# HG changeset patch
# User blanchet
# Date 1351766040 -3600
# Node ID 3b7ad6153322efc9090c588f9bf4040d421b9572
# Parent  ceceb403eb4ecf29eafb8b10ebd25903fbc74ebb
regenerated "SMT_Examples" certificates after soft-timeout change + removed a few needless oracles

diff -r ceceb403eb4e -r 3b7ad6153322 src/HOL/SMT_Examples/SMT_Examples.certs
--- 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
diff -r ceceb403eb4e -r 3b7ad6153322 src/HOL/SMT_Examples/SMT_Tests.certs
--- 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)
+4867997399e05a82038d4f69182ea74d5c78a71f 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)