-#591 := (= 3::Int #274)
-#510 := (= #274 3::Int)
-#316 := (<= #268 1::Int)
-#300 := (= #268 1::Int)
+#25 := f12
+#212 := (f11 f12 #14)
+#9 := 1::Int
+#10 := (f4 f5 1::Int)
+#211 := (f11 f12 #10)
+#213 := (+ #211 #212)
+#214 := (f4 f5 #213)
+#520 := (= #214 #18)
+#518 := (= #18 #214)
+#474 := (= 3::Int #213)
+#383 := (= #213 3::Int)
+#246 := (<= #212 2::Int)
+#236 := (= #212 2::Int)
+decl f1 :: S1
+#3 := f1
 decl f13 :: (-> Int S7 S1)
 decl f14 :: S7
-#34 := f14
-#294 := (f13 1::Int f14)
-decl f1 :: S1
-#4 := f1
-#295 := (= f1 #294)
-#296 := (not #295)
-#539 := [hypothesis]: #296
-#33 := (:var 0 Int)
-#35 := (f13 #33 f14)
-#246 := (pattern #35)
-#39 := (= #33 3::Int)
-#38 := (= #33 2::Int)
-#37 := (= #33 1::Int)
-#114 := (or #37 #38 #39)
-#80 := (= f1 #35)
-#119 := (iff #80 #114)
-#247 := (forall (vars (?v0 Int)) (:pat #246) #119)
-#122 := (forall (vars (?v0 Int)) #119)
-#250 := (iff #122 #247)
-#248 := (iff #119 #119)
-#249 := [refl]: #248
-#251 := [quant-intro #249]: #250
-#169 := (~ #122 #122)
-#167 := (~ #119 #119)
-#168 := [refl]: #167
-#170 := [nnf-pos #168]: #169
-#40 := (or #38 #39)
-#41 := (or #37 #40)
-#36 := (= #35 f1)
-#42 := (iff #36 #41)
-#43 := (forall (vars (?v0 Int)) #42)
-#125 := (iff #43 #122)
-#89 := (= 3::Int #33)
-#86 := (= 2::Int #33)
-#92 := (or #86 #89)
-#83 := (= 1::Int #33)
-#95 := (or #83 #92)
-#98 := (iff #80 #95)
-#101 := (forall (vars (?v0 Int)) #98)
-#123 := (iff #101 #122)
-#120 := (iff #98 #119)
-#117 := (iff #95 #114)
-#115 := (iff #41 #114)
-#116 := [rewrite]: #115
-#112 := (iff #95 #41)
-#110 := (iff #92 #40)
-#106 := (iff #89 #39)
-#107 := [rewrite]: #106
-#104 := (iff #86 #38)
-#105 := [rewrite]: #104
-#111 := [monotonicity #105 #107]: #110
-#108 := (iff #83 #37)
-#109 := [rewrite]: #108
-#113 := [monotonicity #109 #111]: #112
-#118 := [trans #113 #116]: #117
-#121 := [monotonicity #118]: #120
-#124 := [quant-intro #121]: #123
-#102 := (iff #43 #101)
-#99 := (iff #42 #98)
-#96 := (iff #41 #95)
-#93 := (iff #40 #92)
-#90 := (iff #39 #89)
-#91 := [rewrite]: #90
-#87 := (iff #38 #86)
-#88 := [rewrite]: #87
-#94 := [monotonicity #88 #91]: #93
-#84 := (iff #37 #83)
-#85 := [rewrite]: #84
-#97 := [monotonicity #85 #94]: #96
-#81 := (iff #36 #80)
-#82 := [rewrite]: #81
-#100 := [monotonicity #82 #97]: #99
-#103 := [quant-intro #100]: #102
-#126 := [trans #103 #124]: #125
-#79 := [asserted]: #43
-#127 := [mp #79 #126]: #122
-#171 := [mp~ #127 #170]: #122
-#252 := [mp #171 #251]: #247
-#414 := (not #247)
-#530 := (or #414 #295)
-#542 := (= 1::Int 3::Int)
-#543 := (= 1::Int 2::Int)
-#541 := (= 1::Int 1::Int)
-#544 := (or #541 #543 #542)
-#545 := (iff #295 #544)
-#531 := (or #414 #545)
-#533 := (iff #531 #530)
-#535 := (iff #530 #530)
-#536 := [rewrite]: #535
-#526 := (iff #545 #295)
-#1 := true
-#559 := (iff #295 true)
-#527 := (iff #559 #295)
-#528 := [rewrite]: #527
-#560 := (iff #545 #559)
-#557 := (iff #544 true)
-#552 := (or true false false)
-#555 := (iff #552 true)
-#556 := [rewrite]: #555
-#553 := (iff #544 #552)
-#550 := (iff #542 false)
-#551 := [rewrite]: #550
-#548 := (iff #543 false)
-#549 := [rewrite]: #548
-#546 := (iff #541 true)
-#547 := [rewrite]: #546
-#554 := [monotonicity #547 #549 #551]: #553
-#558 := [trans #554 #556]: #557
-#561 := [monotonicity #558]: #560
-#529 := [trans #561 #528]: #526
-#534 := [monotonicity #529]: #533
-#537 := [trans #534 #536]: #533
-#532 := [quant-inst #10]: #531
-#538 := [mp #532 #537]: #530
-#540 := [unit-resolution #538 #252 #539]: false
-#589 := [lemma #540]: #295
-#301 := (or #296 #300)
-#47 := (f4 f5 #33)
-#260 := (pattern #47)
-#48 := (f11 f12 #47)
-#136 := (= #33 #48)
-#143 := (not #80)
-#144 := (or #143 #136)
-#261 := (forall (vars (?v0 Int)) (:pat #246 #260) #144)
-#149 := (forall (vars (?v0 Int)) #144)
-#264 := (iff #149 #261)
-#262 := (iff #144 #144)
-#263 := [refl]: #262
-#265 := [quant-intro #263]: #264
-#179 := (~ #149 #149)
-#177 := (~ #144 #144)
-#178 := [refl]: #177
-#180 := [nnf-pos #178]: #179
-#49 := (= #48 #33)
-#50 := (implies #36 #49)
-#51 := (forall (vars (?v0 Int)) #50)
-#150 := (iff #51 #149)
-#147 := (iff #50 #144)
-#140 := (implies #80 #136)
-#145 := (iff #140 #144)
-#146 := [rewrite]: #145
-#141 := (iff #50 #140)
-#138 := (iff #49 #136)
-#139 := [rewrite]: #138
-#142 := [monotonicity #82 #139]: #141
-#148 := [trans #142 #146]: #147
-#151 := [quant-intro #148]: #150
-#135 := [asserted]: #51
-#154 := [mp #135 #151]: #149
-#181 := [mp~ #154 #180]: #149
-#266 := [mp #181 #265]: #261
-#304 := (not #261)
-#305 := (or #304 #296 #300)
-#293 := (= 1::Int #268)
-#297 := (or #296 #293)
-#306 := (or #304 #297)
-#313 := (iff #306 #305)
-#308 := (or #304 #301)
-#311 := (iff #308 #305)
-#312 := [rewrite]: #311
-#309 := (iff #306 #308)
-#302 := (iff #297 #301)
-#298 := (iff #293 #300)
-#299 := [rewrite]: #298
-#303 := [monotonicity #299]: #302
-#310 := [monotonicity #303]: #309
-#314 := [trans #310 #312]: #313
-#307 := [quant-inst #10]: #306
-#315 := [mp #307 #314]: #305
-#612 := [unit-resolution #315 #266]: #301
-#613 := [unit-resolution #612 #589]: #300
-#428 := (not #300)
-#614 := (or #428 #316)
-#615 := [th-lemma arith triangle-eq]: #614
-#616 := [unit-resolution #615 #613]: #316
-#317 := (>= #268 1::Int)
-#562 := (not #317)
-#563 := [hypothesis]: #562
-#564 := (or #428 #317)
-#565 := [th-lemma arith triangle-eq]: #564
-#566 := [unit-resolution #565 #563]: #428
-#402 := (= #268 3::Int)
-#431 := (not #402)
-#425 := (>= #268 3::Int)
-#567 := (not #425)
-#568 := (or #567 #317)
-#569 := [th-lemma arith farkas 1 1]: #568
-#570 := [unit-resolution #569 #563]: #567
-#571 := (or #431 #425)
-#572 := [th-lemma arith triangle-eq]: #571
-#573 := [unit-resolution #572 #570]: #431
-#403 := (= #268 2::Int)
-#434 := (not #403)
-#427 := (>= #268 2::Int)
-#574 := (not #427)
-#575 := (or #574 #317)
-#576 := [th-lemma arith farkas 1 1]: #575
-#577 := [unit-resolution #576 #563]: #574
-#578 := (or #434 #427)
-#579 := [th-lemma arith triangle-eq]: #578
-#580 := [unit-resolution #579 #577]: #434
-#408 := (or #300 #402 #403)
-#395 := (f13 #268 f14)
-#396 := (= f1 #395)
-#411 := (iff #396 #408)
-#415 := (or #414 #411)
-#406 := (or #300 #403 #402)
-#407 := (iff #396 #406)
-#416 := (or #414 #407)
-#418 := (iff #416 #415)
-#420 := (iff #415 #415)
-#421 := [rewrite]: #420
-#412 := (iff #407 #411)
-#409 := (iff #406 #408)
-#410 := [rewrite]: #409
-#413 := [monotonicity #410]: #412
-#419 := [monotonicity #413]: #418
-#422 := [trans #419 #421]: #418
-#417 := [quant-inst #268]: #416
-#423 := [mp #417 #422]: #415
-#581 := [unit-resolution #423 #252]: #411
-#440 := (not #411)
-#583 := (or #440 #408)
-#253 := (pattern #28)
-#44 := (f13 #28 f14)
-#129 := (= f1 #44)
-#254 := (forall (vars (?v0 S2)) (:pat #253) #129)
-#132 := (forall (vars (?v0 S2)) #129)
-#257 := (iff #132 #254)
-#255 := (iff #129 #129)
-#256 := [refl]: #255
-#258 := [quant-intro #256]: #257
-#174 := (~ #132 #132)
-#172 := (~ #129 #129)
-#173 := [refl]: #172
-#175 := [nnf-pos #173]: #174
-#45 := (= #44 f1)
-#46 := (forall (vars (?v0 S2)) #45)
-#133 := (iff #46 #132)
-#130 := (iff #45 #129)
-#131 := [rewrite]: #130
-#134 := [quant-intro #131]: #133
-#128 := [asserted]: #46
-#137 := [mp #128 #134]: #132
-#176 := [mp~ #137 #175]: #132
-#259 := [mp #176 #258]: #254
-#399 := (not #254)
-#400 := (or #399 #396)
-#401 := [quant-inst #11]: #400
-#582 := [unit-resolution #401 #259]: #396
-#443 := (not #396)
-#444 := (or #440 #443 #408)
-#445 := [def-axiom]: #444
-#584 := [unit-resolution #445 #582]: #583
-#585 := [unit-resolution #584 #581]: #408
-#437 := (not #408)
-#438 := (or #437 #300 #402 #403)
-#439 := [def-axiom]: #438
-#586 := [unit-resolution #439 #585]: #408
-#587 := [unit-resolution #586 #580 #573 #566]: false
-#588 := [lemma #587]: #317
-#340 := (<= #267 2::Int)
-#325 := (= #267 2::Int)
-#319 := (f13 2::Int f14)
-#320 := (= f1 #319)
-#321 := (not #320)
-#660 := [hypothesis]: #321
-#651 := (or #414 #320)
-#627 := (= 2::Int 3::Int)
-#628 := (= 2::Int 2::Int)
-#626 := (= 2::Int 1::Int)
-#629 := (or #626 #628 #627)
-#630 := (iff #320 #629)
-#652 := (or #414 #630)
-#654 := (iff #652 #651)
-#656 := (iff #651 #651)
-#657 := [rewrite]: #656
-#649 := (iff #630 #320)
-#644 := (iff #320 true)
-#647 := (iff #644 #320)
-#648 := [rewrite]: #647
-#645 := (iff #630 #644)
-#642 := (iff #629 true)
-#637 := (or false true false)
-#640 := (iff #637 true)
-#641 := [rewrite]: #640
-#638 := (iff #629 #637)
-#635 := (iff #627 false)
-#636 := [rewrite]: #635
-#633 := (iff #628 true)
-#634 := [rewrite]: #633
-#631 := (iff #626 false)
-#632 := [rewrite]: #631
-#639 := [monotonicity #632 #634 #636]: #638
-#643 := [trans #639 #641]: #642
-#646 := [monotonicity #643]: #645
-#650 := [trans #646 #648]: #649
-#655 := [monotonicity #650]: #654
-#658 := [trans #655 #657]: #654
-#653 := [quant-inst #14]: #652
-#659 := [mp #653 #658]: #651
-#661 := [unit-resolution #659 #252 #660]: false
-#662 := [lemma #661]: #320
-#326 := (or #321 #325)
-#329 := (or #304 #321 #325)
-#318 := (= 2::Int #267)
-#322 := (or #321 #318)
-#330 := (or #304 #322)
-#337 := (iff #330 #329)
-#332 := (or #304 #326)
-#335 := (iff #332 #329)
-#336 := [rewrite]: #335
-#333 := (iff #330 #332)
-#327 := (iff #322 #326)
-#323 := (iff #318 #325)
-#324 := [rewrite]: #323
-#328 := [monotonicity #324]: #327
-#334 := [monotonicity #328]: #333
-#338 := [trans #334 #336]: #337
-#331 := [quant-inst #14]: #330
-#339 := [mp #331 #338]: #329
-#617 := [unit-resolution #339 #266]: #326
-#618 := [unit-resolution #617 #662]: #325
-#483 := (not #325)
-#619 := (or #483 #340)
-#620 := [th-lemma arith triangle-eq]: #619
-#621 := [unit-resolution #620 #618]: #340
-#341 := (>= #267 2::Int)
-#622 := (or #483 #341)
-#623 := [th-lemma arith triangle-eq]: #622
-#624 := [unit-resolution #623 #618]: #341
-#625 := [th-lemma arith eq-propagate -1 -1 -1 -1 #624 #621 #588 #616]: #510
-#592 := [symm #625]: #591
-#593 := [monotonicity #592]: #590
-#20 := (= f7 #19)
-#77 := [asserted]: #20
-#665 := [trans #77 #593]: #664
-#667 := [trans #665 #597]: #666
-#668 := [trans #667 #663]: #153
-#157 := (not #153)
-#54 := (= #53 f7)
-#55 := (not #54)
-#158 := (iff #55 #157)
-#155 := (iff #54 #153)
-#156 := [rewrite]: #155
-#159 := [monotonicity #156]: #158
-#152 := [asserted]: #55
-#162 := [mp #152 #159]: #157
-[unit-resolution #162 #668]: false
-unsat
-fec19a326f20bb7c46f8aaa57650582e09f85345 1 0
-unsat
-3985530df8b42c3cef066c8cd0d44440d8ea6843 1 0
-unsat
-b4de8a8d55c543048b440b0c84f0071b46100a45 1 0
-unsat
-94ef9302298c22689d91dfad87e5b1f5d143d5d6 1 0
-unsat
-84466cebf093560047a32670f44cbc877bb477c9 1 0
-unsat
-579199d37b2cb3378054f9db68fcb9989d990323 1 0
-unsat
-2872ce5ca3a7494f5ba4028b085484fd0433ed9b 1 0
-unsat
-d857d3364e9de34d43d117af226fd9c871330291 1 0
-unsat
-7b5fe4ae09f8bd6fdbd244103d5a0b40235f5a67 1 0
-unsat
-333b09d4a88312b735fa2c0986530dc12f9062b0 1 0
-unsat
-62bb93d4bfd163a4bd1ef9e32841389b2f0701ff 1 0
-unsat
-8a3a338f2631cd760047005189c26535fc42f33b 1 0
-unsat
-e65adab8d8118c2a62881422c4cfa39ea83588c6 1 0
-unsat
-1722e6f38c6c2d0aec0a2dcdf1e1e78adb2e31e3 1 0
-unsat
-fcc7f044a41e9e32b443e735a923af3bab731696 1 0
-unsat
-d283a7edf751ac599eb9ddd0eb05b8f0e5418081 1 0
-unsat
-9826b35d28195f567a43a9988d931aa560cc0e62 1 0
-unsat
-75ecdd955df71dc9013f7eaa0ab5e7c1a3efb520 1 0
-unsat
-731417bf1910ce702bf230518d2ad09e58894b57 1 0
-unsat
-fead099c17f1944309708edb03f92a2c5882b602 1 0
-unsat
-077dfea4c505e6a54f38d0e98e1a237b06f1a2b6 1 0
-unsat
-4968d9eb8b05e0c9bb6bec431e8a3db101fdd07d 1 0
-unsat
-37993c5ba42b0ad3840c52f6978182c665b6a51a 1 0
-unsat
-fc106b34b31aebbcd284a81b86ca12b66f28a082 1 0
-unsat
-50686101f51261c6e69c51c57e81f850810ca021 1 0
-unsat
-7c224e2bf446bb9e771ad899dbf71e71a3387da4 1 0
-unsat
-3c211c7e4bc32a231c616ba0ab783febeec764b9 1 0
-unsat
-3ee74ae7ffc2b7cd44664723e548e33953a1326d 1 0
-unsat
-3bee47654272d37062810bef6736a841e54b7e55 1 0
-unsat
-31692355cdcd02b4c6d5b8823c2c5faa69b5e7c6 1 0
-unsat
-68d8c15a9e52bdbb429d5415b2df29a5b506a165 1 0
-unsat
-4e3281973dda451a73a69c742c6e82a2624514c5 1 0
-unsat
-6da1c460b7745afe557552bcf129475de318b5a5 1 0
-unsat
-2087de823b8b6adb448d7b8612d73f1da92eb202 1 0
-unsat
-67b2b464b1c97af42282ab2b3611abc12748bebc 1 0
-unsat
-4f95bb0ed62abba4e30dd0f6a43e32be94b9504a 1 0
-unsat
-8355b72d160f61ed2bfa2347277cc51be5e403d9 1 0
-unsat
-87f0dff086bc3f2a8c8ae4368ef87fdd33753018 1 0
-unsat
-5d89866e008ca1008aa010cd8ac00375e1e49a76 1 0
-unsat
-f585a3090b2190a907cde398ffc80884fd113697 1 0
-unsat
-8b9c59708c54702afdb72e9234fbe61739dcdcac 1 0
-unsat
-1b8942a7812b6a3825133062469e81170c968122 1 0
-unsat
-7ce8e82cc1e04157aad53db91c119a393f0cc34c 1 0
-unsat
-a7fb4771d1deb25dcf66848f425d54aca604bb1b 1 0
-unsat
-e6b0a173f73465d0bda9435774a6a86f94eab9cd 1 0
-unsat
-1ddab5bc0ef3d61ccee542ac3a7c0d5333bca04e 1 0
-unsat
-e126416a9aaf9380c805079d9ea23f46180b1ead 1 0
-unsat
-a7fcb872e8568eaf8ce860d563685b1a0605dffe 1 0
-unsat
-c1df88859dce165ae1a0fe05398eaab699a73d1a 1 0
-unsat
-bd55640b57c04d5cdd17b87acb77828e12be95d3 1 0
-unsat
-b1a2c4806b409b2f63dd2441827e4310ccc7ce77 1 0
-unsat
-f106177fef6206c2a71499d1adef5ec2644bd1c8 1 0
-unsat
-ab425bfd72799c3278b174059545a5022fbf5950 1 0
-unsat
-61b369fcda1cf2779764b8823aacbec7784d925b 1 0
-unsat
-bbeefb7aa775f6cd1ba85d93b2f5a5511639f5c2 1 0
-unsat
-b09779548402501da93636b75ef7898959d6eb1e 1 0
-unsat
-24791d6e1671b2836e50b921f2d0ceb0f42151b1 1 0
-unsat
-e2a11ab87aeb3ed5913e9512aa10b9ca74213a4b 61 0
-#2 := false
-decl f3 :: (-> S2 S3 S4)
-decl f9 :: S3
-#33 := f9
-decl f4 :: (-> S5 S4 S2)
-decl f10 :: S4
-#35 := f10
-decl f5 :: (-> S6 S3 S5)
-decl f6 :: (-> S7 S2 S6)
-decl f8 :: S2
-#31 := f8
-decl f7 :: S7
-#8 := f7
-#32 := (f6 f7 f8)
-#34 := (f5 #32 f9)
-#36 := (f4 #34 f10)
-#37 := (f3 #36 f9)
-#81 := (= f10 #37)
-#85 := (not #81)
-#38 := (= #37 f10)
-#39 := (not #38)
-#86 := (iff #39 #85)
-#83 := (iff #38 #81)
+#33 := f14
+#224 := (f13 2::Int f14)
+#225 := (= #224 f1)
+#235 := (not #225)
+#513 := [hypothesis]: #235
+#32 := (:var 0 Int)
+#34 := (f13 #32 f14)
+#188 := (pattern #34)
+#38 := (= #32 3::Int)
+#37 := (= #32 2::Int)
+#36 := (= #32 1::Int)
+#82 := (or #36 #37 #38)
+#35 := (= #34 f1)
+#85 := (iff #35 #82)
+#189 := (forall (vars (?v0 Int)) (:pat #188) #85)
+#88 := (forall (vars (?v0 Int)) #85)
+#192 := (iff #88 #189)
+#190 := (iff #85 #85)
+#191 := [refl]: #190
+#193 := [quant-intro #191]: #192
+#109 := (~ #88 #88)
+#107 := (~ #85 #85)
+#108 := [refl]: #107
+#110 := [nnf-pos #108]: #109
+#39 := (or #37 #38)
+#40 := (or #36 #39)
+#41 := (iff #35 #40)
+#42 := (forall (vars (?v0 Int)) #41)
+#89 := (iff #42 #88)
+#86 := (iff #41 #85)
+#83 := (iff #40 #82)
 #84 := [rewrite]: #83
 #87 := [monotonicity #84]: #86
-#80 := [asserted]: #39
-#90 := [mp #80 #87]: #85
-#13 := (:var 0 S4)
-#11 := (:var 1 S3)
-#9 := (:var 2 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#14 := (f4 #12 #13)
-#584 := (pattern #14)
-#15 := (f3 #14 #11)
-#60 := (= #13 #15)
-#585 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #584) #60)
-#63 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #60)
-#588 := (iff #63 #585)
-#586 := (iff #60 #60)
-#587 := [refl]: #586
-#589 := [quant-intro #587]: #588
-#100 := (~ #63 #63)
-#98 := (~ #60 #60)
-#99 := [refl]: #98
-#101 := [nnf-pos #99]: #100
-#16 := (= #15 #13)
-#17 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #16)
-#64 := (iff #17 #63)
-#61 := (iff #16 #60)
-#62 := [rewrite]: #61
-#65 := [quant-intro #62]: #64
-#59 := [asserted]: #17
-#68 := [mp #59 #65]: #63
-#89 := [mp~ #68 #101]: #63
-#590 := [mp #89 #589]: #585
-#167 := (not #585)
-#254 := (or #167 #81)
-#168 := [quant-inst #31 #33 #35]: #254
-[unit-resolution #168 #590 #90]: false
-unsat
-573c26140e97f5551027a6ed7f91a8a26996149c 95 0
-#2 := false
-decl f3 :: (-> S2 S3 S4)
-decl f9 :: S3
-#32 := f9
-decl f10 :: S2
-#35 := f10
-#41 := (f3 f10 f9)
-decl f4 :: (-> S5 S4 S2)
-decl f11 :: S4
-#38 := f11
-decl f5 :: (-> S6 S3 S5)
-decl f8 :: S3
-#31 := f8
-decl f6 :: (-> S7 S2 S6)
-decl f7 :: S7
-#8 := f7
-#36 := (f6 f7 f10)
-#37 := (f5 #36 f8)
-#39 := (f4 #37 f11)
-#40 := (f3 #39 f9)
-#42 := (= #40 #41)
-#175 := (= f11 #40)
-#33 := (= f8 f9)
-#262 := (ite #33 #175 #42)
-#268 := (not #262)
-#94 := (not #42)
-#86 := (or #33 #42)
-#90 := (not #86)
-#34 := (not #33)
-#43 := (implies #34 #42)
-#44 := (not #43)
-#91 := (iff #44 #90)
-#88 := (iff #43 #86)
-#89 := [rewrite]: #88
-#92 := [monotonicity #89]: #91
-#85 := [asserted]: #44
-#95 := [mp #85 #92]: #90
-#96 := [not-or-elim #95]: #94
-#93 := [not-or-elim #95]: #34
-#586 := (or #268 #33 #42)
-#241 := [def-axiom]: #586
-#265 := [unit-resolution #241 #93 #96]: #268
-#24 := (:var 0 S3)
-#22 := (:var 1 S4)
-#20 := (:var 2 S3)
-#18 := (:var 3 S2)
-#19 := (f6 f7 #18)
-#21 := (f5 #19 #20)
-#23 := (f4 #21 #22)
-#25 := (f3 #23 #24)
-#599 := (pattern #25)
-#27 := (f3 #18 #24)
-#115 := (= #25 #27)
-#114 := (= #22 #25)
-#72 := (= #20 #24)
-#102 := (ite #72 #114 #115)
-#600 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #599) #102)
-#107 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #102)
-#603 := (iff #107 #600)
-#601 := (iff #102 #102)
-#602 := [refl]: #601
-#604 := [quant-intro #602]: #603
-#76 := (ite #72 #22 #27)
-#79 := (= #25 #76)
-#82 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #79)
-#104 := (iff #82 #107)
-#103 := (iff #79 #102)
-#106 := [rewrite]: #103
-#105 := [quant-intro #106]: #104
-#100 := (~ #82 #82)
-#99 := (~ #79 #79)
-#112 := [refl]: #99
-#101 := [nnf-pos #112]: #100
-#26 := (= #24 #20)
-#28 := (ite #26 #22 #27)
-#29 := (= #25 #28)
-#30 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #29)
-#83 := (iff #30 #82)
-#80 := (iff #29 #79)
-#77 := (= #28 #76)
-#74 := (iff #26 #72)
-#75 := [rewrite]: #74
-#78 := [monotonicity #75]: #77
-#81 := [monotonicity #78]: #80
-#84 := [quant-intro #81]: #83
-#71 := [asserted]: #30
-#87 := [mp #71 #84]: #82
-#113 := [mp~ #87 #101]: #82
-#116 := [mp #113 #105]: #107
-#605 := [mp #116 #604]: #600
-#194 := (not #600)
-#267 := (or #194 #262)
-#264 := [quant-inst #35 #31 #38 #32]: #267
-[unit-resolution #264 #605 #265]: false
-unsat
-d35743b8d8e626bc0fb89e7618256a033a85cc45 169 0
-#2 := false
-decl f3 :: (-> S2 S3 S4)
-decl f8 :: S3
-#31 := f8
-decl f4 :: (-> S5 S4 S2)
-decl f12 :: S4
-#42 := f12
-decl f5 :: (-> S6 S3 S5)
-decl f9 :: S3
-#32 := f9
-decl f6 :: (-> S7 S2 S6)
-decl f11 :: S4
-#38 := f11
-decl f10 :: S2
-#35 := f10
-decl f7 :: S7
-#8 := f7
-#36 := (f6 f7 f10)
-#37 := (f5 #36 f8)
-#39 := (f4 #37 f11)
-#40 := (f6 f7 #39)
-#41 := (f5 #40 f9)
-#43 := (f4 #41 f12)
-#44 := (f3 #43 f8)
-#89 := (= f11 #44)
-#185 := (f3 #39 f8)
-#276 := (= #44 #185)
-#589 := (iff #276 #89)
-#226 := (iff #89 #276)
-#579 := (= #185 #44)
-#586 := (iff #579 #276)
-#588 := [commutativity]: #586
-#585 := (iff #89 #579)
-#272 := (= f11 #185)
-#13 := (:var 0 S4)
-#11 := (:var 1 S3)
-#9 := (:var 2 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#14 := (f4 #12 #13)
-#603 := (pattern #14)
-#15 := (f3 #14 #11)
-#68 := (= #13 #15)
-#604 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #603) #68)
-#71 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #68)
-#607 := (iff #71 #604)
-#605 := (iff #68 #68)
-#606 := [refl]: #605
-#608 := [quant-intro #606]: #607
-#121 := (~ #71 #71)
-#119 := (~ #68 #68)
-#120 := [refl]: #119
-#122 := [nnf-pos #120]: #121
-#16 := (= #15 #13)
-#17 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #16)
-#72 := (iff #17 #71)
-#69 := (iff #16 #68)
-#70 := [rewrite]: #69
-#73 := [quant-intro #70]: #72
-#67 := [asserted]: #17
-#76 := [mp #67 #73]: #71
-#109 := [mp~ #76 #122]: #71
-#609 := [mp #109 #608]: #604
-#187 := (not #604)
-#274 := (or #187 #272)
-#265 := [quant-inst #35 #31 #38]: #274
-#584 := [unit-resolution #265 #609]: #272
-#221 := [monotonicity #584]: #585
-#227 := [trans #221 #588]: #226
-#587 := [symm #227]: #589
-#277 := (= f12 #44)
-#33 := (= f8 f9)
-#597 := (ite #33 #277 #276)
-#24 := (:var 0 S3)
-#22 := (:var 1 S4)
-#20 := (:var 2 S3)
-#18 := (:var 3 S2)
-#19 := (f6 f7 #18)
-#21 := (f5 #19 #20)
-#23 := (f4 #21 #22)
-#25 := (f3 #23 #24)
-#610 := (pattern #25)
-#27 := (f3 #18 #24)
-#126 := (= #25 #27)
-#125 := (= #22 #25)
-#75 := (= #20 #24)
-#113 := (ite #75 #125 #126)
-#611 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #610) #113)
-#118 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #113)
-#614 := (iff #118 #611)
-#612 := (iff #113 #113)
-#613 := [refl]: #612
-#615 := [quant-intro #613]: #614
-#79 := (ite #75 #22 #27)
-#82 := (= #25 #79)
-#85 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #82)
-#115 := (iff #85 #118)
-#114 := (iff #82 #113)
-#117 := [rewrite]: #114
-#116 := [quant-intro #117]: #115
-#111 := (~ #85 #85)
-#110 := (~ #82 #82)
-#123 := [refl]: #110
-#112 := [nnf-pos #123]: #111
-#26 := (= #24 #20)
-#28 := (ite #26 #22 #27)
-#29 := (= #25 #28)
-#30 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #29)
-#86 := (iff #30 #85)
-#83 := (iff #29 #82)
-#80 := (= #28 #79)
-#77 := (iff #26 #75)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [quant-intro #84]: #86
-#74 := [asserted]: #30
-#90 := [mp #74 #87]: #85
-#124 := [mp~ #90 #112]: #85
-#127 := [mp #124 #116]: #118
-#616 := [mp #127 #615]: #611
-#591 := (not #611)
-#263 := (or #591 #597)
-#275 := (= f9 f8)
-#279 := (ite #275 #277 #276)
-#264 := (or #591 #279)
-#599 := (iff #264 #263)
-#601 := (iff #263 #263)
-#596 := [rewrite]: #601
-#252 := (iff #279 #597)
-#258 := (iff #275 #33)
-#595 := [rewrite]: #258
-#384 := [monotonicity #595]: #252
-#600 := [monotonicity #384]: #599
-#602 := [trans #600 #596]: #599
-#598 := [quant-inst #39 #32 #42 #31]: #264
-#592 := [mp #598 #602]: #263
-#580 := [unit-resolution #592 #616]: #597
-#250 := (not #597)
-#581 := (or #250 #276)
-#34 := (not #33)
-#96 := (or #33 #89)
-#101 := (not #96)
-#45 := (= #44 f11)
-#46 := (implies #34 #45)
-#47 := (not #46)
-#102 := (iff #47 #101)
-#99 := (iff #46 #96)
-#93 := (implies #34 #89)
-#97 := (iff #93 #96)
-#98 := [rewrite]: #97
-#94 := (iff #46 #93)
-#91 := (iff #45 #89)
-#92 := [rewrite]: #91
-#95 := [monotonicity #92]: #94
-#100 := [trans #95 #98]: #99
-#103 := [monotonicity #100]: #102
-#88 := [asserted]: #47
-#106 := [mp #88 #103]: #101
-#104 := [not-or-elim #106]: #34
-#251 := (or #250 #33 #276)
-#594 := [def-axiom]: #251
-#582 := [unit-resolution #594 #104]: #581
-#583 := [unit-resolution #582 #580]: #276
-#590 := [mp #583 #587]: #89
-#105 := (not #89)
-#107 := [not-or-elim #106]: #105
-[unit-resolution #107 #590]: false
-unsat
-71e81e17dffc11bde3007b51f81e62a30ca54d00 81 0
-#2 := false
+#90 := [quant-intro #87]: #89
+#79 := [asserted]: #42
+#91 := [mp #79 #90]: #88
+#111 := [mp~ #91 #110]: #88
+#194 := [mp #111 #193]: #189
+#302 := (not #189)
+#504 := (or #302 #225)
+#481 := (= 2::Int 3::Int)
+#451 := (= 2::Int 2::Int)
+#450 := (= 2::Int 1::Int)
+#482 := (or #450 #451 #481)
+#483 := (iff #225 #482)
+#505 := (or #302 #483)
+#507 := (iff #505 #504)
+#509 := (iff #504 #504)
+#510 := [rewrite]: #509
+#502 := (iff #483 #225)
+#1 := true
+#497 := (iff #225 true)
+#500 := (iff #497 #225)
+#501 := [rewrite]: #500
+#498 := (iff #483 #497)
+#495 := (iff #482 true)
+#490 := (or false true false)
+#493 := (iff #490 true)
+#494 := [rewrite]: #493
+#491 := (iff #482 #490)
+#488 := (iff #481 false)
+#489 := [rewrite]: #488
+#486 := (iff #451 true)
+#487 := [rewrite]: #486
+#484 := (iff #450 false)
+#485 := [rewrite]: #484
+#492 := [monotonicity #485 #487 #489]: #491
+#496 := [trans #492 #494]: #495
+#499 := [monotonicity #496]: #498
+#503 := [trans #499 #501]: #502
+#508 := [monotonicity #503]: #507
+#511 := [trans #508 #510]: #507
+#506 := [quant-inst #13]: #505
+#512 := [mp #506 #511]: #504
+#514 := [unit-resolution #512 #194 #513]: false
+#515 := [lemma #514]: #225
+#237 := (or #235 #236)
+#46 := (f4 f5 #32)
+#202 := (pattern #46)
+#47 := (f11 f12 #46)
+#48 := (= #47 #32)
+#92 := (not #35)
+#93 := (or #92 #48)
+#203 := (forall (vars (?v0 Int)) (:pat #188 #202) #93)
+#96 := (forall (vars (?v0 Int)) #93)
+#206 := (iff #96 #203)
+#204 := (iff #93 #93)
+#205 := [refl]: #204
+#207 := [quant-intro #205]: #206
+#119 := (~ #96 #96)
+#117 := (~ #93 #93)
+#118 := [refl]: #117
+#120 := [nnf-pos #118]: #119
+#49 := (implies #35 #48)
+#50 := (forall (vars (?v0 Int)) #49)
+#97 := (iff #50 #96)
+#94 := (iff #49 #93)
+#95 := [rewrite]: #94
+#98 := [quant-intro #95]: #97
+#81 := [asserted]: #50
+#101 := [mp #81 #98]: #96
+#121 := [mp~ #101 #120]: #96
+#208 := [mp #121 #207]: #203
+#226 := (not #203)
+#240 := (or #226 #235 #236)
+#241 := (or #226 #237)
+#243 := (iff #241 #240)
+#244 := [rewrite]: #243
+#242 := [quant-inst #13]: #241
+#245 := [mp #242 #244]: #240
+#460 := [unit-resolution #245 #208]: #237
+#461 := [unit-resolution #460 #515]: #236
+#312 := (not #236)
+#462 := (or #312 #246)
+#463 := [th-lemma arith triangle-eq]: #462
+#464 := [unit-resolution #463 #461]: #246
+#247 := (>= #212 2::Int)
+#465 := (or #312 #247)
+#466 := [th-lemma arith triangle-eq]: #465
+#467 := [unit-resolution #466 #461]: #247
+#233 := (<= #211 1::Int)
+#222 := (= #211 1::Int)
+#216 := (f13 1::Int f14)
+#217 := (= #216 f1)
+#221 := (not #217)
+#447 := [hypothesis]: #221
+#392 := (or #302 #217)
+#398 := (= 1::Int 3::Int)
+#397 := (= 1::Int 2::Int)
+#396 := (= 1::Int 1::Int)
+#399 := (or #396 #397 #398)
+#400 := (iff #217 #399)
+#393 := (or #302 #400)
+#395 := (iff #393 #392)
+#443 := (iff #392 #392)
+#444 := [rewrite]: #443
+#390 := (iff #400 #217)
+#414 := (iff #217 true)
+#388 := (iff #414 #217)
+#389 := [rewrite]: #388
+#415 := (iff #400 #414)
+#412 := (iff #399 true)
+#407 := (or true false false)
+#410 := (iff #407 true)
+#411 := [rewrite]: #410
+#408 := (iff #399 #407)
+#405 := (iff #398 false)
+#406 := [rewrite]: #405
+#403 := (iff #397 false)
+#404 := [rewrite]: #403
+#401 := (iff #396 true)
+#402 := [rewrite]: #401
+#409 := [monotonicity #402 #404 #406]: #408
+#413 := [trans #409 #411]: #412
+#416 := [monotonicity #413]: #415
+#391 := [trans #416 #389]: #390
+#442 := [monotonicity #391]: #395
+#445 := [trans #442 #444]: #395
+#394 := [quant-inst #9]: #393
+#446 := [mp #394 #445]: #392
+#448 := [unit-resolution #446 #194 #447]: false
+#449 := [lemma #448]: #217
+#223 := (or #221 #222)
+#227 := (or #226 #221 #222)
+#228 := (or #226 #223)
+#230 := (iff #228 #227)
+#231 := [rewrite]: #230
+#229 := [quant-inst #9]: #228
+#232 := [mp #229 #231]: #227
+#468 := [unit-resolution #232 #208]: #223
+#469 := [unit-resolution #468 #449]: #222
+#351 := (not #222)
+#470 := (or #351 #233)
+#471 := [th-lemma arith triangle-eq]: #470
+#472 := [unit-resolution #471 #469]: #233
+#234 := (>= #211 1::Int)
+#386 := (not #234)
+#387 := [hypothesis]: #386
+#417 := (or #351 #234)
+#418 := [th-lemma arith triangle-eq]: #417
+#419 := [unit-resolution #418 #387]: #351
+#333 := (= #211 2::Int)
+#354 := (not #333)
+#348 := (>= #211 2::Int)
+#420 := (not #348)
+#421 := (or #420 #234)
+#422 := [th-lemma arith farkas 1 1]: #421
+#423 := [unit-resolution #422 #387]: #420
+#424 := (or #354 #348)
+#425 := [th-lemma arith triangle-eq]: #424
+#426 := [unit-resolution #425 #423]: #354
+#334 := (= #211 3::Int)
+#357 := (not #334)
+#350 := (>= #211 3::Int)
+#427 := (not #350)
+#428 := (or #427 #234)
+#429 := [th-lemma arith farkas 1 1]: #428
+#430 := [unit-resolution #429 #387]: #427
+#431 := (or #357 #350)
+#432 := [th-lemma arith triangle-eq]: #431
+#433 := [unit-resolution #432 #430]: #357
+#341 := (or #222 #333 #334)
+#289 := (f13 #211 f14)
+#290 := (= #289 f1)
+#342 := (iff #290 #341)
+#345 := (or #302 #342)
+#346 := [quant-inst #211]: #345
+#434 := [unit-resolution #346 #194]: #342
+#363 := (not #342)
+#436 := (or #363 #341)
+#23 := (:var 0 S2)
+#27 := (f11 f12 #23)
+#195 := (pattern #27)
+#43 := (f13 #27 f14)
+#44 := (= #43 f1)
+#196 := (forall (vars (?v0 S2)) (:pat #195) #44)
+#45 := (forall (vars (?v0 S2)) #44)
+#199 := (iff #45 #196)
+#197 := (iff #44 #44)
+#198 := [refl]: #197
+#200 := [quant-intro #198]: #199
+#114 := (~ #45 #45)
+#112 := (~ #44 #44)
+#113 := [refl]: #112
+#115 := [nnf-pos #113]: #114
+#80 := [asserted]: #45
+#116 := [mp~ #80 #115]: #45
+#201 := [mp #116 #200]: #196
+#291 := (not #196)
+#296 := (or #291 #290)
+#297 := [quant-inst #10]: #296
+#435 := [unit-resolution #297 #201]: #290
+#366 := (not #290)
+#367 := (or #363 #366 #341)
+#368 := [def-axiom]: #367
+#437 := [unit-resolution #368 #435]: #436
+#438 := [unit-resolution #437 #434]: #341
+#360 := (not #341)
+#361 := (or #360 #222 #333 #334)
+#362 := [def-axiom]: #361
+#439 := [unit-resolution #362 #438]: #341
+#440 := [unit-resolution #439 #433 #426 #419]: false
+#441 := [lemma #440]: #234
+#473 := [th-lemma arith eq-propagate -1 -1 -1 -1 #441 #472 #467 #464]: #383
+#475 := [symm #473]: #474
+#519 := [monotonicity #475]: #518
+#521 := [symm #519]: #520
+#524 := (= #52 #214)
+#209 := (f9 f10 #10)
+#210 := (f8 #209 #14)
+#215 := (= #210 #214)
+#21 := (:var 1 S2)
+#22 := (f9 f10 #21)
+#24 := (f8 #22 #23)
+#181 := (pattern #24)
+#26 := (f11 f12 #21)
+#28 := (+ #26 #27)
+#29 := (f4 f5 #28)
+#30 := (= #24 #29)
+#182 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #181) #30)
+#31 := (forall (vars (?v0 S2) (?v1 S2)) #30)
+#185 := (iff #31 #182)
+#183 := (iff #30 #30)
+#184 := [refl]: #183
+#186 := [quant-intro #184]: #185
+#104 := (~ #31 #31)
+#102 := (~ #30 #30)
+#103 := [refl]: #102
+#105 := [nnf-pos #103]: #104
+#78 := [asserted]: #31
+#106 := [mp~ #78 #105]: #31
+#187 := [mp #106 #186]: #182
+#218 := (not #182)
+#219 := (or #218 #215)
+#220 := [quant-inst #10 #14]: #219
+#476 := [unit-resolution #220 #187]: #215
+#516 := (= #52 #210)
+#15 := (= f6 #14)
+#76 := [asserted]: #15
+#452 := (= #51 #209)
+#479 := (= #209 #51)
+#477 := (= #10 f3)
+#11 := (= f3 #10)
+#75 := [asserted]: #11
+#478 := [symm #75]: #477
+#480 := [monotonicity #478]: #479
+#453 := [symm #480]: #452
+#517 := [monotonicity #453 #76]: #516
+#525 := [trans #517 #476]: #524
+#527 := [trans #525 #521]: #526
+#528 := [trans #527 #523]: #53
+#54 := (not #53)
+#99 := [asserted]: #54
+[unit-resolution #99 #528]: false
+unsat
+2864d138b390af4e3eeba533641291b4ae179658 1 0
+unsat
+218fdaddec8daf9fe821ad83145a0f41dc0cea69 1 0
+unsat
+e4291661842e19946a32d5d03adcb9efafbd09b2 1 0
+unsat
+c588e986fb0be52b47531527138c9af03115a341 1 0
+unsat
+0a10387ef30e59cf2ddae7f35bfb8acd6ada3dbd 1 0
+unsat
+23eac3c9c6bd3afca4e93ad69fc507b57e5a404f 1 0
+unsat
+11c2a4b88caf165635cfebe8973f704d44d24794 1 0
+unsat
+3a5f958e4a5b70d0ec5d8d00c8ab6d7e7ae3a517 1 0
+unsat
+c2efd82298ced7929b47cff71c32d108136ebb30 1 0
+unsat
+faea053ed25da44e251b8eb4312ac6428fd87ca2 1 0
+unsat
+9532645b849bc944ead9221c89cd2cc80a79542d 1 0
+unsat
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+unsat
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+unsat
[phone]d8c81d0c1fcf765a24b7acc0b8b25 1 0
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+unsat
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+unsat
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+unsat
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+unsat
+1f603b5bd7f43c523a79a6bb10a493b3fa72cc85 1 0
+unsat
+d6873b3ad9377b99f2c3517770dea23f32521508 1 0
+unsat
+e2bd554f5593f9ef15136cabe0aea65dcfdb5188 1 0
+unsat
+4f72565e3d34747b9db8c734bc1f9265d086b52b 1 0
+unsat
+222d8029a2e1d50ba54c31aee7513d2d67ed472e 1 0
+unsat
+bdd3ac024678b853058c58dd381f33bda892d817 1 0
+unsat
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+unsat
+4e11f3d12b4eddfd39e29aa51612229198e08d79 1 0
+unsat
+ed132dc37435ef0c545fb72697366d21ce40b8e1 1 0
+unsat
+1a1d2140097a8893b17dc25e6605282254748963 1 0
+unsat
+a29ebb3637da825c641bd6c6606b77eb08906d93 1 0
+unsat
[phone]a7921466e21b252e0564cb1c6aa577 1 0
+unsat
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+unsat
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+unsat
+7b0e5b05b2ed758f149f0b55b9223ecaaeeb51cf 1 0
+unsat
+eafcdd2983b49d76b5488cea98e3f2f7e52876ba 1 0
+unsat
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+unsat
+594d725c4e08c5276928341fb15c42e790395795 1 0
+unsat
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+unsat
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+unsat
+e2cab523a51c26eaaa7fe0d9e1059e52e750c834 1 0
+unsat
+b1153994e02691ad7f1b18a2cbb489a7165319df 1 0
+unsat
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+unsat
+c50127acd06804ffc4d2b5381e19ed95d4784807 1 0
+unsat
+7dee0163a1aa13072509bd5a8b6706b711964644 1 0
+unsat
[phone]df48367740bbf9c50efea328be41 1 0
+unsat
+697e36dcaec78bc74ef0344cc9bfbab4fcc473fa 1 0
+unsat
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+unsat
+2c70ce922a083eaaef42a1b1541bf29fc3cb7e54 1 0
+unsat
+c03a19c9bc6c365fbc3e7555a82ee1e533d868c7 1 0
+unsat
+3b50e4f33dd2e10584c63c303e2a234d52c44d12 1 0
+unsat
+34f76ecd2c593f21adfb82e04699df605d7dde4f 1 0
+unsat
+13021c851a0cac5f9a6fa998cc01ddbd3e82ecdd 1 0
+unsat
+97ac538214a4420392823c7a3e55c4e4ae0919d9 1 0
+unsat
+bfec2f2aa9b262d9b6b7060b5701a5e3814488b2 1 0
+unsat
+f18271423b6c758ca8234fe9ec2671a9d9855f4f 1 0
+unsat
+1d9d6a45a95fa36e2cf7fdd489e71cf9eebcc402 1 0
+unsat
+466f95c3091f0353c12c0b00d563961d31c7ea6c 1 0
+unsat
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+unsat
+0632b158f9a5c6bb65e1e1b6be57c2c08505527a 47 0
+#2 := false
+decl f10 :: S4
+#34 := f10
 decl f3 :: (-> S2 S3 S4)
 decl f9 :: S3
 #32 := f9
 decl f4 :: (-> S5 S4 S2)
-decl f12 :: S4
-#42 := f12
+decl f5 :: (-> S6 S3 S5)
+decl f6 :: (-> S7 S2 S6)
+decl f8 :: S2
+#30 := f8
+decl f7 :: S7
+#7 := f7
+#31 := (f6 f7 f8)
+#33 := (f5 #31 f9)
+#35 := (f4 #33 f10)
+#36 := (f3 #35 f9)
+#37 := (= #36 f10)
+#38 := (not #37)
+#61 := [asserted]: #38
+#12 := (:var 0 S4)
+#10 := (:var 1 S3)
+#8 := (:var 2 S2)
+#9 := (f6 f7 #8)
+#11 := (f5 #9 #10)
+#13 := (f4 #11 #12)
+#560 := (pattern #13)
+#14 := (f3 #13 #10)
+#15 := (= #14 #12)
+#561 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #560) #15)
+#16 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #15)
+#564 := (iff #16 #561)
+#562 := (iff #15 #15)
+#563 := [refl]: #562
+#565 := [quant-intro #563]: #564
+#73 := (~ #16 #16)
+#71 := (~ #15 #15)
+#72 := [refl]: #71
+#74 := [nnf-pos #72]: #73
+#59 := [asserted]: #16
+#63 := [mp~ #59 #74]: #16
+#566 := [mp #63 #565]: #561
+#145 := (not #561)
+#231 := (or #145 #37)
+#146 := [quant-inst #30 #32 #34]: #231
+[unit-resolution #146 #566 #61]: false
+unsat
+f6aef6296a02dc2bb756eda92687889cb2a54145 87 0
+#2 := false
+decl f9 :: S3
+#31 := f9
+decl f8 :: S3
+#30 := f8
+#32 := (= f8 f9)
+#160 := (= f9 f8)
+decl f3 :: (-> S2 S3 S4)
+decl f10 :: S2
+#34 := f10
+#40 := (f3 f10 f9)
+decl f4 :: (-> S5 S4 S2)
+decl f11 :: S4
+#37 := f11
 decl f5 :: (-> S6 S3 S5)
 decl f6 :: (-> S7 S2 S6)
+decl f7 :: S7
+#7 := f7
+#35 := (f6 f7 f10)
+#36 := (f5 #35 f8)
+#38 := (f4 #36 f11)
+#39 := (f3 #38 f9)
+#41 := (= #39 #40)
+#246 := (= #39 f11)
+#249 := (if #160 #246 #41)
+#23 := (:var 0 S3)
+#21 := (:var 1 S4)
+#19 := (:var 2 S3)
+#17 := (:var 3 S2)
+#18 := (f6 f7 #17)
+#20 := (f5 #18 #19)
+#22 := (f4 #20 #21)
+#24 := (f3 #22 #23)
+#582 := (pattern #24)
+#26 := (f3 #17 #23)
+#95 := (= #24 #26)
+#94 := (= #24 #21)
+#25 := (= #23 #19)
+#82 := (if #25 #94 #95)
+#583 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #582) #82)
+#87 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #82)
+#586 := (iff #87 #583)
+#584 := (iff #82 #82)
+#585 := [refl]: #584
+#587 := [quant-intro #585]: #586
+#27 := (if #25 #21 #26)
+#28 := (= #24 #27)
+#29 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #28)
+#84 := (iff #29 #87)
+#83 := (iff #28 #82)
+#86 := [rewrite]: #83
+#85 := [quant-intro #86]: #84
+#80 := (~ #29 #29)
+#79 := (~ #28 #28)
+#92 := [refl]: #79
+#81 := [nnf-pos #92]: #80
+#65 := [asserted]: #29
+#93 := [mp~ #65 #81]: #29
+#96 := [mp #93 #85]: #87
+#588 := [mp #96 #587]: #583
+#248 := (not #583)
+#252 := (or #248 #249)
+#231 := [quant-inst #34 #30 #37 #31]: #252
+#250 := [unit-resolution #231 #588]: #249
+#567 := (not #249)
+#251 := (or #567 #160)
+#74 := (not #41)
+#67 := (or #32 #41)
+#70 := (not #67)
+#33 := (not #32)
+#42 := (implies #33 #41)
+#43 := (not #42)
+#71 := (iff #43 #70)
+#68 := (iff #42 #67)
+#69 := [rewrite]: #68
+#72 := [monotonicity #69]: #71
+#66 := [asserted]: #43
+#75 := [mp #66 #72]: #70
+#76 := [not-or-elim #75]: #74
+#563 := (or #567 #160 #41)
+#236 := [def-axiom]: #563
+#568 := [unit-resolution #236 #76]: #251
+#574 := [unit-resolution #568 #250]: #160
+#564 := [symm #574]: #32
+#73 := [not-or-elim #75]: #33
+[unit-resolution #73 #564]: false
+unsat
[phone]a6a4924829d934c10beb30bac9d44410 119 0
+#2 := false
 decl f11 :: S4
-#38 := f11
-decl f8 :: S3
-#31 := f8
-decl f10 :: S2
-#35 := f10
-decl f7 :: S7
-#8 := f7
-#36 := (f6 f7 f10)
-#37 := (f5 #36 f8)
-#39 := (f4 #37 f11)
-#40 := (f6 f7 #39)
-#41 := (f5 #40 f9)
-#43 := (f4 #41 f12)
-#44 := (f3 #43 f9)
-#89 := (= f12 #44)
-#105 := (not #89)
-#33 := (= f8 f9)
-#96 := (or #33 #89)
-#101 := (not #96)
-#45 := (= #44 f12)
-#34 := (not #33)
-#46 := (implies #34 #45)
-#47 := (not #46)
-#102 := (iff #47 #101)
-#99 := (iff #46 #96)
-#93 := (implies #34 #89)
-#97 := (iff #93 #96)
-#98 := [rewrite]: #97
-#94 := (iff #46 #93)
-#91 := (iff #45 #89)
-#92 := [rewrite]: #91
-#95 := [monotonicity #92]: #94
-#100 := [trans #95 #98]: #99
-#103 := [monotonicity #100]: #102
-#88 := [asserted]: #47
-#106 := [mp #88 #103]: #101
-#107 := [not-or-elim #106]: #105
-#13 := (:var 0 S4)
-#11 := (:var 1 S3)
-#9 := (:var 2 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#14 := (f4 #12 #13)
-#603 := (pattern #14)
-#15 := (f3 #14 #11)
-#68 := (= #13 #15)
-#604 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #603) #68)
-#71 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #68)
-#607 := (iff #71 #604)
-#605 := (iff #68 #68)
-#606 := [refl]: #605
-#608 := [quant-intro #606]: #607
-#121 := (~ #71 #71)
-#119 := (~ #68 #68)
-#120 := [refl]: #119
-#122 := [nnf-pos #120]: #121
-#16 := (= #15 #13)
-#17 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #16)
-#72 := (iff #17 #71)
-#69 := (iff #16 #68)
-#70 := [rewrite]: #69
-#73 := [quant-intro #70]: #72
-#67 := [asserted]: #17
-#76 := [mp #67 #73]: #71
-#109 := [mp~ #76 #122]: #71
-#609 := [mp #109 #608]: #604
-#187 := (not #604)
-#276 := (or #187 #89)
-#277 := [quant-inst #39 #32 #42]: #276
-[unit-resolution #277 #609 #107]: false
-unsat
-9663363ef61bef2d7fe1deebc3df1c1645a5ab56 90 0
-#2 := false
+#37 := f11
 decl f3 :: (-> S2 S3 S4)
 decl f8 :: S3
-#31 := f8
+#30 := f8
 decl f4 :: (-> S5 S4 S2)
 decl f12 :: S4
 #41 := f12
 decl f5 :: (-> S6 S3 S5)
 decl f9 :: S3
-#32 := f9
+#31 := f9
 decl f6 :: (-> S7 S2 S6)
-decl f11 :: S4
-#37 := f11
 decl f10 :: S2
 #34 := f10
 decl f7 :: S7
-#8 := f7
+#7 := f7
 #35 := (f6 f7 f10)
 #36 := (f5 #35 f8)
 #38 := (f4 #36 f11)
@@ -57604,9908 +54517,2043 @@
 #40 := (f5 #39 f9)
 #42 := (f4 #40 f12)
 #43 := (f3 #42 f8)
-#88 := (= f12 #43)
-#187 := (f3 #42 f9)
-#241 := (= #187 #43)
-#239 := (= #43 #187)
-#33 := (= f8 f9)
-#95 := (not #33)
-#96 := (or #95 #88)
-#101 := (not #96)
-#44 := (= #43 f12)
+#44 := (= #43 f11)
+#162 := (f3 #38 f8)
+#248 := (= #162 f11)
+#12 := (:var 0 S4)
+#10 := (:var 1 S3)
+#8 := (:var 2 S2)
+#9 := (f6 f7 #8)
+#11 := (f5 #9 #10)
+#13 := (f4 #11 #12)
+#578 := (pattern #13)
+#14 := (f3 #13 #10)
+#15 := (= #14 #12)
+#579 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #578) #15)
+#16 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #15)
+#582 := (iff #16 #579)
+#580 := (iff #15 #15)
+#581 := [refl]: #580
+#583 := [quant-intro #581]: #582
+#93 := (~ #16 #16)
+#91 := (~ #15 #15)
+#92 := [refl]: #91
+#94 := [nnf-pos #92]: #93
+#67 := [asserted]: #16
+#81 := [mp~ #67 #94]: #16
+#584 := [mp #81 #583]: #579
+#164 := (not #579)
+#250 := (or #164 #248)
+#241 := [quant-inst #34 #30 #37]: #250
+#234 := [unit-resolution #241 #584]: #248
+#253 := (= #43 #162)
+#252 := (= #43 f12)
+#32 := (= f8 f9)
+#255 := (if #32 #252 #253)
+#23 := (:var 0 S3)
+#21 := (:var 1 S4)
+#19 := (:var 2 S3)
+#17 := (:var 3 S2)
+#18 := (f6 f7 #17)
+#20 := (f5 #18 #19)
+#22 := (f4 #20 #21)
+#24 := (f3 #22 #23)
+#585 := (pattern #24)
+#26 := (f3 #17 #23)
+#98 := (= #24 #26)
+#97 := (= #24 #21)
+#25 := (= #23 #19)
+#85 := (if #25 #97 #98)
+#586 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #585) #85)
+#90 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #85)
+#589 := (iff #90 #586)
+#587 := (iff #85 #85)
+#588 := [refl]: #587
+#590 := [quant-intro #588]: #589
+#27 := (if #25 #21 #26)
+#28 := (= #24 #27)
+#29 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #28)
+#87 := (iff #29 #90)
+#86 := (iff #28 #85)
+#89 := [rewrite]: #86
+#88 := [quant-intro #89]: #87
+#83 := (~ #29 #29)
+#82 := (~ #28 #28)
+#95 := [refl]: #82
+#84 := [nnf-pos #95]: #83
+#68 := [asserted]: #29
+#96 := [mp~ #68 #84]: #29
+#99 := [mp #96 #88]: #90
+#591 := [mp #99 #590]: #586
+#572 := (not #586)
+#228 := (or #572 #255)
+#359 := [quant-inst #38 #31 #41 #30]: #228
+#570 := [unit-resolution #359 #591]: #255
+#566 := (not #255)
+#231 := (or #566 #253)
+#33 := (not #32)
+#70 := (or #32 #44)
+#73 := (not #70)
 #45 := (implies #33 #44)
 #46 := (not #45)
-#102 := (iff #46 #101)
-#99 := (iff #45 #96)
-#92 := (implies #33 #88)
-#97 := (iff #92 #96)
-#98 := [rewrite]: #97
-#93 := (iff #45 #92)
-#90 := (iff #44 #88)
-#91 := [rewrite]: #90
-#94 := [monotonicity #91]: #93
-#100 := [trans #94 #98]: #99
-#103 := [monotonicity #100]: #102
-#87 := [asserted]: #46
-#106 := [mp #87 #103]: #101
-#104 := [not-or-elim #106]: #33
-#240 := [monotonicity #104]: #239
-#242 := [symm #240]: #241
-#274 := (= f12 #187)
-#13 := (:var 0 S4)
-#11 := (:var 1 S3)
-#9 := (:var 2 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#14 := (f4 #12 #13)
-#603 := (pattern #14)
-#15 := (f3 #14 #11)
-#67 := (= #13 #15)
-#604 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #603) #67)
-#70 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #67)
-#607 := (iff #70 #604)
-#605 := (iff #67 #67)
-#606 := [refl]: #605
-#608 := [quant-intro #606]: #607
-#121 := (~ #70 #70)
-#119 := (~ #67 #67)
-#120 := [refl]: #119
-#122 := [nnf-pos #120]: #121
-#16 := (= #15 #13)
-#17 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #16)
-#71 := (iff #17 #70)
-#68 := (iff #16 #67)
-#69 := [rewrite]: #68
-#72 := [quant-intro #69]: #71
-#66 := [asserted]: #17
-#75 := [mp #66 #72]: #70
-#109 := [mp~ #75 #122]: #70
-#609 := [mp #109 #608]: #604
-#265 := (not #604)
-#275 := (or #265 #274)
-#279 := [quant-inst #38 #32 #41]: #275
-#578 := [unit-resolution #279 #609]: #274
-#580 := [trans #578 #242]: #88
-#105 := (not #88)
-#107 := [not-or-elim #106]: #105
-[unit-resolution #107 #580]: false
-unsat
-fb3d1591ff5af89c5578c6ff5cca5ed3529f7307 198 0
+#74 := (iff #46 #73)
+#71 := (iff #45 #70)
+#72 := [rewrite]: #71
+#75 := [monotonicity #72]: #74
+#69 := [asserted]: #46
+#78 := [mp #69 #75]: #73
+#76 := [not-or-elim #78]: #33
+#573 := (or #566 #32 #253)
+#574 := [def-axiom]: #573
+#568 := [unit-resolution #574 #76]: #231
+#227 := [unit-resolution #568 #570]: #253
+#569 := [trans #227 #234]: #44
+#77 := (not #44)
+#79 := [not-or-elim #78]: #77
+[unit-resolution #79 #569]: false
+unsat
+05bfab9a0b912a45a5d23c900aa9736bbf67a50a 66 0
+#2 := false
+decl f12 :: S4
+#41 := f12
+decl f3 :: (-> S2 S3 S4)
+decl f9 :: S3
+#31 := f9
+decl f4 :: (-> S5 S4 S2)
+decl f5 :: (-> S6 S3 S5)
+decl f6 :: (-> S7 S2 S6)
+decl f11 :: S4
+#37 := f11
+decl f8 :: S3
+#30 := f8
+decl f10 :: S2
+#34 := f10
+decl f7 :: S7
+#7 := f7
+#35 := (f6 f7 f10)
+#36 := (f5 #35 f8)
+#38 := (f4 #36 f11)
+#39 := (f6 f7 #38)
+#40 := (f5 #39 f9)
+#42 := (f4 #40 f12)
+#43 := (f3 #42 f9)
+#44 := (= #43 f12)
+#77 := (not #44)
+#32 := (= f8 f9)
+#70 := (or #32 #44)
+#73 := (not #70)
+#33 := (not #32)
+#45 := (implies #33 #44)
+#46 := (not #45)
+#74 := (iff #46 #73)
+#71 := (iff #45 #70)
+#72 := [rewrite]: #71
+#75 := [monotonicity #72]: #74
+#69 := [asserted]: #46
+#78 := [mp #69 #75]: #73
+#79 := [not-or-elim #78]: #77
+#12 := (:var 0 S4)
+#10 := (:var 1 S3)
+#8 := (:var 2 S2)
+#9 := (f6 f7 #8)
+#11 := (f5 #9 #10)
+#13 := (f4 #11 #12)
+#578 := (pattern #13)
+#14 := (f3 #13 #10)
+#15 := (= #14 #12)
+#579 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #578) #15)
+#16 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #15)
+#582 := (iff #16 #579)
+#580 := (iff #15 #15)
+#581 := [refl]: #580
+#583 := [quant-intro #581]: #582
+#93 := (~ #16 #16)
+#91 := (~ #15 #15)
+#92 := [refl]: #91
+#94 := [nnf-pos #92]: #93
+#67 := [asserted]: #16
+#81 := [mp~ #67 #94]: #16
+#584 := [mp #81 #583]: #579
+#164 := (not #579)
+#252 := (or #164 #44)
+#253 := [quant-inst #38 #31 #41]: #252
+[unit-resolution #253 #584 #79]: false
+unsat
+4a487b439b5a71496138881872532bead0355621 73 0
+#2 := false
+decl f12 :: S4
+#40 := f12
+decl f3 :: (-> S2 S3 S4)
+decl f8 :: S3
+#30 := f8
+decl f4 :: (-> S5 S4 S2)
+decl f5 :: (-> S6 S3 S5)
+decl f9 :: S3
+#31 := f9
+decl f6 :: (-> S7 S2 S6)
+decl f11 :: S4
+#36 := f11
+decl f10 :: S2
+#33 := f10
+decl f7 :: S7
+#7 := f7
+#34 := (f6 f7 f10)
+#35 := (f5 #34 f8)
+#37 := (f4 #35 f11)
+#38 := (f6 f7 #37)
+#39 := (f5 #38 f9)
+#41 := (f4 #39 f12)
+#42 := (f3 #41 f8)
+#43 := (= #42 f12)
+#164 := (f3 #41 f9)
+#250 := (= #164 f12)
+#12 := (:var 0 S4)
+#10 := (:var 1 S3)
+#8 := (:var 2 S2)
+#9 := (f6 f7 #8)
+#11 := (f5 #9 #10)
+#13 := (f4 #11 #12)
+#578 := (pattern #13)
+#14 := (f3 #13 #10)
+#15 := (= #14 #12)
+#579 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #578) #15)
+#16 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #15)
+#582 := (iff #16 #579)
+#580 := (iff #15 #15)
+#581 := [refl]: #580
+#583 := [quant-intro #581]: #582
+#93 := (~ #16 #16)
+#91 := (~ #15 #15)
+#92 := [refl]: #91
+#94 := [nnf-pos #92]: #93
+#66 := [asserted]: #16
+#81 := [mp~ #66 #94]: #16
+#584 := [mp #81 #583]: #579
+#241 := (not #579)
+#255 := (or #241 #250)
+#234 := [quant-inst #37 #31 #40]: #255
+#215 := [unit-resolution #234 #584]: #250
+#216 := (= #42 #164)
+#32 := (= f8 f9)
+#69 := (not #32)
+#70 := (or #69 #43)
+#73 := (not #70)
+#44 := (implies #32 #43)
+#45 := (not #44)
+#74 := (iff #45 #73)
+#71 := (iff #44 #70)
+#72 := [rewrite]: #71
+#75 := [monotonicity #72]: #74
+#68 := [asserted]: #45
+#78 := [mp #68 #75]: #73
+#76 := [not-or-elim #78]: #32
+#217 := [monotonicity #76]: #216
+#218 := [trans #217 #215]: #43
+#77 := (not #43)
+#79 := [not-or-elim #78]: #77
+[unit-resolution #79 #218]: false
+unsat
+2f89ec4bff68da07bcf5df08cb44abd1cf304bcc 152 0
 #2 := false
 decl f3 :: (-> S2 S3 S4)
 decl f10 :: S3
-#33 := f10
+#34 := f10
 decl f11 :: S2
-#35 := f11
-#45 := (f3 f11 f10)
+#41 := f11
+#51 := (f3 f11 f10)
 decl f4 :: (-> S5 S4 S2)
-decl f13 :: S4
-#42 := f13
+decl f12 :: S4
+#44 := f12
 decl f5 :: (-> S6 S3 S5)
-decl f9 :: S3
-#32 := f9
+decl f8 :: S3
+#30 := f8
 decl f6 :: (-> S7 S2 S6)
-decl f12 :: S4
-#38 := f12
-decl f8 :: S3
-#31 := f8
 decl f7 :: S7
-#8 := f7
-#36 := (f6 f7 f11)
-#37 := (f5 #36 f8)
-#39 := (f4 #37 f12)
-#40 := (f6 f7 #39)
-#41 := (f5 #40 f9)
-#43 := (f4 #41 f13)
-#44 := (f3 #43 f10)
-#46 := (= #44 #45)
-#258 := (f3 #39 f8)
-#572 := (f4 #37 #258)
-#548 := (f3 #572 f10)
-#377 := (= #548 #45)
-#533 := (= #45 #548)
-#379 := (= #258 #548)
-#180 := (= f8 f10)
-#537 := (ite #180 #379 #533)
-#24 := (:var 0 S3)
-#22 := (:var 1 S4)
-#20 := (:var 2 S3)
-#18 := (:var 3 S2)
-#19 := (f6 f7 #18)
-#21 := (f5 #19 #20)
-#23 := (f4 #21 #22)
-#25 := (f3 #23 #24)
-#604 := (pattern #25)
-#27 := (f3 #18 #24)
-#120 := (= #25 #27)
-#119 := (= #22 #25)
-#76 := (= #20 #24)
-#107 := (ite #76 #119 #120)
-#605 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #604) #107)
-#112 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #107)
-#608 := (iff #112 #605)
-#606 := (iff #107 #107)
-#607 := [refl]: #606
-#609 := [quant-intro #607]: #608
-#80 := (ite #76 #22 #27)
-#83 := (= #25 #80)
-#86 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #83)
-#109 := (iff #86 #112)
-#108 := (iff #83 #107)
-#111 := [rewrite]: #108
-#110 := [quant-intro #111]: #109
-#105 := (~ #86 #86)
-#104 := (~ #83 #83)
-#117 := [refl]: #104
-#106 := [nnf-pos #117]: #105
-#26 := (= #24 #20)
-#28 := (ite #26 #22 #27)
-#29 := (= #25 #28)
-#30 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #29)
-#87 := (iff #30 #86)
-#84 := (iff #29 #83)
-#81 := (= #28 #80)
-#78 := (iff #26 #76)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#85 := [monotonicity #82]: #84
-#88 := [quant-intro #85]: #87
-#75 := [asserted]: #30
-#91 := [mp #75 #88]: #86
-#118 := [mp~ #91 #106]: #86
-#121 := [mp #118 #110]: #112
-#610 := [mp #121 #609]: #605
-#233 := (not #605)
-#420 := (or #233 #537)
-#380 := (ite #180 #379 #377)
-#421 := (or #233 #380)
-#381 := (iff #421 #420)
-#431 := (iff #420 #420)
-#526 := [rewrite]: #431
-#535 := (iff #380 #537)
-#534 := (iff #377 #533)
-#536 := [rewrite]: #534
-#538 := [monotonicity #536]: #535
-#529 := [monotonicity #538]: #381
-#527 := [trans #529 #526]: #381
-#422 := [quant-inst #35 #31 #258 #33]: #421
-#530 := [mp #422 #527]: #420
-#510 := [unit-resolution #530 #610]: #537
-#415 := (not #537)
-#523 := (or #415 #533)
-#267 := (not #180)
-#181 := (= f9 f10)
-#268 := (not #181)
-#179 := (= f8 f9)
-#266 := (not #179)
-#259 := (and #266 #267 #268)
-#34 := (distinct f8 f9 f10)
-#90 := (not #34)
-#92 := (or #90 #46)
-#95 := (not #92)
-#47 := (implies #34 #46)
-#48 := (not #47)
-#96 := (iff #48 #95)
-#93 := (iff #47 #92)
-#94 := [rewrite]: #93
-#97 := [monotonicity #94]: #96
-#89 := [asserted]: #48
-#100 := [mp #89 #97]: #95
-#98 := [not-or-elim #100]: #34
-#246 := (or #90 #259)
-#378 := [def-axiom]: #246
-#512 := [unit-resolution #378 #98]: #259
-#270 := (not #259)
-#272 := (or #270 #267)
-#269 := [def-axiom]: #272
-#522 := [unit-resolution #269 #512]: #267
-#433 := (or #415 #180 #533)
-#426 := [def-axiom]: #433
-#524 := [unit-resolution #426 #522]: #523
-#520 := [unit-resolution #524 #510]: #533
-#505 := [symm #520]: #377
-#506 := (= #44 #548)
-#586 := (f3 #39 f10)
-#502 := (= #586 #548)
-#511 := (= #548 #586)
-#521 := (= #572 #39)
-#532 := (= #258 f12)
-#592 := (= f12 #258)
-#13 := (:var 0 S4)
-#11 := (:var 1 S3)
-#9 := (:var 2 S2)
-#10 := (f6 f7 #9)
-#12 := (f5 #10 #11)
-#14 := (f4 #12 #13)
-#597 := (pattern #14)
-#15 := (f3 #14 #11)
-#69 := (= #13 #15)
-#598 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #597) #69)
-#72 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #69)
-#601 := (iff #72 #598)
-#599 := (iff #69 #69)
-#600 := [refl]: #599
-#602 := [quant-intro #600]: #601
-#115 := (~ #72 #72)
-#113 := (~ #69 #69)
-#114 := [refl]: #113
-#116 := [nnf-pos #114]: #115
-#16 := (= #15 #13)
-#17 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #16)
-#73 := (iff #17 #72)
-#70 := (iff #16 #69)
+#7 := f7
+#42 := (f6 f7 f11)
+#43 := (f5 #42 f8)
+#45 := (f4 #43 f12)
+#281 := (f3 #45 f10)
+#282 := (= #281 #51)
+#568 := (= #281 f12)
+#567 := (= f10 f8)
+#565 := (if #567 #568 #282)
+#23 := (:var 0 S3)
+#21 := (:var 1 S4)
+#19 := (:var 2 S3)
+#17 := (:var 3 S2)
+#18 := (f6 f7 #17)
+#20 := (f5 #18 #19)
+#22 := (f4 #20 #21)
+#24 := (f3 #22 #23)
+#611 := (pattern #24)
+#26 := (f3 #17 #23)
+#128 := (= #24 #26)
+#127 := (= #24 #21)
+#25 := (= #23 #19)
+#111 := (if #25 #127 #128)
+#612 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #611) #111)
+#120 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #111)
+#615 := (iff #120 #612)
+#613 := (iff #111 #111)
+#614 := [refl]: #613
+#616 := [quant-intro #614]: #615
+#27 := (if #25 #21 #26)
+#28 := (= #24 #27)
+#29 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #28)
+#117 := (iff #29 #120)
+#112 := (iff #28 #111)
+#119 := [rewrite]: #112
+#118 := [quant-intro #119]: #117
+#109 := (~ #29 #29)
+#108 := (~ #28 #28)
+#125 := [refl]: #108
+#110 := [nnf-pos #125]: #109
+#76 := [asserted]: #29
+#126 := [mp~ #76 #110]: #29
+#115 := [mp #126 #118]: #120
+#617 := [mp #115 #616]: #612
+#385 := (not #612)
+#570 := (or #385 #565)
+#559 := [quant-inst #41 #30 #44 #34]: #570
+#569 := [unit-resolution #559 #617]: #565
+#561 := (not #567)
+#35 := (= f8 f10)
+#36 := (not #35)
+#546 := (iff #36 #561)
+#551 := (iff #35 #567)
+#566 := (iff #567 #35)
+#550 := [commutativity]: #566
+#552 := [symm #550]: #551
+#547 := [monotonicity #552]: #546
+decl f9 :: S3
+#31 := f9
+#37 := (= f9 f10)
+#38 := (not #37)
+#32 := (= f8 f9)
+#33 := (not #32)
+#85 := (and #33 #36 #38)
+decl f13 :: S4
+#48 := f13
+#46 := (f6 f7 #45)
+#47 := (f5 #46 f9)
+#49 := (f4 #47 f13)
+#50 := (f3 #49 f10)
+#52 := (= #50 #51)
+#88 := (not #85)
+#91 := (or #88 #52)
+#94 := (not #91)
+#39 := (and #36 #38)
+#40 := (and #33 #39)
+#53 := (implies #40 #52)
+#54 := (not #53)
+#97 := (iff #54 #94)
+#78 := (not #40)
+#79 := (or #78 #52)
+#82 := (not #79)
+#95 := (iff #82 #94)
+#92 := (iff #79 #91)
+#89 := (iff #78 #88)
+#86 := (iff #40 #85)
+#87 := [rewrite]: #86
+#90 := [monotonicity #87]: #89
+#93 := [monotonicity #90]: #92
+#96 := [monotonicity #93]: #95
+#83 := (iff #54 #82)
+#80 := (iff #53 #79)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#98 := [trans #84 #96]: #97
+#77 := [asserted]: #54
+#99 := [mp #77 #98]: #94
+#100 := [not-or-elim #99]: #85
+#102 := [and-elim #100]: #36
+#553 := [mp #102 #547]: #561
+#406 := (not #282)
+#104 := (not #52)
+#388 := (iff #104 #406)
+#428 := (iff #52 #282)
+#545 := (iff #282 #52)
+#544 := (= #281 #50)
+#260 := (= #50 #281)
+#279 := (= #50 f13)
+#278 := (= f10 f9)
+#596 := (if #278 #279 #260)
+#592 := (or #385 #596)
+#265 := [quant-inst #45 #31 #48 #34]: #592
+#554 := [unit-resolution #265 #617]: #596
+#599 := (not #278)
+#387 := (iff #38 #599)
+#384 := (iff #37 #278)
+#548 := (iff #278 #37)
+#555 := [commutativity]: #548
+#386 := [symm #555]: #384
+#540 := [monotonicity #386]: #387
+#103 := [and-elim #100]: #38
+#541 := [mp #103 #540]: #599
+#266 := (not #596)
+#602 := (or #266 #278 #260)
+#597 := [def-axiom]: #602
+#543 := [unit-resolution #597 #541 #554]: #260
+#542 := [symm #543]: #544
+#427 := [monotonicity #542]: #545
+#429 := [symm #427]: #428
+#536 := [monotonicity #429]: #388
+#105 := [not-or-elim #99]: #104
+#438 := [mp #105 #536]: #406
+#560 := (not #565)
+#562 := (or #560 #567 #282)
+#563 := [def-axiom]: #562
+[unit-resolution #563 #438 #553 #569]: false
+unsat
+88a85966e07fd047108db907b5b652de257cb18b 39 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S3 S1)
+decl f4 :: S3
+#8 := f4
+decl f10 :: S2
+#40 := f10
+#41 := (f3 f10 f4)
+#42 := (= #41 f1)
+#43 := (not #42)
+#44 := (not #43)
+#70 := (iff #44 #42)
 #71 := [rewrite]: #70
-#74 := [quant-intro #71]: #73
-#68 := [asserted]: #17
-#77 := [mp #68 #74]: #72
-#103 := [mp~ #77 #116]: #72
-#603 := [mp #103 #602]: #598
-#595 := (not #598)
-#590 := (or #595 #592)
-#596 := [quant-inst #35 #31 #38]: #590
-#528 := [unit-resolution #596 #603]: #592
-#519 := [symm #528]: #532
-#513 := [monotonicity #519]: #521
-#518 := [monotonicity #513]: #511
-#503 := [symm #518]: #502
-#244 := (= #44 #586)
-#245 := (= f13 #44)
-#588 := (ite #181 #245 #244)
-#234 := (or #233 #588)
-#235 := [quant-inst #39 #32 #42 #33]: #234
-#525 := [unit-resolution #235 #610]: #588
-#236 := (not #588)
-#515 := (or #236 #244)
-#273 := (or #270 #268)
-#252 := [def-axiom]: #273
-#514 := [unit-resolution #252 #512]: #268
-#576 := (or #236 #181 #244)
-#577 := [def-axiom]: #576
-#516 := [unit-resolution #577 #514]: #515
-#517 := [unit-resolution #516 #525]: #244
-#507 := [trans #517 #503]: #506
-#508 := [trans #507 #505]: #46
-#99 := (not #46)
-#101 := [not-or-elim #100]: #99
-[unit-resolution #101 #508]: false
-unsat
-04f776d0bcdad9344e012498233d6d29f32415f7 31 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f9 :: (-> S5 S1)
-decl f10 :: S5
-#36 := f10
-#37 := (f9 f10)
-#38 := (= #37 f1)
-#39 := (iff #38 #38)
-#40 := (not #39)
-#129 := (iff #40 false)
-#1 := true
-#124 := (not true)
-#127 := (iff #124 false)
-#128 := [rewrite]: #127
-#125 := (iff #40 #124)
-#122 := (iff #39 true)
-#113 := (= f1 #37)
-#117 := (iff #113 #113)
-#120 := (iff #117 true)
-#121 := [rewrite]: #120
-#118 := (iff #39 #117)
-#115 := (iff #38 #113)
-#116 := [rewrite]: #115
-#119 := [monotonicity #116 #116]: #118
-#123 := [trans #119 #121]: #122
-#126 := [monotonicity #123]: #125
-#130 := [trans #126 #128]: #129
-#112 := [asserted]: #40
-[mp #112 #130]: false
-unsat
-618857fa3166a2d5419a42f28019f480aa778950 58 0
-#2 := false
-decl f3 :: (-> S2 S1)
-decl f9 :: S2
-#37 := f9
-#38 := (f3 f9)
-decl f1 :: S1
-#4 := f1
-#114 := (= f1 #38)
-#39 := (= #38 f1)
-#40 := (not #39)
-#41 := (not #40)
-#126 := (iff #41 #114)
-#118 := (not #114)
-#121 := (not #118)
-#124 := (iff #121 #114)
-#125 := [rewrite]: #124
-#122 := (iff #41 #121)
-#119 := (iff #40 #118)
-#116 := (iff #39 #114)
-#117 := [rewrite]: #116
-#120 := [monotonicity #117]: #119
-#123 := [monotonicity #120]: #122
-#127 := [trans #123 #125]: #126
-#113 := [asserted]: #41
-#130 := [mp #113 #127]: #114
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#638 := (pattern #9)
-#62 := (= f1 #9)
-#65 := (not #62)
-#639 := (forall (vars (?v0 S2)) (:pat #638) #65)
-#68 := (forall (vars (?v0 S2)) #65)
-#642 := (iff #68 #639)
-#640 := (iff #65 #65)
-#641 := [refl]: #640
-#643 := [quant-intro #641]: #642
-#144 := (~ #68 #68)
-#142 := (~ #65 #65)
-#143 := [refl]: #142
-#145 := [nnf-pos #143]: #144
+#69 := [asserted]: #44
+#74 := [mp #69 #71]: #42
+#7 := (:var 0 S2)
+#9 := (f3 #7 f4)
+#585 := (pattern #9)
 #10 := (= #9 f1)
 #11 := (not #10)
+#586 := (forall (vars (?v0 S2)) (:pat #585) #11)
 #12 := (forall (vars (?v0 S2)) #11)
-#69 := (iff #12 #68)
-#66 := (iff #11 #65)
-#63 := (iff #10 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#70 := [quant-intro #67]: #69
-#61 := [asserted]: #12
-#73 := [mp #61 #70]: #68
-#129 := [mp~ #73 #145]: #68
-#644 := [mp #129 #643]: #639
-#221 := (not #639)
-#308 := (or #221 #118)
-#222 := [quant-inst #37]: #308
-[unit-resolution #222 #644 #130]: false
-unsat
-421fc4c47d5088f4fa169777ed876d4b4bc85b8f 46 0
-#2 := false
-decl f4 :: (-> S3 S1)
-decl f9 :: S3
-#37 := f9
-#38 := (f4 f9)
-decl f1 :: S1
-#4 := f1
-#113 := (= f1 #38)
-#117 := (not #113)
-#39 := (= #38 f1)
-#40 := (not #39)
-#118 := (iff #40 #117)
-#115 := (iff #39 #113)
-#116 := [rewrite]: #115
-#119 := [monotonicity #116]: #118
-#112 := [asserted]: #40
-#122 := [mp #112 #119]: #117
-#13 := (:var 0 S3)
-#14 := (f4 #13)
-#637 := (pattern #14)
-#71 := (= f1 #14)
-#638 := (forall (vars (?v0 S3)) (:pat #637) #71)
-#75 := (forall (vars (?v0 S3)) #71)
-#641 := (iff #75 #638)
-#639 := (iff #71 #71)
-#640 := [refl]: #639
-#642 := [quant-intro #640]: #641
-#124 := (~ #75 #75)
-#123 := (~ #71 #71)
-#138 := [refl]: #123
-#125 := [nnf-pos #138]: #124
-#15 := (= #14 f1)
-#16 := (forall (vars (?v0 S3)) #15)
-#76 := (iff #16 #75)
-#73 := (iff #15 #71)
-#74 := [rewrite]: #73
-#77 := [quant-intro #74]: #76
-#70 := [asserted]: #16
-#80 := [mp #70 #77]: #75
-#139 := [mp~ #80 #125]: #75
-#643 := [mp #139 #642]: #638
-#213 := (not #638)
-#300 := (or #213 #113)
-#214 := [quant-inst #37]: #300
-[unit-resolution #214 #643 #122]: false
-unsat
-9e3a7aa4371f1826345d223063f64e874bc52086 124 0
-#2 := false
-decl f5 :: (-> S3 S4 S1)
-decl f13 :: S4
-#47 := f13
-decl f6 :: (-> S5 S3 S3)
-decl f12 :: S3
-#45 := f12
-decl f7 :: (-> S3 S5)
-decl f11 :: S3
-#43 := f11
-#44 := (f7 f11)
-#46 := (f6 #44 f12)
-#48 := (f5 #46 f13)
-decl f1 :: S1
-#4 := f1
-#135 := (= f1 #48)
-#154 := (not #135)
-#658 := [hypothesis]: #154
-#52 := (f5 f12 f13)
-#142 := (= f1 #52)
-#50 := (f5 f11 f13)
-#139 := (= f1 #50)
-#145 := (or #139 #142)
-#346 := (or #145 #135)
-#155 := (iff #145 #154)
-#53 := (= #52 f1)
-#51 := (= #50 f1)
-#54 := (or #51 #53)
-#49 := (= #48 f1)
-#55 := (iff #49 #54)
-#56 := (not #55)
-#158 := (iff #56 #155)
-#148 := (iff #135 #145)
-#151 := (not #148)
-#156 := (iff #151 #155)
-#157 := [rewrite]: #156
-#152 := (iff #56 #151)
-#149 := (iff #55 #148)
-#146 := (iff #54 #145)
-#143 := (iff #53 #142)
-#144 := [rewrite]: #143
-#140 := (iff #51 #139)
-#141 := [rewrite]: #140
-#147 := [monotonicity #141 #144]: #146
-#137 := (iff #49 #135)
-#138 := [rewrite]: #137
-#150 := [monotonicity #138 #147]: #149
-#153 := [monotonicity #150]: #152
-#159 := [trans #153 #157]: #158
-#134 := [asserted]: #56
-#162 := [mp #134 #159]: #155
-#272 := (not #155)
-#345 := (or #145 #135 #272)
-#342 := [def-axiom]: #345
-#325 := [unit-resolution #342 #162]: #346
-#330 := [unit-resolution #325 #658]: #145
-#332 := (not #145)
-#661 := (or #135 #332)
-#20 := (:var 0 S4)
-#18 := (:var 1 S3)
-#16 := (:var 2 S3)
-#17 := (f7 #16)
-#19 := (f6 #17 #18)
-#21 := (f5 #19 #20)
-#684 := (pattern #21)
-#25 := (f5 #18 #20)
-#102 := (= f1 #25)
-#23 := (f5 #16 #20)
-#99 := (= f1 #23)
-#105 := (or #99 #102)
-#95 := (= f1 #21)
-#108 := (iff #95 #105)
-#685 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) (:pat #684) #108)
-#111 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #108)
-#688 := (iff #111 #685)
-#686 := (iff #108 #108)
-#687 := [refl]: #686
-#689 := [quant-intro #687]: #688
-#166 := (~ #111 #111)
-#180 := (~ #108 #108)
-#181 := [refl]: #180
-#167 := [nnf-pos #181]: #166
-#26 := (= #25 f1)
-#24 := (= #23 f1)
-#27 := (or #24 #26)
-#22 := (= #21 f1)
-#28 := (iff #22 #27)
-#29 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #28)
-#112 := (iff #29 #111)
-#109 := (iff #28 #108)
-#106 := (iff #27 #105)
-#103 := (iff #26 #102)
-#104 := [rewrite]: #103
-#100 := (iff #24 #99)
-#101 := [rewrite]: #100
-#107 := [monotonicity #101 #104]: #106
-#97 := (iff #22 #95)
-#98 := [rewrite]: #97
-#110 := [monotonicity #98 #107]: #109
-#113 := [quant-intro #110]: #112
-#94 := [asserted]: #29
-#116 := [mp #94 #113]: #111
-#182 := [mp~ #116 #167]: #111
-#690 := [mp #182 #689]: #685
-#331 := (not #685)
-#665 := (or #331 #148)
-#666 := [quant-inst #43 #45 #47]: #665
-#318 := [unit-resolution #666 #690]: #148
-#667 := (or #151 #135 #332)
-#668 := [def-axiom]: #667
-#302 := [unit-resolution #668 #318]: #661
-#645 := [unit-resolution #302 #330 #658]: false
-#306 := [lemma #645]: #135
-#319 := (or #332 #154)
-#662 := (or #332 #154 #272)
-#664 := [def-axiom]: #662
-#451 := [unit-resolution #664 #162]: #319
-#307 := [unit-resolution #451 #306]: #332
-#308 := (or #154 #145)
-#663 := (or #151 #154 #145)
-#669 := [def-axiom]: #663
-#309 := [unit-resolution #669 #318]: #308
-[unit-resolution #309 #307 #306]: false
-unsat
-f06e509678a15cfe1fb09ac8d8cd1679c65b806e 159 0
-#2 := false
-decl f3 :: (-> S3 S2 S1)
-decl f12 :: S2
-#47 := f12
-decl f4 :: S3
-#8 := f4
-#336 := (f3 f4 f12)
-decl f1 :: S1
-#4 := f1
-#333 := (= f1 #336)
-decl f11 :: S3
-#44 := f11
-#50 := (f3 f11 f12)
-#136 := (= f1 #50)
-#337 := (or #136 #333)
-decl f6 :: (-> S5 S3 S3)
-decl f7 :: (-> S3 S5)
-#45 := (f7 f11)
-#46 := (f6 #45 f4)
-#48 := (f3 #46 f12)
-#132 := (= f1 #48)
-#145 := (not #132)
-#653 := [hypothesis]: #145
-#331 := (or #136 #132)
-#146 := (iff #136 #145)
-#51 := (= #50 f1)
-#49 := (= #48 f1)
-#52 := (iff #49 #51)
-#53 := (not #52)
-#149 := (iff #53 #146)
-#139 := (iff #132 #136)
-#142 := (not #139)
-#147 := (iff #142 #146)
-#148 := [rewrite]: #147
-#143 := (iff #53 #142)
-#140 := (iff #52 #139)
-#137 := (iff #51 #136)
-#138 := [rewrite]: #137
-#134 := (iff #49 #132)
-#135 := [rewrite]: #134
-#141 := [monotonicity #135 #138]: #140
-#144 := [monotonicity #141]: #143
-#150 := [trans #144 #148]: #149
-#131 := [asserted]: #53
-#153 := [mp #131 #150]: #146
-#243 := (not #146)
-#330 := (or #136 #132 #243)
-#244 := [def-axiom]: #330
-#245 := [unit-resolution #244 #153]: #331
-#655 := [unit-resolution #245 #653]: #136
-#659 := (not #337)
-#299 := (or #132 #659)
-#316 := (iff #132 #337)
-#9 := (:var 0 S2)
-#20 := (:var 1 S3)
-#18 := (:var 2 S3)
-#19 := (f7 #18)
-#21 := (f6 #19 #20)
-#22 := (f3 #21 #9)
-#675 := (pattern #22)
-#26 := (f3 #20 #9)
-#99 := (= f1 #26)
-#24 := (f3 #18 #9)
-#96 := (= f1 #24)
-#102 := (or #96 #99)
-#92 := (= f1 #22)
-#105 := (iff #92 #102)
-#676 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S2)) (:pat #675) #105)
-#108 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S2)) #105)
-#679 := (iff #108 #676)
-#677 := (iff #105 #105)
-#678 := [refl]: #677
-#680 := [quant-intro #678]: #679
-#157 := (~ #108 #108)
-#171 := (~ #105 #105)
-#172 := [refl]: #171
-#158 := [nnf-pos #172]: #157
-#27 := (= #26 f1)
-#25 := (= #24 f1)
-#28 := (or #25 #27)
-#23 := (= #22 f1)
-#29 := (iff #23 #28)
-#30 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S2)) #29)
-#109 := (iff #30 #108)
-#106 := (iff #29 #105)
-#103 := (iff #28 #102)
-#100 := (iff #27 #99)
-#101 := [rewrite]: #100
-#97 := (iff #25 #96)
-#98 := [rewrite]: #97
-#104 := [monotonicity #98 #101]: #103
-#94 := (iff #23 #92)
-#95 := [rewrite]: #94
-#107 := [monotonicity #95 #104]: #106
-#110 := [quant-intro #107]: #109
-#91 := [asserted]: #30
-#113 := [mp #91 #110]: #108
-#173 := [mp~ #113 #158]: #108
-#681 := [mp #173 #680]: #676
-#310 := (not #676)
-#442 := (or #310 #316)
-#649 := [quant-inst #44 #8 #47]: #442
-#298 := [unit-resolution #649 #681]: #316
-#650 := (not #316)
-#308 := (or #650 #132 #659)
-#313 := [def-axiom]: #308
-#300 := [unit-resolution #313 #298]: #299
-#638 := [unit-resolution #300 #653]: #659
-#332 := (not #136)
-#321 := (or #337 #332)
-#322 := [def-axiom]: #321
-#639 := [unit-resolution #322 #638 #655]: false
-#640 := [lemma #639]: #132
-#641 := (or #145 #337)
-#651 := (or #650 #145 #337)
-#309 := [def-axiom]: #651
-#642 := [unit-resolution #309 #298]: #641
-#644 := [unit-resolution #642 #640]: #337
-#335 := (or #332 #145)
-#323 := (or #332 #145 #243)
-#334 := [def-axiom]: #323
-#263 := [unit-resolution #334 #153]: #335
-#646 := [unit-resolution #263 #640]: #332
-#654 := (or #659 #136 #333)
-#660 := [def-axiom]: #654
-#284 := [unit-resolution #660 #646 #644]: #333
-#10 := (f3 f4 #9)
-#661 := (pattern #10)
-#74 := (= f1 #10)
-#77 := (not #74)
-#662 := (forall (vars (?v0 S2)) (:pat #661) #77)
-#80 := (forall (vars (?v0 S2)) #77)
-#665 := (iff #80 #662)
-#663 := (iff #77 #77)
-#664 := [refl]: #663
-#666 := [quant-intro #664]: #665
-#167 := (~ #80 #80)
-#165 := (~ #77 #77)
-#166 := [refl]: #165
-#168 := [nnf-pos #166]: #167
-#11 := (= #10 f1)
-#12 := (not #11)
-#13 := (forall (vars (?v0 S2)) #12)
-#81 := (iff #13 #80)
-#78 := (iff #12 #77)
-#75 := (iff #11 #74)
-#76 := [rewrite]: #75
-#79 := [monotonicity #76]: #78
-#82 := [quant-intro #79]: #81
-#73 := [asserted]: #13
-#85 := [mp #73 #82]: #80
-#152 := [mp~ #85 #168]: #80
-#667 := [mp #152 #666]: #662
-#656 := (not #333)
-#637 := (not #662)
-#643 := (or #637 #656)
-#279 := [quant-inst #47]: #643
-[unit-resolution #279 #667 #284]: false
-unsat
-14cd77cb80a411e3c351de92a11790bff950543a 133 0
-#2 := false
-decl f4 :: (-> S4 S3 S1)
-decl f12 :: S3
-#47 := f12
-decl f5 :: S4
-#13 := f5
-#228 := (f4 f5 f12)
-decl f1 :: S1
-#4 := f1
-#315 := (= f1 #228)
-#642 := (not #315)
-decl f11 :: S4
-#44 := f11
-#229 := (f4 f11 f12)
-#316 := (= f1 #229)
-#308 := (or #315 #316)
-#293 := (not #308)
-decl f6 :: (-> S5 S4 S4)
-decl f7 :: (-> S4 S5)
-#45 := (f7 f11)
-#46 := (f6 #45 f5)
-#48 := (f4 #46 f12)
-#129 := (= f1 #48)
-#248 := (iff #129 #308)
-#14 := (:var 0 S3)
-#20 := (:var 1 S4)
-#18 := (:var 2 S4)
-#19 := (f7 #18)
-#21 := (f6 #19 #20)
-#22 := (f4 #21 #14)
-#660 := (pattern #22)
-#26 := (f4 #20 #14)
-#96 := (= f1 #26)
-#24 := (f4 #18 #14)
-#93 := (= f1 #24)
-#99 := (or #93 #96)
-#89 := (= f1 #22)
-#102 := (iff #89 #99)
-#661 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S3)) (:pat #660) #102)
-#105 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S3)) #102)
-#664 := (iff #105 #661)
-#662 := (iff #102 #102)
-#663 := [refl]: #662
-#665 := [quant-intro #663]: #664
-#142 := (~ #105 #105)
-#156 := (~ #102 #102)
-#157 := [refl]: #156
-#143 := [nnf-pos #157]: #142
-#27 := (= #26 f1)
-#25 := (= #24 f1)
-#28 := (or #25 #27)
-#23 := (= #22 f1)
-#29 := (iff #23 #28)
-#30 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S3)) #29)
-#106 := (iff #30 #105)
-#103 := (iff #29 #102)
-#100 := (iff #28 #99)
-#97 := (iff #27 #96)
-#98 := [rewrite]: #97
-#94 := (iff #25 #93)
-#95 := [rewrite]: #94
-#101 := [monotonicity #95 #98]: #100
-#91 := (iff #23 #89)
-#92 := [rewrite]: #91
-#104 := [monotonicity #92 #101]: #103
-#107 := [quant-intro #104]: #106
-#88 := [asserted]: #30
-#110 := [mp #88 #107]: #105
-#158 := [mp~ #110 #143]: #105
-#666 := [mp #158 #665]: #661
-#322 := (not #661)
-#301 := (or #322 #248)
-#230 := (or #316 #315)
-#317 := (iff #129 #230)
-#638 := (or #322 #317)
-#295 := (iff #638 #301)
-#634 := (iff #301 #301)
-#306 := [rewrite]: #634
-#321 := (iff #317 #248)
-#319 := (iff #230 #308)
-#320 := [rewrite]: #319
-#318 := [monotonicity #320]: #321
-#427 := [monotonicity #318]: #295
-#307 := [trans #427 #306]: #295
-#640 := [quant-inst #44 #13 #47]: #638
-#641 := [mp #640 #307]: #301
-#624 := [unit-resolution #641 #666]: #248
-#294 := (not #248)
-#625 := (or #294 #293)
-#133 := (not #129)
-#49 := (= #48 f1)
-#50 := (not #49)
-#134 := (iff #50 #133)
-#131 := (iff #49 #129)
-#132 := [rewrite]: #131
-#135 := [monotonicity #132]: #134
-#128 := [asserted]: #50
-#138 := [mp #128 #135]: #133
-#637 := (or #294 #129 #293)
-#278 := [def-axiom]: #637
-#628 := [unit-resolution #278 #138]: #625
-#264 := [unit-resolution #628 #624]: #293
-#643 := (or #308 #642)
-#644 := [def-axiom]: #643
-#629 := [unit-resolution #644 #264]: #642
-#15 := (f4 f5 #14)
-#653 := (pattern #15)
-#81 := (= f1 #15)
-#654 := (forall (vars (?v0 S3)) (:pat #653) #81)
-#85 := (forall (vars (?v0 S3)) #81)
-#657 := (iff #85 #654)
-#655 := (iff #81 #81)
-#656 := [refl]: #655
-#658 := [quant-intro #656]: #657
-#140 := (~ #85 #85)
-#139 := (~ #81 #81)
-#154 := [refl]: #139
-#141 := [nnf-pos #154]: #140
-#16 := (= #15 f1)
-#17 := (forall (vars (?v0 S3)) #16)
-#86 := (iff #17 #85)
-#83 := (iff #16 #81)
-#84 := [rewrite]: #83
-#87 := [quant-intro #84]: #86
-#80 := [asserted]: #17
-#90 := [mp #80 #87]: #85
-#155 := [mp~ #90 #141]: #85
-#659 := [mp #155 #658]: #654
-#626 := (not #654)
-#627 := (or #626 #315)
-#622 := [quant-inst #47]: #627
-[unit-resolution #622 #659 #629]: false
-unsat
-79e2168b4b0ff2f5af8111880c8b7e92b3513c4b 153 0
-#2 := false
-decl f5 :: (-> S3 S4 S1)
-decl f13 :: S4
-#47 := f13
-decl f6 :: (-> S5 S3 S3)
-decl f11 :: S3
-#43 := f11
-decl f7 :: (-> S3 S5)
-decl f12 :: S3
-#45 := f12
-#50 := (f7 f12)
-#51 := (f6 #50 f11)
-#52 := (f5 #51 f13)
-decl f1 :: S1
-#4 := f1
-#138 := (= f1 #52)
-#334 := (not #138)
-#44 := (f7 f11)
-#46 := (f6 #44 f12)
-#48 := (f5 #46 f13)
-#134 := (= f1 #48)
-#147 := (not #134)
-#253 := [hypothesis]: #147
-#333 := (or #138 #134)
-#148 := (iff #138 #147)
-#53 := (= #52 f1)
-#49 := (= #48 f1)
-#54 := (iff #49 #53)
-#55 := (not #54)
-#151 := (iff #55 #148)
-#141 := (iff #134 #138)
-#144 := (not #141)
-#149 := (iff #144 #148)
-#150 := [rewrite]: #149
-#145 := (iff #55 #144)
-#142 := (iff #54 #141)
-#139 := (iff #53 #138)
-#140 := [rewrite]: #139
-#136 := (iff #49 #134)
-#137 := [rewrite]: #136
-#143 := [monotonicity #137 #140]: #142
-#146 := [monotonicity #143]: #145
-#152 := [trans #146 #150]: #151
-#133 := [asserted]: #55
-#155 := [mp #133 #152]: #148
-#245 := (not #148)
-#332 := (or #138 #134 #245)
-#246 := [def-axiom]: #332
-#247 := [unit-resolution #246 #155]: #333
-#632 := [unit-resolution #247 #253]: #138
-#338 := (f5 f11 f13)
-#335 := (= f1 #338)
-#339 := (f5 f12 f13)
-#318 := (= f1 #339)
-#655 := (or #318 #335)
-#652 := (not #655)
-#355 := (or #134 #652)
-#642 := (iff #134 #655)
-#20 := (:var 0 S4)
-#18 := (:var 1 S3)
-#16 := (:var 2 S3)
-#17 := (f7 #16)
-#19 := (f6 #17 #18)
-#21 := (f5 #19 #20)
-#677 := (pattern #21)
-#25 := (f5 #18 #20)
-#101 := (= f1 #25)
-#23 := (f5 #16 #20)
-#98 := (= f1 #23)
-#104 := (or #98 #101)
-#94 := (= f1 #21)
-#107 := (iff #94 #104)
-#678 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) (:pat #677) #107)
-#110 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #107)
-#681 := (iff #110 #678)
-#679 := (iff #107 #107)
-#680 := [refl]: #679
-#682 := [quant-intro #680]: #681
-#159 := (~ #110 #110)
-#173 := (~ #107 #107)
-#174 := [refl]: #173
-#160 := [nnf-pos #174]: #159
-#26 := (= #25 f1)
-#24 := (= #23 f1)
-#27 := (or #24 #26)
-#22 := (= #21 f1)
-#28 := (iff #22 #27)
-#29 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #28)
-#111 := (iff #29 #110)
-#108 := (iff #28 #107)
-#105 := (iff #27 #104)
-#102 := (iff #26 #101)
-#103 := [rewrite]: #102
-#99 := (iff #24 #98)
-#100 := [rewrite]: #99
-#106 := [monotonicity #100 #103]: #105
-#96 := (iff #22 #94)
-#97 := [rewrite]: #96
-#109 := [monotonicity #97 #106]: #108
-#112 := [quant-intro #109]: #111
-#93 := [asserted]: #29
-#115 := [mp #93 #112]: #110
-#175 := [mp~ #115 #160]: #110
-#683 := [mp #175 #682]: #678
-#651 := (not #678)
-#639 := (or #651 #642)
-#312 := (or #335 #318)
-#444 := (iff #134 #312)
-#645 := (or #651 #444)
-#646 := (iff #645 #639)
-#286 := (iff #639 #639)
-#287 := [rewrite]: #286
-#643 := (iff #444 #642)
-#640 := (iff #312 #655)
-#641 := [rewrite]: #640
-#644 := [monotonicity #641]: #643
-#648 := [monotonicity #644]: #646
-#649 := [trans #648 #287]: #646
-#281 := [quant-inst #43 #45 #47]: #645
-#647 := [mp #281 #649]: #639
-#633 := [unit-resolution #647 #683]: #642
-#650 := (not #642)
-#636 := (or #650 #134 #652)
-#637 := [def-axiom]: #636
-#356 := [unit-resolution #637 #633]: #355
-#630 := [unit-resolution #356 #253]: #652
-#631 := (or #334 #655)
-#657 := (iff #138 #655)
-#323 := (or #651 #657)
-#324 := [quant-inst #45 #43 #47]: #323
-#634 := [unit-resolution #324 #683]: #657
-#653 := (not #657)
-#295 := (or #653 #334 #655)
-#638 := [def-axiom]: #295
-#635 := [unit-resolution #638 #634]: #631
-#344 := [unit-resolution #635 #630 #632]: false
-#345 := [lemma #344]: #134
-#337 := (or #334 #147)
-#325 := (or #334 #147 #245)
-#336 := [def-axiom]: #325
-#265 := [unit-resolution #336 #155]: #337
-#346 := [unit-resolution #265 #345]: #334
-#348 := (or #147 #655)
-#343 := (or #650 #147 #655)
-#359 := [def-axiom]: #343
-#626 := [unit-resolution #359 #633]: #348
-#627 := [unit-resolution #626 #345]: #655
-#340 := (or #138 #652)
-#311 := (or #653 #138 #652)
-#654 := [def-axiom]: #311
-#624 := [unit-resolution #654 #634]: #340
-[unit-resolution #624 #627 #346]: false
-unsat
-00b5c7702f2f9d2a9e2bcf2d2e1bc9e9ddd72c8d 126 0
-#2 := false
-decl f5 :: (-> S3 S4 S1)
-decl f12 :: S4
-#46 := f12
-decl f6 :: (-> S5 S3 S3)
-decl f11 :: S3
-#43 := f11
-decl f7 :: (-> S3 S5)
-#44 := (f7 f11)
-#45 := (f6 #44 f11)
-#47 := (f5 #45 f12)
-decl f1 :: S1
-#4 := f1
-#131 := (= f1 #47)
-#144 := (not #131)
-#635 := [hypothesis]: #144
-#49 := (f5 f11 f12)
-#135 := (= f1 #49)
-#330 := (or #135 #131)
-#145 := (iff #135 #144)
-#50 := (= #49 f1)
-#48 := (= #47 f1)
-#51 := (iff #48 #50)
-#52 := (not #51)
-#148 := (iff #52 #145)
-#138 := (iff #131 #135)
-#141 := (not #138)
-#146 := (iff #141 #145)
-#147 := [rewrite]: #146
-#142 := (iff #52 #141)
-#139 := (iff #51 #138)
-#136 := (iff #50 #135)
-#137 := [rewrite]: #136
-#133 := (iff #48 #131)
-#134 := [rewrite]: #133
-#140 := [monotonicity #134 #137]: #139
-#143 := [monotonicity #140]: #142
-#149 := [trans #143 #147]: #148
-#130 := [asserted]: #52
-#152 := [mp #130 #149]: #145
-#242 := (not #145)
-#329 := (or #135 #131 #242)
-#243 := [def-axiom]: #329
-#244 := [unit-resolution #243 #152]: #330
-#296 := [unit-resolution #244 #635]: #135
-#331 := (not #135)
-#298 := (or #131 #331)
-#20 := (:var 0 S4)
-#18 := (:var 1 S3)
-#16 := (:var 2 S3)
-#17 := (f7 #16)
-#19 := (f6 #17 #18)
-#21 := (f5 #19 #20)
-#674 := (pattern #21)
-#25 := (f5 #18 #20)
-#98 := (= f1 #25)
-#23 := (f5 #16 #20)
-#95 := (= f1 #23)
-#101 := (or #95 #98)
-#91 := (= f1 #21)
-#104 := (iff #91 #101)
-#675 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) (:pat #674) #104)
-#107 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #104)
-#678 := (iff #107 #675)
-#676 := (iff #104 #104)
-#677 := [refl]: #676
-#679 := [quant-intro #677]: #678
-#156 := (~ #107 #107)
-#170 := (~ #104 #104)
-#171 := [refl]: #170
-#157 := [nnf-pos #171]: #156
-#26 := (= #25 f1)
-#24 := (= #23 f1)
-#27 := (or #24 #26)
-#22 := (= #21 f1)
-#28 := (iff #22 #27)
-#29 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #28)
-#108 := (iff #29 #107)
-#105 := (iff #28 #104)
-#102 := (iff #27 #101)
-#99 := (iff #26 #98)
-#100 := [rewrite]: #99
-#96 := (iff #24 #95)
-#97 := [rewrite]: #96
-#103 := [monotonicity #97 #100]: #102
-#93 := (iff #22 #91)
-#94 := [rewrite]: #93
-#106 := [monotonicity #94 #103]: #105
-#109 := [quant-intro #106]: #108
-#90 := [asserted]: #29
-#112 := [mp #90 #109]: #107
-#172 := [mp~ #112 #157]: #107
-#680 := [mp #172 #679]: #675
-#309 := (not #675)
-#441 := (or #309 #138)
-#335 := (or #135 #135)
-#332 := (iff #131 #335)
-#648 := (or #309 #332)
-#321 := (iff #648 #441)
-#656 := (iff #441 #441)
-#657 := [rewrite]: #656
-#652 := (iff #332 #138)
-#336 := (iff #335 #135)
-#315 := [rewrite]: #336
-#654 := [monotonicity #315]: #652
-#655 := [monotonicity #654]: #321
-#658 := [trans #655 #657]: #321
-#320 := [quant-inst #43 #43 #46]: #648
-#653 := [mp #320 #658]: #441
-#297 := [unit-resolution #653 #680]: #138
-#659 := (or #141 #131 #331)
-#649 := [def-axiom]: #659
-#299 := [unit-resolution #649 #297]: #298
-#637 := [unit-resolution #299 #296 #635]: false
-#638 := [lemma #637]: #131
-#334 := (or #331 #144)
-#322 := (or #331 #144 #242)
-#333 := [def-axiom]: #322
-#262 := [unit-resolution #333 #152]: #334
-#639 := [unit-resolution #262 #638]: #331
-#640 := (or #144 #135)
-#307 := (or #141 #144 #135)
-#312 := [def-axiom]: #307
-#641 := [unit-resolution #312 #297]: #640
-[unit-resolution #641 #639 #638]: false
-unsat
-36be54782f18afe7f767077c9cb63504fffdbec4 264 0
-#2 := false
-decl f5 :: (-> S3 S4 S1)
-decl f14 :: S4
-#50 := f14
-decl f12 :: S3
-#45 := f12
-#631 := (f5 f12 f14)
-decl f1 :: S1
-#4 := f1
-#344 := (= f1 #631)
-decl f13 :: S3
-#47 := f13
-#342 := (f5 f13 f14)
-#339 := (= f1 #342)
-#629 := (or #339 #344)
-decl f6 :: (-> S5 S3 S3)
-decl f7 :: (-> S3 S5)
-#46 := (f7 f12)
-#48 := (f6 #46 f13)
-#316 := (f5 #48 f14)
-#448 := (= f1 #316)
-#623 := (iff #448 #629)
-#589 := (not #623)
-#601 := (not #629)
-#613 := (not #344)
-decl f11 :: S3
-#43 := f11
-#644 := (f5 f11 f14)
-#645 := (= f1 #644)
-#491 := (or #344 #645)
-#616 := (not #491)
-#44 := (f7 f11)
-#53 := (f6 #44 f12)
-#343 := (f5 #53 f14)
-#322 := (= f1 #343)
-#599 := (iff #322 #491)
-#591 := (not #599)
-#584 := [hypothesis]: #591
-#20 := (:var 0 S4)
-#18 := (:var 1 S3)
-#16 := (:var 2 S3)
-#17 := (f7 #16)
-#19 := (f6 #17 #18)
-#21 := (f5 #19 #20)
-#681 := (pattern #21)
-#25 := (f5 #18 #20)
-#105 := (= f1 #25)
-#23 := (f5 #16 #20)
-#102 := (= f1 #23)
-#108 := (or #102 #105)
-#98 := (= f1 #21)
-#111 := (iff #98 #108)
-#682 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) (:pat #681) #111)
-#114 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #111)
-#685 := (iff #114 #682)
-#683 := (iff #111 #111)
-#684 := [refl]: #683
-#686 := [quant-intro #684]: #685
-#163 := (~ #114 #114)
-#177 := (~ #111 #111)
-#178 := [refl]: #177
-#164 := [nnf-pos #178]: #163
-#26 := (= #25 f1)
-#24 := (= #23 f1)
-#27 := (or #24 #26)
-#22 := (= #21 f1)
-#28 := (iff #22 #27)
-#29 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #28)
-#115 := (iff #29 #114)
-#112 := (iff #28 #111)
-#109 := (iff #27 #108)
-#106 := (iff #26 #105)
-#107 := [rewrite]: #106
-#103 := (iff #24 #102)
-#104 := [rewrite]: #103
-#110 := [monotonicity #104 #107]: #109
-#100 := (iff #22 #98)
-#101 := [rewrite]: #100
-#113 := [monotonicity #101 #110]: #112
-#116 := [quant-intro #113]: #115
-#97 := [asserted]: #29
-#119 := [mp #97 #116]: #114
-#179 := [mp~ #119 #164]: #114
-#687 := [mp #179 #686]: #682
-#655 := (not #682)
-#597 := (or #655 #599)
-#608 := (or #645 #344)
-#490 := (iff #322 #608)
-#600 := (or #655 #490)
-#500 := (iff #600 #597)
-#503 := (iff #597 #597)
-#496 := [rewrite]: #503
-#501 := (iff #490 #599)
-#492 := (iff #608 #491)
-#451 := [rewrite]: #492
-#596 := [monotonicity #451]: #501
-#502 := [monotonicity #596]: #500
-#504 := [trans #502 #496]: #500
-#485 := [quant-inst #43 #45 #50]: #600
-#505 := [mp #485 #504]: #597
-#585 := [unit-resolution #505 #687 #584]: false
-#586 := [lemma #585]: #599
-#662 := (not #322)
-#659 := (or #322 #339)
-#656 := (not #659)
-#54 := (f7 #53)
-#55 := (f6 #54 f13)
-#56 := (f5 #55 f14)
-#142 := (= f1 #56)
-#338 := (not #142)
-#49 := (f6 #44 #48)
-#51 := (f5 #49 f14)
-#138 := (= f1 #51)
-#151 := (not #138)
-#587 := [hypothesis]: #151
-#337 := (or #142 #138)
-#152 := (iff #142 #151)
-#57 := (= #56 f1)
-#52 := (= #51 f1)
-#58 := (iff #52 #57)
-#59 := (not #58)
-#155 := (iff #59 #152)
-#145 := (iff #138 #142)
-#148 := (not #145)
-#153 := (iff #148 #152)
-#154 := [rewrite]: #153
-#149 := (iff #59 #148)
-#146 := (iff #58 #145)
-#143 := (iff #57 #142)
-#144 := [rewrite]: #143
-#140 := (iff #52 #138)
-#141 := [rewrite]: #140
-#147 := [monotonicity #141 #144]: #146
-#150 := [monotonicity #147]: #149
-#156 := [trans #150 #154]: #155
-#137 := [asserted]: #59
-#159 := [mp #137 #156]: #152
-#249 := (not #152)
-#336 := (or #142 #138 #249)
-#250 := [def-axiom]: #336
-#251 := [unit-resolution #250 #159]: #337
-#581 := [unit-resolution #251 #587]: #142
-#572 := (or #338 #659)
-#661 := (iff #142 #659)
-#327 := (or #655 #661)
-#328 := [quant-inst #53 #47 #50]: #327
-#588 := [unit-resolution #328 #687]: #661
-#657 := (not #661)
-#299 := (or #657 #338 #659)
-#642 := [def-axiom]: #299
-#573 := [unit-resolution #642 #588]: #572
-#575 := [unit-resolution #573 #581]: #659
-#665 := (not #339)
-#605 := (or #655 #623)
-#628 := (or #344 #339)
-#632 := (iff #448 #628)
-#625 := (or #655 #632)
-#620 := (iff #625 #605)
-#627 := (iff #605 #605)
-#468 := [rewrite]: #627
-#624 := (iff #632 #623)
-#633 := (iff #628 #629)
-#622 := [rewrite]: #633
-#619 := [monotonicity #622]: #624
-#621 := [monotonicity #619]: #620
-#469 := [trans #621 #468]: #620
-#626 := [quant-inst #45 #47 #50]: #625
-#470 := [mp #626 #469]: #605
-#576 := [unit-resolution #470 #687]: #623
-#566 := (or #589 #601)
-#364 := (not #448)
-#648 := (or #448 #645)
-#637 := (not #648)
-#578 := (or #138 #637)
-#285 := (iff #138 #648)
-#290 := (or #655 #285)
-#646 := (or #645 #448)
-#647 := (iff #138 #646)
-#291 := (or #655 #647)
-#651 := (iff #291 #290)
-#640 := (iff #290 #290)
-#641 := [rewrite]: #640
-#650 := (iff #647 #285)
-#643 := (iff #646 #648)
-#649 := [rewrite]: #643
-#652 := [monotonicity #649]: #650
-#654 := [monotonicity #652]: #651
-#347 := [trans #654 #641]: #651
-#653 := [quant-inst #43 #48 #50]: #291
-#363 := [mp #653 #347]: #290
-#577 := [unit-resolution #363 #687]: #285
-#634 := (not #285)
-#638 := (or #634 #138 #637)
-#635 := [def-axiom]: #638
-#574 := [unit-resolution #635 #577]: #578
-#579 := [unit-resolution #574 #587]: #637
-#365 := (or #648 #364)
-#351 := [def-axiom]: #365
-#565 := [unit-resolution #351 #579]: #364
-#583 := (or #589 #448 #601)
-#580 := [def-axiom]: #583
-#568 := [unit-resolution #580 #565]: #566
-#569 := [unit-resolution #568 #576]: #601
-#612 := (or #629 #665)
-#506 := [def-axiom]: #612
-#570 := [unit-resolution #506 #569]: #665
-#314 := (or #656 #322 #339)
-#319 := [def-axiom]: #314
-#567 := [unit-resolution #319 #570 #575]: #322
-#366 := (not #645)
-#257 := (or #648 #366)
-#636 := [def-axiom]: #257
-#571 := [unit-resolution #636 #579]: #366
-#507 := (or #629 #613)
-#508 := [def-axiom]: #507
-#551 := [unit-resolution #508 #569]: #613
-#617 := (or #616 #344 #645)
-#611 := [def-axiom]: #617
-#552 := [unit-resolution #611 #551 #571]: #616
-#449 := (or #591 #662 #491)
-#450 := [def-axiom]: #449
-#554 := [unit-resolution #450 #552 #567 #586]: false
-#555 := [lemma #554]: #138
-#341 := (or #338 #151)
-#329 := (or #338 #151 #249)
-#340 := [def-axiom]: #329
-#269 := [unit-resolution #340 #159]: #341
-#556 := [unit-resolution #269 #555]: #338
-#557 := (or #142 #656)
-#315 := (or #657 #142 #656)
-#658 := [def-axiom]: #315
-#558 := [unit-resolution #658 #588]: #557
-#559 := [unit-resolution #558 #556]: #656
-#663 := (or #659 #662)
-#664 := [def-axiom]: #663
-#560 := [unit-resolution #664 #559]: #662
-#618 := (or #591 #322 #616)
-#447 := [def-axiom]: #618
-#561 := [unit-resolution #447 #560 #586]: #616
-#614 := (or #491 #613)
-#615 := [def-axiom]: #614
-#562 := [unit-resolution #615 #561]: #613
-#660 := (or #659 #665)
-#666 := [def-axiom]: #660
-#563 := [unit-resolution #666 #559]: #665
-#598 := (or #601 #339 #344)
-#602 := [def-axiom]: #598
-#553 := [unit-resolution #602 #563 #562]: #601
-#564 := (or #151 #648)
-#639 := (or #634 #151 #648)
-#348 := [def-axiom]: #639
-#542 := [unit-resolution #348 #577]: #564
-#543 := [unit-resolution #542 #555]: #648
-#609 := (or #491 #366)
-#610 := [def-axiom]: #609
-#545 := [unit-resolution #610 #561]: #366
-#359 := (or #637 #448 #645)
-#360 := [def-axiom]: #359
-#546 := [unit-resolution #360 #545 #543]: #448
-#582 := (or #589 #364 #629)
-#592 := [def-axiom]: #582
-#547 := [unit-resolution #592 #546 #553]: #589
-[unit-resolution #470 #687 #547]: false
-unsat
-d2f2f1ccdb6d545bd3f136b38b7ffe9f993f5bcd 158 0
-#2 := false
-decl f8 :: (-> S5 S6 S1)
-decl f13 :: S6
-#47 := f13
-decl f12 :: S5
-#45 := f12
-#52 := (f8 f12 f13)
-decl f1 :: S1
-#4 := f1
-#142 := (= f1 #52)
-#196 := (not #142)
-decl f11 :: S5
-#43 := f11
-#50 := (f8 f11 f13)
-#139 := (= f1 #50)
-#195 := (not #139)
-#197 := (or #195 #196)
-#198 := (not #197)
-#339 := [hypothesis]: #198
-decl f9 :: (-> S7 S5 S5)
-decl f10 :: (-> S5 S7)
-#44 := (f10 f11)
-#46 := (f9 #44 f12)
-#48 := (f8 #46 f13)
-#135 := (= f1 #48)
-#154 := (not #135)
-#345 := (or #154 #197)
-#209 := (iff #135 #197)
-#145 := (and #139 #142)
-#155 := (iff #145 #154)
-#212 := (iff #155 #209)
-#204 := (iff #197 #135)
-#210 := (iff #204 #209)
-#211 := [rewrite]: #210
-#207 := (iff #155 #204)
-#201 := (iff #198 #154)
-#205 := (iff #201 #204)
-#206 := [rewrite]: #205
-#202 := (iff #155 #201)
-#199 := (iff #145 #198)
-#200 := [rewrite]: #199
-#203 := [monotonicity #200]: #202
-#208 := [trans #203 #206]: #207
-#213 := [trans #208 #211]: #212
-#53 := (= #52 f1)
-#51 := (= #50 f1)
-#54 := (and #51 #53)
-#49 := (= #48 f1)
-#55 := (iff #49 #54)
-#56 := (not #55)
-#158 := (iff #56 #155)
-#148 := (iff #135 #145)
-#151 := (not #148)
-#156 := (iff #151 #155)
-#157 := [rewrite]: #156
-#152 := (iff #56 #151)
-#149 := (iff #55 #148)
-#146 := (iff #54 #145)
-#143 := (iff #53 #142)
-#144 := [rewrite]: #143
-#140 := (iff #51 #139)
-#141 := [rewrite]: #140
-#147 := [monotonicity #141 #144]: #146
-#137 := (iff #49 #135)
-#138 := [rewrite]: #137
-#150 := [monotonicity #138 #147]: #149
-#153 := [monotonicity #150]: #152
-#159 := [trans #153 #157]: #158
-#134 := [asserted]: #56
-#162 := [mp #134 #159]: #155
-#214 := [mp #162 #213]: #209
-#352 := (not #209)
-#362 := (or #154 #197 #352)
-#366 := [def-axiom]: #362
-#682 := [unit-resolution #366 #214]: #345
-#471 := [unit-resolution #682 #339]: #154
-#338 := (or #135 #197)
-#684 := (iff #135 #198)
-#33 := (:var 0 S6)
-#31 := (:var 1 S5)
-#29 := (:var 2 S5)
-#30 := (f10 #29)
-#32 := (f9 #30 #31)
-#34 := (f8 #32 #33)
-#711 := (pattern #34)
-#38 := (f8 #31 #33)
-#122 := (= f1 #38)
-#187 := (not #122)
-#36 := (f8 #29 #33)
-#119 := (= f1 #36)
-#186 := (not #119)
-#170 := (or #186 #187)
-#171 := (not #170)
-#115 := (= f1 #34)
-#188 := (iff #115 #171)
-#712 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) (:pat #711) #188)
-#191 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) #188)
-#715 := (iff #191 #712)
-#713 := (iff #188 #188)
-#714 := [refl]: #713
-#716 := [quant-intro #714]: #715
-#125 := (and #119 #122)
-#128 := (iff #115 #125)
-#131 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) #128)
-#192 := (iff #131 #191)
-#189 := (iff #128 #188)
-#172 := (iff #125 #171)
-#173 := [rewrite]: #172
-#190 := [monotonicity #173]: #189
-#193 := [quant-intro #190]: #192
-#168 := (~ #131 #131)
-#183 := (~ #128 #128)
-#184 := [refl]: #183
-#169 := [nnf-pos #184]: #168
-#39 := (= #38 f1)
-#37 := (= #36 f1)
-#40 := (and #37 #39)
-#35 := (= #34 f1)
-#41 := (iff #35 #40)
-#42 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) #41)
-#132 := (iff #42 #131)
-#129 := (iff #41 #128)
-#126 := (iff #40 #125)
-#123 := (iff #39 #122)
-#124 := [rewrite]: #123
-#120 := (iff #37 #119)
-#121 := [rewrite]: #120
-#127 := [monotonicity #121 #124]: #126
-#117 := (iff #35 #115)
-#118 := [rewrite]: #117
-#130 := [monotonicity #118 #127]: #129
-#133 := [quant-intro #130]: #132
-#114 := [asserted]: #42
-#136 := [mp #114 #133]: #131
-#185 := [mp~ #136 #169]: #131
-#194 := [mp #185 #193]: #191
-#717 := [mp #194 #716]: #712
-#678 := (not #712)
-#350 := (or #678 #684)
-#351 := [quant-inst #43 #45 #47]: #350
-#680 := [unit-resolution #351 #717]: #684
-#685 := (not #684)
-#686 := (or #685 #135 #197)
-#687 := [def-axiom]: #686
-#681 := [unit-resolution #687 #680]: #338
-#322 := [unit-resolution #681 #471 #339]: false
-#665 := [lemma #322]: #197
-#292 := (or #135 #198)
-#363 := (or #135 #198 #352)
-#364 := [def-axiom]: #363
-#365 := [unit-resolution #364 #214]: #292
-#326 := [unit-resolution #365 #665]: #135
-#327 := (or #154 #198)
-#688 := (or #685 #154 #198)
-#683 := [def-axiom]: #688
-#328 := [unit-resolution #683 #680]: #327
-[unit-resolution #328 #326 #665]: false
-unsat
-7a081c99c642b081ea8cd661453be0f8f15b2aa5 146 0
-#2 := false
-decl f3 :: (-> S3 S2 S1)
-decl f12 :: S2
-#47 := f12
-decl f4 :: S3
-#8 := f4
-#236 := (f3 f4 f12)
-decl f1 :: S1
-#4 := f1
-#323 := (= f1 #236)
-#237 := (not #323)
-decl f11 :: S3
-#44 := f11
-#324 := (f3 f11 f12)
-#238 := (= f1 #324)
-#325 := (not #238)
-#316 := (or #325 #237)
-#327 := (not #316)
-decl f9 :: (-> S7 S3 S3)
-decl f10 :: (-> S3 S7)
-#45 := (f10 f11)
-#46 := (f9 #45 f4)
-#48 := (f3 #46 f12)
-#130 := (= f1 #48)
-#328 := (iff #130 #327)
-#9 := (:var 0 S2)
-#33 := (:var 1 S3)
-#31 := (:var 2 S3)
-#32 := (f10 #31)
-#34 := (f9 #32 #33)
-#35 := (f3 #34 #9)
-#675 := (pattern #35)
-#39 := (f3 #33 #9)
-#117 := (= f1 #39)
-#171 := (not #117)
-#37 := (f3 #31 #9)
-#114 := (= f1 #37)
-#170 := (not #114)
-#154 := (or #170 #171)
-#155 := (not #154)
-#110 := (= f1 #35)
-#172 := (iff #110 #155)
-#676 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S2)) (:pat #675) #172)
-#175 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S2)) #172)
-#679 := (iff #175 #676)
-#677 := (iff #172 #172)
-#678 := [refl]: #677
-#680 := [quant-intro #678]: #679
-#120 := (and #114 #117)
-#123 := (iff #110 #120)
-#126 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S2)) #123)
-#176 := (iff #126 #175)
-#173 := (iff #123 #172)
-#156 := (iff #120 #155)
-#157 := [rewrite]: #156
-#174 := [monotonicity #157]: #173
-#177 := [quant-intro #174]: #176
-#152 := (~ #126 #126)
-#167 := (~ #123 #123)
-#168 := [refl]: #167
-#153 := [nnf-pos #168]: #152
-#40 := (= #39 f1)
-#38 := (= #37 f1)
-#41 := (and #38 #40)
-#36 := (= #35 f1)
-#42 := (iff #36 #41)
-#43 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S2)) #42)
-#127 := (iff #43 #126)
-#124 := (iff #42 #123)
-#121 := (iff #41 #120)
-#118 := (iff #40 #117)
-#119 := [rewrite]: #118
-#115 := (iff #38 #114)
-#116 := [rewrite]: #115
-#122 := [monotonicity #116 #119]: #121
-#112 := (iff #36 #110)
-#113 := [rewrite]: #112
-#125 := [monotonicity #113 #122]: #124
-#128 := [quant-intro #125]: #127
-#109 := [asserted]: #43
-#131 := [mp #109 #128]: #126
-#169 := [mp~ #131 #153]: #126
-#178 := [mp #169 #177]: #175
-#681 := [mp #178 #680]: #676
-#326 := (not #676)
-#330 := (or #326 #328)
-#309 := [quant-inst #44 #8 #47]: #330
-#256 := [unit-resolution #309 #681]: #328
-#315 := (not #328)
-#329 := (or #315 #327)
-#49 := (= #48 f1)
-#50 := (not #49)
-#51 := (not #50)
-#142 := (iff #51 #130)
-#134 := (not #130)
-#137 := (not #134)
-#140 := (iff #137 #130)
-#141 := [rewrite]: #140
-#138 := (iff #51 #137)
-#135 := (iff #50 #134)
-#132 := (iff #49 #130)
-#133 := [rewrite]: #132
-#136 := [monotonicity #133]: #135
-#139 := [monotonicity #136]: #138
-#143 := [trans #139 #141]: #142
-#129 := [asserted]: #51
-#146 := [mp #129 #143]: #130
-#651 := (or #315 #134 #327)
-#652 := [def-axiom]: #651
-#645 := [unit-resolution #652 #146]: #329
-#286 := [unit-resolution #645 #256]: #327
-#303 := (or #316 #323)
-#435 := [def-axiom]: #303
-#629 := [unit-resolution #435 #286]: #323
-#10 := (f3 f4 #9)
-#654 := (pattern #10)
-#72 := (= f1 #10)
-#75 := (not #72)
-#655 := (forall (vars (?v0 S2)) (:pat #654) #75)
-#78 := (forall (vars (?v0 S2)) #75)
-#658 := (iff #78 #655)
-#656 := (iff #75 #75)
-#657 := [refl]: #656
-#659 := [quant-intro #657]: #658
-#160 := (~ #78 #78)
-#158 := (~ #75 #75)
-#159 := [refl]: #158
-#161 := [nnf-pos #159]: #160
-#11 := (= #10 f1)
-#12 := (not #11)
-#13 := (forall (vars (?v0 S2)) #12)
-#79 := (iff #13 #78)
-#76 := (iff #12 #75)
-#73 := (iff #11 #72)
-#74 := [rewrite]: #73
-#77 := [monotonicity #74]: #76
-#80 := [quant-intro #77]: #79
-#71 := [asserted]: #13
-#83 := [mp #71 #80]: #78
-#145 := [mp~ #83 #161]: #78
-#660 := [mp #145 #659]: #655
-#306 := (not #655)
-#644 := (or #306 #237)
-#302 := [quant-inst #47]: #644
-[unit-resolution #302 #660 #629]: false
-unsat
-a553f34a8063e2bd9b0a5e3813ed9795ccc16096 170 0
-#2 := false
-decl f4 :: (-> S4 S3 S1)
-decl f12 :: S3
-#47 := f12
-decl f11 :: S4
-#44 := f11
-#50 := (f4 f11 f12)
-decl f1 :: S1
-#4 := f1
-#136 := (= f1 #50)
-#332 := (not #136)
-decl f9 :: (-> S7 S4 S4)
-decl f5 :: S4
+#589 := (iff #12 #586)
+#587 := (iff #11 #11)
+#588 := [refl]: #587
+#590 := [quant-intro #588]: #589
+#88 := (~ #12 #12)
+#86 := (~ #11 #11)
+#87 := [refl]: #86
+#89 := [nnf-pos #87]: #88
+#65 := [asserted]: #12
+#73 := [mp~ #65 #89]: #12
+#591 := [mp #73 #590]: #586
+#256 := (not #586)
+#171 := (or #256 #43)
+#257 := [quant-inst #40]: #171
+[unit-resolution #257 #591 #74]: false
+unsat
+e52edad337a80ce1b9f167b25fc11aa08d513ef1 34 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S3 S1)
+decl f5 :: S3
 #13 := f5
-decl f10 :: (-> S4 S7)
-#45 := (f10 f11)
-#46 := (f9 #45 f5)
-#48 := (f4 #46 f12)
-#132 := (= f1 #48)
-#336 := (f4 f5 f12)
-#333 := (= f1 #336)
-#337 := (not #333)
-#310 := [hypothesis]: #337
-#14 := (:var 0 S3)
-#15 := (f4 f5 #14)
-#668 := (pattern #15)
-#84 := (= f1 #15)
-#669 := (forall (vars (?v0 S3)) (:pat #668) #84)
-#88 := (forall (vars (?v0 S3)) #84)
-#672 := (iff #88 #669)
-#670 := (iff #84 #84)
-#671 := [refl]: #670
-#673 := [quant-intro #671]: #672
-#155 := (~ #88 #88)
-#154 := (~ #84 #84)
-#169 := [refl]: #154
-#156 := [nnf-pos #169]: #155
-#16 := (= #15 f1)
-#17 := (forall (vars (?v0 S3)) #16)
-#89 := (iff #17 #88)
-#86 := (iff #16 #84)
-#87 := [rewrite]: #86
-#90 := [quant-intro #87]: #89
-#83 := [asserted]: #17
-#93 := [mp #83 #90]: #88
-#170 := [mp~ #93 #156]: #88
-#674 := [mp #170 #673]: #669
-#298 := (not #669)
-#299 := (or #298 #333)
-#300 := [quant-inst #47]: #299
-#442 := [unit-resolution #300 #674 #310]: false
-#638 := [lemma #442]: #333
-#145 := (not #132)
-#639 := [hypothesis]: #145
-#331 := (or #136 #132)
-#146 := (iff #136 #145)
-#51 := (= #50 f1)
-#49 := (= #48 f1)
-#52 := (iff #49 #51)
-#53 := (not #52)
-#149 := (iff #53 #146)
-#139 := (iff #132 #136)
-#142 := (not #139)
-#147 := (iff #142 #146)
-#148 := [rewrite]: #147
-#143 := (iff #53 #142)
-#140 := (iff #52 #139)
-#137 := (iff #51 #136)
-#138 := [rewrite]: #137
-#134 := (iff #49 #132)
-#135 := [rewrite]: #134
-#141 := [monotonicity #135 #138]: #140
-#144 := [monotonicity #141]: #143
-#150 := [trans #144 #148]: #149
-#131 := [asserted]: #53
-#153 := [mp #131 #150]: #146
-#243 := (not #146)
-#330 := (or #136 #132 #243)
-#244 := [def-axiom]: #330
-#245 := [unit-resolution #244 #153]: #331
-#640 := [unit-resolution #245 #639]: #136
-#316 := (or #332 #337)
-#642 := (or #132 #316)
-#653 := (not #316)
-#655 := (iff #132 #653)
-#33 := (:var 1 S4)
-#31 := (:var 2 S4)
-#32 := (f10 #31)
-#34 := (f9 #32 #33)
-#35 := (f4 #34 #14)
-#682 := (pattern #35)
-#39 := (f4 #33 #14)
-#119 := (= f1 #39)
-#178 := (not #119)
-#37 := (f4 #31 #14)
-#116 := (= f1 #37)
-#177 := (not #116)
-#161 := (or #177 #178)
-#162 := (not #161)
-#112 := (= f1 #35)
-#179 := (iff #112 #162)
-#683 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S3)) (:pat #682) #179)
-#182 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S3)) #179)
-#686 := (iff #182 #683)
-#684 := (iff #179 #179)
-#685 := [refl]: #684
-#687 := [quant-intro #685]: #686
-#122 := (and #116 #119)
-#125 := (iff #112 #122)
-#128 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S3)) #125)
-#183 := (iff #128 #182)
-#180 := (iff #125 #179)
-#163 := (iff #122 #162)
-#164 := [rewrite]: #163
-#181 := [monotonicity #164]: #180
-#184 := [quant-intro #181]: #183
-#159 := (~ #128 #128)
-#174 := (~ #125 #125)
-#175 := [refl]: #174
-#160 := [nnf-pos #175]: #159
-#40 := (= #39 f1)
-#38 := (= #37 f1)
-#41 := (and #38 #40)
-#36 := (= #35 f1)
-#42 := (iff #36 #41)
-#43 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S3)) #42)
-#129 := (iff #43 #128)
-#126 := (iff #42 #125)
-#123 := (iff #41 #122)
-#120 := (iff #40 #119)
-#121 := [rewrite]: #120
-#117 := (iff #38 #116)
-#118 := [rewrite]: #117
-#124 := [monotonicity #118 #121]: #123
-#114 := (iff #36 #112)
-#115 := [rewrite]: #114
-#127 := [monotonicity #115 #124]: #126
-#130 := [quant-intro #127]: #129
-#111 := [asserted]: #43
-#133 := [mp #111 #130]: #128
-#176 := [mp~ #133 #160]: #128
-#185 := [mp #176 #184]: #182
-#688 := [mp #185 #687]: #683
-#649 := (not #683)
-#321 := (or #649 #655)
-#322 := [quant-inst #44 #13 #47]: #321
-#641 := [unit-resolution #322 #688]: #655
-#650 := (not #655)
-#308 := (or #650 #132 #316)
-#313 := [def-axiom]: #308
-#637 := [unit-resolution #313 #641]: #642
-#643 := [unit-resolution #637 #639]: #316
-#654 := (or #653 #332 #337)
-#660 := [def-axiom]: #654
-#279 := [unit-resolution #660 #643 #640 #638]: false
-#644 := [lemma #279]: #132
-#335 := (or #332 #145)
-#323 := (or #332 #145 #243)
-#334 := [def-axiom]: #323
-#263 := [unit-resolution #334 #153]: #335
-#646 := [unit-resolution #263 #644]: #332
-#284 := (or #145 #653)
-#651 := (or #650 #145 #653)
-#309 := [def-axiom]: #651
-#285 := [unit-resolution #309 #641]: #284
-#647 := [unit-resolution #285 #644]: #653
-#656 := (or #316 #136)
-#657 := [def-axiom]: #656
-[unit-resolution #657 #647 #646]: false
-unsat
-58bc05f7a76c224bbfdad5d684aa2594b451e197 171 0
-#2 := false
-decl f8 :: (-> S5 S6 S1)
-decl f13 :: S6
-#47 := f13
-decl f9 :: (-> S7 S5 S5)
-decl f11 :: S5
-#43 := f11
-decl f10 :: (-> S5 S7)
-decl f12 :: S5
-#45 := f12
-#50 := (f10 f12)
-#51 := (f9 #50 f11)
-#52 := (f8 #51 f13)
-decl f1 :: S1
-#4 := f1
-#138 := (= f1 #52)
-#334 := (not #138)
-#44 := (f10 f11)
-#46 := (f9 #44 f12)
-#48 := (f8 #46 f13)
-#134 := (= f1 #48)
-#147 := (not #134)
-#636 := [hypothesis]: #147
-#333 := (or #138 #134)
-#148 := (iff #138 #147)
-#53 := (= #52 f1)
-#49 := (= #48 f1)
-#54 := (iff #49 #53)
-#55 := (not #54)
-#151 := (iff #55 #148)
-#141 := (iff #134 #138)
-#144 := (not #141)
-#149 := (iff #144 #148)
-#150 := [rewrite]: #149
-#145 := (iff #55 #144)
-#142 := (iff #54 #141)
-#139 := (iff #53 #138)
-#140 := [rewrite]: #139
-#136 := (iff #49 #134)
-#137 := [rewrite]: #136
-#143 := [monotonicity #137 #140]: #142
-#146 := [monotonicity #143]: #145
-#152 := [trans #146 #150]: #151
-#133 := [asserted]: #55
-#155 := [mp #133 #152]: #148
-#245 := (not #148)
-#332 := (or #138 #134 #245)
-#246 := [def-axiom]: #332
-#247 := [unit-resolution #246 #155]: #333
-#637 := [unit-resolution #247 #636]: #138
-#318 := (f8 f12 f13)
-#655 := (= f1 #318)
-#657 := (not #655)
-#338 := (f8 f11 f13)
-#335 := (= f1 #338)
-#339 := (not #335)
-#323 := (or #339 #657)
-#634 := (or #134 #323)
-#659 := (not #323)
-#650 := (iff #134 #659)
-#33 := (:var 0 S6)
-#31 := (:var 1 S5)
-#29 := (:var 2 S5)
-#30 := (f10 #29)
-#32 := (f9 #30 #31)
-#34 := (f8 #32 #33)
-#684 := (pattern #34)
-#38 := (f8 #31 #33)
-#121 := (= f1 #38)
-#180 := (not #121)
-#36 := (f8 #29 #33)
-#118 := (= f1 #36)
-#179 := (not #118)
-#163 := (or #179 #180)
-#164 := (not #163)
-#114 := (= f1 #34)
-#181 := (iff #114 #164)
-#685 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) (:pat #684) #181)
-#184 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) #181)
-#688 := (iff #184 #685)
-#686 := (iff #181 #181)
-#687 := [refl]: #686
-#689 := [quant-intro #687]: #688
-#124 := (and #118 #121)
-#127 := (iff #114 #124)
-#130 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) #127)
-#185 := (iff #130 #184)
-#182 := (iff #127 #181)
-#165 := (iff #124 #164)
-#166 := [rewrite]: #165
-#183 := [monotonicity #166]: #182
-#186 := [quant-intro #183]: #185
-#161 := (~ #130 #130)
-#176 := (~ #127 #127)
-#177 := [refl]: #176
-#162 := [nnf-pos #177]: #161
-#39 := (= #38 f1)
-#37 := (= #36 f1)
-#40 := (and #37 #39)
-#35 := (= #34 f1)
-#41 := (iff #35 #40)
-#42 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) #41)
-#131 := (iff #42 #130)
-#128 := (iff #41 #127)
-#125 := (iff #40 #124)
-#122 := (iff #39 #121)
-#123 := [rewrite]: #122
-#119 := (iff #37 #118)
-#120 := [rewrite]: #119
-#126 := [monotonicity #120 #123]: #125
-#116 := (iff #35 #114)
-#117 := [rewrite]: #116
-#129 := [monotonicity #117 #126]: #128
-#132 := [quant-intro #129]: #131
-#113 := [asserted]: #42
-#135 := [mp #113 #132]: #130
-#178 := [mp~ #135 #162]: #130
-#187 := [mp #178 #186]: #184
-#690 := [mp #187 #689]: #685
-#310 := (not #685)
-#343 := (or #310 #650)
-#359 := [quant-inst #43 #45 #47]: #343
-#630 := [unit-resolution #359 #690]: #650
-#360 := (not #650)
-#361 := (or #360 #134 #323)
-#347 := [def-axiom]: #361
-#631 := [unit-resolution #347 #630]: #634
-#635 := [unit-resolution #631 #636]: #323
-#345 := (or #334 #659)
-#656 := (iff #138 #659)
-#315 := (or #310 #656)
-#312 := (or #657 #339)
-#444 := (not #312)
-#651 := (iff #138 #444)
-#653 := (or #310 #651)
-#654 := (iff #653 #315)
-#638 := (iff #315 #315)
-#299 := [rewrite]: #638
-#662 := (iff #651 #656)
-#660 := (iff #444 #659)
-#324 := (iff #312 #323)
-#658 := [rewrite]: #324
-#661 := [monotonicity #658]: #660
-#652 := [monotonicity #661]: #662
-#295 := [monotonicity #652]: #654
-#300 := [trans #295 #299]: #654
-#311 := [quant-inst #45 #43 #47]: #653
-#301 := [mp #311 #300]: #315
-#344 := [unit-resolution #301 #690]: #656
-#639 := (not #656)
-#646 := (or #639 #334 #659)
-#648 := [def-axiom]: #646
-#346 := [unit-resolution #648 #344]: #345
-#348 := [unit-resolution #346 #635 #637]: false
-#626 := [lemma #348]: #134
-#337 := (or #334 #147)
-#325 := (or #334 #147 #245)
-#336 := [def-axiom]: #325
-#265 := [unit-resolution #336 #155]: #337
-#627 := [unit-resolution #265 #626]: #334
-#340 := (or #147 #659)
-#362 := (or #360 #147 #659)
-#253 := [def-axiom]: #362
-#624 := [unit-resolution #253 #630]: #340
-#628 := [unit-resolution #624 #626]: #659
-#625 := (or #138 #323)
-#645 := (or #639 #138 #323)
-#281 := [def-axiom]: #645
-#629 := [unit-resolution #281 #344]: #625
-[unit-resolution #629 #628 #627]: false
-unsat
-8d1e77108728c35ede6d03f92ae722f22d8aeeab 147 0
-#2 := false
-decl f8 :: (-> S5 S6 S1)
-decl f12 :: S6
-#46 := f12
-decl f9 :: (-> S7 S5 S5)
-decl f11 :: S5
-#43 := f11
-decl f10 :: (-> S5 S7)
-#44 := (f10 f11)
-#45 := (f9 #44 f11)
-#47 := (f8 #45 f12)
-decl f1 :: S1
-#4 := f1
-#131 := (= f1 #47)
-#144 := (not #131)
-#640 := [hypothesis]: #144
-#49 := (f8 f11 f12)
-#135 := (= f1 #49)
-#330 := (or #135 #131)
-#145 := (iff #135 #144)
+decl f10 :: S2
+#40 := f10
+#41 := (f3 f10 f5)
+#42 := (= #41 f1)
+#43 := (not #42)
+#68 := [asserted]: #43
+#7 := (:var 0 S2)
+#14 := (f3 #7 f5)
+#588 := (pattern #14)
+#15 := (= #14 f1)
+#589 := (forall (vars (?v0 S2)) (:pat #588) #15)
+#16 := (forall (vars (?v0 S2)) #15)
+#592 := (iff #16 #589)
+#590 := (iff #15 #15)
+#591 := [refl]: #590
+#593 := [quant-intro #591]: #592
+#72 := (~ #16 #16)
+#71 := (~ #15 #15)
+#86 := [refl]: #71
+#73 := [nnf-pos #86]: #72
+#65 := [asserted]: #16
+#87 := [mp~ #65 #73]: #16
+#594 := [mp #87 #593]: #589
+#252 := (not #589)
+#167 := (or #252 #42)
+#253 := [quant-inst #40]: #167
+[unit-resolution #253 #594 #68]: false
+unsat
+ad95b138cf36827005b5ec90f511d80185776b0d 87 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S3 S1)
+decl f12 :: S3
+#43 := f12
+decl f10 :: S2
+#40 := f10
+#49 := (f3 f10 f12)
 #50 := (= #49 f1)
+decl f11 :: S3
+#41 := f11
+#47 := (f3 f10 f11)
 #48 := (= #47 f1)
-#51 := (iff #48 #50)
-#52 := (not #51)
-#148 := (iff #52 #145)
-#138 := (iff #131 #135)
-#141 := (not #138)
-#146 := (iff #141 #145)
-#147 := [rewrite]: #146
-#142 := (iff #52 #141)
-#139 := (iff #51 #138)
-#136 := (iff #50 #135)
-#137 := [rewrite]: #136
-#133 := (iff #48 #131)
-#134 := [rewrite]: #133
-#140 := [monotonicity #134 #137]: #139
-#143 := [monotonicity #140]: #142
-#149 := [trans #143 #147]: #148
-#130 := [asserted]: #52
-#152 := [mp #130 #149]: #145
-#242 := (not #145)
-#329 := (or #135 #131 #242)
-#243 := [def-axiom]: #329
-#244 := [unit-resolution #243 #152]: #330
-#641 := [unit-resolution #244 #640]: #135
-#331 := (not #135)
-#642 := (or #131 #331)
-#33 := (:var 0 S6)
-#31 := (:var 1 S5)
-#29 := (:var 2 S5)
-#30 := (f10 #29)
-#32 := (f9 #30 #31)
-#34 := (f8 #32 #33)
-#681 := (pattern #34)
-#38 := (f8 #31 #33)
-#118 := (= f1 #38)
-#177 := (not #118)
-#36 := (f8 #29 #33)
-#115 := (= f1 #36)
-#176 := (not #115)
-#160 := (or #176 #177)
-#161 := (not #160)
-#111 := (= f1 #34)
-#178 := (iff #111 #161)
-#682 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) (:pat #681) #178)
-#181 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) #178)
-#685 := (iff #181 #682)
-#683 := (iff #178 #178)
-#684 := [refl]: #683
-#686 := [quant-intro #684]: #685
-#121 := (and #115 #118)
-#124 := (iff #111 #121)
-#127 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) #124)
-#182 := (iff #127 #181)
-#179 := (iff #124 #178)
-#162 := (iff #121 #161)
-#163 := [rewrite]: #162
-#180 := [monotonicity #163]: #179
-#183 := [quant-intro #180]: #182
-#158 := (~ #127 #127)
-#173 := (~ #124 #124)
-#174 := [refl]: #173
-#159 := [nnf-pos #174]: #158
-#39 := (= #38 f1)
-#37 := (= #36 f1)
-#40 := (and #37 #39)
-#35 := (= #34 f1)
-#41 := (iff #35 #40)
-#42 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) #41)
-#128 := (iff #42 #127)
-#125 := (iff #41 #124)
-#122 := (iff #40 #121)
-#119 := (iff #39 #118)
-#120 := [rewrite]: #119
-#116 := (iff #37 #115)
-#117 := [rewrite]: #116
-#123 := [monotonicity #117 #120]: #122
-#113 := (iff #35 #111)
-#114 := [rewrite]: #113
-#126 := [monotonicity #114 #123]: #125
-#129 := [quant-intro #126]: #128
-#110 := [asserted]: #42
-#132 := [mp #110 #129]: #127
-#175 := [mp~ #132 #159]: #127
-#184 := [mp #175 #183]: #181
-#687 := [mp #184 #686]: #682
-#658 := (not #682)
-#653 := (or #658 #138)
-#335 := (or #331 #331)
-#332 := (not #335)
-#336 := (iff #131 #332)
-#659 := (or #658 #336)
-#307 := (iff #659 #653)
-#650 := (iff #653 #653)
-#308 := [rewrite]: #650
-#656 := (iff #336 #138)
-#321 := (iff #332 #135)
-#654 := (not #331)
-#648 := (iff #654 #135)
-#320 := [rewrite]: #648
-#309 := (iff #332 #654)
-#315 := (iff #335 #331)
-#652 := [rewrite]: #315
-#441 := [monotonicity #652]: #309
-#655 := [trans #441 #320]: #321
-#657 := [monotonicity #655]: #656
-#312 := [monotonicity #657]: #307
-#651 := [trans #312 #308]: #307
-#649 := [quant-inst #43 #43 #46]: #659
-#292 := [mp #649 #651]: #653
-#636 := [unit-resolution #292 #687]: #138
-#635 := (or #141 #131 #331)
-#296 := [def-axiom]: #635
-#278 := [unit-resolution #296 #636]: #642
-#643 := [unit-resolution #278 #641 #640]: false
-#645 := [lemma #643]: #131
-#334 := (or #331 #144)
-#322 := (or #331 #144 #242)
-#333 := [def-axiom]: #322
-#262 := [unit-resolution #333 #152]: #334
-#283 := [unit-resolution #262 #645]: #331
-#284 := (or #144 #135)
-#297 := (or #141 #144 #135)
-#298 := [def-axiom]: #297
-#646 := [unit-resolution #298 #636]: #284
-[unit-resolution #646 #283 #645]: false
-unsat
-3c719dc52c3c9f6d289eb68f38a893d1d68bb5d7 285 0
-#2 := false
-decl f8 :: (-> S5 S6 S1)
-decl f14 :: S6
-#50 := f14
-decl f9 :: (-> S7 S5 S5)
-decl f12 :: S5
-#45 := f12
-decl f10 :: (-> S5 S7)
-decl f11 :: S5
-#43 := f11
-#44 := (f10 f11)
-#53 := (f9 #44 f12)
-#322 := (f8 #53 f14)
-decl f1 :: S1
-#4 := f1
-#659 := (= f1 #322)
-#257 := (f8 f12 f14)
-#636 := (= f1 #257)
-#633 := (not #636)
-#347 := (f8 f11 f14)
-#363 := (= f1 #347)
-#364 := (not #363)
-#622 := (or #364 #633)
-#623 := (not #622)
-#619 := (iff #623 #659)
-#590 := (not #619)
-decl f13 :: S5
-#47 := f13
-#342 := (f8 f13 f14)
-#339 := (= f1 #342)
-#343 := (not #339)
-#492 := (or #343 #633)
-#501 := (not #492)
-#46 := (f10 f12)
-#48 := (f9 #46 f13)
-#654 := (f8 #48 f14)
-#640 := (= f1 #654)
-#502 := (iff #501 #640)
-#595 := (not #502)
-#575 := [hypothesis]: #595
-#33 := (:var 0 S6)
-#31 := (:var 1 S5)
-#29 := (:var 2 S5)
-#30 := (f10 #29)
-#32 := (f9 #30 #31)
-#34 := (f8 #32 #33)
-#688 := (pattern #34)
-#38 := (f8 #31 #33)
-#125 := (= f1 #38)
-#184 := (not #125)
-#36 := (f8 #29 #33)
-#122 := (= f1 #36)
-#183 := (not #122)
-#167 := (or #183 #184)
-#168 := (not #167)
-#118 := (= f1 #34)
-#185 := (iff #118 #168)
-#689 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) (:pat #688) #185)
-#188 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) #185)
-#692 := (iff #188 #689)
-#690 := (iff #185 #185)
-#691 := [refl]: #690
-#693 := [quant-intro #691]: #692
-#128 := (and #122 #125)
-#131 := (iff #118 #128)
-#134 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) #131)
-#189 := (iff #134 #188)
-#186 := (iff #131 #185)
-#169 := (iff #128 #168)
-#170 := [rewrite]: #169
-#187 := [monotonicity #170]: #186
-#190 := [quant-intro #187]: #189
-#165 := (~ #134 #134)
-#180 := (~ #131 #131)
-#181 := [refl]: #180
-#166 := [nnf-pos #181]: #165
-#39 := (= #38 f1)
-#37 := (= #36 f1)
-#40 := (and #37 #39)
-#35 := (= #34 f1)
-#41 := (iff #35 #40)
-#42 := (forall (vars (?v0 S5) (?v1 S5) (?v2 S6)) #41)
-#135 := (iff #42 #134)
-#132 := (iff #41 #131)
-#129 := (iff #40 #128)
-#126 := (iff #39 #125)
-#127 := [rewrite]: #126
-#123 := (iff #37 #122)
-#124 := [rewrite]: #123
-#130 := [monotonicity #124 #127]: #129
-#120 := (iff #35 #118)
-#121 := [rewrite]: #120
-#133 := [monotonicity #121 #130]: #132
-#136 := [quant-intro #133]: #135
-#117 := [asserted]: #42
-#139 := [mp #117 #136]: #134
-#182 := [mp~ #139 #166]: #134
-#191 := [mp #182 #190]: #188
-#694 := [mp #191 #693]: #689
-#314 := (not #689)
-#506 := (or #314 #502)
-#608 := (or #633 #343)
-#490 := (not #608)
-#491 := (iff #640 #490)
-#507 := (or #314 #491)
-#601 := (iff #507 #506)
-#602 := (iff #506 #506)
-#589 := [rewrite]: #602
-#504 := (iff #491 #502)
-#600 := (iff #640 #501)
-#503 := (iff #600 #502)
-#496 := [rewrite]: #503
-#485 := (iff #491 #600)
-#596 := (iff #490 #501)
-#451 := (iff #608 #492)
-#599 := [rewrite]: #451
-#597 := [monotonicity #599]: #596
-#500 := [monotonicity #597]: #485
-#505 := [trans #500 #496]: #504
-#598 := [monotonicity #505]: #601
-#591 := [trans #598 #589]: #601
-#508 := [quant-inst #45 #47 #50]: #507
-#583 := [mp #508 #591]: #506
-#576 := [unit-resolution #583 #694 #575]: false
-#577 := [lemma #576]: #502
-#641 := (not #640)
-#365 := (or #364 #641)
-#351 := (not #365)
-#49 := (f9 #44 #48)
-#51 := (f8 #49 f14)
-#138 := (= f1 #51)
-#151 := (not #138)
-#578 := [hypothesis]: #151
-#579 := (or #138 #365)
-#366 := (iff #138 #351)
-#637 := (or #314 #366)
-#359 := [quant-inst #43 #48 #50]: #637
-#574 := [unit-resolution #359 #694]: #366
-#349 := (not #366)
-#350 := (or #349 #138 #365)
-#352 := [def-axiom]: #350
-#565 := [unit-resolution #352 #574]: #579
-#566 := [unit-resolution #565 #578]: #365
-#605 := (or #314 #619)
-#624 := (iff #659 #623)
-#621 := (or #314 #624)
-#626 := (iff #621 #605)
-#469 := (iff #605 #605)
-#470 := [rewrite]: #469
-#620 := (iff #624 #619)
-#625 := [rewrite]: #620
-#468 := [monotonicity #625]: #626
-#612 := [trans #468 #470]: #626
-#627 := [quant-inst #43 #45 #50]: #621
-#613 := [mp #627 #612]: #605
-#568 := [unit-resolution #613 #694]: #619
-#554 := (or #590 #623)
-#661 := (not #659)
-#327 := (or #343 #661)
-#663 := (not #327)
-#54 := (f10 #53)
-#55 := (f9 #54 f13)
-#56 := (f8 #55 f14)
-#142 := (= f1 #56)
-#337 := (or #142 #138)
-#152 := (iff #142 #151)
-#57 := (= #56 f1)
-#52 := (= #51 f1)
-#58 := (iff #52 #57)
-#59 := (not #58)
-#155 := (iff #59 #152)
-#145 := (iff #138 #142)
-#148 := (not #145)
-#153 := (iff #148 #152)
-#154 := [rewrite]: #153
-#149 := (iff #59 #148)
-#146 := (iff #58 #145)
-#143 := (iff #57 #142)
-#144 := [rewrite]: #143
-#140 := (iff #52 #138)
-#141 := [rewrite]: #140
-#147 := [monotonicity #141 #144]: #146
-#150 := [monotonicity #147]: #149
-#156 := [trans #150 #154]: #155
-#137 := [asserted]: #59
-#159 := [mp #137 #156]: #152
-#249 := (not #152)
-#336 := (or #142 #138 #249)
-#250 := [def-axiom]: #336
-#251 := [unit-resolution #250 #159]: #337
-#569 := [unit-resolution #251 #578]: #142
-#338 := (not #142)
-#567 := (or #338 #663)
-#660 := (iff #142 #663)
-#319 := (or #314 #660)
-#316 := (or #661 #343)
-#448 := (not #316)
-#655 := (iff #142 #448)
-#657 := (or #314 #655)
-#658 := (iff #657 #319)
-#642 := (iff #319 #319)
-#303 := [rewrite]: #642
-#666 := (iff #655 #660)
-#664 := (iff #448 #663)
-#328 := (iff #316 #327)
-#662 := [rewrite]: #328
-#665 := [monotonicity #662]: #664
-#656 := [monotonicity #665]: #666
-#299 := [monotonicity #656]: #658
-#304 := [trans #299 #303]: #658
-#315 := [quant-inst #53 #47 #50]: #657
-#305 := [mp #315 #304]: #319
-#570 := [unit-resolution #305 #694]: #660
-#643 := (not #660)
-#650 := (or #643 #338 #663)
-#652 := [def-axiom]: #650
-#571 := [unit-resolution #652 #570]: #567
-#551 := [unit-resolution #571 #569]: #663
-#645 := (or #327 #659)
-#646 := [def-axiom]: #645
-#552 := [unit-resolution #646 #551]: #659
-#584 := (or #590 #623 #661)
-#585 := [def-axiom]: #584
-#555 := [unit-resolution #585 #552]: #554
-#556 := [unit-resolution #555 #568]: #623
-#614 := (or #622 #363)
-#580 := [def-axiom]: #614
-#557 := [unit-resolution #580 #556]: #363
-#639 := (or #351 #364 #641)
-#348 := [def-axiom]: #639
-#558 := [unit-resolution #348 #557 #566]: #641
-#306 := (or #327 #339)
-#644 := [def-axiom]: #306
-#559 := [unit-resolution #644 #551]: #339
-#582 := (or #622 #636)
-#592 := [def-axiom]: #582
-#560 := [unit-resolution #592 #556]: #636
-#617 := (or #501 #343 #633)
-#611 := [def-axiom]: #617
-#561 := [unit-resolution #611 #560 #559]: #501
-#449 := (or #595 #492 #640)
-#450 := [def-axiom]: #449
-#562 := [unit-resolution #450 #561 #558 #577]: false
-#563 := [lemma #562]: #138
-#553 := (or #151 #351)
-#630 := (or #349 #151 #351)
-#631 := [def-axiom]: #630
-#564 := [unit-resolution #631 #574]: #553
-#542 := [unit-resolution #564 #563]: #351
-#638 := (or #365 #640)
-#635 := [def-axiom]: #638
-#543 := [unit-resolution #635 #542]: #640
-#618 := (or #595 #501 #641)
-#447 := [def-axiom]: #618
-#545 := [unit-resolution #447 #543 #577]: #501
-#610 := (or #492 #636)
-#616 := [def-axiom]: #610
-#546 := [unit-resolution #616 #545]: #636
-#360 := (or #365 #363)
-#634 := [def-axiom]: #360
-#547 := [unit-resolution #634 #542]: #363
-#593 := (or #623 #364 #633)
-#594 := [def-axiom]: #593
-#548 := [unit-resolution #594 #547 #546]: #623
-#341 := (or #338 #151)
-#329 := (or #338 #151 #249)
-#340 := [def-axiom]: #329
-#269 := [unit-resolution #340 #159]: #341
-#549 := [unit-resolution #269 #563]: #338
-#544 := (or #142 #327)
-#649 := (or #643 #142 #327)
-#285 := [def-axiom]: #649
-#550 := [unit-resolution #285 #570]: #544
-#536 := [unit-resolution #550 #549]: #327
-#615 := (or #492 #339)
-#609 := [def-axiom]: #615
-#532 := [unit-resolution #609 #545]: #339
-#647 := (or #663 #343 #661)
-#648 := [def-axiom]: #647
-#533 := [unit-resolution #648 #532 #536]: #661
-#586 := (or #590 #622 #659)
-#587 := [def-axiom]: #586
-#534 := [unit-resolution #587 #533 #548]: #590
-[unit-resolution #613 #694 #534]: false
-unsat
-93dc18f04c0bd27068136e216aafda64d0ca91ea 18 0
-#2 := false
-decl f9 :: S5
-#36 := f9
-#37 := (= f9 f9)
-#38 := (not #37)
-#119 := (iff #38 false)
-#1 := true
-#114 := (not true)
-#117 := (iff #114 false)
-#118 := [rewrite]: #117
-#115 := (iff #38 #114)
-#111 := (iff #37 true)
-#113 := [rewrite]: #111
-#116 := [monotonicity #113]: #115
-#120 := [trans #116 #118]: #119
-#110 := [asserted]: #38
-[mp #110 #120]: false
-unsat
-8021f8e09eb3e47791aed2bed0dafccd5948187d 69 0
-#2 := false
-decl f4 :: (-> S2 S1)
-decl f5 :: S2
-#16 := f5
-#19 := (f4 f5)
-decl f1 :: S1
-#4 := f1
-#66 := (= f1 #19)
-#70 := (not #66)
-#20 := (= #19 f1)
-#21 := (not #20)
-#71 := (iff #21 #70)
-#68 := (iff #20 #66)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#65 := [asserted]: #21
-#75 := [mp #65 #72]: #70
-decl f3 :: (-> S2 S1)
-#17 := (f3 f5)
-#61 := (= f1 #17)
-#18 := (= #17 f1)
-#63 := (iff #18 #61)
-#64 := [rewrite]: #63
-#60 := [asserted]: #18
-#67 := [mp #60 #64]: #61
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#10 := (pattern #9)
-#12 := (f4 #8)
-#45 := (= f1 #12)
-#42 := (= f1 #9)
-#51 := (not #42)
-#52 := (or #51 #45)
-#57 := (forall (vars (?v0 S2)) (:pat #10) #52)
-#85 := (~ #57 #57)
-#83 := (~ #52 #52)
-#84 := [refl]: #83
-#86 := [nnf-pos #84]: #85
-#13 := (= #12 f1)
-#11 := (= #9 f1)
-#14 := (implies #11 #13)
-#15 := (forall (vars (?v0 S2)) (:pat #10) #14)
-#58 := (iff #15 #57)
-#55 := (iff #14 #52)
-#48 := (implies #42 #45)
-#53 := (iff #48 #52)
-#54 := [rewrite]: #53
-#49 := (iff #14 #48)
-#46 := (iff #13 #45)
-#47 := [rewrite]: #46
-#43 := (iff #11 #42)
-#44 := [rewrite]: #43
-#50 := [monotonicity #44 #47]: #49
-#56 := [trans #50 #54]: #55
-#59 := [quant-intro #56]: #58
-#41 := [asserted]: #15
-#62 := [mp #41 #59]: #57
-#74 := [mp~ #62 #86]: #57
-#137 := (not #61)
-#139 := (not #57)
-#226 := (or #139 #137 #66)
-#224 := (or #137 #66)
-#217 := (or #139 #224)
-#229 := (iff #217 #226)
-#157 := [rewrite]: #229
-#228 := [quant-inst #16]: #217
-#230 := [mp #228 #157]: #226
-[unit-resolution #230 #74 #67 #75]: false
-unsat
-51102b6663906c70b84f1c6e3a1a2e429b49188d 112 0
-#2 := false
-decl f5 :: (-> S2 S1)
-decl f6 :: S2
-#19 := f6
-#24 := (f5 f6)
-decl f1 :: S1
-#4 := f1
-#82 := (= f1 #24)
-#86 := (not #82)
-#25 := (= #24 f1)
-#26 := (not #25)
-#87 := (iff #26 #86)
-#84 := (iff #25 #82)
-#85 := [rewrite]: #84
-#88 := [monotonicity #85]: #87
-#81 := [asserted]: #26
-#91 := [mp #81 #88]: #86
-decl f4 :: (-> S2 S1)
-#22 := (f4 f6)
-#77 := (= f1 #22)
-#23 := (= #22 f1)
-#79 := (iff #23 #77)
-#80 := [rewrite]: #79
-#76 := [asserted]: #23
-#83 := [mp #76 #80]: #77
-decl f3 :: (-> S2 S1)
-#20 := (f3 f6)
-#72 := (= f1 #20)
-#21 := (= #20 f1)
-#74 := (iff #21 #72)
-#75 := [rewrite]: #74
-#71 := [asserted]: #21
-#78 := [mp #71 #75]: #72
-#8 := (:var 0 S2)
-#10 := (f4 #8)
-#9 := (f3 #8)
-#11 := (pattern #9 #10)
-#15 := (f5 #8)
-#56 := (= f1 #15)
-#50 := (= f1 #10)
-#105 := (not #50)
-#47 := (= f1 #9)
-#92 := (not #47)
-#112 := (or #92 #105 #56)
-#117 := (forall (vars (?v0 S2)) (:pat #11) #112)
-#53 := (and #47 #50)
-#62 := (not #53)
-#63 := (or #62 #56)
-#68 := (forall (vars (?v0 S2)) (:pat #11) #63)
-#118 := (iff #68 #117)
-#115 := (iff #63 #112)
-#93 := (or #92 #105)
-#109 := (or #93 #56)
-#113 := (iff #109 #112)
-#114 := [rewrite]: #113
-#110 := (iff #63 #109)
-#107 := (iff #62 #93)
-#94 := (not #93)
-#97 := (not #94)
-#96 := (iff #97 #93)
-#106 := [rewrite]: #96
-#98 := (iff #62 #97)
-#99 := (iff #53 #94)
-#100 := [rewrite]: #99
-#95 := [monotonicity #100]: #98
-#108 := [trans #95 #106]: #107
-#111 := [monotonicity #108]: #110
-#116 := [trans #111 #114]: #115
-#119 := [quant-intro #116]: #118
-#103 := (~ #68 #68)
-#101 := (~ #63 #63)
-#102 := [refl]: #101
-#104 := [nnf-pos #102]: #103
-#16 := (= #15 f1)
-#13 := (= #10 f1)
-#12 := (= #9 f1)
-#14 := (and #12 #13)
-#17 := (implies #14 #16)
-#18 := (forall (vars (?v0 S2)) (:pat #11) #17)
-#69 := (iff #18 #68)
-#66 := (iff #17 #63)
-#59 := (implies #53 #56)
-#64 := (iff #59 #63)
-#65 := [rewrite]: #64
-#60 := (iff #17 #59)
-#57 := (iff #16 #56)
-#58 := [rewrite]: #57
-#54 := (iff #14 #53)
-#51 := (iff #13 #50)
-#52 := [rewrite]: #51
-#48 := (iff #12 #47)
-#49 := [rewrite]: #48
-#55 := [monotonicity #49 #52]: #54
-#61 := [monotonicity #55 #58]: #60
-#67 := [trans #61 #65]: #66
-#70 := [quant-intro #67]: #69
-#46 := [asserted]: #18
-#73 := [mp #46 #70]: #68
-#90 := [mp~ #73 #104]: #68
-#120 := [mp #90 #119]: #117
-#178 := (not #77)
-#265 := (not #72)
-#267 := (not #117)
-#258 := (or #267 #265 #178 #82)
-#179 := (or #265 #178 #82)
-#269 := (or #267 #179)
-#198 := (iff #269 #258)
-#271 := [rewrite]: #198
-#270 := [quant-inst #19]: #269
-#268 := [mp #270 #271]: #258
-[unit-resolution #268 #120 #78 #83 #91]: false
-unsat
-1191e209015c2f2f439f124434700d861e089600 149 0
-#2 := false
-decl f3 :: (-> S2 S1)
-decl f6 :: S2
-#21 := f6
-#22 := (f3 f6)
-decl f1 :: S1
-#4 := f1
-#84 := (= f1 #22)
-#264 := (not #84)
-decl f5 :: (-> S2 S1)
-#27 := (f5 f6)
-#95 := (= f1 #27)
-#178 := (or #264 #95)
-decl f4 :: (-> S2 S1)
-#24 := (f4 f6)
-#88 := (= f1 #24)
-#176 := (not #88)
-#268 := (or #176 #95)
-#266 := (not #268)
-#265 := (not #178)
-#586 := (or #265 #266)
-#375 := (not #586)
-#579 := [hypothesis]: #586
-#8 := (:var 0 S2)
-#11 := (f4 #8)
-#12 := (pattern #11)
-#9 := (f3 #8)
-#10 := (pattern #9)
-#65 := (= f1 #11)
-#71 := (not #65)
-#14 := (f5 #8)
-#53 := (= f1 #14)
-#72 := (or #53 #71)
-#116 := (not #72)
-#50 := (= f1 #9)
-#59 := (not #50)
-#60 := (or #59 #53)
-#105 := (not #60)
-#106 := (or #105 #116)
-#107 := (not #106)
-#108 := (forall (vars (?v0 S2)) (:pat #10 #12) #107)
-#77 := (and #60 #72)
-#80 := (forall (vars (?v0 S2)) (:pat #10 #12) #77)
-#109 := (iff #80 #108)
-#110 := (iff #77 #107)
-#111 := [rewrite]: #110
-#117 := [quant-intro #111]: #109
-#114 := (~ #80 #80)
-#112 := (~ #77 #77)
-#113 := [refl]: #112
-#115 := [nnf-pos #113]: #114
-#15 := (= #14 f1)
-#17 := (= #11 f1)
-#18 := (implies #17 #15)
-#13 := (= #9 f1)
-#16 := (implies #13 #15)
-#19 := (and #16 #18)
-#20 := (forall (vars (?v0 S2)) (:pat #10 #12) #19)
-#81 := (iff #20 #80)
-#78 := (iff #19 #77)
-#75 := (iff #18 #72)
-#68 := (implies #65 #53)
-#73 := (iff #68 #72)
-#74 := [rewrite]: #73
-#69 := (iff #18 #68)
-#54 := (iff #15 #53)
-#55 := [rewrite]: #54
-#66 := (iff #17 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67 #55]: #69
-#76 := [trans #70 #74]: #75
-#63 := (iff #16 #60)
-#56 := (implies #50 #53)
-#61 := (iff #56 #60)
-#62 := [rewrite]: #61
-#57 := (iff #16 #56)
-#51 := (iff #13 #50)
-#52 := [rewrite]: #51
-#58 := [monotonicity #52 #55]: #57
-#64 := [trans #58 #62]: #63
-#79 := [monotonicity #64 #76]: #78
-#82 := [quant-intro #79]: #81
-#49 := [asserted]: #20
-#85 := [mp #49 #82]: #80
-#103 := [mp~ #85 #115]: #80
-#118 := [mp #103 #117]: #108
-#255 := (not #108)
-#589 := (or #255 #375)
-#263 := (or #95 #176)
-#177 := (not #263)
-#256 := (or #265 #177)
-#267 := (not #256)
-#590 := (or #255 #267)
-#592 := (iff #590 #589)
-#593 := (iff #589 #589)
-#583 := [rewrite]: #593
-#582 := (iff #267 #375)
-#588 := (iff #256 #586)
-#270 := (iff #177 #266)
-#196 := (iff #263 #268)
-#269 := [rewrite]: #196
-#249 := [monotonicity #269]: #270
-#243 := [monotonicity #249]: #588
-#254 := [monotonicity #243]: #582
-#587 := [monotonicity #254]: #592
-#241 := [trans #587 #583]: #592
-#591 := [quant-inst #21]: #590
-#246 := [mp #591 #241]: #589
-#217 := [unit-resolution #246 #118 #579]: false
-#218 := [lemma #217]: #375
-#574 := (or #586 #178)
-#575 := [def-axiom]: #574
-#580 := [unit-resolution #575 #218]: #178
-#578 := (or #265 #264)
-#99 := (not #95)
-#28 := (= #27 f1)
-#29 := (not #28)
-#100 := (iff #29 #99)
-#97 := (iff #28 #95)
-#98 := [rewrite]: #97
-#101 := [monotonicity #98]: #100
-#94 := [asserted]: #29
-#104 := [mp #94 #101]: #99
-#569 := (or #265 #264 #95)
-#230 := [def-axiom]: #569
-#581 := [unit-resolution #230 #104]: #578
-#567 := [unit-resolution #581 #580]: #264
-#570 := (or #586 #268)
-#576 := [def-axiom]: #570
-#568 := [unit-resolution #576 #218]: #268
-#274 := (or #266 #176)
-#572 := (or #266 #176 #95)
-#573 := [def-axiom]: #572
-#290 := [unit-resolution #573 #104]: #274
-#291 := [unit-resolution #290 #568]: #176
-#91 := (or #84 #88)
-#25 := (= #24 f1)
-#23 := (= #22 f1)
-#26 := (or #23 #25)
-#92 := (iff #26 #91)
-#89 := (iff #25 #88)
-#90 := [rewrite]: #89
-#86 := (iff #23 #84)
-#87 := [rewrite]: #86
-#93 := [monotonicity #87 #90]: #92
-#83 := [asserted]: #26
-#96 := [mp #83 #93]: #91
-[unit-resolution #96 #291 #567]: false
-unsat
-45f8ffe676ed981a383aaab6faaf520b9ff236c9 69 0
-#2 := false
-decl f4 :: (-> S2 S1)
-decl f5 :: S2
-#16 := f5
-#19 := (f4 f5)
-decl f1 :: S1
-#4 := f1
-#66 := (= f1 #19)
-#70 := (not #66)
-#20 := (= #19 f1)
-#21 := (not #20)
-#71 := (iff #21 #70)
-#68 := (iff #20 #66)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#65 := [asserted]: #21
-#75 := [mp #65 #72]: #70
-decl f3 :: (-> S2 S1)
-#17 := (f3 f5)
-#61 := (= f1 #17)
-#18 := (= #17 f1)
-#63 := (iff #18 #61)
-#64 := [rewrite]: #63
-#60 := [asserted]: #18
-#67 := [mp #60 #64]: #61
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#10 := (pattern #9)
-#12 := (f4 #8)
-#45 := (= f1 #12)
-#42 := (= f1 #9)
-#51 := (not #42)
-#52 := (or #51 #45)
-#57 := (forall (vars (?v0 S2)) (:pat #10) #52)
-#85 := (~ #57 #57)
-#83 := (~ #52 #52)
-#84 := [refl]: #83
-#86 := [nnf-pos #84]: #85
-#13 := (= #12 f1)
-#11 := (= #9 f1)
-#14 := (implies #11 #13)
-#15 := (forall (vars (?v0 S2)) (:pat #10) #14)
-#58 := (iff #15 #57)
-#55 := (iff #14 #52)
-#48 := (implies #42 #45)
-#53 := (iff #48 #52)
-#54 := [rewrite]: #53
-#49 := (iff #14 #48)
-#46 := (iff #13 #45)
-#47 := [rewrite]: #46
-#43 := (iff #11 #42)
-#44 := [rewrite]: #43
-#50 := [monotonicity #44 #47]: #49
-#56 := [trans #50 #54]: #55
-#59 := [quant-intro #56]: #58
-#41 := [asserted]: #15
-#62 := [mp #41 #59]: #57
-#74 := [mp~ #62 #86]: #57
-#137 := (not #61)
-#139 := (not #57)
-#226 := (or #139 #137 #66)
-#224 := (or #137 #66)
-#217 := (or #139 #224)
-#229 := (iff #217 #226)
-#157 := [rewrite]: #229
-#228 := [quant-inst #16]: #217
-#230 := [mp #228 #157]: #226
-[unit-resolution #230 #74 #67 #75]: false
-unsat
-ceabafba9f0db45264556e8d9525b667725281c7 76 0
-#2 := false
-decl f4 :: (-> S2 S1)
-decl f5 :: S2
-#15 := f5
-#18 := (f4 f5)
-decl f1 :: S1
-#4 := f1
-#65 := (= f1 #18)
-#69 := (not #65)
-#19 := (= #18 f1)
-#20 := (not #19)
-#70 := (iff #20 #69)
-#67 := (iff #19 #65)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#64 := [asserted]: #20
-#74 := [mp #64 #71]: #69
-decl f3 :: (-> S2 S1)
-#16 := (f3 f5)
-#60 := (= f1 #16)
-#17 := (= #16 f1)
-#62 := (iff #17 #60)
-#63 := [rewrite]: #62
-#59 := [asserted]: #17
-#66 := [mp #59 #63]: #60
-#8 := (:var 0 S2)
-#11 := (f4 #8)
-#555 := (pattern #11)
-#9 := (f3 #8)
-#554 := (pattern #9)
-#44 := (= f1 #11)
-#41 := (= f1 #9)
-#50 := (not #41)
-#51 := (or #50 #44)
-#556 := (forall (vars (?v0 S2)) (:pat #554 #555) #51)
-#56 := (forall (vars (?v0 S2)) #51)
-#559 := (iff #56 #556)
-#557 := (iff #51 #51)
-#558 := [refl]: #557
-#560 := [quant-intro #558]: #559
-#84 := (~ #56 #56)
-#82 := (~ #51 #51)
-#83 := [refl]: #82
-#85 := [nnf-pos #83]: #84
-#12 := (= #11 f1)
-#10 := (= #9 f1)
-#13 := (implies #10 #12)
-#14 := (forall (vars (?v0 S2)) #13)
-#57 := (iff #14 #56)
-#54 := (iff #13 #51)
-#47 := (implies #41 #44)
-#52 := (iff #47 #51)
-#53 := [rewrite]: #52
-#48 := (iff #13 #47)
-#45 := (iff #12 #44)
-#46 := [rewrite]: #45
-#42 := (iff #10 #41)
-#43 := [rewrite]: #42
-#49 := [monotonicity #43 #46]: #48
-#55 := [trans #49 #53]: #54
-#58 := [quant-intro #55]: #57
-#40 := [asserted]: #14
-#61 := [mp #40 #58]: #56
-#73 := [mp~ #61 #85]: #56
-#561 := [mp #73 #560]: #556
-#136 := (not #60)
-#138 := (not #556)
-#225 := (or #138 #136 #65)
-#223 := (or #136 #65)
-#216 := (or #138 #223)
-#228 := (iff #216 #225)
-#156 := [rewrite]: #228
-#227 := [quant-inst #15]: #216
-#229 := [mp #227 #156]: #225
-[unit-resolution #229 #561 #66 #74]: false
-unsat
-7cd7dbb3fbfb0bc76acedbcf070880f3e3e3d434 60 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f4 :: S3
-#9 := f4
-decl f9 :: S2
-#39 := f9
-#40 := (f3 f9 f4)
-decl f1 :: S1
-#4 := f1
-#116 := (= f1 #40)
-#41 := (= #40 f1)
-#42 := (not #41)
-#43 := (not #42)
-#128 := (iff #43 #116)
-#120 := (not #116)
-#123 := (not #120)
-#126 := (iff #123 #116)
-#127 := [rewrite]: #126
-#124 := (iff #43 #123)
-#121 := (iff #42 #120)
-#118 := (iff #41 #116)
-#119 := [rewrite]: #118
-#122 := [monotonicity #119]: #121
-#125 := [monotonicity #122]: #124
-#129 := [trans #125 #127]: #128
-#115 := [asserted]: #43
-#132 := [mp #115 #129]: #116
-#8 := (:var 0 S2)
-#10 := (f3 #8 f4)
-#640 := (pattern #10)
-#64 := (= f1 #10)
-#67 := (not #64)
-#641 := (forall (vars (?v0 S2)) (:pat #640) #67)
-#70 := (forall (vars (?v0 S2)) #67)
-#644 := (iff #70 #641)
-#642 := (iff #67 #67)
-#643 := [refl]: #642
-#645 := [quant-intro #643]: #644
-#146 := (~ #70 #70)
-#144 := (~ #67 #67)
-#145 := [refl]: #144
-#147 := [nnf-pos #145]: #146
-#11 := (= #10 f1)
-#12 := (not #11)
-#13 := (forall (vars (?v0 S2)) #12)
-#71 := (iff #13 #70)
-#68 := (iff #12 #67)
-#65 := (iff #11 #64)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#72 := [quant-intro #69]: #71
-#63 := [asserted]: #13
-#75 := [mp #63 #72]: #70
-#131 := [mp~ #75 #147]: #70
-#646 := [mp #131 #645]: #641
-#223 := (not #641)
-#310 := (or #223 #120)
-#224 := [quant-inst #39]: #310
-[unit-resolution #224 #646 #132]: false
-unsat
-71b592381f7787562afdf512ef22356644e574ef 48 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f5 :: S3
-#14 := f5
-decl f9 :: S2
-#39 := f9
-#40 := (f3 f9 f5)
-decl f1 :: S1
-#4 := f1
-#115 := (= f1 #40)
-#119 := (not #115)
-#41 := (= #40 f1)
-#42 := (not #41)
-#120 := (iff #42 #119)
-#117 := (iff #41 #115)
-#118 := [rewrite]: #117
-#121 := [monotonicity #118]: #120
-#114 := [asserted]: #42
-#124 := [mp #114 #121]: #119
-#8 := (:var 0 S2)
-#15 := (f3 #8 f5)
-#639 := (pattern #15)
-#73 := (= f1 #15)
-#640 := (forall (vars (?v0 S2)) (:pat #639) #73)
-#77 := (forall (vars (?v0 S2)) #73)
-#643 := (iff #77 #640)
-#641 := (iff #73 #73)
-#642 := [refl]: #641
-#644 := [quant-intro #642]: #643
-#126 := (~ #77 #77)
-#125 := (~ #73 #73)
-#140 := [refl]: #125
-#127 := [nnf-pos #140]: #126
-#16 := (= #15 f1)
-#17 := (forall (vars (?v0 S2)) #16)
-#78 := (iff #17 #77)
-#75 := (iff #16 #73)
-#76 := [rewrite]: #75
-#79 := [quant-intro #76]: #78
-#72 := [asserted]: #17
-#82 := [mp #72 #79]: #77
-#141 := [mp~ #82 #127]: #77
-#645 := [mp #141 #644]: #640
-#215 := (not #640)
-#302 := (or #215 #115)
-#216 := [quant-inst #39]: #302
-[unit-resolution #216 #645 #124]: false
-unsat
-164d5a6bdaf120b4948f5b45d9c26eb765a67512 124 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
+#51 := (or #48 #50)
+#270 := (not #51)
+#258 := [hypothesis]: #270
 decl f6 :: (-> S4 S3 S3)
-decl f11 :: S3
-#42 := f11
-decl f7 :: (-> S3 S4)
-decl f10 :: S3
-#40 := f10
-#41 := (f7 f10)
-#43 := (f6 #41 f11)
-decl f9 :: S2
-#39 := f9
-#44 := (f3 f9 #43)
-decl f1 :: S1
-#4 := f1
-#125 := (= f1 #44)
-#144 := (not #125)
-#648 := [hypothesis]: #144
-#48 := (f3 f9 f11)
-#132 := (= f1 #48)
-#46 := (f3 f9 f10)
-#129 := (= f1 #46)
-#135 := (or #129 #132)
-#336 := (or #135 #125)
-#145 := (iff #135 #144)
-#49 := (= #48 f1)
-#47 := (= #46 f1)
-#50 := (or #47 #49)
-#45 := (= #44 f1)
-#51 := (iff #45 #50)
-#52 := (not #51)
-#148 := (iff #52 #145)
-#138 := (iff #125 #135)
-#141 := (not #138)
-#146 := (iff #141 #145)
-#147 := [rewrite]: #146
-#142 := (iff #52 #141)
-#139 := (iff #51 #138)
-#136 := (iff #50 #135)
-#133 := (iff #49 #132)
-#134 := [rewrite]: #133
-#130 := (iff #47 #129)
-#131 := [rewrite]: #130
-#137 := [monotonicity #131 #134]: #136
-#127 := (iff #45 #125)
-#128 := [rewrite]: #127
-#140 := [monotonicity #128 #137]: #139
-#143 := [monotonicity #140]: #142
-#149 := [trans #143 #147]: #148
-#124 := [asserted]: #52
-#152 := [mp #124 #149]: #145
-#262 := (not #145)
-#335 := (or #135 #125 #262)
-#332 := [def-axiom]: #335
-#315 := [unit-resolution #332 #152]: #336
-#320 := [unit-resolution #315 #648]: #135
-#322 := (not #135)
-#651 := (or #125 #322)
+decl f7 :: (-> S5 S3 S4)
+decl f8 :: S5
+#18 := f8
+#42 := (f7 f8 f11)
+#44 := (f6 #42 f12)
+#45 := (f3 f10 #44)
+#46 := (= #45 f1)
+#584 := (or #46 #51)
+#79 := (not #46)
+#80 := (iff #79 #51)
+#52 := (iff #46 #51)
+#53 := (not #52)
+#81 := (iff #53 #80)
+#82 := [rewrite]: #81
+#78 := [asserted]: #53
+#85 := [mp #78 #82]: #80
+#269 := (not #80)
+#246 := (or #46 #51 #269)
+#377 := [def-axiom]: #246
+#257 := [unit-resolution #377 #85]: #584
+#591 := [unit-resolution #257 #258]: #46
+#571 := (or #79 #51)
 #21 := (:var 0 S3)
 #19 := (:var 1 S3)
-#20 := (f7 #19)
+#20 := (f7 f8 #19)
 #22 := (f6 #20 #21)
-#18 := (:var 2 S2)
-#23 := (f3 #18 #22)
-#674 := (pattern #23)
-#27 := (f3 #18 #21)
-#98 := (= f1 #27)
-#25 := (f3 #18 #19)
-#95 := (= f1 #25)
-#101 := (or #95 #98)
-#91 := (= f1 #23)
-#104 := (iff #91 #101)
-#675 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #674) #104)
-#107 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #104)
-#678 := (iff #107 #675)
-#676 := (iff #104 #104)
-#677 := [refl]: #676
-#679 := [quant-intro #677]: #678
-#156 := (~ #107 #107)
-#170 := (~ #104 #104)
-#171 := [refl]: #170
-#157 := [nnf-pos #171]: #156
+#17 := (:var 2 S2)
+#23 := (f3 #17 #22)
+#610 := (pattern #23)
+#27 := (f3 #17 #21)
 #28 := (= #27 f1)
+#25 := (f3 #17 #19)
 #26 := (= #25 f1)
 #29 := (or #26 #28)
 #24 := (= #23 f1)
 #30 := (iff #24 #29)
+#611 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #610) #30)
 #31 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #30)
-#108 := (iff #31 #107)
-#105 := (iff #30 #104)
-#102 := (iff #29 #101)
-#99 := (iff #28 #98)
-#100 := [rewrite]: #99
-#96 := (iff #26 #95)
-#97 := [rewrite]: #96
-#103 := [monotonicity #97 #100]: #102
-#93 := (iff #24 #91)
-#94 := [rewrite]: #93
-#106 := [monotonicity #94 #103]: #105
-#109 := [quant-intro #106]: #108
-#90 := [asserted]: #31
-#112 := [mp #90 #109]: #107
-#172 := [mp~ #112 #157]: #107
-#680 := [mp #172 #679]: #675
-#321 := (not #675)
-#655 := (or #321 #138)
-#656 := [quant-inst #39 #40 #42]: #655
-#308 := [unit-resolution #656 #680]: #138
-#657 := (or #141 #125 #322)
-#658 := [def-axiom]: #657
-#292 := [unit-resolution #658 #308]: #651
-#635 := [unit-resolution #292 #320 #648]: false
-#296 := [lemma #635]: #125
-#309 := (or #322 #144)
-#652 := (or #322 #144 #262)
-#654 := [def-axiom]: #652
-#441 := [unit-resolution #654 #152]: #309
-#297 := [unit-resolution #441 #296]: #322
-#298 := (or #144 #135)
-#653 := (or #141 #144 #135)
-#659 := [def-axiom]: #653
-#299 := [unit-resolution #659 #308]: #298
-[unit-resolution #299 #297 #296]: false
-unsat
-d1bc5c257411f66b4000ce061c39762e6b5b7a04 160 0
-#2 := false
+#614 := (iff #31 #611)
+#612 := (iff #30 #30)
+#613 := [refl]: #612
+#615 := [quant-intro #613]: #614
+#89 := (~ #31 #31)
+#103 := (~ #30 #30)
+#104 := [refl]: #103
+#90 := [nnf-pos #104]: #89
+#76 := [asserted]: #31
+#105 := [mp~ #76 #90]: #31
+#616 := [mp #105 #615]: #611
+#592 := (not #611)
+#593 := (or #592 #52)
+#594 := [quant-inst #40 #41 #43]: #593
+#229 := [unit-resolution #594 #616]: #52
+#585 := (or #53 #79 #51)
+#244 := [def-axiom]: #585
+#233 := [unit-resolution #244 #229]: #571
+#234 := [unit-resolution #233 #591 #258]: false
+#235 := [lemma #234]: #51
+#588 := (or #79 #270)
+#273 := (or #79 #270 #269)
+#252 := [def-axiom]: #273
+#590 := [unit-resolution #252 #85]: #588
+#236 := [unit-resolution #590 #235]: #79
+#573 := (or #46 #270)
+#589 := (or #53 #46 #270)
+#595 := [def-axiom]: #589
+#574 := [unit-resolution #595 #229]: #573
+[unit-resolution #574 #236 #235]: false
+unsat
+a358148b5f0eff69cab7c01e442584acaffb3f96 121 0
+#2 := false
+decl f1 :: S1
+#3 := f1
 decl f3 :: (-> S2 S3 S1)
+decl f6 :: (-> S4 S3 S3)
 decl f4 :: S3
-#9 := f4
-decl f9 :: S2
-#39 := f9
-#325 := (f3 f9 f4)
-decl f1 :: S1
-#4 := f1
-#322 := (= f1 #325)
-decl f10 :: S3
+#8 := f4
+decl f7 :: (-> S5 S3 S4)
+decl f11 :: S3
+#41 := f11
+decl f8 :: S5
+#18 := f8
+#42 := (f7 f8 f11)
+#43 := (f6 #42 f4)
+decl f10 :: S2
 #40 := f10
-#45 := (f3 f9 f10)
-#125 := (= f1 #45)
-#326 := (or #125 #322)
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S3 S4)
-#41 := (f7 f10)
-#42 := (f6 #41 f4)
-#43 := (f3 f9 #42)
-#121 := (= f1 #43)
-#134 := (not #121)
-#642 := [hypothesis]: #134
-#320 := (or #125 #121)
-#135 := (iff #125 #134)
-#46 := (= #45 f1)
-#44 := (= #43 f1)
-#47 := (iff #44 #46)
-#48 := (not #47)
-#138 := (iff #48 #135)
-#128 := (iff #121 #125)
-#131 := (not #128)
-#136 := (iff #131 #135)
-#137 := [rewrite]: #136
-#132 := (iff #48 #131)
-#129 := (iff #47 #128)
-#126 := (iff #46 #125)
-#127 := [rewrite]: #126
-#123 := (iff #44 #121)
-#124 := [rewrite]: #123
-#130 := [monotonicity #124 #127]: #129
-#133 := [monotonicity #130]: #132
-#139 := [trans #133 #137]: #138
-#120 := [asserted]: #48
-#142 := [mp #120 #139]: #135
-#232 := (not #135)
-#319 := (or #125 #121 #232)
-#233 := [def-axiom]: #319
-#234 := [unit-resolution #233 #142]: #320
-#644 := [unit-resolution #234 #642]: #125
-#648 := (not #326)
-#288 := (or #121 #648)
-#305 := (iff #121 #326)
+#44 := (f3 f10 #43)
+#45 := (= #44 f1)
+#75 := (not #45)
+#46 := (f3 f10 f11)
+#47 := (= #46 f1)
+#262 := (not #47)
+#572 := [hypothesis]: #262
+#268 := (or #45 #47)
+#76 := (iff #75 #47)
+#48 := (iff #45 #47)
+#49 := (not #48)
+#77 := (iff #49 #76)
+#78 := [rewrite]: #77
+#74 := [asserted]: #49
+#81 := [mp #74 #78]: #76
+#177 := (not #76)
+#266 := (or #45 #47 #177)
+#267 := [def-axiom]: #266
+#265 := [unit-resolution #267 #81]: #268
+#573 := [unit-resolution #265 #572]: #45
+#269 := (f3 f10 f4)
+#248 := (= #269 f1)
+#584 := (or #47 #248)
+#591 := (not #584)
+#589 := (not #248)
+#242 := [hypothesis]: #248
+#7 := (:var 0 S2)
+#9 := (f3 #7 f4)
+#592 := (pattern #9)
+#10 := (= #9 f1)
+#11 := (not #10)
+#593 := (forall (vars (?v0 S2)) (:pat #592) #11)
+#12 := (forall (vars (?v0 S2)) #11)
+#596 := (iff #12 #593)
+#594 := (iff #11 #11)
+#595 := [refl]: #594
+#597 := [quant-intro #595]: #596
+#95 := (~ #12 #12)
+#93 := (~ #11 #11)
+#94 := [refl]: #93
+#96 := [nnf-pos #94]: #95
+#70 := [asserted]: #12
+#80 := [mp~ #70 #96]: #12
+#598 := [mp #80 #597]: #593
+#232 := (not #593)
+#569 := (or #232 #589)
+#570 := [quant-inst #40]: #569
+#373 := [unit-resolution #570 #598 #242]: false
+#571 := [lemma #373]: #589
+#581 := (or #591 #47 #248)
+#240 := [def-axiom]: #581
+#568 := [unit-resolution #240 #572 #571]: #591
+#211 := (or #75 #584)
+#586 := (iff #45 #584)
 #21 := (:var 0 S3)
 #19 := (:var 1 S3)
-#20 := (f7 #19)
+#20 := (f7 f8 #19)
 #22 := (f6 #20 #21)
-#18 := (:var 2 S2)
-#23 := (f3 #18 #22)
-#664 := (pattern #23)
-#27 := (f3 #18 #21)
-#94 := (= f1 #27)
-#25 := (f3 #18 #19)
-#91 := (= f1 #25)
-#97 := (or #91 #94)
-#87 := (= f1 #23)
-#100 := (iff #87 #97)
-#665 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #664) #100)
-#103 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #100)
-#668 := (iff #103 #665)
-#666 := (iff #100 #100)
-#667 := [refl]: #666
-#669 := [quant-intro #667]: #668
-#146 := (~ #103 #103)
-#160 := (~ #100 #100)
-#161 := [refl]: #160
-#147 := [nnf-pos #161]: #146
+#17 := (:var 2 S2)
+#23 := (f3 #17 #22)
+#606 := (pattern #23)
+#27 := (f3 #17 #21)
 #28 := (= #27 f1)
+#25 := (f3 #17 #19)
 #26 := (= #25 f1)
 #29 := (or #26 #28)
 #24 := (= #23 f1)
 #30 := (iff #24 #29)
+#607 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #606) #30)
 #31 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #30)
-#104 := (iff #31 #103)
-#101 := (iff #30 #100)
-#98 := (iff #29 #97)
-#95 := (iff #28 #94)
-#96 := [rewrite]: #95
-#92 := (iff #26 #91)
-#93 := [rewrite]: #92
-#99 := [monotonicity #93 #96]: #98
-#89 := (iff #24 #87)
-#90 := [rewrite]: #89
-#102 := [monotonicity #90 #99]: #101
-#105 := [quant-intro #102]: #104
-#86 := [asserted]: #31
-#108 := [mp #86 #105]: #103
-#162 := [mp~ #108 #147]: #103
-#670 := [mp #162 #669]: #665
-#299 := (not #665)
-#431 := (or #299 #305)
-#638 := [quant-inst #39 #40 #9]: #431
-#287 := [unit-resolution #638 #670]: #305
-#639 := (not #305)
-#297 := (or #639 #121 #648)
-#302 := [def-axiom]: #297
-#289 := [unit-resolution #302 #287]: #288
-#627 := [unit-resolution #289 #642]: #648
-#321 := (not #125)
-#310 := (or #326 #321)
-#311 := [def-axiom]: #310
-#628 := [unit-resolution #311 #627 #644]: false
-#629 := [lemma #628]: #121
-#630 := (or #134 #326)
-#640 := (or #639 #134 #326)
-#298 := [def-axiom]: #640
-#631 := [unit-resolution #298 #287]: #630
-#633 := [unit-resolution #631 #629]: #326
-#324 := (or #321 #134)
-#312 := (or #321 #134 #232)
-#323 := [def-axiom]: #312
-#252 := [unit-resolution #323 #142]: #324
-#635 := [unit-resolution #252 #629]: #321
-#643 := (or #648 #125 #322)
-#649 := [def-axiom]: #643
-#273 := [unit-resolution #649 #635 #633]: #322
-#8 := (:var 0 S2)
-#10 := (f3 #8 f4)
-#650 := (pattern #10)
-#69 := (= f1 #10)
-#72 := (not #69)
-#651 := (forall (vars (?v0 S2)) (:pat #650) #72)
-#75 := (forall (vars (?v0 S2)) #72)
-#654 := (iff #75 #651)
-#652 := (iff #72 #72)
-#653 := [refl]: #652
-#655 := [quant-intro #653]: #654
-#156 := (~ #75 #75)
-#154 := (~ #72 #72)
-#155 := [refl]: #154
-#157 := [nnf-pos #155]: #156
-#11 := (= #10 f1)
-#12 := (not #11)
-#13 := (forall (vars (?v0 S2)) #12)
-#76 := (iff #13 #75)
-#73 := (iff #12 #72)
-#70 := (iff #11 #69)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#77 := [quant-intro #74]: #76
-#68 := [asserted]: #13
-#80 := [mp #68 #77]: #75
-#141 := [mp~ #80 #157]: #75
-#656 := [mp #141 #655]: #651
-#645 := (not #322)
-#626 := (not #651)
-#632 := (or #626 #645)
-#268 := [quant-inst #39]: #632
-[unit-resolution #268 #656 #273]: false
-unsat
-37e8c2c682de93175c2e3b6573d2a98ccec54dc2 134 0
-#2 := false
+#610 := (iff #31 #607)
+#608 := (iff #30 #30)
+#609 := [refl]: #608
+#611 := [quant-intro #609]: #610
+#85 := (~ #31 #31)
+#99 := (~ #30 #30)
+#100 := [refl]: #99
+#86 := [nnf-pos #100]: #85
+#72 := [asserted]: #31
+#101 := [mp~ #72 #86]: #31
+#612 := [mp #101 #611]: #607
+#580 := (not #607)
+#253 := (or #580 #586)
+#254 := [quant-inst #40 #41 #8]: #253
+#574 := [unit-resolution #254 #612]: #586
+#245 := (not #586)
+#583 := (or #245 #75 #584)
+#225 := [def-axiom]: #583
+#575 := [unit-resolution #225 #574]: #211
+#577 := [unit-resolution #575 #568 #573]: false
+#216 := [lemma #577]: #47
+#264 := (or #75 #262)
+#263 := (or #75 #262 #177)
+#178 := [def-axiom]: #263
+#255 := [unit-resolution #178 #81]: #264
+#217 := [unit-resolution #255 #216]: #75
+#587 := (or #584 #262)
+#588 := [def-axiom]: #587
+#578 := [unit-resolution #588 #216]: #584
+#576 := (or #45 #591)
+#582 := (or #245 #45 #591)
+#241 := [def-axiom]: #582
+#579 := [unit-resolution #241 #574]: #576
+[unit-resolution #579 #578 #217]: false
+unsat
+91c9ceb101c072b8bb603b688737950bad02faa7 90 0
+#2 := false
+decl f1 :: S1
+#3 := f1
 decl f3 :: (-> S2 S3 S1)
 decl f5 :: S3
-#14 := f5
-decl f9 :: S2
-#39 := f9
-#217 := (f3 f9 f5)
-decl f1 :: S1
-#4 := f1
-#304 := (= f1 #217)
-#631 := (not #304)
-decl f10 :: S3
+#13 := f5
+decl f10 :: S2
 #40 := f10
-#218 := (f3 f9 f10)
-#305 := (= f1 #218)
-#297 := (or #304 #305)
-#282 := (not #297)
+#255 := (f3 f10 f5)
+#170 := (= #255 f1)
+#234 := (not #170)
+decl f11 :: S3
+#41 := f11
+#254 := (f3 f10 f11)
+#169 := (= #254 f1)
+#256 := (or #169 #170)
+#245 := (not #256)
 decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S3 S4)
-#41 := (f7 f10)
-#42 := (f6 #41 f5)
-#43 := (f3 f9 #42)
-#118 := (= f1 #43)
-#237 := (iff #118 #297)
+decl f7 :: (-> S5 S3 S4)
+decl f8 :: S5
+#18 := f8
+#42 := (f7 f8 f11)
+#43 := (f6 #42 f5)
+#44 := (f3 f10 #43)
+#45 := (= #44 f1)
+#247 := (iff #45 #256)
 #21 := (:var 0 S3)
 #19 := (:var 1 S3)
-#20 := (f7 #19)
+#20 := (f7 f8 #19)
 #22 := (f6 #20 #21)
-#18 := (:var 2 S2)
-#23 := (f3 #18 #22)
-#649 := (pattern #23)
-#27 := (f3 #18 #21)
-#91 := (= f1 #27)
-#25 := (f3 #18 #19)
-#88 := (= f1 #25)
-#94 := (or #88 #91)
-#84 := (= f1 #23)
-#97 := (iff #84 #94)
-#650 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #649) #97)
-#100 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #97)
-#653 := (iff #100 #650)
-#651 := (iff #97 #97)
-#652 := [refl]: #651
-#654 := [quant-intro #652]: #653
-#131 := (~ #100 #100)
-#145 := (~ #97 #97)
-#146 := [refl]: #145
-#132 := [nnf-pos #146]: #131
+#17 := (:var 2 S2)
+#23 := (f3 #17 #22)
+#598 := (pattern #23)
+#27 := (f3 #17 #21)
 #28 := (= #27 f1)
+#25 := (f3 #17 #19)
 #26 := (= #25 f1)
 #29 := (or #26 #28)
 #24 := (= #23 f1)
 #30 := (iff #24 #29)
+#599 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #598) #30)
 #31 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #30)
-#101 := (iff #31 #100)
-#98 := (iff #30 #97)
-#95 := (iff #29 #94)
-#92 := (iff #28 #91)
-#93 := [rewrite]: #92
-#89 := (iff #26 #88)
-#90 := [rewrite]: #89
-#96 := [monotonicity #90 #93]: #95
-#86 := (iff #24 #84)
-#87 := [rewrite]: #86
-#99 := [monotonicity #87 #96]: #98
-#102 := [quant-intro #99]: #101
-#83 := [asserted]: #31
-#105 := [mp #83 #102]: #100
-#147 := [mp~ #105 #132]: #100
-#655 := [mp #147 #654]: #650
-#311 := (not #650)
-#290 := (or #311 #237)
-#219 := (or #305 #304)
-#306 := (iff #118 #219)
-#627 := (or #311 #306)
-#284 := (iff #627 #290)
-#623 := (iff #290 #290)
-#295 := [rewrite]: #623
-#310 := (iff #306 #237)
-#308 := (iff #219 #297)
-#309 := [rewrite]: #308
-#307 := [monotonicity #309]: #310
-#416 := [monotonicity #307]: #284
-#296 := [trans #416 #295]: #284
-#629 := [quant-inst #39 #40 #14]: #627
-#630 := [mp #629 #296]: #290
-#613 := [unit-resolution #630 #655]: #237
-#283 := (not #237)
-#614 := (or #283 #282)
-#122 := (not #118)
-#44 := (= #43 f1)
-#45 := (not #44)
-#123 := (iff #45 #122)
-#120 := (iff #44 #118)
-#121 := [rewrite]: #120
-#124 := [monotonicity #121]: #123
-#117 := [asserted]: #45
-#127 := [mp #117 #124]: #122
-#626 := (or #283 #118 #282)
-#267 := [def-axiom]: #626
-#617 := [unit-resolution #267 #127]: #614
-#253 := [unit-resolution #617 #613]: #282
-#632 := (or #297 #631)
-#633 := [def-axiom]: #632
-#618 := [unit-resolution #633 #253]: #631
-#8 := (:var 0 S2)
-#15 := (f3 #8 f5)
-#642 := (pattern #15)
-#76 := (= f1 #15)
-#643 := (forall (vars (?v0 S2)) (:pat #642) #76)
-#80 := (forall (vars (?v0 S2)) #76)
-#646 := (iff #80 #643)
-#644 := (iff #76 #76)
-#645 := [refl]: #644
-#647 := [quant-intro #645]: #646
-#129 := (~ #80 #80)
-#128 := (~ #76 #76)
-#143 := [refl]: #128
-#130 := [nnf-pos #143]: #129
-#16 := (= #15 f1)
-#17 := (forall (vars (?v0 S2)) #16)
-#81 := (iff #17 #80)
-#78 := (iff #16 #76)
-#79 := [rewrite]: #78
-#82 := [quant-intro #79]: #81
-#75 := [asserted]: #17
-#85 := [mp #75 #82]: #80
-#144 := [mp~ #85 #130]: #80
-#648 := [mp #144 #647]: #643
-#615 := (not #643)
-#616 := (or #615 #304)
-#611 := [quant-inst #39]: #616
-[unit-resolution #611 #648 #618]: false
-unsat
-8b3671158912b5be83077a5d2f71eae8a40f4427 153 0
-#2 := false
+#602 := (iff #31 #599)
+#600 := (iff #30 #30)
+#601 := [refl]: #600
+#603 := [quant-intro #601]: #602
+#77 := (~ #31 #31)
+#91 := (~ #30 #30)
+#92 := [refl]: #91
+#78 := [nnf-pos #92]: #77
+#69 := [asserted]: #31
+#93 := [mp~ #69 #78]: #31
+#604 := [mp #93 #603]: #599
+#260 := (not #599)
+#257 := (or #260 #247)
+#261 := [quant-inst #40 #41 #13]: #257
+#258 := [unit-resolution #261 #604]: #247
+#580 := (not #247)
+#259 := (or #580 #245)
+#46 := (not #45)
+#71 := [asserted]: #46
+#581 := (or #580 #45 #245)
+#582 := [def-axiom]: #581
+#559 := [unit-resolution #582 #71]: #259
+#221 := [unit-resolution #559 #258]: #245
+#365 := (or #256 #234)
+#572 := [def-axiom]: #365
+#222 := [unit-resolution #572 #221]: #234
+#7 := (:var 0 S2)
+#14 := (f3 #7 f5)
+#591 := (pattern #14)
+#15 := (= #14 f1)
+#592 := (forall (vars (?v0 S2)) (:pat #591) #15)
+#16 := (forall (vars (?v0 S2)) #15)
+#595 := (iff #16 #592)
+#593 := (iff #15 #15)
+#594 := [refl]: #593
+#596 := [quant-intro #594]: #595
+#75 := (~ #16 #16)
+#74 := (~ #15 #15)
+#89 := [refl]: #74
+#76 := [nnf-pos #89]: #75
+#68 := [asserted]: #16
+#90 := [mp~ #68 #76]: #16
+#597 := [mp #90 #596]: #592
+#233 := (not #592)
+#575 := (or #233 #170)
+#217 := [quant-inst #40]: #575
+[unit-resolution #217 #597 #222]: false
+unsat
+f5d17ecef2699af9d85c677d592ffbcac1a42bd5 131 0
+#2 := false
+decl f1 :: S1
+#3 := f1
 decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f10 :: S3
+decl f11 :: S3
+#41 := f11
+decl f10 :: S2
 #40 := f10
-decl f7 :: (-> S3 S4)
-decl f11 :: S3
-#42 := f11
-#46 := (f7 f11)
-#47 := (f6 #46 f10)
-decl f9 :: S2
-#39 := f9
-#48 := (f3 f9 #47)
-decl f1 :: S1
-#4 := f1
-#128 := (= f1 #48)
-#324 := (not #128)
-#41 := (f7 f10)
-#43 := (f6 #41 f11)
-#44 := (f3 f9 #43)
-#124 := (= f1 #44)
-#137 := (not #124)
-#243 := [hypothesis]: #137
-#323 := (or #128 #124)
-#138 := (iff #128 #137)
-#49 := (= #48 f1)
-#45 := (= #44 f1)
-#50 := (iff #45 #49)
-#51 := (not #50)
-#141 := (iff #51 #138)
-#131 := (iff #124 #128)
-#134 := (not #131)
-#139 := (iff #134 #138)
-#140 := [rewrite]: #139
-#135 := (iff #51 #134)
-#132 := (iff #50 #131)
-#129 := (iff #49 #128)
-#130 := [rewrite]: #129
-#126 := (iff #45 #124)
-#127 := [rewrite]: #126
-#133 := [monotonicity #127 #130]: #132
-#136 := [monotonicity #133]: #135
-#142 := [trans #136 #140]: #141
-#123 := [asserted]: #51
-#145 := [mp #123 #142]: #138
-#235 := (not #138)
-#322 := (or #128 #124 #235)
-#236 := [def-axiom]: #322
-#237 := [unit-resolution #236 #145]: #323
-#622 := [unit-resolution #237 #243]: #128
-#328 := (f3 f9 f10)
-#325 := (= f1 #328)
-#329 := (f3 f9 f11)
-#308 := (= f1 #329)
-#645 := (or #308 #325)
-#642 := (not #645)
-#345 := (or #124 #642)
-#632 := (iff #124 #645)
+#272 := (f3 f10 f11)
+#251 := (= #272 f1)
+decl f12 :: S3
+#43 := f12
+#587 := (f3 f10 f12)
+#589 := (= #587 f1)
+#583 := (or #589 #251)
+decl f6 :: (-> S4 S3 S3)
+decl f7 :: (-> S5 S3 S4)
+decl f8 :: S5
+#18 := f8
+#47 := (f7 f8 f12)
+#48 := (f6 #47 f11)
+#49 := (f3 f10 #48)
+#50 := (= #49 f1)
+#245 := (or #251 #589)
+#42 := (f7 f8 f11)
+#44 := (f6 #42 f12)
+#45 := (f3 f10 #44)
+#46 := (= #45 f1)
+#265 := (not #50)
+#574 := [hypothesis]: #265
+#271 := (or #46 #50)
+#78 := (not #46)
+#79 := (iff #78 #50)
+#51 := (iff #46 #50)
+#52 := (not #51)
+#80 := (iff #52 #79)
+#81 := [rewrite]: #80
+#77 := [asserted]: #52
+#84 := [mp #77 #81]: #79
+#180 := (not #79)
+#269 := (or #46 #50 #180)
+#270 := [def-axiom]: #269
+#268 := [unit-resolution #270 #84]: #271
+#575 := [unit-resolution #268 #574]: #46
+#564 := (or #78 #245)
+#376 := (iff #46 #245)
 #21 := (:var 0 S3)
 #19 := (:var 1 S3)
-#20 := (f7 #19)
+#20 := (f7 f8 #19)
 #22 := (f6 #20 #21)
-#18 := (:var 2 S2)
-#23 := (f3 #18 #22)
-#667 := (pattern #23)
-#27 := (f3 #18 #21)
-#97 := (= f1 #27)
-#25 := (f3 #18 #19)
-#94 := (= f1 #25)
-#100 := (or #94 #97)
-#90 := (= f1 #23)
-#103 := (iff #90 #100)
-#668 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #667) #103)
-#106 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #103)
-#671 := (iff #106 #668)
-#669 := (iff #103 #103)
-#670 := [refl]: #669
-#672 := [quant-intro #670]: #671
-#149 := (~ #106 #106)
-#163 := (~ #103 #103)
-#164 := [refl]: #163
-#150 := [nnf-pos #164]: #149
+#17 := (:var 2 S2)
+#23 := (f3 #17 #22)
+#609 := (pattern #23)
+#27 := (f3 #17 #21)
 #28 := (= #27 f1)
+#25 := (f3 #17 #19)
 #26 := (= #25 f1)
 #29 := (or #26 #28)
 #24 := (= #23 f1)
 #30 := (iff #24 #29)
+#610 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #609) #30)
 #31 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #30)
-#107 := (iff #31 #106)
-#104 := (iff #30 #103)
-#101 := (iff #29 #100)
-#98 := (iff #28 #97)
-#99 := [rewrite]: #98
-#95 := (iff #26 #94)
-#96 := [rewrite]: #95
-#102 := [monotonicity #96 #99]: #101
-#92 := (iff #24 #90)
-#93 := [rewrite]: #92
-#105 := [monotonicity #93 #102]: #104
-#108 := [quant-intro #105]: #107
-#89 := [asserted]: #31
-#111 := [mp #89 #108]: #106
-#165 := [mp~ #111 #150]: #106
-#673 := [mp #165 #672]: #668
-#641 := (not #668)
-#629 := (or #641 #632)
-#302 := (or #325 #308)
-#434 := (iff #124 #302)
-#635 := (or #641 #434)
-#636 := (iff #635 #629)
-#276 := (iff #629 #629)
-#277 := [rewrite]: #276
-#633 := (iff #434 #632)
-#630 := (iff #302 #645)
-#631 := [rewrite]: #630
-#634 := [monotonicity #631]: #633
-#638 := [monotonicity #634]: #636
-#639 := [trans #638 #277]: #636
-#271 := [quant-inst #39 #40 #42]: #635
-#637 := [mp #271 #639]: #629
-#623 := [unit-resolution #637 #673]: #632
-#640 := (not #632)
-#626 := (or #640 #124 #642)
-#627 := [def-axiom]: #626
-#346 := [unit-resolution #627 #623]: #345
-#620 := [unit-resolution #346 #243]: #642
-#621 := (or #324 #645)
-#647 := (iff #128 #645)
-#313 := (or #641 #647)
-#314 := [quant-inst #39 #42 #40]: #313
-#624 := [unit-resolution #314 #673]: #647
-#643 := (not #647)
-#285 := (or #643 #324 #645)
-#628 := [def-axiom]: #285
-#625 := [unit-resolution #628 #624]: #621
-#334 := [unit-resolution #625 #620 #622]: false
-#335 := [lemma #334]: #124
-#327 := (or #324 #137)
-#315 := (or #324 #137 #235)
-#326 := [def-axiom]: #315
-#255 := [unit-resolution #326 #145]: #327
-#336 := [unit-resolution #255 #335]: #324
-#338 := (or #137 #645)
-#333 := (or #640 #137 #645)
-#349 := [def-axiom]: #333
-#616 := [unit-resolution #349 #623]: #338
-#617 := [unit-resolution #616 #335]: #645
-#330 := (or #128 #642)
-#301 := (or #643 #128 #642)
-#644 := [def-axiom]: #301
-#614 := [unit-resolution #644 #624]: #330
-[unit-resolution #614 #617 #336]: false
-unsat
-76f35b24758dff3b162e8fc64fc760da00fb55d8 126 0
-#2 := false
+#613 := (iff #31 #610)
+#611 := (iff #30 #30)
+#612 := [refl]: #611
+#614 := [quant-intro #612]: #613
+#88 := (~ #31 #31)
+#102 := (~ #30 #30)
+#103 := [refl]: #102
+#89 := [nnf-pos #103]: #88
+#75 := [asserted]: #31
+#104 := [mp~ #75 #89]: #31
+#615 := [mp #104 #614]: #610
+#257 := (not #610)
+#590 := (or #257 #376)
+#591 := [quant-inst #40 #41 #43]: #590
+#187 := [unit-resolution #591 #615]: #376
+#586 := (not #376)
+#232 := (or #586 #78 #245)
+#233 := [def-axiom]: #232
+#565 := [unit-resolution #233 #187]: #564
+#287 := [unit-resolution #565 #575]: #245
+#594 := (not #589)
+#219 := (not #583)
+#562 := (or #50 #219)
+#256 := (iff #50 #583)
+#576 := (or #257 #256)
+#571 := [quant-inst #40 #43 #41]: #576
+#288 := [unit-resolution #571 #615]: #256
+#579 := (not #256)
+#582 := (or #579 #50 #219)
+#568 := [def-axiom]: #582
+#566 := [unit-resolution #568 #288]: #562
+#563 := [unit-resolution #566 #574]: #219
+#577 := (or #583 #594)
+#214 := [def-axiom]: #577
+#567 := [unit-resolution #214 #563]: #594
+#592 := (not #251)
+#578 := (or #583 #592)
+#580 := [def-axiom]: #578
+#277 := [unit-resolution #580 #563]: #592
+#248 := (not #245)
+#585 := (or #248 #251 #589)
+#244 := [def-axiom]: #585
+#278 := [unit-resolution #244 #277 #567 #287]: false
+#279 := [lemma #278]: #50
+#280 := (or #265 #583)
+#569 := (or #579 #265 #583)
+#276 := [def-axiom]: #569
+#558 := [unit-resolution #276 #288]: #280
+#559 := [unit-resolution #558 #279]: #583
+#267 := (or #78 #265)
+#266 := (or #78 #265 #180)
+#181 := [def-axiom]: #266
+#258 := [unit-resolution #181 #84]: #267
+#273 := [unit-resolution #258 #279]: #78
+#556 := (or #46 #248)
+#228 := (or #586 #46 #248)
+#570 := [def-axiom]: #228
+#560 := [unit-resolution #570 #187]: #556
+#557 := [unit-resolution #560 #273]: #248
+#593 := (or #245 #592)
+#588 := [def-axiom]: #593
+#561 := [unit-resolution #588 #557]: #592
+#584 := (or #245 #594)
+#243 := [def-axiom]: #584
+#550 := [unit-resolution #243 #557]: #594
+#220 := (or #219 #589 #251)
+#581 := [def-axiom]: #220
+[unit-resolution #581 #550 #561 #559]: false
+unsat
+7b7f932ab0a4581fa34b6f91edcffafb0fae6833 95 0
+#2 := false
+decl f1 :: S1
+#3 := f1
 decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f10 :: S3
+decl f11 :: S3
+#41 := f11
+decl f10 :: S2
 #40 := f10
-decl f7 :: (-> S3 S4)
-#41 := (f7 f10)
-#42 := (f6 #41 f10)
-decl f9 :: S2
-#39 := f9
-#43 := (f3 f9 #42)
-decl f1 :: S1
-#4 := f1
-#121 := (= f1 #43)
-#134 := (not #121)
-#625 := [hypothesis]: #134
-#45 := (f3 f9 f10)
-#125 := (= f1 #45)
-#320 := (or #125 #121)
-#135 := (iff #125 #134)
-#46 := (= #45 f1)
-#44 := (= #43 f1)
-#47 := (iff #44 #46)
-#48 := (not #47)
-#138 := (iff #48 #135)
-#128 := (iff #121 #125)
-#131 := (not #128)
-#136 := (iff #131 #135)
-#137 := [rewrite]: #136
-#132 := (iff #48 #131)
-#129 := (iff #47 #128)
-#126 := (iff #46 #125)
-#127 := [rewrite]: #126
-#123 := (iff #44 #121)
-#124 := [rewrite]: #123
-#130 := [monotonicity #124 #127]: #129
-#133 := [monotonicity #130]: #132
-#139 := [trans #133 #137]: #138
-#120 := [asserted]: #48
-#142 := [mp #120 #139]: #135
-#232 := (not #135)
-#319 := (or #125 #121 #232)
-#233 := [def-axiom]: #319
-#234 := [unit-resolution #233 #142]: #320
-#286 := [unit-resolution #234 #625]: #125
-#321 := (not #125)
-#288 := (or #121 #321)
+#46 := (f3 f10 f11)
+#47 := (= #46 f1)
+#262 := (not #47)
+#230 := [hypothesis]: #262
+decl f6 :: (-> S4 S3 S3)
+decl f7 :: (-> S5 S3 S4)
+decl f8 :: S5
+#18 := f8
+#42 := (f7 f8 f11)
+#43 := (f6 #42 f11)
+#44 := (f3 f10 #43)
+#45 := (= #44 f1)
+#268 := (or #45 #47)
+#75 := (not #45)
+#76 := (iff #75 #47)
+#48 := (iff #45 #47)
+#49 := (not #48)
+#77 := (iff #49 #76)
+#78 := [rewrite]: #77
+#74 := [asserted]: #49
+#81 := [mp #74 #78]: #76
+#177 := (not #76)
+#266 := (or #45 #47 #177)
+#267 := [def-axiom]: #266
+#265 := [unit-resolution #267 #81]: #268
+#231 := [unit-resolution #265 #230]: #45
+#569 := (or #75 #47)
 #21 := (:var 0 S3)
 #19 := (:var 1 S3)
-#20 := (f7 #19)
+#20 := (f7 f8 #19)
 #22 := (f6 #20 #21)
-#18 := (:var 2 S2)
-#23 := (f3 #18 #22)
-#664 := (pattern #23)
-#27 := (f3 #18 #21)
-#94 := (= f1 #27)
-#25 := (f3 #18 #19)
-#91 := (= f1 #25)
-#97 := (or #91 #94)
-#87 := (= f1 #23)
-#100 := (iff #87 #97)
-#665 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #664) #100)
-#103 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #100)
-#668 := (iff #103 #665)
-#666 := (iff #100 #100)
-#667 := [refl]: #666
-#669 := [quant-intro #667]: #668
-#146 := (~ #103 #103)
-#160 := (~ #100 #100)
-#161 := [refl]: #160
-#147 := [nnf-pos #161]: #146
+#17 := (:var 2 S2)
+#23 := (f3 #17 #22)
+#606 := (pattern #23)
+#27 := (f3 #17 #21)
 #28 := (= #27 f1)
-#26 := (= #25 f1)
-#29 := (or #26 #28)
-#24 := (= #23 f1)
-#30 := (iff #24 #29)
-#31 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #30)
-#104 := (iff #31 #103)
-#101 := (iff #30 #100)
-#98 := (iff #29 #97)
-#95 := (iff #28 #94)
-#96 := [rewrite]: #95
-#92 := (iff #26 #91)
-#93 := [rewrite]: #92
-#99 := [monotonicity #93 #96]: #98
-#89 := (iff #24 #87)
-#90 := [rewrite]: #89
-#102 := [monotonicity #90 #99]: #101
-#105 := [quant-intro #102]: #104
-#86 := [asserted]: #31
-#108 := [mp #86 #105]: #103
-#162 := [mp~ #108 #147]: #103
-#670 := [mp #162 #669]: #665
-#299 := (not #665)
-#431 := (or #299 #128)
-#325 := (or #125 #125)
-#322 := (iff #121 #325)
-#638 := (or #299 #322)
-#311 := (iff #638 #431)
-#646 := (iff #431 #431)
-#647 := [rewrite]: #646
-#642 := (iff #322 #128)
-#326 := (iff #325 #125)
-#305 := [rewrite]: #326
-#644 := [monotonicity #305]: #642
-#645 := [monotonicity #644]: #311
-#648 := [trans #645 #647]: #311
-#310 := [quant-inst #39 #40 #40]: #638
-#643 := [mp #310 #648]: #431
-#287 := [unit-resolution #643 #670]: #128
-#649 := (or #131 #121 #321)
-#639 := [def-axiom]: #649
-#289 := [unit-resolution #639 #287]: #288
-#627 := [unit-resolution #289 #286 #625]: false
-#628 := [lemma #627]: #121
-#324 := (or #321 #134)
-#312 := (or #321 #134 #232)
-#323 := [def-axiom]: #312
-#252 := [unit-resolution #323 #142]: #324
-#629 := [unit-resolution #252 #628]: #321
-#630 := (or #134 #125)
-#297 := (or #131 #134 #125)
-#302 := [def-axiom]: #297
-#631 := [unit-resolution #302 #287]: #630
-[unit-resolution #631 #629 #628]: false
-unsat
-2ac06f7d84c36d7f3c61e2f783f6f8bf82530665 264 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f11 :: S3
-#42 := f11
-decl f9 :: S2
-#39 := f9
-#621 := (f3 f9 f11)
-decl f1 :: S1
-#4 := f1
-#334 := (= f1 #621)
-decl f12 :: S3
-#44 := f12
-#332 := (f3 f9 f12)
-#329 := (= f1 #332)
-#619 := (or #329 #334)
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S3 S4)
-#43 := (f7 f11)
-#45 := (f6 #43 f12)
-#306 := (f3 f9 #45)
-#438 := (= f1 #306)
-#613 := (iff #438 #619)
-#579 := (not #613)
-#591 := (not #619)
-#603 := (not #334)
-decl f10 :: S3
-#40 := f10
-#634 := (f3 f9 f10)
-#635 := (= f1 #634)
-#481 := (or #334 #635)
-#606 := (not #481)
-#41 := (f7 f10)
-#49 := (f6 #41 f11)
-#333 := (f3 f9 #49)
-#312 := (= f1 #333)
-#589 := (iff #312 #481)
-#581 := (not #589)
-#574 := [hypothesis]: #581
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#20 := (f7 #19)
-#22 := (f6 #20 #21)
-#18 := (:var 2 S2)
-#23 := (f3 #18 #22)
-#671 := (pattern #23)
-#27 := (f3 #18 #21)
-#101 := (= f1 #27)
-#25 := (f3 #18 #19)
-#98 := (= f1 #25)
-#104 := (or #98 #101)
-#94 := (= f1 #23)
-#107 := (iff #94 #104)
-#672 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #671) #107)
-#110 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #107)
-#675 := (iff #110 #672)
-#673 := (iff #107 #107)
-#674 := [refl]: #673
-#676 := [quant-intro #674]: #675
-#153 := (~ #110 #110)
-#167 := (~ #107 #107)
-#168 := [refl]: #167
-#154 := [nnf-pos #168]: #153
-#28 := (= #27 f1)
+#25 := (f3 #17 #19)
 #26 := (= #25 f1)
 #29 := (or #26 #28)
 #24 := (= #23 f1)
 #30 := (iff #24 #29)
+#607 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #606) #30)
 #31 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #30)
-#111 := (iff #31 #110)
-#108 := (iff #30 #107)
-#105 := (iff #29 #104)
-#102 := (iff #28 #101)
-#103 := [rewrite]: #102
-#99 := (iff #26 #98)
-#100 := [rewrite]: #99
-#106 := [monotonicity #100 #103]: #105
-#96 := (iff #24 #94)
-#97 := [rewrite]: #96
-#109 := [monotonicity #97 #106]: #108
-#112 := [quant-intro #109]: #111
-#93 := [asserted]: #31
-#115 := [mp #93 #112]: #110
-#169 := [mp~ #115 #154]: #110
-#677 := [mp #169 #676]: #672
-#645 := (not #672)
-#587 := (or #645 #589)
-#598 := (or #635 #334)
-#480 := (iff #312 #598)
-#590 := (or #645 #480)
-#490 := (iff #590 #587)
-#493 := (iff #587 #587)
-#486 := [rewrite]: #493
-#491 := (iff #480 #589)
-#482 := (iff #598 #481)
-#441 := [rewrite]: #482
-#586 := [monotonicity #441]: #491
-#492 := [monotonicity #586]: #490
-#494 := [trans #492 #486]: #490
-#475 := [quant-inst #39 #40 #42]: #590
-#495 := [mp #475 #494]: #587
-#575 := [unit-resolution #495 #677 #574]: false
-#576 := [lemma #575]: #589
-#652 := (not #312)
-#649 := (or #312 #329)
-#646 := (not #649)
-#50 := (f7 #49)
-#51 := (f6 #50 f12)
-#52 := (f3 f9 #51)
-#132 := (= f1 #52)
-#328 := (not #132)
-#46 := (f6 #41 #45)
-#47 := (f3 f9 #46)
-#128 := (= f1 #47)
-#141 := (not #128)
-#577 := [hypothesis]: #141
-#327 := (or #132 #128)
-#142 := (iff #132 #141)
-#53 := (= #52 f1)
-#48 := (= #47 f1)
-#54 := (iff #48 #53)
-#55 := (not #54)
-#145 := (iff #55 #142)
-#135 := (iff #128 #132)
-#138 := (not #135)
-#143 := (iff #138 #142)
-#144 := [rewrite]: #143
-#139 := (iff #55 #138)
-#136 := (iff #54 #135)
-#133 := (iff #53 #132)
-#134 := [rewrite]: #133
-#130 := (iff #48 #128)
-#131 := [rewrite]: #130
-#137 := [monotonicity #131 #134]: #136
-#140 := [monotonicity #137]: #139
-#146 := [trans #140 #144]: #145
-#127 := [asserted]: #55
-#149 := [mp #127 #146]: #142
-#239 := (not #142)
-#326 := (or #132 #128 #239)
-#240 := [def-axiom]: #326
-#241 := [unit-resolution #240 #149]: #327
-#571 := [unit-resolution #241 #577]: #132
-#562 := (or #328 #649)
-#651 := (iff #132 #649)
-#317 := (or #645 #651)
-#318 := [quant-inst #39 #49 #44]: #317
-#578 := [unit-resolution #318 #677]: #651
-#647 := (not #651)
-#289 := (or #647 #328 #649)
-#632 := [def-axiom]: #289
-#563 := [unit-resolution #632 #578]: #562
-#565 := [unit-resolution #563 #571]: #649
-#655 := (not #329)
-#595 := (or #645 #613)
-#618 := (or #334 #329)
-#622 := (iff #438 #618)
-#615 := (or #645 #622)
-#610 := (iff #615 #595)
-#617 := (iff #595 #595)
-#458 := [rewrite]: #617
-#614 := (iff #622 #613)
-#623 := (iff #618 #619)
-#612 := [rewrite]: #623
-#609 := [monotonicity #612]: #614
-#611 := [monotonicity #609]: #610
-#459 := [trans #611 #458]: #610
-#616 := [quant-inst #39 #42 #44]: #615
-#460 := [mp #616 #459]: #595
-#566 := [unit-resolution #460 #677]: #613
-#556 := (or #579 #591)
-#354 := (not #438)
-#638 := (or #438 #635)
-#627 := (not #638)
-#568 := (or #128 #627)
-#275 := (iff #128 #638)
-#280 := (or #645 #275)
-#636 := (or #635 #438)
-#637 := (iff #128 #636)
-#281 := (or #645 #637)
-#641 := (iff #281 #280)
-#630 := (iff #280 #280)
-#631 := [rewrite]: #630
-#640 := (iff #637 #275)
-#633 := (iff #636 #638)
-#639 := [rewrite]: #633
-#642 := [monotonicity #639]: #640
-#644 := [monotonicity #642]: #641
-#337 := [trans #644 #631]: #641
-#643 := [quant-inst #39 #40 #45]: #281
-#353 := [mp #643 #337]: #280
-#567 := [unit-resolution #353 #677]: #275
-#624 := (not #275)
-#628 := (or #624 #128 #627)
-#625 := [def-axiom]: #628
-#564 := [unit-resolution #625 #567]: #568
-#569 := [unit-resolution #564 #577]: #627
-#355 := (or #638 #354)
-#341 := [def-axiom]: #355
-#555 := [unit-resolution #341 #569]: #354
-#573 := (or #579 #438 #591)
-#570 := [def-axiom]: #573
-#558 := [unit-resolution #570 #555]: #556
-#559 := [unit-resolution #558 #566]: #591
-#602 := (or #619 #655)
-#496 := [def-axiom]: #602
-#560 := [unit-resolution #496 #559]: #655
-#304 := (or #646 #312 #329)
-#309 := [def-axiom]: #304
-#557 := [unit-resolution #309 #560 #565]: #312
-#356 := (not #635)
-#247 := (or #638 #356)
-#626 := [def-axiom]: #247
-#561 := [unit-resolution #626 #569]: #356
-#497 := (or #619 #603)
-#498 := [def-axiom]: #497
-#541 := [unit-resolution #498 #559]: #603
-#607 := (or #606 #334 #635)
-#601 := [def-axiom]: #607
-#542 := [unit-resolution #601 #541 #561]: #606
-#439 := (or #581 #652 #481)
-#440 := [def-axiom]: #439
-#544 := [unit-resolution #440 #542 #557 #576]: false
-#545 := [lemma #544]: #128
-#331 := (or #328 #141)
-#319 := (or #328 #141 #239)
-#330 := [def-axiom]: #319
-#259 := [unit-resolution #330 #149]: #331
-#546 := [unit-resolution #259 #545]: #328
-#547 := (or #132 #646)
-#305 := (or #647 #132 #646)
-#648 := [def-axiom]: #305
-#548 := [unit-resolution #648 #578]: #547
-#549 := [unit-resolution #548 #546]: #646
-#653 := (or #649 #652)
-#654 := [def-axiom]: #653
-#550 := [unit-resolution #654 #549]: #652
-#608 := (or #581 #312 #606)
-#437 := [def-axiom]: #608
-#551 := [unit-resolution #437 #550 #576]: #606
-#604 := (or #481 #603)
-#605 := [def-axiom]: #604
-#552 := [unit-resolution #605 #551]: #603
-#650 := (or #649 #655)
-#656 := [def-axiom]: #650
-#553 := [unit-resolution #656 #549]: #655
-#588 := (or #591 #329 #334)
-#592 := [def-axiom]: #588
-#543 := [unit-resolution #592 #553 #552]: #591
-#554 := (or #141 #638)
-#629 := (or #624 #141 #638)
-#338 := [def-axiom]: #629
-#532 := [unit-resolution #338 #567]: #554
-#533 := [unit-resolution #532 #545]: #638
-#599 := (or #481 #356)
-#600 := [def-axiom]: #599
-#535 := [unit-resolution #600 #551]: #356
-#349 := (or #627 #438 #635)
-#350 := [def-axiom]: #349
-#536 := [unit-resolution #350 #535 #533]: #438
-#572 := (or #579 #354 #619)
-#582 := [def-axiom]: #572
-#537 := [unit-resolution #582 #536 #543]: #579
-[unit-resolution #460 #677 #537]: false
-unsat
-95f37b9506ab4a9ecf6e4bca8da6ce25960cec6d 158 0
-#2 := false
+#610 := (iff #31 #607)
+#608 := (iff #30 #30)
+#609 := [refl]: #608
+#611 := [quant-intro #609]: #610
+#85 := (~ #31 #31)
+#99 := (~ #30 #30)
+#100 := [refl]: #99
+#86 := [nnf-pos #100]: #85
+#72 := [asserted]: #31
+#101 := [mp~ #72 #86]: #31
+#612 := [mp #101 #611]: #607
+#580 := (not #607)
+#253 := (or #580 #48)
+#269 := (or #47 #47)
+#248 := (iff #45 #269)
+#254 := (or #580 #248)
+#588 := (iff #254 #253)
+#590 := (iff #253 #253)
+#585 := [rewrite]: #590
+#242 := (iff #248 #48)
+#584 := (iff #269 #47)
+#586 := [rewrite]: #584
+#373 := [monotonicity #586]: #242
+#589 := [monotonicity #373]: #588
+#591 := [trans #589 #585]: #588
+#587 := [quant-inst #40 #41 #41]: #254
+#581 := [mp #587 #591]: #253
+#232 := [unit-resolution #581 #612]: #48
+#582 := (or #49 #75 #47)
+#241 := [def-axiom]: #582
+#570 := [unit-resolution #241 #232]: #569
+#571 := [unit-resolution #570 #231 #230]: false
+#572 := [lemma #571]: #47
+#264 := (or #75 #262)
+#263 := (or #75 #262 #177)
+#178 := [def-axiom]: #263
+#255 := [unit-resolution #178 #81]: #264
+#573 := [unit-resolution #255 #572]: #75
+#568 := (or #45 #262)
+#240 := (or #49 #45 #262)
+#245 := [def-axiom]: #240
+#574 := [unit-resolution #245 #232]: #568
+[unit-resolution #574 #573 #572]: false
+unsat
+43b21f39caa6691199e92bb505d662d92b79c6d5 194 0
+#2 := false
+decl f1 :: S1
+#3 := f1
 decl f3 :: (-> S2 S3 S1)
-decl f11 :: S3
-#42 := f11
-decl f9 :: S2
-#39 := f9
-#48 := (f3 f9 f11)
-decl f1 :: S1
-#4 := f1
-#132 := (= f1 #48)
-#186 := (not #132)
-decl f10 :: S3
+decl f12 :: S3
+#43 := f12
+decl f10 :: S2
 #40 := f10
-#46 := (f3 f9 f10)
-#129 := (= f1 #46)
-#185 := (not #129)
-#187 := (or #185 #186)
-#188 := (not #187)
-#329 := [hypothesis]: #188
-decl f6 :: (-> S4 S3 S3)
-decl f8 :: (-> S3 S4)
-#41 := (f8 f10)
-#43 := (f6 #41 f11)
-#44 := (f3 f9 #43)
-#125 := (= f1 #44)
-#144 := (not #125)
-#335 := (or #144 #187)
-#199 := (iff #125 #187)
-#135 := (and #129 #132)
-#145 := (iff #135 #144)
-#202 := (iff #145 #199)
-#194 := (iff #187 #125)
-#200 := (iff #194 #199)
-#201 := [rewrite]: #200
-#197 := (iff #145 #194)
-#191 := (iff #188 #144)
-#195 := (iff #191 #194)
-#196 := [rewrite]: #195
-#192 := (iff #145 #191)
-#189 := (iff #135 #188)
-#190 := [rewrite]: #189
-#193 := [monotonicity #190]: #192
-#198 := [trans #193 #196]: #197
-#203 := [trans #198 #201]: #202
-#49 := (= #48 f1)
-#47 := (= #46 f1)
-#50 := (and #47 #49)
-#45 := (= #44 f1)
-#51 := (iff #45 #50)
-#52 := (not #51)
-#148 := (iff #52 #145)
-#138 := (iff #125 #135)
-#141 := (not #138)
-#146 := (iff #141 #145)
-#147 := [rewrite]: #146
-#142 := (iff #52 #141)
-#139 := (iff #51 #138)
-#136 := (iff #50 #135)
-#133 := (iff #49 #132)
-#134 := [rewrite]: #133
-#130 := (iff #47 #129)
-#131 := [rewrite]: #130
-#137 := [monotonicity #131 #134]: #136
-#127 := (iff #45 #125)
-#128 := [rewrite]: #127
-#140 := [monotonicity #128 #137]: #139
-#143 := [monotonicity #140]: #142
-#149 := [trans #143 #147]: #148
-#124 := [asserted]: #52
-#152 := [mp #124 #149]: #145
-#204 := [mp #152 #203]: #199
-#342 := (not #199)
-#352 := (or #144 #187 #342)
-#356 := [def-axiom]: #352
-#672 := [unit-resolution #356 #204]: #335
-#461 := [unit-resolution #672 #329]: #144
-#328 := (or #125 #187)
-#674 := (iff #125 #188)
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#32 := (f8 #19)
-#33 := (f6 #32 #21)
-#18 := (:var 2 S2)
-#34 := (f3 #18 #33)
-#701 := (pattern #34)
-#27 := (f3 #18 #21)
-#98 := (= f1 #27)
-#177 := (not #98)
-#25 := (f3 #18 #19)
-#95 := (= f1 #25)
-#176 := (not #95)
-#160 := (or #176 #177)
-#161 := (not #160)
-#111 := (= f1 #34)
-#178 := (iff #111 #161)
-#702 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #701) #178)
-#181 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #178)
-#705 := (iff #181 #702)
-#703 := (iff #178 #178)
-#704 := [refl]: #703
-#706 := [quant-intro #704]: #705
-#115 := (and #95 #98)
-#118 := (iff #111 #115)
-#121 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #118)
-#182 := (iff #121 #181)
-#179 := (iff #118 #178)
-#162 := (iff #115 #161)
-#163 := [rewrite]: #162
-#180 := [monotonicity #163]: #179
-#183 := [quant-intro #180]: #182
-#158 := (~ #121 #121)
-#173 := (~ #118 #118)
-#174 := [refl]: #173
-#159 := [nnf-pos #174]: #158
-#28 := (= #27 f1)
-#26 := (= #25 f1)
-#36 := (and #26 #28)
-#35 := (= #34 f1)
-#37 := (iff #35 #36)
-#38 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #37)
-#122 := (iff #38 #121)
-#119 := (iff #37 #118)
-#116 := (iff #36 #115)
-#99 := (iff #28 #98)
-#100 := [rewrite]: #99
-#96 := (iff #26 #95)
-#97 := [rewrite]: #96
-#117 := [monotonicity #97 #100]: #116
-#113 := (iff #35 #111)
-#114 := [rewrite]: #113
-#120 := [monotonicity #114 #117]: #119
-#123 := [quant-intro #120]: #122
-#110 := [asserted]: #38
-#126 := [mp #110 #123]: #121
-#175 := [mp~ #126 #159]: #121
-#184 := [mp #175 #183]: #181
-#707 := [mp #184 #706]: #702
-#668 := (not #702)
-#340 := (or #668 #674)
-#341 := [quant-inst #39 #40 #42]: #340
-#670 := [unit-resolution #341 #707]: #674
-#675 := (not #674)
-#676 := (or #675 #125 #187)
-#677 := [def-axiom]: #676
-#671 := [unit-resolution #677 #670]: #328
-#312 := [unit-resolution #671 #461 #329]: false
-#655 := [lemma #312]: #187
-#282 := (or #125 #188)
-#353 := (or #125 #188 #342)
-#354 := [def-axiom]: #353
-#355 := [unit-resolution #354 #204]: #282
-#316 := [unit-resolution #355 #655]: #125
-#317 := (or #144 #188)
-#678 := (or #675 #144 #188)
-#673 := [def-axiom]: #678
-#318 := [unit-resolution #673 #670]: #317
-[unit-resolution #318 #316 #655]: false
-unsat
-453491eb61ee5da70153220378ac3f020b43cd23 147 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f4 :: S3
-#9 := f4
-decl f9 :: S2
-#39 := f9
-#225 := (f3 f9 f4)
-decl f1 :: S1
-#4 := f1
-#312 := (= f1 #225)
-#226 := (not #312)
-decl f10 :: S3
-#40 := f10
-#313 := (f3 f9 f10)
-#227 := (= f1 #313)
-#314 := (not #227)
-#305 := (or #314 #226)
-#316 := (not #305)
-decl f6 :: (-> S4 S3 S3)
-decl f8 :: (-> S3 S4)
-#41 := (f8 f10)
-#42 := (f6 #41 f4)
-#43 := (f3 f9 #42)
-#119 := (= f1 #43)
-#317 := (iff #119 #316)
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#32 := (f8 #19)
-#33 := (f6 #32 #21)
-#18 := (:var 2 S2)
-#34 := (f3 #18 #33)
-#664 := (pattern #34)
-#27 := (f3 #18 #21)
-#92 := (= f1 #27)
-#160 := (not #92)
-#25 := (f3 #18 #19)
-#89 := (= f1 #25)
-#159 := (not #89)
-#143 := (or #159 #160)
-#144 := (not #143)
-#105 := (= f1 #34)
-#161 := (iff #105 #144)
-#665 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #664) #161)
-#164 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #161)
-#668 := (iff #164 #665)
-#666 := (iff #161 #161)
-#667 := [refl]: #666
-#669 := [quant-intro #667]: #668
-#109 := (and #89 #92)
-#112 := (iff #105 #109)
-#115 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #112)
-#165 := (iff #115 #164)
-#162 := (iff #112 #161)
-#145 := (iff #109 #144)
-#146 := [rewrite]: #145
-#163 := [monotonicity #146]: #162
-#166 := [quant-intro #163]: #165
-#141 := (~ #115 #115)
-#156 := (~ #112 #112)
-#157 := [refl]: #156
-#142 := [nnf-pos #157]: #141
-#28 := (= #27 f1)
-#26 := (= #25 f1)
-#36 := (and #26 #28)
-#35 := (= #34 f1)
-#37 := (iff #35 #36)
-#38 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #37)
-#116 := (iff #38 #115)
-#113 := (iff #37 #112)
-#110 := (iff #36 #109)
-#93 := (iff #28 #92)
-#94 := [rewrite]: #93
-#90 := (iff #26 #89)
-#91 := [rewrite]: #90
-#111 := [monotonicity #91 #94]: #110
-#107 := (iff #35 #105)
-#108 := [rewrite]: #107
-#114 := [monotonicity #108 #111]: #113
-#117 := [quant-intro #114]: #116
-#104 := [asserted]: #38
-#120 := [mp #104 #117]: #115
-#158 := [mp~ #120 #142]: #115
-#167 := [mp #158 #166]: #164
-#670 := [mp #167 #669]: #665
-#315 := (not #665)
-#319 := (or #315 #317)
-#298 := [quant-inst #39 #40 #9]: #319
-#245 := [unit-resolution #298 #670]: #317
-#304 := (not #317)
-#318 := (or #304 #316)
-#44 := (= #43 f1)
-#45 := (not #44)
-#46 := (not #45)
-#131 := (iff #46 #119)
-#123 := (not #119)
-#126 := (not #123)
-#129 := (iff #126 #119)
-#130 := [rewrite]: #129
-#127 := (iff #46 #126)
-#124 := (iff #45 #123)
-#121 := (iff #44 #119)
-#122 := [rewrite]: #121
-#125 := [monotonicity #122]: #124
-#128 := [monotonicity #125]: #127
-#132 := [trans #128 #130]: #131
-#118 := [asserted]: #46
-#135 := [mp #118 #132]: #119
-#640 := (or #304 #123 #316)
-#641 := [def-axiom]: #640
-#634 := [unit-resolution #641 #135]: #318
-#275 := [unit-resolution #634 #245]: #316
-#292 := (or #305 #312)
-#424 := [def-axiom]: #292
-#618 := [unit-resolution #424 #275]: #312
-#8 := (:var 0 S2)
-#10 := (f3 #8 f4)
-#643 := (pattern #10)
-#67 := (= f1 #10)
-#70 := (not #67)
-#644 := (forall (vars (?v0 S2)) (:pat #643) #70)
-#73 := (forall (vars (?v0 S2)) #70)
-#647 := (iff #73 #644)
-#645 := (iff #70 #70)
-#646 := [refl]: #645
-#648 := [quant-intro #646]: #647
-#149 := (~ #73 #73)
-#147 := (~ #70 #70)
-#148 := [refl]: #147
-#150 := [nnf-pos #148]: #149
-#11 := (= #10 f1)
-#12 := (not #11)
-#13 := (forall (vars (?v0 S2)) #12)
-#74 := (iff #13 #73)
-#71 := (iff #12 #70)
-#68 := (iff #11 #67)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#75 := [quant-intro #72]: #74
-#66 := [asserted]: #13
-#78 := [mp #66 #75]: #73
-#134 := [mp~ #78 #150]: #73
-#649 := [mp #134 #648]: #644
-#295 := (not #644)
-#633 := (or #295 #226)
-#291 := [quant-inst #39]: #633
-[unit-resolution #291 #649 #618]: false
-unsat
-6f8829ccc8ddcc6f60b1e61de2ed840042d23d2c 171 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f10 :: S3
-#40 := f10
-decl f9 :: S2
-#39 := f9
-#45 := (f3 f9 f10)
-decl f1 :: S1
-#4 := f1
-#125 := (= f1 #45)
-#321 := (not #125)
-decl f6 :: (-> S4 S3 S3)
-decl f5 :: S3
-#14 := f5
-decl f8 :: (-> S3 S4)
-#41 := (f8 f10)
-#42 := (f6 #41 f5)
-#43 := (f3 f9 #42)
-#121 := (= f1 #43)
-#325 := (f3 f9 f5)
-#322 := (= f1 #325)
-#326 := (not #322)
-#299 := [hypothesis]: #326
-#8 := (:var 0 S2)
-#15 := (f3 #8 f5)
-#657 := (pattern #15)
-#79 := (= f1 #15)
-#658 := (forall (vars (?v0 S2)) (:pat #657) #79)
-#83 := (forall (vars (?v0 S2)) #79)
-#661 := (iff #83 #658)
-#659 := (iff #79 #79)
-#660 := [refl]: #659
-#662 := [quant-intro #660]: #661
-#144 := (~ #83 #83)
-#143 := (~ #79 #79)
-#158 := [refl]: #143
-#145 := [nnf-pos #158]: #144
-#16 := (= #15 f1)
-#17 := (forall (vars (?v0 S2)) #16)
-#84 := (iff #17 #83)
-#81 := (iff #16 #79)
-#82 := [rewrite]: #81
-#85 := [quant-intro #82]: #84
-#78 := [asserted]: #17
-#88 := [mp #78 #85]: #83
-#159 := [mp~ #88 #145]: #83
-#663 := [mp #159 #662]: #658
-#287 := (not #658)
-#288 := (or #287 #322)
-#289 := [quant-inst #39]: #288
-#431 := [unit-resolution #289 #663 #299]: false
-#627 := [lemma #431]: #322
-#134 := (not #121)
-#628 := [hypothesis]: #134
-#320 := (or #125 #121)
-#135 := (iff #125 #134)
-#46 := (= #45 f1)
-#44 := (= #43 f1)
-#47 := (iff #44 #46)
-#48 := (not #47)
-#138 := (iff #48 #135)
-#128 := (iff #121 #125)
-#131 := (not #128)
-#136 := (iff #131 #135)
-#137 := [rewrite]: #136
-#132 := (iff #48 #131)
-#129 := (iff #47 #128)
-#126 := (iff #46 #125)
-#127 := [rewrite]: #126
-#123 := (iff #44 #121)
-#124 := [rewrite]: #123
-#130 := [monotonicity #124 #127]: #129
-#133 := [monotonicity #130]: #132
-#139 := [trans #133 #137]: #138
-#120 := [asserted]: #48
-#142 := [mp #120 #139]: #135
-#232 := (not #135)
-#319 := (or #125 #121 #232)
-#233 := [def-axiom]: #319
-#234 := [unit-resolution #233 #142]: #320
-#629 := [unit-resolution #234 #628]: #125
-#305 := (or #321 #326)
-#631 := (or #121 #305)
-#642 := (not #305)
-#644 := (iff #121 #642)
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#32 := (f8 #19)
-#33 := (f6 #32 #21)
-#18 := (:var 2 S2)
-#34 := (f3 #18 #33)
-#671 := (pattern #34)
-#27 := (f3 #18 #21)
-#94 := (= f1 #27)
-#167 := (not #94)
-#25 := (f3 #18 #19)
-#91 := (= f1 #25)
-#166 := (not #91)
-#150 := (or #166 #167)
-#151 := (not #150)
-#107 := (= f1 #34)
-#168 := (iff #107 #151)
-#672 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #671) #168)
-#171 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #168)
-#675 := (iff #171 #672)
-#673 := (iff #168 #168)
-#674 := [refl]: #673
-#676 := [quant-intro #674]: #675
-#111 := (and #91 #94)
-#114 := (iff #107 #111)
-#117 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #114)
-#172 := (iff #117 #171)
-#169 := (iff #114 #168)
-#152 := (iff #111 #151)
-#153 := [rewrite]: #152
-#170 := [monotonicity #153]: #169
-#173 := [quant-intro #170]: #172
-#148 := (~ #117 #117)
-#163 := (~ #114 #114)
-#164 := [refl]: #163
-#149 := [nnf-pos #164]: #148
-#28 := (= #27 f1)
-#26 := (= #25 f1)
-#36 := (and #26 #28)
-#35 := (= #34 f1)
-#37 := (iff #35 #36)
-#38 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #37)
-#118 := (iff #38 #117)
-#115 := (iff #37 #114)
-#112 := (iff #36 #111)
-#95 := (iff #28 #94)
-#96 := [rewrite]: #95
-#92 := (iff #26 #91)
-#93 := [rewrite]: #92
-#113 := [monotonicity #93 #96]: #112
-#109 := (iff #35 #107)
-#110 := [rewrite]: #109
-#116 := [monotonicity #110 #113]: #115
-#119 := [quant-intro #116]: #118
-#106 := [asserted]: #38
-#122 := [mp #106 #119]: #117
-#165 := [mp~ #122 #149]: #117
-#174 := [mp #165 #173]: #171
-#677 := [mp #174 #676]: #672
-#638 := (not #672)
-#310 := (or #638 #644)
-#311 := [quant-inst #39 #40 #14]: #310
-#630 := [unit-resolution #311 #677]: #644
-#639 := (not #644)
-#297 := (or #639 #121 #305)
-#302 := [def-axiom]: #297
-#626 := [unit-resolution #302 #630]: #631
-#632 := [unit-resolution #626 #628]: #305
-#643 := (or #642 #321 #326)
-#649 := [def-axiom]: #643
-#268 := [unit-resolution #649 #632 #629 #627]: false
-#633 := [lemma #268]: #121
-#324 := (or #321 #134)
-#312 := (or #321 #134 #232)
-#323 := [def-axiom]: #312
-#252 := [unit-resolution #323 #142]: #324
-#635 := [unit-resolution #252 #633]: #321
-#273 := (or #134 #642)
-#640 := (or #639 #134 #642)
-#298 := [def-axiom]: #640
-#274 := [unit-resolution #298 #630]: #273
-#636 := [unit-resolution #274 #633]: #642
-#645 := (or #305 #125)
-#646 := [def-axiom]: #645
-[unit-resolution #646 #636 #635]: false
-unsat
-7fb5c9e3c94a5bd9f761d4854f2678f455553edf 171 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f10 :: S3
-#40 := f10
-decl f8 :: (-> S3 S4)
+#581 := (f3 f10 f12)
+#218 := (= #581 f1)
 decl f11 :: S3
-#42 := f11
-#46 := (f8 f11)
-#47 := (f6 #46 f10)
-decl f9 :: S2
-#39 := f9
-#48 := (f3 f9 #47)
-decl f1 :: S1
-#4 := f1
-#128 := (= f1 #48)
-#324 := (not #128)
-#41 := (f8 f10)
-#43 := (f6 #41 f11)
-#44 := (f3 f9 #43)
-#124 := (= f1 #44)
-#137 := (not #124)
-#626 := [hypothesis]: #137
-#323 := (or #128 #124)
-#138 := (iff #128 #137)
-#49 := (= #48 f1)
-#45 := (= #44 f1)
-#50 := (iff #45 #49)
-#51 := (not #50)
-#141 := (iff #51 #138)
-#131 := (iff #124 #128)
-#134 := (not #131)
-#139 := (iff #134 #138)
-#140 := [rewrite]: #139
-#135 := (iff #51 #134)
-#132 := (iff #50 #131)
-#129 := (iff #49 #128)
-#130 := [rewrite]: #129
-#126 := (iff #45 #124)
-#127 := [rewrite]: #126
-#133 := [monotonicity #127 #130]: #132
-#136 := [monotonicity #133]: #135
-#142 := [trans #136 #140]: #141
-#123 := [asserted]: #51
-#145 := [mp #123 #142]: #138
-#235 := (not #138)
-#322 := (or #128 #124 #235)
-#236 := [def-axiom]: #322
-#237 := [unit-resolution #236 #145]: #323
-#627 := [unit-resolution #237 #626]: #128
-#308 := (f3 f9 f11)
-#645 := (= f1 #308)
-#647 := (not #645)
-#328 := (f3 f9 f10)
-#325 := (= f1 #328)
-#329 := (not #325)
-#313 := (or #329 #647)
-#624 := (or #124 #313)
-#649 := (not #313)
-#640 := (iff #124 #649)
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#32 := (f8 #19)
-#33 := (f6 #32 #21)
-#18 := (:var 2 S2)
-#34 := (f3 #18 #33)
-#674 := (pattern #34)
-#27 := (f3 #18 #21)
-#97 := (= f1 #27)
-#170 := (not #97)
-#25 := (f3 #18 #19)
-#94 := (= f1 #25)
-#169 := (not #94)
-#153 := (or #169 #170)
-#154 := (not #153)
-#110 := (= f1 #34)
-#171 := (iff #110 #154)
-#675 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #674) #171)
-#174 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #171)
-#678 := (iff #174 #675)
-#676 := (iff #171 #171)
-#677 := [refl]: #676
-#679 := [quant-intro #677]: #678
-#114 := (and #94 #97)
-#117 := (iff #110 #114)
-#120 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #117)
-#175 := (iff #120 #174)
-#172 := (iff #117 #171)
-#155 := (iff #114 #154)
-#156 := [rewrite]: #155
-#173 := [monotonicity #156]: #172
-#176 := [quant-intro #173]: #175
-#151 := (~ #120 #120)
-#166 := (~ #117 #117)
-#167 := [refl]: #166
-#152 := [nnf-pos #167]: #151
-#28 := (= #27 f1)
-#26 := (= #25 f1)
-#36 := (and #26 #28)
-#35 := (= #34 f1)
-#37 := (iff #35 #36)
-#38 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #37)
-#121 := (iff #38 #120)
-#118 := (iff #37 #117)
-#115 := (iff #36 #114)
-#98 := (iff #28 #97)
-#99 := [rewrite]: #98
-#95 := (iff #26 #94)
-#96 := [rewrite]: #95
-#116 := [monotonicity #96 #99]: #115
-#112 := (iff #35 #110)
-#113 := [rewrite]: #112
-#119 := [monotonicity #113 #116]: #118
-#122 := [quant-intro #119]: #121
-#109 := [asserted]: #38
-#125 := [mp #109 #122]: #120
-#168 := [mp~ #125 #152]: #120
-#177 := [mp #168 #176]: #174
-#680 := [mp #177 #679]: #675
-#300 := (not #675)
-#333 := (or #300 #640)
-#349 := [quant-inst #39 #40 #42]: #333
-#620 := [unit-resolution #349 #680]: #640
-#350 := (not #640)
-#351 := (or #350 #124 #313)
-#337 := [def-axiom]: #351
-#621 := [unit-resolution #337 #620]: #624
-#625 := [unit-resolution #621 #626]: #313
-#335 := (or #324 #649)
-#646 := (iff #128 #649)
-#305 := (or #300 #646)
-#302 := (or #647 #329)
-#434 := (not #302)
-#641 := (iff #128 #434)
-#643 := (or #300 #641)
-#644 := (iff #643 #305)
-#628 := (iff #305 #305)
-#289 := [rewrite]: #628
-#652 := (iff #641 #646)
-#650 := (iff #434 #649)
-#314 := (iff #302 #313)
-#648 := [rewrite]: #314
-#651 := [monotonicity #648]: #650
-#642 := [monotonicity #651]: #652
-#285 := [monotonicity #642]: #644
-#290 := [trans #285 #289]: #644
-#301 := [quant-inst #39 #42 #40]: #643
-#291 := [mp #301 #290]: #305
-#334 := [unit-resolution #291 #680]: #646
-#629 := (not #646)
-#636 := (or #629 #324 #649)
-#638 := [def-axiom]: #636
-#336 := [unit-resolution #638 #334]: #335
-#338 := [unit-resolution #336 #625 #627]: false
-#616 := [lemma #338]: #124
-#327 := (or #324 #137)
-#315 := (or #324 #137 #235)
-#326 := [def-axiom]: #315
-#255 := [unit-resolution #326 #145]: #327
-#617 := [unit-resolution #255 #616]: #324
-#330 := (or #137 #649)
-#352 := (or #350 #137 #649)
-#243 := [def-axiom]: #352
-#614 := [unit-resolution #243 #620]: #330
-#618 := [unit-resolution #614 #616]: #649
-#615 := (or #128 #313)
-#635 := (or #629 #128 #313)
-#271 := [def-axiom]: #635
-#619 := [unit-resolution #271 #334]: #615
-[unit-resolution #619 #618 #617]: false
-unsat
-894705c4ef9337c77fce76fc097ee92668a964e4 147 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f10 :: S3
-#40 := f10
-decl f8 :: (-> S3 S4)
-#41 := (f8 f10)
-#42 := (f6 #41 f10)
-decl f9 :: S2
-#39 := f9
-#43 := (f3 f9 #42)
-decl f1 :: S1
-#4 := f1
-#121 := (= f1 #43)
-#134 := (not #121)
-#630 := [hypothesis]: #134
-#45 := (f3 f9 f10)
-#125 := (= f1 #45)
-#320 := (or #125 #121)
-#135 := (iff #125 #134)
-#46 := (= #45 f1)
-#44 := (= #43 f1)
-#47 := (iff #44 #46)
-#48 := (not #47)
-#138 := (iff #48 #135)
-#128 := (iff #121 #125)
-#131 := (not #128)
-#136 := (iff #131 #135)
-#137 := [rewrite]: #136
-#132 := (iff #48 #131)
-#129 := (iff #47 #128)
-#126 := (iff #46 #125)
-#127 := [rewrite]: #126
-#123 := (iff #44 #121)
-#124 := [rewrite]: #123
-#130 := [monotonicity #124 #127]: #129
-#133 := [monotonicity #130]: #132
-#139 := [trans #133 #137]: #138
-#120 := [asserted]: #48
-#142 := [mp #120 #139]: #135
-#232 := (not #135)
-#319 := (or #125 #121 #232)
-#233 := [def-axiom]: #319
-#234 := [unit-resolution #233 #142]: #320
-#631 := [unit-resolution #234 #630]: #125
-#321 := (not #125)
-#632 := (or #121 #321)
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#32 := (f8 #19)
-#33 := (f6 #32 #21)
-#18 := (:var 2 S2)
-#34 := (f3 #18 #33)
-#671 := (pattern #34)
-#27 := (f3 #18 #21)
-#94 := (= f1 #27)
-#167 := (not #94)
-#25 := (f3 #18 #19)
-#91 := (= f1 #25)
-#166 := (not #91)
-#150 := (or #166 #167)
-#151 := (not #150)
-#107 := (= f1 #34)
-#168 := (iff #107 #151)
-#672 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #671) #168)
-#171 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #168)
-#675 := (iff #171 #672)
-#673 := (iff #168 #168)
-#674 := [refl]: #673
-#676 := [quant-intro #674]: #675
-#111 := (and #91 #94)
-#114 := (iff #107 #111)
-#117 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #114)
-#172 := (iff #117 #171)
-#169 := (iff #114 #168)
-#152 := (iff #111 #151)
-#153 := [rewrite]: #152
-#170 := [monotonicity #153]: #169
-#173 := [quant-intro #170]: #172
-#148 := (~ #117 #117)
-#163 := (~ #114 #114)
-#164 := [refl]: #163
-#149 := [nnf-pos #164]: #148
-#28 := (= #27 f1)
-#26 := (= #25 f1)
-#36 := (and #26 #28)
-#35 := (= #34 f1)
-#37 := (iff #35 #36)
-#38 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #37)
-#118 := (iff #38 #117)
-#115 := (iff #37 #114)
-#112 := (iff #36 #111)
-#95 := (iff #28 #94)
-#96 := [rewrite]: #95
-#92 := (iff #26 #91)
-#93 := [rewrite]: #92
-#113 := [monotonicity #93 #96]: #112
-#109 := (iff #35 #107)
-#110 := [rewrite]: #109
-#116 := [monotonicity #110 #113]: #115
-#119 := [quant-intro #116]: #118
-#106 := [asserted]: #38
-#122 := [mp #106 #119]: #117
-#165 := [mp~ #122 #149]: #117
-#174 := [mp #165 #173]: #171
-#677 := [mp #174 #676]: #672
-#648 := (not #672)
-#643 := (or #648 #128)
-#325 := (or #321 #321)
-#322 := (not #325)
-#326 := (iff #121 #322)
-#649 := (or #648 #326)
-#297 := (iff #649 #643)
-#640 := (iff #643 #643)
-#298 := [rewrite]: #640
-#646 := (iff #326 #128)
-#311 := (iff #322 #125)
-#644 := (not #321)
-#638 := (iff #644 #125)
-#310 := [rewrite]: #638
-#299 := (iff #322 #644)
-#305 := (iff #325 #321)
-#642 := [rewrite]: #305
-#431 := [monotonicity #642]: #299
-#645 := [trans #431 #310]: #311
-#647 := [monotonicity #645]: #646
-#302 := [monotonicity #647]: #297
-#641 := [trans #302 #298]: #297
-#639 := [quant-inst #39 #40 #40]: #649
-#282 := [mp #639 #641]: #643
-#626 := [unit-resolution #282 #677]: #128
-#625 := (or #131 #121 #321)
-#286 := [def-axiom]: #625
-#268 := [unit-resolution #286 #626]: #632
-#633 := [unit-resolution #268 #631 #630]: false
-#635 := [lemma #633]: #121
-#324 := (or #321 #134)
-#312 := (or #321 #134 #232)
-#323 := [def-axiom]: #312
-#252 := [unit-resolution #323 #142]: #324
-#273 := [unit-resolution #252 #635]: #321
-#274 := (or #134 #125)
-#287 := (or #131 #134 #125)
-#288 := [def-axiom]: #287
-#636 := [unit-resolution #288 #626]: #274
-[unit-resolution #636 #273 #635]: false
-unsat
-6bc0dc7cf7d78f36cf0c61d5f399a6c019b36218 285 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f11 :: S3
-#42 := f11
-decl f8 :: (-> S3 S4)
-decl f10 :: S3
-#40 := f10
-#41 := (f8 f10)
-#49 := (f6 #41 f11)
-decl f9 :: S2
-#39 := f9
-#312 := (f3 f9 #49)
-decl f1 :: S1
-#4 := f1
-#649 := (= f1 #312)
-#247 := (f3 f9 f11)
-#626 := (= f1 #247)
-#623 := (not #626)
-#337 := (f3 f9 f10)
-#353 := (= f1 #337)
-#354 := (not #353)
-#612 := (or #354 #623)
-#613 := (not #612)
-#609 := (iff #613 #649)
-#580 := (not #609)
-decl f12 :: S3
-#44 := f12
-#332 := (f3 f9 f12)
-#329 := (= f1 #332)
-#333 := (not #329)
-#482 := (or #333 #623)
-#491 := (not #482)
-#43 := (f8 f11)
-#45 := (f6 #43 f12)
-#644 := (f3 f9 #45)
-#630 := (= f1 #644)
-#492 := (iff #491 #630)
-#585 := (not #492)
-#565 := [hypothesis]: #585
-#21 := (:var 0 S3)
-#19 := (:var 1 S3)
-#32 := (f8 #19)
-#33 := (f6 #32 #21)
-#18 := (:var 2 S2)
-#34 := (f3 #18 #33)
-#678 := (pattern #34)
-#27 := (f3 #18 #21)
-#101 := (= f1 #27)
-#174 := (not #101)
-#25 := (f3 #18 #19)
-#98 := (= f1 #25)
-#173 := (not #98)
-#157 := (or #173 #174)
-#158 := (not #157)
-#114 := (= f1 #34)
-#175 := (iff #114 #158)
-#679 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #678) #175)
-#178 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #175)
-#682 := (iff #178 #679)
-#680 := (iff #175 #175)
-#681 := [refl]: #680
-#683 := [quant-intro #681]: #682
-#118 := (and #98 #101)
-#121 := (iff #114 #118)
-#124 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #121)
-#179 := (iff #124 #178)
-#176 := (iff #121 #175)
-#159 := (iff #118 #158)
-#160 := [rewrite]: #159
-#177 := [monotonicity #160]: #176
-#180 := [quant-intro #177]: #179
-#155 := (~ #124 #124)
-#170 := (~ #121 #121)
-#171 := [refl]: #170
-#156 := [nnf-pos #171]: #155
-#28 := (= #27 f1)
-#26 := (= #25 f1)
-#36 := (and #26 #28)
-#35 := (= #34 f1)
-#37 := (iff #35 #36)
-#38 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #37)
-#125 := (iff #38 #124)
-#122 := (iff #37 #121)
-#119 := (iff #36 #118)
-#102 := (iff #28 #101)
-#103 := [rewrite]: #102
-#99 := (iff #26 #98)
-#100 := [rewrite]: #99
-#120 := [monotonicity #100 #103]: #119
-#116 := (iff #35 #114)
-#117 := [rewrite]: #116
-#123 := [monotonicity #117 #120]: #122
-#126 := [quant-intro #123]: #125
-#113 := [asserted]: #38
-#129 := [mp #113 #126]: #124
-#172 := [mp~ #129 #156]: #124
-#181 := [mp #172 #180]: #178
-#684 := [mp #181 #683]: #679
-#304 := (not #679)
-#496 := (or #304 #492)
-#598 := (or #623 #333)
-#480 := (not #598)
-#481 := (iff #630 #480)
-#497 := (or #304 #481)
-#591 := (iff #497 #496)
-#592 := (iff #496 #496)
-#579 := [rewrite]: #592
-#494 := (iff #481 #492)
-#590 := (iff #630 #491)
-#493 := (iff #590 #492)
-#486 := [rewrite]: #493
-#475 := (iff #481 #590)
-#586 := (iff #480 #491)
-#441 := (iff #598 #482)
-#589 := [rewrite]: #441
-#587 := [monotonicity #589]: #586
-#490 := [monotonicity #587]: #475
-#495 := [trans #490 #486]: #494
-#588 := [monotonicity #495]: #591
-#581 := [trans #588 #579]: #591
-#498 := [quant-inst #39 #42 #44]: #497
-#573 := [mp #498 #581]: #496
-#566 := [unit-resolution #573 #684 #565]: false
-#567 := [lemma #566]: #492
-#631 := (not #630)
-#355 := (or #354 #631)
-#341 := (not #355)
-#46 := (f6 #41 #45)
-#47 := (f3 f9 #46)
-#128 := (= f1 #47)
-#141 := (not #128)
-#568 := [hypothesis]: #141
-#569 := (or #128 #355)
-#356 := (iff #128 #341)
-#627 := (or #304 #356)
-#349 := [quant-inst #39 #40 #45]: #627
-#564 := [unit-resolution #349 #684]: #356
-#339 := (not #356)
-#340 := (or #339 #128 #355)
-#342 := [def-axiom]: #340
-#555 := [unit-resolution #342 #564]: #569
-#556 := [unit-resolution #555 #568]: #355
-#595 := (or #304 #609)
-#614 := (iff #649 #613)
-#611 := (or #304 #614)
-#616 := (iff #611 #595)
-#459 := (iff #595 #595)
-#460 := [rewrite]: #459
-#610 := (iff #614 #609)
-#615 := [rewrite]: #610
-#458 := [monotonicity #615]: #616
-#602 := [trans #458 #460]: #616
-#617 := [quant-inst #39 #40 #42]: #611
-#603 := [mp #617 #602]: #595
-#558 := [unit-resolution #603 #684]: #609
-#544 := (or #580 #613)
-#651 := (not #649)
-#317 := (or #333 #651)
-#653 := (not #317)
-#50 := (f8 #49)
-#51 := (f6 #50 f12)
-#52 := (f3 f9 #51)
-#132 := (= f1 #52)
-#327 := (or #132 #128)
-#142 := (iff #132 #141)
-#53 := (= #52 f1)
-#48 := (= #47 f1)
-#54 := (iff #48 #53)
-#55 := (not #54)
-#145 := (iff #55 #142)
-#135 := (iff #128 #132)
-#138 := (not #135)
-#143 := (iff #138 #142)
-#144 := [rewrite]: #143
-#139 := (iff #55 #138)
-#136 := (iff #54 #135)
-#133 := (iff #53 #132)
-#134 := [rewrite]: #133
-#130 := (iff #48 #128)
-#131 := [rewrite]: #130
-#137 := [monotonicity #131 #134]: #136
-#140 := [monotonicity #137]: #139
-#146 := [trans #140 #144]: #145
-#127 := [asserted]: #55
-#149 := [mp #127 #146]: #142
-#239 := (not #142)
-#326 := (or #132 #128 #239)
-#240 := [def-axiom]: #326
-#241 := [unit-resolution #240 #149]: #327
-#559 := [unit-resolution #241 #568]: #132
-#328 := (not #132)
-#557 := (or #328 #653)
-#650 := (iff #132 #653)
-#309 := (or #304 #650)
-#306 := (or #651 #333)
-#438 := (not #306)
-#645 := (iff #132 #438)
-#647 := (or #304 #645)
-#648 := (iff #647 #309)
-#632 := (iff #309 #309)
-#293 := [rewrite]: #632
-#656 := (iff #645 #650)
-#654 := (iff #438 #653)
-#318 := (iff #306 #317)
-#652 := [rewrite]: #318
-#655 := [monotonicity #652]: #654
-#646 := [monotonicity #655]: #656
-#289 := [monotonicity #646]: #648
-#294 := [trans #289 #293]: #648
-#305 := [quant-inst #39 #49 #44]: #647
-#295 := [mp #305 #294]: #309
-#560 := [unit-resolution #295 #684]: #650
-#633 := (not #650)
-#640 := (or #633 #328 #653)
-#642 := [def-axiom]: #640
-#561 := [unit-resolution #642 #560]: #557
-#541 := [unit-resolution #561 #559]: #653
-#635 := (or #317 #649)
-#636 := [def-axiom]: #635
-#542 := [unit-resolution #636 #541]: #649
-#574 := (or #580 #613 #651)
-#575 := [def-axiom]: #574
-#545 := [unit-resolution #575 #542]: #544
-#546 := [unit-resolution #545 #558]: #613
-#604 := (or #612 #353)
-#570 := [def-axiom]: #604
-#547 := [unit-resolution #570 #546]: #353
-#629 := (or #341 #354 #631)
-#338 := [def-axiom]: #629
-#548 := [unit-resolution #338 #547 #556]: #631
-#296 := (or #317 #329)
-#634 := [def-axiom]: #296
-#549 := [unit-resolution #634 #541]: #329
-#572 := (or #612 #626)
-#582 := [def-axiom]: #572
-#550 := [unit-resolution #582 #546]: #626
-#607 := (or #491 #333 #623)
-#601 := [def-axiom]: #607
-#551 := [unit-resolution #601 #550 #549]: #491
-#439 := (or #585 #482 #630)
-#440 := [def-axiom]: #439
-#552 := [unit-resolution #440 #551 #548 #567]: false
-#553 := [lemma #552]: #128
-#543 := (or #141 #341)
-#620 := (or #339 #141 #341)
-#621 := [def-axiom]: #620
-#554 := [unit-resolution #621 #564]: #543
-#532 := [unit-resolution #554 #553]: #341
-#628 := (or #355 #630)
-#625 := [def-axiom]: #628
-#533 := [unit-resolution #625 #532]: #630
-#608 := (or #585 #491 #631)
-#437 := [def-axiom]: #608
-#535 := [unit-resolution #437 #533 #567]: #491
-#600 := (or #482 #626)
-#606 := [def-axiom]: #600
-#536 := [unit-resolution #606 #535]: #626
-#350 := (or #355 #353)
-#624 := [def-axiom]: #350
-#537 := [unit-resolution #624 #532]: #353
-#583 := (or #613 #354 #623)
-#584 := [def-axiom]: #583
-#538 := [unit-resolution #584 #537 #536]: #613
-#331 := (or #328 #141)
-#319 := (or #328 #141 #239)
-#330 := [def-axiom]: #319
-#259 := [unit-resolution #330 #149]: #331
-#539 := [unit-resolution #259 #553]: #328
-#534 := (or #132 #317)
-#639 := (or #633 #132 #317)
-#275 := [def-axiom]: #639
-#540 := [unit-resolution #275 #560]: #534
-#526 := [unit-resolution #540 #539]: #317
-#605 := (or #482 #329)
-#599 := [def-axiom]: #605
-#522 := [unit-resolution #599 #535]: #329
-#637 := (or #653 #333 #651)
-#638 := [def-axiom]: #637
-#523 := [unit-resolution #638 #522 #526]: #651
-#576 := (or #580 #612 #649)
-#577 := [def-axiom]: #576
-#524 := [unit-resolution #577 #523 #538]: #580
-[unit-resolution #603 #684 #524]: false
-unsat
-a7bc4cb1c082efb5c0f6c878be007f36211e0adf 20 0
-#2 := false
-decl f12 :: (-> S3 S3)
-decl f4 :: S3
-#8 := f4
-#48 := (f12 f4)
-#49 := (= #48 #48)
-#50 := (not #49)
-#145 := (iff #50 false)
-#1 := true
-#140 := (not true)
-#143 := (iff #140 false)
-#144 := [rewrite]: #143
-#141 := (iff #50 #140)
-#137 := (iff #49 true)
-#139 := [rewrite]: #137
-#142 := [monotonicity #139]: #141
-#146 := [trans #142 #144]: #145
-#136 := [asserted]: #50
-[mp #136 #146]: false
-unsat
-eac8197a82f6b3a5c2024430d69641bb761b0abc 60 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f4 :: S3
-#9 := f4
-decl f10 :: S2
-#41 := f10
-#42 := (f3 f10 f4)
-decl f1 :: S1
-#4 := f1
-#118 := (= f1 #42)
-#43 := (= #42 f1)
-#44 := (not #43)
-#45 := (not #44)
-#130 := (iff #45 #118)
-#122 := (not #118)
-#125 := (not #122)
-#128 := (iff #125 #118)
-#129 := [rewrite]: #128
-#126 := (iff #45 #125)
-#123 := (iff #44 #122)
-#120 := (iff #43 #118)
-#121 := [rewrite]: #120
-#124 := [monotonicity #121]: #123
-#127 := [monotonicity #124]: #126
-#131 := [trans #127 #129]: #130
-#117 := [asserted]: #45
-#134 := [mp #117 #131]: #118
-#8 := (:var 0 S2)
-#10 := (f3 #8 f4)
-#642 := (pattern #10)
-#66 := (= f1 #10)
-#69 := (not #66)
-#643 := (forall (vars (?v0 S2)) (:pat #642) #69)
-#72 := (forall (vars (?v0 S2)) #69)
-#646 := (iff #72 #643)
-#644 := (iff #69 #69)
-#645 := [refl]: #644
-#647 := [quant-intro #645]: #646
-#148 := (~ #72 #72)
-#146 := (~ #69 #69)
-#147 := [refl]: #146
-#149 := [nnf-pos #147]: #148
-#11 := (= #10 f1)
-#12 := (not #11)
-#13 := (forall (vars (?v0 S2)) #12)
-#73 := (iff #13 #72)
-#70 := (iff #12 #69)
-#67 := (iff #11 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#74 := [quant-intro #71]: #73
-#65 := [asserted]: #13
-#77 := [mp #65 #74]: #72
-#133 := [mp~ #77 #149]: #72
-#648 := [mp #133 #647]: #643
-#225 := (not #643)
-#312 := (or #225 #122)
-#226 := [quant-inst #41]: #312
-[unit-resolution #226 #648 #134]: false
-unsat
-32295808d649b2df10d022ec20bfa2f501001522 48 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f5 :: S3
-#14 := f5
-decl f10 :: S2
-#41 := f10
-#42 := (f3 f10 f5)
-decl f1 :: S1
-#4 := f1
-#117 := (= f1 #42)
-#121 := (not #117)
-#43 := (= #42 f1)
-#44 := (not #43)
-#122 := (iff #44 #121)
-#119 := (iff #43 #117)
-#120 := [rewrite]: #119
-#123 := [monotonicity #120]: #122
-#116 := [asserted]: #44
-#126 := [mp #116 #123]: #121
-#8 := (:var 0 S2)
-#15 := (f3 #8 f5)
-#641 := (pattern #15)
-#75 := (= f1 #15)
-#642 := (forall (vars (?v0 S2)) (:pat #641) #75)
-#79 := (forall (vars (?v0 S2)) #75)
-#645 := (iff #79 #642)
-#643 := (iff #75 #75)
-#644 := [refl]: #643
-#646 := [quant-intro #644]: #645
-#128 := (~ #79 #79)
-#127 := (~ #75 #75)
-#142 := [refl]: #127
-#129 := [nnf-pos #142]: #128
-#16 := (= #15 f1)
-#17 := (forall (vars (?v0 S2)) #16)
-#80 := (iff #17 #79)
-#77 := (iff #16 #75)
-#78 := [rewrite]: #77
-#81 := [quant-intro #78]: #80
-#74 := [asserted]: #17
-#84 := [mp #74 #81]: #79
-#143 := [mp~ #84 #129]: #79
-#647 := [mp #143 #646]: #642
-#217 := (not #642)
-#304 := (or #217 #117)
-#218 := [quant-inst #41]: #304
-[unit-resolution #218 #647 #126]: false
-unsat
-dfe83e391823f1cbfcca9d6fb06c0ae74a22248a 126 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f12 :: S3
-#44 := f12
-decl f7 :: (-> S5 S3 S4)
-decl f11 :: S3
-#42 := f11
-decl f8 :: S5
-#19 := f8
-#43 := (f7 f8 f11)
-#45 := (f6 #43 f12)
-decl f10 :: S2
-#41 := f10
-#46 := (f3 f10 #45)
-decl f1 :: S1
-#4 := f1
-#127 := (= f1 #46)
-#146 := (not #127)
-#650 := [hypothesis]: #146
-#50 := (f3 f10 f12)
-#134 := (= f1 #50)
-#48 := (f3 f10 f11)
-#131 := (= f1 #48)
-#137 := (or #131 #134)
-#338 := (or #137 #127)
-#147 := (iff #137 #146)
-#51 := (= #50 f1)
-#49 := (= #48 f1)
-#52 := (or #49 #51)
-#47 := (= #46 f1)
-#53 := (iff #47 #52)
-#54 := (not #53)
-#150 := (iff #54 #147)
-#140 := (iff #127 #137)
-#143 := (not #140)
-#148 := (iff #143 #147)
-#149 := [rewrite]: #148
-#144 := (iff #54 #143)
-#141 := (iff #53 #140)
-#138 := (iff #52 #137)
-#135 := (iff #51 #134)
-#136 := [rewrite]: #135
-#132 := (iff #49 #131)
-#133 := [rewrite]: #132
-#139 := [monotonicity #133 #136]: #138
-#129 := (iff #47 #127)
-#130 := [rewrite]: #129
-#142 := [monotonicity #130 #139]: #141
-#145 := [monotonicity #142]: #144
-#151 := [trans #145 #149]: #150
-#126 := [asserted]: #54
-#154 := [mp #126 #151]: #147
-#264 := (not #147)
-#337 := (or #137 #127 #264)
-#334 := [def-axiom]: #337
-#317 := [unit-resolution #334 #154]: #338
-#322 := [unit-resolution #317 #650]: #137
-#324 := (not #137)
-#653 := (or #127 #324)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#21 := (f7 f8 #20)
-#23 := (f6 #21 #22)
-#18 := (:var 2 S2)
-#24 := (f3 #18 #23)
-#676 := (pattern #24)
-#28 := (f3 #18 #22)
-#100 := (= f1 #28)
-#26 := (f3 #18 #20)
-#97 := (= f1 #26)
-#103 := (or #97 #100)
-#93 := (= f1 #24)
-#106 := (iff #93 #103)
-#677 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #676) #106)
-#109 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #106)
-#680 := (iff #109 #677)
-#678 := (iff #106 #106)
-#679 := [refl]: #678
-#681 := [quant-intro #679]: #680
-#158 := (~ #109 #109)
-#172 := (~ #106 #106)
-#173 := [refl]: #172
-#159 := [nnf-pos #173]: #158
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#30 := (or #27 #29)
-#25 := (= #24 f1)
-#31 := (iff #25 #30)
-#32 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #31)
-#110 := (iff #32 #109)
-#107 := (iff #31 #106)
-#104 := (iff #30 #103)
-#101 := (iff #29 #100)
-#102 := [rewrite]: #101
-#98 := (iff #27 #97)
-#99 := [rewrite]: #98
-#105 := [monotonicity #99 #102]: #104
-#95 := (iff #25 #93)
-#96 := [rewrite]: #95
-#108 := [monotonicity #96 #105]: #107
-#111 := [quant-intro #108]: #110
-#92 := [asserted]: #32
-#114 := [mp #92 #111]: #109
-#174 := [mp~ #114 #159]: #109
-#682 := [mp #174 #681]: #677
-#323 := (not #677)
-#657 := (or #323 #140)
-#658 := [quant-inst #41 #42 #44]: #657
-#310 := [unit-resolution #658 #682]: #140
-#659 := (or #143 #127 #324)
-#660 := [def-axiom]: #659
-#294 := [unit-resolution #660 #310]: #653
-#637 := [unit-resolution #294 #322 #650]: false
-#298 := [lemma #637]: #127
-#311 := (or #324 #146)
-#654 := (or #324 #146 #264)
-#656 := [def-axiom]: #654
-#443 := [unit-resolution #656 #154]: #311
-#299 := [unit-resolution #443 #298]: #324
-#300 := (or #146 #137)
-#655 := (or #143 #146 #137)
-#661 := [def-axiom]: #655
-#301 := [unit-resolution #661 #310]: #300
-[unit-resolution #301 #299 #298]: false
-unsat
-54d5adcc9aa92b5c35a0e590a6651cbf7d0b828e 162 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f4 :: S3
-#9 := f4
-decl f10 :: S2
-#41 := f10
-#327 := (f3 f10 f4)
-decl f1 :: S1
-#4 := f1
-#324 := (= f1 #327)
-decl f11 :: S3
-#42 := f11
-#47 := (f3 f10 f11)
-#127 := (= f1 #47)
-#328 := (or #127 #324)
+#41 := f11
+#276 := (f3 f10 f11)
+#255 := (= #276 f1)
+#570 := (or #255 #218)
 decl f6 :: (-> S4 S3 S3)
 decl f7 :: (-> S5 S3 S4)
 decl f8 :: S5
-#19 := f8
-#43 := (f7 f8 f11)
-#44 := (f6 #43 f4)
-#45 := (f3 f10 #44)
-#123 := (= f1 #45)
-#136 := (not #123)
-#644 := [hypothesis]: #136
-#322 := (or #127 #123)
-#137 := (iff #127 #136)
-#48 := (= #47 f1)
-#46 := (= #45 f1)
-#49 := (iff #46 #48)
-#50 := (not #49)
-#140 := (iff #50 #137)
-#130 := (iff #123 #127)
-#133 := (not #130)
-#138 := (iff #133 #137)
-#139 := [rewrite]: #138
-#134 := (iff #50 #133)
-#131 := (iff #49 #130)
-#128 := (iff #48 #127)
-#129 := [rewrite]: #128
-#125 := (iff #46 #123)
-#126 := [rewrite]: #125
-#132 := [monotonicity #126 #129]: #131
-#135 := [monotonicity #132]: #134
-#141 := [trans #135 #139]: #140
-#122 := [asserted]: #50
-#144 := [mp #122 #141]: #137
-#234 := (not #137)
-#321 := (or #127 #123 #234)
-#235 := [def-axiom]: #321
-#236 := [unit-resolution #235 #144]: #322
-#646 := [unit-resolution #236 #644]: #127
-#650 := (not #328)
-#290 := (or #123 #650)
-#307 := (iff #123 #328)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#21 := (f7 f8 #20)
-#23 := (f6 #21 #22)
-#18 := (:var 2 S2)
-#24 := (f3 #18 #23)
-#666 := (pattern #24)
-#28 := (f3 #18 #22)
-#96 := (= f1 #28)
-#26 := (f3 #18 #20)
-#93 := (= f1 #26)
-#99 := (or #93 #96)
-#89 := (= f1 #24)
-#102 := (iff #89 #99)
-#667 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #666) #102)
-#105 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #102)
-#670 := (iff #105 #667)
-#668 := (iff #102 #102)
-#669 := [refl]: #668
-#671 := [quant-intro #669]: #670
-#148 := (~ #105 #105)
-#162 := (~ #102 #102)
-#163 := [refl]: #162
-#149 := [nnf-pos #163]: #148
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#30 := (or #27 #29)
-#25 := (= #24 f1)
-#31 := (iff #25 #30)
-#32 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #31)
-#106 := (iff #32 #105)
-#103 := (iff #31 #102)
-#100 := (iff #30 #99)
-#97 := (iff #29 #96)
-#98 := [rewrite]: #97
-#94 := (iff #27 #93)
-#95 := [rewrite]: #94
-#101 := [monotonicity #95 #98]: #100
-#91 := (iff #25 #89)
-#92 := [rewrite]: #91
-#104 := [monotonicity #92 #101]: #103
-#107 := [quant-intro #104]: #106
-#88 := [asserted]: #32
-#110 := [mp #88 #107]: #105
-#164 := [mp~ #110 #149]: #105
-#672 := [mp #164 #671]: #667
-#301 := (not #667)
-#433 := (or #301 #307)
-#640 := [quant-inst #41 #42 #9]: #433
-#289 := [unit-resolution #640 #672]: #307
-#641 := (not #307)
-#299 := (or #641 #123 #650)
-#304 := [def-axiom]: #299
-#291 := [unit-resolution #304 #289]: #290
-#629 := [unit-resolution #291 #644]: #650
-#323 := (not #127)
-#312 := (or #328 #323)
-#313 := [def-axiom]: #312
-#630 := [unit-resolution #313 #629 #646]: false
-#631 := [lemma #630]: #123
-#632 := (or #136 #328)
-#642 := (or #641 #136 #328)
-#300 := [def-axiom]: #642
-#633 := [unit-resolution #300 #289]: #632
-#635 := [unit-resolution #633 #631]: #328
-#326 := (or #323 #136)
-#314 := (or #323 #136 #234)
-#325 := [def-axiom]: #314
-#254 := [unit-resolution #325 #144]: #326
-#637 := [unit-resolution #254 #631]: #323
-#645 := (or #650 #127 #324)
-#651 := [def-axiom]: #645
-#275 := [unit-resolution #651 #637 #635]: #324
-#8 := (:var 0 S2)
-#10 := (f3 #8 f4)
-#652 := (pattern #10)
-#71 := (= f1 #10)
-#74 := (not #71)
-#653 := (forall (vars (?v0 S2)) (:pat #652) #74)
-#77 := (forall (vars (?v0 S2)) #74)
-#656 := (iff #77 #653)
-#654 := (iff #74 #74)
-#655 := [refl]: #654
-#657 := [quant-intro #655]: #656
-#158 := (~ #77 #77)
-#156 := (~ #74 #74)
-#157 := [refl]: #156
-#159 := [nnf-pos #157]: #158
-#11 := (= #10 f1)
-#12 := (not #11)
-#13 := (forall (vars (?v0 S2)) #12)
-#78 := (iff #13 #77)
-#75 := (iff #12 #74)
-#72 := (iff #11 #71)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#79 := [quant-intro #76]: #78
-#70 := [asserted]: #13
-#82 := [mp #70 #79]: #77
-#143 := [mp~ #82 #159]: #77
-#658 := [mp #143 #657]: #653
-#647 := (not #324)
-#628 := (not #653)
-#634 := (or #628 #647)
-#270 := [quant-inst #41]: #634
-[unit-resolution #270 #658 #275]: false
-unsat
-6579b339206079120a92afc0dda92279c34507ae 136 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f5 :: S3
-#14 := f5
-decl f10 :: S2
-#41 := f10
-#219 := (f3 f10 f5)
-decl f1 :: S1
-#4 := f1
-#306 := (= f1 #219)
-#633 := (not #306)
-decl f11 :: S3
-#42 := f11
-#220 := (f3 f10 f11)
-#307 := (= f1 #220)
-#299 := (or #306 #307)
-#284 := (not #299)
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f8 :: S5
-#19 := f8
-#43 := (f7 f8 f11)
-#44 := (f6 #43 f5)
-#45 := (f3 f10 #44)
-#120 := (= f1 #45)
-#239 := (iff #120 #299)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#21 := (f7 f8 #20)
-#23 := (f6 #21 #22)
-#18 := (:var 2 S2)
-#24 := (f3 #18 #23)
-#651 := (pattern #24)
-#28 := (f3 #18 #22)
-#93 := (= f1 #28)
-#26 := (f3 #18 #20)
-#90 := (= f1 #26)
-#96 := (or #90 #93)
-#86 := (= f1 #24)
-#99 := (iff #86 #96)
-#652 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #651) #99)
-#102 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #99)
-#655 := (iff #102 #652)
-#653 := (iff #99 #99)
-#654 := [refl]: #653
-#656 := [quant-intro #654]: #655
-#133 := (~ #102 #102)
-#147 := (~ #99 #99)
-#148 := [refl]: #147
-#134 := [nnf-pos #148]: #133
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#30 := (or #27 #29)
-#25 := (= #24 f1)
-#31 := (iff #25 #30)
-#32 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #31)
-#103 := (iff #32 #102)
-#100 := (iff #31 #99)
-#97 := (iff #30 #96)
-#94 := (iff #29 #93)
-#95 := [rewrite]: #94
-#91 := (iff #27 #90)
-#92 := [rewrite]: #91
-#98 := [monotonicity #92 #95]: #97
-#88 := (iff #25 #86)
-#89 := [rewrite]: #88
-#101 := [monotonicity #89 #98]: #100
-#104 := [quant-intro #101]: #103
-#85 := [asserted]: #32
-#107 := [mp #85 #104]: #102
-#149 := [mp~ #107 #134]: #102
-#657 := [mp #149 #656]: #652
-#313 := (not #652)
-#292 := (or #313 #239)
-#221 := (or #307 #306)
-#308 := (iff #120 #221)
-#629 := (or #313 #308)
-#286 := (iff #629 #292)
-#625 := (iff #292 #292)
-#297 := [rewrite]: #625
-#312 := (iff #308 #239)
-#310 := (iff #221 #299)
-#311 := [rewrite]: #310
-#309 := [monotonicity #311]: #312
-#418 := [monotonicity #309]: #286
-#298 := [trans #418 #297]: #286
-#631 := [quant-inst #41 #42 #14]: #629
-#632 := [mp #631 #298]: #292
-#615 := [unit-resolution #632 #657]: #239
-#285 := (not #239)
-#616 := (or #285 #284)
-#124 := (not #120)
-#46 := (= #45 f1)
-#47 := (not #46)
-#125 := (iff #47 #124)
-#122 := (iff #46 #120)
-#123 := [rewrite]: #122
-#126 := [monotonicity #123]: #125
-#119 := [asserted]: #47
-#129 := [mp #119 #126]: #124
-#628 := (or #285 #120 #284)
-#269 := [def-axiom]: #628
-#619 := [unit-resolution #269 #129]: #616
-#255 := [unit-resolution #619 #615]: #284
-#634 := (or #299 #633)
-#635 := [def-axiom]: #634
-#620 := [unit-resolution #635 #255]: #633
-#8 := (:var 0 S2)
-#15 := (f3 #8 f5)
-#644 := (pattern #15)
-#78 := (= f1 #15)
-#645 := (forall (vars (?v0 S2)) (:pat #644) #78)
-#82 := (forall (vars (?v0 S2)) #78)
-#648 := (iff #82 #645)
-#646 := (iff #78 #78)
-#647 := [refl]: #646
-#649 := [quant-intro #647]: #648
-#131 := (~ #82 #82)
-#130 := (~ #78 #78)
-#145 := [refl]: #130
-#132 := [nnf-pos #145]: #131
-#16 := (= #15 f1)
-#17 := (forall (vars (?v0 S2)) #16)
-#83 := (iff #17 #82)
-#80 := (iff #16 #78)
-#81 := [rewrite]: #80
-#84 := [quant-intro #81]: #83
-#77 := [asserted]: #17
-#87 := [mp #77 #84]: #82
-#146 := [mp~ #87 #132]: #82
-#650 := [mp #146 #649]: #645
-#617 := (not #645)
-#618 := (or #617 #306)
-#613 := [quant-inst #41]: #618
-[unit-resolution #613 #650 #620]: false
-unsat
-21f3225a60811428730067e610d6913c3bcb0df3 155 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f11 :: S3
-#42 := f11
-decl f7 :: (-> S5 S3 S4)
-decl f12 :: S3
-#44 := f12
-decl f8 :: S5
-#19 := f8
-#48 := (f7 f8 f12)
-#49 := (f6 #48 f11)
-decl f10 :: S2
-#41 := f10
-#50 := (f3 f10 #49)
-decl f1 :: S1
-#4 := f1
-#130 := (= f1 #50)
-#326 := (not #130)
-#43 := (f7 f8 f11)
-#45 := (f6 #43 f12)
-#46 := (f3 f10 #45)
-#126 := (= f1 #46)
-#139 := (not #126)
-#245 := [hypothesis]: #139
-#325 := (or #130 #126)
-#140 := (iff #130 #139)
-#51 := (= #50 f1)
-#47 := (= #46 f1)
-#52 := (iff #47 #51)
-#53 := (not #52)
-#143 := (iff #53 #140)
-#133 := (iff #126 #130)
-#136 := (not #133)
-#141 := (iff #136 #140)
-#142 := [rewrite]: #141
-#137 := (iff #53 #136)
-#134 := (iff #52 #133)
-#131 := (iff #51 #130)
-#132 := [rewrite]: #131
-#128 := (iff #47 #126)
-#129 := [rewrite]: #128
-#135 := [monotonicity #129 #132]: #134
-#138 := [monotonicity #135]: #137
-#144 := [trans #138 #142]: #143
-#125 := [asserted]: #53
-#147 := [mp #125 #144]: #140
-#237 := (not #140)
-#324 := (or #130 #126 #237)
-#238 := [def-axiom]: #324
-#239 := [unit-resolution #238 #147]: #325
-#624 := [unit-resolution #239 #245]: #130
-#330 := (f3 f10 f11)
-#327 := (= f1 #330)
-#331 := (f3 f10 f12)
-#310 := (= f1 #331)
-#647 := (or #310 #327)
-#644 := (not #647)
-#347 := (or #126 #644)
-#634 := (iff #126 #647)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#21 := (f7 f8 #20)
-#23 := (f6 #21 #22)
-#18 := (:var 2 S2)
-#24 := (f3 #18 #23)
-#669 := (pattern #24)
-#28 := (f3 #18 #22)
-#99 := (= f1 #28)
-#26 := (f3 #18 #20)
-#96 := (= f1 #26)
-#102 := (or #96 #99)
-#92 := (= f1 #24)
-#105 := (iff #92 #102)
-#670 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #669) #105)
-#108 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #105)
-#673 := (iff #108 #670)
-#671 := (iff #105 #105)
-#672 := [refl]: #671
-#674 := [quant-intro #672]: #673
-#151 := (~ #108 #108)
-#165 := (~ #105 #105)
-#166 := [refl]: #165
-#152 := [nnf-pos #166]: #151
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#30 := (or #27 #29)
-#25 := (= #24 f1)
-#31 := (iff #25 #30)
-#32 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #31)
-#109 := (iff #32 #108)
-#106 := (iff #31 #105)
-#103 := (iff #30 #102)
-#100 := (iff #29 #99)
-#101 := [rewrite]: #100
-#97 := (iff #27 #96)
-#98 := [rewrite]: #97
-#104 := [monotonicity #98 #101]: #103
-#94 := (iff #25 #92)
-#95 := [rewrite]: #94
-#107 := [monotonicity #95 #104]: #106
-#110 := [quant-intro #107]: #109
-#91 := [asserted]: #32
-#113 := [mp #91 #110]: #108
-#167 := [mp~ #113 #152]: #108
-#675 := [mp #167 #674]: #670
-#643 := (not #670)
-#631 := (or #643 #634)
-#304 := (or #327 #310)
-#436 := (iff #126 #304)
-#637 := (or #643 #436)
-#638 := (iff #637 #631)
-#278 := (iff #631 #631)
-#279 := [rewrite]: #278
-#635 := (iff #436 #634)
-#632 := (iff #304 #647)
-#633 := [rewrite]: #632
-#636 := [monotonicity #633]: #635
-#640 := [monotonicity #636]: #638
-#641 := [trans #640 #279]: #638
-#273 := [quant-inst #41 #42 #44]: #637
-#639 := [mp #273 #641]: #631
-#625 := [unit-resolution #639 #675]: #634
-#642 := (not #634)
-#628 := (or #642 #126 #644)
-#629 := [def-axiom]: #628
-#348 := [unit-resolution #629 #625]: #347
-#622 := [unit-resolution #348 #245]: #644
-#623 := (or #326 #647)
-#649 := (iff #130 #647)
-#315 := (or #643 #649)
-#316 := [quant-inst #41 #44 #42]: #315
-#626 := [unit-resolution #316 #675]: #649
-#645 := (not #649)
-#287 := (or #645 #326 #647)
-#630 := [def-axiom]: #287
-#627 := [unit-resolution #630 #626]: #623
-#336 := [unit-resolution #627 #622 #624]: false
-#337 := [lemma #336]: #126
-#329 := (or #326 #139)
-#317 := (or #326 #139 #237)
-#328 := [def-axiom]: #317
-#257 := [unit-resolution #328 #147]: #329
-#338 := [unit-resolution #257 #337]: #326
-#340 := (or #139 #647)
-#335 := (or #642 #139 #647)
-#351 := [def-axiom]: #335
-#618 := [unit-resolution #351 #625]: #340
-#619 := [unit-resolution #618 #337]: #647
-#332 := (or #130 #644)
-#303 := (or #645 #130 #644)
-#646 := [def-axiom]: #303
-#616 := [unit-resolution #646 #626]: #332
-[unit-resolution #616 #619 #338]: false
-unsat
-0a38803d5203ebb9de80029b1e5de8bcd8e8f404 128 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f11 :: S3
-#42 := f11
-decl f7 :: (-> S5 S3 S4)
-decl f8 :: S5
-#19 := f8
-#43 := (f7 f8 f11)
-#44 := (f6 #43 f11)
-decl f10 :: S2
-#41 := f10
-#45 := (f3 f10 #44)
-decl f1 :: S1
-#4 := f1
-#123 := (= f1 #45)
-#136 := (not #123)
-#627 := [hypothesis]: #136
-#47 := (f3 f10 f11)
-#127 := (= f1 #47)
-#322 := (or #127 #123)
-#137 := (iff #127 #136)
-#48 := (= #47 f1)
-#46 := (= #45 f1)
-#49 := (iff #46 #48)
-#50 := (not #49)
-#140 := (iff #50 #137)
-#130 := (iff #123 #127)
-#133 := (not #130)
-#138 := (iff #133 #137)
-#139 := [rewrite]: #138
-#134 := (iff #50 #133)
-#131 := (iff #49 #130)
-#128 := (iff #48 #127)
-#129 := [rewrite]: #128
-#125 := (iff #46 #123)
-#126 := [rewrite]: #125
-#132 := [monotonicity #126 #129]: #131
-#135 := [monotonicity #132]: #134
-#141 := [trans #135 #139]: #140
-#122 := [asserted]: #50
-#144 := [mp #122 #141]: #137
-#234 := (not #137)
-#321 := (or #127 #123 #234)
-#235 := [def-axiom]: #321
-#236 := [unit-resolution #235 #144]: #322
-#288 := [unit-resolution #236 #627]: #127
-#323 := (not #127)
-#290 := (or #123 #323)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#21 := (f7 f8 #20)
-#23 := (f6 #21 #22)
-#18 := (:var 2 S2)
-#24 := (f3 #18 #23)
-#666 := (pattern #24)
-#28 := (f3 #18 #22)
-#96 := (= f1 #28)
-#26 := (f3 #18 #20)
-#93 := (= f1 #26)
-#99 := (or #93 #96)
-#89 := (= f1 #24)
-#102 := (iff #89 #99)
-#667 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #666) #102)
-#105 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #102)
-#670 := (iff #105 #667)
-#668 := (iff #102 #102)
-#669 := [refl]: #668
-#671 := [quant-intro #669]: #670
-#148 := (~ #105 #105)
-#162 := (~ #102 #102)
-#163 := [refl]: #162
-#149 := [nnf-pos #163]: #148
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#30 := (or #27 #29)
-#25 := (= #24 f1)
-#31 := (iff #25 #30)
-#32 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #31)
-#106 := (iff #32 #105)
-#103 := (iff #31 #102)
-#100 := (iff #30 #99)
-#97 := (iff #29 #96)
-#98 := [rewrite]: #97
-#94 := (iff #27 #93)
-#95 := [rewrite]: #94
-#101 := [monotonicity #95 #98]: #100
-#91 := (iff #25 #89)
-#92 := [rewrite]: #91
-#104 := [monotonicity #92 #101]: #103
-#107 := [quant-intro #104]: #106
-#88 := [asserted]: #32
-#110 := [mp #88 #107]: #105
-#164 := [mp~ #110 #149]: #105
-#672 := [mp #164 #671]: #667
-#301 := (not #667)
-#433 := (or #301 #130)
-#327 := (or #127 #127)
-#324 := (iff #123 #327)
-#640 := (or #301 #324)
-#313 := (iff #640 #433)
-#648 := (iff #433 #433)
-#649 := [rewrite]: #648
-#644 := (iff #324 #130)
-#328 := (iff #327 #127)
-#307 := [rewrite]: #328
-#646 := [monotonicity #307]: #644
-#647 := [monotonicity #646]: #313
-#650 := [trans #647 #649]: #313
-#312 := [quant-inst #41 #42 #42]: #640
-#645 := [mp #312 #650]: #433
-#289 := [unit-resolution #645 #672]: #130
-#651 := (or #133 #123 #323)
-#641 := [def-axiom]: #651
-#291 := [unit-resolution #641 #289]: #290
-#629 := [unit-resolution #291 #288 #627]: false
-#630 := [lemma #629]: #123
-#326 := (or #323 #136)
-#314 := (or #323 #136 #234)
-#325 := [def-axiom]: #314
-#254 := [unit-resolution #325 #144]: #326
-#631 := [unit-resolution #254 #630]: #323
-#632 := (or #136 #127)
-#299 := (or #133 #136 #127)
-#304 := [def-axiom]: #299
-#633 := [unit-resolution #304 #289]: #632
-[unit-resolution #633 #631 #630]: false
-unsat
-a9b4d2c6d5d71402741164958baf8befeec2192a 266 0
-#2 := false
+#18 := f8
+#42 := (f7 f8 f11)
+#50 := (f6 #42 f12)
+#587 := (f3 f10 #50)
+#260 := (= #587 f1)
+#567 := (iff #260 #570)
+#379 := (not #567)
+#548 := (not #570)
+#284 := (not #218)
+decl f13 :: S3
+#45 := f13
+#578 := (f3 f10 f13)
+#579 := (= #578 f1)
+#571 := (or #218 #579)
+#564 := (not #571)
+#44 := (f7 f8 f12)
+#46 := (f6 #44 f13)
+#591 := (f3 f10 #46)
+#593 := (= #591 f1)
+#281 := (iff #593 #571)
+#543 := (not #281)
+#400 := [hypothesis]: #543
+#21 := (:var 0 S3)
+#19 := (:var 1 S3)
+#20 := (f7 f8 #19)
+#22 := (f6 #20 #21)
+#17 := (:var 2 S2)
+#23 := (f3 #17 #22)
+#613 := (pattern #23)
+#27 := (f3 #17 #21)
+#28 := (= #27 f1)
+#25 := (f3 #17 #19)
+#26 := (= #25 f1)
+#29 := (or #26 #28)
+#24 := (= #23 f1)
+#30 := (iff #24 #29)
+#614 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #613) #30)
+#31 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #30)
+#617 := (iff #31 #614)
+#615 := (iff #30 #30)
+#616 := [refl]: #615
+#618 := [quant-intro #616]: #617
+#92 := (~ #31 #31)
+#106 := (~ #30 #30)
+#107 := [refl]: #106
+#93 := [nnf-pos #107]: #92
+#79 := [asserted]: #31
+#108 := [mp~ #79 #93]: #31
+#619 := [mp #108 #618]: #614
+#261 := (not #614)
+#402 := (or #261 #281)
+#544 := [quant-inst #40 #43 #45]: #402
+#401 := [unit-resolution #544 #619 #400]: false
+#537 := [lemma #401]: #281
+#598 := (not #593)
+#249 := (or #255 #593)
+#252 := (not #249)
+#47 := (f6 #42 #46)
+#48 := (f3 f10 #47)
+#49 := (= #48 f1)
+#82 := (not #49)
+#51 := (f7 f8 #50)
+#52 := (f6 #51 f13)
+#53 := (f3 f10 #52)
+#54 := (= #53 f1)
+#269 := (not #54)
+#559 := [hypothesis]: #269
+#275 := (or #49 #54)
+#83 := (iff #82 #54)
+#55 := (iff #49 #54)
+#56 := (not #55)
+#84 := (iff #56 #83)
+#85 := [rewrite]: #84
+#81 := [asserted]: #56
+#88 := [mp #81 #85]: #83
+#184 := (not #83)
+#273 := (or #49 #54 #184)
+#274 := [def-axiom]: #273
+#272 := [unit-resolution #274 #88]: #275
+#282 := [unit-resolution #272 #559]: #49
+#424 := (or #82 #249)
+#380 := (iff #49 #249)
+#594 := (or #261 #380)
+#595 := [quant-inst #40 #41 #46]: #594
+#423 := [unit-resolution #595 #619]: #380
+#590 := (not #380)
+#236 := (or #590 #82 #249)
+#237 := [def-axiom]: #236
+#383 := [unit-resolution #237 #423]: #424
+#531 := [unit-resolution #383 #282]: #249
+#596 := (not #255)
+#283 := (or #261 #567)
+#545 := [quant-inst #40 #41 #43]: #283
+#433 := [unit-resolution #545 #619]: #567
+#434 := (or #379 #548)
+#223 := (not #260)
+#580 := (or #260 #579)
+#573 := (not #580)
+#529 := (or #54 #573)
+#575 := (iff #54 #580)
+#582 := (or #261 #575)
+#584 := [quant-inst #40 #50 #45]: #582
+#528 := [unit-resolution #584 #619]: #575
+#296 := (not #575)
+#297 := (or #296 #54 #573)
+#298 := [def-axiom]: #297
+#532 := [unit-resolution #298 #528]: #529
+#417 := [unit-resolution #532 #559]: #573
+#224 := (or #580 #223)
+#585 := [def-axiom]: #224
+#432 := [unit-resolution #585 #417]: #223
+#381 := (or #379 #260 #548)
+#382 := [def-axiom]: #381
+#435 := [unit-resolution #382 #432]: #434
+#428 := [unit-resolution #435 #433]: #548
+#546 := (or #570 #596)
+#547 := [def-axiom]: #546
+#436 := [unit-resolution #547 #428]: #596
+#589 := (or #252 #255 #593)
+#248 := [def-axiom]: #589
+#437 := [unit-resolution #248 #436 #531]: #593
+#583 := (not #579)
+#586 := (or #580 #583)
+#572 := [def-axiom]: #586
+#438 := [unit-resolution #572 #417]: #583
+#541 := (or #570 #284)
+#542 := [def-axiom]: #541
+#439 := [unit-resolution #542 #428]: #284
+#561 := (or #564 #218 #579)
+#565 := [def-axiom]: #561
+#440 := [unit-resolution #565 #439 #438]: #564
+#556 := (or #543 #598 #571)
+#551 := [def-axiom]: #556
+#533 := [unit-resolution #551 #440 #437 #537]: false
+#530 := [lemma #533]: #54
+#271 := (or #82 #269)
+#270 := (or #82 #269 #184)
+#185 := [def-axiom]: #270
+#262 := [unit-resolution #185 #88]: #271
+#549 := [unit-resolution #262 #530]: #82
+#550 := (or #49 #252)
+#232 := (or #590 #49 #252)
+#574 := [def-axiom]: #232
+#523 := [unit-resolution #574 #423]: #550
+#515 := [unit-resolution #523 #549]: #252
+#588 := (or #249 #598)
+#247 := [def-axiom]: #588
+#512 := [unit-resolution #247 #515]: #598
+#554 := (or #543 #593 #564)
+#555 := [def-axiom]: #554
+#514 := [unit-resolution #555 #512 #537]: #564
+#562 := (or #571 #284)
+#563 := [def-axiom]: #562
+#524 := [unit-resolution #563 #514]: #284
+#597 := (or #249 #596)
+#592 := [def-axiom]: #597
+#525 := [unit-resolution #592 #515]: #596
+#535 := (or #548 #255 #218)
+#536 := [def-axiom]: #535
+#526 := [unit-resolution #536 #525 #524]: #548
+#522 := (or #269 #580)
+#191 := (or #296 #269 #580)
+#568 := [def-axiom]: #191
+#527 := [unit-resolution #568 #528]: #522
+#516 := [unit-resolution #527 #530]: #580
+#277 := (or #571 #583)
+#560 := [def-axiom]: #277
+#517 := [unit-resolution #560 #514]: #583
+#280 := (or #573 #260 #579)
+#295 := [def-axiom]: #280
+#518 := [unit-resolution #295 #517 #516]: #260
+#538 := (or #379 #223 #570)
+#539 := [def-axiom]: #538
+#519 := [unit-resolution #539 #518 #526]: #379
+[unit-resolution #545 #619 #519]: false
+unsat
+397d6346cfc96d3be794b9edcc58a3e463721e51 116 0
+#2 := false
+decl f1 :: S1
+#3 := f1
 decl f3 :: (-> S2 S3 S1)
 decl f12 :: S3
-#44 := f12
+#43 := f12
 decl f10 :: S2
-#41 := f10
-#623 := (f3 f10 f12)
-decl f1 :: S1
-#4 := f1
-#336 := (= f1 #623)
-decl f13 :: S3
-#46 := f13
-#334 := (f3 f10 f13)
-#331 := (= f1 #334)
-#621 := (or #331 #336)
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f8 :: S5
-#19 := f8
-#45 := (f7 f8 f12)
-#47 := (f6 #45 f13)
-#308 := (f3 f10 #47)
-#440 := (= f1 #308)
-#615 := (iff #440 #621)
-#581 := (not #615)
-#593 := (not #621)
-#605 := (not #336)
-decl f11 :: S3
-#42 := f11
-#636 := (f3 f10 f11)
-#637 := (= f1 #636)
-#483 := (or #336 #637)
-#608 := (not #483)
-#43 := (f7 f8 f11)
-#51 := (f6 #43 f12)
-#335 := (f3 f10 #51)
-#314 := (= f1 #335)
-#591 := (iff #314 #483)
-#583 := (not #591)
-#576 := [hypothesis]: #583
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#21 := (f7 f8 #20)
-#23 := (f6 #21 #22)
-#18 := (:var 2 S2)
-#24 := (f3 #18 #23)
-#673 := (pattern #24)
-#28 := (f3 #18 #22)
-#103 := (= f1 #28)
-#26 := (f3 #18 #20)
-#100 := (= f1 #26)
-#106 := (or #100 #103)
-#96 := (= f1 #24)
-#109 := (iff #96 #106)
-#674 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #673) #109)
-#112 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #109)
-#677 := (iff #112 #674)
-#675 := (iff #109 #109)
-#676 := [refl]: #675
-#678 := [quant-intro #676]: #677
-#155 := (~ #112 #112)
-#169 := (~ #109 #109)
-#170 := [refl]: #169
-#156 := [nnf-pos #170]: #155
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#30 := (or #27 #29)
-#25 := (= #24 f1)
-#31 := (iff #25 #30)
-#32 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #31)
-#113 := (iff #32 #112)
-#110 := (iff #31 #109)
-#107 := (iff #30 #106)
-#104 := (iff #29 #103)
-#105 := [rewrite]: #104
-#101 := (iff #27 #100)
-#102 := [rewrite]: #101
-#108 := [monotonicity #102 #105]: #107
-#98 := (iff #25 #96)
-#99 := [rewrite]: #98
-#111 := [monotonicity #99 #108]: #110
-#114 := [quant-intro #111]: #113
-#95 := [asserted]: #32
-#117 := [mp #95 #114]: #112
-#171 := [mp~ #117 #156]: #112
-#679 := [mp #171 #678]: #674
-#647 := (not #674)
-#589 := (or #647 #591)
-#600 := (or #637 #336)
-#482 := (iff #314 #600)
-#592 := (or #647 #482)
-#492 := (iff #592 #589)
-#495 := (iff #589 #589)
-#488 := [rewrite]: #495
-#493 := (iff #482 #591)
-#484 := (iff #600 #483)
-#443 := [rewrite]: #484
-#588 := [monotonicity #443]: #493
-#494 := [monotonicity #588]: #492
-#496 := [trans #494 #488]: #492
-#477 := [quant-inst #41 #42 #44]: #592
-#497 := [mp #477 #496]: #589
-#577 := [unit-resolution #497 #679 #576]: false
-#578 := [lemma #577]: #591
-#654 := (not #314)
-#651 := (or #314 #331)
-#648 := (not #651)
-#52 := (f7 f8 #51)
-#53 := (f6 #52 f13)
-#54 := (f3 f10 #53)
-#134 := (= f1 #54)
-#330 := (not #134)
-#48 := (f6 #43 #47)
-#49 := (f3 f10 #48)
-#130 := (= f1 #49)
-#143 := (not #130)
-#579 := [hypothesis]: #143
-#329 := (or #134 #130)
-#144 := (iff #134 #143)
-#55 := (= #54 f1)
+#40 := f10
+#49 := (f3 f10 f12)
 #50 := (= #49 f1)
-#56 := (iff #50 #55)
-#57 := (not #56)
-#147 := (iff #57 #144)
-#137 := (iff #130 #134)
-#140 := (not #137)
-#145 := (iff #140 #144)
-#146 := [rewrite]: #145
-#141 := (iff #57 #140)
-#138 := (iff #56 #137)
-#135 := (iff #55 #134)
-#136 := [rewrite]: #135
-#132 := (iff #50 #130)
-#133 := [rewrite]: #132
-#139 := [monotonicity #133 #136]: #138
-#142 := [monotonicity #139]: #141
-#148 := [trans #142 #146]: #147
-#129 := [asserted]: #57
-#151 := [mp #129 #148]: #144
-#241 := (not #144)
-#328 := (or #134 #130 #241)
-#242 := [def-axiom]: #328
-#243 := [unit-resolution #242 #151]: #329
-#573 := [unit-resolution #243 #579]: #134
-#564 := (or #330 #651)
-#653 := (iff #134 #651)
-#319 := (or #647 #653)
-#320 := [quant-inst #41 #51 #46]: #319
-#580 := [unit-resolution #320 #679]: #653
-#649 := (not #653)
-#291 := (or #649 #330 #651)
-#634 := [def-axiom]: #291
-#565 := [unit-resolution #634 #580]: #564
-#567 := [unit-resolution #565 #573]: #651
-#657 := (not #331)
-#597 := (or #647 #615)
-#620 := (or #336 #331)
-#624 := (iff #440 #620)
-#617 := (or #647 #624)
-#612 := (iff #617 #597)
-#619 := (iff #597 #597)
-#460 := [rewrite]: #619
-#616 := (iff #624 #615)
-#625 := (iff #620 #621)
-#614 := [rewrite]: #625
-#611 := [monotonicity #614]: #616
-#613 := [monotonicity #611]: #612
-#461 := [trans #613 #460]: #612
-#618 := [quant-inst #41 #44 #46]: #617
-#462 := [mp #618 #461]: #597
-#568 := [unit-resolution #462 #679]: #615
-#558 := (or #581 #593)
-#356 := (not #440)
-#640 := (or #440 #637)
-#629 := (not #640)
-#570 := (or #130 #629)
-#277 := (iff #130 #640)
-#282 := (or #647 #277)
-#638 := (or #637 #440)
-#639 := (iff #130 #638)
-#283 := (or #647 #639)
-#643 := (iff #283 #282)
-#632 := (iff #282 #282)
-#633 := [rewrite]: #632
-#642 := (iff #639 #277)
-#635 := (iff #638 #640)
-#641 := [rewrite]: #635
-#644 := [monotonicity #641]: #642
-#646 := [monotonicity #644]: #643
-#339 := [trans #646 #633]: #643
-#645 := [quant-inst #41 #42 #47]: #283
-#355 := [mp #645 #339]: #282
-#569 := [unit-resolution #355 #679]: #277
-#626 := (not #277)
-#630 := (or #626 #130 #629)
-#627 := [def-axiom]: #630
-#566 := [unit-resolution #627 #569]: #570
-#571 := [unit-resolution #566 #579]: #629
-#357 := (or #640 #356)
-#343 := [def-axiom]: #357
-#557 := [unit-resolution #343 #571]: #356
-#575 := (or #581 #440 #593)
-#572 := [def-axiom]: #575
-#560 := [unit-resolution #572 #557]: #558
-#561 := [unit-resolution #560 #568]: #593
-#604 := (or #621 #657)
-#498 := [def-axiom]: #604
-#562 := [unit-resolution #498 #561]: #657
-#306 := (or #648 #314 #331)
-#311 := [def-axiom]: #306
-#559 := [unit-resolution #311 #562 #567]: #314
-#358 := (not #637)
-#249 := (or #640 #358)
-#628 := [def-axiom]: #249
-#563 := [unit-resolution #628 #571]: #358
-#499 := (or #621 #605)
-#500 := [def-axiom]: #499
-#543 := [unit-resolution #500 #561]: #605
-#609 := (or #608 #336 #637)
-#603 := [def-axiom]: #609
-#544 := [unit-resolution #603 #543 #563]: #608
-#441 := (or #583 #654 #483)
-#442 := [def-axiom]: #441
-#546 := [unit-resolution #442 #544 #559 #578]: false
-#547 := [lemma #546]: #130
-#333 := (or #330 #143)
-#321 := (or #330 #143 #241)
-#332 := [def-axiom]: #321
-#261 := [unit-resolution #332 #151]: #333
-#548 := [unit-resolution #261 #547]: #330
-#549 := (or #134 #648)
-#307 := (or #649 #134 #648)
-#650 := [def-axiom]: #307
-#550 := [unit-resolution #650 #580]: #549
-#551 := [unit-resolution #550 #548]: #648
-#655 := (or #651 #654)
-#656 := [def-axiom]: #655
-#552 := [unit-resolution #656 #551]: #654
-#610 := (or #583 #314 #608)
-#439 := [def-axiom]: #610
-#553 := [unit-resolution #439 #552 #578]: #608
-#606 := (or #483 #605)
-#607 := [def-axiom]: #606
-#554 := [unit-resolution #607 #553]: #605
-#652 := (or #651 #657)
-#658 := [def-axiom]: #652
-#555 := [unit-resolution #658 #551]: #657
-#590 := (or #593 #331 #336)
-#594 := [def-axiom]: #590
-#545 := [unit-resolution #594 #555 #554]: #593
-#556 := (or #143 #640)
-#631 := (or #626 #143 #640)
-#340 := [def-axiom]: #631
-#534 := [unit-resolution #340 #569]: #556
-#535 := [unit-resolution #534 #547]: #640
-#601 := (or #483 #358)
-#602 := [def-axiom]: #601
-#537 := [unit-resolution #602 #553]: #358
-#351 := (or #629 #440 #637)
-#352 := [def-axiom]: #351
-#538 := [unit-resolution #352 #537 #535]: #440
-#574 := (or #581 #356 #621)
-#584 := [def-axiom]: #574
-#539 := [unit-resolution #584 #538 #545]: #581
-[unit-resolution #462 #679 #539]: false
-unsat
-c3c3648cfba9d6c85cac6f8d51a3b06b08975178 160 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f12 :: S3
-#44 := f12
-decl f10 :: S2
-#41 := f10
-#50 := (f3 f10 f12)
-decl f1 :: S1
-#4 := f1
-#134 := (= f1 #50)
-#188 := (not #134)
+#119 := (not #50)
 decl f11 :: S3
-#42 := f11
-#48 := (f3 f10 f11)
-#131 := (= f1 #48)
-#187 := (not #131)
-#189 := (or #187 #188)
-#190 := (not #189)
-#331 := [hypothesis]: #190
+#41 := f11
+#47 := (f3 f10 f11)
+#48 := (= #47 f1)
+#118 := (not #48)
+#120 := (or #118 #119)
+#121 := (not #120)
+#599 := [hypothesis]: #121
 decl f6 :: (-> S4 S3 S3)
 decl f7 :: (-> S5 S3 S4)
 decl f9 :: S5
-#33 := f9
-#43 := (f7 f9 f11)
-#45 := (f6 #43 f12)
-#46 := (f3 f10 #45)
-#127 := (= f1 #46)
-#146 := (not #127)
-#337 := (or #146 #189)
-#201 := (iff #127 #189)
-#137 := (and #131 #134)
-#147 := (iff #137 #146)
-#204 := (iff #147 #201)
-#196 := (iff #189 #127)
-#202 := (iff #196 #201)
-#203 := [rewrite]: #202
-#199 := (iff #147 #196)
-#193 := (iff #190 #146)
-#197 := (iff #193 #196)
-#198 := [rewrite]: #197
-#194 := (iff #147 #193)
-#191 := (iff #137 #190)
-#192 := [rewrite]: #191
-#195 := [monotonicity #192]: #194
-#200 := [trans #195 #198]: #199
-#205 := [trans #200 #203]: #204
-#51 := (= #50 f1)
-#49 := (= #48 f1)
-#52 := (and #49 #51)
-#47 := (= #46 f1)
-#53 := (iff #47 #52)
-#54 := (not #53)
-#150 := (iff #54 #147)
-#140 := (iff #127 #137)
-#143 := (not #140)
-#148 := (iff #143 #147)
-#149 := [rewrite]: #148
-#144 := (iff #54 #143)
-#141 := (iff #53 #140)
-#138 := (iff #52 #137)
-#135 := (iff #51 #134)
-#136 := [rewrite]: #135
-#132 := (iff #49 #131)
-#133 := [rewrite]: #132
-#139 := [monotonicity #133 #136]: #138
-#129 := (iff #47 #127)
-#130 := [rewrite]: #129
-#142 := [monotonicity #130 #139]: #141
-#145 := [monotonicity #142]: #144
-#151 := [trans #145 #149]: #150
-#126 := [asserted]: #54
-#154 := [mp #126 #151]: #147
-#206 := [mp #154 #205]: #201
-#344 := (not #201)
-#354 := (or #146 #189 #344)
-#358 := [def-axiom]: #354
-#674 := [unit-resolution #358 #206]: #337
-#463 := [unit-resolution #674 #331]: #146
-#330 := (or #127 #189)
-#676 := (iff #127 #190)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#34 := (f7 f9 #20)
-#35 := (f6 #34 #22)
-#18 := (:var 2 S2)
-#36 := (f3 #18 #35)
-#703 := (pattern #36)
-#28 := (f3 #18 #22)
-#100 := (= f1 #28)
-#179 := (not #100)
-#26 := (f3 #18 #20)
-#97 := (= f1 #26)
-#178 := (not #97)
-#162 := (or #178 #179)
-#163 := (not #162)
-#113 := (= f1 #36)
-#180 := (iff #113 #163)
-#704 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #703) #180)
-#183 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #180)
-#707 := (iff #183 #704)
-#705 := (iff #180 #180)
-#706 := [refl]: #705
-#708 := [quant-intro #706]: #707
-#117 := (and #97 #100)
-#120 := (iff #113 #117)
-#123 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #120)
-#184 := (iff #123 #183)
-#181 := (iff #120 #180)
-#164 := (iff #117 #163)
-#165 := [rewrite]: #164
-#182 := [monotonicity #165]: #181
-#185 := [quant-intro #182]: #184
-#160 := (~ #123 #123)
-#175 := (~ #120 #120)
-#176 := [refl]: #175
-#161 := [nnf-pos #176]: #160
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#38 := (and #27 #29)
-#37 := (= #36 f1)
-#39 := (iff #37 #38)
-#40 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #39)
-#124 := (iff #40 #123)
-#121 := (iff #39 #120)
-#118 := (iff #38 #117)
-#101 := (iff #29 #100)
-#102 := [rewrite]: #101
-#98 := (iff #27 #97)
-#99 := [rewrite]: #98
-#119 := [monotonicity #99 #102]: #118
-#115 := (iff #37 #113)
-#116 := [rewrite]: #115
-#122 := [monotonicity #116 #119]: #121
-#125 := [quant-intro #122]: #124
-#112 := [asserted]: #40
-#128 := [mp #112 #125]: #123
-#177 := [mp~ #128 #161]: #123
-#186 := [mp #177 #185]: #183
-#709 := [mp #186 #708]: #704
-#670 := (not #704)
-#342 := (or #670 #676)
-#343 := [quant-inst #41 #42 #44]: #342
-#672 := [unit-resolution #343 #709]: #676
-#677 := (not #676)
-#678 := (or #677 #127 #189)
-#679 := [def-axiom]: #678
-#673 := [unit-resolution #679 #672]: #330
-#314 := [unit-resolution #673 #463 #331]: false
-#657 := [lemma #314]: #189
-#284 := (or #127 #190)
-#355 := (or #127 #190 #344)
-#356 := [def-axiom]: #355
-#357 := [unit-resolution #356 #206]: #284
-#318 := [unit-resolution #357 #657]: #127
-#319 := (or #146 #190)
-#680 := (or #677 #146 #190)
-#675 := [def-axiom]: #680
-#320 := [unit-resolution #675 #672]: #319
-[unit-resolution #320 #318 #657]: false
-unsat
-1adc4d295cebee376081ce9f5a9d0e96c2943423 149 0
-#2 := false
+#32 := f9
+#42 := (f7 f9 f11)
+#44 := (f6 #42 f12)
+#45 := (f3 f10 #44)
+#46 := (= #45 f1)
+#79 := (not #46)
+#605 := (or #79 #120)
+#127 := (iff #46 #120)
+#51 := (and #48 #50)
+#80 := (iff #79 #51)
+#130 := (iff #80 #127)
+#124 := (iff #79 #121)
+#128 := (iff #124 #127)
+#129 := [rewrite]: #128
+#125 := (iff #80 #124)
+#122 := (iff #51 #121)
+#123 := [rewrite]: #122
+#126 := [monotonicity #123]: #125
+#131 := [trans #126 #129]: #130
+#52 := (iff #46 #51)
+#53 := (not #52)
+#81 := (iff #53 #80)
+#82 := [rewrite]: #81
+#78 := [asserted]: #53
+#85 := [mp #78 #82]: #80
+#132 := [mp #85 #131]: #127
+#285 := (not #127)
+#267 := (or #79 #120 #285)
+#603 := [def-axiom]: #267
+#261 := [unit-resolution #603 #132]: #605
+#272 := [unit-resolution #261 #599]: #79
+#244 := (or #46 #120)
+#392 := (iff #46 #121)
+#21 := (:var 0 S3)
+#19 := (:var 1 S3)
+#33 := (f7 f9 #19)
+#34 := (f6 #33 #21)
+#17 := (:var 2 S2)
+#35 := (f3 #17 #34)
+#632 := (pattern #35)
+#27 := (f3 #17 #21)
+#28 := (= #27 f1)
+#110 := (not #28)
+#25 := (f3 #17 #19)
+#26 := (= #25 f1)
+#109 := (not #26)
+#93 := (or #109 #110)
+#94 := (not #93)
+#36 := (= #35 f1)
+#111 := (iff #36 #94)
+#633 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #632) #111)
+#114 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #111)
+#636 := (iff #114 #633)
+#634 := (iff #111 #111)
+#635 := [refl]: #634
+#637 := [quant-intro #635]: #636
+#37 := (and #26 #28)
+#38 := (iff #36 #37)
+#39 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #38)
+#115 := (iff #39 #114)
+#112 := (iff #38 #111)
+#95 := (iff #37 #94)
+#96 := [rewrite]: #95
+#113 := [monotonicity #96]: #112
+#116 := [quant-intro #113]: #115
+#91 := (~ #39 #39)
+#106 := (~ #38 #38)
+#107 := [refl]: #106
+#92 := [nnf-pos #107]: #91
+#77 := [asserted]: #39
+#108 := [mp~ #77 #92]: #39
+#117 := [mp #108 #116]: #114
+#638 := [mp #117 #637]: #633
+#273 := (not #633)
+#606 := (or #273 #392)
+#607 := [quant-inst #40 #41 #43]: #606
+#602 := [unit-resolution #607 #638]: #392
+#608 := (not #392)
+#609 := (or #608 #46 #120)
+#604 := [def-axiom]: #609
+#586 := [unit-resolution #604 #602]: #244
+#248 := [unit-resolution #586 #272 #599]: false
+#249 := [lemma #248]: #120
+#284 := (or #46 #121)
+#286 := (or #46 #121 #285)
+#287 := [def-axiom]: #286
+#288 := [unit-resolution #287 #132]: #284
+#250 := [unit-resolution #288 #249]: #46
+#251 := (or #79 #121)
+#610 := (or #608 #79 #121)
+#600 := [def-axiom]: #610
+#588 := [unit-resolution #600 #602]: #251
+[unit-resolution #588 #250 #249]: false
+unsat
+25e43ea74050b29942998055a45c2dfa635fcffe 109 0
+#2 := false
+decl f1 :: S1
+#3 := f1
 decl f3 :: (-> S2 S3 S1)
 decl f4 :: S3
-#9 := f4
+#8 := f4
 decl f10 :: S2
-#41 := f10
-#227 := (f3 f10 f4)
-decl f1 :: S1
-#4 := f1
-#314 := (= f1 #227)
-#228 := (not #314)
+#40 := f10
+#174 := (f3 f10 f4)
+#260 := (= #174 f1)
+#251 := (not #260)
 decl f11 :: S3
-#42 := f11
-#315 := (f3 f10 f11)
-#229 := (= f1 #315)
-#316 := (not #229)
-#307 := (or #316 #228)
-#318 := (not #307)
+#41 := f11
+#258 := (f3 f10 f11)
+#173 := (= #258 f1)
+#259 := (not #173)
+#262 := (or #259 #251)
+#263 := (not #262)
+decl f6 :: (-> S4 S3 S3)
+decl f7 :: (-> S5 S3 S4)
+decl f9 :: S5
+#32 := f9
+#42 := (f7 f9 f11)
+#43 := (f6 #42 f4)
+#44 := (f3 f10 #43)
+#45 := (= #44 f1)
+#264 := (iff #45 #263)
+#21 := (:var 0 S3)
+#19 := (:var 1 S3)
+#33 := (f7 f9 #19)
+#34 := (f6 #33 #21)
+#17 := (:var 2 S2)
+#35 := (f3 #17 #34)
+#609 := (pattern #35)
+#27 := (f3 #17 #21)
+#28 := (= #27 f1)
+#102 := (not #28)
+#25 := (f3 #17 #19)
+#26 := (= #25 f1)
+#101 := (not #26)
+#85 := (or #101 #102)
+#86 := (not #85)
+#36 := (= #35 f1)
+#103 := (iff #36 #86)
+#610 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #609) #103)
+#106 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #103)
+#613 := (iff #106 #610)
+#611 := (iff #103 #103)
+#612 := [refl]: #611
+#614 := [quant-intro #612]: #613
+#37 := (and #26 #28)
+#38 := (iff #36 #37)
+#39 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #38)
+#107 := (iff #39 #106)
+#104 := (iff #38 #103)
+#87 := (iff #37 #86)
+#88 := [rewrite]: #87
+#105 := [monotonicity #88]: #104
+#108 := [quant-intro #105]: #107
+#83 := (~ #39 #39)
+#98 := (~ #38 #38)
+#99 := [refl]: #98
+#84 := [nnf-pos #99]: #83
+#71 := [asserted]: #39
+#100 := [mp~ #71 #84]: #39
+#109 := [mp #100 #108]: #106
+#615 := [mp #109 #614]: #610
+#244 := (not #610)
+#580 := (or #244 #264)
+#582 := [quant-inst #40 #41 #8]: #580
+#261 := [unit-resolution #582 #615]: #264
+#584 := (not #264)
+#265 := (or #584 #263)
+#46 := (not #45)
+#47 := (not #46)
+#73 := (iff #47 #45)
+#74 := [rewrite]: #73
+#72 := [asserted]: #47
+#77 := [mp #72 #74]: #45
+#581 := (or #584 #46 #263)
+#587 := [def-axiom]: #581
+#563 := [unit-resolution #587 #77]: #265
+#225 := [unit-resolution #563 #261]: #263
+#576 := (or #262 #260)
+#249 := [def-axiom]: #576
+#226 := [unit-resolution #249 #225]: #260
+#7 := (:var 0 S2)
+#9 := (f3 #7 f4)
+#588 := (pattern #9)
+#10 := (= #9 f1)
+#11 := (not #10)
+#589 := (forall (vars (?v0 S2)) (:pat #588) #11)
+#12 := (forall (vars (?v0 S2)) #11)
+#592 := (iff #12 #589)
+#590 := (iff #11 #11)
+#591 := [refl]: #590
+#593 := [quant-intro #591]: #592
+#91 := (~ #12 #12)
+#89 := (~ #11 #11)
+#90 := [refl]: #89
+#92 := [nnf-pos #90]: #91
+#68 := [asserted]: #12
+#76 := [mp~ #68 #92]: #12
+#594 := [mp #76 #593]: #589
+#237 := (not #589)
+#579 := (or #237 #251)
+#221 := [quant-inst #40]: #579
+[unit-resolution #221 #594 #226]: false
+unsat
+aea5829d512de2728ecad3b816f4fb373d3860ab 131 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S3 S1)
+decl f5 :: S3
+#13 := f5
+decl f10 :: S2
+#40 := f10
+#269 := (f3 f10 f5)
+#248 := (= #269 f1)
+#584 := (not #248)
+decl f11 :: S3
+#41 := f11
+#46 := (f3 f10 f11)
+#47 := (= #46 f1)
 decl f6 :: (-> S4 S3 S3)
 decl f7 :: (-> S5 S3 S4)
 decl f9 :: S5
-#33 := f9
-#43 := (f7 f9 f11)
-#44 := (f6 #43 f4)
-#45 := (f3 f10 #44)
-#121 := (= f1 #45)
-#319 := (iff #121 #318)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#34 := (f7 f9 #20)
-#35 := (f6 #34 #22)
-#18 := (:var 2 S2)
-#36 := (f3 #18 #35)
-#666 := (pattern #36)
-#28 := (f3 #18 #22)
-#94 := (= f1 #28)
-#162 := (not #94)
-#26 := (f3 #18 #20)
-#91 := (= f1 #26)
-#161 := (not #91)
-#145 := (or #161 #162)
-#146 := (not #145)
-#107 := (= f1 #36)
-#163 := (iff #107 #146)
-#667 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #666) #163)
-#166 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #163)
-#670 := (iff #166 #667)
-#668 := (iff #163 #163)
-#669 := [refl]: #668
-#671 := [quant-intro #669]: #670
-#111 := (and #91 #94)
-#114 := (iff #107 #111)
-#117 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #114)
-#167 := (iff #117 #166)
-#164 := (iff #114 #163)
-#147 := (iff #111 #146)
-#148 := [rewrite]: #147
-#165 := [monotonicity #148]: #164
-#168 := [quant-intro #165]: #167
-#143 := (~ #117 #117)
-#158 := (~ #114 #114)
-#159 := [refl]: #158
-#144 := [nnf-pos #159]: #143
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#38 := (and #27 #29)
-#37 := (= #36 f1)
-#39 := (iff #37 #38)
-#40 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #39)
-#118 := (iff #40 #117)
-#115 := (iff #39 #114)
-#112 := (iff #38 #111)
-#95 := (iff #29 #94)
-#96 := [rewrite]: #95
-#92 := (iff #27 #91)
-#93 := [rewrite]: #92
-#113 := [monotonicity #93 #96]: #112
-#109 := (iff #37 #107)
-#110 := [rewrite]: #109
-#116 := [monotonicity #110 #113]: #115
-#119 := [quant-intro #116]: #118
-#106 := [asserted]: #40
-#122 := [mp #106 #119]: #117
-#160 := [mp~ #122 #144]: #117
-#169 := [mp #160 #168]: #166
-#672 := [mp #169 #671]: #667
-#317 := (not #667)
-#321 := (or #317 #319)
-#300 := [quant-inst #41 #42 #9]: #321
-#247 := [unit-resolution #300 #672]: #319
-#306 := (not #319)
-#320 := (or #306 #318)
-#46 := (= #45 f1)
-#47 := (not #46)
-#48 := (not #47)
-#133 := (iff #48 #121)
-#125 := (not #121)
-#128 := (not #125)
-#131 := (iff #128 #121)
-#132 := [rewrite]: #131
-#129 := (iff #48 #128)
-#126 := (iff #47 #125)
-#123 := (iff #46 #121)
-#124 := [rewrite]: #123
-#127 := [monotonicity #124]: #126
-#130 := [monotonicity #127]: #129
-#134 := [trans #130 #132]: #133
-#120 := [asserted]: #48
-#137 := [mp #120 #134]: #121
-#642 := (or #306 #125 #318)
-#643 := [def-axiom]: #642
-#636 := [unit-resolution #643 #137]: #320
-#277 := [unit-resolution #636 #247]: #318
-#294 := (or #307 #314)
-#426 := [def-axiom]: #294
-#620 := [unit-resolution #426 #277]: #314
-#8 := (:var 0 S2)
-#10 := (f3 #8 f4)
-#645 := (pattern #10)
-#69 := (= f1 #10)
-#72 := (not #69)
-#646 := (forall (vars (?v0 S2)) (:pat #645) #72)
-#75 := (forall (vars (?v0 S2)) #72)
-#649 := (iff #75 #646)
-#647 := (iff #72 #72)
-#648 := [refl]: #647
-#650 := [quant-intro #648]: #649
-#151 := (~ #75 #75)
-#149 := (~ #72 #72)
-#150 := [refl]: #149
-#152 := [nnf-pos #150]: #151
-#11 := (= #10 f1)
-#12 := (not #11)
-#13 := (forall (vars (?v0 S2)) #12)
-#76 := (iff #13 #75)
-#73 := (iff #12 #72)
-#70 := (iff #11 #69)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#77 := [quant-intro #74]: #76
-#68 := [asserted]: #13
-#80 := [mp #68 #77]: #75
-#136 := [mp~ #80 #152]: #75
-#651 := [mp #136 #650]: #646
-#297 := (not #646)
-#635 := (or #297 #228)
-#293 := [quant-inst #41]: #635
-[unit-resolution #293 #651 #620]: false
-unsat
-27fbc35929f013c0b43884a593f3f377821cad64 173 0
-#2 := false
+#32 := f9
+#42 := (f7 f9 f11)
+#43 := (f6 #42 f5)
+#44 := (f3 f10 #43)
+#45 := (= #44 f1)
+#262 := (not #47)
+#580 := [hypothesis]: #262
+#268 := (or #45 #47)
+#75 := (not #45)
+#76 := (iff #75 #47)
+#48 := (iff #45 #47)
+#49 := (not #48)
+#77 := (iff #49 #76)
+#78 := [rewrite]: #77
+#74 := [asserted]: #49
+#81 := [mp #74 #78]: #76
+#177 := (not #76)
+#266 := (or #45 #47 #177)
+#267 := [def-axiom]: #266
+#265 := [unit-resolution #267 #81]: #268
+#253 := [unit-resolution #265 #580]: #45
+#586 := (or #262 #584)
+#589 := (or #586 #47)
+#590 := [def-axiom]: #589
+#232 := [unit-resolution #590 #580]: #586
+#242 := (not #586)
+#570 := (or #75 #242)
+#373 := (iff #45 #242)
+#21 := (:var 0 S3)
+#19 := (:var 1 S3)
+#33 := (f7 f9 #19)
+#34 := (f6 #33 #21)
+#17 := (:var 2 S2)
+#35 := (f3 #17 #34)
+#613 := (pattern #35)
+#27 := (f3 #17 #21)
+#28 := (= #27 f1)
+#106 := (not #28)
+#25 := (f3 #17 #19)
+#26 := (= #25 f1)
+#105 := (not #26)
+#89 := (or #105 #106)
+#90 := (not #89)
+#36 := (= #35 f1)
+#107 := (iff #36 #90)
+#614 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #613) #107)
+#110 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #107)
+#617 := (iff #110 #614)
+#615 := (iff #107 #107)
+#616 := [refl]: #615
+#618 := [quant-intro #616]: #617
+#37 := (and #26 #28)
+#38 := (iff #36 #37)
+#39 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #38)
+#111 := (iff #39 #110)
+#108 := (iff #38 #107)
+#91 := (iff #37 #90)
+#92 := [rewrite]: #91
+#109 := [monotonicity #92]: #108
+#112 := [quant-intro #109]: #111
+#87 := (~ #39 #39)
+#102 := (~ #38 #38)
+#103 := [refl]: #102
+#88 := [nnf-pos #103]: #87
+#73 := [asserted]: #39
+#104 := [mp~ #73 #88]: #39
+#113 := [mp #104 #112]: #110
+#619 := [mp #113 #618]: #614
+#254 := (not #614)
+#587 := (or #254 #373)
+#588 := [quant-inst #40 #41 #13]: #587
+#569 := [unit-resolution #588 #619]: #373
+#245 := (not #373)
+#583 := (or #245 #75 #242)
+#225 := [def-axiom]: #583
+#571 := [unit-resolution #225 #569]: #570
+#572 := [unit-resolution #571 #232 #253]: false
+#573 := [lemma #572]: #47
+#264 := (or #75 #262)
+#263 := (or #75 #262 #177)
+#178 := [def-axiom]: #263
+#255 := [unit-resolution #178 #81]: #264
+#568 := [unit-resolution #255 #573]: #75
+#574 := (or #45 #586)
+#582 := (or #245 #45 #586)
+#241 := [def-axiom]: #582
+#216 := [unit-resolution #241 #569]: #574
+#217 := [unit-resolution #216 #568]: #586
+#581 := (or #242 #262 #584)
+#240 := [def-axiom]: #581
+#578 := [unit-resolution #240 #217 #573]: #584
+#7 := (:var 0 S2)
+#14 := (f3 #7 f5)
+#599 := (pattern #14)
+#15 := (= #14 f1)
+#600 := (forall (vars (?v0 S2)) (:pat #599) #15)
+#16 := (forall (vars (?v0 S2)) #15)
+#603 := (iff #16 #600)
+#601 := (iff #15 #15)
+#602 := [refl]: #601
+#604 := [quant-intro #602]: #603
+#83 := (~ #16 #16)
+#82 := (~ #15 #15)
+#97 := [refl]: #82
+#84 := [nnf-pos #97]: #83
+#71 := [asserted]: #16
+#98 := [mp~ #71 #84]: #16
+#605 := [mp #98 #604]: #600
+#211 := (not #600)
+#575 := (or #211 #248)
+#577 := [quant-inst #40]: #575
+[unit-resolution #577 #605 #578]: false
+unsat
+2c368a83b5623f0f697753a8fe91229b9ba6f049 144 0
+#2 := false
+decl f1 :: S1
+#3 := f1
 decl f3 :: (-> S2 S3 S1)
 decl f11 :: S3
-#42 := f11
+#41 := f11
 decl f10 :: S2
-#41 := f10
-#47 := (f3 f10 f11)
-decl f1 :: S1
-#4 := f1
-#127 := (= f1 #47)
-#323 := (not #127)
+#40 := f10
+#272 := (f3 f10 f11)
+#251 := (= #272 f1)
+#587 := (not #251)
+decl f12 :: S3
+#43 := f12
+#589 := (f3 f10 f12)
+#245 := (= #589 f1)
+#376 := (not #245)
+#590 := (or #376 #587)
+#591 := (not #590)
 decl f6 :: (-> S4 S3 S3)
-decl f5 :: S3
-#14 := f5
+decl f7 :: (-> S5 S3 S4)
+decl f9 :: S5
+#32 := f9
+#47 := (f7 f9 f12)
+#48 := (f6 #47 f11)
+#49 := (f3 f10 #48)
+#50 := (= #49 f1)
+#265 := (not #50)
+#575 := [hypothesis]: #265
+#187 := (or #50 #590)
+#574 := (iff #50 #591)
+#21 := (:var 0 S3)
+#19 := (:var 1 S3)
+#33 := (f7 f9 #19)
+#34 := (f6 #33 #21)
+#17 := (:var 2 S2)
+#35 := (f3 #17 #34)
+#616 := (pattern #35)
+#27 := (f3 #17 #21)
+#28 := (= #27 f1)
+#109 := (not #28)
+#25 := (f3 #17 #19)
+#26 := (= #25 f1)
+#108 := (not #26)
+#92 := (or #108 #109)
+#93 := (not #92)
+#36 := (= #35 f1)
+#110 := (iff #36 #93)
+#617 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #616) #110)
+#113 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #110)
+#620 := (iff #113 #617)
+#618 := (iff #110 #110)
+#619 := [refl]: #618
+#621 := [quant-intro #619]: #620
+#37 := (and #26 #28)
+#38 := (iff #36 #37)
+#39 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #38)
+#114 := (iff #39 #113)
+#111 := (iff #38 #110)
+#94 := (iff #37 #93)
+#95 := [rewrite]: #94
+#112 := [monotonicity #95]: #111
+#115 := [quant-intro #112]: #114
+#90 := (~ #39 #39)
+#105 := (~ #38 #38)
+#106 := [refl]: #105
+#91 := [nnf-pos #106]: #90
+#76 := [asserted]: #39
+#107 := [mp~ #76 #91]: #39
+#116 := [mp #107 #115]: #113
+#622 := [mp #116 #621]: #617
+#592 := (not #617)
+#571 := (or #592 #574)
+#577 := [quant-inst #40 #43 #41]: #571
+#576 := [unit-resolution #577 #622]: #574
+#579 := (not #574)
+#582 := (or #579 #50 #590)
+#568 := [def-axiom]: #582
+#564 := [unit-resolution #568 #576]: #187
+#565 := [unit-resolution #564 #575]: #590
+#583 := (or #587 #376)
+#256 := (not #583)
+#42 := (f7 f9 f11)
+#44 := (f6 #42 f12)
+#45 := (f3 f10 #44)
+#46 := (= #45 f1)
+#271 := (or #46 #50)
+#78 := (not #46)
+#79 := (iff #78 #50)
+#51 := (iff #46 #50)
+#52 := (not #51)
+#80 := (iff #52 #79)
+#81 := [rewrite]: #80
+#77 := [asserted]: #52
+#84 := [mp #77 #81]: #79
+#180 := (not #79)
+#269 := (or #46 #50 #180)
+#270 := [def-axiom]: #269
+#268 := [unit-resolution #270 #84]: #271
+#287 := [unit-resolution #268 #575]: #46
+#562 := (or #78 #256)
+#257 := (iff #46 #256)
+#593 := (or #592 #257)
+#588 := [quant-inst #40 #41 #43]: #593
+#288 := [unit-resolution #588 #622]: #257
+#586 := (not #257)
+#232 := (or #586 #78 #256)
+#233 := [def-axiom]: #232
+#566 := [unit-resolution #233 #288]: #562
+#563 := [unit-resolution #566 #287]: #256
+#594 := (or #583 #251)
+#584 := [def-axiom]: #594
+#567 := [unit-resolution #584 #563]: #251
+#243 := (or #583 #245)
+#248 := [def-axiom]: #243
+#277 := [unit-resolution #248 #563]: #245
+#220 := (or #591 #376 #587)
+#581 := [def-axiom]: #220
+#278 := [unit-resolution #581 #277 #567 #565]: false
+#279 := [lemma #278]: #50
+#280 := (or #265 #591)
+#569 := (or #579 #265 #591)
+#276 := [def-axiom]: #569
+#558 := [unit-resolution #276 #576]: #280
+#559 := [unit-resolution #558 #279]: #591
+#580 := (or #590 #251)
+#219 := [def-axiom]: #580
+#273 := [unit-resolution #219 #559]: #251
+#267 := (or #78 #265)
+#266 := (or #78 #265 #180)
+#181 := [def-axiom]: #266
+#258 := [unit-resolution #181 #84]: #267
+#556 := [unit-resolution #258 #279]: #78
+#560 := (or #46 #583)
+#228 := (or #586 #46 #583)
+#570 := [def-axiom]: #228
+#557 := [unit-resolution #570 #288]: #560
+#561 := [unit-resolution #557 #556]: #583
+#214 := (or #590 #245)
+#578 := [def-axiom]: #214
+#550 := [unit-resolution #578 #559]: #245
+#585 := (or #256 #587 #376)
+#244 := [def-axiom]: #585
+[unit-resolution #244 #550 #561 #273]: false
+unsat
+786e0baa52e956eb38ebe0e784a4d54d1b6938d2 116 0
+#2 := false
+decl f1 :: S1
+#3 := f1
+decl f3 :: (-> S2 S3 S1)
+decl f11 :: S3
+#41 := f11
+decl f10 :: S2
+#40 := f10
+#46 := (f3 f10 f11)
+#47 := (= #46 f1)
+#262 := (not #47)
+#568 := [hypothesis]: #262
+decl f6 :: (-> S4 S3 S3)
 decl f7 :: (-> S5 S3 S4)
 decl f9 :: S5
-#33 := f9
-#43 := (f7 f9 f11)
-#44 := (f6 #43 f5)
-#45 := (f3 f10 #44)
-#123 := (= f1 #45)
-#327 := (f3 f10 f5)
-#324 := (= f1 #327)
-#328 := (not #324)
-#301 := [hypothesis]: #328
-#8 := (:var 0 S2)
-#15 := (f3 #8 f5)
-#659 := (pattern #15)
-#81 := (= f1 #15)
-#660 := (forall (vars (?v0 S2)) (:pat #659) #81)
-#85 := (forall (vars (?v0 S2)) #81)
-#663 := (iff #85 #660)
-#661 := (iff #81 #81)
-#662 := [refl]: #661
-#664 := [quant-intro #662]: #663
-#146 := (~ #85 #85)
-#145 := (~ #81 #81)
-#160 := [refl]: #145
-#147 := [nnf-pos #160]: #146
-#16 := (= #15 f1)
-#17 := (forall (vars (?v0 S2)) #16)
-#86 := (iff #17 #85)
-#83 := (iff #16 #81)
-#84 := [rewrite]: #83
-#87 := [quant-intro #84]: #86
-#80 := [asserted]: #17
-#90 := [mp #80 #87]: #85
-#161 := [mp~ #90 #147]: #85
-#665 := [mp #161 #664]: #660
-#289 := (not #660)
-#290 := (or #289 #324)
-#291 := [quant-inst #41]: #290
-#433 := [unit-resolution #291 #665 #301]: false
-#629 := [lemma #433]: #324
-#136 := (not #123)
-#630 := [hypothesis]: #136
-#322 := (or #127 #123)
-#137 := (iff #127 #136)
-#48 := (= #47 f1)
-#46 := (= #45 f1)
-#49 := (iff #46 #48)
-#50 := (not #49)
-#140 := (iff #50 #137)
-#130 := (iff #123 #127)
-#133 := (not #130)
-#138 := (iff #133 #137)
-#139 := [rewrite]: #138
-#134 := (iff #50 #133)
-#131 := (iff #49 #130)
-#128 := (iff #48 #127)
-#129 := [rewrite]: #128
-#125 := (iff #46 #123)
-#126 := [rewrite]: #125
-#132 := [monotonicity #126 #129]: #131
-#135 := [monotonicity #132]: #134
-#141 := [trans #135 #139]: #140
-#122 := [asserted]: #50
-#144 := [mp #122 #141]: #137
-#234 := (not #137)
-#321 := (or #127 #123 #234)
-#235 := [def-axiom]: #321
-#236 := [unit-resolution #235 #144]: #322
-#631 := [unit-resolution #236 #630]: #127
-#307 := (or #323 #328)
-#633 := (or #123 #307)
-#644 := (not #307)
-#646 := (iff #123 #644)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#34 := (f7 f9 #20)
-#35 := (f6 #34 #22)
-#18 := (:var 2 S2)
-#36 := (f3 #18 #35)
-#673 := (pattern #36)
-#28 := (f3 #18 #22)
-#96 := (= f1 #28)
-#169 := (not #96)
-#26 := (f3 #18 #20)
-#93 := (= f1 #26)
-#168 := (not #93)
-#152 := (or #168 #169)
-#153 := (not #152)
-#109 := (= f1 #36)
-#170 := (iff #109 #153)
-#674 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #673) #170)
-#173 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #170)
-#677 := (iff #173 #674)
-#675 := (iff #170 #170)
-#676 := [refl]: #675
-#678 := [quant-intro #676]: #677
-#113 := (and #93 #96)
-#116 := (iff #109 #113)
-#119 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #116)
-#174 := (iff #119 #173)
-#171 := (iff #116 #170)
-#154 := (iff #113 #153)
-#155 := [rewrite]: #154
-#172 := [monotonicity #155]: #171
-#175 := [quant-intro #172]: #174
-#150 := (~ #119 #119)
-#165 := (~ #116 #116)
-#166 := [refl]: #165
-#151 := [nnf-pos #166]: #150
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#38 := (and #27 #29)
-#37 := (= #36 f1)
-#39 := (iff #37 #38)
-#40 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #39)
-#120 := (iff #40 #119)
-#117 := (iff #39 #116)
-#114 := (iff #38 #113)
-#97 := (iff #29 #96)
-#98 := [rewrite]: #97
-#94 := (iff #27 #93)
-#95 := [rewrite]: #94
-#115 := [monotonicity #95 #98]: #114
-#111 := (iff #37 #109)
-#112 := [rewrite]: #111
-#118 := [monotonicity #112 #115]: #117
-#121 := [quant-intro #118]: #120
-#108 := [asserted]: #40
-#124 := [mp #108 #121]: #119
-#167 := [mp~ #124 #151]: #119
-#176 := [mp #167 #175]: #173
-#679 := [mp #176 #678]: #674
-#640 := (not #674)
-#312 := (or #640 #646)
-#313 := [quant-inst #41 #42 #14]: #312
-#632 := [unit-resolution #313 #679]: #646
-#641 := (not #646)
-#299 := (or #641 #123 #307)
-#304 := [def-axiom]: #299
-#628 := [unit-resolution #304 #632]: #633
-#634 := [unit-resolution #628 #630]: #307
-#645 := (or #644 #323 #328)
-#651 := [def-axiom]: #645
-#270 := [unit-resolution #651 #634 #631 #629]: false
-#635 := [lemma #270]: #123
-#326 := (or #323 #136)
-#314 := (or #323 #136 #234)
-#325 := [def-axiom]: #314
-#254 := [unit-resolution #325 #144]: #326
-#637 := [unit-resolution #254 #635]: #323
-#275 := (or #136 #644)
-#642 := (or #641 #136 #644)
-#300 := [def-axiom]: #642
-#276 := [unit-resolution #300 #632]: #275
-#638 := [unit-resolution #276 #635]: #644
-#647 := (or #307 #127)
-#648 := [def-axiom]: #647
-[unit-resolution #648 #638 #637]: false
-unsat
-fa1e213c15b8e9288bf16d2dc4bd96e3c7fb5c7e 173 0
-#2 := false
+#32 := f9
+#42 := (f7 f9 f11)
+#43 := (f6 #42 f11)
+#44 := (f3 f10 #43)
+#45 := (= #44 f1)
+#268 := (or #45 #47)
+#75 := (not #45)
+#76 := (iff #75 #47)
+#48 := (iff #45 #47)
+#49 := (not #48)
+#77 := (iff #49 #76)
+#78 := [rewrite]: #77
+#74 := [asserted]: #49
+#81 := [mp #74 #78]: #76
+#177 := (not #76)
+#266 := (or #45 #47 #177)
+#267 := [def-axiom]: #266
+#265 := [unit-resolution #267 #81]: #268
+#574 := [unit-resolution #265 #568]: #45
+#575 := (or #75 #47)
+#21 := (:var 0 S3)
+#19 := (:var 1 S3)
+#33 := (f7 f9 #19)
+#34 := (f6 #33 #21)
+#17 := (:var 2 S2)
+#35 := (f3 #17 #34)
+#613 := (pattern #35)
+#27 := (f3 #17 #21)
+#28 := (= #27 f1)
+#106 := (not #28)
+#25 := (f3 #17 #19)
+#26 := (= #25 f1)
+#105 := (not #26)
+#89 := (or #105 #106)
+#90 := (not #89)
+#36 := (= #35 f1)
+#107 := (iff #36 #90)
+#614 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #613) #107)
+#110 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #107)
+#617 := (iff #110 #614)
+#615 := (iff #107 #107)
+#616 := [refl]: #615
+#618 := [quant-intro #616]: #617
+#37 := (and #26 #28)
+#38 := (iff #36 #37)
+#39 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #38)
+#111 := (iff #39 #110)
+#108 := (iff #38 #107)
+#91 := (iff #37 #90)
+#92 := [rewrite]: #91
+#109 := [monotonicity #92]: #108
+#112 := [quant-intro #109]: #111
+#87 := (~ #39 #39)
+#102 := (~ #38 #38)
+#103 := [refl]: #102
+#88 := [nnf-pos #103]: #87
+#73 := [asserted]: #39
+#104 := [mp~ #73 #88]: #39
+#113 := [mp #104 #112]: #110
+#619 := [mp #113 #618]: #614
+#591 := (not #614)
+#581 := (or #591 #48)
+#269 := (or #262 #262)
+#248 := (not #269)
+#584 := (iff #45 #248)
+#240 := (or #591 #584)
+#582 := (iff #240 #581)
+#583 := (iff #581 #581)
+#225 := [rewrite]: #583
+#590 := (iff #584 #48)
+#588 := (iff #248 #47)
+#373 := (not #262)
+#254 := (iff #373 #47)
+#587 := [rewrite]: #254
+#580 := (iff #248 #373)
+#586 := (iff #269 #262)
+#242 := [rewrite]: #586
+#253 := [monotonicity #242]: #580
+#589 := [trans #253 #587]: #588
+#585 := [monotonicity #589]: #590
+#241 := [monotonicity #585]: #582
+#567 := [trans #241 #225]: #582
+#245 := [quant-inst #40 #41 #41]: #240
+#229 := [mp #245 #567]: #581
+#211 := [unit-resolution #229 #619]: #48
+#232 := (or #49 #75 #47)
+#569 := [def-axiom]: #232
+#577 := [unit-resolution #569 #211]: #575
+#216 := [unit-resolution #577 #574 #568]: false
+#217 := [lemma #216]: #47
+#264 := (or #75 #262)
+#263 := (or #75 #262 #177)
+#178 := [def-axiom]: #263
+#255 := [unit-resolution #178 #81]: #264
+#578 := [unit-resolution #255 #217]: #75
+#576 := (or #45 #262)
+#230 := (or #49 #45 #262)
+#231 := [def-axiom]: #230
+#579 := [unit-resolution #231 #211]: #576
+[unit-resolution #579 #578 #217]: false
+unsat
+62139c25ee961075afc011e9d98f3a2524600355 207 0
+#2 := false
+decl f1 :: S1
+#3 := f1
 decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f11 :: S3
-#42 := f11
-decl f7 :: (-> S5 S3 S4)
+decl f13 :: S3
+#45 := f13
+decl f10 :: S2
+#40 := f10
+#579 := (f3 f10 f13)
+#580 := (= #579 f1)
+#575 := (not #580)
 decl f12 :: S3
-#44 := f12
-decl f9 :: S5
-#33 := f9
-#48 := (f7 f9 f12)
-#49 := (f6 #48 f11)
-decl f10 :: S2
-#41 := f10
-#50 := (f3 f10 #49)
-decl f1 :: S1
-#4 := f1
-#130 := (= f1 #50)
-#326 := (not #130)
-#43 := (f7 f9 f11)
-#45 := (f6 #43 f12)
-#46 := (f3 f10 #45)
-#126 := (= f1 #46)
-#139 := (not #126)
-#628 := [hypothesis]: #139
-#325 := (or #130 #126)
-#140 := (iff #130 #139)
-#51 := (= #50 f1)
-#47 := (= #46 f1)
-#52 := (iff #47 #51)
-#53 := (not #52)
-#143 := (iff #53 #140)
-#133 := (iff #126 #130)
-#136 := (not #133)
-#141 := (iff #136 #140)
-#142 := [rewrite]: #141
-#137 := (iff #53 #136)
-#134 := (iff #52 #133)
-#131 := (iff #51 #130)
-#132 := [rewrite]: #131
-#128 := (iff #47 #126)
-#129 := [rewrite]: #128
-#135 := [monotonicity #129 #132]: #134
-#138 := [monotonicity #135]: #137
-#144 := [trans #138 #142]: #143
-#125 := [asserted]: #53
-#147 := [mp #125 #144]: #140
-#237 := (not #140)
-#324 := (or #130 #126 #237)
-#238 := [def-axiom]: #324
-#239 := [unit-resolution #238 #147]: #325
-#629 := [unit-resolution #239 #628]: #130
-#310 := (f3 f10 f12)
-#647 := (= f1 #310)
-#649 := (not #647)
-#330 := (f3 f10 f11)
-#327 := (= f1 #330)
-#331 := (not #327)
-#315 := (or #331 #649)
-#626 := (or #126 #315)
-#651 := (not #315)
-#642 := (iff #126 #651)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#34 := (f7 f9 #20)
-#35 := (f6 #34 #22)
-#18 := (:var 2 S2)
-#36 := (f3 #18 #35)
-#676 := (pattern #36)
-#28 := (f3 #18 #22)
-#99 := (= f1 #28)
-#172 := (not #99)
-#26 := (f3 #18 #20)
-#96 := (= f1 #26)
-#171 := (not #96)
-#155 := (or #171 #172)
-#156 := (not #155)
-#112 := (= f1 #36)
-#173 := (iff #112 #156)
-#677 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #676) #173)
-#176 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #173)
-#680 := (iff #176 #677)
-#678 := (iff #173 #173)
-#679 := [refl]: #678
-#681 := [quant-intro #679]: #680
-#116 := (and #96 #99)
-#119 := (iff #112 #116)
-#122 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #119)
-#177 := (iff #122 #176)
-#174 := (iff #119 #173)
-#157 := (iff #116 #156)
-#158 := [rewrite]: #157
-#175 := [monotonicity #158]: #174
-#178 := [quant-intro #175]: #177
-#153 := (~ #122 #122)
-#168 := (~ #119 #119)
-#169 := [refl]: #168
-#154 := [nnf-pos #169]: #153
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#38 := (and #27 #29)
-#37 := (= #36 f1)
-#39 := (iff #37 #38)
-#40 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #39)
-#123 := (iff #40 #122)
-#120 := (iff #39 #119)
-#117 := (iff #38 #116)
-#100 := (iff #29 #99)
-#101 := [rewrite]: #100
-#97 := (iff #27 #96)
-#98 := [rewrite]: #97
-#118 := [monotonicity #98 #101]: #117
-#114 := (iff #37 #112)
-#115 := [rewrite]: #114
-#121 := [monotonicity #115 #118]: #120
-#124 := [quant-intro #121]: #123
-#111 := [asserted]: #40
-#127 := [mp #111 #124]: #122
-#170 := [mp~ #127 #154]: #122
-#179 := [mp #170 #178]: #176
-#682 := [mp #179 #681]: #677
-#302 := (not #677)
-#335 := (or #302 #642)
-#351 := [quant-inst #41 #42 #44]: #335
-#622 := [unit-resolution #351 #682]: #642
-#352 := (not #642)
-#353 := (or #352 #126 #315)
-#339 := [def-axiom]: #353
-#623 := [unit-resolution #339 #622]: #626
-#627 := [unit-resolution #623 #628]: #315
-#337 := (or #326 #651)
-#648 := (iff #130 #651)
-#307 := (or #302 #648)
-#304 := (or #649 #331)
-#436 := (not #304)
-#643 := (iff #130 #436)
-#645 := (or #302 #643)
-#646 := (iff #645 #307)
-#630 := (iff #307 #307)
-#291 := [rewrite]: #630
-#654 := (iff #643 #648)
-#652 := (iff #436 #651)
-#316 := (iff #304 #315)
-#650 := [rewrite]: #316
-#653 := [monotonicity #650]: #652
-#644 := [monotonicity #653]: #654
-#287 := [monotonicity #644]: #646
-#292 := [trans #287 #291]: #646
-#303 := [quant-inst #41 #44 #42]: #645
-#293 := [mp #303 #292]: #307
-#336 := [unit-resolution #293 #682]: #648
-#631 := (not #648)
-#638 := (or #631 #326 #651)
-#640 := [def-axiom]: #638
-#338 := [unit-resolution #640 #336]: #337
-#340 := [unit-resolution #338 #627 #629]: false
-#618 := [lemma #340]: #126
-#329 := (or #326 #139)
-#317 := (or #326 #139 #237)
-#328 := [def-axiom]: #317
-#257 := [unit-resolution #328 #147]: #329
-#619 := [unit-resolution #257 #618]: #326
-#332 := (or #139 #651)
-#354 := (or #352 #139 #651)
-#245 := [def-axiom]: #354
-#616 := [unit-resolution #245 #622]: #332
-#620 := [unit-resolution #616 #618]: #651
-#617 := (or #130 #315)
-#637 := (or #631 #130 #315)
-#273 := [def-axiom]: #637
-#621 := [unit-resolution #273 #336]: #617
-[unit-resolution #621 #620 #619]: false
-unsat
-8424513290e59440c92fec106021e2354c2f6a1c 149 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
+#43 := f12
+#584 := (f3 f10 f12)
+#223 := (= #584 f1)
+#570 := (not #223)
+#567 := (or #570 #575)
+#571 := (not #567)
 decl f6 :: (-> S4 S3 S3)
-decl f11 :: S3
-#42 := f11
 decl f7 :: (-> S5 S3 S4)
 decl f9 :: S5
-#33 := f9
-#43 := (f7 f9 f11)
-#44 := (f6 #43 f11)
-decl f10 :: S2
-#41 := f10
-#45 := (f3 f10 #44)
-decl f1 :: S1
-#4 := f1
-#123 := (= f1 #45)
-#136 := (not #123)
-#632 := [hypothesis]: #136
-#47 := (f3 f10 f11)
-#127 := (= f1 #47)
-#322 := (or #127 #123)
-#137 := (iff #127 #136)
-#48 := (= #47 f1)
-#46 := (= #45 f1)
-#49 := (iff #46 #48)
-#50 := (not #49)
-#140 := (iff #50 #137)
-#130 := (iff #123 #127)
-#133 := (not #130)
-#138 := (iff #133 #137)
-#139 := [rewrite]: #138
-#134 := (iff #50 #133)
-#131 := (iff #49 #130)
-#128 := (iff #48 #127)
-#129 := [rewrite]: #128
-#125 := (iff #46 #123)
-#126 := [rewrite]: #125
-#132 := [monotonicity #126 #129]: #131
-#135 := [monotonicity #132]: #134
-#141 := [trans #135 #139]: #140
-#122 := [asserted]: #50
-#144 := [mp #122 #141]: #137
-#234 := (not #137)
-#321 := (or #127 #123 #234)
-#235 := [def-axiom]: #321
-#236 := [unit-resolution #235 #144]: #322
-#633 := [unit-resolution #236 #632]: #127
-#323 := (not #127)
-#634 := (or #123 #323)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#34 := (f7 f9 #20)
-#35 := (f6 #34 #22)
-#18 := (:var 2 S2)
-#36 := (f3 #18 #35)
-#673 := (pattern #36)
-#28 := (f3 #18 #22)
-#96 := (= f1 #28)
-#169 := (not #96)
-#26 := (f3 #18 #20)
-#93 := (= f1 #26)
-#168 := (not #93)
-#152 := (or #168 #169)
-#153 := (not #152)
-#109 := (= f1 #36)
-#170 := (iff #109 #153)
-#674 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #673) #170)
-#173 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #170)
-#677 := (iff #173 #674)
-#675 := (iff #170 #170)
-#676 := [refl]: #675
-#678 := [quant-intro #676]: #677
-#113 := (and #93 #96)
-#116 := (iff #109 #113)
-#119 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #116)
-#174 := (iff #119 #173)
-#171 := (iff #116 #170)
-#154 := (iff #113 #153)
-#155 := [rewrite]: #154
-#172 := [monotonicity #155]: #171
-#175 := [quant-intro #172]: #174
-#150 := (~ #119 #119)
-#165 := (~ #116 #116)
-#166 := [refl]: #165
-#151 := [nnf-pos #166]: #150
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#38 := (and #27 #29)
-#37 := (= #36 f1)
-#39 := (iff #37 #38)
-#40 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #39)
-#120 := (iff #40 #119)
-#117 := (iff #39 #116)
-#114 := (iff #38 #113)
-#97 := (iff #29 #96)
-#98 := [rewrite]: #97
-#94 := (iff #27 #93)
-#95 := [rewrite]: #94
-#115 := [monotonicity #95 #98]: #114
-#111 := (iff #37 #109)
-#112 := [rewrite]: #111
-#118 := [monotonicity #112 #115]: #117
-#121 := [quant-intro #118]: #120
-#108 := [asserted]: #40
-#124 := [mp #108 #121]: #119
-#167 := [mp~ #124 #151]: #119
-#176 := [mp #167 #175]: #173
-#679 := [mp #176 #678]: #674
-#650 := (not #674)
-#645 := (or #650 #130)
-#327 := (or #323 #323)
-#324 := (not #327)
-#328 := (iff #123 #324)
-#651 := (or #650 #328)
-#299 := (iff #651 #645)
-#642 := (iff #645 #645)
-#300 := [rewrite]: #642
-#648 := (iff #328 #130)
-#313 := (iff #324 #127)
-#646 := (not #323)
-#640 := (iff #646 #127)
-#312 := [rewrite]: #640
-#301 := (iff #324 #646)
-#307 := (iff #327 #323)
-#644 := [rewrite]: #307
-#433 := [monotonicity #644]: #301
-#647 := [trans #433 #312]: #313
-#649 := [monotonicity #647]: #648
-#304 := [monotonicity #649]: #299
-#643 := [trans #304 #300]: #299
-#641 := [quant-inst #41 #42 #42]: #651
-#284 := [mp #641 #643]: #645
-#628 := [unit-resolution #284 #679]: #130
-#627 := (or #133 #123 #323)
-#288 := [def-axiom]: #627
-#270 := [unit-resolution #288 #628]: #634
-#635 := [unit-resolution #270 #633 #632]: false
-#637 := [lemma #635]: #123
-#326 := (or #323 #136)
-#314 := (or #323 #136 #234)
-#325 := [def-axiom]: #314
-#254 := [unit-resolution #325 #144]: #326
-#275 := [unit-resolution #254 #637]: #323
-#276 := (or #136 #127)
-#289 := (or #133 #136 #127)
-#290 := [def-axiom]: #289
-#638 := [unit-resolution #290 #628]: #276
-[unit-resolution #638 #275 #637]: false
-unsat
-5973328496eea1e33493c38f9af9d86965f67ad9 287 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f12 :: S3
-#44 := f12
-decl f7 :: (-> S5 S3 S4)
+#32 := f9
+#44 := (f7 f9 f12)
+#46 := (f6 #44 f13)
+#593 := (f3 f10 #46)
+#249 := (= #593 f1)
+#281 := (iff #249 #571)
+#379 := (not #281)
 decl f11 :: S3
-#42 := f11
-decl f9 :: S5
-#33 := f9
-#43 := (f7 f9 f11)
-#51 := (f6 #43 f12)
-decl f10 :: S2
-#41 := f10
-#314 := (f3 f10 #51)
-decl f1 :: S1
-#4 := f1
-#651 := (= f1 #314)
-#249 := (f3 f10 f12)
-#628 := (= f1 #249)
-#625 := (not #628)
-#339 := (f3 f10 f11)
-#355 := (= f1 #339)
-#356 := (not #355)
-#614 := (or #356 #625)
-#615 := (not #614)
-#611 := (iff #615 #651)
-#582 := (not #611)
-decl f13 :: S3
-#46 := f13
-#334 := (f3 f10 f13)
-#331 := (= f1 #334)
-#335 := (not #331)
-#484 := (or #335 #625)
-#493 := (not #484)
-#45 := (f7 f9 f12)
-#47 := (f6 #45 f13)
-#646 := (f3 f10 #47)
-#632 := (= f1 #646)
-#494 := (iff #493 #632)
-#587 := (not #494)
-#567 := [hypothesis]: #587
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#34 := (f7 f9 #20)
-#35 := (f6 #34 #22)
-#18 := (:var 2 S2)
-#36 := (f3 #18 #35)
-#680 := (pattern #36)
-#28 := (f3 #18 #22)
-#103 := (= f1 #28)
-#176 := (not #103)
-#26 := (f3 #18 #20)
-#100 := (= f1 #26)
-#175 := (not #100)
-#159 := (or #175 #176)
-#160 := (not #159)
-#116 := (= f1 #36)
-#177 := (iff #116 #160)
-#681 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #680) #177)
-#180 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #177)
-#684 := (iff #180 #681)
-#682 := (iff #177 #177)
-#683 := [refl]: #682
-#685 := [quant-intro #683]: #684
-#120 := (and #100 #103)
-#123 := (iff #116 #120)
-#126 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #123)
-#181 := (iff #126 #180)
-#178 := (iff #123 #177)
-#161 := (iff #120 #160)
-#162 := [rewrite]: #161
-#179 := [monotonicity #162]: #178
-#182 := [quant-intro #179]: #181
-#157 := (~ #126 #126)
-#172 := (~ #123 #123)
-#173 := [refl]: #172
-#158 := [nnf-pos #173]: #157
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#38 := (and #27 #29)
-#37 := (= #36 f1)
-#39 := (iff #37 #38)
-#40 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #39)
-#127 := (iff #40 #126)
-#124 := (iff #39 #123)
-#121 := (iff #38 #120)
-#104 := (iff #29 #103)
-#105 := [rewrite]: #104
-#101 := (iff #27 #100)
-#102 := [rewrite]: #101
-#122 := [monotonicity #102 #105]: #121
-#118 := (iff #37 #116)
-#119 := [rewrite]: #118
-#125 := [monotonicity #119 #122]: #124
-#128 := [quant-intro #125]: #127
-#115 := [asserted]: #40
-#131 := [mp #115 #128]: #126
-#174 := [mp~ #131 #158]: #126
-#183 := [mp #174 #182]: #180
-#686 := [mp #183 #685]: #681
-#306 := (not #681)
-#498 := (or #306 #494)
-#600 := (or #625 #335)
-#482 := (not #600)
-#483 := (iff #632 #482)
-#499 := (or #306 #483)
-#593 := (iff #499 #498)
-#594 := (iff #498 #498)
-#581 := [rewrite]: #594
-#496 := (iff #483 #494)
-#592 := (iff #632 #493)
-#495 := (iff #592 #494)
-#488 := [rewrite]: #495
-#477 := (iff #483 #592)
-#588 := (iff #482 #493)
-#443 := (iff #600 #484)
-#591 := [rewrite]: #443
-#589 := [monotonicity #591]: #588
-#492 := [monotonicity #589]: #477
-#497 := [trans #492 #488]: #496
-#590 := [monotonicity #497]: #593
-#583 := [trans #590 #581]: #593
-#500 := [quant-inst #41 #44 #46]: #499
-#575 := [mp #500 #583]: #498
-#568 := [unit-resolution #575 #686 #567]: false
-#569 := [lemma #568]: #494
-#633 := (not #632)
-#357 := (or #356 #633)
-#343 := (not #357)
-#48 := (f6 #43 #47)
-#49 := (f3 f10 #48)
-#130 := (= f1 #49)
-#143 := (not #130)
-#570 := [hypothesis]: #143
-#571 := (or #130 #357)
-#358 := (iff #130 #343)
-#629 := (or #306 #358)
-#351 := [quant-inst #41 #42 #47]: #629
-#566 := [unit-resolution #351 #686]: #358
-#341 := (not #358)
-#342 := (or #341 #130 #357)
-#344 := [def-axiom]: #342
-#557 := [unit-resolution #344 #566]: #571
-#558 := [unit-resolution #557 #570]: #357
-#597 := (or #306 #611)
-#616 := (iff #651 #615)
-#613 := (or #306 #616)
-#618 := (iff #613 #597)
-#461 := (iff #597 #597)
-#462 := [rewrite]: #461
-#612 := (iff #616 #611)
-#617 := [rewrite]: #612
-#460 := [monotonicity #617]: #618
-#604 := [trans #460 #462]: #618
-#619 := [quant-inst #41 #42 #44]: #613
-#605 := [mp #619 #604]: #597
-#560 := [unit-resolution #605 #686]: #611
-#546 := (or #582 #615)
-#653 := (not #651)
-#319 := (or #335 #653)
-#655 := (not #319)
-#52 := (f7 f9 #51)
-#53 := (f6 #52 f13)
-#54 := (f3 f10 #53)
-#134 := (= f1 #54)
-#329 := (or #134 #130)
-#144 := (iff #134 #143)
-#55 := (= #54 f1)
-#50 := (= #49 f1)
-#56 := (iff #50 #55)
-#57 := (not #56)
-#147 := (iff #57 #144)
-#137 := (iff #130 #134)
-#140 := (not #137)
-#145 := (iff #140 #144)
-#146 := [rewrite]: #145
-#141 := (iff #57 #140)
-#138 := (iff #56 #137)
-#135 := (iff #55 #134)
-#136 := [rewrite]: #135
-#132 := (iff #50 #130)
-#133 := [rewrite]: #132
-#139 := [monotonicity #133 #136]: #138
-#142 := [monotonicity #139]: #141
-#148 := [trans #142 #146]: #147
-#129 := [asserted]: #57
-#151 := [mp #129 #148]: #144
-#241 := (not #144)
-#328 := (or #134 #130 #241)
-#242 := [def-axiom]: #328
-#243 := [unit-resolution #242 #151]: #329
-#561 := [unit-resolution #243 #570]: #134
-#330 := (not #134)
-#559 := (or #330 #655)
-#652 := (iff #134 #655)
-#311 := (or #306 #652)
-#308 := (or #653 #335)
-#440 := (not #308)
-#647 := (iff #134 #440)
-#649 := (or #306 #647)
-#650 := (iff #649 #311)
-#634 := (iff #311 #311)
-#295 := [rewrite]: #634
-#658 := (iff #647 #652)
-#656 := (iff #440 #655)
-#320 := (iff #308 #319)
-#654 := [rewrite]: #320
-#657 := [monotonicity #654]: #656
-#648 := [monotonicity #657]: #658
-#291 := [monotonicity #648]: #650
-#296 := [trans #291 #295]: #650
-#307 := [quant-inst #41 #51 #46]: #649
-#297 := [mp #307 #296]: #311
-#562 := [unit-resolution #297 #686]: #652
-#635 := (not #652)
-#642 := (or #635 #330 #655)
-#644 := [def-axiom]: #642
-#563 := [unit-resolution #644 #562]: #559
-#543 := [unit-resolution #563 #561]: #655
-#637 := (or #319 #651)
-#638 := [def-axiom]: #637
-#544 := [unit-resolution #638 #543]: #651
-#576 := (or #582 #615 #653)
-#577 := [def-axiom]: #576
-#547 := [unit-resolution #577 #544]: #546
-#548 := [unit-resolution #547 #560]: #615
-#606 := (or #614 #355)
-#572 := [def-axiom]: #606
-#549 := [unit-resolution #572 #548]: #355
-#631 := (or #343 #356 #633)
-#340 := [def-axiom]: #631
-#550 := [unit-resolution #340 #549 #558]: #633
-#298 := (or #319 #331)
-#636 := [def-axiom]: #298
-#551 := [unit-resolution #636 #543]: #331
-#574 := (or #614 #628)
-#584 := [def-axiom]: #574
-#552 := [unit-resolution #584 #548]: #628
-#609 := (or #493 #335 #625)
-#603 := [def-axiom]: #609
-#553 := [unit-resolution #603 #552 #551]: #493
-#441 := (or #587 #484 #632)
-#442 := [def-axiom]: #441
-#554 := [unit-resolution #442 #553 #550 #569]: false
-#555 := [lemma #554]: #130
-#545 := (or #143 #343)
-#622 := (or #341 #143 #343)
-#623 := [def-axiom]: #622
-#556 := [unit-resolution #623 #566]: #545
-#534 := [unit-resolution #556 #555]: #343
-#630 := (or #357 #632)
-#627 := [def-axiom]: #630
-#535 := [unit-resolution #627 #534]: #632
-#610 := (or #587 #493 #633)
-#439 := [def-axiom]: #610
-#537 := [unit-resolution #439 #535 #569]: #493
-#602 := (or #484 #628)
-#608 := [def-axiom]: #602
-#538 := [unit-resolution #608 #537]: #628
-#352 := (or #357 #355)
-#626 := [def-axiom]: #352
-#539 := [unit-resolution #626 #534]: #355
-#585 := (or #615 #356 #625)
-#586 := [def-axiom]: #585
-#540 := [unit-resolution #586 #539 #538]: #615
-#333 := (or #330 #143)
-#321 := (or #330 #143 #241)
-#332 := [def-axiom]: #321
-#261 := [unit-resolution #332 #151]: #333
-#541 := [unit-resolution #261 #555]: #330
-#536 := (or #134 #319)
-#641 := (or #635 #134 #319)
-#277 := [def-axiom]: #641
-#542 := [unit-resolution #277 #562]: #536
-#528 := [unit-resolution #542 #541]: #319
-#607 := (or #484 #331)
-#601 := [def-axiom]: #607
-#524 := [unit-resolution #601 #537]: #331
-#639 := (or #655 #335 #653)
-#640 := [def-axiom]: #639
-#525 := [unit-resolution #640 #524 #528]: #653
-#578 := (or #582 #614 #651)
-#579 := [def-axiom]: #578
-#526 := [unit-resolution #579 #525 #540]: #582
-[unit-resolution #605 #686 #526]: false
-unsat
-6c759b8f06a9510b6e4f2c41f45fd7a908ea138f 22 0
+#41 := f11
+#276 := (f3 f10 f11)
+#255 := (= #276 f1)
+#591 := (not #255)
+#282 := (or #591 #570)
+#283 := (not #282)
+#42 := (f7 f9 f11)
+#50 := (f6 #42 f12)
+#594 := (f3 f10 #50)
+#595 := (= #594 f1)
+#400 := (iff #595 #283)
+#543 := (not #400)
+#401 := [hypothesis]: #543
+#21 := (:var 0 S3)
+#19 := (:var 1 S3)
+#33 := (f7 f9 #19)
+#34 := (f6 #33 #21)
+#17 := (:var 2 S2)
+#35 := (f3 #17 #34)
+#620 := (pattern #35)
+#27 := (f3 #17 #21)
+#28 := (= #27 f1)
+#113 := (not #28)
+#25 := (f3 #17 #19)
+#26 := (= #25 f1)
+#112 := (not #26)
+#96 := (or #112 #113)
+#97 := (not #96)
+#36 := (= #35 f1)
+#114 := (iff #36 #97)
+#621 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #620) #114)
+#117 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #114)
+#624 := (iff #117 #621)
+#622 := (iff #114 #114)
+#623 := [refl]: #622
+#625 := [quant-intro #623]: #624
+#37 := (and #26 #28)
+#38 := (iff #36 #37)
+#39 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #38)
+#118 := (iff #39 #117)
+#115 := (iff #38 #114)
+#98 := (iff #37 #97)
+#99 := [rewrite]: #98
+#116 := [monotonicity #99]: #115
+#119 := [quant-intro #116]: #118
+#94 := (~ #39 #39)
+#109 := (~ #38 #38)
+#110 := [refl]: #109
+#95 := [nnf-pos #110]: #94
+#80 := [asserted]: #39
+#111 := [mp~ #80 #95]: #39
+#120 := [mp #111 #119]: #117
+#626 := [mp #120 #625]: #621
+#596 := (not #621)
+#544 := (or #596 #400)
+#545 := [quant-inst #40 #41 #43]: #544
+#402 := [unit-resolution #545 #626 #401]: false
+#537 := [lemma #402]: #400
+#578 := (not #595)
+#581 := (or #578 #575)
+#218 := (not #581)
+#51 := (f7 f9 #50)
+#52 := (f6 #51 f13)
+#53 := (f3 f10 #52)
+#54 := (= #53 f1)
+#380 := (not #249)
+#587 := (or #591 #380)
+#260 := (not #587)
+#47 := (f6 #42 #46)
+#48 := (f3 f10 #47)
+#49 := (= #48 f1)
+#269 := (not #54)
+#559 := [hypothesis]: #269
+#275 := (or #49 #54)
+#82 := (not #49)
+#83 := (iff #82 #54)
+#55 := (iff #49 #54)
+#56 := (not #55)
+#84 := (iff #56 #83)
+#85 := [rewrite]: #84
+#81 := [asserted]: #56
+#88 := [mp #81 #85]: #83
+#184 := (not #83)
+#273 := (or #49 #54 #184)
+#274 := [def-axiom]: #273
+#272 := [unit-resolution #274 #88]: #275
+#284 := [unit-resolution #272 #559]: #49
+#424 := (or #82 #260)
+#261 := (iff #49 #260)
+#597 := (or #596 #261)
+#592 := [quant-inst #40 #41 #46]: #597
+#423 := [unit-resolution #592 #626]: #261
+#590 := (not #261)
+#236 := (or #590 #82 #260)
+#237 := [def-axiom]: #236
+#383 := [unit-resolution #237 #423]: #424
+#531 := [unit-resolution #383 #284]: #260
+#598 := (or #587 #255)
+#588 := [def-axiom]: #598
+#433 := [unit-resolution #588 #531]: #255
+#562 := (or #596 #281)
+#546 := [quant-inst #40 #43 #45]: #562
+#528 := [unit-resolution #546 #626]: #281
+#532 := (or #379 #571)
+#247 := (or #587 #249)
+#252 := [def-axiom]: #247
+#529 := [unit-resolution #252 #531]: #249
+#535 := (or #379 #380 #571)
+#536 := [def-axiom]: #535
+#417 := [unit-resolution #536 #529]: #532
+#432 := [unit-resolution #417 #528]: #571
+#547 := (or #567 #223)
+#541 := [def-axiom]: #547
+#434 := [unit-resolution #541 #432]: #223
+#561 := (or #283 #591 #570)
+#565 := [def-axiom]: #561
+#435 := [unit-resolution #565 #434 #433]: #283
+#436 := (or #54 #581)
+#582 := (iff #54 #218)
+#224 := (or #596 #582)
+#585 := [quant-inst #40 #50 #45]: #224
+#428 := [unit-resolution #585 #626]: #582
+#296 := (not #582)
+#297 := (or #296 #54 #581)
+#298 := [def-axiom]: #297
+#437 := [unit-resolution #298 #428]: #436
+#438 := [unit-resolution #437 #559]: #581
+#542 := (or #567 #580)
+#548 := [def-axiom]: #542
+#439 := [unit-resolution #548 #432]: #580
+#280 := (or #218 #578 #575)
+#295 := [def-axiom]: #280
+#440 := [unit-resolution #295 #439 #438]: #578
+#554 := (or #543 #595 #282)
+#555 := [def-axiom]: #554
+#533 := [unit-resolution #555 #440 #435 #537]: false
+#530 := [lemma #533]: #54
+#549 := (or #269 #218)
+#191 := (or #296 #269 #218)
+#568 := [def-axiom]: #191
+#550 := [unit-resolution #568 #428]: #549
+#523 := [unit-resolution #550 #530]: #218
+#583 := (or #581 #595)
+#586 := [def-axiom]: #583
+#515 := [unit-resolution #586 #523]: #595
+#556 := (or #543 #578 #283)
+#551 := [def-axiom]: #556
+#512 := [unit-resolution #551 #515 #537]: #283
+#560 := (or #282 #223)
+#564 := [def-axiom]: #560
+#514 := [unit-resolution #564 #512]: #223
+#572 := (or #581 #580)
+#573 := [def-axiom]: #572
+#524 := [unit-resolution #573 #523]: #580
+#381 := (or #571 #570 #575)
+#382 := [def-axiom]: #381
+#525 := [unit-resolution #382 #524 #514]: #571
+#271 := (or #82 #269)
+#270 := (or #82 #269 #184)
+#185 := [def-axiom]: #270
+#262 := [unit-resolution #185 #88]: #271
+#526 := [unit-resolution #262 #530]: #82
+#522 := (or #49 #587)
+#232 := (or #590 #49 #587)
+#574 := [def-axiom]: #232
+#527 := [unit-resolution #574 #423]: #522
+#516 := [unit-resolution #527 #526]: #587
+#563 := (or #282 #255)
+#277 := [def-axiom]: #563
+#517 := [unit-resolution #277 #512]: #255
+#589 := (or #260 #591 #380)
+#248 := [def-axiom]: #589
+#518 := [unit-resolution #248 #517 #516]: #380
+#538 := (or #379 #249 #567)
+#539 := [def-axiom]: #538
+#519 := [unit-resolution #539 #518 #525]: #379
+[unit-resolution #546 #626 #519]: false
+unsat
+c39c54f907aa2283011df5d842bdfd51c1629e0d 22 0
 #2 := false
 decl f13 :: (-> S7 S3 S4)
 decl f4 :: S3
-#8 := f4
+#7 := f4
 decl f14 :: S7
-#50 := f14
-#51 := (f13 f14 f4)
-#52 := (= #51 #51)
-#53 := (not #52)
-#148 := (iff #53 false)
-#1 := true
-#143 := (not true)
-#146 := (iff #143 false)
-#147 := [rewrite]: #146
-#144 := (iff #53 #143)
-#140 := (iff #52 true)
-#142 := [rewrite]: #140
-#145 := [monotonicity #142]: #144
-#149 := [trans #145 #147]: #148
-#139 := [asserted]: #53
-[mp #139 #149]: false
-unsat
-eac8197a82f6b3a5c2024430d69641bb761b0abc 60 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f4 :: S3
-#9 := f4
-decl f10 :: S2
-#41 := f10
-#42 := (f3 f10 f4)
-decl f1 :: S1
-#4 := f1
-#118 := (= f1 #42)
-#43 := (= #42 f1)
-#44 := (not #43)
-#45 := (not #44)
-#130 := (iff #45 #118)
-#122 := (not #118)
-#125 := (not #122)
-#128 := (iff #125 #118)
-#129 := [rewrite]: #128
-#126 := (iff #45 #125)
-#123 := (iff #44 #122)
-#120 := (iff #43 #118)
-#121 := [rewrite]: #120
-#124 := [monotonicity #121]: #123
-#127 := [monotonicity #124]: #126
-#131 := [trans #127 #129]: #130
-#117 := [asserted]: #45
-#134 := [mp #117 #131]: #118
-#8 := (:var 0 S2)
-#10 := (f3 #8 f4)
-#642 := (pattern #10)
-#66 := (= f1 #10)
-#69 := (not #66)
-#643 := (forall (vars (?v0 S2)) (:pat #642) #69)
-#72 := (forall (vars (?v0 S2)) #69)
-#646 := (iff #72 #643)
-#644 := (iff #69 #69)
-#645 := [refl]: #644
-#647 := [quant-intro #645]: #646
-#148 := (~ #72 #72)
-#146 := (~ #69 #69)
-#147 := [refl]: #146
-#149 := [nnf-pos #147]: #148
-#11 := (= #10 f1)
-#12 := (not #11)
-#13 := (forall (vars (?v0 S2)) #12)
-#73 := (iff #13 #72)
-#70 := (iff #12 #69)
-#67 := (iff #11 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#74 := [quant-intro #71]: #73
-#65 := [asserted]: #13
-#77 := [mp #65 #74]: #72
-#133 := [mp~ #77 #149]: #72
-#648 := [mp #133 #647]: #643
-#225 := (not #643)
-#312 := (or #225 #122)
-#226 := [quant-inst #41]: #312
-[unit-resolution #226 #648 #134]: false
-unsat
-32295808d649b2df10d022ec20bfa2f501001522 48 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f5 :: S3
-#14 := f5
-decl f10 :: S2
-#41 := f10
-#42 := (f3 f10 f5)
-decl f1 :: S1
-#4 := f1
-#117 := (= f1 #42)
-#121 := (not #117)
-#43 := (= #42 f1)
-#44 := (not #43)
-#122 := (iff #44 #121)
-#119 := (iff #43 #117)
-#120 := [rewrite]: #119
-#123 := [monotonicity #120]: #122
-#116 := [asserted]: #44
-#126 := [mp #116 #123]: #121
-#8 := (:var 0 S2)
-#15 := (f3 #8 f5)
-#641 := (pattern #15)
-#75 := (= f1 #15)
-#642 := (forall (vars (?v0 S2)) (:pat #641) #75)
-#79 := (forall (vars (?v0 S2)) #75)
-#645 := (iff #79 #642)
-#643 := (iff #75 #75)
-#644 := [refl]: #643
-#646 := [quant-intro #644]: #645
-#128 := (~ #79 #79)
-#127 := (~ #75 #75)
-#142 := [refl]: #127
-#129 := [nnf-pos #142]: #128
-#16 := (= #15 f1)
-#17 := (forall (vars (?v0 S2)) #16)
-#80 := (iff #17 #79)
-#77 := (iff #16 #75)
-#78 := [rewrite]: #77
-#81 := [quant-intro #78]: #80
-#74 := [asserted]: #17
-#84 := [mp #74 #81]: #79
-#143 := [mp~ #84 #129]: #79
-#647 := [mp #143 #646]: #642
-#217 := (not #642)
-#304 := (or #217 #117)
-#218 := [quant-inst #41]: #304
-[unit-resolution #218 #647 #126]: false
-unsat
-dfe83e391823f1cbfcca9d6fb06c0ae74a22248a 126 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f12 :: S3
-#44 := f12
-decl f7 :: (-> S5 S3 S4)
-decl f11 :: S3
-#42 := f11
-decl f8 :: S5
-#19 := f8
-#43 := (f7 f8 f11)
-#45 := (f6 #43 f12)
-decl f10 :: S2
-#41 := f10
-#46 := (f3 f10 #45)
-decl f1 :: S1
-#4 := f1
-#127 := (= f1 #46)
-#146 := (not #127)
-#650 := [hypothesis]: #146
-#50 := (f3 f10 f12)
-#134 := (= f1 #50)
-#48 := (f3 f10 f11)
-#131 := (= f1 #48)
-#137 := (or #131 #134)
-#338 := (or #137 #127)
-#147 := (iff #137 #146)
-#51 := (= #50 f1)
-#49 := (= #48 f1)
-#52 := (or #49 #51)
-#47 := (= #46 f1)
-#53 := (iff #47 #52)
-#54 := (not #53)
-#150 := (iff #54 #147)
-#140 := (iff #127 #137)
-#143 := (not #140)
-#148 := (iff #143 #147)
-#149 := [rewrite]: #148
-#144 := (iff #54 #143)
-#141 := (iff #53 #140)
-#138 := (iff #52 #137)
-#135 := (iff #51 #134)
-#136 := [rewrite]: #135
-#132 := (iff #49 #131)
-#133 := [rewrite]: #132
-#139 := [monotonicity #133 #136]: #138
-#129 := (iff #47 #127)
-#130 := [rewrite]: #129
-#142 := [monotonicity #130 #139]: #141
-#145 := [monotonicity #142]: #144
-#151 := [trans #145 #149]: #150
-#126 := [asserted]: #54
-#154 := [mp #126 #151]: #147
-#264 := (not #147)
-#337 := (or #137 #127 #264)
-#334 := [def-axiom]: #337
-#317 := [unit-resolution #334 #154]: #338
-#322 := [unit-resolution #317 #650]: #137
-#324 := (not #137)
-#653 := (or #127 #324)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#21 := (f7 f8 #20)
-#23 := (f6 #21 #22)
-#18 := (:var 2 S2)
-#24 := (f3 #18 #23)
-#676 := (pattern #24)
-#28 := (f3 #18 #22)
-#100 := (= f1 #28)
-#26 := (f3 #18 #20)
-#97 := (= f1 #26)
-#103 := (or #97 #100)
-#93 := (= f1 #24)
-#106 := (iff #93 #103)
-#677 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #676) #106)
-#109 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #106)
-#680 := (iff #109 #677)
-#678 := (iff #106 #106)
-#679 := [refl]: #678
-#681 := [quant-intro #679]: #680
-#158 := (~ #109 #109)
-#172 := (~ #106 #106)
-#173 := [refl]: #172
-#159 := [nnf-pos #173]: #158
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#30 := (or #27 #29)
-#25 := (= #24 f1)
-#31 := (iff #25 #30)
-#32 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #31)
-#110 := (iff #32 #109)
-#107 := (iff #31 #106)
-#104 := (iff #30 #103)
-#101 := (iff #29 #100)
-#102 := [rewrite]: #101
-#98 := (iff #27 #97)
-#99 := [rewrite]: #98
-#105 := [monotonicity #99 #102]: #104
-#95 := (iff #25 #93)
-#96 := [rewrite]: #95
-#108 := [monotonicity #96 #105]: #107
-#111 := [quant-intro #108]: #110
-#92 := [asserted]: #32
-#114 := [mp #92 #111]: #109
-#174 := [mp~ #114 #159]: #109
-#682 := [mp #174 #681]: #677
-#323 := (not #677)
-#657 := (or #323 #140)
-#658 := [quant-inst #41 #42 #44]: #657
-#310 := [unit-resolution #658 #682]: #140
-#659 := (or #143 #127 #324)
-#660 := [def-axiom]: #659
-#294 := [unit-resolution #660 #310]: #653
-#637 := [unit-resolution #294 #322 #650]: false
-#298 := [lemma #637]: #127
-#311 := (or #324 #146)
-#654 := (or #324 #146 #264)
-#656 := [def-axiom]: #654
-#443 := [unit-resolution #656 #154]: #311
-#299 := [unit-resolution #443 #298]: #324
-#300 := (or #146 #137)
-#655 := (or #143 #146 #137)
-#661 := [def-axiom]: #655
-#301 := [unit-resolution #661 #310]: #300
-[unit-resolution #301 #299 #298]: false
-unsat
-54d5adcc9aa92b5c35a0e590a6651cbf7d0b828e 162 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f4 :: S3
-#9 := f4
-decl f10 :: S2
-#41 := f10
-#327 := (f3 f10 f4)
-decl f1 :: S1
-#4 := f1
-#324 := (= f1 #327)
-decl f11 :: S3
-#42 := f11
-#47 := (f3 f10 f11)
-#127 := (= f1 #47)
-#328 := (or #127 #324)
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f8 :: S5
-#19 := f8
-#43 := (f7 f8 f11)
-#44 := (f6 #43 f4)
-#45 := (f3 f10 #44)
-#123 := (= f1 #45)
-#136 := (not #123)
-#644 := [hypothesis]: #136
-#322 := (or #127 #123)
-#137 := (iff #127 #136)
-#48 := (= #47 f1)
-#46 := (= #45 f1)
-#49 := (iff #46 #48)
-#50 := (not #49)
-#140 := (iff #50 #137)
-#130 := (iff #123 #127)
-#133 := (not #130)
-#138 := (iff #133 #137)
-#139 := [rewrite]: #138
-#134 := (iff #50 #133)
-#131 := (iff #49 #130)
-#128 := (iff #48 #127)
-#129 := [rewrite]: #128
-#125 := (iff #46 #123)
-#126 := [rewrite]: #125
-#132 := [monotonicity #126 #129]: #131
-#135 := [monotonicity #132]: #134
-#141 := [trans #135 #139]: #140
-#122 := [asserted]: #50
-#144 := [mp #122 #141]: #137
-#234 := (not #137)
-#321 := (or #127 #123 #234)
-#235 := [def-axiom]: #321
-#236 := [unit-resolution #235 #144]: #322
-#646 := [unit-resolution #236 #644]: #127
-#650 := (not #328)
-#290 := (or #123 #650)
-#307 := (iff #123 #328)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#21 := (f7 f8 #20)
-#23 := (f6 #21 #22)
-#18 := (:var 2 S2)
-#24 := (f3 #18 #23)
-#666 := (pattern #24)
-#28 := (f3 #18 #22)
-#96 := (= f1 #28)
-#26 := (f3 #18 #20)
-#93 := (= f1 #26)
-#99 := (or #93 #96)
-#89 := (= f1 #24)
-#102 := (iff #89 #99)
-#667 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #666) #102)
-#105 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #102)
-#670 := (iff #105 #667)
-#668 := (iff #102 #102)
-#669 := [refl]: #668
-#671 := [quant-intro #669]: #670
-#148 := (~ #105 #105)
-#162 := (~ #102 #102)
-#163 := [refl]: #162
-#149 := [nnf-pos #163]: #148
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#30 := (or #27 #29)
-#25 := (= #24 f1)
-#31 := (iff #25 #30)
-#32 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #31)
-#106 := (iff #32 #105)
-#103 := (iff #31 #102)
-#100 := (iff #30 #99)
-#97 := (iff #29 #96)
-#98 := [rewrite]: #97
-#94 := (iff #27 #93)
-#95 := [rewrite]: #94
-#101 := [monotonicity #95 #98]: #100
-#91 := (iff #25 #89)
-#92 := [rewrite]: #91
-#104 := [monotonicity #92 #101]: #103
-#107 := [quant-intro #104]: #106
-#88 := [asserted]: #32
-#110 := [mp #88 #107]: #105
-#164 := [mp~ #110 #149]: #105
-#672 := [mp #164 #671]: #667
-#301 := (not #667)
-#433 := (or #301 #307)
-#640 := [quant-inst #41 #42 #9]: #433
-#289 := [unit-resolution #640 #672]: #307
-#641 := (not #307)
-#299 := (or #641 #123 #650)
-#304 := [def-axiom]: #299
-#291 := [unit-resolution #304 #289]: #290
-#629 := [unit-resolution #291 #644]: #650
-#323 := (not #127)
-#312 := (or #328 #323)
-#313 := [def-axiom]: #312
-#630 := [unit-resolution #313 #629 #646]: false
-#631 := [lemma #630]: #123
-#632 := (or #136 #328)
-#642 := (or #641 #136 #328)
-#300 := [def-axiom]: #642
-#633 := [unit-resolution #300 #289]: #632
-#635 := [unit-resolution #633 #631]: #328
-#326 := (or #323 #136)
-#314 := (or #323 #136 #234)
-#325 := [def-axiom]: #314
-#254 := [unit-resolution #325 #144]: #326
-#637 := [unit-resolution #254 #631]: #323
-#645 := (or #650 #127 #324)
-#651 := [def-axiom]: #645
-#275 := [unit-resolution #651 #637 #635]: #324
-#8 := (:var 0 S2)
-#10 := (f3 #8 f4)
-#652 := (pattern #10)
-#71 := (= f1 #10)
-#74 := (not #71)
-#653 := (forall (vars (?v0 S2)) (:pat #652) #74)
-#77 := (forall (vars (?v0 S2)) #74)
-#656 := (iff #77 #653)
-#654 := (iff #74 #74)
-#655 := [refl]: #654
-#657 := [quant-intro #655]: #656
-#158 := (~ #77 #77)
-#156 := (~ #74 #74)
-#157 := [refl]: #156
-#159 := [nnf-pos #157]: #158
-#11 := (= #10 f1)
-#12 := (not #11)
-#13 := (forall (vars (?v0 S2)) #12)
-#78 := (iff #13 #77)
-#75 := (iff #12 #74)
-#72 := (iff #11 #71)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#79 := [quant-intro #76]: #78
-#70 := [asserted]: #13
-#82 := [mp #70 #79]: #77
-#143 := [mp~ #82 #159]: #77
-#658 := [mp #143 #657]: #653
-#647 := (not #324)
-#628 := (not #653)
-#634 := (or #628 #647)
-#270 := [quant-inst #41]: #634
-[unit-resolution #270 #658 #275]: false
-unsat
-6579b339206079120a92afc0dda92279c34507ae 136 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f5 :: S3
-#14 := f5
-decl f10 :: S2
-#41 := f10
-#219 := (f3 f10 f5)
-decl f1 :: S1
-#4 := f1
-#306 := (= f1 #219)
-#633 := (not #306)
-decl f11 :: S3
-#42 := f11
-#220 := (f3 f10 f11)
-#307 := (= f1 #220)
-#299 := (or #306 #307)
-#284 := (not #299)
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f8 :: S5
-#19 := f8
-#43 := (f7 f8 f11)
-#44 := (f6 #43 f5)
-#45 := (f3 f10 #44)
-#120 := (= f1 #45)
-#239 := (iff #120 #299)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#21 := (f7 f8 #20)
-#23 := (f6 #21 #22)
-#18 := (:var 2 S2)
-#24 := (f3 #18 #23)
-#651 := (pattern #24)
-#28 := (f3 #18 #22)
-#93 := (= f1 #28)
-#26 := (f3 #18 #20)
-#90 := (= f1 #26)
-#96 := (or #90 #93)
-#86 := (= f1 #24)
-#99 := (iff #86 #96)
-#652 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #651) #99)
-#102 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #99)
-#655 := (iff #102 #652)
-#653 := (iff #99 #99)
-#654 := [refl]: #653
-#656 := [quant-intro #654]: #655
-#133 := (~ #102 #102)
-#147 := (~ #99 #99)
-#148 := [refl]: #147
-#134 := [nnf-pos #148]: #133
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#30 := (or #27 #29)
-#25 := (= #24 f1)
-#31 := (iff #25 #30)
-#32 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #31)
-#103 := (iff #32 #102)
-#100 := (iff #31 #99)
-#97 := (iff #30 #96)
-#94 := (iff #29 #93)
-#95 := [rewrite]: #94
-#91 := (iff #27 #90)
-#92 := [rewrite]: #91
-#98 := [monotonicity #92 #95]: #97
-#88 := (iff #25 #86)
-#89 := [rewrite]: #88
-#101 := [monotonicity #89 #98]: #100
-#104 := [quant-intro #101]: #103
-#85 := [asserted]: #32
-#107 := [mp #85 #104]: #102
-#149 := [mp~ #107 #134]: #102
-#657 := [mp #149 #656]: #652
-#313 := (not #652)
-#292 := (or #313 #239)
-#221 := (or #307 #306)
-#308 := (iff #120 #221)
-#629 := (or #313 #308)
-#286 := (iff #629 #292)
-#625 := (iff #292 #292)
-#297 := [rewrite]: #625
-#312 := (iff #308 #239)
-#310 := (iff #221 #299)
-#311 := [rewrite]: #310
-#309 := [monotonicity #311]: #312
-#418 := [monotonicity #309]: #286
-#298 := [trans #418 #297]: #286
-#631 := [quant-inst #41 #42 #14]: #629
-#632 := [mp #631 #298]: #292
-#615 := [unit-resolution #632 #657]: #239
-#285 := (not #239)
-#616 := (or #285 #284)
-#124 := (not #120)
-#46 := (= #45 f1)
-#47 := (not #46)
-#125 := (iff #47 #124)
-#122 := (iff #46 #120)
-#123 := [rewrite]: #122
-#126 := [monotonicity #123]: #125
-#119 := [asserted]: #47
-#129 := [mp #119 #126]: #124
-#628 := (or #285 #120 #284)
-#269 := [def-axiom]: #628
-#619 := [unit-resolution #269 #129]: #616
-#255 := [unit-resolution #619 #615]: #284
-#634 := (or #299 #633)
-#635 := [def-axiom]: #634
-#620 := [unit-resolution #635 #255]: #633
-#8 := (:var 0 S2)
-#15 := (f3 #8 f5)
-#644 := (pattern #15)
-#78 := (= f1 #15)
-#645 := (forall (vars (?v0 S2)) (:pat #644) #78)
-#82 := (forall (vars (?v0 S2)) #78)
-#648 := (iff #82 #645)
-#646 := (iff #78 #78)
-#647 := [refl]: #646
-#649 := [quant-intro #647]: #648
-#131 := (~ #82 #82)
-#130 := (~ #78 #78)
-#145 := [refl]: #130
-#132 := [nnf-pos #145]: #131
-#16 := (= #15 f1)
-#17 := (forall (vars (?v0 S2)) #16)
-#83 := (iff #17 #82)
-#80 := (iff #16 #78)
-#81 := [rewrite]: #80
-#84 := [quant-intro #81]: #83
-#77 := [asserted]: #17
-#87 := [mp #77 #84]: #82
-#146 := [mp~ #87 #132]: #82
-#650 := [mp #146 #649]: #645
-#617 := (not #645)
-#618 := (or #617 #306)
-#613 := [quant-inst #41]: #618
-[unit-resolution #613 #650 #620]: false
-unsat
-21f3225a60811428730067e610d6913c3bcb0df3 155 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f11 :: S3
-#42 := f11
-decl f7 :: (-> S5 S3 S4)
-decl f12 :: S3
-#44 := f12
-decl f8 :: S5
-#19 := f8
-#48 := (f7 f8 f12)
-#49 := (f6 #48 f11)
-decl f10 :: S2
-#41 := f10
-#50 := (f3 f10 #49)
-decl f1 :: S1
-#4 := f1
-#130 := (= f1 #50)
-#326 := (not #130)
-#43 := (f7 f8 f11)
-#45 := (f6 #43 f12)
-#46 := (f3 f10 #45)
-#126 := (= f1 #46)
-#139 := (not #126)
-#245 := [hypothesis]: #139
-#325 := (or #130 #126)
-#140 := (iff #130 #139)
-#51 := (= #50 f1)
-#47 := (= #46 f1)
-#52 := (iff #47 #51)
-#53 := (not #52)
-#143 := (iff #53 #140)
-#133 := (iff #126 #130)
-#136 := (not #133)
-#141 := (iff #136 #140)
-#142 := [rewrite]: #141
-#137 := (iff #53 #136)
-#134 := (iff #52 #133)
-#131 := (iff #51 #130)
-#132 := [rewrite]: #131
-#128 := (iff #47 #126)
-#129 := [rewrite]: #128
-#135 := [monotonicity #129 #132]: #134
-#138 := [monotonicity #135]: #137
-#144 := [trans #138 #142]: #143
-#125 := [asserted]: #53
-#147 := [mp #125 #144]: #140
-#237 := (not #140)
-#324 := (or #130 #126 #237)
-#238 := [def-axiom]: #324
-#239 := [unit-resolution #238 #147]: #325
-#624 := [unit-resolution #239 #245]: #130
-#330 := (f3 f10 f11)
-#327 := (= f1 #330)
-#331 := (f3 f10 f12)
-#310 := (= f1 #331)
-#647 := (or #310 #327)
-#644 := (not #647)
-#347 := (or #126 #644)
-#634 := (iff #126 #647)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#21 := (f7 f8 #20)
-#23 := (f6 #21 #22)
-#18 := (:var 2 S2)
-#24 := (f3 #18 #23)
-#669 := (pattern #24)
-#28 := (f3 #18 #22)
-#99 := (= f1 #28)
-#26 := (f3 #18 #20)
-#96 := (= f1 #26)
-#102 := (or #96 #99)
-#92 := (= f1 #24)
-#105 := (iff #92 #102)
-#670 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #669) #105)
-#108 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #105)
-#673 := (iff #108 #670)
-#671 := (iff #105 #105)
-#672 := [refl]: #671
-#674 := [quant-intro #672]: #673
-#151 := (~ #108 #108)
-#165 := (~ #105 #105)
-#166 := [refl]: #165
-#152 := [nnf-pos #166]: #151
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#30 := (or #27 #29)
-#25 := (= #24 f1)
-#31 := (iff #25 #30)
-#32 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #31)
-#109 := (iff #32 #108)
-#106 := (iff #31 #105)
-#103 := (iff #30 #102)
-#100 := (iff #29 #99)
-#101 := [rewrite]: #100
-#97 := (iff #27 #96)
-#98 := [rewrite]: #97
-#104 := [monotonicity #98 #101]: #103
-#94 := (iff #25 #92)
-#95 := [rewrite]: #94
-#107 := [monotonicity #95 #104]: #106
-#110 := [quant-intro #107]: #109
-#91 := [asserted]: #32
-#113 := [mp #91 #110]: #108
-#167 := [mp~ #113 #152]: #108
-#675 := [mp #167 #674]: #670
-#643 := (not #670)
-#631 := (or #643 #634)
-#304 := (or #327 #310)
-#436 := (iff #126 #304)
-#637 := (or #643 #436)
-#638 := (iff #637 #631)
-#278 := (iff #631 #631)
-#279 := [rewrite]: #278
-#635 := (iff #436 #634)
-#632 := (iff #304 #647)
-#633 := [rewrite]: #632
-#636 := [monotonicity #633]: #635
-#640 := [monotonicity #636]: #638
-#641 := [trans #640 #279]: #638
-#273 := [quant-inst #41 #42 #44]: #637
-#639 := [mp #273 #641]: #631
-#625 := [unit-resolution #639 #675]: #634
-#642 := (not #634)
-#628 := (or #642 #126 #644)
-#629 := [def-axiom]: #628
-#348 := [unit-resolution #629 #625]: #347
-#622 := [unit-resolution #348 #245]: #644
-#623 := (or #326 #647)
-#649 := (iff #130 #647)
-#315 := (or #643 #649)
-#316 := [quant-inst #41 #44 #42]: #315
-#626 := [unit-resolution #316 #675]: #649
-#645 := (not #649)
-#287 := (or #645 #326 #647)
-#630 := [def-axiom]: #287
-#627 := [unit-resolution #630 #626]: #623
-#336 := [unit-resolution #627 #622 #624]: false
-#337 := [lemma #336]: #126
-#329 := (or #326 #139)
-#317 := (or #326 #139 #237)
-#328 := [def-axiom]: #317
-#257 := [unit-resolution #328 #147]: #329
-#338 := [unit-resolution #257 #337]: #326
-#340 := (or #139 #647)
-#335 := (or #642 #139 #647)
-#351 := [def-axiom]: #335
-#618 := [unit-resolution #351 #625]: #340
-#619 := [unit-resolution #618 #337]: #647
-#332 := (or #130 #644)
-#303 := (or #645 #130 #644)
-#646 := [def-axiom]: #303
-#616 := [unit-resolution #646 #626]: #332
-[unit-resolution #616 #619 #338]: false
-unsat
-0a38803d5203ebb9de80029b1e5de8bcd8e8f404 128 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f11 :: S3
-#42 := f11
-decl f7 :: (-> S5 S3 S4)
-decl f8 :: S5
-#19 := f8
-#43 := (f7 f8 f11)
-#44 := (f6 #43 f11)
-decl f10 :: S2
-#41 := f10
-#45 := (f3 f10 #44)
-decl f1 :: S1
-#4 := f1
-#123 := (= f1 #45)
-#136 := (not #123)
-#627 := [hypothesis]: #136
-#47 := (f3 f10 f11)
-#127 := (= f1 #47)
-#322 := (or #127 #123)
-#137 := (iff #127 #136)
-#48 := (= #47 f1)
-#46 := (= #45 f1)
-#49 := (iff #46 #48)
-#50 := (not #49)
-#140 := (iff #50 #137)
-#130 := (iff #123 #127)
-#133 := (not #130)
-#138 := (iff #133 #137)
-#139 := [rewrite]: #138
-#134 := (iff #50 #133)
-#131 := (iff #49 #130)
-#128 := (iff #48 #127)
-#129 := [rewrite]: #128
-#125 := (iff #46 #123)
-#126 := [rewrite]: #125
-#132 := [monotonicity #126 #129]: #131
-#135 := [monotonicity #132]: #134
-#141 := [trans #135 #139]: #140
-#122 := [asserted]: #50
-#144 := [mp #122 #141]: #137
-#234 := (not #137)
-#321 := (or #127 #123 #234)
-#235 := [def-axiom]: #321
-#236 := [unit-resolution #235 #144]: #322
-#288 := [unit-resolution #236 #627]: #127
-#323 := (not #127)
-#290 := (or #123 #323)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#21 := (f7 f8 #20)
-#23 := (f6 #21 #22)
-#18 := (:var 2 S2)
-#24 := (f3 #18 #23)
-#666 := (pattern #24)
-#28 := (f3 #18 #22)
-#96 := (= f1 #28)
-#26 := (f3 #18 #20)
-#93 := (= f1 #26)
-#99 := (or #93 #96)
-#89 := (= f1 #24)
-#102 := (iff #89 #99)
-#667 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #666) #102)
-#105 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #102)
-#670 := (iff #105 #667)
-#668 := (iff #102 #102)
-#669 := [refl]: #668
-#671 := [quant-intro #669]: #670
-#148 := (~ #105 #105)
-#162 := (~ #102 #102)
-#163 := [refl]: #162
-#149 := [nnf-pos #163]: #148
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#30 := (or #27 #29)
-#25 := (= #24 f1)
-#31 := (iff #25 #30)
-#32 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #31)
-#106 := (iff #32 #105)
-#103 := (iff #31 #102)
-#100 := (iff #30 #99)
-#97 := (iff #29 #96)
-#98 := [rewrite]: #97
-#94 := (iff #27 #93)
-#95 := [rewrite]: #94
-#101 := [monotonicity #95 #98]: #100
-#91 := (iff #25 #89)
-#92 := [rewrite]: #91
-#104 := [monotonicity #92 #101]: #103
-#107 := [quant-intro #104]: #106
-#88 := [asserted]: #32
-#110 := [mp #88 #107]: #105
-#164 := [mp~ #110 #149]: #105
-#672 := [mp #164 #671]: #667
-#301 := (not #667)
-#433 := (or #301 #130)
-#327 := (or #127 #127)
-#324 := (iff #123 #327)
-#640 := (or #301 #324)
-#313 := (iff #640 #433)
-#648 := (iff #433 #433)
-#649 := [rewrite]: #648
-#644 := (iff #324 #130)
-#328 := (iff #327 #127)
-#307 := [rewrite]: #328
-#646 := [monotonicity #307]: #644
-#647 := [monotonicity #646]: #313
-#650 := [trans #647 #649]: #313
-#312 := [quant-inst #41 #42 #42]: #640
-#645 := [mp #312 #650]: #433
-#289 := [unit-resolution #645 #672]: #130
-#651 := (or #133 #123 #323)
-#641 := [def-axiom]: #651
-#291 := [unit-resolution #641 #289]: #290
-#629 := [unit-resolution #291 #288 #627]: false
-#630 := [lemma #629]: #123
-#326 := (or #323 #136)
-#314 := (or #323 #136 #234)
-#325 := [def-axiom]: #314
-#254 := [unit-resolution #325 #144]: #326
-#631 := [unit-resolution #254 #630]: #323
-#632 := (or #136 #127)
-#299 := (or #133 #136 #127)
-#304 := [def-axiom]: #299
-#633 := [unit-resolution #304 #289]: #632
-[unit-resolution #633 #631 #630]: false
-unsat
-a9b4d2c6d5d71402741164958baf8befeec2192a 266 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f12 :: S3
-#44 := f12
-decl f10 :: S2
-#41 := f10
-#623 := (f3 f10 f12)
-decl f1 :: S1
-#4 := f1
-#336 := (= f1 #623)
-decl f13 :: S3
-#46 := f13
-#334 := (f3 f10 f13)
-#331 := (= f1 #334)
-#621 := (or #331 #336)
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f8 :: S5
-#19 := f8
-#45 := (f7 f8 f12)
-#47 := (f6 #45 f13)
-#308 := (f3 f10 #47)
-#440 := (= f1 #308)
-#615 := (iff #440 #621)
-#581 := (not #615)
-#593 := (not #621)
-#605 := (not #336)
-decl f11 :: S3
-#42 := f11
-#636 := (f3 f10 f11)
-#637 := (= f1 #636)
-#483 := (or #336 #637)
-#608 := (not #483)
-#43 := (f7 f8 f11)
-#51 := (f6 #43 f12)
-#335 := (f3 f10 #51)
-#314 := (= f1 #335)
-#591 := (iff #314 #483)
-#583 := (not #591)
-#576 := [hypothesis]: #583
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#21 := (f7 f8 #20)
-#23 := (f6 #21 #22)
-#18 := (:var 2 S2)
-#24 := (f3 #18 #23)
-#673 := (pattern #24)
-#28 := (f3 #18 #22)
-#103 := (= f1 #28)
-#26 := (f3 #18 #20)
-#100 := (= f1 #26)
-#106 := (or #100 #103)
-#96 := (= f1 #24)
-#109 := (iff #96 #106)
-#674 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #673) #109)
-#112 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #109)
-#677 := (iff #112 #674)
-#675 := (iff #109 #109)
-#676 := [refl]: #675
-#678 := [quant-intro #676]: #677
-#155 := (~ #112 #112)
-#169 := (~ #109 #109)
-#170 := [refl]: #169
-#156 := [nnf-pos #170]: #155
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#30 := (or #27 #29)
-#25 := (= #24 f1)
-#31 := (iff #25 #30)
-#32 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #31)
-#113 := (iff #32 #112)
-#110 := (iff #31 #109)
-#107 := (iff #30 #106)
-#104 := (iff #29 #103)
-#105 := [rewrite]: #104
-#101 := (iff #27 #100)
-#102 := [rewrite]: #101
-#108 := [monotonicity #102 #105]: #107
-#98 := (iff #25 #96)
-#99 := [rewrite]: #98
-#111 := [monotonicity #99 #108]: #110
-#114 := [quant-intro #111]: #113
-#95 := [asserted]: #32
-#117 := [mp #95 #114]: #112
-#171 := [mp~ #117 #156]: #112
-#679 := [mp #171 #678]: #674
-#647 := (not #674)
-#589 := (or #647 #591)
-#600 := (or #637 #336)
-#482 := (iff #314 #600)
-#592 := (or #647 #482)
-#492 := (iff #592 #589)
-#495 := (iff #589 #589)
-#488 := [rewrite]: #495
-#493 := (iff #482 #591)
-#484 := (iff #600 #483)
-#443 := [rewrite]: #484
-#588 := [monotonicity #443]: #493
-#494 := [monotonicity #588]: #492
-#496 := [trans #494 #488]: #492
-#477 := [quant-inst #41 #42 #44]: #592
-#497 := [mp #477 #496]: #589
-#577 := [unit-resolution #497 #679 #576]: false
-#578 := [lemma #577]: #591
-#654 := (not #314)
-#651 := (or #314 #331)
-#648 := (not #651)
-#52 := (f7 f8 #51)
-#53 := (f6 #52 f13)
-#54 := (f3 f10 #53)
-#134 := (= f1 #54)
-#330 := (not #134)
-#48 := (f6 #43 #47)
-#49 := (f3 f10 #48)
-#130 := (= f1 #49)
-#143 := (not #130)
-#579 := [hypothesis]: #143
-#329 := (or #134 #130)
-#144 := (iff #134 #143)
-#55 := (= #54 f1)
-#50 := (= #49 f1)
-#56 := (iff #50 #55)
-#57 := (not #56)
-#147 := (iff #57 #144)
-#137 := (iff #130 #134)
-#140 := (not #137)
-#145 := (iff #140 #144)
-#146 := [rewrite]: #145
-#141 := (iff #57 #140)
-#138 := (iff #56 #137)
-#135 := (iff #55 #134)
-#136 := [rewrite]: #135
-#132 := (iff #50 #130)
-#133 := [rewrite]: #132
-#139 := [monotonicity #133 #136]: #138
-#142 := [monotonicity #139]: #141
-#148 := [trans #142 #146]: #147
-#129 := [asserted]: #57
-#151 := [mp #129 #148]: #144
-#241 := (not #144)
-#328 := (or #134 #130 #241)
-#242 := [def-axiom]: #328
-#243 := [unit-resolution #242 #151]: #329
-#573 := [unit-resolution #243 #579]: #134
-#564 := (or #330 #651)
-#653 := (iff #134 #651)
-#319 := (or #647 #653)
-#320 := [quant-inst #41 #51 #46]: #319
-#580 := [unit-resolution #320 #679]: #653
-#649 := (not #653)
-#291 := (or #649 #330 #651)
-#634 := [def-axiom]: #291
-#565 := [unit-resolution #634 #580]: #564
-#567 := [unit-resolution #565 #573]: #651
-#657 := (not #331)
-#597 := (or #647 #615)
-#620 := (or #336 #331)
-#624 := (iff #440 #620)
-#617 := (or #647 #624)
-#612 := (iff #617 #597)
-#619 := (iff #597 #597)
-#460 := [rewrite]: #619
-#616 := (iff #624 #615)
-#625 := (iff #620 #621)
-#614 := [rewrite]: #625
-#611 := [monotonicity #614]: #616
-#613 := [monotonicity #611]: #612
-#461 := [trans #613 #460]: #612
-#618 := [quant-inst #41 #44 #46]: #617
-#462 := [mp #618 #461]: #597
-#568 := [unit-resolution #462 #679]: #615
-#558 := (or #581 #593)
-#356 := (not #440)
-#640 := (or #440 #637)
-#629 := (not #640)
-#570 := (or #130 #629)
-#277 := (iff #130 #640)
-#282 := (or #647 #277)
-#638 := (or #637 #440)
-#639 := (iff #130 #638)
-#283 := (or #647 #639)
-#643 := (iff #283 #282)
-#632 := (iff #282 #282)
-#633 := [rewrite]: #632
-#642 := (iff #639 #277)
-#635 := (iff #638 #640)
-#641 := [rewrite]: #635
-#644 := [monotonicity #641]: #642
-#646 := [monotonicity #644]: #643
-#339 := [trans #646 #633]: #643
-#645 := [quant-inst #41 #42 #47]: #283
-#355 := [mp #645 #339]: #282
-#569 := [unit-resolution #355 #679]: #277
-#626 := (not #277)
-#630 := (or #626 #130 #629)
-#627 := [def-axiom]: #630
-#566 := [unit-resolution #627 #569]: #570
-#571 := [unit-resolution #566 #579]: #629
-#357 := (or #640 #356)
-#343 := [def-axiom]: #357
-#557 := [unit-resolution #343 #571]: #356
-#575 := (or #581 #440 #593)
-#572 := [def-axiom]: #575
-#560 := [unit-resolution #572 #557]: #558
-#561 := [unit-resolution #560 #568]: #593
-#604 := (or #621 #657)
-#498 := [def-axiom]: #604
-#562 := [unit-resolution #498 #561]: #657
-#306 := (or #648 #314 #331)
-#311 := [def-axiom]: #306
-#559 := [unit-resolution #311 #562 #567]: #314
-#358 := (not #637)
-#249 := (or #640 #358)
-#628 := [def-axiom]: #249
-#563 := [unit-resolution #628 #571]: #358
-#499 := (or #621 #605)
-#500 := [def-axiom]: #499
-#543 := [unit-resolution #500 #561]: #605
-#609 := (or #608 #336 #637)
-#603 := [def-axiom]: #609
-#544 := [unit-resolution #603 #543 #563]: #608
-#441 := (or #583 #654 #483)
-#442 := [def-axiom]: #441
-#546 := [unit-resolution #442 #544 #559 #578]: false
-#547 := [lemma #546]: #130
-#333 := (or #330 #143)
-#321 := (or #330 #143 #241)
-#332 := [def-axiom]: #321
-#261 := [unit-resolution #332 #151]: #333
-#548 := [unit-resolution #261 #547]: #330
-#549 := (or #134 #648)
-#307 := (or #649 #134 #648)
-#650 := [def-axiom]: #307
-#550 := [unit-resolution #650 #580]: #549
-#551 := [unit-resolution #550 #548]: #648
-#655 := (or #651 #654)
-#656 := [def-axiom]: #655
-#552 := [unit-resolution #656 #551]: #654
-#610 := (or #583 #314 #608)
-#439 := [def-axiom]: #610
-#553 := [unit-resolution #439 #552 #578]: #608
-#606 := (or #483 #605)
-#607 := [def-axiom]: #606
-#554 := [unit-resolution #607 #553]: #605
-#652 := (or #651 #657)
-#658 := [def-axiom]: #652
-#555 := [unit-resolution #658 #551]: #657
-#590 := (or #593 #331 #336)
-#594 := [def-axiom]: #590
-#545 := [unit-resolution #594 #555 #554]: #593
-#556 := (or #143 #640)
-#631 := (or #626 #143 #640)
-#340 := [def-axiom]: #631
-#534 := [unit-resolution #340 #569]: #556
-#535 := [unit-resolution #534 #547]: #640
-#601 := (or #483 #358)
-#602 := [def-axiom]: #601
-#537 := [unit-resolution #602 #553]: #358
-#351 := (or #629 #440 #637)
-#352 := [def-axiom]: #351
-#538 := [unit-resolution #352 #537 #535]: #440
-#574 := (or #581 #356 #621)
-#584 := [def-axiom]: #574
-#539 := [unit-resolution #584 #538 #545]: #581
-[unit-resolution #462 #679 #539]: false
-unsat
-c3c3648cfba9d6c85cac6f8d51a3b06b08975178 160 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f12 :: S3
-#44 := f12
-decl f10 :: S2
-#41 := f10
-#50 := (f3 f10 f12)
-decl f1 :: S1
-#4 := f1
-#134 := (= f1 #50)
-#188 := (not #134)
-decl f11 :: S3
-#42 := f11
-#48 := (f3 f10 f11)
-#131 := (= f1 #48)
-#187 := (not #131)
-#189 := (or #187 #188)
-#190 := (not #189)
-#331 := [hypothesis]: #190
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f9 :: S5
-#33 := f9
-#43 := (f7 f9 f11)
-#45 := (f6 #43 f12)
-#46 := (f3 f10 #45)
-#127 := (= f1 #46)
-#146 := (not #127)
-#337 := (or #146 #189)
-#201 := (iff #127 #189)
-#137 := (and #131 #134)
-#147 := (iff #137 #146)
-#204 := (iff #147 #201)
-#196 := (iff #189 #127)
-#202 := (iff #196 #201)
-#203 := [rewrite]: #202
-#199 := (iff #147 #196)
-#193 := (iff #190 #146)
-#197 := (iff #193 #196)
-#198 := [rewrite]: #197
-#194 := (iff #147 #193)
-#191 := (iff #137 #190)
-#192 := [rewrite]: #191
-#195 := [monotonicity #192]: #194
-#200 := [trans #195 #198]: #199
-#205 := [trans #200 #203]: #204
-#51 := (= #50 f1)
-#49 := (= #48 f1)
-#52 := (and #49 #51)
-#47 := (= #46 f1)
-#53 := (iff #47 #52)
-#54 := (not #53)
-#150 := (iff #54 #147)
-#140 := (iff #127 #137)
-#143 := (not #140)
-#148 := (iff #143 #147)
-#149 := [rewrite]: #148
-#144 := (iff #54 #143)
-#141 := (iff #53 #140)
-#138 := (iff #52 #137)
-#135 := (iff #51 #134)
-#136 := [rewrite]: #135
-#132 := (iff #49 #131)
-#133 := [rewrite]: #132
-#139 := [monotonicity #133 #136]: #138
-#129 := (iff #47 #127)
-#130 := [rewrite]: #129
-#142 := [monotonicity #130 #139]: #141
-#145 := [monotonicity #142]: #144
-#151 := [trans #145 #149]: #150
-#126 := [asserted]: #54
-#154 := [mp #126 #151]: #147
-#206 := [mp #154 #205]: #201
-#344 := (not #201)
-#354 := (or #146 #189 #344)
-#358 := [def-axiom]: #354
-#674 := [unit-resolution #358 #206]: #337
-#463 := [unit-resolution #674 #331]: #146
-#330 := (or #127 #189)
-#676 := (iff #127 #190)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#34 := (f7 f9 #20)
-#35 := (f6 #34 #22)
-#18 := (:var 2 S2)
-#36 := (f3 #18 #35)
-#703 := (pattern #36)
-#28 := (f3 #18 #22)
-#100 := (= f1 #28)
-#179 := (not #100)
-#26 := (f3 #18 #20)
-#97 := (= f1 #26)
-#178 := (not #97)
-#162 := (or #178 #179)
-#163 := (not #162)
-#113 := (= f1 #36)
-#180 := (iff #113 #163)
-#704 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #703) #180)
-#183 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #180)
-#707 := (iff #183 #704)
-#705 := (iff #180 #180)
-#706 := [refl]: #705
-#708 := [quant-intro #706]: #707
-#117 := (and #97 #100)
-#120 := (iff #113 #117)
-#123 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #120)
-#184 := (iff #123 #183)
-#181 := (iff #120 #180)
-#164 := (iff #117 #163)
-#165 := [rewrite]: #164
-#182 := [monotonicity #165]: #181
-#185 := [quant-intro #182]: #184
-#160 := (~ #123 #123)
-#175 := (~ #120 #120)
-#176 := [refl]: #175
-#161 := [nnf-pos #176]: #160
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#38 := (and #27 #29)
-#37 := (= #36 f1)
-#39 := (iff #37 #38)
-#40 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #39)
-#124 := (iff #40 #123)
-#121 := (iff #39 #120)
-#118 := (iff #38 #117)
-#101 := (iff #29 #100)
-#102 := [rewrite]: #101
-#98 := (iff #27 #97)
-#99 := [rewrite]: #98
-#119 := [monotonicity #99 #102]: #118
-#115 := (iff #37 #113)
-#116 := [rewrite]: #115
-#122 := [monotonicity #116 #119]: #121
-#125 := [quant-intro #122]: #124
-#112 := [asserted]: #40
-#128 := [mp #112 #125]: #123
-#177 := [mp~ #128 #161]: #123
-#186 := [mp #177 #185]: #183
-#709 := [mp #186 #708]: #704
-#670 := (not #704)
-#342 := (or #670 #676)
-#343 := [quant-inst #41 #42 #44]: #342
-#672 := [unit-resolution #343 #709]: #676
-#677 := (not #676)
-#678 := (or #677 #127 #189)
-#679 := [def-axiom]: #678
-#673 := [unit-resolution #679 #672]: #330
-#314 := [unit-resolution #673 #463 #331]: false
-#657 := [lemma #314]: #189
-#284 := (or #127 #190)
-#355 := (or #127 #190 #344)
-#356 := [def-axiom]: #355
-#357 := [unit-resolution #356 #206]: #284
-#318 := [unit-resolution #357 #657]: #127
-#319 := (or #146 #190)
-#680 := (or #677 #146 #190)
-#675 := [def-axiom]: #680
-#320 := [unit-resolution #675 #672]: #319
-[unit-resolution #320 #318 #657]: false
-unsat
-1adc4d295cebee376081ce9f5a9d0e96c2943423 149 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f4 :: S3
-#9 := f4
-decl f10 :: S2
-#41 := f10
-#227 := (f3 f10 f4)
-decl f1 :: S1
-#4 := f1
-#314 := (= f1 #227)
-#228 := (not #314)
-decl f11 :: S3
-#42 := f11
-#315 := (f3 f10 f11)
-#229 := (= f1 #315)
-#316 := (not #229)
-#307 := (or #316 #228)
-#318 := (not #307)
-decl f6 :: (-> S4 S3 S3)
-decl f7 :: (-> S5 S3 S4)
-decl f9 :: S5
-#33 := f9
-#43 := (f7 f9 f11)
-#44 := (f6 #43 f4)
-#45 := (f3 f10 #44)
-#121 := (= f1 #45)
-#319 := (iff #121 #318)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#34 := (f7 f9 #20)
-#35 := (f6 #34 #22)
-#18 := (:var 2 S2)
-#36 := (f3 #18 #35)
-#666 := (pattern #36)
-#28 := (f3 #18 #22)
-#94 := (= f1 #28)
-#162 := (not #94)
-#26 := (f3 #18 #20)
-#91 := (= f1 #26)
-#161 := (not #91)
-#145 := (or #161 #162)
-#146 := (not #145)
-#107 := (= f1 #36)
-#163 := (iff #107 #146)
-#667 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #666) #163)
-#166 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #163)
-#670 := (iff #166 #667)
-#668 := (iff #163 #163)
-#669 := [refl]: #668
-#671 := [quant-intro #669]: #670
-#111 := (and #91 #94)
-#114 := (iff #107 #111)
-#117 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #114)
-#167 := (iff #117 #166)
-#164 := (iff #114 #163)
-#147 := (iff #111 #146)
-#148 := [rewrite]: #147
-#165 := [monotonicity #148]: #164
-#168 := [quant-intro #165]: #167
-#143 := (~ #117 #117)
-#158 := (~ #114 #114)
-#159 := [refl]: #158
-#144 := [nnf-pos #159]: #143
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#38 := (and #27 #29)
-#37 := (= #36 f1)
-#39 := (iff #37 #38)
-#40 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #39)
-#118 := (iff #40 #117)
-#115 := (iff #39 #114)
-#112 := (iff #38 #111)
-#95 := (iff #29 #94)
-#96 := [rewrite]: #95
-#92 := (iff #27 #91)
-#93 := [rewrite]: #92
-#113 := [monotonicity #93 #96]: #112
-#109 := (iff #37 #107)
-#110 := [rewrite]: #109
-#116 := [monotonicity #110 #113]: #115
-#119 := [quant-intro #116]: #118
-#106 := [asserted]: #40
-#122 := [mp #106 #119]: #117
-#160 := [mp~ #122 #144]: #117
-#169 := [mp #160 #168]: #166
-#672 := [mp #169 #671]: #667
-#317 := (not #667)
-#321 := (or #317 #319)
-#300 := [quant-inst #41 #42 #9]: #321
-#247 := [unit-resolution #300 #672]: #319
-#306 := (not #319)
-#320 := (or #306 #318)
-#46 := (= #45 f1)
-#47 := (not #46)
-#48 := (not #47)
-#133 := (iff #48 #121)
-#125 := (not #121)
-#128 := (not #125)
-#131 := (iff #128 #121)
-#132 := [rewrite]: #131
-#129 := (iff #48 #128)
-#126 := (iff #47 #125)
-#123 := (iff #46 #121)
-#124 := [rewrite]: #123
-#127 := [monotonicity #124]: #126
-#130 := [monotonicity #127]: #129
-#134 := [trans #130 #132]: #133
-#120 := [asserted]: #48
-#137 := [mp #120 #134]: #121
-#642 := (or #306 #125 #318)
-#643 := [def-axiom]: #642
-#636 := [unit-resolution #643 #137]: #320
-#277 := [unit-resolution #636 #247]: #318
-#294 := (or #307 #314)
-#426 := [def-axiom]: #294
-#620 := [unit-resolution #426 #277]: #314
-#8 := (:var 0 S2)
-#10 := (f3 #8 f4)
-#645 := (pattern #10)
-#69 := (= f1 #10)
-#72 := (not #69)
-#646 := (forall (vars (?v0 S2)) (:pat #645) #72)
-#75 := (forall (vars (?v0 S2)) #72)
-#649 := (iff #75 #646)
-#647 := (iff #72 #72)
-#648 := [refl]: #647
-#650 := [quant-intro #648]: #649
-#151 := (~ #75 #75)
-#149 := (~ #72 #72)
-#150 := [refl]: #149
-#152 := [nnf-pos #150]: #151
-#11 := (= #10 f1)
-#12 := (not #11)
-#13 := (forall (vars (?v0 S2)) #12)
-#76 := (iff #13 #75)
-#73 := (iff #12 #72)
-#70 := (iff #11 #69)
-#71 := [rewrite]: #70
-#74 := [monotonicity #71]: #73
-#77 := [quant-intro #74]: #76
-#68 := [asserted]: #13
-#80 := [mp #68 #77]: #75
-#136 := [mp~ #80 #152]: #75
-#651 := [mp #136 #650]: #646
-#297 := (not #646)
-#635 := (or #297 #228)
-#293 := [quant-inst #41]: #635
-[unit-resolution #293 #651 #620]: false
-unsat
-27fbc35929f013c0b43884a593f3f377821cad64 173 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f11 :: S3
-#42 := f11
-decl f10 :: S2
-#41 := f10
-#47 := (f3 f10 f11)
-decl f1 :: S1
-#4 := f1
-#127 := (= f1 #47)
-#323 := (not #127)
-decl f6 :: (-> S4 S3 S3)
-decl f5 :: S3
-#14 := f5
-decl f7 :: (-> S5 S3 S4)
-decl f9 :: S5
-#33 := f9
-#43 := (f7 f9 f11)
-#44 := (f6 #43 f5)
-#45 := (f3 f10 #44)
-#123 := (= f1 #45)
-#327 := (f3 f10 f5)
-#324 := (= f1 #327)
-#328 := (not #324)
-#301 := [hypothesis]: #328
-#8 := (:var 0 S2)
-#15 := (f3 #8 f5)
-#659 := (pattern #15)
-#81 := (= f1 #15)
-#660 := (forall (vars (?v0 S2)) (:pat #659) #81)
-#85 := (forall (vars (?v0 S2)) #81)
-#663 := (iff #85 #660)
-#661 := (iff #81 #81)
-#662 := [refl]: #661
-#664 := [quant-intro #662]: #663
-#146 := (~ #85 #85)
-#145 := (~ #81 #81)
-#160 := [refl]: #145
-#147 := [nnf-pos #160]: #146
-#16 := (= #15 f1)
-#17 := (forall (vars (?v0 S2)) #16)
-#86 := (iff #17 #85)
-#83 := (iff #16 #81)
-#84 := [rewrite]: #83
-#87 := [quant-intro #84]: #86
-#80 := [asserted]: #17
-#90 := [mp #80 #87]: #85
-#161 := [mp~ #90 #147]: #85
-#665 := [mp #161 #664]: #660
-#289 := (not #660)
-#290 := (or #289 #324)
-#291 := [quant-inst #41]: #290
-#433 := [unit-resolution #291 #665 #301]: false
-#629 := [lemma #433]: #324
-#136 := (not #123)
-#630 := [hypothesis]: #136
-#322 := (or #127 #123)
-#137 := (iff #127 #136)
-#48 := (= #47 f1)
-#46 := (= #45 f1)
-#49 := (iff #46 #48)
-#50 := (not #49)
-#140 := (iff #50 #137)
-#130 := (iff #123 #127)
-#133 := (not #130)
-#138 := (iff #133 #137)
-#139 := [rewrite]: #138
-#134 := (iff #50 #133)
-#131 := (iff #49 #130)
-#128 := (iff #48 #127)
-#129 := [rewrite]: #128
-#125 := (iff #46 #123)
-#126 := [rewrite]: #125
-#132 := [monotonicity #126 #129]: #131
-#135 := [monotonicity #132]: #134
-#141 := [trans #135 #139]: #140
-#122 := [asserted]: #50
-#144 := [mp #122 #141]: #137
-#234 := (not #137)
-#321 := (or #127 #123 #234)
-#235 := [def-axiom]: #321
-#236 := [unit-resolution #235 #144]: #322
-#631 := [unit-resolution #236 #630]: #127
-#307 := (or #323 #328)
-#633 := (or #123 #307)
-#644 := (not #307)
-#646 := (iff #123 #644)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#34 := (f7 f9 #20)
-#35 := (f6 #34 #22)
-#18 := (:var 2 S2)
-#36 := (f3 #18 #35)
-#673 := (pattern #36)
-#28 := (f3 #18 #22)
-#96 := (= f1 #28)
-#169 := (not #96)
-#26 := (f3 #18 #20)
-#93 := (= f1 #26)
-#168 := (not #93)
-#152 := (or #168 #169)
-#153 := (not #152)
-#109 := (= f1 #36)
-#170 := (iff #109 #153)
-#674 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #673) #170)
-#173 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #170)
-#677 := (iff #173 #674)
-#675 := (iff #170 #170)
-#676 := [refl]: #675
-#678 := [quant-intro #676]: #677
-#113 := (and #93 #96)
-#116 := (iff #109 #113)
-#119 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #116)
-#174 := (iff #119 #173)
-#171 := (iff #116 #170)
-#154 := (iff #113 #153)
-#155 := [rewrite]: #154
-#172 := [monotonicity #155]: #171
-#175 := [quant-intro #172]: #174
-#150 := (~ #119 #119)
-#165 := (~ #116 #116)
-#166 := [refl]: #165
-#151 := [nnf-pos #166]: #150
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#38 := (and #27 #29)
-#37 := (= #36 f1)
-#39 := (iff #37 #38)
-#40 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #39)
-#120 := (iff #40 #119)
-#117 := (iff #39 #116)
-#114 := (iff #38 #113)
-#97 := (iff #29 #96)
-#98 := [rewrite]: #97
-#94 := (iff #27 #93)
-#95 := [rewrite]: #94
-#115 := [monotonicity #95 #98]: #114
-#111 := (iff #37 #109)
-#112 := [rewrite]: #111
-#118 := [monotonicity #112 #115]: #117
-#121 := [quant-intro #118]: #120
-#108 := [asserted]: #40
-#124 := [mp #108 #121]: #119
-#167 := [mp~ #124 #151]: #119
-#176 := [mp #167 #175]: #173
-#679 := [mp #176 #678]: #674
-#640 := (not #674)
-#312 := (or #640 #646)
-#313 := [quant-inst #41 #42 #14]: #312
-#632 := [unit-resolution #313 #679]: #646
-#641 := (not #646)
-#299 := (or #641 #123 #307)
-#304 := [def-axiom]: #299
-#628 := [unit-resolution #304 #632]: #633
-#634 := [unit-resolution #628 #630]: #307
-#645 := (or #644 #323 #328)
-#651 := [def-axiom]: #645
-#270 := [unit-resolution #651 #634 #631 #629]: false
-#635 := [lemma #270]: #123
-#326 := (or #323 #136)
-#314 := (or #323 #136 #234)
-#325 := [def-axiom]: #314
-#254 := [unit-resolution #325 #144]: #326
-#637 := [unit-resolution #254 #635]: #323
-#275 := (or #136 #644)
-#642 := (or #641 #136 #644)
-#300 := [def-axiom]: #642
-#276 := [unit-resolution #300 #632]: #275
-#638 := [unit-resolution #276 #635]: #644
-#647 := (or #307 #127)
-#648 := [def-axiom]: #647
-[unit-resolution #648 #638 #637]: false
-unsat
-fa1e213c15b8e9288bf16d2dc4bd96e3c7fb5c7e 173 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f11 :: S3
-#42 := f11
-decl f7 :: (-> S5 S3 S4)
-decl f12 :: S3
-#44 := f12
-decl f9 :: S5
-#33 := f9
-#48 := (f7 f9 f12)
-#49 := (f6 #48 f11)
-decl f10 :: S2
-#41 := f10
-#50 := (f3 f10 #49)
-decl f1 :: S1
-#4 := f1
-#130 := (= f1 #50)
-#326 := (not #130)
-#43 := (f7 f9 f11)
-#45 := (f6 #43 f12)
-#46 := (f3 f10 #45)
-#126 := (= f1 #46)
-#139 := (not #126)
-#628 := [hypothesis]: #139
-#325 := (or #130 #126)
-#140 := (iff #130 #139)
-#51 := (= #50 f1)
-#47 := (= #46 f1)
-#52 := (iff #47 #51)
-#53 := (not #52)
-#143 := (iff #53 #140)
-#133 := (iff #126 #130)
-#136 := (not #133)
-#141 := (iff #136 #140)
-#142 := [rewrite]: #141
-#137 := (iff #53 #136)
-#134 := (iff #52 #133)
-#131 := (iff #51 #130)
-#132 := [rewrite]: #131
-#128 := (iff #47 #126)
-#129 := [rewrite]: #128
-#135 := [monotonicity #129 #132]: #134
-#138 := [monotonicity #135]: #137
-#144 := [trans #138 #142]: #143
-#125 := [asserted]: #53
-#147 := [mp #125 #144]: #140
-#237 := (not #140)
-#324 := (or #130 #126 #237)
-#238 := [def-axiom]: #324
-#239 := [unit-resolution #238 #147]: #325
-#629 := [unit-resolution #239 #628]: #130
-#310 := (f3 f10 f12)
-#647 := (= f1 #310)
-#649 := (not #647)
-#330 := (f3 f10 f11)
-#327 := (= f1 #330)
-#331 := (not #327)
-#315 := (or #331 #649)
-#626 := (or #126 #315)
-#651 := (not #315)
-#642 := (iff #126 #651)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#34 := (f7 f9 #20)
-#35 := (f6 #34 #22)
-#18 := (:var 2 S2)
-#36 := (f3 #18 #35)
-#676 := (pattern #36)
-#28 := (f3 #18 #22)
-#99 := (= f1 #28)
-#172 := (not #99)
-#26 := (f3 #18 #20)
-#96 := (= f1 #26)
-#171 := (not #96)
-#155 := (or #171 #172)
-#156 := (not #155)
-#112 := (= f1 #36)
-#173 := (iff #112 #156)
-#677 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #676) #173)
-#176 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #173)
-#680 := (iff #176 #677)
-#678 := (iff #173 #173)
-#679 := [refl]: #678
-#681 := [quant-intro #679]: #680
-#116 := (and #96 #99)
-#119 := (iff #112 #116)
-#122 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #119)
-#177 := (iff #122 #176)
-#174 := (iff #119 #173)
-#157 := (iff #116 #156)
-#158 := [rewrite]: #157
-#175 := [monotonicity #158]: #174
-#178 := [quant-intro #175]: #177
-#153 := (~ #122 #122)
-#168 := (~ #119 #119)
-#169 := [refl]: #168
-#154 := [nnf-pos #169]: #153
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#38 := (and #27 #29)
-#37 := (= #36 f1)
-#39 := (iff #37 #38)
-#40 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #39)
-#123 := (iff #40 #122)
-#120 := (iff #39 #119)
-#117 := (iff #38 #116)
-#100 := (iff #29 #99)
-#101 := [rewrite]: #100
-#97 := (iff #27 #96)
-#98 := [rewrite]: #97
-#118 := [monotonicity #98 #101]: #117
-#114 := (iff #37 #112)
-#115 := [rewrite]: #114
-#121 := [monotonicity #115 #118]: #120
-#124 := [quant-intro #121]: #123
-#111 := [asserted]: #40
-#127 := [mp #111 #124]: #122
-#170 := [mp~ #127 #154]: #122
-#179 := [mp #170 #178]: #176
-#682 := [mp #179 #681]: #677
-#302 := (not #677)
-#335 := (or #302 #642)
-#351 := [quant-inst #41 #42 #44]: #335
-#622 := [unit-resolution #351 #682]: #642
-#352 := (not #642)
-#353 := (or #352 #126 #315)
-#339 := [def-axiom]: #353
-#623 := [unit-resolution #339 #622]: #626
-#627 := [unit-resolution #623 #628]: #315
-#337 := (or #326 #651)
-#648 := (iff #130 #651)
-#307 := (or #302 #648)
-#304 := (or #649 #331)
-#436 := (not #304)
-#643 := (iff #130 #436)
-#645 := (or #302 #643)
-#646 := (iff #645 #307)
-#630 := (iff #307 #307)
-#291 := [rewrite]: #630
-#654 := (iff #643 #648)
-#652 := (iff #436 #651)
-#316 := (iff #304 #315)
-#650 := [rewrite]: #316
-#653 := [monotonicity #650]: #652
-#644 := [monotonicity #653]: #654
-#287 := [monotonicity #644]: #646
-#292 := [trans #287 #291]: #646
-#303 := [quant-inst #41 #44 #42]: #645
-#293 := [mp #303 #292]: #307
-#336 := [unit-resolution #293 #682]: #648
-#631 := (not #648)
-#638 := (or #631 #326 #651)
-#640 := [def-axiom]: #638
-#338 := [unit-resolution #640 #336]: #337
-#340 := [unit-resolution #338 #627 #629]: false
-#618 := [lemma #340]: #126
-#329 := (or #326 #139)
-#317 := (or #326 #139 #237)
-#328 := [def-axiom]: #317
-#257 := [unit-resolution #328 #147]: #329
-#619 := [unit-resolution #257 #618]: #326
-#332 := (or #139 #651)
-#354 := (or #352 #139 #651)
-#245 := [def-axiom]: #354
-#616 := [unit-resolution #245 #622]: #332
-#620 := [unit-resolution #616 #618]: #651
-#617 := (or #130 #315)
-#637 := (or #631 #130 #315)
-#273 := [def-axiom]: #637
-#621 := [unit-resolution #273 #336]: #617
-[unit-resolution #621 #620 #619]: false
-unsat
-8424513290e59440c92fec106021e2354c2f6a1c 149 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f11 :: S3
-#42 := f11
-decl f7 :: (-> S5 S3 S4)
-decl f9 :: S5
-#33 := f9
-#43 := (f7 f9 f11)
-#44 := (f6 #43 f11)
-decl f10 :: S2
-#41 := f10
-#45 := (f3 f10 #44)
-decl f1 :: S1
-#4 := f1
-#123 := (= f1 #45)
-#136 := (not #123)
-#632 := [hypothesis]: #136
-#47 := (f3 f10 f11)
-#127 := (= f1 #47)
-#322 := (or #127 #123)
-#137 := (iff #127 #136)
-#48 := (= #47 f1)
-#46 := (= #45 f1)
-#49 := (iff #46 #48)
-#50 := (not #49)
-#140 := (iff #50 #137)
-#130 := (iff #123 #127)
-#133 := (not #130)
-#138 := (iff #133 #137)
-#139 := [rewrite]: #138
-#134 := (iff #50 #133)
-#131 := (iff #49 #130)
-#128 := (iff #48 #127)
-#129 := [rewrite]: #128
-#125 := (iff #46 #123)
-#126 := [rewrite]: #125
-#132 := [monotonicity #126 #129]: #131
-#135 := [monotonicity #132]: #134
-#141 := [trans #135 #139]: #140
-#122 := [asserted]: #50
-#144 := [mp #122 #141]: #137
-#234 := (not #137)
-#321 := (or #127 #123 #234)
-#235 := [def-axiom]: #321
-#236 := [unit-resolution #235 #144]: #322
-#633 := [unit-resolution #236 #632]: #127
-#323 := (not #127)
-#634 := (or #123 #323)
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#34 := (f7 f9 #20)
-#35 := (f6 #34 #22)
-#18 := (:var 2 S2)
-#36 := (f3 #18 #35)
-#673 := (pattern #36)
-#28 := (f3 #18 #22)
-#96 := (= f1 #28)
-#169 := (not #96)
-#26 := (f3 #18 #20)
-#93 := (= f1 #26)
-#168 := (not #93)
-#152 := (or #168 #169)
-#153 := (not #152)
-#109 := (= f1 #36)
-#170 := (iff #109 #153)
-#674 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #673) #170)
-#173 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #170)
-#677 := (iff #173 #674)
-#675 := (iff #170 #170)
-#676 := [refl]: #675
-#678 := [quant-intro #676]: #677
-#113 := (and #93 #96)
-#116 := (iff #109 #113)
-#119 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #116)
-#174 := (iff #119 #173)
-#171 := (iff #116 #170)
-#154 := (iff #113 #153)
-#155 := [rewrite]: #154
-#172 := [monotonicity #155]: #171
-#175 := [quant-intro #172]: #174
-#150 := (~ #119 #119)
-#165 := (~ #116 #116)
-#166 := [refl]: #165
-#151 := [nnf-pos #166]: #150
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#38 := (and #27 #29)
-#37 := (= #36 f1)
-#39 := (iff #37 #38)
-#40 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #39)
-#120 := (iff #40 #119)
-#117 := (iff #39 #116)
-#114 := (iff #38 #113)
-#97 := (iff #29 #96)
-#98 := [rewrite]: #97
-#94 := (iff #27 #93)
-#95 := [rewrite]: #94
-#115 := [monotonicity #95 #98]: #114
-#111 := (iff #37 #109)
-#112 := [rewrite]: #111
-#118 := [monotonicity #112 #115]: #117
-#121 := [quant-intro #118]: #120
-#108 := [asserted]: #40
-#124 := [mp #108 #121]: #119
-#167 := [mp~ #124 #151]: #119
-#176 := [mp #167 #175]: #173
-#679 := [mp #176 #678]: #674
-#650 := (not #674)
-#645 := (or #650 #130)
-#327 := (or #323 #323)
-#324 := (not #327)
-#328 := (iff #123 #324)
-#651 := (or #650 #328)
-#299 := (iff #651 #645)
-#642 := (iff #645 #645)
-#300 := [rewrite]: #642
-#648 := (iff #328 #130)
-#313 := (iff #324 #127)
-#646 := (not #323)
-#640 := (iff #646 #127)
-#312 := [rewrite]: #640
-#301 := (iff #324 #646)
-#307 := (iff #327 #323)
-#644 := [rewrite]: #307
-#433 := [monotonicity #644]: #301
-#647 := [trans #433 #312]: #313
-#649 := [monotonicity #647]: #648
-#304 := [monotonicity #649]: #299
-#643 := [trans #304 #300]: #299
-#641 := [quant-inst #41 #42 #42]: #651
-#284 := [mp #641 #643]: #645
-#628 := [unit-resolution #284 #679]: #130
-#627 := (or #133 #123 #323)
-#288 := [def-axiom]: #627
-#270 := [unit-resolution #288 #628]: #634
-#635 := [unit-resolution #270 #633 #632]: false
-#637 := [lemma #635]: #123
-#326 := (or #323 #136)
-#314 := (or #323 #136 #234)
-#325 := [def-axiom]: #314
-#254 := [unit-resolution #325 #144]: #326
-#275 := [unit-resolution #254 #637]: #323
-#276 := (or #136 #127)
-#289 := (or #133 #136 #127)
-#290 := [def-axiom]: #289
-#638 := [unit-resolution #290 #628]: #276
-[unit-resolution #638 #275 #637]: false
-unsat
-5973328496eea1e33493c38f9af9d86965f67ad9 287 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f6 :: (-> S4 S3 S3)
-decl f12 :: S3
-#44 := f12
-decl f7 :: (-> S5 S3 S4)
-decl f11 :: S3
-#42 := f11
-decl f9 :: S5
-#33 := f9
-#43 := (f7 f9 f11)
-#51 := (f6 #43 f12)
-decl f10 :: S2
-#41 := f10
-#314 := (f3 f10 #51)
-decl f1 :: S1
-#4 := f1
-#651 := (= f1 #314)
-#249 := (f3 f10 f12)
-#628 := (= f1 #249)
-#625 := (not #628)
-#339 := (f3 f10 f11)
-#355 := (= f1 #339)
-#356 := (not #355)
-#614 := (or #356 #625)
-#615 := (not #614)
-#611 := (iff #615 #651)
-#582 := (not #611)
-decl f13 :: S3
-#46 := f13
-#334 := (f3 f10 f13)
-#331 := (= f1 #334)
-#335 := (not #331)
-#484 := (or #335 #625)
-#493 := (not #484)
-#45 := (f7 f9 f12)
-#47 := (f6 #45 f13)
-#646 := (f3 f10 #47)
-#632 := (= f1 #646)
-#494 := (iff #493 #632)
-#587 := (not #494)
-#567 := [hypothesis]: #587
-#22 := (:var 0 S3)
-#20 := (:var 1 S3)
-#34 := (f7 f9 #20)
-#35 := (f6 #34 #22)
-#18 := (:var 2 S2)
-#36 := (f3 #18 #35)
-#680 := (pattern #36)
-#28 := (f3 #18 #22)
-#103 := (= f1 #28)
-#176 := (not #103)
-#26 := (f3 #18 #20)
-#100 := (= f1 #26)
-#175 := (not #100)
-#159 := (or #175 #176)
-#160 := (not #159)
-#116 := (= f1 #36)
-#177 := (iff #116 #160)
-#681 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) (:pat #680) #177)
-#180 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #177)
-#684 := (iff #180 #681)
-#682 := (iff #177 #177)
-#683 := [refl]: #682
-#685 := [quant-intro #683]: #684
-#120 := (and #100 #103)
-#123 := (iff #116 #120)
-#126 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #123)
-#181 := (iff #126 #180)
-#178 := (iff #123 #177)
-#161 := (iff #120 #160)
-#162 := [rewrite]: #161
-#179 := [monotonicity #162]: #178
-#182 := [quant-intro #179]: #181
-#157 := (~ #126 #126)
-#172 := (~ #123 #123)
-#173 := [refl]: #172
-#158 := [nnf-pos #173]: #157
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#38 := (and #27 #29)
-#37 := (= #36 f1)
-#39 := (iff #37 #38)
-#40 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #39)
-#127 := (iff #40 #126)
-#124 := (iff #39 #123)
-#121 := (iff #38 #120)
-#104 := (iff #29 #103)
-#105 := [rewrite]: #104
-#101 := (iff #27 #100)
-#102 := [rewrite]: #101
-#122 := [monotonicity #102 #105]: #121
-#118 := (iff #37 #116)
-#119 := [rewrite]: #118
-#125 := [monotonicity #119 #122]: #124
-#128 := [quant-intro #125]: #127
-#115 := [asserted]: #40
-#131 := [mp #115 #128]: #126
-#174 := [mp~ #131 #158]: #126
-#183 := [mp #174 #182]: #180
-#686 := [mp #183 #685]: #681
-#306 := (not #681)
-#498 := (or #306 #494)
-#600 := (or #625 #335)
-#482 := (not #600)
-#483 := (iff #632 #482)
-#499 := (or #306 #483)
-#593 := (iff #499 #498)
-#594 := (iff #498 #498)
-#581 := [rewrite]: #594
-#496 := (iff #483 #494)
-#592 := (iff #632 #493)
-#495 := (iff #592 #494)
-#488 := [rewrite]: #495
-#477 := (iff #483 #592)
-#588 := (iff #482 #493)
-#443 := (iff #600 #484)
-#591 := [rewrite]: #443
-#589 := [monotonicity #591]: #588
-#492 := [monotonicity #589]: #477
-#497 := [trans #492 #488]: #496
-#590 := [monotonicity #497]: #593
-#583 := [trans #590 #581]: #593
-#500 := [quant-inst #41 #44 #46]: #499
-#575 := [mp #500 #583]: #498
-#568 := [unit-resolution #575 #686 #567]: false
-#569 := [lemma #568]: #494
-#633 := (not #632)
-#357 := (or #356 #633)
-#343 := (not #357)
-#48 := (f6 #43 #47)
-#49 := (f3 f10 #48)
-#130 := (= f1 #49)
-#143 := (not #130)
-#570 := [hypothesis]: #143
-#571 := (or #130 #357)
-#358 := (iff #130 #343)
-#629 := (or #306 #358)
-#351 := [quant-inst #41 #42 #47]: #629
-#566 := [unit-resolution #351 #686]: #358
-#341 := (not #358)
-#342 := (or #341 #130 #357)
-#344 := [def-axiom]: #342
-#557 := [unit-resolution #344 #566]: #571
-#558 := [unit-resolution #557 #570]: #357
-#597 := (or #306 #611)
-#616 := (iff #651 #615)
-#613 := (or #306 #616)
-#618 := (iff #613 #597)
-#461 := (iff #597 #597)
-#462 := [rewrite]: #461
-#612 := (iff #616 #611)
-#617 := [rewrite]: #612
-#460 := [monotonicity #617]: #618
-#604 := [trans #460 #462]: #618
-#619 := [quant-inst #41 #42 #44]: #613
-#605 := [mp #619 #604]: #597
-#560 := [unit-resolution #605 #686]: #611
-#546 := (or #582 #615)
-#653 := (not #651)
-#319 := (or #335 #653)
-#655 := (not #319)
-#52 := (f7 f9 #51)
-#53 := (f6 #52 f13)
-#54 := (f3 f10 #53)
-#134 := (= f1 #54)
-#329 := (or #134 #130)
-#144 := (iff #134 #143)
-#55 := (= #54 f1)
-#50 := (= #49 f1)
-#56 := (iff #50 #55)
-#57 := (not #56)
-#147 := (iff #57 #144)
-#137 := (iff #130 #134)
-#140 := (not #137)
-#145 := (iff #140 #144)
-#146 := [rewrite]: #145
-#141 := (iff #57 #140)
-#138 := (iff #56 #137)
-#135 := (iff #55 #134)
-#136 := [rewrite]: #135
-#132 := (iff #50 #130)
-#133 := [rewrite]: #132
-#139 := [monotonicity #133 #136]: #138
-#142 := [monotonicity #139]: #141
-#148 := [trans #142 #146]: #147
-#129 := [asserted]: #57
-#151 := [mp #129 #148]: #144
-#241 := (not #144)
-#328 := (or #134 #130 #241)
-#242 := [def-axiom]: #328
-#243 := [unit-resolution #242 #151]: #329
-#561 := [unit-resolution #243 #570]: #134
-#330 := (not #134)
-#559 := (or #330 #655)
-#652 := (iff #134 #655)
-#311 := (or #306 #652)
-#308 := (or #653 #335)
-#440 := (not #308)
-#647 := (iff #134 #440)
-#649 := (or #306 #647)
-#650 := (iff #649 #311)
-#634 := (iff #311 #311)
-#295 := [rewrite]: #634
-#658 := (iff #647 #652)
-#656 := (iff #440 #655)
-#320 := (iff #308 #319)
-#654 := [rewrite]: #320
-#657 := [monotonicity #654]: #656
-#648 := [monotonicity #657]: #658
-#291 := [monotonicity #648]: #650
-#296 := [trans #291 #295]: #650
-#307 := [quant-inst #41 #51 #46]: #649
-#297 := [mp #307 #296]: #311
-#562 := [unit-resolution #297 #686]: #652
-#635 := (not #652)
-#642 := (or #635 #330 #655)
-#644 := [def-axiom]: #642
-#563 := [unit-resolution #644 #562]: #559
-#543 := [unit-resolution #563 #561]: #655
-#637 := (or #319 #651)
-#638 := [def-axiom]: #637
-#544 := [unit-resolution #638 #543]: #651
-#576 := (or #582 #615 #653)
-#577 := [def-axiom]: #576
-#547 := [unit-resolution #577 #544]: #546
-#548 := [unit-resolution #547 #560]: #615
-#606 := (or #614 #355)
-#572 := [def-axiom]: #606
-#549 := [unit-resolution #572 #548]: #355
-#631 := (or #343 #356 #633)
-#340 := [def-axiom]: #631
-#550 := [unit-resolution #340 #549 #558]: #633
-#298 := (or #319 #331)
-#636 := [def-axiom]: #298
-#551 := [unit-resolution #636 #543]: #331
-#574 := (or #614 #628)
-#584 := [def-axiom]: #574
-#552 := [unit-resolution #584 #548]: #628
-#609 := (or #493 #335 #625)
-#603 := [def-axiom]: #609
-#553 := [unit-resolution #603 #552 #551]: #493
-#441 := (or #587 #484 #632)
-#442 := [def-axiom]: #441
-#554 := [unit-resolution #442 #553 #550 #569]: false
-#555 := [lemma #554]: #130
-#545 := (or #143 #343)
-#622 := (or #341 #143 #343)
-#623 := [def-axiom]: #622
-#556 := [unit-resolution #623 #566]: #545
-#534 := [unit-resolution #556 #555]: #343
-#630 := (or #357 #632)
-#627 := [def-axiom]: #630
-#535 := [unit-resolution #627 #534]: #632
-#610 := (or #587 #493 #633)
-#439 := [def-axiom]: #610
-#537 := [unit-resolution #439 #535 #569]: #493
-#602 := (or #484 #628)
-#608 := [def-axiom]: #602
-#538 := [unit-resolution #608 #537]: #628
-#352 := (or #357 #355)
-#626 := [def-axiom]: #352
-#539 := [unit-resolution #626 #534]: #355
-#585 := (or #615 #356 #625)
-#586 := [def-axiom]: #585
-#540 := [unit-resolution #586 #539 #538]: #615
-#333 := (or #330 #143)
-#321 := (or #330 #143 #241)
-#332 := [def-axiom]: #321
-#261 := [unit-resolution #332 #151]: #333
-#541 := [unit-resolution #261 #555]: #330
-#536 := (or #134 #319)
-#641 := (or #635 #134 #319)
-#277 := [def-axiom]: #641
-#542 := [unit-resolution #277 #562]: #536
-#528 := [unit-resolution #542 #541]: #319
-#607 := (or #484 #331)
-#601 := [def-axiom]: #607
-#524 := [unit-resolution #601 #537]: #331
-#639 := (or #655 #335 #653)
-#640 := [def-axiom]: #639
-#525 := [unit-resolution #640 #524 #528]: #653
-#578 := (or #582 #614 #651)
-#579 := [def-axiom]: #578
-#526 := [unit-resolution #579 #525 #540]: #582
-[unit-resolution #605 #686 #526]: false
-unsat
-6c759b8f06a9510b6e4f2c41f45fd7a908ea138f 22 0
-#2 := false
-decl f13 :: (-> S7 S3 S4)
-decl f4 :: S3
-#8 := f4
-decl f14 :: S7
-#50 := f14
-#51 := (f13 f14 f4)
-#52 := (= #51 #51)
-#53 := (not #52)
-#148 := (iff #53 false)
-#1 := true
-#143 := (not true)
-#146 := (iff #143 false)
-#147 := [rewrite]: #146
-#144 := (iff #53 #143)
-#140 := (iff #52 true)
-#142 := [rewrite]: #140
-#145 := [monotonicity #142]: #144
-#149 := [trans #145 #147]: #148
-#139 := [asserted]: #53
-[mp #139 #149]: false
-unsat
-f09576464eb9a729afbe3fe966b57e4354456502 30 0
-#2 := false
-decl f4 :: (-> S3 S4)
-decl f6 :: S3
-#16 := f6
-#17 := (f4 f6)
-decl f3 :: (-> S2 S4)
-decl f5 :: S2
-#14 := f5
-#15 := (f3 f5)
-#18 := (= #15 #17)
-#19 := (not #18)
-#41 := [asserted]: #19
-#9 := (:var 0 S3)
-#10 := (f4 #9)
-#7 := (:var 1 S2)
-#8 := (f3 #7)
-#11 := (pattern #8 #10)
-#12 := (= #8 #10)
-#13 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #11) #12)
-#51 := (~ #13 #13)
-#49 := (~ #12 #12)
-#50 := [refl]: #49
-#52 := [nnf-pos #50]: #51
-#40 := [asserted]: #13
-#43 := [mp~ #40 #52]: #13
-#111 := (not #13)
-#197 := (or #111 #18)
-#112 := [quant-inst #14 #16]: #197
-[unit-resolution #112 #43 #41]: false
-unsat
-5a4509215da405eb20d4081e74524f90aaca407d 1 0
-unsat
-ec561a73aaf24cad28c298d64ff90ab9419e03b9 1 0
-unsat
-99895ba337908a50454cc51cd8d58f8c9973a5d8 1 0
-unsat
-f66af12ea27f7d59df586df568e3d48733d0c2ad 1 0
-unsat
-98a1d35ce489ce400102751e60b482d34ba4c100 1 0
-unsat
-997d0c877f7a6af3978a25e9a11fe86be44aa3d7 1 0
-unsat
-dec47d92e2bc6704596ff538272e4aa7dad033f8 1 0
-unsat
-79ff64606be9eaf1430551196cf6a56b904cd2f0 1 0
-unsat
-9ddb2d0aa5571f810dbdcf99f2a9c0dd91892822 1 0
-unsat
-383af2a9be136c8b9da304961ed7781d6d8b67da 1 0
-unsat
-8a45fca8152b4b73650f0bdadc7b4837d03b0e4f 1 0
-unsat
-028cbfc14838b1039241d56404b98b994249bd70 1 0
-unsat
-0c3c93869b86cd3cceaa64f6505c6b53e5a0d5f5 1 0
-unsat
-da5a18ce51a6fcaf95a5da1f3cf6ec44d50d2911 1 0
-unsat
-b326e9b62ea312d34250c299905421b42e169a3d 1 0
-unsat
-2df9f9573f4c3d690e8e9d39a01fbee0d0dabfca 1 0
-unsat
-64fe45c879d2ce11b605b7ccbadec44b7474cdb3 1 0
-unsat
-27388d866d376a195719342119d2c39bddbbda5e 1 0
-unsat
-4fdb33415d645476800f24bc2645077ed20fbcc7 1 0
-unsat
-34954aeef00ac521d8d6983ea46bbdde741af613 1 0
-unsat
-c975ecb6377964929f32ae1b30fbd693a2969c6a 1 0
-unsat
-5c9a9ffe9941b81f90170c912034e8b681bc281f 1 0
-unsat
-26a6ebeac1bb75693d61408e7c0984072dfbd2df 1 0
-unsat
-2f894a623075d62f46fa0487301d3cff02b03b4d 123 0
-#2 := false
-decl f4 :: S2
-#8 := f4
-decl f3 :: S2
-#7 := f3
-#9 := (= f3 f4)
-decl inj!0 :: (-> S3 S2)
-decl f6 :: (-> S2 S3)
-#28 := (f6 f4)
-#179 := (inj!0 #28)
-#265 := (= #179 f4)
-#18 := (:var 0 S2)
-#19 := (f6 #18)
-#112 := (pattern #19)
-#111 := (inj!0 #19)
-#108 := (= #111 #18)
-#594 := (forall (vars (k!0 S2)) (:pat #112) #108)
-#113 := (forall (vars (k!0 S2)) (:pat #112) #108)
-#595 := (iff #113 #594)
-#597 := (iff #594 #594)
-#598 := [rewrite]: #597
-#596 := [rewrite]: #595
-#599 := [trans #596 #598]: #595
-#16 := (:var 1 S2)
-#21 := (= #18 #16)
-#17 := (f6 #16)
-#20 := (= #17 #19)
-#54 := (not #20)
-#55 := (or #54 #21)
-#58 := (forall (vars (?v0 S2) (?v1 S2)) #55)
-#114 := (iff #58 #113)
-#115 := [rewrite]: #114
-#118 := (~ #58 #58)
-#116 := (~ #55 #55)
-#117 := [refl]: #116
-#119 := [nnf-pos #117]: #118
-decl f5 :: S2
-#11 := f5
-#14 := (= f4 f5)
-#15 := (not #14)
-#12 := (= f3 f5)
-#13 := (not #12)
-#10 := (not #9)
-#82 := (and #10 #13 #15 #58)
-#27 := (f6 f3)
-#29 := (= #27 #28)
-#30 := (not #29)
-#85 := (not #82)
-#88 := (or #85 #30)
-#91 := (not #88)
-#22 := (implies #20 #21)
-#23 := (forall (vars (?v0 S2) (?v1 S2)) #22)
-#24 := (and #15 #23)
-#25 := (and #13 #24)
-#26 := (and #10 #25)
-#31 := (implies #26 #30)
-#32 := (not #31)
-#94 := (iff #32 #91)
-#61 := (and #15 #58)
-#64 := (and #13 #61)
-#67 := (and #10 #64)
-#73 := (not #67)
-#74 := (or #73 #30)
-#79 := (not #74)
-#92 := (iff #79 #91)
-#89 := (iff #74 #88)
-#86 := (iff #73 #85)
-#83 := (iff #67 #82)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#90 := [monotonicity #87]: #89
-#93 := [monotonicity #90]: #92
-#80 := (iff #32 #79)
-#77 := (iff #31 #74)
-#70 := (implies #67 #30)
-#75 := (iff #70 #74)
-#76 := [rewrite]: #75
-#71 := (iff #31 #70)
-#68 := (iff #26 #67)
-#65 := (iff #25 #64)
-#62 := (iff #24 #61)
-#59 := (iff #23 #58)
-#56 := (iff #22 #55)
-#57 := [rewrite]: #56
-#60 := [quant-intro #57]: #59
-#63 := [monotonicity #60]: #62
-#66 := [monotonicity #63]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#78 := [trans #72 #76]: #77
-#81 := [monotonicity #78]: #80
-#95 := [trans #81 #93]: #94
-#53 := [asserted]: #32
-#96 := [mp #53 #95]: #91
-#97 := [not-or-elim #96]: #82
-#101 := [and-elim #97]: #58
-#110 := [mp~ #101 #119]: #58
-#109 := [mp #110 #115]: #113
-#600 := [mp #109 #599]: #594
-#180 := (not #594)
-#270 := (or #180 #265)
-#267 := [quant-inst #8]: #270
-#250 := [unit-resolution #267 #600]: #265
-#590 := (= f3 #179)
-#178 := (inj!0 #27)
-#256 := (= #178 #179)
-#244 := (= #179 #178)
-#269 := (= #28 #27)
-#102 := [not-or-elim #96]: #29
-#271 := [symm #102]: #269
-#375 := [monotonicity #271]: #244
-#589 := [symm #375]: #256
-#582 := (= f3 #178)
-#264 := (= #178 f3)
-#266 := (or #180 #264)
-#257 := [quant-inst #7]: #266
-#268 := [unit-resolution #257 #600]: #264
-#255 := [symm #268]: #582
-#591 := [trans #255 #589]: #590
-#592 := [trans #591 #250]: #9
-#98 := [and-elim #97]: #10
-[unit-resolution #98 #592]: false
-unsat
-dbb5533c26f60f0a5c965d87e1dfccfd73b06e07 152 0
-#2 := false
-decl f3 :: (-> S2 S3 S4)
-decl f10 :: S3
-#34 := f10
-decl f11 :: S2
-#41 := f11
-#51 := (f3 f11 f10)
-decl f4 :: (-> S5 S4 S2)
-decl f12 :: S4
-#44 := f12
-decl f5 :: (-> S6 S3 S5)
-decl f8 :: S3
-#30 := f8
-decl f6 :: (-> S7 S2 S6)
-decl f7 :: S7
-#7 := f7
-#42 := (f6 f7 f11)
-#43 := (f5 #42 f8)
-#45 := (f4 #43 f12)
-#281 := (f3 #45 f10)
-#282 := (= #281 #51)
-#568 := (= #281 f12)
-#567 := (= f10 f8)
-#565 := (if #567 #568 #282)
-#23 := (:var 0 S3)
-#21 := (:var 1 S4)
-#19 := (:var 2 S3)
-#17 := (:var 3 S2)
-#18 := (f6 f7 #17)
-#20 := (f5 #18 #19)
-#22 := (f4 #20 #21)
-#24 := (f3 #22 #23)
-#611 := (pattern #24)
-#26 := (f3 #17 #23)
-#128 := (= #24 #26)
-#127 := (= #24 #21)
-#25 := (= #23 #19)
-#111 := (if #25 #127 #128)
-#612 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #611) #111)
-#120 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #111)
-#615 := (iff #120 #612)
-#613 := (iff #111 #111)
-#614 := [refl]: #613
-#616 := [quant-intro #614]: #615
-#27 := (if #25 #21 #26)
-#28 := (= #24 #27)
-#29 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #28)
-#117 := (iff #29 #120)
-#112 := (iff #28 #111)
-#119 := [rewrite]: #112
-#118 := [quant-intro #119]: #117
-#109 := (~ #29 #29)
-#108 := (~ #28 #28)
-#125 := [refl]: #108
-#110 := [nnf-pos #125]: #109
-#76 := [asserted]: #29
-#126 := [mp~ #76 #110]: #29
-#115 := [mp #126 #118]: #120
-#617 := [mp #115 #616]: #612
-#385 := (not #612)
-#570 := (or #385 #565)
-#559 := [quant-inst #41 #30 #44 #34]: #570
-#569 := [unit-resolution #559 #617]: #565
-#561 := (not #567)
-#35 := (= f8 f10)
-#36 := (not #35)
-#546 := (iff #36 #561)
-#551 := (iff #35 #567)
-#566 := (iff #567 #35)
-#550 := [commutativity]: #566
-#552 := [symm #550]: #551
-#547 := [monotonicity #552]: #546
-decl f9 :: S3
-#31 := f9
-#37 := (= f9 f10)
-#38 := (not #37)
-#32 := (= f8 f9)
-#33 := (not #32)
-#85 := (and #33 #36 #38)
-decl f13 :: S4
-#48 := f13
-#46 := (f6 f7 #45)
-#47 := (f5 #46 f9)
-#49 := (f4 #47 f13)
-#50 := (f3 #49 f10)
-#52 := (= #50 #51)
-#88 := (not #85)
-#91 := (or #88 #52)
-#94 := (not #91)
-#39 := (and #36 #38)
-#40 := (and #33 #39)
-#53 := (implies #40 #52)
-#54 := (not #53)
-#97 := (iff #54 #94)
-#78 := (not #40)
-#79 := (or #78 #52)
-#82 := (not #79)
-#95 := (iff #82 #94)
-#92 := (iff #79 #91)
-#89 := (iff #78 #88)
-#86 := (iff #40 #85)
-#87 := [rewrite]: #86
-#90 := [monotonicity #87]: #89
-#93 := [monotonicity #90]: #92
-#96 := [monotonicity #93]: #95
-#83 := (iff #54 #82)
-#80 := (iff #53 #79)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#98 := [trans #84 #96]: #97
-#77 := [asserted]: #54
-#99 := [mp #77 #98]: #94
-#100 := [not-or-elim #99]: #85
-#102 := [and-elim #100]: #36
-#553 := [mp #102 #547]: #561
-#406 := (not #282)
-#104 := (not #52)
-#388 := (iff #104 #406)
-#428 := (iff #52 #282)
-#545 := (iff #282 #52)
-#544 := (= #281 #50)
-#260 := (= #50 #281)
-#279 := (= #50 f13)
-#278 := (= f10 f9)
-#596 := (if #278 #279 #260)
-#592 := (or #385 #596)
-#265 := [quant-inst #45 #31 #48 #34]: #592
-#554 := [unit-resolution #265 #617]: #596
-#599 := (not #278)
-#387 := (iff #38 #599)
-#384 := (iff #37 #278)
-#548 := (iff #278 #37)
-#555 := [commutativity]: #548
-#386 := [symm #555]: #384
-#540 := [monotonicity #386]: #387
-#103 := [and-elim #100]: #38
-#541 := [mp #103 #540]: #599
-#266 := (not #596)
-#602 := (or #266 #278 #260)
-#597 := [def-axiom]: #602
-#543 := [unit-resolution #597 #541 #554]: #260
-#542 := [symm #543]: #544
-#427 := [monotonicity #542]: #545
-#429 := [symm #427]: #428
-#536 := [monotonicity #429]: #388
-#105 := [not-or-elim #99]: #104
-#438 := [mp #105 #536]: #406
-#560 := (not #565)
-#562 := (or #560 #567 #282)
-#563 := [def-axiom]: #562
-[unit-resolution #563 #438 #553 #569]: false
-unsat
+#49 := f14
+#50 := (f13 f14 f4)
+#51 := (= #50 #50)
+#52 := (not #51)
+#86 := (iff #52 false)
+#1 := true
+#81 := (not true)
+#84 := (iff #81 false)
+#85 := [rewrite]: #84
+#82 := (iff #52 #81)
+#79 := (iff #51 true)
+#80 := [rewrite]: #79
+#83 := [monotonicity #80]: #82
+#87 := [trans #83 #85]: #86
+#78 := [asserted]: #52
+[mp #78 #87]: false
+unsat

--- a/src/HOL/SMT_Examples/SMT_Tests.thy	Wed Oct 31 11:23:21 2012 +0100
+++ b/src/HOL/SMT_Examples/SMT_Tests.thy	Thu Nov 01 11:34:00 2012 +0100
@@ -126,15 +126,14 @@
   "\<not>((\<exists>x. \<not>P x) \<and> ((\<exists>x. P x) \<or> (\<exists>x. P x \<and> Q x)) \<and> \<not>(\<exists>x. P x))"
   by smt+
 
-lemma  (* only without proofs: *)
+lemma
   "\<exists>x y. x = y"
   "\<exists>x. P x \<longrightarrow> (\<exists>y. P x \<and> P y)"
   "(\<exists>x. P x) \<or> R \<longleftrightarrow> (\<exists>x. P x \<or> R)"
   "\<exists>x. P x \<longrightarrow> P a \<and> P b"
-  "\<exists>x. (\<exists>y. P y) \<longrightarrow> P x" 
+  "\<exists>x. (\<exists>y. P y) \<longrightarrow> P x"
   "(\<exists>x. Q \<longrightarrow> P x) \<longleftrightarrow> (Q \<longrightarrow> (\<exists>x. P x))"
-  using [[smt_oracle=true, z3_options="AUTO_CONFIG=false SATURATE=true"]]
-  by smt+
+by smt+
 
 lemma
   "(\<not>(\<exists>x. P x)) \<longleftrightarrow> (\<forall>x. \<not> P x)"
@@ -144,7 +143,7 @@
   "(\<forall>x y. R x y = x) \<and> (\<forall>x. \<exists>y. R x y) = (\<forall>x. R x c) \<longrightarrow> (\<exists>y. R x y) = R x c"
   by smt+
 
-lemma  (* only without proofs: *)
+lemma
   "\<forall>x. \<exists>y. f x y = f x (g x)"
   "(\<not>\<not>(\<exists>x. P x)) \<longleftrightarrow> (\<not>(\<forall>x. \<not> P x))"
   "\<forall>u. \<exists>v. \<forall>w. \<exists>x. f u v w x = f u (g u) w (h u w)"
@@ -153,7 +152,6 @@
   "(\<exists>x. \<forall>y. P x \<longleftrightarrow> P y) \<longrightarrow> ((\<exists>x. P x) \<longleftrightarrow> (\<forall>y. P y))"
   "\<exists>z. P z \<longrightarrow> (\<forall>x. P x)"
   "(\<exists>y. \<forall>x. R x y) \<longrightarrow> (\<forall>x. \<exists>y. R x y)"
-  using [[smt_oracle=true]]
   by smt+
 
 lemma
@@ -563,7 +561,7 @@
   "x < 0 \<longrightarrow> -x > 0"
   by smt+
 
-lemma 
+lemma
   "(x::real) - 0 = x"
   "0 - x = -x"
   "x < y \<longrightarrow> x - y < 0"

--- a/src/HOL/SMT_Examples/SMT_Word_Examples.certs	Wed Oct 31 11:23:21 2012 +0100
+++ b/src/HOL/SMT_Examples/SMT_Word_Examples.certs	Thu Nov 01 11:34:00 2012 +0100
@@ -1,56 +1,56 @@
-1dea21d7f83bf3c8744889b87efdd51ec9b13522 1 0
+76e44ee5933c173533f6c97186112ffd01a35ae7 1 0
 unsat
-e4079c456b2eef2ac4a460a64f6113e3f4e0c166 1 0
+ab57bdb94d69bdaba64439f9bb267d64807e1b5e 1 0
 unsat
-4528ee18a87d7e792c3e551fc6891303a56cdeaa 1 0
[phone]b7622bd35b4dfc98f7cffcbc6c68d8f 1 0
 unsat
-3cf263d3d9abc6c9f43b2caeff18d80706c67c3f 1 0
+788a14cdbdb52ecdc7af1170ffad340615282c1d 1 0
 unsat
-82b1dcef093ff559df687ea978391118da7ebc2f 1 0
+975e232ce6b6ffe7dec903c82ba2e55be9be4b55 1 0
 unsat
-c1fab913bcaeaa11e2a73c6525b382ee9afa489d 1 0
+6b59badfb0234682536bb0ad166188999b0c6ddc 1 0
 unsat
-a093424324d5a32372ddb295c1512be60f121da4 1 0
+3382bcdf1086a48fcafa193342eaa14b3d909da5 1 0
 unsat
-f23e2d7a4ec6d24d260c37b661aec80bc88aa232 1 0
+b70039502c53afd0aa36eb84a1b69ddb2aa2d889 1 0
 unsat
-d47155609b280ddaa63574797e5ef4ac587325e4 1 0
+1708d764034dbf13b2c2700d611d5ffa101211d9 1 0
 unsat
-44e79df6588d993672eca866baec13c5f54343e7 1 0
+c477e950ae95e3b24973c8c733ec2bea8b9b2d38 1 0
 unsat
-cee1aca69943693cc464a3a3718ce011a9251c2e 1 0
+1093c5f8705b619e8a7be9b8025eeb457136ec3e 1 0
 unsat
-d994fef5ffc2e32ad58ff2c458322e61b69933f3 1 0
+dd3396716b2da248d8c9added0ceea02fef4ba84 1 0
 unsat
-3dd14db324dcd5277297ef4a7c6d0e288cd627ca 1 0
+bdcc1e71a24633edb63d0dd3ba120c65e846f3ce 1 0
 unsat
-3cdb3c6fc67b95c3af80c236175e971746e9d49f 1 0
+e2eacbb801fda7d852db0c81474cb853fd1c712b 1 0
 unsat
-fb681fce74f688cee5fec2e557d7d2f77a772f64 1 0
+f0d4a4b3c8c63de26b273932bfe1395e8b793560 1 0
 unsat
-dcac8a123cd5019a4174294cf01f82aa809aa855 1 0
+88c2d9cc032fd024a08d4ba295900da6bce5f5d4 1 0
 unsat
-12722d9dd871f78b7cf1d8c71c8b3895df97231b 1 0
+1bcdaf67c99875bf6db184c44d694d9acd5f4fe6 1 0
 unsat
-dd2ea04983b1210e07bd977332f5928c281333a8 1 0
+c00707370876ed215f3713cd85573c4763ec2a26 1 0
 unsat
-64c9fe73f7ca3832f4daec3b66d94e4f6c730fa5 1 0
+1cb480a8b9f94702afaeb571497b186daedb1ef8 1 0
 unsat
-72d447be1e4c7ba9ad39300590a185b5ff3d7a54 1 0
+9e8b9e428288ae30c668e8f03352d15d8e286432 1 0
 unsat
-f9acba6675baa1463a0fbd893377a528d3bb0de9 1 0
+196c4a9a6b5640282f300e93c54ff8eb71316ff5 1 0
 unsat
-9b6b36788fe27138833728937e7dba8ad83d5703 1 0
[phone]b49208eb8677e518d5be0f42b61b38 1 0
 unsat
-9e722a42cab872ac3674f51a989dbbdd036d2789 1 0
+55f83dbb53da0f4b9428053cd94f44601bcaa774 1 0
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