# HG changeset patch
# User boehmes
# Date 1288086379 -7200
# Node ID a462d5207aa6ead74bd6e128d6e18e168d60d56b
# Parent  7f58a9a843c2bf638e2104f60f553dc5e830d30a
changed SMT configuration options; updated SMT certificates

diff -r 7f58a9a843c2 -r a462d5207aa6 src/HOL/Boogie/Examples/Boogie_Dijkstra.certs
--- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Tue Oct 26 11:45:12 2010 +0200
+++ b/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Tue Oct 26 11:46:19 2010 +0200
@@ -1,4 +1,4 @@
-585d6a826013e58a18631a689e131cc7e15b8538 6889 0
+a959f1dced399224414912ad7379705a61749faa 6889 0
 #2 := false
 decl f11 :: (-> S5 S2 S1)
 decl ?v1!7 :: (-> S2 S2)
diff -r 7f58a9a843c2 -r a462d5207aa6 src/HOL/Boogie/Examples/Boogie_Dijkstra.thy
--- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.thy	Tue Oct 26 11:45:12 2010 +0200
+++ b/src/HOL/Boogie/Examples/Boogie_Dijkstra.thy	Tue Oct 26 11:46:19 2010 +0200
@@ -83,9 +83,9 @@
 
 declare [[smt_certificates="~~/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs"]]
 declare [[smt_fixed=true]]
+declare [[smt_oracle=false]]
 
 boogie_vc Dijkstra
-  using [[z3_proofs=true]]
   by boogie
 
 boogie_end 
diff -r 7f58a9a843c2 -r a462d5207aa6 src/HOL/Boogie/Examples/Boogie_Max.certs
--- a/src/HOL/Boogie/Examples/Boogie_Max.certs	Tue Oct 26 11:45:12 2010 +0200
+++ b/src/HOL/Boogie/Examples/Boogie_Max.certs	Tue Oct 26 11:46:19 2010 +0200
@@ -1,4 +1,4 @@
-3e8da1e086888bc525192984192051f1e39c6752 2224 0
+16ee32e23503be38842c16c90807e66120a960ee 2224 0
 #2 := false
 #8 := 0::int
 decl f5 :: (-> int int)
diff -r 7f58a9a843c2 -r a462d5207aa6 src/HOL/Boogie/Examples/Boogie_Max.thy
--- a/src/HOL/Boogie/Examples/Boogie_Max.thy	Tue Oct 26 11:45:12 2010 +0200
+++ b/src/HOL/Boogie/Examples/Boogie_Max.thy	Tue Oct 26 11:46:19 2010 +0200
@@ -40,9 +40,9 @@
 
 declare [[smt_certificates="~~/src/HOL/Boogie/Examples/Boogie_Max.certs"]]
 declare [[smt_fixed=true]]
+declare [[smt_oracle=false]]
 
 boogie_vc max
-  using [[z3_proofs=true]]
   by boogie
 
 boogie_end
diff -r 7f58a9a843c2 -r a462d5207aa6 src/HOL/Boogie/Examples/VCC_Max.certs
--- a/src/HOL/Boogie/Examples/VCC_Max.certs	Tue Oct 26 11:45:12 2010 +0200
+++ b/src/HOL/Boogie/Examples/VCC_Max.certs	Tue Oct 26 11:46:19 2010 +0200
@@ -1,4 +1,4 @@
-a2095afb5c01aff7b980eece0ecc2b89ecf5e46c 7862 0
+5815fb85125ba62bb3b4a150604c8978e5a08a22 7862 0
 #2 := false
 decl f111 :: (-> S4 S5 int)
 decl f67 :: (-> S5 int S3 S5)
diff -r 7f58a9a843c2 -r a462d5207aa6 src/HOL/Boogie/Examples/VCC_Max.thy
--- a/src/HOL/Boogie/Examples/VCC_Max.thy	Tue Oct 26 11:45:12 2010 +0200
+++ b/src/HOL/Boogie/Examples/VCC_Max.thy	Tue Oct 26 11:46:19 2010 +0200
@@ -48,11 +48,11 @@
 
 declare [[smt_certificates="~~/src/HOL/Boogie/Examples/VCC_Max.certs"]]
 declare [[smt_fixed=true]]
+declare [[smt_oracle=false]]
 
 boogie_status
 
 boogie_vc maximum
-  using [[z3_proofs=true]]
   by boogie
 
 boogie_end
diff -r 7f58a9a843c2 -r a462d5207aa6 src/HOL/Multivariate_Analysis/Integration.certs
--- a/src/HOL/Multivariate_Analysis/Integration.certs	Tue Oct 26 11:45:12 2010 +0200
+++ b/src/HOL/Multivariate_Analysis/Integration.certs	Tue Oct 26 11:46:19 2010 +0200
@@ -1,1976 +1,243 @@
-2e3a7f41999e849037c0bc39fd6c0ffa4f5b7eb6 910 0
+19e9a49723add29f06290682aca290aa2ab968ea 238 0
 #2 := false
-#369 := 0::real
-decl f8 :: (-> S5 S2 real)
-decl f11 :: (-> S4 S2)
-decl f7 :: S4
-#13 := f7
-#20 := (f11 f7)
-decl f21 :: (-> S3 S5)
+#48 := 0::real
+decl f19 :: (-> S3 S10 real)
+decl f20 :: S10
+#43 := f20
 decl f4 :: S3
 #8 := f4
-#101 := (f21 f4)
-#1205 := (f8 #101 #20)
-#367 := -1::real
-#1507 := (* -1::real #1205)
-decl f19 :: S3
-#60 := f19
-#88 := (f21 f19)
-#1037 := (f8 #88 #20)
-#1698 := (+ #1037 #1507)
-#1765 := (>= #1698 0::real)
-#1697 := (= #1037 #1205)
-decl f10 :: S5
-#19 := f10
-#21 := (f8 f10 #20)
-#1208 := (= #21 #1205)
-decl f12 :: S5
-#22 := f12
-#1129 := (f8 f12 #20)
-#1207 := (= #1129 #1205)
-decl f6 :: (-> S2 S4)
-#84 := (f6 #20)
-#351 := (= f7 #84)
-#1211 := (ite #351 #1208 #1207)
-decl f9 :: S5
-#16 := f9
-#31 := (f8 f9 #20)
-#1206 := (= #31 #1205)
-#70 := 0::int
-decl f5 :: (-> S4 int)
-#1041 := (f5 #84)
-#155 := -1::int
-#1051 := (* -1::int #1041)
-#14 := (f5 f7)
-#1097 := (+ #14 #1051)
-#1098 := (<= #1097 0::int)
-#1214 := (ite #1098 #1211 #1206)
-#9 := (:var 0 S2)
-#17 := (f8 f9 #9)
-#697 := (pattern #17)
-#23 := (f8 f12 #9)
-#696 := (pattern #23)
-#102 := (f8 #101 #9)
-#695 := (pattern #102)
-#11 := (f6 #9)
-#694 := (pattern #11)
-#580 := (= #17 #102)
-#578 := (= #23 #102)
-#577 := (= #21 #102)
-#18 := (= #11 f7)
-#579 := (ite #18 #577 #578)
-#158 := (* -1::int #14)
-#12 := (f5 #11)
-#159 := (+ #12 #158)
-#157 := (>= #159 0::int)
-#581 := (ite #157 #579 #580)
-#698 := (forall (vars (?v0 S2)) (:pat #694 #695 #696 #697) #581)
-#584 := (forall (vars (?v0 S2)) #581)
-#701 := (iff #584 #698)
-#699 := (iff #581 #581)
-#700 := [refl]: #699
-#702 := [quant-intro #700]: #701
-#24 := (ite #18 #21 #23)
-#165 := (ite #157 #24 #17)
-#486 := (= #102 #165)
-#487 := (forall (vars (?v0 S2)) #486)
-#585 := (iff #487 #584)
-#582 := (iff #486 #581)
-#583 := [rewrite]: #582
-#586 := [quant-intro #583]: #585
-#480 := (~ #487 #487)
-#482 := (~ #486 #486)
-#483 := [refl]: #482
-#481 := [nnf-pos #483]: #480
-decl f3 :: (-> S3 S2 real)
-#10 := (f3 f4 #9)
-#170 := (= #10 #165)
-#173 := (forall (vars (?v0 S2)) #170)
-#488 := (iff #173 #487)
-#130 := (:var 1 S3)
-#133 := (f3 #130 #9)
-#131 := (f21 #130)
-#132 := (f8 #131 #9)
-#134 := (= #132 #133)
-#135 := (forall (vars (?v0 S3) (?v1 S2)) #134)
-#441 := [asserted]: #135
-#489 := [rewrite* #441]: #488
-#15 := (< #12 #14)
-#25 := (ite #15 #17 #24)
-#26 := (= #10 #25)
-#27 := (forall (vars (?v0 S2)) #26)
-#174 := (iff #27 #173)
-#171 := (iff #26 #170)
-#168 := (= #25 #165)
-#156 := (not #157)
-#162 := (ite #156 #17 #24)
+#58 := (f19 f4 f20)
+#109 := -1::real
+#153 := (* -1::real #58)
+decl f5 :: (-> S4 S5 real)
+decl f8 :: S5
+#13 := f8
+decl f22 :: S4
+#54 := f22
+#55 := (f5 f22 f8)
+#154 := (+ #55 #153)
+#137 := (* -1::real #55)
+#144 := (+ #137 #58)
+#188 := (<= #154 0::real)
+#195 := (ite #188 #144 #154)
+#451 := (* -1::real #195)
+#452 := (+ #144 #451)
+#453 := (<= #452 0::real)
+#435 := (= #144 #195)
+decl f21 :: S4
+#45 := f21
+#46 := (f5 f21 f8)
+decl f9 :: S3
+#17 := f9
+#44 := (f19 f9 f20)
+#120 := (* -1::real #44)
+#121 := (+ #120 #46)
+#110 := (* -1::real #46)
+#111 := (+ #44 #110)
+#216 := (>= #111 0::real)
+#223 := (ite #216 #111 #121)
+#447 := (* -1::real #223)
+#450 := (+ #121 #447)
+#454 := (<= #450 0::real)
+#442 := (= #121 #223)
+#217 := (not #216)
+#455 := [hypothesis]: #216
+#184 := (+ #44 #153)
+#185 := (<= #184 0::real)
+#206 := -3::real
+#234 := (* -3::real #223)
+#235 := (+ #137 #234)
+#236 := (+ #46 #235)
+#237 := (<= #236 0::real)
+#238 := (not #237)
+#207 := (* -3::real #195)
+#208 := (+ #137 #207)
+#209 := (+ #46 #208)
+#210 := (<= #209 0::real)
+#211 := (not #210)
+#249 := (and #185 #211 #238)
+#65 := (<= #44 #58)
+#56 := (- #46 #55)
+#52 := 3::real
+#59 := (- #58 #55)
+#61 := (- #59)
+#60 := (< #59 0::real)
+#62 := (ite #60 #61 #59)
+#63 := (* #62 3::real)
+#64 := (< #63 #56)
+#66 := (and #64 #65)
+#47 := (- #44 #46)
+#50 := (- #47)
+#49 := (< #47 0::real)
+#51 := (ite #49 #50 #47)
+#53 := (* #51 3::real)
+#57 := (< #53 #56)
+#67 := (and #57 #66)
+#254 := (iff #67 #249)
+#138 := (+ #46 #137)
+#147 := (< #144 0::real)
+#159 := (ite #147 #154 #144)
+#165 := (* 3::real #159)
+#170 := (< #165 #138)
+#176 := (and #65 #170)
+#114 := (< #111 0::real)
+#126 := (ite #114 #121 #111)
+#132 := (* 3::real #126)
+#141 := (< #132 #138)
+#181 := (and #141 #176)
+#252 := (iff #181 #249)
+#243 := (and #185 #211)
+#246 := (and #238 #243)
+#250 := (iff #246 #249)
+#251 := [rewrite]: #250
+#247 := (iff #181 #246)
+#244 := (iff #176 #243)
+#214 := (iff #170 #211)
+#200 := (* 3::real #195)
+#203 := (< #200 #138)
+#212 := (iff #203 #211)
+#213 := [rewrite]: #212
+#204 := (iff #170 #203)
+#201 := (= #165 #200)
+#198 := (= #159 #195)
+#189 := (not #188)
+#192 := (ite #189 #154 #144)
+#196 := (= #192 #195)
+#197 := [rewrite]: #196
+#193 := (= #159 #192)
+#190 := (iff #147 #189)
+#191 := [rewrite]: #190
+#194 := [monotonicity #191]: #193
+#199 := [trans #194 #197]: #198
+#202 := [monotonicity #199]: #201
+#205 := [monotonicity #202]: #204
+#215 := [trans #205 #213]: #214
+#186 := (iff #65 #185)
+#187 := [rewrite]: #186
+#245 := [monotonicity #187 #215]: #244
+#241 := (iff #141 #238)
+#228 := (* 3::real #223)
+#231 := (< #228 #138)
+#239 := (iff #231 #238)
+#240 := [rewrite]: #239
+#232 := (iff #141 #231)
+#229 := (= #132 #228)
+#226 := (= #126 #223)
+#220 := (ite #217 #121 #111)
+#224 := (= #220 #223)
+#225 := [rewrite]: #224
+#221 := (= #126 #220)
+#218 := (iff #114 #217)
+#219 := [rewrite]: #218
+#222 := [monotonicity #219]: #221
+#227 := [trans #222 #225]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#242 := [trans #233 #240]: #241
+#248 := [monotonicity #242 #245]: #247
+#253 := [trans #248 #251]: #252
+#182 := (iff #67 #181)
+#179 := (iff #66 #176)
+#173 := (and #170 #65)
+#177 := (iff #173 #176)
+#178 := [rewrite]: #177
+#174 := (iff #66 #173)
+#171 := (iff #64 #170)
+#139 := (= #56 #138)
+#140 := [rewrite]: #139
+#168 := (= #63 #165)
+#162 := (* #159 3::real)
 #166 := (= #162 #165)
 #167 := [rewrite]: #166
-#163 := (= #25 #162)
-#160 := (iff #15 #156)
-#161 := [rewrite]: #160
+#163 := (= #63 #162)
+#160 := (= #62 #159)
+#145 := (= #59 #144)
+#146 := [rewrite]: #145
+#157 := (= #61 #154)
+#150 := (- #144)
+#155 := (= #150 #154)
+#156 := [rewrite]: #155
+#151 := (= #61 #150)
+#152 := [monotonicity #146]: #151
+#158 := [trans #152 #156]: #157
+#148 := (iff #60 #147)
+#149 := [monotonicity #146]: #148
+#161 := [monotonicity #149 #158 #146]: #160
 #164 := [monotonicity #161]: #163
 #169 := [trans #164 #167]: #168
-#172 := [monotonicity #169]: #171
-#175 := [quant-intro #172]: #174
-#152 := [asserted]: #27
-#176 := [mp #152 #175]: #173
-#490 := [mp #176 #489]: #487
-#478 := [mp~ #490 #481]: #487
-#587 := [mp #478 #586]: #584
-#703 := [mp #587 #702]: #698
-#962 := (not #698)
-#1217 := (or #962 #1214)
-#85 := (= #84 f7)
-#1209 := (ite #85 #1208 #1207)
-#1088 := (+ #1041 #158)
-#1089 := (>= #1088 0::int)
-#1210 := (ite #1089 #1209 #1206)
-#1218 := (or #962 #1210)
-#1220 := (iff #1218 #1217)
-#1222 := (iff #1217 #1217)
-#1223 := [rewrite]: #1222
-#1215 := (iff #1210 #1214)
-#1212 := (iff #1209 #1211)
-#353 := (iff #85 #351)
-#354 := [rewrite]: #353
-#1213 := [monotonicity #354]: #1212
-#1101 := (iff #1089 #1098)
-#1091 := (+ #158 #1041)
-#1094 := (>= #1091 0::int)
-#1099 := (iff #1094 #1098)
-#1100 := [rewrite]: #1099
-#1095 := (iff #1089 #1094)
-#1092 := (= #1088 #1091)
-#1093 := [rewrite]: #1092
-#1096 := [monotonicity #1093]: #1095
-#1102 := [trans #1096 #1100]: #1101
-#1216 := [monotonicity #1102 #1213]: #1215
-#1221 := [monotonicity #1216]: #1220
-#1224 := [trans #1221 #1223]: #1220
-#1219 := [quant-inst]: #1218
-#1225 := [mp #1219 #1224]: #1217
-#1767 := [unit-resolution #1225 #703]: #1214
-#1396 := (= #14 #1041)
-#1718 := (= #1041 #14)
-#350 := [asserted]: #85
-#357 := [mp #350 #354]: #351
-#1717 := [symm #357]: #85
-#1719 := [monotonicity #1717]: #1718
-#1749 := [symm #1719]: #1396
-#1750 := (not #1396)
-#1768 := (or #1750 #1098)
-#1769 := [th-lemma]: #1768
-#1770 := [unit-resolution #1769 #1749]: #1098
-#1116 := (not #1098)
-#1238 := (not #1214)
-#1239 := (or #1238 #1116 #1211)
-#1240 := [def-axiom]: #1239
-#1771 := [unit-resolution #1240 #1770 #1767]: #1211
-#1226 := (not #1211)
-#1772 := (or #1226 #1208)
-#1227 := (not #351)
-#1228 := (or #1226 #1227 #1208)
-#1229 := [def-axiom]: #1228
-#1773 := [unit-resolution #1229 #357]: #1772
-#1774 := [unit-resolution #1773 #1771]: #1208
-#1811 := (= #1037 #21)
-#1038 := (= #21 #1037)
-decl f16 :: S4
-#40 := f16
-#41 := (f5 f16)
-#1052 := (+ #41 #1051)
-#1053 := (<= #1052 0::int)
-#1074 := (not #1053)
-#196 := (* -1::int #41)
-#1665 := (+ #14 #196)
-#1666 := (>= #1665 0::int)
-#1754 := (not #1666)
-#1679 := (<= #1665 0::int)
-#44 := (f11 f16)
-#82 := (f6 #44)
-#778 := (f5 #82)
-#788 := (* -1::int #778)
-#835 := (+ #14 #788)
-#836 := (<= #835 0::int)
-decl f18 :: S3
-#55 := f18
-#98 := (f21 f18)
-#823 := (f8 #98 #44)
-#45 := (f8 f10 #44)
-#824 := (= #45 #823)
-#863 := (not #824)
-decl f15 :: S3
-#38 := f15
-#93 := (f21 f15)
-#902 := (f8 #93 #44)
-#1699 := (= #823 #902)
-#1759 := (not #1699)
-#1793 := (iff #1759 #863)
-#1791 := (iff #1699 #824)
-#1786 := (= #823 #45)
-#1789 := (iff #1786 #824)
-#1790 := [commutativity]: #1789
-#1787 := (iff #1699 #1786)
-#1784 := (= #902 #45)
-#905 := (= #45 #902)
-#869 := (f8 f12 #44)
-#904 := (= #869 #902)
-#347 := (= f16 #82)
-#908 := (ite #347 #905 #904)
-#867 := (f8 f9 #44)
-#903 := (= #867 #902)
-#789 := (+ #41 #788)
-#790 := (<= #789 0::int)
-#911 := (ite #790 #908 #903)
-#94 := (f8 #93 #9)
-#713 := (pattern #94)
-#602 := (= #17 #94)
-#600 := (= #23 #94)
-#599 := (= #45 #94)
-#43 := (= #11 f16)
-#601 := (ite #43 #599 #600)
-#197 := (+ #12 #196)
-#195 := (>= #197 0::int)
-#603 := (ite #195 #601 #602)
-#714 := (forall (vars (?v0 S2)) (:pat #694 #713 #696 #697) #603)
-#606 := (forall (vars (?v0 S2)) #603)
-#717 := (iff #606 #714)
-#715 := (iff #603 #603)
-#716 := [refl]: #715
-#718 := [quant-intro #716]: #717
-#46 := (ite #43 #45 #23)
-#203 := (ite #195 #46 #17)
-#497 := (= #94 #203)
-#498 := (forall (vars (?v0 S2)) #497)
-#607 := (iff #498 #606)
-#604 := (iff #497 #603)
-#605 := [rewrite]: #604
-#608 := [quant-intro #605]: #607
-#470 := (~ #498 #498)
-#472 := (~ #497 #497)
-#473 := [refl]: #472
-#471 := [nnf-pos #473]: #470
-#39 := (f3 f15 #9)
-#208 := (= #39 #203)
-#211 := (forall (vars (?v0 S2)) #208)
-#499 := (iff #211 #498)
-#500 := [rewrite* #441]: #499
-#42 := (< #12 #41)
-#47 := (ite #42 #17 #46)
-#48 := (= #39 #47)
-#49 := (forall (vars (?v0 S2)) #48)
-#212 := (iff #49 #211)
-#209 := (iff #48 #208)
-#206 := (= #47 #203)
-#194 := (not #195)
-#200 := (ite #194 #17 #46)
-#204 := (= #200 #203)
-#205 := [rewrite]: #204
-#201 := (= #47 #200)
-#198 := (iff #42 #194)
-#199 := [rewrite]: #198
-#202 := [monotonicity #199]: #201
-#207 := [trans #202 #205]: #206
-#210 := [monotonicity #207]: #209
-#213 := [quant-intro #210]: #212
-#154 := [asserted]: #49
-#214 := [mp #154 #213]: #211
-#501 := [mp #214 #500]: #498
-#468 := [mp~ #501 #471]: #498
-#609 := [mp #468 #608]: #606
-#719 := [mp #609 #718]: #714
-#914 := (not #714)
-#915 := (or #914 #911)
-#83 := (= #82 f16)
-#906 := (ite #83 #905 #904)
-#779 := (+ #778 #196)
-#780 := (>= #779 0::int)
-#907 := (ite #780 #906 #903)
-#916 := (or #914 #907)
-#918 := (iff #916 #915)
-#920 := (iff #915 #915)
-#921 := [rewrite]: #920
-#912 := (iff #907 #911)
-#909 := (iff #906 #908)
-#348 := (iff #83 #347)
-#349 := [rewrite]: #348
-#910 := [monotonicity #349]: #909
-#793 := (iff #780 #790)
-#782 := (+ #196 #778)
-#785 := (>= #782 0::int)
-#791 := (iff #785 #790)
-#792 := [rewrite]: #791
-#786 := (iff #780 #785)
-#783 := (= #779 #782)
-#784 := [rewrite]: #783
-#787 := [monotonicity #784]: #786
-#794 := [trans #787 #792]: #793
-#913 := [monotonicity #794 #910]: #912
-#919 := [monotonicity #913]: #918
-#922 := [trans #919 #921]: #918
-#917 := [quant-inst]: #916
-#923 := [mp #917 #922]: #915
-#1776 := [unit-resolution #923 #719]: #911
-#1394 := (= #41 #778)
-#1674 := (= #778 #41)
-#346 := [asserted]: #83
-#352 := [mp #346 #349]: #347
-#1673 := [symm #352]: #83
-#1675 := [monotonicity #1673]: #1674
-#1676 := [symm #1675]: #1394
-#1739 := (not #1394)
-#1777 := (or #1739 #790)
-#1778 := [th-lemma]: #1777
-#1779 := [unit-resolution #1778 #1676]: #790
-#812 := (not #790)
-#936 := (not #911)
-#937 := (or #936 #812 #908)
-#938 := [def-axiom]: #937
-#1780 := [unit-resolution #938 #1779 #1776]: #908
-#924 := (not #908)
-#1781 := (or #924 #905)
-#925 := (not #347)
-#926 := (or #924 #925 #905)
-#927 := [def-axiom]: #926
-#1782 := [unit-resolution #927 #352]: #1781
-#1783 := [unit-resolution #1782 #1780]: #905
-#1785 := [symm #1783]: #1784
-#1788 := [monotonicity #1785]: #1787
-#1792 := [trans #1788 #1790]: #1791
-#1794 := [monotonicity #1792]: #1793
-#1462 := (* -1::real #902)
-#1709 := (+ #823 #1462)
-#1711 := (>= #1709 0::real)
-#1708 := (not #1711)
-decl f22 :: S5
-#90 := f22
-#1463 := (f8 f22 #44)
-#1466 := (* -1::real #1463)
-#1477 := (+ #902 #1466)
-#1478 := (<= #1477 0::real)
-#1502 := (not #1478)
-#774 := (f8 #88 #44)
-#1467 := (+ #774 #1466)
-#1468 := (>= #1467 0::real)
-#1483 := (or #1468 #1478)
-#1486 := (not #1483)
-#91 := (f8 f22 #9)
-#761 := (pattern #91)
-#89 := (f8 #88 #9)
-#734 := (pattern #89)
-#376 := (* -1::real #94)
-#377 := (+ #91 #376)
-#375 := (>= #377 0::real)
-#371 := (* -1::real #91)
-#372 := (+ #89 #371)
-#370 := (>= #372 0::real)
-#561 := (or #370 #375)
-#562 := (not #561)
-#762 := (forall (vars (?v0 S2)) (:pat #734 #761 #713) #562)
-#565 := (forall (vars (?v0 S2)) #562)
-#765 := (iff #565 #762)
-#763 := (iff #562 #562)
-#764 := [refl]: #763
-#766 := [quant-intro #764]: #765
-#378 := (not #375)
-#368 := (not #370)
-#381 := (and #368 #378)
-#384 := (forall (vars (?v0 S2)) #381)
-#566 := (iff #384 #565)
-#563 := (iff #381 #562)
-#564 := [rewrite]: #563
-#567 := [quant-intro #564]: #566
-#553 := (~ #384 #384)
-#551 := (~ #381 #381)
-#552 := [refl]: #551
-#554 := [nnf-pos #552]: #553
-#394 := (* -1::real #102)
-#395 := (+ #91 #394)
-#393 := (>= #395 0::real)
-#396 := (not #393)
-#99 := (f8 #98 #9)
-#387 := (* -1::real #99)
-#388 := (+ #91 #387)
-#389 := (<= #388 0::real)
-#390 := (not #389)
-#399 := (and #390 #396)
-#402 := (forall (vars (?v0 S2)) #399)
-#405 := (and #384 #402)
-#103 := (< #91 #102)
-#100 := (< #99 #91)
-#104 := (and #100 #103)
-#105 := (forall (vars (?v0 S2)) #104)
-#95 := (< #91 #94)
-#92 := (< #89 #91)
-#96 := (and #92 #95)
-#97 := (forall (vars (?v0 S2)) #96)
-#106 := (and #97 #105)
-#406 := (iff #106 #405)
-#403 := (iff #105 #402)
-#400 := (iff #104 #399)
-#397 := (iff #103 #396)
-#398 := [rewrite]: #397
-#391 := (iff #100 #390)
-#392 := [rewrite]: #391
-#401 := [monotonicity #392 #398]: #400
-#404 := [quant-intro #401]: #403
-#385 := (iff #97 #384)
-#382 := (iff #96 #381)
-#379 := (iff #95 #378)
-#380 := [rewrite]: #379
-#373 := (iff #92 #368)
-#374 := [rewrite]: #373
-#383 := [monotonicity #374 #380]: #382
-#386 := [quant-intro #383]: #385
-#407 := [monotonicity #386 #404]: #406
-#363 := [asserted]: #106
-#408 := [mp #363 #407]: #405
-#409 := [and-elim #408]: #384
-#555 := [mp~ #409 #554]: #384
-#568 := [mp #555 #567]: #565
-#767 := [mp #568 #766]: #762
-#1489 := (not #762)
-#1490 := (or #1489 #1486)
-#1464 := (+ #1463 #1462)
-#1465 := (>= #1464 0::real)
-#1469 := (or #1468 #1465)
-#1470 := (not #1469)
-#1491 := (or #1489 #1470)
-#1493 := (iff #1491 #1490)
-#1495 := (iff #1490 #1490)
-#1496 := [rewrite]: #1495
-#1487 := (iff #1470 #1486)
-#1484 := (iff #1469 #1483)
-#1481 := (iff #1465 #1478)
-#1471 := (+ #1462 #1463)
-#1474 := (>= #1471 0::real)
-#1479 := (iff #1474 #1478)
-#1480 := [rewrite]: #1479
-#1475 := (iff #1465 #1474)
-#1472 := (= #1464 #1471)
-#1473 := [rewrite]: #1472
-#1476 := [monotonicity #1473]: #1475
-#1482 := [trans #1476 #1480]: #1481
-#1485 := [monotonicity #1482]: #1484
-#1488 := [monotonicity #1485]: #1487
-#1494 := [monotonicity #1488]: #1493
-#1497 := [trans #1494 #1496]: #1493
-#1492 := [quant-inst]: #1491
-#1498 := [mp #1492 #1497]: #1490
-#1701 := [unit-resolution #1498 #767]: #1486
-#1503 := (or #1483 #1502)
-#1504 := [def-axiom]: #1503
-#1702 := [unit-resolution #1504 #1701]: #1502
-#1579 := (+ #823 #1466)
-#1580 := (>= #1579 0::real)
-#1612 := (not #1580)
-#946 := (f8 #101 #44)
-#1591 := (+ #946 #1466)
-#1592 := (<= #1591 0::real)
-#1597 := (or #1580 #1592)
-#1600 := (not #1597)
-#727 := (pattern #99)
-#569 := (or #389 #393)
-#570 := (not #569)
-#768 := (forall (vars (?v0 S2)) (:pat #761 #727 #695) #570)
-#573 := (forall (vars (?v0 S2)) #570)
-#771 := (iff #573 #768)
-#769 := (iff #570 #570)
-#770 := [refl]: #769
-#772 := [quant-intro #770]: #771
-#574 := (iff #402 #573)
-#571 := (iff #399 #570)
-#572 := [rewrite]: #571
-#575 := [quant-intro #572]: #574
-#558 := (~ #402 #402)
-#556 := (~ #399 #399)
-#557 := [refl]: #556
-#559 := [nnf-pos #557]: #558
-#410 := [and-elim #408]: #402
-#560 := [mp~ #410 #559]: #402
-#576 := [mp #560 #575]: #573
-#773 := [mp #576 #772]: #768
-#1547 := (not #768)
-#1603 := (or #1547 #1600)
-#1565 := (* -1::real #946)
-#1566 := (+ #1463 #1565)
-#1567 := (>= #1566 0::real)
-#1568 := (* -1::real #823)
-#1569 := (+ #1463 #1568)
-#1570 := (<= #1569 0::real)
-#1571 := (or #1570 #1567)
-#1572 := (not #1571)
-#1604 := (or #1547 #1572)
-#1606 := (iff #1604 #1603)
-#1608 := (iff #1603 #1603)
-#1609 := [rewrite]: #1608
-#1601 := (iff #1572 #1600)
-#1598 := (iff #1571 #1597)
-#1595 := (iff #1567 #1592)
-#1585 := (+ #1565 #1463)
-#1588 := (>= #1585 0::real)
-#1593 := (iff #1588 #1592)
-#1594 := [rewrite]: #1593
-#1589 := (iff #1567 #1588)
-#1586 := (= #1566 #1585)
-#1587 := [rewrite]: #1586
-#1590 := [monotonicity #1587]: #1589
-#1596 := [trans #1590 #1594]: #1595
-#1583 := (iff #1570 #1580)
-#1573 := (+ #1568 #1463)
-#1576 := (<= #1573 0::real)
-#1581 := (iff #1576 #1580)
-#1582 := [rewrite]: #1581
-#1577 := (iff #1570 #1576)
-#1574 := (= #1569 #1573)
-#1575 := [rewrite]: #1574
-#1578 := [monotonicity #1575]: #1577
-#1584 := [trans #1578 #1582]: #1583
-#1599 := [monotonicity #1584 #1596]: #1598
-#1602 := [monotonicity #1599]: #1601
-#1607 := [monotonicity #1602]: #1606
-#1610 := [trans #1607 #1609]: #1606
-#1605 := [quant-inst]: #1604
-#1611 := [mp #1605 #1610]: #1603
-#1703 := [unit-resolution #1611 #773]: #1600
-#1613 := (or #1597 #1612)
-#1614 := [def-axiom]: #1613
-#1704 := [unit-resolution #1614 #1703]: #1612
-#1713 := (or #1708 #1580 #1478)
-#1714 := [th-lemma]: #1713
-#1715 := [unit-resolution #1714 #1704 #1702]: #1708
-#1760 := (or #1759 #1711)
-#1761 := [th-lemma]: #1760
-#1775 := [unit-resolution #1761 #1715]: #1759
-#1795 := [mp #1775 #1794]: #863
-#1797 := (or #836 #824)
-decl f14 :: S5
-#32 := f14
-#776 := (f8 f14 #44)
-#825 := (= #776 #823)
-#841 := (ite #836 #825 #824)
-#30 := (f8 f10 #9)
-#706 := (pattern #30)
-#33 := (f8 f14 #9)
-#705 := (pattern #33)
-#620 := (= #30 #99)
-#619 := (= #33 #99)
-#621 := (ite #157 #619 #620)
-#728 := (forall (vars (?v0 S2)) (:pat #694 #705 #727 #706) #621)
-#624 := (forall (vars (?v0 S2)) #621)
-#731 := (iff #624 #728)
-#729 := (iff #621 #621)
-#730 := [refl]: #729
-#732 := [quant-intro #730]: #731
-#235 := (ite #157 #33 #30)
-#508 := (= #99 #235)
-#509 := (forall (vars (?v0 S2)) #508)
-#625 := (iff #509 #624)
-#622 := (iff #508 #621)
-#623 := [rewrite]: #622
-#626 := [quant-intro #623]: #625
-#460 := (~ #509 #509)
-#462 := (~ #508 #508)
-#463 := [refl]: #462
-#461 := [nnf-pos #463]: #460
-#56 := (f3 f18 #9)
-#240 := (= #56 #235)
-#243 := (forall (vars (?v0 S2)) #240)
-#510 := (iff #243 #509)
-#511 := [rewrite* #441]: #510
-#57 := (ite #15 #30 #33)
-#58 := (= #56 #57)
-#59 := (forall (vars (?v0 S2)) #58)
-#244 := (iff #59 #243)
-#241 := (iff #58 #240)
-#238 := (= #57 #235)
-#232 := (ite #156 #30 #33)
-#236 := (= #232 #235)
-#237 := [rewrite]: #236
-#233 := (= #57 #232)
-#234 := [monotonicity #161]: #233
-#239 := [trans #234 #237]: #238
-#242 := [monotonicity #239]: #241
-#245 := [quant-intro #242]: #244
-#193 := [asserted]: #59
-#246 := [mp #193 #245]: #243
-#512 := [mp #246 #511]: #509
-#530 := [mp~ #512 #461]: #509
-#627 := [mp #530 #626]: #624
-#733 := [mp #627 #732]: #728
-#844 := (not #728)
-#845 := (or #844 #841)
-#826 := (+ #778 #158)
-#827 := (>= #826 0::int)
-#828 := (ite #827 #825 #824)
-#846 := (or #844 #828)
-#848 := (iff #846 #845)
-#850 := (iff #845 #845)
-#851 := [rewrite]: #850
-#842 := (iff #828 #841)
-#839 := (iff #827 #836)
-#829 := (+ #158 #778)
-#832 := (>= #829 0::int)
-#837 := (iff #832 #836)
-#838 := [rewrite]: #837
-#833 := (iff #827 #832)
-#830 := (= #826 #829)
-#831 := [rewrite]: #830
-#834 := [monotonicity #831]: #833
-#840 := [trans #834 #838]: #839
-#843 := [monotonicity #840]: #842
-#849 := [monotonicity #843]: #848
-#852 := [trans #849 #851]: #848
-#847 := [quant-inst]: #846
-#853 := [mp #847 #852]: #845
-#1796 := [unit-resolution #853 #733]: #841
-#854 := (not #841)
-#858 := (or #854 #836 #824)
-#859 := [def-axiom]: #858
-#1798 := [unit-resolution #859 #1796]: #1797
-#1799 := [unit-resolution #1798 #1795]: #836
-#855 := (not #836)
-#1746 := (or #1679 #855)
-#1738 := [hypothesis]: #836
-#1395 := (>= #789 0::int)
-#1740 := (or #1739 #1395)
-#1741 := [th-lemma]: #1740
-#1742 := [unit-resolution #1741 #1676]: #1395
-#1743 := (not #1679)
-#1744 := [hypothesis]: #1743
-#1745 := [th-lemma #1744 #1742 #1738]: false
-#1747 := [lemma #1745]: #1746
-#1800 := [unit-resolution #1747 #1799]: #1679
-#1803 := (or #1743 #1754)
-#1712 := (= #14 #41)
-#1736 := (not #1712)
-#356 := (= f7 f16)
-#953 := (= f7 #82)
-decl f20 :: (-> int S4)
-#1398 := (f20 #778)
-#1727 := (= #1398 #82)
-#1399 := (= #82 #1398)
-#65 := (:var 0 S4)
-#66 := (f5 #65)
-#741 := (pattern #66)
-#67 := (f20 #66)
-#247 := (= #65 #67)
-#742 := (forall (vars (?v0 S4)) (:pat #741) #247)
-#265 := (forall (vars (?v0 S4)) #247)
-#745 := (iff #265 #742)
-#743 := (iff #247 #247)
-#744 := [refl]: #743
-#746 := [quant-intro #744]: #745
-#538 := (~ #265 #265)
-#536 := (~ #247 #247)
-#537 := [refl]: #536
-#539 := [nnf-pos #537]: #538
-#68 := (= #67 #65)
-#69 := (forall (vars (?v0 S4)) #68)
-#266 := (iff #69 #265)
-#263 := (iff #68 #247)
-#264 := [rewrite]: #263
-#267 := [quant-intro #264]: #266
-#231 := [asserted]: #69
-#270 := [mp #231 #267]: #265
-#540 := [mp~ #270 #539]: #265
-#747 := [mp #540 #746]: #742
-#1294 := (not #742)
-#1402 := (or #1294 #1399)
-#1403 := [quant-inst]: #1402
-#1672 := [unit-resolution #1403 #747]: #1399
-#1728 := [symm #1672]: #1727
-#1731 := (= f7 #1398)
-#1400 := (f20 #1041)
-#1725 := (= #1400 #1398)
-#1722 := (= #1041 #778)
-#1720 := (= #1041 #41)
-#1716 := [hypothesis]: #1712
-#1721 := [trans #1719 #1716]: #1720
-#1723 := [trans #1721 #1676]: #1722
-#1726 := [monotonicity #1723]: #1725
-#1729 := (= f7 #1400)
-#1401 := (= #84 #1400)
-#1406 := (or #1294 #1401)
-#1407 := [quant-inst]: #1406
-#1724 := [unit-resolution #1407 #747]: #1401
-#1730 := [trans #357 #1724]: #1729
-#1732 := [trans #1730 #1726]: #1731
-#1733 := [trans #1732 #1728]: #953
-#1734 := [trans #1733 #1673]: #356
-#360 := (not #356)
-#86 := (= f16 f7)
-#87 := (not #86)
-#361 := (iff #87 #360)
-#358 := (iff #86 #356)
-#359 := [rewrite]: #358
-#362 := [monotonicity #359]: #361
-#355 := [asserted]: #87
-#365 := [mp #355 #362]: #360
-#1735 := [unit-resolution #365 #1734]: false
-#1737 := [lemma #1735]: #1736
-#1801 := (or #1712 #1743 #1754)
-#1802 := [th-lemma]: #1801
-#1804 := [unit-resolution #1802 #1737]: #1803
-#1805 := [unit-resolution #1804 #1800]: #1754
-#1757 := (or #1666 #1074)
-#1748 := [hypothesis]: #1053
-#1397 := (>= #1097 0::int)
-#1751 := (or #1750 #1397)
-#1752 := [th-lemma]: #1751
-#1753 := [unit-resolution #1752 #1749]: #1397
-#1755 := [hypothesis]: #1754
-#1756 := [th-lemma #1755 #1753 #1748]: false
-#1758 := [lemma #1756]: #1757
-#1806 := [unit-resolution #1758 #1805]: #1074
-#1808 := (or #1053 #1038)
-#1039 := (f8 f14 #20)
-#1058 := (= #1037 #1039)
-#1061 := (ite #1053 #1058 #1038)
-#629 := (= #30 #89)
-#628 := (= #33 #89)
-#630 := (ite #195 #628 #629)
-#735 := (forall (vars (?v0 S2)) (:pat #694 #705 #734 #706) #630)
-#633 := (forall (vars (?v0 S2)) #630)
-#738 := (iff #633 #735)
-#736 := (iff #630 #630)
-#737 := [refl]: #736
-#739 := [quant-intro #737]: #738
-#251 := (ite #195 #33 #30)
-#513 := (= #89 #251)
-#514 := (forall (vars (?v0 S2)) #513)
-#634 := (iff #514 #633)
-#631 := (iff #513 #630)
-#632 := [rewrite]: #631
-#635 := [quant-intro #632]: #634
-#533 := (~ #514 #514)
-#531 := (~ #513 #513)
-#532 := [refl]: #531
-#534 := [nnf-pos #532]: #533
-#61 := (f3 f19 #9)
-#256 := (= #61 #251)
-#259 := (forall (vars (?v0 S2)) #256)
-#515 := (iff #259 #514)
-#516 := [rewrite* #441]: #515
-#62 := (ite #42 #30 #33)
-#63 := (= #61 #62)
-#64 := (forall (vars (?v0 S2)) #63)
-#260 := (iff #64 #259)
-#257 := (iff #63 #256)
-#254 := (= #62 #251)
-#248 := (ite #194 #30 #33)
-#252 := (= #248 #251)
-#253 := [rewrite]: #252
-#249 := (= #62 #248)
-#250 := [monotonicity #199]: #249
-#255 := [trans #250 #253]: #254
-#258 := [monotonicity #255]: #257
-#261 := [quant-intro #258]: #260
-#215 := [asserted]: #64
-#262 := [mp #215 #261]: #259
-#517 := [mp #262 #516]: #514
-#535 := [mp~ #517 #534]: #514
-#636 := [mp #535 #635]: #633
-#740 := [mp #636 #739]: #735
-#801 := (not #735)
-#1064 := (or #801 #1061)
-#1040 := (= #1039 #1037)
-#1042 := (+ #1041 #196)
-#1043 := (>= #1042 0::int)
-#1044 := (ite #1043 #1040 #1038)
-#1065 := (or #801 #1044)
-#1067 := (iff #1065 #1064)
-#1069 := (iff #1064 #1064)
-#1070 := [rewrite]: #1069
-#1062 := (iff #1044 #1061)
-#1059 := (iff #1040 #1058)
-#1060 := [rewrite]: #1059
-#1056 := (iff #1043 #1053)
-#1045 := (+ #196 #1041)
-#1048 := (>= #1045 0::int)
-#1054 := (iff #1048 #1053)
-#1055 := [rewrite]: #1054
-#1049 := (iff #1043 #1048)
-#1046 := (= #1042 #1045)
-#1047 := [rewrite]: #1046
-#1050 := [monotonicity #1047]: #1049
-#1057 := [trans #1050 #1055]: #1056
-#1063 := [monotonicity #1057 #1060]: #1062
-#1068 := [monotonicity #1063]: #1067
-#1071 := [trans #1068 #1070]: #1067
-#1066 := [quant-inst]: #1065
-#1072 := [mp #1066 #1071]: #1064
-#1807 := [unit-resolution #1072 #740]: #1061
-#1073 := (not #1061)
-#1077 := (or #1073 #1053 #1038)
-#1078 := [def-axiom]: #1077
-#1809 := [unit-resolution #1078 #1807]: #1808
-#1810 := [unit-resolution #1809 #1806]: #1038
-#1812 := [symm #1810]: #1811
-#1813 := [trans #1812 #1774]: #1697
-#1814 := (not #1697)
-#1815 := (or #1814 #1765)
-#1816 := [th-lemma]: #1815
-#1817 := [unit-resolution #1816 #1813]: #1765
-#1508 := (f8 f22 #20)
-#1522 := (* -1::real #1508)
-#1535 := (+ #1205 #1522)
-#1536 := (<= #1535 0::real)
-#1560 := (not #1536)
-#1085 := (f8 #98 #20)
-#1523 := (+ #1085 #1522)
-#1524 := (>= #1523 0::real)
-#1541 := (or #1524 #1536)
-#1544 := (not #1541)
-#1548 := (or #1547 #1544)
-#1509 := (+ #1508 #1507)
-#1510 := (>= #1509 0::real)
-#1511 := (* -1::real #1085)
-#1512 := (+ #1508 #1511)
-#1513 := (<= #1512 0::real)
-#1514 := (or #1513 #1510)
-#1515 := (not #1514)
-#1549 := (or #1547 #1515)
-#1551 := (iff #1549 #1548)
-#1553 := (iff #1548 #1548)
-#1554 := [rewrite]: #1553
-#1545 := (iff #1515 #1544)
-#1542 := (iff #1514 #1541)
-#1539 := (iff #1510 #1536)
-#1529 := (+ #1507 #1508)
-#1532 := (>= #1529 0::real)
-#1537 := (iff #1532 #1536)
-#1538 := [rewrite]: #1537
-#1533 := (iff #1510 #1532)
-#1530 := (= #1509 #1529)
-#1531 := [rewrite]: #1530
-#1534 := [monotonicity #1531]: #1533
-#1540 := [trans #1534 #1538]: #1539
-#1527 := (iff #1513 #1524)
-#1516 := (+ #1511 #1508)
-#1519 := (<= #1516 0::real)
-#1525 := (iff #1519 #1524)
-#1526 := [rewrite]: #1525
-#1520 := (iff #1513 #1519)
-#1517 := (= #1512 #1516)
-#1518 := [rewrite]: #1517
-#1521 := [monotonicity #1518]: #1520
-#1528 := [trans #1521 #1526]: #1527
-#1543 := [monotonicity #1528 #1540]: #1542
-#1546 := [monotonicity #1543]: #1545
-#1552 := [monotonicity #1546]: #1551
-#1555 := [trans #1552 #1554]: #1551
-#1550 := [quant-inst]: #1549
-#1556 := [mp #1550 #1555]: #1548
-#1818 := [unit-resolution #1556 #773]: #1544
-#1561 := (or #1541 #1560)
-#1562 := [def-axiom]: #1561
-#1819 := [unit-resolution #1562 #1818]: #1560
-#1623 := (+ #1037 #1522)
-#1624 := (>= #1623 0::real)
-#1654 := (not #1624)
-#1158 := (f8 #93 #20)
-#1633 := (+ #1158 #1522)
-#1634 := (<= #1633 0::real)
-#1639 := (or #1624 #1634)
-#1642 := (not #1639)
-#1645 := (or #1489 #1642)
-#1620 := (* -1::real #1158)
-#1621 := (+ #1508 #1620)
-#1622 := (>= #1621 0::real)
-#1625 := (or #1624 #1622)
-#1626 := (not #1625)
-#1646 := (or #1489 #1626)
-#1648 := (iff #1646 #1645)
-#1650 := (iff #1645 #1645)
-#1651 := [rewrite]: #1650
-#1643 := (iff #1626 #1642)
-#1640 := (iff #1625 #1639)
-#1637 := (iff #1622 #1634)
-#1627 := (+ #1620 #1508)
-#1630 := (>= #1627 0::real)
-#1635 := (iff #1630 #1634)
-#1636 := [rewrite]: #1635
-#1631 := (iff #1622 #1630)
-#1628 := (= #1621 #1627)
-#1629 := [rewrite]: #1628
-#1632 := [monotonicity #1629]: #1631
-#1638 := [trans #1632 #1636]: #1637
-#1641 := [monotonicity #1638]: #1640
-#1644 := [monotonicity #1641]: #1643
-#1649 := [monotonicity #1644]: #1648
-#1652 := [trans #1649 #1651]: #1648
-#1647 := [quant-inst]: #1646
-#1653 := [mp #1647 #1652]: #1645
-#1820 := [unit-resolution #1653 #767]: #1642
-#1655 := (or #1639 #1654)
-#1656 := [def-axiom]: #1655
-#1821 := [unit-resolution #1656 #1820]: #1654
-[th-lemma #1821 #1819 #1817]: false
+#172 := [monotonicity #169 #140]: #171
+#175 := [monotonicity #172]: #174
+#180 := [trans #175 #178]: #179
+#142 := (iff #57 #141)
+#135 := (= #53 #132)
+#129 := (* #126 3::real)
+#133 := (= #129 #132)
+#134 := [rewrite]: #133
+#130 := (= #53 #129)
+#127 := (= #51 #126)
+#112 := (= #47 #111)
+#113 := [rewrite]: #112
+#124 := (= #50 #121)
+#117 := (- #111)
+#122 := (= #117 #121)
+#123 := [rewrite]: #122
+#118 := (= #50 #117)
+#119 := [monotonicity #113]: #118
+#125 := [trans #119 #123]: #124
+#115 := (iff #49 #114)
+#116 := [monotonicity #113]: #115
+#128 := [monotonicity #116 #125 #113]: #127
+#131 := [monotonicity #128]: #130
+#136 := [trans #131 #134]: #135
+#143 := [monotonicity #136 #140]: #142
+#183 := [monotonicity #143 #180]: #182
+#255 := [trans #183 #253]: #254
+#108 := [asserted]: #67
+#256 := [mp #108 #255]: #249
+#257 := [and-elim #256]: #185
+#259 := [and-elim #256]: #238
+#448 := (+ #111 #447)
+#449 := (<= #448 0::real)
+#441 := (= #111 #223)
+#443 := (or #217 #441)
+#444 := [def-axiom]: #443
+#467 := [unit-resolution #444 #455]: #441
+#468 := (not #441)
+#469 := (or #468 #449)
+#470 := [th-lemma]: #469
+#471 := [unit-resolution #470 #467]: #449
+#463 := (or #189 #217)
+#456 := [hypothesis]: #188
+#258 := [and-elim #256]: #211
+#437 := (or #189 #435)
+#438 := [def-axiom]: #437
+#457 := [unit-resolution #438 #456]: #435
+#458 := (not #435)
+#459 := (or #458 #453)
+#460 := [th-lemma]: #459
+#461 := [unit-resolution #460 #457]: #453
+#462 := [th-lemma #257 #461 #258 #456 #455]: false
+#464 := [lemma #462]: #463
+#472 := [unit-resolution #464 #455]: #189
+#473 := [th-lemma #472 #471 #259 #257 #455]: false
+#474 := [lemma #473]: #217
+#445 := (or #216 #442)
+#446 := [def-axiom]: #445
+#475 := [unit-resolution #446 #474]: #442
+#476 := (not #442)
+#477 := (or #476 #454)
+#478 := [th-lemma]: #477
+#479 := [unit-resolution #478 #475]: #454
+#481 := (not #185)
+#480 := (not #454)
+#482 := (or #188 #480 #237 #481 #216)
+#483 := [th-lemma]: #482
+#484 := [unit-resolution #483 #257 #474 #259 #479]: #188
+#485 := [unit-resolution #438 #484]: #435
+#486 := [unit-resolution #460 #485]: #453
+[th-lemma #479 #259 #257 #474 #258 #486]: false
 unsat
-6c73093b27236ef09bc4a53162dee78b6dc31895 422 0
-#2 := false
-decl f12 :: S2
-#42 := f12
-decl f5 :: S2
-#25 := f5
-#45 := (= f5 f12)
-decl f3 :: (-> int S2)
-decl f4 :: (-> S2 int)
-#43 := (f4 f12)
-#598 := (f3 #43)
-#696 := (= #598 f12)
-#599 := (= f12 #598)
-#8 := (:var 0 S2)
-#9 := (f4 #8)
-#551 := (pattern #9)
-#10 := (f3 #9)
-#98 := (= #8 #10)
-#552 := (forall (vars (?v0 S2)) (:pat #551) #98)
-#101 := (forall (vars (?v0 S2)) #98)
-#555 := (iff #101 #552)
-#553 := (iff #98 #98)
-#554 := [refl]: #553
-#556 := [quant-intro #554]: #555
-#455 := (~ #101 #101)
-#457 := (~ #98 #98)
-#458 := [refl]: #457
-#456 := [nnf-pos #458]: #455
-#11 := (= #10 #8)
-#12 := (forall (vars (?v0 S2)) #11)
-#102 := (iff #12 #101)
-#99 := (iff #11 #98)
-#100 := [rewrite]: #99
-#103 := [quant-intro #100]: #102
-#97 := [asserted]: #12
-#106 := [mp #97 #103]: #101
-#453 := [mp~ #106 #456]: #101
-#557 := [mp #453 #556]: #552
-#600 := (not #552)
-#605 := (or #600 #599)
-#606 := [quant-inst]: #605
-#690 := [unit-resolution #606 #557]: #599
-#697 := [symm #690]: #696
-#698 := (= f5 #598)
-#26 := (f4 f5)
-#596 := (f3 #26)
-#694 := (= #596 #598)
-#692 := (= #598 #596)
-#688 := (= #43 #26)
-#686 := (= #26 #43)
-#13 := 0::int
-#231 := -1::int
-#234 := (* -1::int #43)
-#235 := (+ #26 #234)
-#295 := (<= #235 0::int)
-#74 := (<= #26 #43)
-#393 := (iff #74 #295)
-#394 := [rewrite]: #393
-#346 := [asserted]: #74
-#395 := [mp #346 #394]: #295
-#233 := (>= #235 0::int)
-decl f6 :: (-> S3 S4 real)
-decl f8 :: (-> S2 S4)
-#29 := (f8 f5)
-decl f7 :: S3
-#28 := f7
-#30 := (f6 f7 #29)
-decl f9 :: S3
-#31 := f9
-#32 := (f6 f9 #29)
-#46 := (f8 f12)
-decl f11 :: S3
-#37 := f11
-#47 := (f6 f11 #46)
-#48 := (ite #45 #47 #32)
-#241 := (ite #233 #48 #30)
-#572 := (= #30 #241)
-#658 := (not #572)
-#199 := 0::real
-#197 := -1::real
-#249 := (* -1::real #241)
-#647 := (+ #30 #249)
-#648 := (<= #647 0::real)
-#652 := (not #648)
-#650 := [hypothesis]: #648
-decl f10 :: S3
-#34 := f10
-#35 := (f6 f10 #29)
-#250 := (+ #35 #249)
-#251 := (<= #250 0::real)
-#252 := (not #251)
-#38 := (f6 f11 #29)
-decl f13 :: S3
-#51 := f13
-#52 := (f6 f13 #29)
-#260 := (ite #233 #52 #38)
-#269 := (* -1::real #260)
-#270 := (+ #35 #269)
-#268 := (>= #270 0::real)
-#271 := (not #268)
-#276 := (and #252 #271)
-#44 := (< #26 #43)
-#53 := (ite #44 #38 #52)
-#54 := (< #35 #53)
-#49 := (ite #44 #30 #48)
-#50 := (< #49 #35)
-#55 := (and #50 #54)
-#277 := (iff #55 #276)
-#274 := (iff #54 #271)
-#265 := (< #35 #260)
-#272 := (iff #265 #271)
-#273 := [rewrite]: #272
-#266 := (iff #54 #265)
-#263 := (= #53 #260)
-#232 := (not #233)
-#257 := (ite #232 #38 #52)
-#261 := (= #257 #260)
-#262 := [rewrite]: #261
-#258 := (= #53 #257)
-#236 := (iff #44 #232)
-#237 := [rewrite]: #236
-#259 := [monotonicity #237]: #258
-#264 := [trans #259 #262]: #263
-#267 := [monotonicity #264]: #266
-#275 := [trans #267 #273]: #274
-#255 := (iff #50 #252)
-#246 := (< #241 #35)
-#253 := (iff #246 #252)
-#254 := [rewrite]: #253
-#247 := (iff #50 #246)
-#244 := (= #49 #241)
-#238 := (ite #232 #30 #48)
-#242 := (= #238 #241)
-#243 := [rewrite]: #242
-#239 := (= #49 #238)
-#240 := [monotonicity #237]: #239
-#245 := [trans #240 #243]: #244
-#248 := [monotonicity #245]: #247
-#256 := [trans #248 #254]: #255
-#278 := [monotonicity #256 #275]: #277
-#183 := [asserted]: #55
-#279 := [mp #183 #278]: #276
-#280 := [and-elim #279]: #252
-#201 := (* -1::real #35)
-#217 := (+ #30 #201)
-#218 := (<= #217 0::real)
-#219 := (not #218)
-#202 := (+ #32 #201)
-#200 := (>= #202 0::real)
-#198 := (not #200)
-#224 := (and #198 #219)
-#27 := (< #26 #26)
-#39 := (ite #27 #38 #30)
-#40 := (< #35 #39)
-#33 := (ite #27 #30 #32)
-#36 := (< #33 #35)
-#41 := (and #36 #40)
-#225 := (iff #41 #224)
-#222 := (iff #40 #219)
-#214 := (< #35 #30)
-#220 := (iff #214 #219)
-#221 := [rewrite]: #220
-#215 := (iff #40 #214)
-#212 := (= #39 #30)
-#207 := (ite false #38 #30)
-#210 := (= #207 #30)
-#211 := [rewrite]: #210
-#208 := (= #39 #207)
-#185 := (iff #27 false)
-#186 := [rewrite]: #185
-#209 := [monotonicity #186]: #208
-#213 := [trans #209 #211]: #212
-#216 := [monotonicity #213]: #215
-#223 := [trans #216 #221]: #222
-#205 := (iff #36 #198)
-#194 := (< #32 #35)
-#203 := (iff #194 #198)
-#204 := [rewrite]: #203
-#195 := (iff #36 #194)
-#192 := (= #33 #32)
-#187 := (ite false #30 #32)
-#190 := (= #187 #32)
-#191 := [rewrite]: #190
-#188 := (= #33 #187)
-#189 := [monotonicity #186]: #188
-#193 := [trans #189 #191]: #192
-#196 := [monotonicity #193]: #195
-#206 := [trans #196 #204]: #205
-#226 := [monotonicity #206 #223]: #225
-#182 := [asserted]: #41
-#227 := [mp #182 #226]: #224
-#229 := [and-elim #227]: #219
-#651 := [th-lemma #229 #280 #650]: false
-#653 := [lemma #651]: #652
-#657 := [hypothesis]: #572
-#659 := (or #658 #648)
-#660 := [th-lemma]: #659
-#661 := [unit-resolution #660 #657 #653]: false
-#662 := [lemma #661]: #658
-#582 := (or #233 #572)
-#583 := [def-axiom]: #582
-#685 := [unit-resolution #583 #662]: #233
-#687 := [th-lemma #685 #395]: #686
-#689 := [symm #687]: #688
-#693 := [monotonicity #689]: #692
-#695 := [symm #693]: #694
-#597 := (= f5 #596)
-#601 := (or #600 #597)
-#602 := [quant-inst]: #601
-#691 := [unit-resolution #602 #557]: #597
-#699 := [trans #691 #695]: #698
-#700 := [trans #699 #697]: #45
-#575 := (not #45)
-#63 := (f6 f13 #46)
-#283 := (ite #45 #30 #63)
-#466 := (* -1::real #283)
-#642 := (+ #30 #466)
-#644 := (>= #642 0::real)
-#590 := (= #30 #283)
-#666 := [hypothesis]: #45
-#592 := (or #575 #590)
-#593 := [def-axiom]: #592
-#667 := [unit-resolution #593 #666]: #590
-#668 := (not #590)
-#669 := (or #668 #644)
-#670 := [th-lemma]: #669
-#671 := [unit-resolution #670 #667]: #644
-#60 := (f6 f10 #46)
-#362 := (* -1::real #60)
-#363 := (+ #47 #362)
-#361 := (>= #363 0::real)
-#360 := (not #361)
-#379 := (* -1::real #63)
-#380 := (+ #60 #379)
-#378 := (>= #380 0::real)
-#381 := (not #378)
-#386 := (and #360 #381)
-#68 := (< #43 #43)
-#71 := (ite #68 #47 #63)
-#72 := (< #60 #71)
-#57 := (f6 f7 #46)
-#69 := (ite #68 #57 #47)
-#70 := (< #69 #60)
-#73 := (and #70 #72)
-#387 := (iff #73 #386)
-#384 := (iff #72 #381)
-#375 := (< #60 #63)
-#382 := (iff #375 #381)
-#383 := [rewrite]: #382
-#376 := (iff #72 #375)
-#373 := (= #71 #63)
-#368 := (ite false #47 #63)
-#371 := (= #368 #63)
-#372 := [rewrite]: #371
-#369 := (= #71 #368)
-#348 := (iff #68 false)
-#349 := [rewrite]: #348
-#370 := [monotonicity #349]: #369
-#374 := [trans #370 #372]: #373
-#377 := [monotonicity #374]: #376
-#385 := [trans #377 #383]: #384
-#366 := (iff #70 #360)
-#357 := (< #47 #60)
-#364 := (iff #357 #360)
-#365 := [rewrite]: #364
-#358 := (iff #70 #357)
-#355 := (= #69 #47)
-#350 := (ite false #57 #47)
-#353 := (= #350 #47)
-#354 := [rewrite]: #353
-#351 := (= #69 #350)
-#352 := [monotonicity #349]: #351
-#356 := [trans #352 #354]: #355
-#359 := [monotonicity #356]: #358
-#367 := [trans #359 #365]: #366
-#388 := [monotonicity #367 #385]: #387
-#345 := [asserted]: #73
-#389 := [mp #345 #388]: #386
-#390 := [and-elim #389]: #360
-#399 := (* -1::real #57)
-#400 := (+ #47 #399)
-#398 := (>= #400 0::real)
-#58 := (f6 f9 #46)
-#407 := (* -1::real #58)
-#408 := (+ #57 #407)
-#406 := (>= #408 0::real)
-#402 := (+ #47 #379)
-#403 := (<= #402 0::real)
-#417 := (and #398 #403 #406)
-#77 := (<= #47 #63)
-#76 := (<= #57 #47)
-#78 := (and #76 #77)
-#75 := (<= #58 #57)
-#79 := (and #75 #78)
-#420 := (iff #79 #417)
-#411 := (and #398 #403)
-#414 := (and #406 #411)
-#418 := (iff #414 #417)
-#419 := [rewrite]: #418
-#415 := (iff #79 #414)
-#412 := (iff #78 #411)
-#404 := (iff #77 #403)
-#405 := [rewrite]: #404
-#397 := (iff #76 #398)
-#401 := [rewrite]: #397
-#413 := [monotonicity #401 #405]: #412
-#409 := (iff #75 #406)
-#410 := [rewrite]: #409
-#416 := [monotonicity #410 #413]: #415
-#421 := [trans #416 #419]: #420
-#347 := [asserted]: #79
-#422 := [mp #347 #421]: #417
-#423 := [and-elim #422]: #398
-#655 := (+ #30 #399)
-#656 := (<= #655 0::real)
-#654 := (= #30 #57)
-#676 := (= #57 #30)
-#674 := (= #46 #29)
-#672 := (= #29 #46)
-#673 := [monotonicity #666]: #672
-#675 := [symm #673]: #674
-#677 := [monotonicity #675]: #676
-#678 := [symm #677]: #654
-#679 := (not #654)
-#680 := (or #679 #656)
-#681 := [th-lemma]: #680
-#682 := [unit-resolution #681 #678]: #656
-#469 := (+ #60 #466)
-#472 := (>= #469 0::real)
-#445 := (not #472)
-#321 := (ite #295 #283 #47)
-#331 := (* -1::real #321)
-#332 := (+ #60 #331)
-#330 := (>= #332 0::real)
-#329 := (not #330)
-#446 := (iff #329 #445)
-#473 := (iff #330 #472)
-#470 := (= #332 #469)
-#467 := (= #331 #466)
-#464 := (= #321 #283)
-#1 := true
-#459 := (ite true #283 #47)
-#462 := (= #459 #283)
-#463 := [rewrite]: #462
-#460 := (= #321 #459)
-#451 := (iff #295 true)
-#452 := [iff-true #395]: #451
-#461 := [monotonicity #452]: #460
-#465 := [trans #461 #463]: #464
-#468 := [monotonicity #465]: #467
-#471 := [monotonicity #468]: #470
-#474 := [monotonicity #471]: #473
-#475 := [monotonicity #474]: #446
-#302 := (ite #295 #58 #57)
-#310 := (* -1::real #302)
-#311 := (+ #60 #310)
-#312 := (<= #311 0::real)
-#313 := (not #312)
-#337 := (and #313 #329)
-#62 := (= f12 f5)
-#64 := (ite #62 #30 #63)
-#56 := (< #43 #26)
-#65 := (ite #56 #47 #64)
-#66 := (< #60 #65)
-#59 := (ite #56 #57 #58)
-#61 := (< #59 #60)
-#67 := (and #61 #66)
-#340 := (iff #67 #337)
-#286 := (ite #56 #47 #283)
-#289 := (< #60 #286)
-#292 := (and #61 #289)
-#338 := (iff #292 #337)
-#335 := (iff #289 #329)
-#326 := (< #60 #321)
-#333 := (iff #326 #329)
-#334 := [rewrite]: #333
-#327 := (iff #289 #326)
-#324 := (= #286 #321)
-#296 := (not #295)
-#318 := (ite #296 #47 #283)
-#322 := (= #318 #321)
-#323 := [rewrite]: #322
-#319 := (= #286 #318)
-#297 := (iff #56 #296)
-#298 := [rewrite]: #297
-#320 := [monotonicity #298]: #319
-#325 := [trans #320 #323]: #324
-#328 := [monotonicity #325]: #327
-#336 := [trans #328 #334]: #335
-#316 := (iff #61 #313)
-#307 := (< #302 #60)
-#314 := (iff #307 #313)
-#315 := [rewrite]: #314
-#308 := (iff #61 #307)
-#305 := (= #59 #302)
-#299 := (ite #296 #57 #58)
-#303 := (= #299 #302)
-#304 := [rewrite]: #303
-#300 := (= #59 #299)
-#301 := [monotonicity #298]: #300
-#306 := [trans #301 #304]: #305
-#309 := [monotonicity #306]: #308
-#317 := [trans #309 #315]: #316
-#339 := [monotonicity #317 #336]: #338
-#293 := (iff #67 #292)
-#290 := (iff #66 #289)
-#287 := (= #65 #286)
-#284 := (= #64 #283)
-#230 := (iff #62 #45)
-#282 := [rewrite]: #230
-#285 := [monotonicity #282]: #284
-#288 := [monotonicity #285]: #287
-#291 := [monotonicity #288]: #290
-#294 := [monotonicity #291]: #293
-#341 := [trans #294 #339]: #340
-#184 := [asserted]: #67
-#342 := [mp #184 #341]: #337
-#344 := [and-elim #342]: #329
-#476 := [mp #344 #475]: #445
-#683 := [th-lemma #476 #682 #423 #390 #671]: false
-#684 := [lemma #683]: #575
-[unit-resolution #684 #700]: false
-unsat
-5ee060971856d2def7cc6d40549073dace7efe45 428 0
-#2 := false
-decl f12 :: S2
-#42 := f12
-decl f5 :: S2
-#25 := f5
-#49 := (= f5 f12)
-decl f3 :: (-> int S2)
-decl f4 :: (-> S2 int)
-#43 := (f4 f12)
-#593 := (f3 #43)
-#691 := (= #593 f12)
-#594 := (= f12 #593)
-#8 := (:var 0 S2)
-#9 := (f4 #8)
-#546 := (pattern #9)
-#10 := (f3 #9)
-#98 := (= #8 #10)
-#547 := (forall (vars (?v0 S2)) (:pat #546) #98)
-#101 := (forall (vars (?v0 S2)) #98)
-#550 := (iff #101 #547)
-#548 := (iff #98 #98)
-#549 := [refl]: #548
-#551 := [quant-intro #549]: #550
-#461 := (~ #101 #101)
-#463 := (~ #98 #98)
-#464 := [refl]: #463
-#462 := [nnf-pos #464]: #461
-#11 := (= #10 #8)
-#12 := (forall (vars (?v0 S2)) #11)
-#102 := (iff #12 #101)
-#99 := (iff #11 #98)
-#100 := [rewrite]: #99
-#103 := [quant-intro #100]: #102
-#97 := [asserted]: #12
-#106 := [mp #97 #103]: #101
-#459 := [mp~ #106 #462]: #101
-#552 := [mp #459 #551]: #547
-#595 := (not #547)
-#600 := (or #595 #594)
-#601 := [quant-inst]: #600
-#685 := [unit-resolution #601 #552]: #594
-#692 := [symm #685]: #691
-#693 := (= f5 #593)
-#26 := (f4 f5)
-#591 := (f3 #26)
-#689 := (= #591 #593)
-#687 := (= #593 #591)
-#683 := (= #43 #26)
-#681 := (= #26 #43)
-#13 := 0::int
-#232 := -1::int
-#235 := (* -1::int #43)
-#236 := (+ #26 #235)
-#301 := (<= #236 0::int)
-#74 := (<= #26 #43)
-#398 := (iff #74 #301)
-#399 := [rewrite]: #398
-#352 := [asserted]: #74
-#400 := [mp #352 #399]: #301
-#234 := (>= #236 0::int)
-decl f6 :: (-> S3 S4 real)
-decl f8 :: (-> S2 S4)
-#29 := (f8 f5)
-decl f9 :: S3
-#31 := f9
-#32 := (f6 f9 #29)
-decl f11 :: S3
-#37 := f11
-#38 := (f6 f11 #29)
-#50 := (f8 f12)
-decl f7 :: S3
-#28 := f7
-#51 := (f6 f7 #50)
-#52 := (ite #49 #51 #38)
-#261 := (ite #234 #52 #32)
-#573 := (= #32 #261)
-#653 := (not #573)
-#199 := 0::real
-#197 := -1::real
-#270 := (* -1::real #261)
-#645 := (+ #32 #270)
-#647 := (>= #645 0::real)
-#650 := (not #647)
-#648 := [hypothesis]: #647
-decl f10 :: S3
-#34 := f10
-#35 := (f6 f10 #29)
-#271 := (+ #35 #270)
-#269 := (>= #271 0::real)
-#272 := (not #269)
-#30 := (f6 f7 #29)
-decl f13 :: S3
-#45 := f13
-#46 := (f6 f13 #29)
-#242 := (ite #234 #46 #30)
-#250 := (* -1::real #242)
-#251 := (+ #35 #250)
-#252 := (<= #251 0::real)
-#253 := (not #252)
-#277 := (and #253 #272)
-#44 := (< #26 #43)
-#53 := (ite #44 #32 #52)
-#54 := (< #35 #53)
-#47 := (ite #44 #30 #46)
-#48 := (< #47 #35)
-#55 := (and #48 #54)
-#278 := (iff #55 #277)
-#275 := (iff #54 #272)
-#266 := (< #35 #261)
-#273 := (iff #266 #272)
-#274 := [rewrite]: #273
-#267 := (iff #54 #266)
-#264 := (= #53 #261)
-#233 := (not #234)
-#258 := (ite #233 #32 #52)
-#262 := (= #258 #261)
-#263 := [rewrite]: #262
-#259 := (= #53 #258)
-#237 := (iff #44 #233)
-#238 := [rewrite]: #237
-#260 := [monotonicity #238]: #259
-#265 := [trans #260 #263]: #264
-#268 := [monotonicity #265]: #267
-#276 := [trans #268 #274]: #275
-#256 := (iff #48 #253)
-#247 := (< #242 #35)
-#254 := (iff #247 #253)
-#255 := [rewrite]: #254
-#248 := (iff #48 #247)
-#245 := (= #47 #242)
-#239 := (ite #233 #30 #46)
-#243 := (= #239 #242)
-#244 := [rewrite]: #243
-#240 := (= #47 #239)
-#241 := [monotonicity #238]: #240
-#246 := [trans #241 #244]: #245
-#249 := [monotonicity #246]: #248
-#257 := [trans #249 #255]: #256
-#279 := [monotonicity #257 #276]: #278
-#183 := [asserted]: #55
-#280 := [mp #183 #279]: #277
-#282 := [and-elim #280]: #272
-#201 := (* -1::real #35)
-#202 := (+ #32 #201)
-#200 := (>= #202 0::real)
-#198 := (not #200)
-#218 := (* -1::real #38)
-#219 := (+ #35 #218)
-#217 := (>= #219 0::real)
-#220 := (not #217)
-#225 := (and #198 #220)
-#27 := (< #26 #26)
-#39 := (ite #27 #32 #38)
-#40 := (< #35 #39)
-#33 := (ite #27 #30 #32)
-#36 := (< #33 #35)
-#41 := (and #36 #40)
-#226 := (iff #41 #225)
-#223 := (iff #40 #220)
-#214 := (< #35 #38)
-#221 := (iff #214 #220)
-#222 := [rewrite]: #221
-#215 := (iff #40 #214)
-#212 := (= #39 #38)
-#207 := (ite false #32 #38)
-#210 := (= #207 #38)
-#211 := [rewrite]: #210
-#208 := (= #39 #207)
-#185 := (iff #27 false)
-#186 := [rewrite]: #185
-#209 := [monotonicity #186]: #208
-#213 := [trans #209 #211]: #212
-#216 := [monotonicity #213]: #215
-#224 := [trans #216 #222]: #223
-#205 := (iff #36 #198)
-#194 := (< #32 #35)
-#203 := (iff #194 #198)
-#204 := [rewrite]: #203
-#195 := (iff #36 #194)
-#192 := (= #33 #32)
-#187 := (ite false #30 #32)
-#190 := (= #187 #32)
-#191 := [rewrite]: #190
-#188 := (= #33 #187)
-#189 := [monotonicity #186]: #188
-#193 := [trans #189 #191]: #192
-#196 := [monotonicity #193]: #195
-#206 := [trans #196 #204]: #205
-#227 := [monotonicity #206 #224]: #226
-#182 := [asserted]: #41
-#228 := [mp #182 #227]: #225
-#229 := [and-elim #228]: #198
-#649 := [th-lemma #229 #282 #648]: false
-#651 := [lemma #649]: #650
-#652 := [hypothesis]: #573
-#654 := (or #653 #647)
-#655 := [th-lemma]: #654
-#656 := [unit-resolution #655 #652 #651]: false
-#657 := [lemma #656]: #653
-#583 := (or #234 #573)
-#584 := [def-axiom]: #583
-#680 := [unit-resolution #584 #657]: #234
-#682 := [th-lemma #680 #400]: #681
-#684 := [symm #682]: #683
-#688 := [monotonicity #684]: #687
-#690 := [symm #688]: #689
-#592 := (= f5 #591)
-#596 := (or #595 #592)
-#597 := [quant-inst]: #596
-#686 := [unit-resolution #597 #552]: #592
-#694 := [trans #686 #690]: #693
-#695 := [trans #694 #692]: #49
-#576 := (not #49)
-#58 := (f6 f13 #50)
-#284 := (ite #49 #32 #58)
-#472 := (* -1::real #284)
-#637 := (+ #32 #472)
-#638 := (<= #637 0::real)
-#585 := (= #32 #284)
-#661 := [hypothesis]: #49
-#587 := (or #576 #585)
-#588 := [def-axiom]: #587
-#662 := [unit-resolution #588 #661]: #585
-#663 := (not #585)
-#664 := (or #663 #638)
-#665 := [th-lemma]: #664
-#666 := [unit-resolution #665 #662]: #638
-#61 := (f6 f10 #50)
-#368 := (* -1::real #61)
-#384 := (+ #51 #368)
-#385 := (<= #384 0::real)
-#386 := (not #385)
-#369 := (+ #58 #368)
-#367 := (>= #369 0::real)
-#366 := (not #367)
-#391 := (and #366 #386)
-#63 := (f6 f9 #50)
-#68 := (< #43 #43)
-#71 := (ite #68 #63 #51)
-#72 := (< #61 #71)
-#69 := (ite #68 #51 #58)
-#70 := (< #69 #61)
-#73 := (and #70 #72)
-#392 := (iff #73 #391)
-#389 := (iff #72 #386)
-#381 := (< #61 #51)
-#387 := (iff #381 #386)
-#388 := [rewrite]: #387
-#382 := (iff #72 #381)
-#379 := (= #71 #51)
-#374 := (ite false #63 #51)
-#377 := (= #374 #51)
-#378 := [rewrite]: #377
-#375 := (= #71 #374)
-#354 := (iff #68 false)
-#355 := [rewrite]: #354
-#376 := [monotonicity #355]: #375
-#380 := [trans #376 #378]: #379
-#383 := [monotonicity #380]: #382
-#390 := [trans #383 #388]: #389
-#372 := (iff #70 #366)
-#363 := (< #58 #61)
-#370 := (iff #363 #366)
-#371 := [rewrite]: #370
-#364 := (iff #70 #363)
-#361 := (= #69 #58)
-#356 := (ite false #51 #58)
-#359 := (= #356 #58)
-#360 := [rewrite]: #359
-#357 := (= #69 #356)
-#358 := [monotonicity #355]: #357
-#362 := [trans #358 #360]: #361
-#365 := [monotonicity #362]: #364
-#373 := [trans #365 #371]: #372
-#393 := [monotonicity #373 #390]: #392
-#351 := [asserted]: #73
-#394 := [mp #351 #393]: #391
-#396 := [and-elim #394]: #386
-#402 := (* -1::real #63)
-#403 := (+ #51 #402)
-#404 := (<= #403 0::real)
-#414 := (* -1::real #58)
-#415 := (+ #51 #414)
-#413 := (>= #415 0::real)
-#64 := (f6 f11 #50)
-#407 := (* -1::real #64)
-#408 := (+ #63 #407)
-#409 := (<= #408 0::real)
-#423 := (and #404 #409 #413)
-#77 := (<= #63 #64)
-#76 := (<= #51 #63)
-#78 := (and #76 #77)
-#75 := (<= #58 #51)
-#79 := (and #75 #78)
-#426 := (iff #79 #423)
-#417 := (and #404 #409)
-#420 := (and #413 #417)
-#424 := (iff #420 #423)
-#425 := [rewrite]: #424
-#421 := (iff #79 #420)
-#418 := (iff #78 #417)
-#410 := (iff #77 #409)
-#411 := [rewrite]: #410
-#405 := (iff #76 #404)
-#406 := [rewrite]: #405
-#419 := [monotonicity #406 #411]: #418
-#412 := (iff #75 #413)
-#416 := [rewrite]: #412
-#422 := [monotonicity #416 #419]: #421
-#427 := [trans #422 #425]: #426
-#353 := [asserted]: #79
-#428 := [mp #353 #427]: #423
-#429 := [and-elim #428]: #404
-#642 := (+ #32 #402)
-#644 := (>= #642 0::real)
-#641 := (= #32 #63)
-#671 := (= #63 #32)
-#669 := (= #50 #29)
-#667 := (= #29 #50)
-#668 := [monotonicity #661]: #667
-#670 := [symm #668]: #669
-#672 := [monotonicity #670]: #671
-#673 := [symm #672]: #641
-#674 := (not #641)
-#675 := (or #674 #644)
-#676 := [th-lemma]: #675
-#677 := [unit-resolution #676 #673]: #644
-#475 := (+ #61 #472)
-#478 := (<= #475 0::real)
-#451 := (not #478)
-#327 := (ite #301 #284 #51)
-#335 := (* -1::real #327)
-#336 := (+ #61 #335)
-#337 := (<= #336 0::real)
-#338 := (not #337)
-#452 := (iff #338 #451)
-#479 := (iff #337 #478)
-#476 := (= #336 #475)
-#473 := (= #335 #472)
-#470 := (= #327 #284)
-#1 := true
-#465 := (ite true #284 #51)
-#468 := (= #465 #284)
-#469 := [rewrite]: #468
-#466 := (= #327 #465)
-#457 := (iff #301 true)
-#458 := [iff-true #400]: #457
-#467 := [monotonicity #458]: #466
-#471 := [trans #467 #469]: #470
-#474 := [monotonicity #471]: #473
-#477 := [monotonicity #474]: #476
-#480 := [monotonicity #477]: #479
-#481 := [monotonicity #480]: #452
-#308 := (ite #301 #64 #63)
-#318 := (* -1::real #308)
-#319 := (+ #61 #318)
-#317 := (>= #319 0::real)
-#316 := (not #317)
-#343 := (and #316 #338)
-#56 := (< #43 #26)
-#65 := (ite #56 #63 #64)
-#66 := (< #61 #65)
-#57 := (= f12 f5)
-#59 := (ite #57 #32 #58)
-#60 := (ite #56 #51 #59)
-#62 := (< #60 #61)
-#67 := (and #62 #66)
-#346 := (iff #67 #343)
-#287 := (ite #56 #51 #284)
-#290 := (< #287 #61)
-#296 := (and #66 #290)
-#344 := (iff #296 #343)
-#341 := (iff #290 #338)
-#332 := (< #327 #61)
-#339 := (iff #332 #338)
-#340 := [rewrite]: #339
-#333 := (iff #290 #332)
-#330 := (= #287 #327)
-#302 := (not #301)
-#324 := (ite #302 #51 #284)
-#328 := (= #324 #327)
-#329 := [rewrite]: #328
-#325 := (= #287 #324)
-#303 := (iff #56 #302)
-#304 := [rewrite]: #303
-#326 := [monotonicity #304]: #325
-#331 := [trans #326 #329]: #330
-#334 := [monotonicity #331]: #333
-#342 := [trans #334 #340]: #341
-#322 := (iff #66 #316)
-#313 := (< #61 #308)
-#320 := (iff #313 #316)
-#321 := [rewrite]: #320
-#314 := (iff #66 #313)
-#311 := (= #65 #308)
-#305 := (ite #302 #63 #64)
-#309 := (= #305 #308)
-#310 := [rewrite]: #309
-#306 := (= #65 #305)
-#307 := [monotonicity #304]: #306
-#312 := [trans #307 #310]: #311
-#315 := [monotonicity #312]: #314
-#323 := [trans #315 #321]: #322
-#345 := [monotonicity #323 #342]: #344
-#299 := (iff #67 #296)
-#293 := (and #290 #66)
-#297 := (iff #293 #296)
-#298 := [rewrite]: #297
-#294 := (iff #67 #293)
-#291 := (iff #62 #290)
-#288 := (= #60 #287)
-#285 := (= #59 #284)
-#231 := (iff #57 #49)
-#283 := [rewrite]: #231
-#286 := [monotonicity #283]: #285
-#289 := [monotonicity #286]: #288
-#292 := [monotonicity #289]: #291
-#295 := [monotonicity #292]: #294
-#300 := [trans #295 #298]: #299
-#347 := [trans #300 #345]: #346
-#184 := [asserted]: #67
-#348 := [mp #184 #347]: #343
-#350 := [and-elim #348]: #338
-#482 := [mp #350 #481]: #451
-#678 := [th-lemma #482 #677 #429 #396 #666]: false
-#679 := [lemma #678]: #576
-[unit-resolution #679 #695]: false
-unsat
-ca942f6174c1f53254d5ef1b69b0e75f0d4027d4 208 0
-#2 := false
-#37 := 0::real
-decl f13 :: (-> S6 S7 real)
-decl f17 :: S7
-#32 := f17
-decl f18 :: S6
-#34 := f18
-#35 := (f13 f18 f17)
-decl f14 :: (-> S8 S9 S6)
-decl f16 :: S9
-#30 := f16
-decl f15 :: (-> S2 S8)
-decl f5 :: S2
-#11 := f5
-#29 := (f15 f5)
-#31 := (f14 #29 f16)
-#33 := (f13 #31 f17)
-#96 := -1::real
-#107 := (* -1::real #33)
-#108 := (+ #107 #35)
-#97 := (* -1::real #35)
-#98 := (+ #33 #97)
-#135 := (>= #98 0::real)
-#142 := (ite #135 #98 #108)
-#150 := (* -1::real #142)
-#383 := (+ #108 #150)
-#384 := (<= #383 0::real)
-#369 := (= #108 #142)
-#136 := (not #135)
-decl f3 :: S2
-#8 := f3
-#47 := (f15 f3)
-#48 := (f14 #47 f16)
-#49 := (f13 #48 f17)
-#172 := (* -1::real #49)
-decl f19 :: S6
-#41 := f19
-#42 := (f13 f19 f17)
-#173 := (+ #42 #172)
-#116 := (* -1::real #42)
-#163 := (+ #116 #49)
-#184 := (<= #173 0::real)
-#191 := (ite #184 #163 #173)
-#199 := (* -1::real #191)
-#382 := (+ #173 #199)
-#385 := (<= #382 0::real)
-#375 := (= #173 #191)
-#185 := (not #184)
-#386 := [hypothesis]: #184
-#394 := (or #136 #185)
-#125 := -1/3::real
-#126 := (* -1/3::real #42)
-#200 := (+ #126 #199)
-#123 := 1/3::real
-#124 := (* 1/3::real #35)
-#201 := (+ #124 #200)
-#202 := (<= #201 0::real)
-#203 := (not #202)
-#44 := 3::real
-#43 := (- #35 #42)
-#45 := (/ #43 3::real)
-#50 := (- #49 #42)
-#52 := (- #50)
-#51 := (< #50 0::real)
-#53 := (ite #51 #52 #50)
-#54 := (< #53 #45)
-#208 := (iff #54 #203)
-#127 := (+ #124 #126)
-#166 := (< #163 0::real)
-#178 := (ite #166 #173 #163)
-#181 := (< #178 #127)
-#206 := (iff #181 #203)
-#196 := (< #191 #127)
-#204 := (iff #196 #203)
-#205 := [rewrite]: #204
-#197 := (iff #181 #196)
-#194 := (= #178 #191)
-#188 := (ite #185 #173 #163)
-#192 := (= #188 #191)
-#193 := [rewrite]: #192
-#189 := (= #178 #188)
-#186 := (iff #166 #185)
-#187 := [rewrite]: #186
-#190 := [monotonicity #187]: #189
-#195 := [trans #190 #193]: #194
-#198 := [monotonicity #195]: #197
-#207 := [trans #198 #205]: #206
-#182 := (iff #54 #181)
-#130 := (= #45 #127)
-#117 := (+ #35 #116)
-#120 := (/ #117 3::real)
-#128 := (= #120 #127)
-#129 := [rewrite]: #128
-#121 := (= #45 #120)
-#118 := (= #43 #117)
-#119 := [rewrite]: #118
-#122 := [monotonicity #119]: #121
-#131 := [trans #122 #129]: #130
-#179 := (= #53 #178)
-#164 := (= #50 #163)
-#165 := [rewrite]: #164
-#176 := (= #52 #173)
-#169 := (- #163)
-#174 := (= #169 #173)
-#175 := [rewrite]: #174
-#170 := (= #52 #169)
-#171 := [monotonicity #165]: #170
-#177 := [trans #171 #175]: #176
-#167 := (iff #51 #166)
-#168 := [monotonicity #165]: #167
-#180 := [monotonicity #168 #177 #165]: #179
-#183 := [monotonicity #180 #131]: #182
-#209 := [trans #183 #207]: #208
-#162 := [asserted]: #54
-#210 := [mp #162 #209]: #203
-#380 := (+ #163 #199)
-#381 := (<= #380 0::real)
-#374 := (= #163 #191)
-#376 := (or #185 #374)
-#377 := [def-axiom]: #376
-#387 := [unit-resolution #377 #386]: #374
-#388 := (not #374)
-#389 := (or #388 #381)
-#390 := [th-lemma]: #389
-#391 := [unit-resolution #390 #387]: #381
-#392 := [hypothesis]: #135
-#214 := (+ #33 #172)
-#215 := (<= #214 0::real)
-#55 := (<= #33 #49)
-#216 := (iff #55 #215)
-#217 := [rewrite]: #216
-#211 := [asserted]: #55
-#218 := [mp #211 #217]: #215
-#393 := [th-lemma #218 #392 #391 #210 #386]: false
-#395 := [lemma #393]: #394
-#396 := [unit-resolution #395 #386]: #136
-#151 := (+ #126 #150)
-#152 := (+ #124 #151)
-#153 := (<= #152 0::real)
-#154 := (not #153)
-#36 := (- #33 #35)
-#39 := (- #36)
-#38 := (< #36 0::real)
-#40 := (ite #38 #39 #36)
-#46 := (< #40 #45)
-#159 := (iff #46 #154)
-#101 := (< #98 0::real)
-#113 := (ite #101 #108 #98)
-#132 := (< #113 #127)
-#157 := (iff #132 #154)
-#147 := (< #142 #127)
-#155 := (iff #147 #154)
-#156 := [rewrite]: #155
-#148 := (iff #132 #147)
-#145 := (= #113 #142)
-#139 := (ite #136 #108 #98)
-#143 := (= #139 #142)
-#144 := [rewrite]: #143
-#140 := (= #113 #139)
-#137 := (iff #101 #136)
-#138 := [rewrite]: #137
-#141 := [monotonicity #138]: #140
-#146 := [trans #141 #144]: #145
-#149 := [monotonicity #146]: #148
-#158 := [trans #149 #156]: #157
-#133 := (iff #46 #132)
-#114 := (= #40 #113)
-#99 := (= #36 #98)
-#100 := [rewrite]: #99
-#111 := (= #39 #108)
-#104 := (- #98)
-#109 := (= #104 #108)
-#110 := [rewrite]: #109
-#105 := (= #39 #104)
-#106 := [monotonicity #100]: #105
-#112 := [trans #106 #110]: #111
-#102 := (iff #38 #101)
-#103 := [monotonicity #100]: #102
-#115 := [monotonicity #103 #112 #100]: #114
-#134 := [monotonicity #115 #131]: #133
-#160 := [trans #134 #158]: #159
-#95 := [asserted]: #46
-#161 := [mp #95 #160]: #154
-#372 := (or #135 #369)
-#373 := [def-axiom]: #372
-#397 := [unit-resolution #373 #396]: #369
-#398 := (not #369)
-#399 := (or #398 #384)
-#400 := [th-lemma]: #399
-#401 := [unit-resolution #400 #397]: #384
-#402 := [th-lemma #401 #161 #391 #210 #218 #396]: false
-#403 := [lemma #402]: #185
-#378 := (or #184 #375)
-#379 := [def-axiom]: #378
-#406 := [unit-resolution #379 #403]: #375
-#407 := (not #375)
-#408 := (or #407 #385)
-#409 := [th-lemma]: #408
-#410 := [unit-resolution #409 #406]: #385
-#412 := (not #215)
-#411 := (not #385)
-#413 := (or #136 #411 #412 #202 #184)
-#414 := [th-lemma]: #413
-#415 := [unit-resolution #414 #403 #210 #218 #410]: #136
-#416 := [unit-resolution #373 #415]: #369
-#417 := [unit-resolution #400 #416]: #384
-[th-lemma #410 #218 #210 #403 #161 #417]: false
-unsat
-504ce5f4f6961a0f59840c0aa303f063d46936a5 333 0
+96c3a1d2dea133da23272bb1832adcfffc19c650 333 0
 #2 := false
 #11 := 0::real
 decl ?v2!1 :: real
@@ -2304,173 +571,7 @@
 #408 := [lemma #407]: #230
 [th-lemma #406 #301 #408 #396 #303]: false
 unsat
-024080ea9e6de105c72225d6d55cc8b136a93933 165 0
-#2 := false
-#22 := 0::real
-decl f3 :: (-> S3 S2 real)
-decl ?v0!0 :: S2
-#118 := ?v0!0
-decl f5 :: S3
-#11 := f5
-#119 := (f3 f5 ?v0!0)
-#49 := -1::real
-#117 := (* -1::real #119)
-decl f4 :: S3
-#8 := f4
-#115 := (f3 f4 ?v0!0)
-#120 := (+ #115 #117)
-#121 := (>= #120 0::real)
-decl f6 :: (-> S2 S4 S1)
-decl f7 :: (-> S4 S4 S4)
-decl f9 :: (-> S2 S4 S4)
-decl f11 :: S4
-#17 := f11
-decl f10 :: S2
-#16 := f10
-#18 := (f9 f10 f11)
-decl f8 :: S4
-#15 := f8
-#19 := (f7 f8 #18)
-#123 := (f6 ?v0!0 #19)
-decl f1 :: S1
-#4 := f1
-#124 := (= f1 #123)
-#9 := (:var 0 S2)
-#12 := (f3 f5 #9)
-#81 := (* -1::real #12)
-#10 := (f3 f4 #9)
-#82 := (+ #10 #81)
-#83 := (>= #82 0::real)
-#84 := (not #83)
-#89 := (forall (vars (?v1 S2)) #84)
-#158 := (and #89 #121 #124)
-#122 := (not #121)
-#133 := (not #122)
-#125 := (not #124)
-#130 := (not #125)
-#143 := (and #130 #133 #89)
-#161 := (iff #143 #158)
-#155 := (and #124 #121 #89)
-#159 := (iff #155 #158)
-#160 := [rewrite]: #159
-#156 := (iff #143 #155)
-#153 := (iff #133 #121)
-#154 := [rewrite]: #153
-#151 := (iff #130 #124)
-#152 := [rewrite]: #151
-#157 := [monotonicity #152 #154]: #156
-#162 := [trans #157 #160]: #161
-#92 := (not #89)
-#20 := (f6 #9 #19)
-#46 := (= f1 #20)
-#60 := (not #46)
-#101 := (or #60 #84 #92)
-#106 := (forall (vars (?v0 S2)) #101)
-#109 := (not #106)
-#146 := (~ #109 #143)
-#126 := (or #125 #122 #92)
-#127 := (not #126)
-#144 := (~ #127 #143)
-#140 := (not #92)
-#141 := (~ #140 #89)
-#138 := (~ #89 #89)
-#136 := (~ #84 #84)
-#137 := [refl]: #136
-#139 := [nnf-pos #137]: #138
-#142 := [nnf-neg #139]: #141
-#134 := (~ #133 #133)
-#135 := [refl]: #134
-#131 := (~ #130 #130)
-#132 := [refl]: #131
-#145 := [nnf-neg #132 #135 #142]: #144
-#128 := (~ #109 #127)
-#129 := [sk]: #128
-#147 := [trans #129 #145]: #146
-#23 := (- #12 #10)
-#24 := (< 0::real #23)
-#21 := (= #20 f1)
-#25 := (implies #21 #24)
-#13 := (< #10 #12)
-#14 := (forall (vars (?v1 S2)) #13)
-#26 := (implies #14 #25)
-#27 := (forall (vars (?v0 S2)) #26)
-#28 := (not #27)
-#112 := (iff #28 #109)
-#50 := (* -1::real #10)
-#51 := (+ #50 #12)
-#54 := (< 0::real #51)
-#61 := (or #60 #54)
-#69 := (not #14)
-#70 := (or #69 #61)
-#75 := (forall (vars (?v0 S2)) #70)
-#78 := (not #75)
-#110 := (iff #78 #109)
-#107 := (iff #75 #106)
-#104 := (iff #70 #101)
-#95 := (or #60 #84)
-#98 := (or #92 #95)
-#102 := (iff #98 #101)
-#103 := [rewrite]: #102
-#99 := (iff #70 #98)
-#96 := (iff #61 #95)
-#85 := (iff #54 #84)
-#86 := [rewrite]: #85
-#97 := [monotonicity #86]: #96
-#93 := (iff #69 #92)
-#90 := (iff #14 #89)
-#87 := (iff #13 #84)
-#88 := [rewrite]: #87
-#91 := [quant-intro #88]: #90
-#94 := [monotonicity #91]: #93
-#100 := [monotonicity #94 #97]: #99
-#105 := [trans #100 #103]: #104
-#108 := [quant-intro #105]: #107
-#111 := [monotonicity #108]: #110
-#79 := (iff #28 #78)
-#76 := (iff #27 #75)
-#73 := (iff #26 #70)
-#66 := (implies #14 #61)
-#71 := (iff #66 #70)
-#72 := [rewrite]: #71
-#67 := (iff #26 #66)
-#64 := (iff #25 #61)
-#57 := (implies #46 #54)
-#62 := (iff #57 #61)
-#63 := [rewrite]: #62
-#58 := (iff #25 #57)
-#55 := (iff #24 #54)
-#52 := (= #23 #51)
-#53 := [rewrite]: #52
-#56 := [monotonicity #53]: #55
-#47 := (iff #21 #46)
-#48 := [rewrite]: #47
-#59 := [monotonicity #48 #56]: #58
-#65 := [trans #59 #63]: #64
-#68 := [monotonicity #65]: #67
-#74 := [trans #68 #72]: #73
-#77 := [quant-intro #74]: #76
-#80 := [monotonicity #77]: #79
-#113 := [trans #80 #111]: #112
-#45 := [asserted]: #28
-#114 := [mp #45 #113]: #109
-#148 := [mp~ #114 #147]: #143
-#149 := [mp #148 #162]: #158
-#163 := [and-elim #149]: #121
-#223 := (pattern #12)
-#222 := (pattern #10)
-#224 := (forall (vars (?v1 S2)) (:pat #222 #223) #84)
-#227 := (iff #89 #224)
-#225 := (iff #84 #84)
-#226 := [refl]: #225
-#228 := [quant-intro #226]: #227
-#150 := [and-elim #149]: #89
-#229 := [mp #150 #228]: #224
-#232 := (not #224)
-#233 := (or #232 #122)
-#234 := [quant-inst]: #233
-[unit-resolution #234 #229 #163]: false
-unsat
-116b1dd4c85396a326f34f6c1266b1ad85116049 57 0
+d083434592d4f729dd1c100279aa204b663fa35c 57 0
 #2 := false
 decl f13 :: (-> S4 S4 S5)
 #44 := (:var 0 S4)
@@ -2528,810 +629,827 @@
 #264 := [quant-inst]: #263
 [unit-resolution #264 #269 #258]: false
 unsat
-74073317ccefcdf35878e5154f8155d12c8475cf 91 0
+93a3d21a7f84dc839f14b9a0cfcafdfff6c6b0f1 318 0
 #2 := false
-#43 := 0::real
-decl f3 :: (-> S2 S3 real)
-decl f5 :: S3
-#9 := f5
-decl f6 :: S2
-#11 := f6
-#12 := (f3 f6 f5)
-#40 := -1::real
-#41 := (* -1::real #12)
-decl f4 :: S2
-#8 := f4
-#10 := (f3 f4 f5)
-#42 := (+ #10 #41)
-#135 := (>= #42 0::real)
-#160 := (not #135)
-#48 := (= #10 #12)
-#60 := (not #48)
-#19 := (= #12 #10)
-#20 := (not #19)
-#61 := (iff #20 #60)
-#58 := (iff #19 #48)
-#59 := [rewrite]: #58
-#62 := [monotonicity #59]: #61
-#39 := [asserted]: #20
-#65 := [mp #39 #62]: #60
-#163 := (or #48 #160)
-#44 := (<= #42 0::real)
-#13 := (<= #10 #12)
-#45 := (iff #13 #44)
-#46 := [rewrite]: #45
-#37 := [asserted]: #13
-#47 := [mp #37 #46]: #44
-#159 := (not #44)
-#161 := (or #48 #159 #160)
-#162 := [th-lemma]: #161
-#164 := [unit-resolution #162 #47]: #163
-#165 := [unit-resolution #164 #65]: #160
-#14 := (:var 0 S3)
-#16 := (f3 f4 #14)
-#128 := (pattern #16)
-#15 := (f3 f6 #14)
-#127 := (pattern #15)
-#49 := (* -1::real #16)
-#50 := (+ #15 #49)
-#51 := (<= #50 0::real)
-#129 := (forall (vars (?v0 S3)) (:pat #127 #128) #51)
-#54 := (forall (vars (?v0 S3)) #51)
-#132 := (iff #54 #129)
-#130 := (iff #51 #51)
-#131 := [refl]: #130
-#133 := [quant-intro #131]: #132
-#69 := (~ #54 #54)
-#71 := (~ #51 #51)
-#72 := [refl]: #71
-#70 := [nnf-pos #72]: #69
-#17 := (<= #15 #16)
-#18 := (forall (vars (?v0 S3)) #17)
-#55 := (iff #18 #54)
-#52 := (iff #17 #51)
-#53 := [rewrite]: #52
-#56 := [quant-intro #53]: #55
-#38 := [asserted]: #18
-#57 := [mp #38 #56]: #54
-#67 := [mp~ #57 #70]: #54
-#134 := [mp #67 #133]: #129
-#149 := (not #129)
-#150 := (or #149 #135)
-#136 := (* -1::real #10)
-#137 := (+ #12 #136)
-#138 := (<= #137 0::real)
-#151 := (or #149 #138)
-#153 := (iff #151 #150)
-#155 := (iff #150 #150)
-#156 := [rewrite]: #155
-#147 := (iff #138 #135)
-#139 := (+ #136 #12)
-#142 := (<= #139 0::real)
-#145 := (iff #142 #135)
-#146 := [rewrite]: #145
-#143 := (iff #138 #142)
-#140 := (= #137 #139)
-#141 := [rewrite]: #140
-#144 := [monotonicity #141]: #143
-#148 := [trans #144 #146]: #147
-#154 := [monotonicity #148]: #153
-#157 := [trans #154 #156]: #153
-#152 := [quant-inst]: #151
-#158 := [mp #152 #157]: #150
-[unit-resolution #158 #134 #165]: false
-unsat
-9ecd5f8eb0c8f78bd68a366175093e04632f1f73 149 0
-#2 := false
-#23 := 0::real
-decl f3 :: (-> S2 S3 real)
-decl f5 :: S3
-#9 := f5
-decl f6 :: S2
-#11 := f6
-#12 := (f3 f6 f5)
-#49 := -1::real
-#161 := (* -1::real #12)
-decl f4 :: S2
-#8 := f4
-#10 := (f3 f4 f5)
-#208 := (+ #10 #161)
-#210 := (>= #208 0::real)
-#13 := (= #10 #12)
-#45 := [asserted]: #13
-#213 := (not #13)
-#214 := (or #213 #210)
-#215 := [th-lemma]: #214
-#216 := [unit-resolution #215 #45]: #210
-decl f7 :: S2
-#16 := f7
-#26 := (f3 f7 f5)
-#165 := (* -1::real #26)
-#166 := (+ #10 #165)
-#212 := (>= #166 0::real)
-#227 := (not #212)
-#211 := (= #10 #26)
-#221 := (not #211)
-#67 := (= #12 #26)
-#75 := (not #67)
-#222 := (iff #75 #221)
-#219 := (iff #67 #211)
-#217 := (iff #211 #67)
-#218 := [monotonicity #45]: #217
-#220 := [symm #218]: #219
-#223 := [monotonicity #220]: #222
-#27 := (= #26 #12)
-#28 := (not #27)
-#76 := (iff #28 #75)
-#73 := (iff #27 #67)
-#74 := [rewrite]: #73
-#77 := [monotonicity #74]: #76
-#48 := [asserted]: #28
-#80 := [mp #48 #77]: #75
-#224 := [mp #80 #223]: #221
-#230 := (or #211 #227)
-#167 := (<= #166 0::real)
-#177 := (+ #12 #165)
-#178 := (>= #177 0::real)
-#183 := (not #178)
+#25 := 0::real
+decl f8 :: (-> S4 S2 real)
+decl f11 :: S2
+#40 := f11
+decl f9 :: S4
+#32 := f9
+#47 := (f8 f9 f11)
+decl f12 :: S4
+#44 := f12
+#45 := (f8 f12 f11)
+#192 := -1::real
+#232 := (* -1::real #45)
+#233 := (+ #232 #47)
+decl f5 :: real
+#26 := f5
+#268 := (* -1::real #47)
+#271 := (+ #45 #268)
+#274 := (+ f5 #271)
+#275 := (<= #274 0::real)
+#278 := (ite #275 f5 #233)
+#593 := (* -1::real #278)
+#594 := (+ f5 #593)
+#595 := (<= #594 0::real)
+#603 := (not #595)
+#223 := 1/2::real
+#281 := (* 1/2::real #278)
+#457 := (<= #281 0::real)
+#292 := (= #281 0::real)
+#306 := (<= #271 0::real)
+decl f10 :: S4
+#34 := f10
+#43 := (f8 f10 f11)
+#302 := (+ #43 #232)
+#303 := (<= #302 0::real)
+#309 := (and #303 #306)
+#13 := 0::int
+decl f4 :: (-> S2 int)
+#41 := (f4 f11)
+#178 := -1::int
+#213 := (* -1::int #41)
+decl f6 :: (-> S3 S2)
+decl f7 :: S3
+#28 := f7
+#29 := (f6 f7)
+#30 := (f4 #29)
+#214 := (+ #30 #213)
+#215 := (<= #214 0::int)
+#312 := (or #215 #309)
+#225 := (* 1/2::real #47)
+#272 := (+ #232 #225)
+#224 := (* 1/2::real #43)
+#273 := (+ #224 #272)
+#270 := (>= #273 0::real)
+#321 := (and #270 #292 #312)
+#52 := 2::real
+#55 := (- #47 #45)
+#56 := (<= f5 #55)
+#57 := (ite #56 f5 #55)
+#58 := (/ #57 2::real)
+#59 := (+ #45 #58)
+#60 := (= #59 #45)
+#51 := (+ #43 #47)
+#53 := (/ #51 2::real)
+#54 := (<= #45 #53)
+#61 := (and #54 #60)
+#48 := (<= #45 #47)
+#46 := (<= #43 #45)
+#49 := (and #46 #48)
+#42 := (< #41 #30)
+#50 := (implies #42 #49)
+#62 := (and #50 #61)
+#326 := (iff #62 #321)
+#236 := (<= f5 #233)
+#239 := (ite #236 f5 #233)
+#245 := (* 1/2::real #239)
+#250 := (+ #45 #245)
+#256 := (= #45 #250)
+#226 := (+ #224 #225)
+#229 := (<= #45 #226)
+#261 := (and #229 #256)
+#212 := (not #42)
+#220 := (or #212 #49)
+#264 := (and #220 #261)
+#324 := (iff #264 #321)
+#315 := (and #270 #292)
+#318 := (and #312 #315)
+#322 := (iff #318 #321)
+#323 := [rewrite]: #322
+#319 := (iff #264 #318)
+#316 := (iff #261 #315)
+#293 := (iff #256 #292)
+#284 := (+ #45 #281)
+#287 := (= #45 #284)
+#290 := (iff #287 #292)
+#291 := [rewrite]: #290
+#288 := (iff #256 #287)
+#285 := (= #250 #284)
+#282 := (= #245 #281)
+#279 := (= #239 #278)
+#276 := (iff #236 #275)
+#277 := [rewrite]: #276
+#280 := [monotonicity #277]: #279
+#283 := [monotonicity #280]: #282
+#286 := [monotonicity #283]: #285
+#289 := [monotonicity #286]: #288
+#294 := [trans #289 #291]: #293
+#267 := (iff #229 #270)
+#269 := [rewrite]: #267
+#317 := [monotonicity #269 #294]: #316
+#313 := (iff #220 #312)
+#310 := (iff #49 #309)
+#307 := (iff #48 #306)
+#308 := [rewrite]: #307
+#304 := (iff #46 #303)
+#305 := [rewrite]: #304
+#311 := [monotonicity #305 #308]: #310
+#300 := (iff #212 #215)
+#216 := (not #215)
+#295 := (not #216)
+#298 := (iff #295 #215)
+#299 := [rewrite]: #298
+#296 := (iff #212 #295)
+#217 := (iff #42 #216)
+#218 := [rewrite]: #217
+#297 := [monotonicity #218]: #296
+#301 := [trans #297 #299]: #300
+#314 := [monotonicity #301 #311]: #313
+#320 := [monotonicity #314 #317]: #319
+#325 := [trans #320 #323]: #324
+#265 := (iff #62 #264)
+#262 := (iff #61 #261)
+#259 := (iff #60 #256)
+#253 := (= #250 #45)
+#257 := (iff #253 #256)
+#258 := [rewrite]: #257
+#254 := (iff #60 #253)
+#251 := (= #59 #250)
+#248 := (= #58 #245)
+#242 := (/ #239 2::real)
+#246 := (= #242 #245)
+#247 := [rewrite]: #246
+#243 := (= #58 #242)
+#240 := (= #57 #239)
+#234 := (= #55 #233)
+#235 := [rewrite]: #234
+#237 := (iff #56 #236)
+#238 := [monotonicity #235]: #237
+#241 := [monotonicity #238 #235]: #240
+#244 := [monotonicity #241]: #243
+#249 := [trans #244 #247]: #248
+#252 := [monotonicity #249]: #251
+#255 := [monotonicity #252]: #254
+#260 := [trans #255 #258]: #259
+#230 := (iff #54 #229)
+#227 := (= #53 #226)
+#228 := [rewrite]: #227
+#231 := [monotonicity #228]: #230
+#263 := [monotonicity #231 #260]: #262
+#221 := (iff #50 #220)
+#222 := [rewrite]: #221
+#266 := [monotonicity #222 #263]: #265
+#327 := [trans #266 #325]: #326
+#211 := [asserted]: #62
+#328 := [mp #211 #327]: #321
+#330 := [and-elim #328]: #292
+#597 := (not #292)
+#598 := (or #597 #457)
+#599 := [th-lemma]: #598
+#600 := [unit-resolution #599 #330]: #457
+#601 := [hypothesis]: #595
+#167 := (<= f5 0::real)
 #168 := (not #167)
-#186 := (or #168 #183)
-#189 := (not #186)
-#14 := (:var 0 S3)
-#19 := (f3 f6 #14)
-#154 := (pattern #19)
-#17 := (f3 f7 #14)
-#153 := (pattern #17)
-#15 := (f3 f4 #14)
-#152 := (pattern #15)
-#55 := (* -1::real #19)
-#56 := (+ #17 #55)
-#57 := (<= #56 0::real)
-#82 := (not #57)
-#50 := (* -1::real #17)
-#51 := (+ #15 #50)
-#52 := (<= #51 0::real)
-#85 := (not #52)
-#83 := (or #85 #82)
-#81 := (not #83)
-#155 := (forall (vars (?v0 S3)) (:pat #152 #153 #154) #81)
-#91 := (forall (vars (?v0 S3)) #81)
-#158 := (iff #91 #155)
-#156 := (iff #81 #81)
-#157 := [refl]: #156
-#159 := [quant-intro #157]: #158
-#60 := (and #52 #57)
-#63 := (forall (vars (?v0 S3)) #60)
-#92 := (iff #63 #91)
-#78 := (iff #60 #81)
-#90 := [rewrite]: #78
-#93 := [quant-intro #90]: #92
-#86 := (~ #63 #63)
-#88 := (~ #60 #60)
-#89 := [refl]: #88
-#87 := [nnf-pos #89]: #86
-#20 := (<= #17 #19)
-#18 := (<= #15 #17)
-#21 := (and #18 #20)
-#22 := (forall (vars (?v0 S3)) #21)
-#64 := (iff #22 #63)
-#61 := (iff #21 #60)
-#58 := (iff #20 #57)
-#59 := [rewrite]: #58
-#53 := (iff #18 #52)
-#54 := [rewrite]: #53
-#62 := [monotonicity #54 #59]: #61
-#65 := [quant-intro #62]: #64
-#46 := [asserted]: #22
-#66 := [mp #46 #65]: #63
-#84 := [mp~ #66 #87]: #63
-#94 := [mp #84 #93]: #91
-#160 := [mp #94 #159]: #155
-#192 := (not #155)
-#193 := (or #192 #189)
-#162 := (+ #26 #161)
-#163 := (<= #162 0::real)
-#164 := (not #163)
-#169 := (or #168 #164)
-#170 := (not #169)
-#194 := (or #192 #170)
-#196 := (iff #194 #193)
-#198 := (iff #193 #193)
-#199 := [rewrite]: #198
-#190 := (iff #170 #189)
-#187 := (iff #169 #186)
-#184 := (iff #164 #183)
-#181 := (iff #163 #178)
-#171 := (+ #161 #26)
-#174 := (<= #171 0::real)
-#179 := (iff #174 #178)
-#180 := [rewrite]: #179
-#175 := (iff #163 #174)
-#172 := (= #162 #171)
-#173 := [rewrite]: #172
-#176 := [monotonicity #173]: #175
-#182 := [trans #176 #180]: #181
-#185 := [monotonicity #182]: #184
-#188 := [monotonicity #185]: #187
-#191 := [monotonicity #188]: #190
-#197 := [monotonicity #191]: #196
-#200 := [trans #197 #199]: #196
-#195 := [quant-inst]: #194
-#201 := [mp #195 #200]: #193
-#225 := [unit-resolution #201 #160]: #189
-#202 := (or #186 #167)
-#203 := [def-axiom]: #202
-#226 := [unit-resolution #203 #225]: #167
-#228 := (or #211 #168 #227)
-#229 := [th-lemma]: #228
-#231 := [unit-resolution #229 #226]: #230
-#232 := [unit-resolution #231 #224]: #227
-#204 := (or #186 #178)
-#205 := [def-axiom]: #204
-#233 := [unit-resolution #205 #225]: #178
-[th-lemma #233 #232 #216]: false
-unsat
-ada412db5ba79d588ff49226c319d0dae76f5f87 271 0
-#2 := false
-#8 := 0::real
-decl f4 :: (-> S3 S2 real)
-decl f7 :: S2
-#19 := f7
-decl f5 :: S3
-#11 := f5
-#24 := (f4 f5 f7)
-decl f8 :: S3
-#21 := f8
-#22 := (f4 f8 f7)
-#66 := -1::real
-#87 := (* -1::real #22)
-#88 := (+ #87 #24)
-decl f3 :: real
-#9 := f3
-#148 := (* -1::real #24)
-#149 := (+ #22 #148)
-#150 := (+ f3 #149)
-#151 := (<= #150 0::real)
-#154 := (ite #151 f3 #88)
-#320 := (* -1::real #154)
-#321 := (+ f3 #320)
-#322 := (<= #321 0::real)
-#329 := (not #322)
-#65 := 1/2::real
-#157 := (* 1/2::real #154)
-#289 := (<= #157 0::real)
-#168 := (= #157 0::real)
-#178 := (<= #149 0::real)
-decl f6 :: S3
-#14 := f6
-#20 := (f4 f6 f7)
-#174 := (+ #20 #87)
-#175 := (<= #174 0::real)
-#181 := (and #175 #178)
-#184 := (not #181)
-#171 := (not #168)
-#80 := (* 1/2::real #24)
-#145 := (+ #87 #80)
-#79 := (* 1/2::real #20)
-#146 := (+ #79 #145)
-#143 := (>= #146 0::real)
-#141 := (not #143)
-#193 := (or #141 #171 #184)
-#198 := (not #193)
-#28 := 2::real
-#31 := (- #24 #22)
-#32 := (<= f3 #31)
-#33 := (ite #32 f3 #31)
-#34 := (/ #33 2::real)
-#35 := (+ #22 #34)
-#36 := (= #35 #22)
+#27 := (< 0::real f5)
+#169 := (iff #27 #168)
+#170 := [rewrite]: #169
+#164 := [asserted]: #27
+#171 := [mp #164 #170]: #168
+#602 := [th-lemma #171 #601 #600]: false
+#604 := [lemma #602]: #603
+#450 := (= f5 #278)
+#451 := (= #233 #278)
+#613 := (not #451)
+#596 := (+ #233 #593)
+#605 := (<= #596 0::real)
+#610 := (not #605)
+#532 := (+ #43 #268)
+#533 := (>= #532 0::real)
+#538 := (not #533)
+#210 := [asserted]: #42
+#219 := [mp #210 #218]: #216
+#8 := (:var 0 S2)
+#35 := (f8 f10 #8)
+#443 := (pattern #35)
+#33 := (f8 f9 #8)
+#442 := (pattern #33)
+#9 := (f4 #8)
+#422 := (pattern #9)
+#193 := (* -1::real #35)
+#194 := (+ #33 #193)
+#195 := (<= #194 0::real)
+#198 := (not #195)
+#181 := (* -1::int #30)
+#182 := (+ #9 #181)
+#180 := (>= #182 0::int)
+#201 := (or #180 #198)
+#444 := (forall (vars (?v0 S2)) (:pat #422 #442 #443) #201)
+#204 := (forall (vars (?v0 S2)) #201)
+#447 := (iff #204 #444)
+#445 := (iff #201 #201)
+#446 := [refl]: #445
+#448 := [quant-intro #446]: #447
+#362 := (~ #204 #204)
+#332 := (~ #201 #201)
+#361 := [refl]: #332
+#363 := [nnf-pos #361]: #362
+#36 := (<= #33 #35)
 #37 := (not #36)
-#27 := (+ #20 #24)
-#29 := (/ #27 2::real)
-#30 := (<= #22 #29)
-#38 := (implies #30 #37)
-#25 := (<= #22 #24)
-#23 := (<= #20 #22)
-#26 := (and #23 #25)
-#39 := (implies #26 #38)
-#40 := (not #39)
-#201 := (iff #40 #198)
-#91 := (<= f3 #88)
-#94 := (ite #91 f3 #88)
-#100 := (* 1/2::real #94)
-#105 := (+ #22 #100)
-#111 := (= #22 #105)
-#116 := (not #111)
-#81 := (+ #79 #80)
-#84 := (<= #22 #81)
-#122 := (not #84)
-#123 := (or #122 #116)
-#131 := (not #26)
-#132 := (or #131 #123)
-#137 := (not #132)
-#199 := (iff #137 #198)
-#196 := (iff #132 #193)
-#187 := (or #141 #171)
-#190 := (or #184 #187)
-#194 := (iff #190 #193)
-#195 := [rewrite]: #194
-#191 := (iff #132 #190)
-#188 := (iff #123 #187)
-#172 := (iff #116 #171)
-#169 := (iff #111 #168)
-#160 := (+ #22 #157)
-#163 := (= #22 #160)
-#166 := (iff #163 #168)
-#167 := [rewrite]: #166
-#164 := (iff #111 #163)
-#161 := (= #105 #160)
-#158 := (= #100 #157)
-#155 := (= #94 #154)
-#152 := (iff #91 #151)
-#153 := [rewrite]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [monotonicity #162]: #164
-#170 := [trans #165 #167]: #169
-#173 := [monotonicity #170]: #172
-#144 := (iff #122 #141)
-#140 := (iff #84 #143)
-#142 := [rewrite]: #140
-#147 := [monotonicity #142]: #144
-#189 := [monotonicity #147 #173]: #188
-#185 := (iff #131 #184)
-#182 := (iff #26 #181)
-#179 := (iff #25 #178)
-#180 := [rewrite]: #179
-#176 := (iff #23 #175)
-#177 := [rewrite]: #176
-#183 := [monotonicity #177 #180]: #182
-#186 := [monotonicity #183]: #185
-#192 := [monotonicity #186 #189]: #191
-#197 := [trans #192 #195]: #196
+#31 := (< #9 #30)
+#38 := (implies #31 #37)
+#39 := (forall (vars (?v0 S2)) #38)
+#207 := (iff #39 #204)
+#166 := (not #31)
+#172 := (or #166 #37)
+#175 := (forall (vars (?v0 S2)) #172)
+#205 := (iff #175 #204)
+#202 := (iff #172 #201)
+#199 := (iff #37 #198)
+#196 := (iff #36 #195)
+#197 := [rewrite]: #196
 #200 := [monotonicity #197]: #199
-#138 := (iff #40 #137)
-#135 := (iff #39 #132)
-#128 := (implies #26 #123)
-#133 := (iff #128 #132)
-#134 := [rewrite]: #133
-#129 := (iff #39 #128)
-#126 := (iff #38 #123)
-#119 := (implies #84 #116)
-#124 := (iff #119 #123)
-#125 := [rewrite]: #124
-#120 := (iff #38 #119)
-#117 := (iff #37 #116)
-#114 := (iff #36 #111)
-#108 := (= #105 #22)
-#112 := (iff #108 #111)
-#113 := [rewrite]: #112
-#109 := (iff #36 #108)
-#106 := (= #35 #105)
-#103 := (= #34 #100)
-#97 := (/ #94 2::real)
-#101 := (= #97 #100)
-#102 := [rewrite]: #101
-#98 := (= #34 #97)
-#95 := (= #33 #94)
-#89 := (= #31 #88)
-#90 := [rewrite]: #89
-#92 := (iff #32 #91)
-#93 := [monotonicity #90]: #92
-#96 := [monotonicity #93 #90]: #95
-#99 := [monotonicity #96]: #98
-#104 := [trans #99 #102]: #103
-#107 := [monotonicity #104]: #106
-#110 := [monotonicity #107]: #109
-#115 := [trans #110 #113]: #114
-#118 := [monotonicity #115]: #117
-#85 := (iff #30 #84)
-#82 := (= #29 #81)
-#83 := [rewrite]: #82
-#86 := [monotonicity #83]: #85
-#121 := [monotonicity #86 #118]: #120
-#127 := [trans #121 #125]: #126
-#130 := [monotonicity #127]: #129
-#136 := [trans #130 #134]: #135
-#139 := [monotonicity #136]: #138
-#202 := [trans #139 #200]: #201
-#59 := [asserted]: #40
-#203 := [mp #59 #202]: #198
-#205 := [not-or-elim #203]: #168
-#324 := (or #171 #289)
-#325 := [th-lemma]: #324
-#326 := [unit-resolution #325 #205]: #289
-#327 := [hypothesis]: #322
-#60 := (<= f3 0::real)
-#61 := (not #60)
-#10 := (< 0::real f3)
-#62 := (iff #10 #61)
-#63 := [rewrite]: #62
-#57 := [asserted]: #10
-#64 := [mp #57 #63]: #61
-#328 := [th-lemma #64 #327 #326]: false
-#330 := [lemma #328]: #329
-#282 := (= f3 #154)
-#283 := (= #88 #154)
-#339 := (not #283)
-#323 := (+ #88 #320)
-#331 := (<= #323 0::real)
-#336 := (not #331)
-#301 := (+ #20 #148)
-#302 := (>= #301 0::real)
-#307 := (not #302)
-#12 := (:var 0 S2)
-#15 := (f4 f6 #12)
-#275 := (pattern #15)
-#13 := (f4 f5 #12)
-#274 := (pattern #13)
-#67 := (* -1::real #15)
-#68 := (+ #13 #67)
-#69 := (<= #68 0::real)
-#218 := (not #69)
-#276 := (forall (vars (?v0 S2)) (:pat #274 #275) #218)
-#223 := (forall (vars (?v0 S2)) #218)
-#279 := (iff #223 #276)
-#277 := (iff #218 #218)
-#278 := [refl]: #277
-#280 := [quant-intro #278]: #279
-#72 := (exists (vars (?v0 S2)) #69)
-#75 := (not #72)
-#220 := (~ #75 #223)
-#219 := (~ #218 #218)
-#222 := [refl]: #219
-#221 := [nnf-neg #222]: #220
-#16 := (<= #13 #15)
-#17 := (exists (vars (?v0 S2)) #16)
-#18 := (not #17)
-#76 := (iff #18 #75)
-#73 := (iff #17 #72)
-#70 := (iff #16 #69)
-#71 := [rewrite]: #70
-#74 := [quant-intro #71]: #73
-#77 := [monotonicity #74]: #76
-#58 := [asserted]: #18
-#78 := [mp #58 #77]: #75
-#216 := [mp~ #78 #221]: #223
-#281 := [mp #216 #280]: #276
-#310 := (not #276)
-#311 := (or #310 #307)
-#291 := (* -1::real #20)
-#292 := (+ #24 #291)
-#293 := (<= #292 0::real)
-#294 := (not #293)
-#312 := (or #310 #294)
-#314 := (iff #312 #311)
-#316 := (iff #311 #311)
-#317 := [rewrite]: #316
-#308 := (iff #294 #307)
-#305 := (iff #293 #302)
-#295 := (+ #291 #24)
-#298 := (<= #295 0::real)
-#303 := (iff #298 #302)
-#304 := [rewrite]: #303
-#299 := (iff #293 #298)
-#296 := (= #292 #295)
-#297 := [rewrite]: #296
-#300 := [monotonicity #297]: #299
-#306 := [trans #300 #304]: #305
-#309 := [monotonicity #306]: #308
-#315 := [monotonicity #309]: #314
-#318 := [trans #315 #317]: #314
-#313 := [quant-inst]: #312
-#319 := [mp #313 #318]: #311
-#333 := [unit-resolution #319 #281]: #307
-#204 := [not-or-elim #203]: #143
-#334 := [hypothesis]: #331
-#335 := [th-lemma #334 #204 #333 #326]: false
-#337 := [lemma #335]: #336
-#338 := [hypothesis]: #283
-#340 := (or #339 #331)
-#341 := [th-lemma]: #340
-#342 := [unit-resolution #341 #338 #337]: false
-#343 := [lemma #342]: #339
-#287 := (or #151 #283)
-#288 := [def-axiom]: #287
-#344 := [unit-resolution #288 #343]: #151
-#284 := (not #151)
-#285 := (or #284 #282)
-#286 := [def-axiom]: #285
-#345 := [unit-resolution #286 #344]: #282
-#346 := (not #282)
-#347 := (or #346 #322)
-#348 := [th-lemma]: #347
-[unit-resolution #348 #345 #330]: false
+#190 := (iff #166 #180)
+#179 := (not #180)
+#185 := (not #179)
+#188 := (iff #185 #180)
+#189 := [rewrite]: #188
+#186 := (iff #166 #185)
+#183 := (iff #31 #179)
+#184 := [rewrite]: #183
+#187 := [monotonicity #184]: #186
+#191 := [trans #187 #189]: #190
+#203 := [monotonicity #191 #200]: #202
+#206 := [quant-intro #203]: #205
+#176 := (iff #39 #175)
+#173 := (iff #38 #172)
+#174 := [rewrite]: #173
+#177 := [quant-intro #174]: #176
+#208 := [trans #177 #206]: #207
+#165 := [asserted]: #39
+#209 := [mp #165 #208]: #204
+#364 := [mp~ #209 #363]: #204
+#449 := [mp #364 #448]: #444
+#544 := (not #444)
+#545 := (or #544 #215 #538)
+#507 := (* -1::real #43)
+#508 := (+ #47 #507)
+#511 := (<= #508 0::real)
+#512 := (not #511)
+#513 := (+ #41 #181)
+#514 := (>= #513 0::int)
+#515 := (or #514 #512)
+#546 := (or #544 #515)
+#553 := (iff #546 #545)
+#541 := (or #215 #538)
+#548 := (or #544 #541)
+#551 := (iff #548 #545)
+#552 := [rewrite]: #551
+#549 := (iff #546 #548)
+#542 := (iff #515 #541)
+#539 := (iff #512 #538)
+#536 := (iff #511 #533)
+#526 := (+ #507 #47)
+#529 := (<= #526 0::real)
+#534 := (iff #529 #533)
+#535 := [rewrite]: #534
+#530 := (iff #511 #529)
+#527 := (= #508 #526)
+#528 := [rewrite]: #527
+#531 := [monotonicity #528]: #530
+#537 := [trans #531 #535]: #536
+#540 := [monotonicity #537]: #539
+#524 := (iff #514 #215)
+#516 := (+ #181 #41)
+#519 := (>= #516 0::int)
+#522 := (iff #519 #215)
+#523 := [rewrite]: #522
+#520 := (iff #514 #519)
+#517 := (= #513 #516)
+#518 := [rewrite]: #517
+#521 := [monotonicity #518]: #520
+#525 := [trans #521 #523]: #524
+#543 := [monotonicity #525 #540]: #542
+#550 := [monotonicity #543]: #549
+#554 := [trans #550 #552]: #553
+#547 := [quant-inst]: #546
+#555 := [mp #547 #554]: #545
+#607 := [unit-resolution #555 #449 #219]: #538
+#329 := [and-elim #328]: #270
+#608 := [hypothesis]: #605
+#609 := [th-lemma #608 #329 #607 #600]: false
+#611 := [lemma #609]: #610
+#612 := [hypothesis]: #451
+#614 := (or #613 #605)
+#615 := [th-lemma]: #614
+#616 := [unit-resolution #615 #612 #611]: false
+#617 := [lemma #616]: #613
+#455 := (or #275 #451)
+#456 := [def-axiom]: #455
+#618 := [unit-resolution #456 #617]: #275
+#452 := (not #275)
+#453 := (or #452 #450)
+#454 := [def-axiom]: #453
+#619 := [unit-resolution #454 #618]: #450
+#620 := (not #450)
+#621 := (or #620 #595)
+#622 := [th-lemma]: #621
+[unit-resolution #622 #619 #604]: false
 unsat
-3f6125a99a8cb462db3a2586a1eae0021b892091 288 0
+26bfbe5c6decad8b4a2114b85a11ff3552d6b060 295 0
 #2 := false
-#8 := 0::real
-decl f4 :: (-> S3 S2 real)
+#25 := 0::real
+decl f8 :: (-> S4 S2 real)
+decl f11 :: S2
+#40 := f11
+decl f12 :: S4
+#44 := f12
+#45 := (f8 f12 f11)
+decl f10 :: S4
+#34 := f10
+#43 := (f8 f10 f11)
+#199 := -1::real
+#263 := (* -1::real #43)
+#264 := (+ #263 #45)
+decl f5 :: real
+#26 := f5
+#242 := (* -1::real #45)
+#331 := (+ #43 #242)
+#332 := (+ f5 #331)
+#333 := (<= #332 0::real)
+#336 := (ite #333 f5 #264)
+#666 := (* -1::real #336)
+#667 := (+ f5 #666)
+#668 := (<= #667 0::real)
+#676 := (not #668)
+#230 := 1/2::real
+#414 := (* 1/2::real #336)
+#531 := (<= #414 0::real)
+#415 := (= #414 0::real)
+#284 := -1/2::real
+#339 := (* -1/2::real #336)
+#342 := (+ #45 #339)
+decl f9 :: S4
+#32 := f9
+#47 := (f8 f9 f11)
+#243 := (+ #242 #47)
+#316 := (* -1::real #47)
+#317 := (+ #45 #316)
+#318 := (+ f5 #317)
+#319 := (<= #318 0::real)
+#322 := (ite #319 f5 #243)
+#325 := (* 1/2::real #322)
+#328 := (+ #45 #325)
+#232 := (* 1/2::real #47)
+#312 := (+ #242 #232)
+#231 := (* 1/2::real #43)
+#313 := (+ #231 #312)
+#310 := (>= #313 0::real)
+#345 := (ite #310 #328 #342)
+#348 := (= #45 #345)
+#418 := (iff #348 #415)
+#411 := (= #45 #342)
+#416 := (iff #411 #415)
+#417 := [rewrite]: #416
+#412 := (iff #348 #411)
+#409 := (= #345 #342)
+#404 := (ite false #328 #342)
+#407 := (= #404 #342)
+#408 := [rewrite]: #407
+#405 := (= #345 #404)
+#402 := (iff #310 false)
+#309 := (not #310)
+#361 := (<= #317 0::real)
+#358 := (<= #331 0::real)
+#364 := (and #358 #361)
+#13 := 0::int
+decl f4 :: (-> S2 int)
+#41 := (f4 f11)
+#185 := -1::int
+#220 := (* -1::int #41)
+decl f6 :: (-> S3 S2)
+decl f7 :: S3
+#28 := f7
+#29 := (f6 f7)
+#30 := (f4 #29)
+#221 := (+ #30 #220)
+#222 := (<= #221 0::int)
+#367 := (or #222 #364)
+#376 := (and #309 #348 #367)
+#52 := 2::real
+#61 := (- #45 #43)
+#62 := (<= f5 #61)
+#63 := (ite #62 f5 #61)
+#64 := (/ #63 2::real)
+#65 := (- #45 #64)
+#56 := (- #47 #45)
+#57 := (<= f5 #56)
+#58 := (ite #57 f5 #56)
+#59 := (/ #58 2::real)
+#60 := (+ #45 #59)
+#51 := (+ #43 #47)
+#53 := (/ #51 2::real)
+#55 := (<= #45 #53)
+#66 := (ite #55 #60 #65)
+#67 := (= #66 #45)
+#54 := (< #53 #45)
+#68 := (and #54 #67)
+#48 := (<= #45 #47)
+#46 := (<= #43 #45)
+#49 := (and #46 #48)
+#42 := (< #41 #30)
+#50 := (implies #42 #49)
+#69 := (and #50 #68)
+#381 := (iff #69 #376)
+#267 := (<= f5 #264)
+#270 := (ite #267 f5 #264)
+#285 := (* -1/2::real #270)
+#286 := (+ #45 #285)
+#246 := (<= f5 #243)
+#249 := (ite #246 f5 #243)
+#255 := (* 1/2::real #249)
+#260 := (+ #45 #255)
+#233 := (+ #231 #232)
+#239 := (<= #45 #233)
+#291 := (ite #239 #260 #286)
+#297 := (= #45 #291)
+#236 := (< #233 #45)
+#302 := (and #236 #297)
+#219 := (not #42)
+#227 := (or #219 #49)
+#305 := (and #227 #302)
+#379 := (iff #305 #376)
+#370 := (and #309 #348)
+#373 := (and #367 #370)
+#377 := (iff #373 #376)
+#378 := [rewrite]: #377
+#374 := (iff #305 #373)
+#371 := (iff #302 #370)
+#349 := (iff #297 #348)
+#346 := (= #291 #345)
+#343 := (= #286 #342)
+#340 := (= #285 #339)
+#337 := (= #270 #336)
+#334 := (iff #267 #333)
+#335 := [rewrite]: #334
+#338 := [monotonicity #335]: #337
+#341 := [monotonicity #338]: #340
+#344 := [monotonicity #341]: #343
+#329 := (= #260 #328)
+#326 := (= #255 #325)
+#323 := (= #249 #322)
+#320 := (iff #246 #319)
+#321 := [rewrite]: #320
+#324 := [monotonicity #321]: #323
+#327 := [monotonicity #324]: #326
+#330 := [monotonicity #327]: #329
+#315 := (iff #239 #310)
+#314 := [rewrite]: #315
+#347 := [monotonicity #314 #330 #344]: #346
+#350 := [monotonicity #347]: #349
+#308 := (iff #236 #309)
+#311 := [rewrite]: #308
+#372 := [monotonicity #311 #350]: #371
+#368 := (iff #227 #367)
+#365 := (iff #49 #364)
+#362 := (iff #48 #361)
+#363 := [rewrite]: #362
+#359 := (iff #46 #358)
+#360 := [rewrite]: #359
+#366 := [monotonicity #360 #363]: #365
+#356 := (iff #219 #222)
+#223 := (not #222)
+#351 := (not #223)
+#354 := (iff #351 #222)
+#355 := [rewrite]: #354
+#352 := (iff #219 #351)
+#224 := (iff #42 #223)
+#225 := [rewrite]: #224
+#353 := [monotonicity #225]: #352
+#357 := [trans #353 #355]: #356
+#369 := [monotonicity #357 #366]: #368
+#375 := [monotonicity #369 #372]: #374
+#380 := [trans #375 #378]: #379
+#306 := (iff #69 #305)
+#303 := (iff #68 #302)
+#300 := (iff #67 #297)
+#294 := (= #291 #45)
+#298 := (iff #294 #297)
+#299 := [rewrite]: #298
+#295 := (iff #67 #294)
+#292 := (= #66 #291)
+#289 := (= #65 #286)
+#276 := (* 1/2::real #270)
+#281 := (- #45 #276)
+#287 := (= #281 #286)
+#288 := [rewrite]: #287
+#282 := (= #65 #281)
+#279 := (= #64 #276)
+#273 := (/ #270 2::real)
+#277 := (= #273 #276)
+#278 := [rewrite]: #277
+#274 := (= #64 #273)
+#271 := (= #63 #270)
+#265 := (= #61 #264)
+#266 := [rewrite]: #265
+#268 := (iff #62 #267)
+#269 := [monotonicity #266]: #268
+#272 := [monotonicity #269 #266]: #271
+#275 := [monotonicity #272]: #274
+#280 := [trans #275 #278]: #279
+#283 := [monotonicity #280]: #282
+#290 := [trans #283 #288]: #289
+#261 := (= #60 #260)
+#258 := (= #59 #255)
+#252 := (/ #249 2::real)
+#256 := (= #252 #255)
+#257 := [rewrite]: #256
+#253 := (= #59 #252)
+#250 := (= #58 #249)
+#244 := (= #56 #243)
+#245 := [rewrite]: #244
+#247 := (iff #57 #246)
+#248 := [monotonicity #245]: #247
+#251 := [monotonicity #248 #245]: #250
+#254 := [monotonicity #251]: #253
+#259 := [trans #254 #257]: #258
+#262 := [monotonicity #259]: #261
+#240 := (iff #55 #239)
+#234 := (= #53 #233)
+#235 := [rewrite]: #234
+#241 := [monotonicity #235]: #240
+#293 := [monotonicity #241 #262 #290]: #292
+#296 := [monotonicity #293]: #295
+#301 := [trans #296 #299]: #300
+#237 := (iff #54 #236)
+#238 := [monotonicity #235]: #237
+#304 := [monotonicity #238 #301]: #303
+#228 := (iff #50 #227)
+#229 := [rewrite]: #228
+#307 := [monotonicity #229 #304]: #306
+#382 := [trans #307 #380]: #381
+#218 := [asserted]: #69
+#383 := [mp #218 #382]: #376
+#384 := [and-elim #383]: #309
+#403 := [iff-false #384]: #402
+#406 := [monotonicity #403]: #405
+#410 := [trans #406 #408]: #409
+#413 := [monotonicity #410]: #412
+#419 := [trans #413 #417]: #418
+#385 := [and-elim #383]: #348
+#420 := [mp #385 #419]: #415
+#670 := (not #415)
+#671 := (or #670 #531)
+#672 := [th-lemma]: #671
+#673 := [unit-resolution #672 #420]: #531
+#674 := [hypothesis]: #668
+#174 := (<= f5 0::real)
+#175 := (not #174)
+#27 := (< 0::real f5)
+#176 := (iff #27 #175)
+#177 := [rewrite]: #176
+#171 := [asserted]: #27
+#178 := [mp #171 #177]: #175
+#675 := [th-lemma #178 #674 #673]: false
+#677 := [lemma #675]: #676
+#524 := (= f5 #336)
+#525 := (= #264 #336)
+#685 := (not #525)
+#669 := (+ #264 #666)
+#678 := (<= #669 0::real)
+#682 := (not #678)
+#428 := (iff #367 #364)
+#423 := (or false #364)
+#426 := (iff #423 #364)
+#427 := [rewrite]: #426
+#424 := (iff #367 #423)
+#400 := (iff #222 false)
+#217 := [asserted]: #42
+#226 := [mp #217 #225]: #223
+#401 := [iff-false #226]: #400
+#425 := [monotonicity #401]: #424
+#429 := [trans #425 #427]: #428
+#386 := [and-elim #383]: #367
+#430 := [mp #386 #429]: #364
+#422 := [and-elim #430]: #361
+#680 := [hypothesis]: #678
+#681 := [th-lemma #680 #422 #384 #673]: false
+#683 := [lemma #681]: #682
+#684 := [hypothesis]: #525
+#686 := (or #685 #678)
+#687 := [th-lemma]: #686
+#688 := [unit-resolution #687 #684 #683]: false
+#689 := [lemma #688]: #685
+#529 := (or #333 #525)
+#530 := [def-axiom]: #529
+#690 := [unit-resolution #530 #689]: #333
+#526 := (not #333)
+#527 := (or #526 #524)
+#528 := [def-axiom]: #527
+#691 := [unit-resolution #528 #690]: #524
+#692 := (not #524)
+#693 := (or #692 #668)
+#694 := [th-lemma]: #693
+[unit-resolution #694 #691 #677]: false
+unsat
+5d75e298a98eb55cd39dacd22665bd3062cf5345 204 0
+#2 := false
+#46 := 0::real
+decl f5 :: (-> S3 S2 real)
 decl f7 :: S2
-#19 := f7
+#26 := f7
+decl f11 :: S3
+#38 := f11
+#49 := (f5 f11 f7)
+#183 := -1::real
+#349 := (* -1::real #49)
 decl f8 :: S3
-#21 := f8
-#22 := (f4 f8 f7)
+#28 := f8
+#29 := (f5 f8 f7)
+#362 := (+ #29 #349)
+#363 := (>= #362 0::real)
+#368 := (not #363)
 decl f6 :: S3
-#14 := f6
-#20 := (f4 f6 f7)
-#73 := -1::real
-#118 := (* -1::real #20)
-#119 := (+ #118 #22)
-decl f3 :: real
-#9 := f3
-#97 := (* -1::real #22)
-#211 := (+ #20 #97)
-#212 := (+ f3 #211)
-#213 := (<= #212 0::real)
-#216 := (ite #213 f3 #119)
-#397 := (* -1::real #216)
-#398 := (+ f3 #397)
-#399 := (<= #398 0::real)
-#407 := (not #399)
-#72 := 1/2::real
-#287 := (* 1/2::real #216)
-#367 := (<= #287 0::real)
-#288 := (= #287 0::real)
-#139 := -1/2::real
-#219 := (* -1/2::real #216)
-#222 := (+ #22 #219)
-decl f5 :: S3
-#11 := f5
-#24 := (f4 f5 f7)
-#98 := (+ #97 #24)
-#196 := (* -1::real #24)
-#197 := (+ #22 #196)
-#198 := (+ f3 #197)
-#199 := (<= #198 0::real)
-#202 := (ite #199 f3 #98)
-#205 := (* 1/2::real #202)
-#208 := (+ #22 #205)
-#87 := (* 1/2::real #24)
-#185 := (+ #97 #87)
-#86 := (* 1/2::real #20)
-#186 := (+ #86 #185)
-#183 := (>= #186 0::real)
-#225 := (ite #183 #208 #222)
-#228 := (= #22 #225)
-#291 := (iff #228 #288)
-#284 := (= #22 #222)
-#289 := (iff #284 #288)
-#290 := [rewrite]: #289
-#285 := (iff #228 #284)
-#282 := (= #225 #222)
-#277 := (ite false #208 #222)
-#280 := (= #277 #222)
-#281 := [rewrite]: #280
-#278 := (= #225 #277)
-#275 := (iff #183 false)
-#182 := (not #183)
-#237 := (<= #197 0::real)
-#234 := (<= #211 0::real)
-#240 := (and #234 #237)
-#243 := (not #240)
-#231 := (not #228)
-#252 := (or #183 #231 #243)
-#257 := (not #252)
-#28 := 2::real
-#37 := (- #22 #20)
-#38 := (<= f3 #37)
-#39 := (ite #38 f3 #37)
-#40 := (/ #39 2::real)
-#41 := (- #22 #40)
-#32 := (- #24 #22)
-#33 := (<= f3 #32)
-#34 := (ite #33 f3 #32)
-#35 := (/ #34 2::real)
-#36 := (+ #22 #35)
-#27 := (+ #20 #24)
-#29 := (/ #27 2::real)
-#31 := (<= #22 #29)
-#42 := (ite #31 #36 #41)
-#43 := (= #42 #22)
-#44 := (not #43)
-#30 := (< #29 #22)
-#45 := (implies #30 #44)
-#25 := (<= #22 #24)
-#23 := (<= #20 #22)
-#26 := (and #23 #25)
-#46 := (implies #26 #45)
-#47 := (not #46)
-#260 := (iff #47 #257)
-#122 := (<= f3 #119)
-#125 := (ite #122 f3 #119)
-#140 := (* -1/2::real #125)
-#141 := (+ #22 #140)
-#101 := (<= f3 #98)
-#104 := (ite #101 f3 #98)
-#110 := (* 1/2::real #104)
-#115 := (+ #22 #110)
-#88 := (+ #86 #87)
-#94 := (<= #22 #88)
-#146 := (ite #94 #115 #141)
-#152 := (= #22 #146)
-#157 := (not #152)
-#91 := (< #88 #22)
-#163 := (not #91)
-#164 := (or #163 #157)
-#172 := (not #26)
-#173 := (or #172 #164)
-#178 := (not #173)
-#258 := (iff #178 #257)
-#255 := (iff #173 #252)
-#246 := (or #183 #231)
-#249 := (or #243 #246)
-#253 := (iff #249 #252)
-#254 := [rewrite]: #253
-#250 := (iff #173 #249)
-#247 := (iff #164 #246)
-#232 := (iff #157 #231)
-#229 := (iff #152 #228)
-#226 := (= #146 #225)
-#223 := (= #141 #222)
-#220 := (= #140 #219)
-#217 := (= #125 #216)
-#214 := (iff #122 #213)
+#25 := f6
+#27 := (f5 f6 f7)
+#350 := (+ #27 #349)
+#351 := (<= #350 0::real)
+#352 := (not #351)
+#371 := (or #352 #368)
+#374 := (not #371)
+#8 := (:var 0 S2)
+#41 := (f5 f8 #8)
+#333 := (pattern #41)
+#39 := (f5 f11 #8)
+#332 := (pattern #39)
+#37 := (f5 f6 #8)
+#331 := (pattern #37)
+decl f4 :: (-> S2 int)
+#9 := (f4 #8)
+#311 := (pattern #9)
+#189 := (* -1::real #41)
+#190 := (+ #39 #189)
+#191 := (<= #190 0::real)
+#242 := (not #191)
+#184 := (* -1::real #39)
+#185 := (+ #37 #184)
+#186 := (<= #185 0::real)
+#241 := (not #186)
+#243 := (or #241 #242)
+#244 := (not #243)
+#13 := 0::int
+decl f9 :: (-> S4 S2)
+decl f10 :: S4
+#32 := f10
+#33 := (f9 f10)
+#34 := (f4 #33)
+#157 := -1::int
+#160 := (* -1::int #34)
+#173 := (+ #9 #160)
+#172 := (>= #173 0::int)
+#247 := (or #172 #244)
+#334 := (forall (vars (?v0 S2)) (:pat #311 #331 #332 #333) #247)
+#250 := (forall (vars (?v0 S2)) #247)
+#337 := (iff #250 #334)
+#335 := (iff #247 #247)
+#336 := [refl]: #335
+#338 := [quant-intro #336]: #337
+#194 := (and #186 #191)
+#197 := (or #172 #194)
+#200 := (forall (vars (?v0 S2)) #197)
+#251 := (iff #200 #250)
+#248 := (iff #197 #247)
+#245 := (iff #194 #244)
+#246 := [rewrite]: #245
+#249 := [monotonicity #246]: #248
+#252 := [quant-intro #249]: #251
+#219 := (~ #200 #200)
+#224 := (~ #197 #197)
+#222 := [refl]: #224
+#239 := [nnf-pos #222]: #219
+#42 := (<= #39 #41)
+#40 := (<= #37 #39)
+#43 := (and #40 #42)
+#36 := (< #9 #34)
+#44 := (implies #36 #43)
+#45 := (forall (vars (?v0 S2)) #44)
+#203 := (iff #45 #200)
+#156 := (not #36)
+#165 := (or #156 #43)
+#168 := (forall (vars (?v0 S2)) #165)
+#201 := (iff #168 #200)
+#198 := (iff #165 #197)
+#195 := (iff #43 #194)
+#192 := (iff #42 #191)
+#193 := [rewrite]: #192
+#187 := (iff #40 #186)
+#188 := [rewrite]: #187
+#196 := [monotonicity #188 #193]: #195
+#181 := (iff #156 #172)
+#171 := (not #172)
+#176 := (not #171)
+#179 := (iff #176 #172)
+#180 := [rewrite]: #179
+#177 := (iff #156 #176)
+#174 := (iff #36 #171)
+#175 := [rewrite]: #174
+#178 := [monotonicity #175]: #177
+#182 := [trans #178 #180]: #181
+#199 := [monotonicity #182 #196]: #198
+#202 := [quant-intro #199]: #201
+#169 := (iff #45 #168)
+#166 := (iff #44 #165)
+#167 := [rewrite]: #166
+#170 := [quant-intro #167]: #169
+#204 := [trans #170 #202]: #203
+#155 := [asserted]: #45
+#205 := [mp #155 #204]: #200
+#240 := [mp~ #205 #239]: #200
+#253 := [mp #240 #252]: #250
+#339 := [mp #253 #338]: #334
+#31 := (f4 f7)
+#161 := (+ #31 #160)
+#159 := (>= #161 0::int)
+#158 := (not #159)
+#35 := (< #31 #34)
+#162 := (iff #35 #158)
+#163 := [rewrite]: #162
+#154 := [asserted]: #35
+#164 := [mp #154 #163]: #158
+#380 := (not #334)
+#381 := (or #380 #159 #374)
+#342 := (* -1::real #29)
+#343 := (+ #49 #342)
+#347 := (<= #343 0::real)
+#348 := (not #347)
+#353 := (or #352 #348)
+#354 := (not #353)
+#355 := (or #159 #354)
+#382 := (or #380 #355)
+#389 := (iff #382 #381)
+#377 := (or #159 #374)
+#384 := (or #380 #377)
+#387 := (iff #384 #381)
+#388 := [rewrite]: #387
+#385 := (iff #382 #384)
+#378 := (iff #355 #377)
+#375 := (iff #354 #374)
+#372 := (iff #353 #371)
+#369 := (iff #348 #368)
+#366 := (iff #347 #363)
+#356 := (+ #342 #49)
+#359 := (<= #356 0::real)
+#364 := (iff #359 #363)
+#365 := [rewrite]: #364
+#360 := (iff #347 #359)
+#357 := (= #343 #356)
+#358 := [rewrite]: #357
+#361 := [monotonicity #358]: #360
+#367 := [trans #361 #365]: #366
+#370 := [monotonicity #367]: #369
+#373 := [monotonicity #370]: #372
+#376 := [monotonicity #373]: #375
+#379 := [monotonicity #376]: #378
+#386 := [monotonicity #379]: #385
+#390 := [trans #386 #388]: #389
+#383 := [quant-inst]: #382
+#391 := [mp #383 #390]: #381
+#513 := [unit-resolution #391 #164 #339]: #374
+#394 := (or #371 #363)
+#395 := [def-axiom]: #394
+#514 := [unit-resolution #395 #513]: #363
+#475 := (>= #350 0::real)
+#524 := (not #475)
+#474 := (= #27 #49)
+#519 := (not #474)
+#208 := (= #29 #49)
+#216 := (not #208)
+#520 := (iff #216 #519)
+#517 := (iff #208 #474)
+#515 := (iff #474 #208)
+#30 := (= #27 #29)
+#153 := [asserted]: #30
+#516 := [monotonicity #153]: #515
+#518 := [symm #516]: #517
+#521 := [monotonicity #518]: #520
+#50 := (= #49 #29)
+#51 := (not #50)
+#217 := (iff #51 #216)
+#214 := (iff #50 #208)
 #215 := [rewrite]: #214
 #218 := [monotonicity #215]: #217
-#221 := [monotonicity #218]: #220
-#224 := [monotonicity #221]: #223
-#209 := (= #115 #208)
-#206 := (= #110 #205)
-#203 := (= #104 #202)
-#200 := (iff #101 #199)
-#201 := [rewrite]: #200
-#204 := [monotonicity #201]: #203
-#207 := [monotonicity #204]: #206
-#210 := [monotonicity #207]: #209
-#195 := (iff #94 #183)
-#194 := [rewrite]: #195
-#227 := [monotonicity #194 #210 #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#192 := (iff #163 #183)
-#187 := (not #182)
-#190 := (iff #187 #183)
-#191 := [rewrite]: #190
-#188 := (iff #163 #187)
-#181 := (iff #91 #182)
-#184 := [rewrite]: #181
-#189 := [monotonicity #184]: #188
-#193 := [trans #189 #191]: #192
-#248 := [monotonicity #193 #233]: #247
-#244 := (iff #172 #243)
-#241 := (iff #26 #240)
-#238 := (iff #25 #237)
-#239 := [rewrite]: #238
-#235 := (iff #23 #234)
-#236 := [rewrite]: #235
-#242 := [monotonicity #236 #239]: #241
-#245 := [monotonicity #242]: #244
-#251 := [monotonicity #245 #248]: #250
-#256 := [trans #251 #254]: #255
-#259 := [monotonicity #256]: #258
-#179 := (iff #47 #178)
-#176 := (iff #46 #173)
-#169 := (implies #26 #164)
-#174 := (iff #169 #173)
-#175 := [rewrite]: #174
-#170 := (iff #46 #169)
-#167 := (iff #45 #164)
-#160 := (implies #91 #157)
-#165 := (iff #160 #164)
-#166 := [rewrite]: #165
-#161 := (iff #45 #160)
-#158 := (iff #44 #157)
-#155 := (iff #43 #152)
-#149 := (= #146 #22)
-#153 := (iff #149 #152)
-#154 := [rewrite]: #153
-#150 := (iff #43 #149)
-#147 := (= #42 #146)
-#144 := (= #41 #141)
-#131 := (* 1/2::real #125)
-#136 := (- #22 #131)
-#142 := (= #136 #141)
-#143 := [rewrite]: #142
-#137 := (= #41 #136)
-#134 := (= #40 #131)
-#128 := (/ #125 2::real)
-#132 := (= #128 #131)
-#133 := [rewrite]: #132
-#129 := (= #40 #128)
-#126 := (= #39 #125)
-#120 := (= #37 #119)
-#121 := [rewrite]: #120
-#123 := (iff #38 #122)
-#124 := [monotonicity #121]: #123
-#127 := [monotonicity #124 #121]: #126
-#130 := [monotonicity #127]: #129
-#135 := [trans #130 #133]: #134
-#138 := [monotonicity #135]: #137
-#145 := [trans #138 #143]: #144
-#116 := (= #36 #115)
-#113 := (= #35 #110)
-#107 := (/ #104 2::real)
-#111 := (= #107 #110)
-#112 := [rewrite]: #111
-#108 := (= #35 #107)
-#105 := (= #34 #104)
-#99 := (= #32 #98)
-#100 := [rewrite]: #99
-#102 := (iff #33 #101)
-#103 := [monotonicity #100]: #102
-#106 := [monotonicity #103 #100]: #105
-#109 := [monotonicity #106]: #108
-#114 := [trans #109 #112]: #113
-#117 := [monotonicity #114]: #116
-#95 := (iff #31 #94)
-#89 := (= #29 #88)
-#90 := [rewrite]: #89
-#96 := [monotonicity #90]: #95
-#148 := [monotonicity #96 #117 #145]: #147
-#151 := [monotonicity #148]: #150
-#156 := [trans #151 #154]: #155
-#159 := [monotonicity #156]: #158
-#92 := (iff #30 #91)
-#93 := [monotonicity #90]: #92
-#162 := [monotonicity #93 #159]: #161
-#168 := [trans #162 #166]: #167
-#171 := [monotonicity #168]: #170
-#177 := [trans #171 #175]: #176
-#180 := [monotonicity #177]: #179
-#261 := [trans #180 #259]: #260
-#66 := [asserted]: #47
-#262 := [mp #66 #261]: #257
-#263 := [not-or-elim #262]: #182
-#276 := [iff-false #263]: #275
-#279 := [monotonicity #276]: #278
-#283 := [trans #279 #281]: #282
-#286 := [monotonicity #283]: #285
-#292 := [trans #286 #290]: #291
-#264 := [not-or-elim #262]: #228
-#293 := [mp #264 #292]: #288
-#401 := (not #288)
-#402 := (or #401 #367)
-#403 := [th-lemma]: #402
-#404 := [unit-resolution #403 #293]: #367
-#405 := [hypothesis]: #399
-#67 := (<= f3 0::real)
-#68 := (not #67)
-#10 := (< 0::real f3)
-#69 := (iff #10 #68)
-#70 := [rewrite]: #69
-#64 := [asserted]: #10
-#71 := [mp #64 #70]: #68
-#406 := [th-lemma #71 #405 #404]: false
-#408 := [lemma #406]: #407
-#360 := (= f3 #216)
-#361 := (= #119 #216)
-#416 := (not #361)
-#400 := (+ #119 #397)
-#409 := (<= #400 0::real)
-#413 := (not #409)
-#265 := [not-or-elim #262]: #240
-#267 := [and-elim #265]: #237
-#411 := [hypothesis]: #409
-#412 := [th-lemma #411 #267 #263 #404]: false
-#414 := [lemma #412]: #413
-#415 := [hypothesis]: #361
-#417 := (or #416 #409)
-#418 := [th-lemma]: #417
-#419 := [unit-resolution #418 #415 #414]: false
-#420 := [lemma #419]: #416
-#365 := (or #213 #361)
-#366 := [def-axiom]: #365
-#421 := [unit-resolution #366 #420]: #213
-#362 := (not #213)
-#363 := (or #362 #360)
-#364 := [def-axiom]: #363
-#422 := [unit-resolution #364 #421]: #360
-#423 := (not #360)
-#424 := (or #423 #399)
-#425 := [th-lemma]: #424
-[unit-resolution #425 #422 #408]: false
+#207 := [asserted]: #51
+#221 := [mp #207 #218]: #216
+#522 := [mp #221 #521]: #519
+#527 := (or #474 #524)
+#392 := (or #371 #351)
+#393 := [def-axiom]: #392
+#523 := [unit-resolution #393 #513]: #351
+#525 := (or #474 #352 #524)
+#526 := [th-lemma]: #525
+#528 := [unit-resolution #526 #523]: #527
+#529 := [unit-resolution #528 #522]: #524
+#471 := (+ #27 #342)
+#473 := (>= #471 0::real)
+#530 := (not #30)
+#531 := (or #530 #473)
+#532 := [th-lemma]: #531
+#533 := [unit-resolution #532 #153]: #473
+[th-lemma #533 #529 #514]: false
 unsat
-2dea73fd0603d00ddaec5e14116c465addb0b89e 870 0
+7b235442f6856a575f67cb04d6eaa03042f5336e 870 0
 #2 := false
 #11 := 0::real
 decl f5 :: real
@@ -4202,5165 +2320,3 @@
 #949 := [unit-resolution #948 #945]: #819
 [th-lemma #926 #949 #646 #648 #899 #651 #938 #944 #644 #642]: false
 unsat
-fda4738b9d427b4c846961908e5b41bb384b40b6 89 0
-f1 -> val!2
-f2 -> val!0
-f23 -> val!1
-f24 -> val!12
-f7 -> val!20
-f25 -> val!18
-f21 -> val!3
-f10 -> val!5
-f9 -> val!6
-f14 -> val!7
-f16 -> val!8
-f4 -> val!10
-f13 -> val!13
-f15 -> val!14
-f31 -> val!17
-f22 -> {
-  val!1 val!12 -> val!2
-  else -> val!2
-}
-f6 -> {
-  val!18 -> val!21
-  else -> val!21
-}
-f5 -> {
-  val!20 -> 7720
-  val!21 -> 7719
-  val!17 -> 8365
-  val!18 -> 1796
-  val!19 -> 1797
-  val!15 -> 1
-  val!22 -> 8366
-  else -> 8366
-}
-f20 -> {
-  val!3 -> val!19
-  else -> val!19
-}
-f26 -> {
-  val!18 val!19 -> val!4
-  else -> val!4
-}
-f8 -> {
-  val!5 val!18 -> 0
-  val!6 val!18 -> 0
-  val!7 val!18 -> 0
-  val!1 val!18 -> -1
-  else -> -1
-}
-f28 -> {
-  val!8 -> val!9
-  val!10 -> val!11
-  else -> val!11
-}
-f27 -> {
-  val!9 val!11 -> val!12
-  else -> val!12
-}
-f17 -> {
-  1 -> val!15
-  8366 -> val!22
-  8365 -> val!17
-  1796 -> val!18
-  1797 -> val!19
-  7720 -> val!20
-  7719 -> val!21
-  else -> val!21
-}
-f30 -> {
-  val!15 val!22 -> val!16
-  else -> val!16
-}
-f29 -> {
-  val!20 val!16 -> val!2
-  else -> val!2
-}
-f3 -> {
-  val!13 val!18 -> 0
-  val!8 val!18 -> 0
-  val!14 val!18 -> 0
-  val!10 val!18 -> 0
-  else -> 0
-}
-f18 -> (ite (forall (?v2 S2)
-              (or (not (= f1 (f19 ?v2 (f20 f21))))
-                  (<= (+ (f8 #1 ?v2) (* -1 (f8 #2 ?v2))) 0))
-              :qid {k!45})
-            f1
-            (f18!0 #0 #1))
-unknown
-7f975502da925ceb9dd4add3271a5a407e743846 262 0
-f1 -> val!7
-f2 -> val!0
-f16 -> val!2
-f7 -> val!4
-f27 -> val!25
-f28 -> val!12
-f18 -> val!8
-f4 -> val!10
-f13 -> val!13
-f17 -> val!14
-f12 -> val!16
-f9 -> val!17
-f14 -> val!18
-f10 -> val!19
-f15 -> val!20
-f19 -> val!21
-f24 -> val!23
-f11 -> {
-  val!2 -> val!1
-  val!4 -> val!3
-  else -> val!3
-}
-f6 -> {
-  val!1 -> val!2
-  val!3 -> val!4
-  val!26 -> val!29
-  val!4 -> val!28
-  val!25 -> val!29
-  val!2 -> val!27
-  val!5 -> val!29
-  val!27 -> val!30
-  val!28 -> val!4
-  val!29 -> val!31
-  val!30 -> val!4
-  val!31 -> val!2
-  else -> val!2
-}
-f20 -> {
-  1 -> val!5
-  7720 -> val!26
-  7719 -> val!25
-  14272 -> val!2
-  14270 -> val!4
-  8365 -> val!27
-  14269 -> val!28
-  14271 -> val!29
-  8457 -> val!30
-  0 -> val!31
-  else -> val!31
-}
-f26 -> {
-  val!5 val!25 -> val!6
-  val!5 val!26 -> val!15
-  else -> val!15
-}
-f25 -> {
-  val!2 val!6 -> val!7
-  val!4 val!6 -> val!7
-  val!4 val!15 -> val!7
-  else -> val!7
-}
-f23 -> {
-  val!8 -> val!9
-  val!10 -> val!11
-  val!21 -> val!22
-  val!20 -> val!24
-  else -> val!24
-}
-f29 -> {
-  val!9 val!11 -> val!12
-  else -> val!12
-}
-f5 -> {
-  val!25 -> 7719
-  val!2 -> 14272
-  val!4 -> 14270
-  val!5 -> 1
-  val!26 -> 7720
-  val!29 -> 14271
-  val!28 -> 14269
-  val!27 -> 8365
-  val!30 -> 8457
-  val!31 -> 0
-  else -> 0
-}
-f3 -> {
-  val!21 val!1 -> 2
-  val!8 val!1 -> 2
-  val!14 val!1 -> 3
-  val!20 val!1 -> 4
-  val!10 val!1 -> 3
-  val!13 val!1 -> 2
-  val!21 val!3 -> 7
-  val!8 val!3 -> 5
-  val!14 val!3 -> 6
-  val!20 val!3 -> 8
-  val!10 val!3 -> 7
-  val!13 val!3 -> 8
-  val!13 val!4 -> 29
-  val!10 val!2 -> 30
-  val!10 val!5 -> 36
-  val!10 val!4 -> 31
-  val!10 val!25 -> 37
-  val!10 val!26 -> 38
-  val!13 val!2 -> 32
-  val!13 val!5 -> 39
-  val!13 val!25 -> 40
-  val!13 val!26 -> 41
-  val!20 val!2 -> 30
-  val!20 val!5 -> 33
-  val!20 val!4 -> 31
-  val!20 val!25 -> 34
-  val!20 val!26 -> 35
-  val!14 val!2 -> 30
-  val!14 val!5 -> 36
-  val!14 val!4 -> 31
-  val!14 val!25 -> 37
-  val!14 val!26 -> 38
-  val!8 val!2 -> 32
-  val!8 val!5 -> 39
-  val!8 val!4 -> 29
-  val!8 val!25 -> 40
-  val!8 val!26 -> 41
-  val!21 val!2 -> 32
-  val!21 val!5 -> 42
-  val!21 val!4 -> 29
-  val!21 val!25 -> 43
-  val!21 val!26 -> 44
-  val!10 val!29 -> 73
-  val!10 val!28 -> 7
-  val!10 val!27 -> 75
-  val!13 val!29 -> 78
-  val!13 val!28 -> 8
-  val!13 val!27 -> 80
-  val!20 val!29 -> 73
-  val!20 val!28 -> 74
-  val!20 val!27 -> 75
-  val!14 val!29 -> 73
-  val!14 val!28 -> 76
-  val!14 val!27 -> 75
-  val!8 val!29 -> 78
-  val!8 val!28 -> 77
-  val!8 val!27 -> 80
-  val!21 val!29 -> 78
-  val!21 val!28 -> 79
-  val!21 val!27 -> 80
-  val!10 val!30 -> 7
-  val!13 val!30 -> 8
-  val!20 val!30 -> 93
-  val!14 val!30 -> 94
-  val!8 val!30 -> 95
-  val!21 val!30 -> 96
-  val!10 val!31 -> 101
-  val!13 val!31 -> 102
-  val!20 val!31 -> 4
-  val!14 val!31 -> 101
-  val!8 val!31 -> 102
-  val!21 val!31 -> 102
-  else -> 102
-}
-f8 -> {
-  val!18 val!1 -> 2
-  val!19 val!1 -> 4
-  val!16 val!1 -> 3
-  val!19 val!3 -> 7
-  val!17 val!3 -> 8
-  val!18 val!3 -> 5
-  val!16 val!3 -> 6
-  val!23 val!25 -> 0
-  val!9 val!25 -> -1
-  val!11 val!25 -> 1
-  val!24 val!25 -> 1
-  val!22 val!25 -> -1
-  val!23 val!2 -> 0
-  val!9 val!2 -> -1
-  val!11 val!2 -> 1
-  val!24 val!2 -> 1
-  val!22 val!2 -> -1
-  val!23 val!4 -> 0
-  val!9 val!4 -> -1
-  val!11 val!4 -> 1
-  val!24 val!4 -> 1
-  val!22 val!4 -> -1
-  val!23 val!5 -> 0
-  val!9 val!5 -> -1
-  val!11 val!5 -> 1
-  val!24 val!5 -> 1
-  val!22 val!5 -> -1
-  val!23 val!26 -> 0
-  val!9 val!26 -> -1
-  val!11 val!26 -> 1
-  val!24 val!26 -> 1
-  val!22 val!26 -> -1
-  val!17 val!2 -> 30
-  val!16 val!5 -> 36
-  val!17 val!5 -> 33
-  val!17 val!4 -> 31
-  val!16 val!25 -> 37
-  val!17 val!25 -> 34
-  val!16 val!26 -> 38
-  val!17 val!26 -> 35
-  val!19 val!2 -> 32
-  val!18 val!5 -> 39
-  val!19 val!5 -> 42
-  val!19 val!4 -> 29
-  val!18 val!25 -> 40
-  val!19 val!25 -> 43
-  val!18 val!26 -> 41
-  val!19 val!26 -> 44
-  val!23 val!3 -> 0
-  val!22 val!3 -> -1
-  val!24 val!3 -> 1
-  val!23 val!1 -> 0
-  val!22 val!1 -> -1
-  val!24 val!1 -> 1
-  val!11 val!3 -> 1
-  val!9 val!3 -> -1
-  val!11 val!1 -> 1
-  val!9 val!1 -> -1
-  val!23 val!27 -> 0
-  val!9 val!27 -> -1
-  val!11 val!27 -> 1
-  val!24 val!27 -> 1
-  val!22 val!27 -> -1
-  val!23 val!28 -> 0
-  val!9 val!28 -> -1
-  val!11 val!28 -> 1
-  val!24 val!28 -> 1
-  val!22 val!28 -> -1
-  val!23 val!29 -> 0
-  val!9 val!29 -> -1
-  val!11 val!29 -> 1
-  val!24 val!29 -> 1
-  val!22 val!29 -> -1
-  val!17 val!29 -> 73
-  val!16 val!28 -> 76
-  val!17 val!28 -> 74
-  val!17 val!27 -> 75
-  val!19 val!29 -> 78
-  val!18 val!28 -> 77
-  val!19 val!28 -> 79
-  val!19 val!27 -> 80
-  val!23 val!31 -> 0
-  val!9 val!31 -> -1
-  val!11 val!31 -> 1
-  val!24 val!31 -> 1
-  val!22 val!31 -> -1
-  val!23 val!30 -> 0
-  val!9 val!30 -> -1
-  val!11 val!30 -> 1
-  val!24 val!30 -> 1
-  val!22 val!30 -> -1
-  val!16 val!30 -> 94
-  val!17 val!30 -> 93
-  val!18 val!30 -> 95
-  val!19 val!30 -> 96
-  val!16 val!31 -> 101
-  val!18 val!31 -> 102
-  else -> 102
-}
-f32 -> (f30 (f31 #0) #1)
-unknown
-bd6da22de14f35502495633a6d03f6d719a5ebda 538 0
-f1 -> val!7
-f2 -> val!0
-f16 -> val!2
-f7 -> val!4
-f27 -> val!27
-f28 -> val!12
-f18 -> val!8
-f4 -> val!10
-f13 -> val!13
-f17 -> val!14
-f12 -> val!16
-f9 -> val!17
-f14 -> val!18
-f10 -> val!19
-f15 -> val!20
-f19 -> val!21
-f24 -> val!23
-f22 -> val!25
-f11 -> {
-  val!2 -> val!1
-  val!4 -> val!3
-  else -> val!3
-}
-f6 -> {
-  val!1 -> val!2
-  val!3 -> val!4
-  val!30 -> val!44
-  val!2 -> val!31
-  val!27 -> val!32
-  val!5 -> val!33
-  val!4 -> val!34
-  val!31 -> val!37
-  val!32 -> val!35
-  val!34 -> val!36
-  val!33 -> val!38
-  val!36 -> val!44
-  val!37 -> val!41
-  val!38 -> val!39
-  val!35 -> val!40
-  val!39 -> val!46
-  val!40 -> val!43
-  val!41 -> val!42
-  val!42 -> val!50
-  val!43 -> val!44
-  val!44 -> val!45
-  val!45 -> val!48
-  val!46 -> val!47
-  val!47 -> val!49
-  val!48 -> val!48
-  val!49 -> val!44
-  val!50 -> val!44
-  else -> val!44
-}
-f20 -> {
-  1 -> val!5
-  7720 -> val!30
-  7719 -> val!27
-  13211 -> val!2
-  13214 -> val!4
-  2944 -> val!31
-  8366 -> val!32
-  5724 -> val!33
-  1597 -> val!34
-  1176 -> val!35
-  1143 -> val!36
-  8753 -> val!37
-  10625 -> val!38
-  4877 -> val!39
-  2854 -> val!40
-  13213 -> val!41
-  5166 -> val!42
-  13216 -> val!43
-  6737 -> val!46
-  2853 -> val!45
-  1276 -> val!47
-  13210 -> val!48
-  2140 -> val!49
-  13212 -> val!44
-  10932 -> val!50
-  else -> val!50
-}
-f26 -> {
-  val!5 val!27 -> val!6
-  val!5 val!30 -> val!15
-  else -> val!15
-}
-f25 -> {
-  val!2 val!6 -> val!7
-  val!4 val!6 -> val!7
-  val!4 val!15 -> val!7
-  else -> val!7
-}
-f23 -> {
-  val!8 -> val!9
-  val!10 -> val!11
-  val!21 -> val!22
-  val!20 -> val!24
-  else -> val!24
-}
-f29 -> {
-  val!9 val!11 -> val!12
-  else -> val!12
-}
-f5 -> {
-  val!27 -> 7719
-  val!2 -> 13211
-  val!4 -> 13214
-  val!5 -> 1
-  val!30 -> 7720
-  val!31 -> 2944
-  val!32 -> 8366
-  val!33 -> 5724
-  val!34 -> 1597
-  val!37 -> 8753
-  val!35 -> 1176
-  val!36 -> 1143
-  val!38 -> 10625
-  val!41 -> 13213
-  val!39 -> 4877
-  val!40 -> 2854
-  val!46 -> 6737
-  val!43 -> 13216
-  val!48 -> 13210
-  val!42 -> 5166
-  val!50 -> 10932
-  val!44 -> 13212
-  val!45 -> 2853
-  val!47 -> 1276
-  val!49 -> 2140
-  else -> 2140
-}
-f21 -> {
-  val!25 -> val!26
-  else -> val!26
-}
-f3 -> {
-  val!21 val!1 -> 2
-  val!8 val!1 -> 4
-  val!14 val!1 -> 3
-  val!20 val!1 -> 4
-  val!10 val!1 -> 3
-  val!13 val!1 -> 4
-  val!21 val!3 -> 5
-  val!8 val!3 -> 5
-  val!14 val!3 -> 6
-  val!20 val!3 -> 6
-  val!10 val!3 -> 7
-  val!13 val!3 -> 8
-  val!10 val!30 -> 37
-  val!13 val!36 -> 30
-  val!10 val!36 -> 96
-  val!10 val!40 -> 32
-  val!21 val!27 -> 40
-  val!20 val!27 -> 35
-  val!21 val!2 -> 38
-  val!20 val!2 -> 33
-  val!10 val!27 -> 35
-  val!8 val!27 -> 40
-  val!10 val!4 -> 36
-  val!8 val!4 -> 41
-  val!10 val!2 -> 33
-  val!8 val!2 -> 38
-  val!21 val!4 -> 41
-  val!20 val!4 -> 36
-  val!10 val!5 -> 34
-  val!8 val!5 -> 39
-  val!8 val!30 -> 42
-  val!21 val!30 -> 43
-  val!20 val!30 -> 29
-  val!21 val!5 -> 39
-  val!20 val!5 -> 34
-  val!13 val!2 -> 38
-  val!13 val!5 -> 39
-  val!13 val!27 -> 40
-  val!13 val!4 -> 41
-  val!13 val!30 -> 42
-  val!14 val!2 -> 33
-  val!14 val!5 -> 34
-  val!14 val!27 -> 35
-  val!14 val!4 -> 36
-  val!14 val!30 -> 37
-  val!10 val!34 -> 70
-  val!8 val!34 -> 74
-  val!10 val!33 -> 68
-  val!8 val!33 -> 72
-  val!21 val!32 -> 73
-  val!20 val!32 -> 69
-  val!21 val!34 -> 74
-  val!20 val!34 -> 70
-  val!21 val!33 -> 72
-  val!20 val!33 -> 68
-  val!10 val!31 -> 67
-  val!8 val!31 -> 71
-  val!21 val!31 -> 71
-  val!20 val!31 -> 67
-  val!10 val!32 -> 69
-  val!8 val!32 -> 73
-  val!13 val!31 -> 71
-  val!13 val!33 -> 72
-  val!13 val!32 -> 73
-  val!13 val!34 -> 74
-  val!14 val!31 -> 67
-  val!14 val!33 -> 68
-  val!14 val!32 -> 69
-  val!14 val!34 -> 70
-  val!10 val!37 -> 98
-  val!8 val!37 -> 102
-  val!21 val!37 -> 103
-  val!20 val!37 -> 97
-  val!21 val!35 -> 104
-  val!20 val!35 -> 99
-  val!10 val!35 -> 99
-  val!8 val!35 -> 104
-  val!21 val!38 -> 100
-  val!20 val!38 -> 95
-  val!21 val!36 -> 101
-  val!20 val!36 -> 31
-  val!8 val!36 -> 30
-  val!10 val!38 -> 95
-  val!8 val!38 -> 100
-  val!13 val!38 -> 100
-  val!13 val!37 -> 102
-  val!13 val!35 -> 104
-  val!14 val!38 -> 95
-  val!14 val!36 -> 96
-  val!14 val!37 -> 98
-  val!14 val!35 -> 99
-  val!10 val!39 -> 125
-  val!8 val!39 -> 128
-  val!10 val!41 -> 127
-  val!8 val!41 -> 130
-  val!21 val!39 -> 128
-  val!20 val!39 -> 125
-  val!21 val!41 -> 130
-  val!20 val!41 -> 127
-  val!21 val!40 -> 131
-  val!20 val!40 -> 32
-  val!8 val!40 -> 131
-  val!13 val!39 -> 128
-  val!13 val!41 -> 130
-  val!13 val!40 -> 131
-  val!14 val!39 -> 125
-  val!14 val!41 -> 127
-  val!14 val!40 -> 32
-  val!10 val!48 -> 153
-  val!8 val!48 -> 159
-  val!8 val!42 -> 158
-  val!10 val!42 -> 152
-  val!21 val!43 -> 161
-  val!20 val!43 -> 154
-  val!21 val!48 -> 159
-  val!20 val!48 -> 153
-  val!10 val!43 -> 155
-  val!8 val!43 -> 160
-  val!10 val!46 -> 157
-  val!8 val!46 -> 163
-  val!21 val!46 -> 163
-  val!20 val!46 -> 157
-  val!20 val!42 -> 152
-  val!21 val!42 -> 158
-  val!13 val!42 -> 158
-  val!13 val!48 -> 159
-  val!13 val!43 -> 160
-  val!13 val!46 -> 163
-  val!14 val!42 -> 152
-  val!14 val!48 -> 153
-  val!14 val!43 -> 155
-  val!14 val!46 -> 157
-  val!21 val!44 -> 129
-  val!20 val!44 -> 126
-  val!10 val!44 -> 126
-  val!8 val!44 -> 129
-  val!20 val!47 -> 186
-  val!21 val!47 -> 189
-  val!10 val!47 -> 186
-  val!8 val!47 -> 189
-  val!21 val!50 -> 188
-  val!20 val!50 -> 184
-  val!10 val!50 -> 185
-  val!8 val!50 -> 187
-  val!13 val!44 -> 129
-  val!13 val!50 -> 187
-  val!13 val!47 -> 189
-  val!14 val!44 -> 126
-  val!14 val!50 -> 185
-  val!14 val!47 -> 186
-  val!10 val!45 -> 156
-  val!8 val!45 -> 162
-  val!10 val!49 -> 207
-  val!8 val!49 -> 208
-  val!21 val!45 -> 162
-  val!20 val!45 -> 156
-  val!21 val!49 -> 209
-  val!20 val!49 -> 206
-  val!13 val!45 -> 162
-  val!13 val!49 -> 208
-  val!14 val!45 -> 156
-  val!14 val!49 -> 207
-  else -> 207
-}
-f8 -> {
-  val!18 val!1 -> 2
-  val!19 val!1 -> 4
-  val!17 val!1 -> 3
-  val!19 val!3 -> 7
-  val!17 val!3 -> 8
-  val!18 val!3 -> 5
-  val!16 val!3 -> 6
-  val!23 val!27 -> 0
-  val!9 val!27 -> -1
-  val!11 val!27 -> 1
-  val!24 val!27 -> 1
-  val!22 val!27 -> -1
-  val!23 val!2 -> 0
-  val!9 val!2 -> -1
-  val!11 val!2 -> 1
-  val!24 val!2 -> 1
-  val!22 val!2 -> -1
-  val!23 val!4 -> 0
-  val!9 val!4 -> -1
-  val!11 val!4 -> 1
-  val!24 val!4 -> 1
-  val!22 val!4 -> -1
-  val!23 val!5 -> 0
-  val!9 val!5 -> -1
-  val!11 val!5 -> 1
-  val!24 val!5 -> 1
-  val!22 val!5 -> -1
-  val!22 val!1 -> -1
-  val!9 val!3 -> -1
-  val!24 val!1 -> 1
-  val!11 val!3 -> 1
-  val!23 val!30 -> 0
-  val!9 val!30 -> -1
-  val!11 val!30 -> 1
-  val!24 val!30 -> 1
-  val!22 val!30 -> -1
-  val!16 val!30 -> 29
-  val!16 val!36 -> 31
-  val!16 val!40 -> 32
-  val!9 val!1 -> -1
-  val!11 val!1 -> 1
-  val!22 val!3 -> -1
-  val!24 val!3 -> 1
-  val!17 val!2 -> 33
-  val!17 val!5 -> 34
-  val!17 val!27 -> 35
-  val!17 val!4 -> 36
-  val!17 val!30 -> 37
-  val!19 val!2 -> 38
-  val!19 val!5 -> 39
-  val!19 val!27 -> 40
-  val!19 val!4 -> 41
-  val!18 val!30 -> 43
-  val!19 val!30 -> 42
-  val!23 val!3 -> 0
-  val!23 val!1 -> 0
-  val!23 val!31 -> 0
-  val!9 val!31 -> -1
-  val!11 val!31 -> 1
-  val!24 val!31 -> 1
-  val!22 val!31 -> -1
-  val!23 val!33 -> 0
-  val!9 val!33 -> -1
-  val!11 val!33 -> 1
-  val!24 val!33 -> 1
-  val!22 val!33 -> -1
-  val!23 val!32 -> 0
-  val!9 val!32 -> -1
-  val!11 val!32 -> 1
-  val!24 val!32 -> 1
-  val!22 val!32 -> -1
-  val!23 val!34 -> 0
-  val!9 val!34 -> -1
-  val!11 val!34 -> 1
-  val!24 val!34 -> 1
-  val!22 val!34 -> -1
-  val!17 val!31 -> 67
-  val!17 val!33 -> 68
-  val!17 val!32 -> 69
-  val!17 val!34 -> 70
-  val!19 val!31 -> 71
-  val!19 val!33 -> 72
-  val!19 val!32 -> 73
-  val!19 val!34 -> 74
-  val!23 val!37 -> 0
-  val!9 val!37 -> -1
-  val!11 val!37 -> 1
-  val!24 val!37 -> 1
-  val!22 val!37 -> -1
-  val!23 val!38 -> 0
-  val!9 val!38 -> -1
-  val!11 val!38 -> 1
-  val!24 val!38 -> 1
-  val!22 val!38 -> -1
-  val!23 val!35 -> 0
-  val!9 val!35 -> -1
-  val!11 val!35 -> 1
-  val!24 val!35 -> 1
-  val!22 val!35 -> -1
-  val!23 val!36 -> 0
-  val!9 val!36 -> -1
-  val!11 val!36 -> 1
-  val!24 val!36 -> 1
-  val!22 val!36 -> -1
-  val!17 val!38 -> 95
-  val!17 val!36 -> 96
-  val!16 val!37 -> 97
-  val!17 val!37 -> 98
-  val!17 val!35 -> 99
-  val!19 val!38 -> 100
-  val!18 val!36 -> 101
-  val!19 val!36 -> 30
-  val!18 val!37 -> 103
-  val!19 val!37 -> 102
-  val!19 val!35 -> 104
-  val!23 val!39 -> 0
-  val!9 val!39 -> -1
-  val!11 val!39 -> 1
-  val!24 val!39 -> 1
-  val!22 val!39 -> -1
-  val!23 val!41 -> 0
-  val!9 val!41 -> -1
-  val!11 val!41 -> 1
-  val!24 val!41 -> 1
-  val!22 val!41 -> -1
-  val!23 val!40 -> 0
-  val!9 val!40 -> -1
-  val!11 val!40 -> 1
-  val!24 val!40 -> 1
-  val!22 val!40 -> -1
-  val!17 val!39 -> 125
-  val!17 val!41 -> 127
-  val!19 val!39 -> 128
-  val!19 val!41 -> 130
-  val!18 val!40 -> 131
-  val!23 val!48 -> 0
-  val!9 val!48 -> -1
-  val!11 val!48 -> 1
-  val!24 val!48 -> 1
-  val!22 val!48 -> -1
-  val!23 val!46 -> 0
-  val!9 val!46 -> -1
-  val!11 val!46 -> 1
-  val!24 val!46 -> 1
-  val!22 val!46 -> -1
-  val!23 val!42 -> 0
-  val!11 val!42 -> 1
-  val!9 val!42 -> -1
-  val!22 val!42 -> -1
-  val!24 val!42 -> 1
-  val!23 val!43 -> 0
-  val!9 val!43 -> -1
-  val!11 val!43 -> 1
-  val!24 val!43 -> 1
-  val!22 val!43 -> -1
-  val!17 val!42 -> 152
-  val!17 val!48 -> 153
-  val!16 val!43 -> 154
-  val!17 val!43 -> 155
-  val!17 val!46 -> 157
-  val!19 val!42 -> 158
-  val!19 val!48 -> 159
-  val!18 val!43 -> 161
-  val!19 val!43 -> 160
-  val!19 val!46 -> 163
-  val!23 val!50 -> 0
-  val!9 val!50 -> -1
-  val!11 val!50 -> 1
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-  val!22 val!47 -> -1
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-  val!17 val!44 -> 126
-  val!16 val!50 -> 184
-  val!17 val!50 -> 185
-  val!17 val!47 -> 186
-  val!19 val!44 -> 129
-  val!18 val!50 -> 188
-  val!19 val!50 -> 187
-  val!19 val!47 -> 189
-  val!23 val!45 -> 0
-  val!9 val!45 -> -1
-  val!11 val!45 -> 1
-  val!24 val!45 -> 1
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-  val!22 val!49 -> -1
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-  val!16 val!49 -> 206
-  val!17 val!49 -> 207
-  val!19 val!45 -> 162
-  val!18 val!49 -> 209
-  val!19 val!49 -> 208
-  else -> 208
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-  val!5 val!26 -> val!54
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-  val!34 val!26 -> val!56
-  val!33 val!26 -> val!57
-  val!32 val!26 -> val!58
-  val!31 val!26 -> val!59
-  val!37 val!26 -> val!60
-  val!35 val!26 -> val!61
-  val!38 val!26 -> val!62
-  val!36 val!26 -> val!63
-  val!39 val!26 -> val!64
-  val!41 val!26 -> val!65
-  val!40 val!26 -> val!67
-  val!48 val!26 -> val!68
-  val!42 val!26 -> val!69
-  val!43 val!26 -> val!71
-  val!46 val!26 -> val!72
-  val!44 val!26 -> val!66
-  val!47 val!26 -> val!73
-  val!50 val!26 -> val!74
-  val!45 val!26 -> val!70
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-}
-unknown
-68b48c983404c9f923b5c2c801b81a1ebfa54f09 60 0
-f1 -> val!0
-f2 -> val!1
-f7 -> val!3
-f8 -> val!5
-f12 -> val!13
-f11 -> val!6
-f17 -> val!8
-f18 -> val!9
-f16 -> val!10
-f20 -> val!11
-f14 -> val!12
-f6 -> {
-  val!3 -> val!2
-  val!5 -> val!4
-  else -> val!4
-}
-f5 -> {
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-  val!4 -> val!5
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-}
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-  val!14 -> 1
-  val!3 -> 3
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-}
-f3 -> {
-  1 -> val!14
-  2 -> val!5
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-  3 -> val!3
-  0 -> val!17
-  1236 -> val!4
-  else -> val!4
-}
-f10 -> {
-  val!6 val!13 -> val!7
-  else -> val!7
-}
-f13 -> {
-  val!12 -> val!17
-  else -> val!17
-}
-f9 -> {
-  val!3 val!7 -> val!15
-  val!5 val!7 -> val!16
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-}
-f15 -> {
-  val!9 val!2 -> 0
-  val!8 val!2 -> -1
-  val!10 val!2 -> 1
-  val!11 val!2 -> 1
-  else -> 1
-}
-unknown
-2cf0827cf5826be278dbca8a4dccba886e2b01ef 611 0
-f1 -> val!7
-f2 -> val!0
-f16 -> val!2
-f7 -> val!4
-f24 -> val!31
-f29 -> val!16
-f18 -> val!8
-f4 -> val!10
-f13 -> val!12
-f17 -> val!14
-f12 -> val!18
-f9 -> val!19
-f14 -> val!20
-f10 -> val!21
-f15 -> val!22
-f19 -> val!23
-f23 -> val!24
-f28 -> val!27
-f26 -> val!29
-f11 -> {
-  val!2 -> val!1
-  val!4 -> val!3
-  else -> val!3
-}
-f6 -> {
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-  val!3 -> val!4
-  val!36 -> val!40
-  val!31 -> val!41
-  val!5 -> val!37
-  val!2 -> val!38
-  val!4 -> val!39
-  val!37 -> val!43
-  val!38 -> val!54
-  val!39 -> val!44
-  val!40 -> val!45
-  val!41 -> val!42
-  val!43 -> val!47
-  val!44 -> val!46
-  val!45 -> val!56
-  val!42 -> val!51
-  val!46 -> val!53
-  val!47 -> val!48
-  val!48 -> val!49
-  val!49 -> val!50
-  val!50 -> val!49
-  val!51 -> val!52
-  val!54 -> val!59
-  val!53 -> val!55
-  val!57 -> val!54
-  val!55 -> val!2
-  val!56 -> val!58
-  val!52 -> val!57
-  val!58 -> val!54
-  val!59 -> val!60
-  val!60 -> val!86
-  val!86 -> val!2
-  else -> val!2
-}
-f20 -> {
-  1 -> val!5
-  7720 -> val!36
-  7719 -> val!31
-  31267 -> val!2
-  36564 -> val!4
-  8366 -> val!37
-  9246 -> val!38
-  8852 -> val!39
-  0 -> val!40
-  2944 -> val!41
-  26221 -> val!42
-  29498 -> val!43
-  15353 -> val!44
-  6996 -> val!45
-  2997 -> val!46
-  9245 -> val!47
-  19679 -> val!49
-  45859 -> val!50
-  9531 -> val!51
-  24738 -> val!52
-  30204 -> val!57
-  9247 -> val!53
-  23570 -> val!55
-  26809 -> val!56
-  23086 -> val!58
-  5529 -> val!59
-  36563 -> val!60
-  36565 -> val!48
-  27246 -> val!86
-  31266 -> val!54
-  else -> val!54
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-f22 -> {
-  val!5 val!31 -> val!6
-  val!5 val!36 -> val!17
-  val!24 val!31 -> val!25
-  else -> val!25
-}
-f21 -> {
-  val!2 val!6 -> val!7
-  val!4 val!6 -> val!7
-  val!4 val!17 -> val!7
-  val!2 val!25 -> val!32
-  val!4 val!25 -> val!33
-  else -> val!33
-}
-f27 -> {
-  val!8 -> val!9
-  val!10 -> val!11
-  val!12 -> val!13
-  val!14 -> val!15
-  val!23 -> val!26
-  val!22 -> val!28
-  else -> val!28
-}
-f30 -> {
-  val!13 val!15 -> val!16
-  else -> val!16
-}
-f5 -> {
-  val!31 -> 7719
-  val!2 -> 31267
-  val!4 -> 36564
-  val!5 -> 1
-  val!36 -> 7720
-  val!40 -> 0
-  val!41 -> 2944
-  val!37 -> 8366
-  val!38 -> 9246
-  val!39 -> 8852
-  val!44 -> 15353
-  val!43 -> 29498
-  val!42 -> 26221
-  val!45 -> 6996
-  val!46 -> 2997
-  val!56 -> 26809
-  val!51 -> 9531
-  val!53 -> 9247
-  val!47 -> 9245
-  val!48 -> 36565
-  val!49 -> 19679
-  val!50 -> 45859
-  val!52 -> 24738
-  val!59 -> 5529
-  val!55 -> 23570
-  val!54 -> 31266
-  val!58 -> 23086
-  val!57 -> 30204
-  val!60 -> 36563
-  val!86 -> 27246
-  else -> 27246
-}
-f25 -> {
-  val!29 -> val!30
-  else -> val!30
-}
-f3 -> {
-  val!23 val!1 -> 2
-  val!8 val!1 -> 4
-  val!14 val!1 -> 3
-  val!22 val!1 -> 4
-  val!10 val!1 -> 3
-  val!12 val!1 -> 4
-  val!23 val!3 -> 5
-  val!8 val!3 -> 5
-  val!14 val!3 -> 6
-  val!22 val!3 -> 6
-  val!10 val!3 -> 7
-  val!12 val!3 -> 8
-  val!22 val!31 -> 32
-  val!22 val!37 -> 62
-  val!22 val!40 -> 60
-  val!22 val!43 -> 88
-  val!10 val!5 -> 30
-  val!8 val!5 -> 35
-  val!22 val!60 -> 150
-  val!23 val!36 -> 37
-  val!22 val!36 -> 31
-  val!23 val!31 -> 36
-  val!10 val!2 -> 28
-  val!8 val!2 -> 33
-  val!23 val!5 -> 35
-  val!22 val!5 -> 30
-  val!10 val!31 -> 32
-  val!8 val!31 -> 36
-  val!23 val!2 -> 33
-  val!22 val!2 -> 28
-  val!10 val!4 -> 29
-  val!8 val!4 -> 34
-  val!23 val!4 -> 34
-  val!22 val!4 -> 29
-  val!10 val!36 -> 31
-  val!8 val!36 -> 37
-  val!12 val!2 -> 33
-  val!12 val!4 -> 34
-  val!12 val!5 -> 35
-  val!12 val!31 -> 36
-  val!12 val!36 -> 37
-  val!14 val!2 -> 28
-  val!14 val!4 -> 29
-  val!14 val!5 -> 30
-  val!14 val!31 -> 32
-  val!14 val!36 -> 31
-  val!10 val!38 -> 59
-  val!8 val!38 -> 64
-  val!23 val!38 -> 64
-  val!22 val!38 -> 59
-  val!10 val!39 -> 58
-  val!8 val!39 -> 63
-  val!10 val!37 -> 62
-  val!8 val!37 -> 67
-  val!23 val!39 -> 63
-  val!22 val!39 -> 58
-  val!10 val!40 -> 60
-  val!8 val!40 -> 65
-  val!23 val!40 -> 65
-  val!23 val!41 -> 66
-  val!22 val!41 -> 61
-  val!23 val!37 -> 67
-  val!10 val!41 -> 61
-  val!8 val!41 -> 66
-  val!12 val!39 -> 63
-  val!12 val!38 -> 64
-  val!12 val!40 -> 65
-  val!12 val!41 -> 66
-  val!12 val!37 -> 67
-  val!14 val!39 -> 58
-  val!14 val!38 -> 59
-  val!14 val!40 -> 60
-  val!14 val!41 -> 61
-  val!14 val!37 -> 62
-  val!10 val!42 -> 89
-  val!8 val!42 -> 93
-  val!23 val!54 -> 94
-  val!22 val!54 -> 90
-  val!10 val!43 -> 88
-  val!8 val!43 -> 92
-  val!23 val!43 -> 92
-  val!23 val!42 -> 93
-  val!22 val!42 -> 89
-  val!23 val!44 -> 95
-  val!22 val!44 -> 91
-  val!10 val!44 -> 91
-  val!8 val!44 -> 95
-  val!10 val!54 -> 90
-  val!8 val!54 -> 94
-  val!23 val!45 -> 107
-  val!22 val!45 -> 106
-  val!10 val!45 -> 106
-  val!8 val!45 -> 107
-  val!12 val!43 -> 92
-  val!12 val!42 -> 93
-  val!12 val!54 -> 94
-  val!12 val!44 -> 95
-  val!14 val!43 -> 88
-  val!14 val!42 -> 89
-  val!14 val!54 -> 90
-  val!14 val!44 -> 91
-  val!12 val!45 -> 107
-  val!14 val!45 -> 106
-  val!10 val!46 -> 118
-  val!8 val!46 -> 122
-  val!23 val!46 -> 122
-  val!22 val!46 -> 118
-  val!23 val!47 -> 123
-  val!22 val!47 -> 127
-  val!8 val!59 -> 126
-  val!10 val!59 -> 120
-  val!23 val!59 -> 125
-  val!22 val!59 -> 119
-  val!10 val!47 -> 127
-  val!8 val!47 -> 123
-  val!10 val!51 -> 116
-  val!8 val!51 -> 124
-  val!23 val!51 -> 124
-  val!22 val!51 -> 116
-  val!23 val!56 -> 121
-  val!22 val!56 -> 117
-  val!10 val!56 -> 117
-  val!8 val!56 -> 121
-  val!12 val!56 -> 121
-  val!12 val!46 -> 122
-  val!12 val!47 -> 123
-  val!12 val!51 -> 124
-  val!12 val!59 -> 126
-  val!14 val!56 -> 117
-  val!14 val!46 -> 118
-  val!14 val!47 -> 127
-  val!14 val!51 -> 116
-  val!14 val!59 -> 120
-  val!23 val!58 -> 153
-  val!22 val!58 -> 148
-  val!10 val!53 -> 151
-  val!8 val!53 -> 156
-  val!23 val!53 -> 156
-  val!22 val!53 -> 151
-  val!10 val!48 -> 149
-  val!8 val!48 -> 154
-  val!23 val!48 -> 154
-  val!22 val!48 -> 149
-  val!23 val!52 -> 157
-  val!22 val!52 -> 152
-  val!10 val!58 -> 148
-  val!8 val!58 -> 153
-  val!10 val!60 -> 150
-  val!8 val!60 -> 155
-  val!10 val!52 -> 152
-  val!8 val!52 -> 157
-  val!23 val!60 -> 155
-  val!12 val!58 -> 153
-  val!12 val!48 -> 154
-  val!12 val!60 -> 155
-  val!12 val!53 -> 156
-  val!12 val!52 -> 157
-  val!14 val!58 -> 148
-  val!14 val!48 -> 149
-  val!14 val!60 -> 150
-  val!14 val!53 -> 151
-  val!14 val!52 -> 152
-  val!23 val!49 -> 186
-  val!22 val!49 -> 187
-  val!10 val!55 -> 179
-  val!8 val!55 -> 182
-  val!23 val!55 -> 178
-  val!22 val!55 -> 4
-  val!10 val!86 -> 181
-  val!8 val!86 -> 184
-  val!23 val!86 -> 185
-  val!22 val!86 -> 4
-  val!23 val!57 -> 183
-  val!22 val!57 -> 180
-  val!10 val!49 -> 187
-  val!8 val!49 -> 186
-  val!8 val!57 -> 183
-  val!10 val!57 -> 180
-  val!12 val!55 -> 182
-  val!12 val!57 -> 183
-  val!12 val!86 -> 184
-  val!12 val!49 -> 186
-  val!14 val!55 -> 179
-  val!14 val!57 -> 180
-  val!14 val!86 -> 181
-  val!14 val!49 -> 187
-  val!23 val!50 -> 205
-  val!22 val!50 -> 204
-  val!10 val!50 -> 204
-  val!8 val!50 -> 205
-  val!12 val!50 -> 205
-  val!14 val!50 -> 204
-  else -> 204
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-f8 -> {
-  val!20 val!1 -> 2
-  val!21 val!1 -> 4
-  val!19 val!1 -> 3
-  val!21 val!3 -> 7
-  val!19 val!3 -> 8
-  val!20 val!3 -> 5
-  val!18 val!3 -> 6
-  val!27 val!31 -> 0
-  val!9 val!31 -> -1
-  val!11 val!31 -> 1
-  val!28 val!31 -> 1
-  val!26 val!31 -> -1
-  val!27 val!2 -> 0
-  val!9 val!2 -> -1
-  val!11 val!2 -> 1
-  val!28 val!2 -> 1
-  val!26 val!2 -> -1
-  val!27 val!4 -> 0
-  val!9 val!4 -> -1
-  val!11 val!4 -> 1
-  val!28 val!4 -> 1
-  val!26 val!4 -> -1
-  val!27 val!5 -> 0
-  val!9 val!5 -> -1
-  val!11 val!5 -> 1
-  val!28 val!5 -> 1
-  val!26 val!5 -> -1
-  val!9 val!36 -> -1
-  val!27 val!36 -> 0
-  val!11 val!36 -> 1
-  val!28 val!36 -> 1
-  val!26 val!36 -> -1
-  val!19 val!2 -> 28
-  val!19 val!4 -> 29
-  val!19 val!5 -> 30
-  val!19 val!36 -> 31
-  val!19 val!31 -> 32
-  val!21 val!2 -> 33
-  val!21 val!4 -> 34
-  val!21 val!5 -> 35
-  val!21 val!31 -> 36
-  val!21 val!36 -> 37
-  val!27 val!38 -> 0
-  val!9 val!38 -> -1
-  val!11 val!38 -> 1
-  val!28 val!38 -> 1
-  val!26 val!38 -> -1
-  val!27 val!39 -> 0
-  val!9 val!39 -> -1
-  val!11 val!39 -> 1
-  val!28 val!39 -> 1
-  val!26 val!39 -> -1
-  val!27 val!37 -> 0
-  val!9 val!37 -> -1
-  val!11 val!37 -> 1
-  val!28 val!37 -> 1
-  val!26 val!37 -> -1
-  val!27 val!40 -> 0
-  val!9 val!40 -> -1
-  val!11 val!40 -> 1
-  val!28 val!40 -> 1
-  val!26 val!40 -> -1
-  val!27 val!41 -> 0
-  val!9 val!41 -> -1
-  val!11 val!41 -> 1
-  val!28 val!41 -> 1
-  val!26 val!41 -> -1
-  val!19 val!39 -> 58
-  val!19 val!38 -> 59
-  val!19 val!40 -> 60
-  val!19 val!41 -> 61
-  val!19 val!37 -> 62
-  val!21 val!39 -> 63
-  val!21 val!38 -> 64
-  val!21 val!40 -> 65
-  val!21 val!41 -> 66
-  val!21 val!37 -> 67
-  val!27 val!44 -> 0
-  val!9 val!44 -> -1
-  val!11 val!44 -> 1
-  val!28 val!44 -> 1
-  val!26 val!44 -> -1
-  val!27 val!45 -> 0
-  val!9 val!45 -> -1
-  val!11 val!45 -> 1
-  val!28 val!45 -> 1
-  val!26 val!45 -> -1
-  val!27 val!42 -> 0
-  val!9 val!42 -> -1
-  val!11 val!42 -> 1
-  val!28 val!42 -> 1
-  val!26 val!42 -> -1
-  val!27 val!43 -> 0
-  val!9 val!43 -> -1
-  val!11 val!43 -> 1
-  val!28 val!43 -> 1
-  val!26 val!43 -> -1
-  val!19 val!43 -> 88
-  val!19 val!42 -> 89
-  val!19 val!54 -> 90
-  val!19 val!44 -> 91
-  val!21 val!43 -> 92
-  val!21 val!42 -> 93
-  val!21 val!54 -> 94
-  val!21 val!44 -> 95
-  val!27 val!47 -> 0
-  val!9 val!47 -> -1
-  val!11 val!47 -> 1
-  val!28 val!47 -> 1
-  val!26 val!47 -> -1
-  val!27 val!59 -> 0
-  val!11 val!59 -> 1
-  val!9 val!59 -> -1
-  val!28 val!59 -> 1
-  val!26 val!59 -> -1
-  val!27 val!46 -> 0
-  val!9 val!46 -> -1
-  val!11 val!46 -> 1
-  val!28 val!46 -> 1
-  val!26 val!46 -> -1
-  val!19 val!45 -> 106
-  val!21 val!45 -> 107
-  val!27 val!51 -> 0
-  val!9 val!51 -> -1
-  val!11 val!51 -> 1
-  val!28 val!51 -> 1
-  val!26 val!51 -> -1
-  val!27 val!56 -> 0
-  val!9 val!56 -> -1
-  val!11 val!56 -> 1
-  val!28 val!56 -> 1
-  val!26 val!56 -> -1
-  val!19 val!56 -> 117
-  val!19 val!46 -> 118
-  val!18 val!47 -> 127
-  val!19 val!51 -> 116
-  val!18 val!59 -> 119
-  val!19 val!59 -> 120
-  val!21 val!56 -> 121
-  val!21 val!46 -> 122
-  val!20 val!47 -> 123
-  val!21 val!51 -> 124
-  val!20 val!59 -> 125
-  val!21 val!59 -> 126
-  val!27 val!58 -> 0
-  val!9 val!58 -> -1
-  val!11 val!58 -> 1
-  val!28 val!58 -> 1
-  val!26 val!58 -> -1
-  val!27 val!53 -> 0
-  val!9 val!53 -> -1
-  val!11 val!53 -> 1
-  val!28 val!53 -> 1
-  val!26 val!53 -> -1
-  val!27 val!48 -> 0
-  val!9 val!48 -> -1
-  val!11 val!48 -> 1
-  val!28 val!48 -> 1
-  val!26 val!48 -> -1
-  val!27 val!52 -> 0
-  val!9 val!52 -> -1
-  val!11 val!52 -> 1
-  val!28 val!52 -> 1
-  val!26 val!52 -> -1
-  val!27 val!60 -> 0
-  val!9 val!60 -> -1
-  val!11 val!60 -> 1
-  val!26 val!60 -> -1
-  val!28 val!60 -> 1
-  val!19 val!58 -> 148
-  val!19 val!48 -> 149
-  val!19 val!60 -> 150
-  val!19 val!53 -> 151
-  val!19 val!52 -> 152
-  val!21 val!58 -> 153
-  val!21 val!48 -> 154
-  val!21 val!60 -> 155
-  val!21 val!53 -> 156
-  val!21 val!52 -> 157
-  val!27 val!49 -> 0
-  val!9 val!49 -> -1
-  val!11 val!49 -> 1
-  val!28 val!49 -> 1
-  val!26 val!49 -> -1
-  val!27 val!86 -> 0
-  val!9 val!86 -> -1
-  val!11 val!86 -> 1
-  val!28 val!86 -> 1
-  val!26 val!86 -> -1
-  val!27 val!55 -> 0
-  val!9 val!55 -> -1
-  val!11 val!55 -> 1
-  val!28 val!55 -> 1
-  val!26 val!55 -> -1
-  val!27 val!57 -> 0
-  val!11 val!57 -> 1
-  val!9 val!57 -> -1
-  val!28 val!57 -> 1
-  val!26 val!57 -> -1
-  val!19 val!55 -> 179
-  val!19 val!57 -> 180
-  val!19 val!86 -> 181
-  val!18 val!49 -> 187
-  val!20 val!55 -> 178
-  val!21 val!55 -> 182
-  val!21 val!57 -> 183
-  val!20 val!86 -> 185
-  val!21 val!86 -> 184
-  val!20 val!49 -> 186
-  val!27 val!50 -> 0
-  val!9 val!50 -> -1
-  val!11 val!50 -> 1
-  val!28 val!50 -> 1
-  val!26 val!50 -> -1
-  val!27 val!54 -> 0
-  val!9 val!54 -> -1
-  val!11 val!54 -> 1
-  val!28 val!54 -> 1
-  val!26 val!54 -> -1
-  val!19 val!50 -> 204
-  val!21 val!50 -> 205
-  else -> 205
-}
-f31 -> {
-  val!1 val!30 -> val!34
-  val!3 val!30 -> val!35
-  val!5 val!30 -> val!61
-  val!36 val!30 -> val!62
-  val!31 val!30 -> val!63
-  val!2 val!30 -> val!64
-  val!4 val!30 -> val!65
-  val!38 val!30 -> val!66
-  val!39 val!30 -> val!67
-  val!37 val!30 -> val!68
-  val!40 val!30 -> val!69
-  val!41 val!30 -> val!70
-  val!42 val!30 -> val!71
-  val!54 val!30 -> val!72
-  val!43 val!30 -> val!73
-  val!44 val!30 -> val!74
-  val!45 val!30 -> val!75
-  val!46 val!30 -> val!76
-  val!47 val!30 -> val!77
-  val!59 val!30 -> val!78
-  val!51 val!30 -> val!79
-  val!56 val!30 -> val!80
-  val!58 val!30 -> val!81
-  val!53 val!30 -> val!82
-  val!48 val!30 -> val!83
-  val!52 val!30 -> val!84
-  val!60 val!30 -> val!85
-  val!49 val!30 -> val!87
-  val!55 val!30 -> val!88
-  val!86 val!30 -> val!89
-  val!57 val!30 -> val!90
-  val!50 val!30 -> val!91
-  else -> val!91
-}
-unknown
-a1ff1dee861d393a5412b6a4273eb86deab7593f 77 0
-f1 -> val!0
-f2 -> val!1
-f7 -> val!3
-f8 -> val!5
-f14 -> val!6
-f11 -> val!7
-f12 -> val!8
-f17 -> val!10
-f18 -> val!11
-f16 -> val!12
-f20 -> val!13
-f19 -> val!14
-f6 -> {
-  val!3 -> val!2
-  val!5 -> val!4
-  else -> val!4
-}
-f5 -> {
-  val!2 -> val!3
-  val!4 -> val!5
-  val!16 -> val!19
-  val!5 -> val!16
-  val!19 -> val!16
-  val!3 -> val!16
-  else -> val!16
-}
-f13 -> {
-  val!6 -> val!15
-  else -> val!15
-}
-f4 -> {
-  val!15 -> 40
-  val!5 -> 2
-  val!16 -> 1
-  val!3 -> 3
-  val!4 -> 1276
-  val!19 -> 0
-  else -> 0
-}
-f3 -> {
-  1 -> val!16
-  40 -> val!15
-  2 -> val!5
-  3 -> val!3
-  0 -> val!19
-  1276 -> val!4
-  else -> val!4
-}
-f10 -> {
-  val!7 val!8 -> val!9
-  else -> val!9
-}
-f9 -> {
-  val!3 val!9 -> val!17
-  val!5 val!9 -> val!18
-  else -> val!18
-}
-f15 -> {
-  val!11 val!2 -> 0
-  val!10 val!2 -> -1
-  val!12 val!2 -> 1
-  val!13 val!2 -> 1
-  val!11 val!16 -> 0
-  val!12 val!16 -> -1
-  val!14 val!16 -> 1
-  val!11 val!3 -> 0
-  val!12 val!3 -> -1
-  val!14 val!3 -> 1
-  val!11 val!5 -> 0
-  val!12 val!5 -> -1
-  val!14 val!5 -> 1
-  val!11 val!19 -> 0
-  val!12 val!19 -> -1
-  val!14 val!19 -> 1
-  else -> 1
-}
-unknown
-26a56d9f61c23c26da64882e31e65a36923764cb 72 0
-f1 -> val!0
-f2 -> val!1
-f7 -> val!3
-f8 -> val!5
-f12 -> val!13
-f11 -> val!6
-f17 -> val!8
-f18 -> val!9
-f16 -> val!10
-f20 -> val!11
-f19 -> val!12
-f6 -> {
-  val!3 -> val!2
-  val!5 -> val!4
-  else -> val!4
-}
-f5 -> {
-  val!2 -> val!3
-  val!4 -> val!5
-  val!3 -> val!17
-  val!14 -> val!14
-  val!5 -> val!14
-  val!17 -> val!14
-  else -> val!14
-}
-f4 -> {
-  val!13 -> 40
-  val!5 -> 2
-  val!14 -> 1
-  val!3 -> 3
-  val!4 -> 1276
-  val!17 -> 0
-  else -> 0
-}
-f3 -> {
-  1 -> val!14
-  40 -> val!13
-  2 -> val!5
-  3 -> val!3
-  1276 -> val!4
-  0 -> val!17
-  else -> val!17
-}
-f10 -> {
-  val!6 val!13 -> val!7
-  else -> val!7
-}
-f9 -> {
-  val!3 val!7 -> val!15
-  val!5 val!7 -> val!16
-  else -> val!16
-}
-f15 -> {
-  val!9 val!2 -> 0
-  val!8 val!2 -> -1
-  val!10 val!2 -> 1
-  val!11 val!2 -> 1
-  val!9 val!3 -> 0
-  val!10 val!3 -> -1
-  val!12 val!3 -> 1
-  val!9 val!14 -> 0
-  val!10 val!14 -> -1
-  val!12 val!14 -> 1
-  val!9 val!5 -> 0
-  val!10 val!5 -> -1
-  val!12 val!5 -> 1
-  val!9 val!17 -> 0
-  val!10 val!17 -> -1
-  val!12 val!17 -> 1
-  else -> 1
-}
-unknown
-a4a52206bfedbc1fa95069df86dc718ab11f5b3a 59 0
-f1 -> val!0
-f2 -> val!1
-f7 -> val!3
-f8 -> val!5
-f17 -> val!6
-f20 -> val!7
-f19 -> val!8
-f18 -> val!9
-f16 -> val!10
-f14 -> val!11
-f11 -> val!12
-f12 -> val!13
-f6 -> {
-  val!3 -> val!2
-  val!5 -> val!4
-  else -> val!4
-}
-f5 -> {
-  val!2 -> val!3
-  val!4 -> val!5
-  else -> val!5
-}
-f15 -> {
-  val!6 val!2 -> 0
-  val!7 val!2 -> 1
-  val!8 val!2 -> -1
-  val!6 val!4 -> 0
-  val!9 val!4 -> 1
-  val!10 val!4 -> -1
-  else -> -1
-}
-f4 -> {
-  val!3 -> 1237
-  val!5 -> 1238
-  val!15 -> 8957
-  val!16 -> 1
-  else -> 1
-}
-f13 -> {
-  val!11 -> val!15
-  else -> val!15
-}
-f3 -> {
-  1 -> val!16
-  1237 -> val!3
-  1238 -> val!5
-  8957 -> val!15
-  else -> val!15
-}
-f10 -> {
-  val!12 val!13 -> val!14
-  else -> val!14
-}
-f9 -> {
-  val!3 val!14 -> val!17
-  val!5 val!14 -> val!18
-  else -> val!18
-}
-unknown
-14333af854a5b65017dd8bd92066cf80fe83d74b 43 0
-f1 -> val!0
-f2 -> val!1
-f15 -> val!2
-f6 -> val!9
-f12 -> val!3
-f16 -> val!4
-f5 -> val!9
-f13 -> val!5
-f10 -> val!7
-f8 -> val!8
-f11 -> {
-  val!9 -> val!6
-  else -> val!6
-}
-f9 -> {
-  val!5 val!6 -> 1
-  val!3 val!6 -> 0
-  val!4 val!6 -> 1
-  val!2 val!6 -> -1
-  val!7 val!6 -> -1
-  else -> -1
-}
-f4 -> {
-  val!9 -> 7720
-  val!10 -> 7758
-  val!11 -> 1
-  else -> 1
-}
-f14 -> {
-  val!6 -> val!9
-  else -> val!9
-}
-f7 -> {
-  val!8 -> val!10
-  else -> val!10
-}
-f3 -> {
-  1 -> val!11
-  7720 -> val!9
-  7758 -> val!10
-  else -> val!10
-}
-unknown
-5f2c36ac6c49043bec7b255aa0d7a0c690b930a4 21 0
-f1 -> val!0
-f2 -> val!1
-f17 -> val!2
-f4 -> val!4
-f14 -> val!7
-f16 -> val!9
-f7 -> val!12
-f10 -> val!12
-f20 -> {
-  val!2 -> val!3
-  val!4 -> val!5
-  val!7 -> val!8
-  val!9 -> val!10
-  else -> val!10
-}
-f19 -> {
-  val!3 val!5 -> val!6
-  val!8 val!10 -> val!11
-  else -> val!11
-}
-unknown
-4bd0e90cc9ab46b702c811a3ea671a168ec22aba 65 0
-f1 -> val!0
-f2 -> val!1
-f14 -> val!19
-f21 -> val!3
-f13 -> val!6
-f23 -> val!8
-f17 -> val!9
-f16 -> val!11
-f4 -> val!13
-f7 -> val!19
-f10 -> val!15
-f9 -> val!16
-f12 -> val!17
-f15 -> val!18
-f11 -> {
-  val!19 -> val!2
-  else -> val!2
-}
-f20 -> {
-  val!3 -> val!4
-  else -> val!4
-}
-f19 -> {
-  val!2 val!4 -> val!5
-  else -> val!5
-}
-f22 -> {
-  val!6 -> val!7
-  val!9 -> val!10
-  val!11 -> val!12
-  val!13 -> val!14
-  else -> val!14
-}
-f8 -> {
-  val!7 val!2 -> -1
-  val!8 val!2 -> 0
-  val!10 val!2 -> 1
-  val!12 val!2 -> -1
-  val!14 val!2 -> 1
-  val!15 val!2 -> 0
-  val!16 val!2 -> -1
-  val!17 val!2 -> 1
-  val!18 val!2 -> 0
-  else -> 0
-}
-f5 -> {
-  val!19 -> 0
-  else -> 0
-}
-f18 -> {
-  0 -> val!19
-  else -> val!19
-}
-f6 -> {
-  val!2 -> val!19
-  else -> val!19
-}
-f3 -> {
-  val!13 val!2 -> 0
-  val!6 val!2 -> -1
-  val!11 val!2 -> 0
-  val!9 val!2 -> 1
-  else -> 1
-}
-unknown
-cdc3b5c1b7947a0fe95f5d2f65f941e2774116a3 63 0
-f1 -> val!0
-f2 -> val!1
-f14 -> val!17
-f21 -> val!3
-f13 -> val!6
-f23 -> val!8
-f17 -> val!9
-f16 -> val!11
-f4 -> val!13
-f7 -> val!17
-f10 -> val!15
-f9 -> val!16
-f11 -> {
-  val!17 -> val!2
-  else -> val!2
-}
-f20 -> {
-  val!3 -> val!4
-  else -> val!4
-}
-f19 -> {
-  val!2 val!4 -> val!5
-  else -> val!5
-}
-f22 -> {
-  val!6 -> val!7
-  val!9 -> val!10
-  val!11 -> val!12
-  val!13 -> val!14
-  else -> val!14
-}
-f8 -> {
-  val!7 val!2 -> -1
-  val!8 val!2 -> 0
-  val!10 val!2 -> 1
-  val!12 val!2 -> -1
-  val!14 val!2 -> 1
-  val!15 val!2 -> 0
-  val!16 val!2 -> 2
-  else -> 2
-}
-f5 -> {
-  val!17 -> 1
-  val!18 -> 0
-  else -> 0
-}
-f18 -> {
-  1 -> val!17
-  0 -> val!18
-  else -> val!18
-}
-f3 -> {
-  val!13 val!2 -> 2
-  val!11 val!2 -> 0
-  val!6 val!2 -> 0
-  val!9 val!2 -> 2
-  else -> 2
-}
-f6 -> {
-  val!2 -> val!18
-  else -> val!18
-}
-unknown
-e7b427c80202d9c4c29f2a9278c2bcdecdabe460 42 0
-f1 -> val!0
-f2 -> val!1
-f3 -> val!2
-f4 -> val!2
-f5 -> val!3
-f6 -> val!3
-f18 -> val!4
-f19 -> val!5
-f20 -> val!6
-f17 -> val!8
-f23 -> val!14
-f13 -> {
-  val!4 val!5 -> 0
-  val!6 val!5 -> -3
-  val!10 val!5 -> 0
-  val!13 val!5 -> 0
-  else -> 0
-}
-f16 -> {
-  val!3 -> val!7
-  val!2 -> val!11
-  else -> val!11
-}
-f15 -> {
-  val!7 val!8 -> val!9
-  val!11 val!8 -> val!12
-  else -> val!12
-}
-f14 -> {
-  val!9 val!4 -> val!10
-  val!12 val!6 -> val!13
-  else -> val!13
-}
-f22 -> {
-  val!14 -> val!15
-  else -> val!15
-}
-f21 -> {
-  val!5 val!15 -> val!16
-  else -> val!16
-}
-unknown
-fc367e02b7e503644f5c70cc9716512639619a51 52 0
-f1 -> val!0
-f2 -> val!1
-f3 -> val!2
-f4 -> val!2
-f5 -> val!3
-f6 -> val!3
-f20 -> val!4
-f21 -> val!15
-f22 -> val!5
-f19 -> val!7
-f25 -> val!13
-f15 -> {
-  val!4 val!15 -> 6
-  val!5 val!15 -> 0
-  val!9 val!15 -> 1
-  val!12 val!15 -> -1
-  else -> -1
-}
-f18 -> {
-  val!3 -> val!6
-  val!2 -> val!10
-  else -> val!10
-}
-f17 -> {
-  val!6 val!7 -> val!8
-  val!10 val!7 -> val!11
-  else -> val!11
-}
-f16 -> {
-  val!8 val!4 -> val!9
-  val!11 val!5 -> val!12
-  else -> val!12
-}
-f24 -> {
-  val!13 -> val!16
-  else -> val!16
-}
-f23 -> {
-  val!15 val!16 -> val!14
-  else -> val!14
-}
-f14 -> {
-  val!15 -> 0
-  val!16 -> 1
-  else -> 1
-}
-f13 -> {
-  0 -> val!15
-  1 -> val!16
-  else -> val!16
-}
-unknown
-2b6a5d632b112638788d36706b106b4e4d10b262 35 0
-f1 -> val!0
-f2 -> val!1
-f3 -> val!2
-f4 -> val!2
-f5 -> val!3
-f6 -> val!3
-f18 -> val!4
-f19 -> val!5
-f20 -> val!6
-f17 -> val!8
-f13 -> {
-  val!4 val!5 -> 0
-  val!6 val!5 -> -3
-  val!10 val!5 -> 0
-  val!13 val!5 -> 0
-  val!9 val!5 -> 0
-  val!12 val!5 -> 0
-  else -> 0
-}
-f16 -> {
-  val!3 -> val!7
-  val!2 -> val!11
-  else -> val!11
-}
-f15 -> {
-  val!7 val!8 -> val!9
-  val!11 val!8 -> val!12
-  else -> val!12
-}
-f14 -> {
-  val!9 val!4 -> val!10
-  val!12 val!6 -> val!13
-  else -> val!13
-}
-unknown
-6220e161feeb3d35604e0055563cdf27e5108197 35 0
-f1 -> val!0
-f2 -> val!1
-f8 -> val!2
-f12 -> val!2
-f11 -> val!3
-f13 -> val!3
-f22 -> val!4
-f9 -> val!5
-f23 -> val!6
-f10 -> val!7
-f21 -> val!8
-f4 -> val!9
-f5 -> {
-  val!4 val!5 -> 3
-  val!6 val!5 -> 0
-  val!11 val!5 -> 0
-  val!13 val!5 -> 0
-  else -> 0
-}
-f20 -> {
-  val!7 val!8 -> 3
-  val!9 val!8 -> 0
-  else -> 0
-}
-f7 -> {
-  val!3 -> val!10
-  val!2 -> val!12
-  else -> val!12
-}
-f24 -> {
-  val!10 val!8 -> val!11
-  val!12 val!8 -> val!13
-  else -> val!13
-}
-unknown
-c29b6c64de39317156c532c91451be225c15adb2 238 0
-#2 := false
-#48 := 0::real
-decl f19 :: (-> S3 S10 real)
-decl f20 :: S10
-#43 := f20
-decl f4 :: S3
-#8 := f4
-#58 := (f19 f4 f20)
-#109 := -1::real
-#153 := (* -1::real #58)
-decl f5 :: (-> S4 S5 real)
-decl f8 :: S5
-#13 := f8
-decl f22 :: S4
-#54 := f22
-#55 := (f5 f22 f8)
-#154 := (+ #55 #153)
-#137 := (* -1::real #55)
-#144 := (+ #137 #58)
-#188 := (<= #154 0::real)
-#195 := (ite #188 #144 #154)
-#451 := (* -1::real #195)
-#452 := (+ #144 #451)
-#453 := (<= #452 0::real)
-#435 := (= #144 #195)
-decl f21 :: S4
-#45 := f21
-#46 := (f5 f21 f8)
-decl f9 :: S3
-#17 := f9
-#44 := (f19 f9 f20)
-#120 := (* -1::real #44)
-#121 := (+ #120 #46)
-#110 := (* -1::real #46)
-#111 := (+ #44 #110)
-#216 := (>= #111 0::real)
-#223 := (ite #216 #111 #121)
-#447 := (* -1::real #223)
-#450 := (+ #121 #447)
-#454 := (<= #450 0::real)
-#442 := (= #121 #223)
-#217 := (not #216)
-#455 := [hypothesis]: #216
-#184 := (+ #44 #153)
-#185 := (<= #184 0::real)
-#206 := -3::real
-#234 := (* -3::real #223)
-#235 := (+ #137 #234)
-#236 := (+ #46 #235)
-#237 := (<= #236 0::real)
-#238 := (not #237)
-#207 := (* -3::real #195)
-#208 := (+ #137 #207)
-#209 := (+ #46 #208)
-#210 := (<= #209 0::real)
-#211 := (not #210)
-#249 := (and #185 #211 #238)
-#65 := (<= #44 #58)
-#56 := (- #46 #55)
-#52 := 3::real
-#59 := (- #58 #55)
-#61 := (- #59)
-#60 := (< #59 0::real)
-#62 := (ite #60 #61 #59)
-#63 := (* #62 3::real)
-#64 := (< #63 #56)
-#66 := (and #64 #65)
-#47 := (- #44 #46)
-#50 := (- #47)
-#49 := (< #47 0::real)
-#51 := (ite #49 #50 #47)
-#53 := (* #51 3::real)
-#57 := (< #53 #56)
-#67 := (and #57 #66)
-#254 := (iff #67 #249)
-#138 := (+ #46 #137)
-#147 := (< #144 0::real)
-#159 := (ite #147 #154 #144)
-#165 := (* 3::real #159)
-#170 := (< #165 #138)
-#176 := (and #65 #170)
-#114 := (< #111 0::real)
-#126 := (ite #114 #121 #111)
-#132 := (* 3::real #126)
-#141 := (< #132 #138)
-#181 := (and #141 #176)
-#252 := (iff #181 #249)
-#243 := (and #185 #211)
-#246 := (and #238 #243)
-#250 := (iff #246 #249)
-#251 := [rewrite]: #250
-#247 := (iff #181 #246)
-#244 := (iff #176 #243)
-#214 := (iff #170 #211)
-#200 := (* 3::real #195)
-#203 := (< #200 #138)
-#212 := (iff #203 #211)
-#213 := [rewrite]: #212
-#204 := (iff #170 #203)
-#201 := (= #165 #200)
-#198 := (= #159 #195)
-#189 := (not #188)
-#192 := (ite #189 #154 #144)
-#196 := (= #192 #195)
-#197 := [rewrite]: #196
-#193 := (= #159 #192)
-#190 := (iff #147 #189)
-#191 := [rewrite]: #190
-#194 := [monotonicity #191]: #193
-#199 := [trans #194 #197]: #198
-#202 := [monotonicity #199]: #201
-#205 := [monotonicity #202]: #204
-#215 := [trans #205 #213]: #214
-#186 := (iff #65 #185)
-#187 := [rewrite]: #186
-#245 := [monotonicity #187 #215]: #244
-#241 := (iff #141 #238)
-#228 := (* 3::real #223)
-#231 := (< #228 #138)
-#239 := (iff #231 #238)
-#240 := [rewrite]: #239
-#232 := (iff #141 #231)
-#229 := (= #132 #228)
-#226 := (= #126 #223)
-#220 := (ite #217 #121 #111)
-#224 := (= #220 #223)
-#225 := [rewrite]: #224
-#221 := (= #126 #220)
-#218 := (iff #114 #217)
-#219 := [rewrite]: #218
-#222 := [monotonicity #219]: #221
-#227 := [trans #222 #225]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#242 := [trans #233 #240]: #241
-#248 := [monotonicity #242 #245]: #247
-#253 := [trans #248 #251]: #252
-#182 := (iff #67 #181)
-#179 := (iff #66 #176)
-#173 := (and #170 #65)
-#177 := (iff #173 #176)
-#178 := [rewrite]: #177
-#174 := (iff #66 #173)
-#171 := (iff #64 #170)
-#139 := (= #56 #138)
-#140 := [rewrite]: #139
-#168 := (= #63 #165)
-#162 := (* #159 3::real)
-#166 := (= #162 #165)
-#167 := [rewrite]: #166
-#163 := (= #63 #162)
-#160 := (= #62 #159)
-#145 := (= #59 #144)
-#146 := [rewrite]: #145
-#157 := (= #61 #154)
-#150 := (- #144)
-#155 := (= #150 #154)
-#156 := [rewrite]: #155
-#151 := (= #61 #150)
-#152 := [monotonicity #146]: #151
-#158 := [trans #152 #156]: #157
-#148 := (iff #60 #147)
-#149 := [monotonicity #146]: #148
-#161 := [monotonicity #149 #158 #146]: #160
-#164 := [monotonicity #161]: #163
-#169 := [trans #164 #167]: #168
-#172 := [monotonicity #169 #140]: #171
-#175 := [monotonicity #172]: #174
-#180 := [trans #175 #178]: #179
-#142 := (iff #57 #141)
-#135 := (= #53 #132)
-#129 := (* #126 3::real)
-#133 := (= #129 #132)
-#134 := [rewrite]: #133
-#130 := (= #53 #129)
-#127 := (= #51 #126)
-#112 := (= #47 #111)
-#113 := [rewrite]: #112
-#124 := (= #50 #121)
-#117 := (- #111)
-#122 := (= #117 #121)
-#123 := [rewrite]: #122
-#118 := (= #50 #117)
-#119 := [monotonicity #113]: #118
-#125 := [trans #119 #123]: #124
-#115 := (iff #49 #114)
-#116 := [monotonicity #113]: #115
-#128 := [monotonicity #116 #125 #113]: #127
-#131 := [monotonicity #128]: #130
-#136 := [trans #131 #134]: #135
-#143 := [monotonicity #136 #140]: #142
-#183 := [monotonicity #143 #180]: #182
-#255 := [trans #183 #253]: #254
-#108 := [asserted]: #67
-#256 := [mp #108 #255]: #249
-#257 := [and-elim #256]: #185
-#259 := [and-elim #256]: #238
-#448 := (+ #111 #447)
-#449 := (<= #448 0::real)
-#441 := (= #111 #223)
-#443 := (or #217 #441)
-#444 := [def-axiom]: #443
-#467 := [unit-resolution #444 #455]: #441
-#468 := (not #441)
-#469 := (or #468 #449)
-#470 := [th-lemma]: #469
-#471 := [unit-resolution #470 #467]: #449
-#463 := (or #189 #217)
-#456 := [hypothesis]: #188
-#258 := [and-elim #256]: #211
-#437 := (or #189 #435)
-#438 := [def-axiom]: #437
-#457 := [unit-resolution #438 #456]: #435
-#458 := (not #435)
-#459 := (or #458 #453)
-#460 := [th-lemma]: #459
-#461 := [unit-resolution #460 #457]: #453
-#462 := [th-lemma #257 #461 #258 #456 #455]: false
-#464 := [lemma #462]: #463
-#472 := [unit-resolution #464 #455]: #189
-#473 := [th-lemma #472 #471 #259 #257 #455]: false
-#474 := [lemma #473]: #217
-#445 := (or #216 #442)
-#446 := [def-axiom]: #445
-#475 := [unit-resolution #446 #474]: #442
-#476 := (not #442)
-#477 := (or #476 #454)
-#478 := [th-lemma]: #477
-#479 := [unit-resolution #478 #475]: #454
-#481 := (not #185)
-#480 := (not #454)
-#482 := (or #188 #480 #237 #481 #216)
-#483 := [th-lemma]: #482
-#484 := [unit-resolution #483 #257 #474 #259 #479]: #188
-#485 := [unit-resolution #438 #484]: #435
-#486 := [unit-resolution #460 #485]: #453
-[th-lemma #479 #259 #257 #474 #258 #486]: false
-unsat
-e14093e1f049d6c695e00b050a39f30b5ee75c84 41 0
-f1 -> val!6
-f2 -> val!0
-?v0!0 -> val!11
-f12 -> val!1
-f14 -> val!2
-f15 -> val!3
-f9 -> val!7
-f8 -> val!8
-f6 -> val!9
-f13 -> {
-  val!2 val!3 -> val!4
-  else -> val!4
-}
-f11 -> {
-  val!1 val!4 -> val!5
-  else -> val!5
-}
-f10 -> {
-  val!11 val!5 -> val!6
-  else -> val!6
-}
-f7 -> {
-  val!7 val!11 -> 0
-  val!8 val!11 -> 0
-  else -> 0
-}
-f5 -> {
-  val!9 -> val!10
-  else -> val!10
-}
-f4 -> {
-  val!10 -> 0
-  val!11 -> 38
-  else -> 38
-}
-f3 -> {
-  0 -> val!10
-  38 -> val!11
-  else -> val!11
-}
-unknown
-b39ccddf1d4f138215d1b195d383905c9937a82f 44 0
-f1 -> val!7
-f2 -> val!0
-?v0!0 -> val!11
-f6 -> val!1
-f14 -> val!3
-f15 -> val!4
-f9 -> val!8
-f8 -> val!9
-f5 -> {
-  val!1 -> val!10
-  else -> val!10
-}
-f12 -> {
-  val!10 -> val!2
-  else -> val!2
-}
-f13 -> {
-  val!3 val!4 -> val!5
-  else -> val!5
-}
-f11 -> {
-  val!2 val!5 -> val!6
-  else -> val!6
-}
-f10 -> {
-  val!11 val!6 -> val!7
-  else -> val!7
-}
-f7 -> {
-  val!8 val!11 -> 0
-  val!9 val!11 -> 0
-  else -> 0
-}
-f4 -> {
-  val!10 -> 0
-  val!11 -> 38
-  else -> 38
-}
-f3 -> {
-  0 -> val!10
-  38 -> val!11
-  else -> val!11
-}
-unknown
-e03a7d5d1030a490d5669c1c764d61d605302d39 48 0
-f1 -> val!6
-f2 -> val!0
-f5 -> val!9
-f7 -> val!1
-?v0!0 -> val!11
-f15 -> val!3
-f10 -> val!7
-f9 -> val!8
-f4 -> {
-  val!9 -> 0
-  val!10 -> 1
-  val!11 -> 1237
-  else -> 1237
-}
-f6 -> {
-  val!1 -> val!10
-  else -> val!10
-}
-f13 -> {
-  val!10 -> val!2
-  else -> val!2
-}
-f14 -> {
-  val!9 val!3 -> val!4
-  else -> val!4
-}
-f12 -> {
-  val!2 val!4 -> val!5
-  else -> val!5
-}
-f11 -> {
-  val!11 val!5 -> val!6
-  else -> val!6
-}
-f8 -> {
-  val!7 val!11 -> 0
-  val!8 val!11 -> 0
-  val!7 val!9 -> -1
-  val!8 val!9 -> 0
-  else -> 0
-}
-f3 -> {
-  0 -> val!9
-  1 -> val!10
-  1237 -> val!11
-  else -> val!11
-}
-unknown
-e7836464956771492f5454e164bcd43446470f5a 48 0
-f1 -> val!6
-f2 -> val!0
-f5 -> val!9
-f7 -> val!1
-?v0!0 -> val!11
-f15 -> val!3
-f10 -> val!7
-f9 -> val!8
-f4 -> {
-  val!9 -> 0
-  val!10 -> 1
-  val!11 -> 1237
-  else -> 1237
-}
-f6 -> {
-  val!1 -> val!10
-  else -> val!10
-}
-f13 -> {
-  val!10 -> val!2
-  else -> val!2
-}
-f14 -> {
-  val!9 val!3 -> val!4
-  else -> val!4
-}
-f12 -> {
-  val!2 val!4 -> val!5
-  else -> val!5
-}
-f11 -> {
-  val!11 val!5 -> val!6
-  else -> val!6
-}
-f8 -> {
-  val!7 val!11 -> 0
-  val!8 val!11 -> 0
-  val!7 val!9 -> 1
-  val!8 val!9 -> 0
-  else -> 0
-}
-f3 -> {
-  0 -> val!9
-  1 -> val!10
-  1237 -> val!11
-  else -> val!11
-}
-unknown
-94aef9051873492c2e350c3ee8f6b777964eebe4 147 0
-#2 := false
-#159 := 0::real
-decl f8 :: (-> S4 S2 real)
-decl f5 :: S2
-#25 := f5
-decl f10 :: S4
-#33 := f10
-#34 := (f8 f10 f5)
-#156 := -1::real
-#157 := (* -1::real #34)
-decl f9 :: S4
-#31 := f9
-#32 := (f8 f9 f5)
-#158 := (+ #32 #157)
-#315 := (>= #158 0::real)
-#392 := (not #315)
-#202 := (= #32 #34)
-#205 := (not #202)
-#43 := (= #34 #32)
-#44 := (not #43)
-#206 := (iff #44 #205)
-#203 := (iff #43 #202)
-#204 := [rewrite]: #203
-#207 := [monotonicity #204]: #206
-#201 := [asserted]: #44
-#210 := [mp #201 #207]: #205
-#395 := (or #202 #392)
-#160 := (<= #158 0::real)
-#13 := 0::int
-decl f4 :: (-> S2 int)
-decl f6 :: (-> S3 S2)
-decl f7 :: S3
-#27 := f7
-#28 := (f6 f7)
-#29 := (f4 #28)
-#149 := -1::int
-#152 := (* -1::int #29)
-#26 := (f4 f5)
-#153 := (+ #26 #152)
-#151 := (>= #153 0::int)
-#150 := (not #151)
-#163 := (and #150 #160)
-#35 := (<= #32 #34)
-#30 := (< #26 #29)
-#36 := (and #30 #35)
-#164 := (iff #36 #163)
-#161 := (iff #35 #160)
-#162 := [rewrite]: #161
-#154 := (iff #30 #150)
-#155 := [rewrite]: #154
-#165 := [monotonicity #155 #162]: #164
-#146 := [asserted]: #36
-#166 := [mp #146 #165]: #163
-#168 := [and-elim #166]: #160
-#391 := (not #160)
-#393 := (or #202 #391 #392)
-#394 := [th-lemma]: #393
-#396 := [unit-resolution #394 #168]: #395
-#397 := [unit-resolution #396 #210]: #392
-#8 := (:var 0 S2)
-#39 := (f8 f9 #8)
-#308 := (pattern #39)
-#38 := (f8 f10 #8)
-#307 := (pattern #38)
-#9 := (f4 #8)
-#287 := (pattern #9)
-#187 := (* -1::real #39)
-#188 := (+ #38 #187)
-#189 := (<= #188 0::real)
-#177 := (+ #9 #152)
-#176 := (>= #177 0::int)
-#192 := (or #176 #189)
-#309 := (forall (vars (?v0 S2)) (:pat #287 #307 #308) #192)
-#195 := (forall (vars (?v0 S2)) #192)
-#312 := (iff #195 #309)
-#310 := (iff #192 #192)
-#311 := [refl]: #310
-#313 := [quant-intro #311]: #312
-#227 := (~ #195 #195)
-#208 := (~ #192 #192)
-#226 := [refl]: #208
-#228 := [nnf-pos #226]: #227
-#40 := (<= #38 #39)
-#37 := (< #9 #29)
-#41 := (implies #37 #40)
-#42 := (forall (vars (?v0 S2)) #41)
-#198 := (iff #42 #195)
-#148 := (not #37)
-#169 := (or #148 #40)
-#172 := (forall (vars (?v0 S2)) #169)
-#196 := (iff #172 #195)
-#193 := (iff #169 #192)
-#190 := (iff #40 #189)
-#191 := [rewrite]: #190
-#185 := (iff #148 #176)
-#175 := (not #176)
-#180 := (not #175)
-#183 := (iff #180 #176)
-#184 := [rewrite]: #183
-#181 := (iff #148 #180)
-#178 := (iff #37 #175)
-#179 := [rewrite]: #178
-#182 := [monotonicity #179]: #181
-#186 := [trans #182 #184]: #185
-#194 := [monotonicity #186 #191]: #193
-#197 := [quant-intro #194]: #196
-#173 := (iff #42 #172)
-#170 := (iff #41 #169)
-#171 := [rewrite]: #170
-#174 := [quant-intro #171]: #173
-#199 := [trans #174 #197]: #198
-#147 := [asserted]: #42
-#200 := [mp #147 #199]: #195
-#229 := [mp~ #200 #228]: #195
-#314 := [mp #229 #313]: #309
-#167 := [and-elim #166]: #150
-#338 := (not #309)
-#339 := (or #338 #151 #315)
-#318 := (* -1::real #32)
-#319 := (+ #34 #318)
-#323 := (<= #319 0::real)
-#324 := (or #151 #323)
-#340 := (or #338 #324)
-#347 := (iff #340 #339)
-#335 := (or #151 #315)
-#342 := (or #338 #335)
-#345 := (iff #342 #339)
-#346 := [rewrite]: #345
-#343 := (iff #340 #342)
-#336 := (iff #324 #335)
-#333 := (iff #323 #315)
-#325 := (+ #318 #34)
-#328 := (<= #325 0::real)
-#331 := (iff #328 #315)
-#332 := [rewrite]: #331
-#329 := (iff #323 #328)
-#326 := (= #319 #325)
-#327 := [rewrite]: #326
-#330 := [monotonicity #327]: #329
-#334 := [trans #330 #332]: #333
-#337 := [monotonicity #334]: #336
-#344 := [monotonicity #337]: #343
-#348 := [trans #344 #346]: #347
-#341 := [quant-inst]: #340
-#349 := [mp #341 #348]: #339
-[unit-resolution #349 #167 #314 #397]: false
-unsat
-a776c8d80c92e36c87766b3cd2a3d1707a6a4f17 29 0
-f1 -> val!0
-f2 -> val!1
-f6 -> val!2
-f7 -> val!7
-f8 -> val!3
-f12 -> 1
-f11 -> val!4
-f10 -> val!5
-f5 -> {
-  val!2 val!7 -> 0
-  val!3 val!7 -> 0
-  val!4 val!7 -> 1
-  else -> 1
-}
-f9 -> {
-  val!5 -> val!6
-  else -> val!6
-}
-f4 -> {
-  val!6 -> 0
-  val!7 -> 7719
-  else -> 7719
-}
-f3 -> {
-  0 -> val!6
-  7719 -> val!7
-  else -> val!7
-}
-unknown
-2b1630352ec036f9060c61ea0f08be80276b84d2 29 0
-f1 -> val!0
-f2 -> val!1
-f6 -> val!2
-f7 -> val!7
-f8 -> val!3
-f12 -> 1
-f11 -> val!4
-f10 -> val!5
-f5 -> {
-  val!2 val!7 -> 0
-  val!3 val!7 -> 0
-  val!4 val!7 -> 1
-  else -> 1
-}
-f9 -> {
-  val!5 -> val!6
-  else -> val!6
-}
-f4 -> {
-  val!6 -> 0
-  val!7 -> 7719
-  else -> 7719
-}
-f3 -> {
-  0 -> val!6
-  7719 -> val!7
-  else -> val!7
-}
-unknown
-478564f7f355dca34baaecde71bc3afeb25b293b 204 0
-#2 := false
-#46 := 0::real
-decl f5 :: (-> S3 S2 real)
-decl f7 :: S2
-#26 := f7
-decl f11 :: S3
-#38 := f11
-#49 := (f5 f11 f7)
-#183 := -1::real
-#349 := (* -1::real #49)
-decl f8 :: S3
-#28 := f8
-#29 := (f5 f8 f7)
-#362 := (+ #29 #349)
-#363 := (>= #362 0::real)
-#368 := (not #363)
-decl f6 :: S3
-#25 := f6
-#27 := (f5 f6 f7)
-#350 := (+ #27 #349)
-#351 := (<= #350 0::real)
-#352 := (not #351)
-#371 := (or #352 #368)
-#374 := (not #371)
-#8 := (:var 0 S2)
-#41 := (f5 f8 #8)
-#333 := (pattern #41)
-#39 := (f5 f11 #8)
-#332 := (pattern #39)
-#37 := (f5 f6 #8)
-#331 := (pattern #37)
-decl f4 :: (-> S2 int)
-#9 := (f4 #8)
-#311 := (pattern #9)
-#189 := (* -1::real #41)
-#190 := (+ #39 #189)
-#191 := (<= #190 0::real)
-#242 := (not #191)
-#184 := (* -1::real #39)
-#185 := (+ #37 #184)
-#186 := (<= #185 0::real)
-#241 := (not #186)
-#243 := (or #241 #242)
-#244 := (not #243)
-#13 := 0::int
-decl f9 :: (-> S4 S2)
-decl f10 :: S4
-#32 := f10
-#33 := (f9 f10)
-#34 := (f4 #33)
-#157 := -1::int
-#160 := (* -1::int #34)
-#173 := (+ #9 #160)
-#172 := (>= #173 0::int)
-#247 := (or #172 #244)
-#334 := (forall (vars (?v0 S2)) (:pat #311 #331 #332 #333) #247)
-#250 := (forall (vars (?v0 S2)) #247)
-#337 := (iff #250 #334)
-#335 := (iff #247 #247)
-#336 := [refl]: #335
-#338 := [quant-intro #336]: #337
-#194 := (and #186 #191)
-#197 := (or #172 #194)
-#200 := (forall (vars (?v0 S2)) #197)
-#251 := (iff #200 #250)
-#248 := (iff #197 #247)
-#245 := (iff #194 #244)
-#246 := [rewrite]: #245
-#249 := [monotonicity #246]: #248
-#252 := [quant-intro #249]: #251
-#219 := (~ #200 #200)
-#224 := (~ #197 #197)
-#222 := [refl]: #224
-#239 := [nnf-pos #222]: #219
-#42 := (<= #39 #41)
-#40 := (<= #37 #39)
-#43 := (and #40 #42)
-#36 := (< #9 #34)
-#44 := (implies #36 #43)
-#45 := (forall (vars (?v0 S2)) #44)
-#203 := (iff #45 #200)
-#156 := (not #36)
-#165 := (or #156 #43)
-#168 := (forall (vars (?v0 S2)) #165)
-#201 := (iff #168 #200)
-#198 := (iff #165 #197)
-#195 := (iff #43 #194)
-#192 := (iff #42 #191)
-#193 := [rewrite]: #192
-#187 := (iff #40 #186)
-#188 := [rewrite]: #187
-#196 := [monotonicity #188 #193]: #195
-#181 := (iff #156 #172)
-#171 := (not #172)
-#176 := (not #171)
-#179 := (iff #176 #172)
-#180 := [rewrite]: #179
-#177 := (iff #156 #176)
-#174 := (iff #36 #171)
-#175 := [rewrite]: #174
-#178 := [monotonicity #175]: #177
-#182 := [trans #178 #180]: #181
-#199 := [monotonicity #182 #196]: #198
-#202 := [quant-intro #199]: #201
-#169 := (iff #45 #168)
-#166 := (iff #44 #165)
-#167 := [rewrite]: #166
-#170 := [quant-intro #167]: #169
-#204 := [trans #170 #202]: #203
-#155 := [asserted]: #45
-#205 := [mp #155 #204]: #200
-#240 := [mp~ #205 #239]: #200
-#253 := [mp #240 #252]: #250
-#339 := [mp #253 #338]: #334
-#31 := (f4 f7)
-#161 := (+ #31 #160)
-#159 := (>= #161 0::int)
-#158 := (not #159)
-#35 := (< #31 #34)
-#162 := (iff #35 #158)
-#163 := [rewrite]: #162
-#154 := [asserted]: #35
-#164 := [mp #154 #163]: #158
-#380 := (not #334)
-#381 := (or #380 #159 #374)
-#342 := (* -1::real #29)
-#343 := (+ #49 #342)
-#347 := (<= #343 0::real)
-#348 := (not #347)
-#353 := (or #352 #348)
-#354 := (not #353)
-#355 := (or #159 #354)
-#382 := (or #380 #355)
-#389 := (iff #382 #381)
-#377 := (or #159 #374)
-#384 := (or #380 #377)
-#387 := (iff #384 #381)
-#388 := [rewrite]: #387
-#385 := (iff #382 #384)
-#378 := (iff #355 #377)
-#375 := (iff #354 #374)
-#372 := (iff #353 #371)
-#369 := (iff #348 #368)
-#366 := (iff #347 #363)
-#356 := (+ #342 #49)
-#359 := (<= #356 0::real)
-#364 := (iff #359 #363)
-#365 := [rewrite]: #364
-#360 := (iff #347 #359)
-#357 := (= #343 #356)
-#358 := [rewrite]: #357
-#361 := [monotonicity #358]: #360
-#367 := [trans #361 #365]: #366
-#370 := [monotonicity #367]: #369
-#373 := [monotonicity #370]: #372
-#376 := [monotonicity #373]: #375
-#379 := [monotonicity #376]: #378
-#386 := [monotonicity #379]: #385
-#390 := [trans #386 #388]: #389
-#383 := [quant-inst]: #382
-#391 := [mp #383 #390]: #381
-#513 := [unit-resolution #391 #164 #339]: #374
-#394 := (or #371 #363)
-#395 := [def-axiom]: #394
-#514 := [unit-resolution #395 #513]: #363
-#475 := (>= #350 0::real)
-#524 := (not #475)
-#474 := (= #27 #49)
-#519 := (not #474)
-#208 := (= #29 #49)
-#216 := (not #208)
-#520 := (iff #216 #519)
-#517 := (iff #208 #474)
-#515 := (iff #474 #208)
-#30 := (= #27 #29)
-#153 := [asserted]: #30
-#516 := [monotonicity #153]: #515
-#518 := [symm #516]: #517
-#521 := [monotonicity #518]: #520
-#50 := (= #49 #29)
-#51 := (not #50)
-#217 := (iff #51 #216)
-#214 := (iff #50 #208)
-#215 := [rewrite]: #214
-#218 := [monotonicity #215]: #217
-#207 := [asserted]: #51
-#221 := [mp #207 #218]: #216
-#522 := [mp #221 #521]: #519
-#527 := (or #474 #524)
-#392 := (or #371 #351)
-#393 := [def-axiom]: #392
-#523 := [unit-resolution #393 #513]: #351
-#525 := (or #474 #352 #524)
-#526 := [th-lemma]: #525
-#528 := [unit-resolution #526 #523]: #527
-#529 := [unit-resolution #528 #522]: #524
-#471 := (+ #27 #342)
-#473 := (>= #471 0::real)
-#530 := (not #30)
-#531 := (or #530 #473)
-#532 := [th-lemma]: #531
-#533 := [unit-resolution #532 #153]: #473
-[th-lemma #533 #529 #514]: false
-unsat
-07499e3240b5b9ff9168a39bf4f0848339ecb137 29 0
-f5 -> 1
-f12 -> val!0
-f11 -> val!7
-f9 -> val!1
-f1 -> val!2
-f2 -> val!3
-f10 -> val!4
-f7 -> val!5
-f8 -> {
-  val!0 val!7 -> 0
-  val!1 val!7 -> 0
-  val!4 val!7 -> 0
-  else -> 0
-}
-f6 -> {
-  val!5 -> val!6
-  else -> val!6
-}
-f4 -> {
-  val!6 -> 0
-  val!7 -> 38
-  else -> 38
-}
-f3 -> {
-  0 -> val!6
-  38 -> val!7
-  else -> val!7
-}
-unknown
-3521e5c8a799f779cef25ded86c422c58ebfc7fd 318 0
-#2 := false
-#25 := 0::real
-decl f8 :: (-> S4 S2 real)
-decl f11 :: S2
-#40 := f11
-decl f9 :: S4
-#32 := f9
-#47 := (f8 f9 f11)
-decl f12 :: S4
-#44 := f12
-#45 := (f8 f12 f11)
-#192 := -1::real
-#232 := (* -1::real #45)
-#233 := (+ #232 #47)
-decl f5 :: real
-#26 := f5
-#268 := (* -1::real #47)
-#271 := (+ #45 #268)
-#274 := (+ f5 #271)
-#275 := (<= #274 0::real)
-#278 := (ite #275 f5 #233)
-#593 := (* -1::real #278)
-#594 := (+ f5 #593)
-#595 := (<= #594 0::real)
-#603 := (not #595)
-#223 := 1/2::real
-#281 := (* 1/2::real #278)
-#457 := (<= #281 0::real)
-#292 := (= #281 0::real)
-#306 := (<= #271 0::real)
-decl f10 :: S4
-#34 := f10
-#43 := (f8 f10 f11)
-#302 := (+ #43 #232)
-#303 := (<= #302 0::real)
-#309 := (and #303 #306)
-#13 := 0::int
-decl f4 :: (-> S2 int)
-#41 := (f4 f11)
-#178 := -1::int
-#213 := (* -1::int #41)
-decl f6 :: (-> S3 S2)
-decl f7 :: S3
-#28 := f7
-#29 := (f6 f7)
-#30 := (f4 #29)
-#214 := (+ #30 #213)
-#215 := (<= #214 0::int)
-#312 := (or #215 #309)
-#225 := (* 1/2::real #47)
-#272 := (+ #232 #225)
-#224 := (* 1/2::real #43)
-#273 := (+ #224 #272)
-#270 := (>= #273 0::real)
-#321 := (and #270 #292 #312)
-#52 := 2::real
-#55 := (- #47 #45)
-#56 := (<= f5 #55)
-#57 := (ite #56 f5 #55)
-#58 := (/ #57 2::real)
-#59 := (+ #45 #58)
-#60 := (= #59 #45)
-#51 := (+ #43 #47)
-#53 := (/ #51 2::real)
-#54 := (<= #45 #53)
-#61 := (and #54 #60)
-#48 := (<= #45 #47)
-#46 := (<= #43 #45)
-#49 := (and #46 #48)
-#42 := (< #41 #30)
-#50 := (implies #42 #49)
-#62 := (and #50 #61)
-#326 := (iff #62 #321)
-#236 := (<= f5 #233)
-#239 := (ite #236 f5 #233)
-#245 := (* 1/2::real #239)
-#250 := (+ #45 #245)
-#256 := (= #45 #250)
-#226 := (+ #224 #225)
-#229 := (<= #45 #226)
-#261 := (and #229 #256)
-#212 := (not #42)
-#220 := (or #212 #49)
-#264 := (and #220 #261)
-#324 := (iff #264 #321)
-#315 := (and #270 #292)
-#318 := (and #312 #315)
-#322 := (iff #318 #321)
-#323 := [rewrite]: #322
-#319 := (iff #264 #318)
-#316 := (iff #261 #315)
-#293 := (iff #256 #292)
-#284 := (+ #45 #281)
-#287 := (= #45 #284)
-#290 := (iff #287 #292)
-#291 := [rewrite]: #290
-#288 := (iff #256 #287)
-#285 := (= #250 #284)
-#282 := (= #245 #281)
-#279 := (= #239 #278)
-#276 := (iff #236 #275)
-#277 := [rewrite]: #276
-#280 := [monotonicity #277]: #279
-#283 := [monotonicity #280]: #282
-#286 := [monotonicity #283]: #285
-#289 := [monotonicity #286]: #288
-#294 := [trans #289 #291]: #293
-#267 := (iff #229 #270)
-#269 := [rewrite]: #267
-#317 := [monotonicity #269 #294]: #316
-#313 := (iff #220 #312)
-#310 := (iff #49 #309)
-#307 := (iff #48 #306)
-#308 := [rewrite]: #307
-#304 := (iff #46 #303)
-#305 := [rewrite]: #304
-#311 := [monotonicity #305 #308]: #310
-#300 := (iff #212 #215)
-#216 := (not #215)
-#295 := (not #216)
-#298 := (iff #295 #215)
-#299 := [rewrite]: #298
-#296 := (iff #212 #295)
-#217 := (iff #42 #216)
-#218 := [rewrite]: #217
-#297 := [monotonicity #218]: #296
-#301 := [trans #297 #299]: #300
-#314 := [monotonicity #301 #311]: #313
-#320 := [monotonicity #314 #317]: #319
-#325 := [trans #320 #323]: #324
-#265 := (iff #62 #264)
-#262 := (iff #61 #261)
-#259 := (iff #60 #256)
-#253 := (= #250 #45)
-#257 := (iff #253 #256)
-#258 := [rewrite]: #257
-#254 := (iff #60 #253)
-#251 := (= #59 #250)
-#248 := (= #58 #245)
-#242 := (/ #239 2::real)
-#246 := (= #242 #245)
-#247 := [rewrite]: #246
-#243 := (= #58 #242)
-#240 := (= #57 #239)
-#234 := (= #55 #233)
-#235 := [rewrite]: #234
-#237 := (iff #56 #236)
-#238 := [monotonicity #235]: #237
-#241 := [monotonicity #238 #235]: #240
-#244 := [monotonicity #241]: #243
-#249 := [trans #244 #247]: #248
-#252 := [monotonicity #249]: #251
-#255 := [monotonicity #252]: #254
-#260 := [trans #255 #258]: #259
-#230 := (iff #54 #229)
-#227 := (= #53 #226)
-#228 := [rewrite]: #227
-#231 := [monotonicity #228]: #230
-#263 := [monotonicity #231 #260]: #262
-#221 := (iff #50 #220)
-#222 := [rewrite]: #221
-#266 := [monotonicity #222 #263]: #265
-#327 := [trans #266 #325]: #326
-#211 := [asserted]: #62
-#328 := [mp #211 #327]: #321
-#330 := [and-elim #328]: #292
-#597 := (not #292)
-#598 := (or #597 #457)
-#599 := [th-lemma]: #598
-#600 := [unit-resolution #599 #330]: #457
-#601 := [hypothesis]: #595
-#167 := (<= f5 0::real)
-#168 := (not #167)
-#27 := (< 0::real f5)
-#169 := (iff #27 #168)
-#170 := [rewrite]: #169
-#164 := [asserted]: #27
-#171 := [mp #164 #170]: #168
-#602 := [th-lemma #171 #601 #600]: false
-#604 := [lemma #602]: #603
-#450 := (= f5 #278)
-#451 := (= #233 #278)
-#613 := (not #451)
-#596 := (+ #233 #593)
-#605 := (<= #596 0::real)
-#610 := (not #605)
-#532 := (+ #43 #268)
-#533 := (>= #532 0::real)
-#538 := (not #533)
-#210 := [asserted]: #42
-#219 := [mp #210 #218]: #216
-#8 := (:var 0 S2)
-#35 := (f8 f10 #8)
-#443 := (pattern #35)
-#33 := (f8 f9 #8)
-#442 := (pattern #33)
-#9 := (f4 #8)
-#422 := (pattern #9)
-#193 := (* -1::real #35)
-#194 := (+ #33 #193)
-#195 := (<= #194 0::real)
-#198 := (not #195)
-#181 := (* -1::int #30)
-#182 := (+ #9 #181)
-#180 := (>= #182 0::int)
-#201 := (or #180 #198)
-#444 := (forall (vars (?v0 S2)) (:pat #422 #442 #443) #201)
-#204 := (forall (vars (?v0 S2)) #201)
-#447 := (iff #204 #444)
-#445 := (iff #201 #201)
-#446 := [refl]: #445
-#448 := [quant-intro #446]: #447
-#362 := (~ #204 #204)
-#332 := (~ #201 #201)
-#361 := [refl]: #332
-#363 := [nnf-pos #361]: #362
-#36 := (<= #33 #35)
-#37 := (not #36)
-#31 := (< #9 #30)
-#38 := (implies #31 #37)
-#39 := (forall (vars (?v0 S2)) #38)
-#207 := (iff #39 #204)
-#166 := (not #31)
-#172 := (or #166 #37)
-#175 := (forall (vars (?v0 S2)) #172)
-#205 := (iff #175 #204)
-#202 := (iff #172 #201)
-#199 := (iff #37 #198)
-#196 := (iff #36 #195)
-#197 := [rewrite]: #196
-#200 := [monotonicity #197]: #199
-#190 := (iff #166 #180)
-#179 := (not #180)
-#185 := (not #179)
-#188 := (iff #185 #180)
-#189 := [rewrite]: #188
-#186 := (iff #166 #185)
-#183 := (iff #31 #179)
-#184 := [rewrite]: #183
-#187 := [monotonicity #184]: #186
-#191 := [trans #187 #189]: #190
-#203 := [monotonicity #191 #200]: #202
-#206 := [quant-intro #203]: #205
-#176 := (iff #39 #175)
-#173 := (iff #38 #172)
-#174 := [rewrite]: #173
-#177 := [quant-intro #174]: #176
-#208 := [trans #177 #206]: #207
-#165 := [asserted]: #39
-#209 := [mp #165 #208]: #204
-#364 := [mp~ #209 #363]: #204
-#449 := [mp #364 #448]: #444
-#544 := (not #444)
-#545 := (or #544 #215 #538)
-#507 := (* -1::real #43)
-#508 := (+ #47 #507)
-#511 := (<= #508 0::real)
-#512 := (not #511)
-#513 := (+ #41 #181)
-#514 := (>= #513 0::int)
-#515 := (or #514 #512)
-#546 := (or #544 #515)
-#553 := (iff #546 #545)
-#541 := (or #215 #538)
-#548 := (or #544 #541)
-#551 := (iff #548 #545)
-#552 := [rewrite]: #551
-#549 := (iff #546 #548)
-#542 := (iff #515 #541)
-#539 := (iff #512 #538)
-#536 := (iff #511 #533)
-#526 := (+ #507 #47)
-#529 := (<= #526 0::real)
-#534 := (iff #529 #533)
-#535 := [rewrite]: #534
-#530 := (iff #511 #529)
-#527 := (= #508 #526)
-#528 := [rewrite]: #527
-#531 := [monotonicity #528]: #530
-#537 := [trans #531 #535]: #536
-#540 := [monotonicity #537]: #539
-#524 := (iff #514 #215)
-#516 := (+ #181 #41)
-#519 := (>= #516 0::int)
-#522 := (iff #519 #215)
-#523 := [rewrite]: #522
-#520 := (iff #514 #519)
-#517 := (= #513 #516)
-#518 := [rewrite]: #517
-#521 := [monotonicity #518]: #520
-#525 := [trans #521 #523]: #524
-#543 := [monotonicity #525 #540]: #542
-#550 := [monotonicity #543]: #549
-#554 := [trans #550 #552]: #553
-#547 := [quant-inst]: #546
-#555 := [mp #547 #554]: #545
-#607 := [unit-resolution #555 #449 #219]: #538
-#329 := [and-elim #328]: #270
-#608 := [hypothesis]: #605
-#609 := [th-lemma #608 #329 #607 #600]: false
-#611 := [lemma #609]: #610
-#612 := [hypothesis]: #451
-#614 := (or #613 #605)
-#615 := [th-lemma]: #614
-#616 := [unit-resolution #615 #612 #611]: false
-#617 := [lemma #616]: #613
-#455 := (or #275 #451)
-#456 := [def-axiom]: #455
-#618 := [unit-resolution #456 #617]: #275
-#452 := (not #275)
-#453 := (or #452 #450)
-#454 := [def-axiom]: #453
-#619 := [unit-resolution #454 #618]: #450
-#620 := (not #450)
-#621 := (or #620 #595)
-#622 := [th-lemma]: #621
-[unit-resolution #622 #619 #604]: false
-unsat
-f7a332c4ab50576b47f6154d9c204a030b7f3346 295 0
-#2 := false
-#25 := 0::real
-decl f8 :: (-> S4 S2 real)
-decl f11 :: S2
-#40 := f11
-decl f12 :: S4
-#44 := f12
-#45 := (f8 f12 f11)
-decl f10 :: S4
-#34 := f10
-#43 := (f8 f10 f11)
-#199 := -1::real
-#263 := (* -1::real #43)
-#264 := (+ #263 #45)
-decl f5 :: real
-#26 := f5
-#242 := (* -1::real #45)
-#331 := (+ #43 #242)
-#332 := (+ f5 #331)
-#333 := (<= #332 0::real)
-#336 := (ite #333 f5 #264)
-#666 := (* -1::real #336)
-#667 := (+ f5 #666)
-#668 := (<= #667 0::real)
-#676 := (not #668)
-#230 := 1/2::real
-#414 := (* 1/2::real #336)
-#531 := (<= #414 0::real)
-#415 := (= #414 0::real)
-#284 := -1/2::real
-#339 := (* -1/2::real #336)
-#342 := (+ #45 #339)
-decl f9 :: S4
-#32 := f9
-#47 := (f8 f9 f11)
-#243 := (+ #242 #47)
-#316 := (* -1::real #47)
-#317 := (+ #45 #316)
-#318 := (+ f5 #317)
-#319 := (<= #318 0::real)
-#322 := (ite #319 f5 #243)
-#325 := (* 1/2::real #322)
-#328 := (+ #45 #325)
-#232 := (* 1/2::real #47)
-#312 := (+ #242 #232)
-#231 := (* 1/2::real #43)
-#313 := (+ #231 #312)
-#310 := (>= #313 0::real)
-#345 := (ite #310 #328 #342)
-#348 := (= #45 #345)
-#418 := (iff #348 #415)
-#411 := (= #45 #342)
-#416 := (iff #411 #415)
-#417 := [rewrite]: #416
-#412 := (iff #348 #411)
-#409 := (= #345 #342)
-#404 := (ite false #328 #342)
-#407 := (= #404 #342)
-#408 := [rewrite]: #407
-#405 := (= #345 #404)
-#402 := (iff #310 false)
-#309 := (not #310)
-#361 := (<= #317 0::real)
-#358 := (<= #331 0::real)
-#364 := (and #358 #361)
-#13 := 0::int
-decl f4 :: (-> S2 int)
-#41 := (f4 f11)
-#185 := -1::int
-#220 := (* -1::int #41)
-decl f6 :: (-> S3 S2)
-decl f7 :: S3
-#28 := f7
-#29 := (f6 f7)
-#30 := (f4 #29)
-#221 := (+ #30 #220)
-#222 := (<= #221 0::int)
-#367 := (or #222 #364)
-#376 := (and #309 #348 #367)
-#52 := 2::real
-#61 := (- #45 #43)
-#62 := (<= f5 #61)
-#63 := (ite #62 f5 #61)
-#64 := (/ #63 2::real)
-#65 := (- #45 #64)
-#56 := (- #47 #45)
-#57 := (<= f5 #56)
-#58 := (ite #57 f5 #56)
-#59 := (/ #58 2::real)
-#60 := (+ #45 #59)
-#51 := (+ #43 #47)
-#53 := (/ #51 2::real)
-#55 := (<= #45 #53)
-#66 := (ite #55 #60 #65)
-#67 := (= #66 #45)
-#54 := (< #53 #45)
-#68 := (and #54 #67)
-#48 := (<= #45 #47)
-#46 := (<= #43 #45)
-#49 := (and #46 #48)
-#42 := (< #41 #30)
-#50 := (implies #42 #49)
-#69 := (and #50 #68)
-#381 := (iff #69 #376)
-#267 := (<= f5 #264)
-#270 := (ite #267 f5 #264)
-#285 := (* -1/2::real #270)
-#286 := (+ #45 #285)
-#246 := (<= f5 #243)
-#249 := (ite #246 f5 #243)
-#255 := (* 1/2::real #249)
-#260 := (+ #45 #255)
-#233 := (+ #231 #232)
-#239 := (<= #45 #233)
-#291 := (ite #239 #260 #286)
-#297 := (= #45 #291)
-#236 := (< #233 #45)
-#302 := (and #236 #297)
-#219 := (not #42)
-#227 := (or #219 #49)
-#305 := (and #227 #302)
-#379 := (iff #305 #376)
-#370 := (and #309 #348)
-#373 := (and #367 #370)
-#377 := (iff #373 #376)
-#378 := [rewrite]: #377
-#374 := (iff #305 #373)
-#371 := (iff #302 #370)
-#349 := (iff #297 #348)
-#346 := (= #291 #345)
-#343 := (= #286 #342)
-#340 := (= #285 #339)
-#337 := (= #270 #336)
-#334 := (iff #267 #333)
-#335 := [rewrite]: #334
-#338 := [monotonicity #335]: #337
-#341 := [monotonicity #338]: #340
-#344 := [monotonicity #341]: #343
-#329 := (= #260 #328)
-#326 := (= #255 #325)
-#323 := (= #249 #322)
-#320 := (iff #246 #319)
-#321 := [rewrite]: #320
-#324 := [monotonicity #321]: #323
-#327 := [monotonicity #324]: #326
-#330 := [monotonicity #327]: #329
-#315 := (iff #239 #310)
-#314 := [rewrite]: #315
-#347 := [monotonicity #314 #330 #344]: #346
-#350 := [monotonicity #347]: #349
-#308 := (iff #236 #309)
-#311 := [rewrite]: #308
-#372 := [monotonicity #311 #350]: #371
-#368 := (iff #227 #367)
-#365 := (iff #49 #364)
-#362 := (iff #48 #361)
-#363 := [rewrite]: #362
-#359 := (iff #46 #358)
-#360 := [rewrite]: #359
-#366 := [monotonicity #360 #363]: #365
-#356 := (iff #219 #222)
-#223 := (not #222)
-#351 := (not #223)
-#354 := (iff #351 #222)
-#355 := [rewrite]: #354
-#352 := (iff #219 #351)
-#224 := (iff #42 #223)
-#225 := [rewrite]: #224
-#353 := [monotonicity #225]: #352
-#357 := [trans #353 #355]: #356
-#369 := [monotonicity #357 #366]: #368
-#375 := [monotonicity #369 #372]: #374
-#380 := [trans #375 #378]: #379
-#306 := (iff #69 #305)
-#303 := (iff #68 #302)
-#300 := (iff #67 #297)
-#294 := (= #291 #45)
-#298 := (iff #294 #297)
-#299 := [rewrite]: #298
-#295 := (iff #67 #294)
-#292 := (= #66 #291)
-#289 := (= #65 #286)
-#276 := (* 1/2::real #270)
-#281 := (- #45 #276)
-#287 := (= #281 #286)
-#288 := [rewrite]: #287
-#282 := (= #65 #281)
-#279 := (= #64 #276)
-#273 := (/ #270 2::real)
-#277 := (= #273 #276)
-#278 := [rewrite]: #277
-#274 := (= #64 #273)
-#271 := (= #63 #270)
-#265 := (= #61 #264)
-#266 := [rewrite]: #265
-#268 := (iff #62 #267)
-#269 := [monotonicity #266]: #268
-#272 := [monotonicity #269 #266]: #271
-#275 := [monotonicity #272]: #274
-#280 := [trans #275 #278]: #279
-#283 := [monotonicity #280]: #282
-#290 := [trans #283 #288]: #289
-#261 := (= #60 #260)
-#258 := (= #59 #255)
-#252 := (/ #249 2::real)
-#256 := (= #252 #255)
-#257 := [rewrite]: #256
-#253 := (= #59 #252)
-#250 := (= #58 #249)
-#244 := (= #56 #243)
-#245 := [rewrite]: #244
-#247 := (iff #57 #246)
-#248 := [monotonicity #245]: #247
-#251 := [monotonicity #248 #245]: #250
-#254 := [monotonicity #251]: #253
-#259 := [trans #254 #257]: #258
-#262 := [monotonicity #259]: #261
-#240 := (iff #55 #239)
-#234 := (= #53 #233)
-#235 := [rewrite]: #234
-#241 := [monotonicity #235]: #240
-#293 := [monotonicity #241 #262 #290]: #292
-#296 := [monotonicity #293]: #295
-#301 := [trans #296 #299]: #300
-#237 := (iff #54 #236)
-#238 := [monotonicity #235]: #237
-#304 := [monotonicity #238 #301]: #303
-#228 := (iff #50 #227)
-#229 := [rewrite]: #228
-#307 := [monotonicity #229 #304]: #306
-#382 := [trans #307 #380]: #381
-#218 := [asserted]: #69
-#383 := [mp #218 #382]: #376
-#384 := [and-elim #383]: #309
-#403 := [iff-false #384]: #402
-#406 := [monotonicity #403]: #405
-#410 := [trans #406 #408]: #409
-#413 := [monotonicity #410]: #412
-#419 := [trans #413 #417]: #418
-#385 := [and-elim #383]: #348
-#420 := [mp #385 #419]: #415
-#670 := (not #415)
-#671 := (or #670 #531)
-#672 := [th-lemma]: #671
-#673 := [unit-resolution #672 #420]: #531
-#674 := [hypothesis]: #668
-#174 := (<= f5 0::real)
-#175 := (not #174)
-#27 := (< 0::real f5)
-#176 := (iff #27 #175)
-#177 := [rewrite]: #176
-#171 := [asserted]: #27
-#178 := [mp #171 #177]: #175
-#675 := [th-lemma #178 #674 #673]: false
-#677 := [lemma #675]: #676
-#524 := (= f5 #336)
-#525 := (= #264 #336)
-#685 := (not #525)
-#669 := (+ #264 #666)
-#678 := (<= #669 0::real)
-#682 := (not #678)
-#428 := (iff #367 #364)
-#423 := (or false #364)
-#426 := (iff #423 #364)
-#427 := [rewrite]: #426
-#424 := (iff #367 #423)
-#400 := (iff #222 false)
-#217 := [asserted]: #42
-#226 := [mp #217 #225]: #223
-#401 := [iff-false #226]: #400
-#425 := [monotonicity #401]: #424
-#429 := [trans #425 #427]: #428
-#386 := [and-elim #383]: #367
-#430 := [mp #386 #429]: #364
-#422 := [and-elim #430]: #361
-#680 := [hypothesis]: #678
-#681 := [th-lemma #680 #422 #384 #673]: false
-#683 := [lemma #681]: #682
-#684 := [hypothesis]: #525
-#686 := (or #685 #678)
-#687 := [th-lemma]: #686
-#688 := [unit-resolution #687 #684 #683]: false
-#689 := [lemma #688]: #685
-#529 := (or #333 #525)
-#530 := [def-axiom]: #529
-#690 := [unit-resolution #530 #689]: #333
-#526 := (not #333)
-#527 := (or #526 #524)
-#528 := [def-axiom]: #527
-#691 := [unit-resolution #528 #690]: #524
-#692 := (not #524)
-#693 := (or #692 #668)
-#694 := [th-lemma]: #693
-[unit-resolution #694 #691 #677]: false
-unsat
-5c9bfd1097eaec646745ccbc19c98d1ba847f0f5 308 0
-#2 := false
-#10 := 0::real
-decl f6 :: real
-#15 := f6
-#143 := (<= f6 0::real)
-#144 := (not #143)
-decl f5 :: real
-#13 := f5
-#53 := -1::real
-#203 := (* -1::real f5)
-decl f4 :: real
-#8 := f4
-#204 := (+ f4 #203)
-#202 := (>= #204 0::real)
-decl f3 :: (-> real real)
-#9 := (f3 f4)
-#54 := (* -1::real #9)
-#154 := (>= #9 0::real)
-#161 := (ite #154 #9 #54)
-#166 := (* f6 #161)
-#187 := (* f5 #166)
-#193 := (* -1::real #187)
-#66 := (* #9 f6)
-#78 := (* f4 #66)
-#72 := (* f5 f6)
-#73 := (* #9 #72)
-#96 := (* -1::real #73)
-#97 := (+ #96 #78)
-#84 := (* -1::real #78)
-#85 := (+ #73 #84)
-#172 := (>= #85 0::real)
-#179 := (ite #172 #85 #97)
-#194 := (+ #179 #193)
-#169 := (* f4 #166)
-#195 := (+ #169 #194)
-#196 := (<= #195 0::real)
-#11 := (= #9 0::real)
-#223 := (or #11 #143 #196 #202)
-#228 := (not #223)
-#18 := (- #9)
-#17 := (< #9 0::real)
-#19 := (ite #17 #18 #9)
-#20 := (* f6 #19)
-#30 := (* f5 #20)
-#22 := (* f6 #9)
-#24 := (* f4 #22)
-#23 := (* f5 #22)
-#25 := (- #23 #24)
-#27 := (- #25)
-#26 := (< #25 0::real)
-#28 := (ite #26 #27 #25)
-#21 := (* f4 #20)
-#29 := (+ #21 #28)
-#31 := (<= #29 #30)
-#16 := (< 0::real f6)
-#32 := (implies #16 #31)
-#14 := (< f4 f5)
-#33 := (implies #14 #32)
-#12 := (not #11)
-#34 := (implies #12 #33)
-#35 := (not #34)
-#231 := (iff #35 #228)
-#57 := (ite #17 #54 #9)
-#60 := (* f6 #57)
-#108 := (* f5 #60)
-#90 := (< #85 0::real)
-#102 := (ite #90 #97 #85)
-#63 := (* f4 #60)
-#105 := (+ #63 #102)
-#111 := (<= #105 #108)
-#117 := (not #16)
-#118 := (or #117 #111)
-#126 := (not #14)
-#127 := (or #126 #118)
-#135 := (or #11 #127)
-#140 := (not #135)
-#229 := (iff #140 #228)
-#226 := (iff #135 #223)
-#214 := (or #143 #196)
-#217 := (or #202 #214)
-#220 := (or #11 #217)
-#224 := (iff #220 #223)
-#225 := [rewrite]: #224
-#221 := (iff #135 #220)
-#218 := (iff #127 #217)
-#215 := (iff #118 #214)
-#199 := (iff #111 #196)
-#184 := (+ #169 #179)
-#190 := (<= #184 #187)
-#197 := (iff #190 #196)
-#198 := [rewrite]: #197
-#191 := (iff #111 #190)
-#188 := (= #108 #187)
-#167 := (= #60 #166)
-#164 := (= #57 #161)
-#155 := (not #154)
-#158 := (ite #155 #54 #9)
-#162 := (= #158 #161)
-#163 := [rewrite]: #162
-#159 := (= #57 #158)
-#156 := (iff #17 #155)
-#157 := [rewrite]: #156
-#160 := [monotonicity #157]: #159
-#165 := [trans #160 #163]: #164
-#168 := [monotonicity #165]: #167
-#189 := [monotonicity #168]: #188
-#185 := (= #105 #184)
-#182 := (= #102 #179)
-#173 := (not #172)
-#176 := (ite #173 #97 #85)
-#180 := (= #176 #179)
-#181 := [rewrite]: #180
-#177 := (= #102 #176)
-#174 := (iff #90 #173)
-#175 := [rewrite]: #174
-#178 := [monotonicity #175]: #177
-#183 := [trans #178 #181]: #182
-#170 := (= #63 #169)
-#171 := [monotonicity #168]: #170
-#186 := [monotonicity #171 #183]: #185
-#192 := [monotonicity #186 #189]: #191
-#200 := [trans #192 #198]: #199
-#152 := (iff #117 #143)
-#147 := (not #144)
-#150 := (iff #147 #143)
-#151 := [rewrite]: #150
-#148 := (iff #117 #147)
-#145 := (iff #16 #144)
-#146 := [rewrite]: #145
-#149 := [monotonicity #146]: #148
-#153 := [trans #149 #151]: #152
-#216 := [monotonicity #153 #200]: #215
-#212 := (iff #126 #202)
-#201 := (not #202)
-#207 := (not #201)
-#210 := (iff #207 #202)
-#211 := [rewrite]: #210
-#208 := (iff #126 #207)
-#205 := (iff #14 #201)
-#206 := [rewrite]: #205
-#209 := [monotonicity #206]: #208
-#213 := [trans #209 #211]: #212
-#219 := [monotonicity #213 #216]: #218
-#222 := [monotonicity #219]: #221
-#227 := [trans #222 #225]: #226
-#230 := [monotonicity #227]: #229
-#141 := (iff #35 #140)
-#138 := (iff #34 #135)
-#132 := (implies #12 #127)
-#136 := (iff #132 #135)
-#137 := [rewrite]: #136
-#133 := (iff #34 #132)
-#130 := (iff #33 #127)
-#123 := (implies #14 #118)
-#128 := (iff #123 #127)
-#129 := [rewrite]: #128
-#124 := (iff #33 #123)
-#121 := (iff #32 #118)
-#114 := (implies #16 #111)
-#119 := (iff #114 #118)
-#120 := [rewrite]: #119
-#115 := (iff #32 #114)
-#112 := (iff #31 #111)
-#109 := (= #30 #108)
-#61 := (= #20 #60)
-#58 := (= #19 #57)
-#55 := (= #18 #54)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#62 := [monotonicity #59]: #61
-#110 := [monotonicity #62]: #109
-#106 := (= #29 #105)
-#103 := (= #28 #102)
-#88 := (= #25 #85)
-#81 := (- #73 #78)
-#86 := (= #81 #85)
-#87 := [rewrite]: #86
-#82 := (= #25 #81)
-#79 := (= #24 #78)
-#67 := (= #22 #66)
-#68 := [rewrite]: #67
-#80 := [monotonicity #68]: #79
-#76 := (= #23 #73)
-#69 := (* f5 #66)
-#74 := (= #69 #73)
-#75 := [rewrite]: #74
-#70 := (= #23 #69)
-#71 := [monotonicity #68]: #70
-#77 := [trans #71 #75]: #76
-#83 := [monotonicity #77 #80]: #82
-#89 := [trans #83 #87]: #88
-#100 := (= #27 #97)
-#93 := (- #85)
-#98 := (= #93 #97)
-#99 := [rewrite]: #98
-#94 := (= #27 #93)
-#95 := [monotonicity #89]: #94
-#101 := [trans #95 #99]: #100
-#91 := (iff #26 #90)
-#92 := [monotonicity #89]: #91
-#104 := [monotonicity #92 #101 #89]: #103
-#64 := (= #21 #63)
-#65 := [monotonicity #62]: #64
-#107 := [monotonicity #65 #104]: #106
-#113 := [monotonicity #107 #110]: #112
-#116 := [monotonicity #113]: #115
-#122 := [trans #116 #120]: #121
-#125 := [monotonicity #122]: #124
-#131 := [trans #125 #129]: #130
-#134 := [monotonicity #131]: #133
-#139 := [trans #134 #137]: #138
-#142 := [monotonicity #139]: #141
-#232 := [trans #142 #230]: #231
-#52 := [asserted]: #35
-#233 := [mp #52 #232]: #228
-#235 := [not-or-elim #233]: #144
-#241 := (<= #9 0::real)
-#317 := (not #241)
-#251 := (= #54 #161)
-#290 := (not #251)
-#236 := (not #196)
-#237 := [not-or-elim #233]: #236
-#239 := (* -1::real #179)
-#299 := (+ #97 #239)
-#301 := (>= #299 0::real)
-#247 := (= #97 #179)
-#246 := (= #85 #179)
-#280 := (not #246)
-#250 := (= #9 #161)
-#264 := (not #250)
-#254 := (+ #85 #239)
-#256 := (>= #254 0::real)
-#279 := [hypothesis]: #246
-#281 := (or #280 #256)
-#282 := [th-lemma]: #281
-#283 := [unit-resolution #282 #279]: #256
-#255 := (<= #254 0::real)
-#284 := (or #280 #255)
-#285 := [th-lemma]: #284
-#286 := [unit-resolution #285 #279]: #255
-#273 := (not #256)
-#272 := (not #255)
-#274 := (or #264 #272 #273)
-#261 := [hypothesis]: #256
-#262 := [hypothesis]: #255
-#257 := (* -1::real #161)
-#258 := (+ #9 #257)
-#260 := (>= #258 0::real)
-#263 := [hypothesis]: #250
-#265 := (or #264 #260)
-#266 := [th-lemma]: #265
-#267 := [unit-resolution #266 #263]: #260
-#259 := (<= #258 0::real)
-#268 := (or #264 #259)
-#269 := [th-lemma]: #268
-#270 := [unit-resolution #269 #263]: #259
-#271 := [th-lemma #270 #267 #262 #261 #237]: false
-#275 := [lemma #271]: #274
-#287 := [unit-resolution #275 #286 #283]: #264
-#252 := (or #155 #250)
-#253 := [def-axiom]: #252
-#288 := [unit-resolution #253 #287]: #155
-#238 := [not-or-elim #233]: #201
-#276 := (+ #54 #257)
-#278 := (>= #276 0::real)
-#248 := (or #154 #251)
-#249 := [def-axiom]: #248
-#289 := [unit-resolution #249 #288]: #251
-#291 := (or #290 #278)
-#292 := [th-lemma]: #291
-#293 := [unit-resolution #292 #289]: #278
-#277 := (<= #276 0::real)
-#294 := (or #290 #277)
-#295 := [th-lemma]: #294
-#296 := [unit-resolution #295 #289]: #277
-#297 := [th-lemma #296 #293 #286 #283 #237 #238 #288 #235]: false
-#298 := [lemma #297]: #280
-#244 := (or #173 #246)
-#245 := [def-axiom]: #244
-#302 := [unit-resolution #245 #298]: #173
-#242 := (or #172 #247)
-#243 := [def-axiom]: #242
-#303 := [unit-resolution #243 #302]: #247
-#304 := (not #247)
-#305 := (or #304 #301)
-#306 := [th-lemma]: #305
-#307 := [unit-resolution #306 #303]: #301
-#300 := (<= #299 0::real)
-#308 := (or #304 #300)
-#309 := [th-lemma]: #308
-#310 := [unit-resolution #309 #303]: #300
-#311 := [hypothesis]: #251
-#312 := [unit-resolution #292 #311]: #278
-#313 := [unit-resolution #295 #311]: #277
-#314 := [th-lemma #313 #312 #310 #307 #237]: false
-#315 := [lemma #314]: #290
-#316 := [unit-resolution #249 #315]: #154
-#320 := (or #317 #155)
-#234 := [not-or-elim #233]: #12
-#318 := (or #11 #317 #155)
-#319 := [th-lemma]: #318
-#321 := [unit-resolution #319 #234]: #320
-#322 := [unit-resolution #321 #316]: #317
-#323 := [unit-resolution #253 #316]: #250
-#324 := [unit-resolution #266 #323]: #260
-#325 := [unit-resolution #269 #323]: #259
-[th-lemma #325 #324 #310 #307 #237 #238 #322 #235]: false
-unsat
-9171919cd704be8e7c103a2053e7cd7353c1a910 19 0
-f1 -> val!0
-f2 -> val!1
-f3 -> 0
-f4 -> 1
-f5 -> 1
-f6 -> {
-  0 -> 3
-  else -> 3
-}
-f7 -> {
-  3 -> 1
-  8 -> 1
-  else -> 1
-}
-f8 -> {
-  1236 3 -> 8
-  else -> 8
-}
-unknown
-2890cc0ea13f6a8b550bc60d1dd56915e31e1ba5 386 0
-#2 := false
-#11 := 0::real
-decl f5 :: real
-#12 := f5
-#62 := (<= f5 0::real)
-#63 := (not #62)
-#13 := (< 0::real f5)
-#64 := (iff #13 #63)
-#65 := [rewrite]: #64
-#51 := [asserted]: #13
-#66 := [mp #51 #65]: #63
-decl f4 :: real
-#9 := f4
-#53 := -1::real
-#56 := (* -1::real f4)
-decl f3 :: real
-#8 := f3
-#57 := (+ f3 #56)
-#55 := (>= #57 0::real)
-#54 := (not #55)
-#10 := (< f3 f4)
-#58 := (iff #10 #54)
-#59 := [rewrite]: #58
-#50 := [asserted]: #10
-#60 := [mp #50 #59]: #54
-decl f6 :: (-> real real)
-#14 := (f6 f3)
-#99 := (* -1::real #14)
-#152 := (>= #14 0::real)
-#159 := (ite #152 #14 #99)
-#271 := (<= #159 0::real)
-#336 := (not #271)
-#252 := (<= #14 0::real)
-#397 := (not #252)
-#153 := (not #152)
-#384 := [hypothesis]: #153
-#267 := (* -1::real #159)
-#305 := (+ #99 #267)
-#306 := (<= #305 0::real)
-#241 := (= #99 #159)
-#244 := (or #152 #241)
-#245 := [def-axiom]: #244
-#385 := [unit-resolution #245 #384]: #241
-#314 := (not #241)
-#318 := (or #314 #306)
-#319 := [th-lemma]: #318
-#386 := [unit-resolution #319 #385]: #306
-#337 := (not #306)
-#338 := (or #336 #152 #337)
-#339 := [th-lemma]: #338
-#387 := [unit-resolution #339 #386 #384]: #336
-#81 := (* f4 f5)
-#90 := 1/8::real
-#93 := (* 1/8::real #81)
-#79 := (* f3 f5)
-#91 := -1/8::real
-#92 := (* -1/8::real #79)
-#94 := (+ #92 #93)
-#164 := (/ #94 #159)
-#170 := (<= #164 0::real)
-#176 := (* #14 #164)
-#188 := (* -1::real #176)
-#183 := (>= #176 0::real)
-#194 := (ite #183 #176 #188)
-#203 := (* -1/8::real #81)
-#204 := (+ #203 #194)
-#202 := (* 1/8::real #79)
-#205 := (+ #202 #204)
-#206 := (<= #205 0::real)
-#382 := (or #206 #314)
-#237 := (not #206)
-#273 := [hypothesis]: #237
-#263 := (* -1::real #194)
-#348 := (+ #188 #263)
-#350 := (>= #348 0::real)
-#247 := (= #188 #194)
-#182 := (not #183)
-#246 := (= #176 #194)
-#325 := (not #246)
-#346 := (or #325 #206)
-#226 := (= #14 #159)
-#293 := (not #226)
-#264 := (+ #176 #263)
-#266 := (>= #264 0::real)
-#324 := [hypothesis]: #246
-#326 := (or #325 #266)
-#327 := [th-lemma]: #326
-#328 := [unit-resolution #327 #324]: #266
-#265 := (<= #264 0::real)
-#329 := (or #325 #265)
-#330 := [th-lemma]: #329
-#331 := [unit-resolution #330 #324]: #265
-#302 := (not #266)
-#301 := (not #265)
-#303 := (or #293 #301 #302 #206)
-#254 := (* #159 #164)
-#258 := (+ #203 #254)
-#259 := (+ #202 #258)
-#257 := (>= #259 0::real)
-#260 := (= #259 0::real)
-#253 := (= #159 0::real)
-#277 := (not #253)
-#15 := (= #14 0::real)
-#16 := (not #15)
-#278 := (iff #16 #277)
-#275 := (iff #15 #253)
-#274 := [hypothesis]: #226
-#276 := [monotonicity #274]: #275
-#279 := [monotonicity #276]: #278
-#171 := (not #170)
-#211 := (and #171 #206)
-#214 := (or #15 #211)
-#217 := (not #214)
-#19 := 8::real
-#17 := (- f4 f3)
-#18 := (* f5 #17)
-#20 := (/ #18 8::real)
-#22 := (- #14)
-#21 := (< #14 0::real)
-#23 := (ite #21 #22 #14)
-#24 := (/ #20 #23)
-#26 := (* #24 #14)
-#28 := (- #26)
-#27 := (< #26 0::real)
-#29 := (ite #27 #28 #26)
-#30 := (<= #29 #20)
-#25 := (< 0::real #24)
-#31 := (and #25 #30)
-#32 := (implies #16 #31)
-#33 := (not #32)
-#220 := (iff #33 #217)
-#102 := (ite #21 #99 #14)
-#105 := (/ #94 #102)
-#114 := (* #14 #105)
-#125 := (* -1::real #114)
-#119 := (< #114 0::real)
-#130 := (ite #119 #125 #114)
-#133 := (<= #130 #94)
-#108 := (< 0::real #105)
-#136 := (and #108 #133)
-#61 := (= 0::real #14)
-#142 := (or #61 #136)
-#147 := (not #142)
-#218 := (iff #147 #217)
-#215 := (iff #142 #214)
-#212 := (iff #136 #211)
-#209 := (iff #133 #206)
-#199 := (<= #194 #94)
-#207 := (iff #199 #206)
-#208 := [rewrite]: #207
-#200 := (iff #133 #199)
-#197 := (= #130 #194)
-#191 := (ite #182 #188 #176)
-#195 := (= #191 #194)
-#196 := [rewrite]: #195
-#192 := (= #130 #191)
-#177 := (= #114 #176)
-#165 := (= #105 #164)
-#162 := (= #102 #159)
-#156 := (ite #153 #99 #14)
-#160 := (= #156 #159)
-#161 := [rewrite]: #160
-#157 := (= #102 #156)
-#154 := (iff #21 #153)
-#155 := [rewrite]: #154
-#158 := [monotonicity #155]: #157
-#163 := [trans #158 #161]: #162
-#166 := [monotonicity #163]: #165
-#178 := [monotonicity #166]: #177
-#189 := (= #125 #188)
-#190 := [monotonicity #178]: #189
-#186 := (iff #119 #182)
-#179 := (< #176 0::real)
-#184 := (iff #179 #182)
-#185 := [rewrite]: #184
-#180 := (iff #119 #179)
-#181 := [monotonicity #178]: #180
-#187 := [trans #181 #185]: #186
-#193 := [monotonicity #187 #190 #178]: #192
-#198 := [trans #193 #196]: #197
-#201 := [monotonicity #198]: #200
-#210 := [trans #201 #208]: #209
-#174 := (iff #108 #171)
-#167 := (< 0::real #164)
-#172 := (iff #167 #171)
-#173 := [rewrite]: #172
-#168 := (iff #108 #167)
-#169 := [monotonicity #166]: #168
-#175 := [trans #169 #173]: #174
-#213 := [monotonicity #175 #210]: #212
-#150 := (iff #61 #15)
-#151 := [rewrite]: #150
-#216 := [monotonicity #151 #213]: #215
-#219 := [monotonicity #216]: #218
-#148 := (iff #33 #147)
-#145 := (iff #32 #142)
-#69 := (not #61)
-#139 := (implies #69 #136)
-#143 := (iff #139 #142)
-#144 := [rewrite]: #143
-#140 := (iff #32 #139)
-#137 := (iff #31 #136)
-#134 := (iff #30 #133)
-#97 := (= #20 #94)
-#80 := (* -1::real #79)
-#82 := (+ #80 #81)
-#87 := (/ #82 8::real)
-#95 := (= #87 #94)
-#96 := [rewrite]: #95
-#88 := (= #20 #87)
-#85 := (= #18 #82)
-#72 := (* -1::real f3)
-#73 := (+ #72 f4)
-#76 := (* f5 #73)
-#83 := (= #76 #82)
-#84 := [rewrite]: #83
-#77 := (= #18 #76)
-#74 := (= #17 #73)
-#75 := [rewrite]: #74
-#78 := [monotonicity #75]: #77
-#86 := [trans #78 #84]: #85
-#89 := [monotonicity #86]: #88
-#98 := [trans #89 #96]: #97
-#131 := (= #29 #130)
-#117 := (= #26 #114)
-#111 := (* #105 #14)
-#115 := (= #111 #114)
-#116 := [rewrite]: #115
-#112 := (= #26 #111)
-#106 := (= #24 #105)
-#103 := (= #23 #102)
-#100 := (= #22 #99)
-#101 := [rewrite]: #100
-#104 := [monotonicity #101]: #103
-#107 := [monotonicity #98 #104]: #106
-#113 := [monotonicity #107]: #112
-#118 := [trans #113 #116]: #117
-#128 := (= #28 #125)
-#122 := (- #114)
-#126 := (= #122 #125)
-#127 := [rewrite]: #126
-#123 := (= #28 #122)
-#124 := [monotonicity #118]: #123
-#129 := [trans #124 #127]: #128
-#120 := (iff #27 #119)
-#121 := [monotonicity #118]: #120
-#132 := [monotonicity #121 #129 #118]: #131
-#135 := [monotonicity #132 #98]: #134
-#109 := (iff #25 #108)
-#110 := [monotonicity #107]: #109
-#138 := [monotonicity #110 #135]: #137
-#70 := (iff #16 #69)
-#67 := (iff #15 #61)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#141 := [monotonicity #71 #138]: #140
-#146 := [trans #141 #144]: #145
-#149 := [monotonicity #146]: #148
-#221 := [trans #149 #219]: #220
-#52 := [asserted]: #33
-#222 := [mp #52 #221]: #217
-#223 := [not-or-elim #222]: #16
-#280 := [mp #223 #279]: #277
-#281 := (or #253 #260)
-#282 := [th-lemma]: #281
-#283 := [unit-resolution #282 #280]: #260
-#284 := (not #260)
-#285 := (or #284 #257)
-#286 := [th-lemma]: #285
-#287 := [unit-resolution #286 #283]: #257
-#256 := (<= #259 0::real)
-#288 := (or #284 #256)
-#289 := [th-lemma]: #288
-#290 := [unit-resolution #289 #283]: #256
-#291 := [hypothesis]: #266
-#292 := [hypothesis]: #265
-#268 := (+ #14 #267)
-#270 := (>= #268 0::real)
-#294 := (or #293 #270)
-#295 := [th-lemma]: #294
-#296 := [unit-resolution #295 #274]: #270
-#269 := (<= #268 0::real)
-#297 := (or #293 #269)
-#298 := [th-lemma]: #297
-#299 := [unit-resolution #298 #274]: #269
-#300 := [th-lemma #299 #296 #292 #291 #290 #287 #273]: false
-#304 := [lemma #300]: #303
-#332 := [unit-resolution #304 #331 #328 #273]: #293
-#242 := (or #153 #226)
-#243 := [def-axiom]: #242
-#333 := [unit-resolution #243 #332]: #153
-#334 := [unit-resolution #245 #333]: #241
-#335 := [unit-resolution #319 #334]: #306
-#340 := [unit-resolution #339 #333 #335]: #336
-#322 := (or #284 #301 #302 #206)
-#308 := [hypothesis]: #260
-#309 := [unit-resolution #286 #308]: #257
-#310 := [unit-resolution #289 #308]: #256
-#307 := (>= #305 0::real)
-#311 := [unit-resolution #304 #292 #291 #273]: #293
-#312 := [unit-resolution #243 #311]: #153
-#313 := [unit-resolution #245 #312]: #241
-#315 := (or #314 #307)
-#316 := [th-lemma]: #315
-#317 := [unit-resolution #316 #313]: #307
-#320 := [unit-resolution #319 #313]: #306
-#321 := [th-lemma #320 #317 #292 #291 #310 #309 #273 #60 #66]: false
-#323 := [lemma #321]: #322
-#341 := [unit-resolution #323 #331 #328 #273]: #284
-#342 := [unit-resolution #282 #341]: #253
-#343 := (or #277 #271)
-#344 := [th-lemma]: #343
-#345 := [unit-resolution #344 #342 #340]: false
-#347 := [lemma #345]: #346
-#365 := [unit-resolution #347 #273]: #325
-#248 := (or #182 #246)
-#249 := [def-axiom]: #248
-#366 := [unit-resolution #249 #365]: #182
-#250 := (or #183 #247)
-#251 := [def-axiom]: #250
-#367 := [unit-resolution #251 #366]: #247
-#368 := (not #247)
-#369 := (or #368 #350)
-#370 := [th-lemma]: #369
-#371 := [unit-resolution #370 #367]: #350
-#349 := (<= #348 0::real)
-#372 := (or #368 #349)
-#373 := [th-lemma]: #372
-#374 := [unit-resolution #373 #367]: #349
-#351 := [hypothesis]: #253
-#352 := [unit-resolution #344 #351]: #271
-#357 := (iff #16 #293)
-#355 := (iff #15 #226)
-#353 := (iff #226 #15)
-#354 := [monotonicity #351]: #353
-#356 := [symm #354]: #355
-#358 := [monotonicity #356]: #357
-#359 := [mp #223 #358]: #293
-#360 := [unit-resolution #243 #359]: #153
-#361 := [unit-resolution #339 #360 #352]: #337
-#362 := [unit-resolution #245 #360]: #241
-#363 := [unit-resolution #319 #362 #361]: false
-#364 := [lemma #363]: #277
-#375 := [unit-resolution #282 #364]: #260
-#376 := [unit-resolution #286 #375]: #257
-#377 := [unit-resolution #289 #375]: #256
-#378 := [hypothesis]: #241
-#379 := [unit-resolution #316 #378]: #307
-#380 := [unit-resolution #319 #378]: #306
-#381 := [th-lemma #380 #379 #377 #376 #374 #371 #273]: false
-#383 := [lemma #381]: #382
-#388 := [unit-resolution #383 #385]: #206
-#238 := (or #170 #237)
-#224 := (not #211)
-#229 := (iff #224 #238)
-#239 := (not #238)
-#236 := (not #239)
-#231 := (iff #236 #238)
-#232 := [rewrite]: #231
-#233 := (iff #224 #236)
-#240 := (iff #211 #239)
-#235 := [rewrite]: #240
-#234 := [monotonicity #235]: #233
-#230 := [trans #234 #232]: #229
-#225 := [not-or-elim #222]: #224
-#228 := [mp #225 #230]: #238
-#389 := [unit-resolution #228 #388]: #170
-#390 := [th-lemma #377 #376 #389 #387 #60 #66]: false
-#391 := [lemma #390]: #152
-#400 := (or #397 #153)
-#398 := (or #15 #397 #153)
-#399 := [th-lemma]: #398
-#401 := [unit-resolution #399 #223]: #400
-#402 := [unit-resolution #401 #391]: #397
-#392 := [unit-resolution #243 #391]: #226
-#394 := [unit-resolution #298 #392]: #269
-#403 := (not #269)
-#404 := (or #336 #252 #403)
-#405 := [th-lemma]: #404
-#406 := [unit-resolution #405 #394 #402]: #336
-#393 := [unit-resolution #295 #392]: #270
-#395 := [th-lemma #394 #393 #377 #376 #374 #371 #273 #60 #66]: false
-#396 := [lemma #395]: #206
-#407 := [unit-resolution #228 #396]: #170
-[th-lemma #377 #376 #407 #406 #60 #66]: false
-unsat
-726e0e73e0888d06cfe039319b4774bfabee92ef 421 0
-#2 := false
-#10 := 0::real
-decl f6 :: real
-#15 := f6
-#150 := (<= f6 0::real)
-#151 := (not #150)
-decl f5 :: real
-#13 := f5
-#53 := -1::real
-#223 := (* -1::real f5)
-decl f4 :: real
-#8 := f4
-#224 := (+ f4 #223)
-#225 := (>= #224 0::real)
-decl f3 :: (-> real real)
-#9 := (f3 f4)
-#81 := (* -1::real #9)
-#161 := (>= #9 0::real)
-#168 := (ite #161 #9 #81)
-#63 := (* f5 f6)
-#72 := 1/8::real
-#75 := (* 1/8::real #63)
-#61 := (* f4 f6)
-#73 := -1/8::real
-#74 := (* -1/8::real #61)
-#76 := (+ #74 #75)
-#173 := (/ #76 #168)
-#185 := (* #9 #173)
-#197 := (* -1::real #185)
-#192 := (>= #185 0::real)
-#203 := (ite #192 #185 #197)
-#212 := (* -1/8::real #63)
-#213 := (+ #212 #203)
-#211 := (* 1/8::real #61)
-#214 := (+ #211 #213)
-#215 := (<= #214 0::real)
-#179 := (<= #173 0::real)
-#180 := (not #179)
-#220 := (and #180 #215)
-#11 := (= #9 0::real)
-#245 := (or #11 #150 #220 #225)
-#250 := (not #245)
-#19 := 8::real
-#17 := (- f5 f4)
-#18 := (* f6 #17)
-#20 := (/ #18 8::real)
-#22 := (- #9)
-#21 := (< #9 0::real)
-#23 := (ite #21 #22 #9)
-#24 := (/ #20 #23)
-#26 := (* #24 #9)
-#28 := (- #26)
-#27 := (< #26 0::real)
-#29 := (ite #27 #28 #26)
-#30 := (<= #29 #20)
-#25 := (< 0::real #24)
-#31 := (and #25 #30)
-#16 := (< 0::real f6)
-#32 := (implies #16 #31)
-#14 := (< f4 f5)
-#33 := (implies #14 #32)
-#12 := (not #11)
-#34 := (implies #12 #33)
-#35 := (not #34)
-#253 := (iff #35 #250)
-#84 := (ite #21 #81 #9)
-#87 := (/ #76 #84)
-#96 := (* #9 #87)
-#107 := (* -1::real #96)
-#101 := (< #96 0::real)
-#112 := (ite #101 #107 #96)
-#115 := (<= #112 #76)
-#90 := (< 0::real #87)
-#118 := (and #90 #115)
-#124 := (not #16)
-#125 := (or #124 #118)
-#133 := (not #14)
-#134 := (or #133 #125)
-#142 := (or #11 #134)
-#147 := (not #142)
-#251 := (iff #147 #250)
-#248 := (iff #142 #245)
-#236 := (or #150 #220)
-#239 := (or #225 #236)
-#242 := (or #11 #239)
-#246 := (iff #242 #245)
-#247 := [rewrite]: #246
-#243 := (iff #142 #242)
-#240 := (iff #134 #239)
-#237 := (iff #125 #236)
-#221 := (iff #118 #220)
-#218 := (iff #115 #215)
-#208 := (<= #203 #76)
-#216 := (iff #208 #215)
-#217 := [rewrite]: #216
-#209 := (iff #115 #208)
-#206 := (= #112 #203)
-#191 := (not #192)
-#200 := (ite #191 #197 #185)
-#204 := (= #200 #203)
-#205 := [rewrite]: #204
-#201 := (= #112 #200)
-#186 := (= #96 #185)
-#174 := (= #87 #173)
-#171 := (= #84 #168)
-#162 := (not #161)
-#165 := (ite #162 #81 #9)
-#169 := (= #165 #168)
-#170 := [rewrite]: #169
-#166 := (= #84 #165)
-#163 := (iff #21 #162)
-#164 := [rewrite]: #163
-#167 := [monotonicity #164]: #166
-#172 := [trans #167 #170]: #171
-#175 := [monotonicity #172]: #174
-#187 := [monotonicity #175]: #186
-#198 := (= #107 #197)
-#199 := [monotonicity #187]: #198
-#195 := (iff #101 #191)
-#188 := (< #185 0::real)
-#193 := (iff #188 #191)
-#194 := [rewrite]: #193
-#189 := (iff #101 #188)
-#190 := [monotonicity #187]: #189
-#196 := [trans #190 #194]: #195
-#202 := [monotonicity #196 #199 #187]: #201
-#207 := [trans #202 #205]: #206
-#210 := [monotonicity #207]: #209
-#219 := [trans #210 #217]: #218
-#183 := (iff #90 #180)
-#176 := (< 0::real #173)
-#181 := (iff #176 #180)
-#182 := [rewrite]: #181
-#177 := (iff #90 #176)
-#178 := [monotonicity #175]: #177
-#184 := [trans #178 #182]: #183
-#222 := [monotonicity #184 #219]: #221
-#159 := (iff #124 #150)
-#154 := (not #151)
-#157 := (iff #154 #150)
-#158 := [rewrite]: #157
-#155 := (iff #124 #154)
-#152 := (iff #16 #151)
-#153 := [rewrite]: #152
-#156 := [monotonicity #153]: #155
-#160 := [trans #156 #158]: #159
-#238 := [monotonicity #160 #222]: #237
-#234 := (iff #133 #225)
-#226 := (not #225)
-#229 := (not #226)
-#232 := (iff #229 #225)
-#233 := [rewrite]: #232
-#230 := (iff #133 #229)
-#227 := (iff #14 #226)
-#228 := [rewrite]: #227
-#231 := [monotonicity #228]: #230
-#235 := [trans #231 #233]: #234
-#241 := [monotonicity #235 #238]: #240
-#244 := [monotonicity #241]: #243
-#249 := [trans #244 #247]: #248
-#252 := [monotonicity #249]: #251
-#148 := (iff #35 #147)
-#145 := (iff #34 #142)
-#139 := (implies #12 #134)
-#143 := (iff #139 #142)
-#144 := [rewrite]: #143
-#140 := (iff #34 #139)
-#137 := (iff #33 #134)
-#130 := (implies #14 #125)
-#135 := (iff #130 #134)
-#136 := [rewrite]: #135
-#131 := (iff #33 #130)
-#128 := (iff #32 #125)
-#121 := (implies #16 #118)
-#126 := (iff #121 #125)
-#127 := [rewrite]: #126
-#122 := (iff #32 #121)
-#119 := (iff #31 #118)
-#116 := (iff #30 #115)
-#79 := (= #20 #76)
-#62 := (* -1::real #61)
-#64 := (+ #62 #63)
-#69 := (/ #64 8::real)
-#77 := (= #69 #76)
-#78 := [rewrite]: #77
-#70 := (= #20 #69)
-#67 := (= #18 #64)
-#54 := (* -1::real f4)
-#55 := (+ #54 f5)
-#58 := (* f6 #55)
-#65 := (= #58 #64)
-#66 := [rewrite]: #65
-#59 := (= #18 #58)
-#56 := (= #17 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#68 := [trans #60 #66]: #67
-#71 := [monotonicity #68]: #70
-#80 := [trans #71 #78]: #79
-#113 := (= #29 #112)
-#99 := (= #26 #96)
-#93 := (* #87 #9)
-#97 := (= #93 #96)
-#98 := [rewrite]: #97
-#94 := (= #26 #93)
-#88 := (= #24 #87)
-#85 := (= #23 #84)
-#82 := (= #22 #81)
-#83 := [rewrite]: #82
-#86 := [monotonicity #83]: #85
-#89 := [monotonicity #80 #86]: #88
-#95 := [monotonicity #89]: #94
-#100 := [trans #95 #98]: #99
-#110 := (= #28 #107)
-#104 := (- #96)
-#108 := (= #104 #107)
-#109 := [rewrite]: #108
-#105 := (= #28 #104)
-#106 := [monotonicity #100]: #105
-#111 := [trans #106 #109]: #110
-#102 := (iff #27 #101)
-#103 := [monotonicity #100]: #102
-#114 := [monotonicity #103 #111 #100]: #113
-#117 := [monotonicity #114 #80]: #116
-#91 := (iff #25 #90)
-#92 := [monotonicity #89]: #91
-#120 := [monotonicity #92 #117]: #119
-#123 := [monotonicity #120]: #122
-#129 := [trans #123 #127]: #128
-#132 := [monotonicity #129]: #131
-#138 := [trans #132 #136]: #137
-#141 := [monotonicity #138]: #140
-#146 := [trans #141 #144]: #145
-#149 := [monotonicity #146]: #148
-#254 := [trans #149 #252]: #253
-#52 := [asserted]: #35
-#255 := [mp #52 #254]: #250
-#257 := [not-or-elim #255]: #151
-#260 := [not-or-elim #255]: #226
-#306 := (<= #168 0::real)
-#371 := (not #306)
-#287 := (<= #9 0::real)
-#432 := (not #287)
-#419 := [hypothesis]: #162
-#302 := (* -1::real #168)
-#340 := (+ #81 #302)
-#341 := (<= #340 0::real)
-#276 := (= #81 #168)
-#279 := (or #161 #276)
-#280 := [def-axiom]: #279
-#420 := [unit-resolution #280 #419]: #276
-#349 := (not #276)
-#353 := (or #349 #341)
-#354 := [th-lemma]: #353
-#421 := [unit-resolution #354 #420]: #341
-#372 := (not #341)
-#373 := (or #371 #161 #372)
-#374 := [th-lemma]: #373
-#422 := [unit-resolution #374 #421 #419]: #371
-#417 := (or #215 #349)
-#272 := (not #215)
-#308 := [hypothesis]: #272
-#298 := (* -1::real #203)
-#383 := (+ #197 #298)
-#385 := (>= #383 0::real)
-#282 := (= #197 #203)
-#281 := (= #185 #203)
-#360 := (not #281)
-#381 := (or #360 #215)
-#261 := (= #9 #168)
-#328 := (not #261)
-#299 := (+ #185 #298)
-#301 := (>= #299 0::real)
-#359 := [hypothesis]: #281
-#361 := (or #360 #301)
-#362 := [th-lemma]: #361
-#363 := [unit-resolution #362 #359]: #301
-#300 := (<= #299 0::real)
-#364 := (or #360 #300)
-#365 := [th-lemma]: #364
-#366 := [unit-resolution #365 #359]: #300
-#337 := (not #301)
-#336 := (not #300)
-#338 := (or #328 #336 #337 #215)
-#289 := (* #168 #173)
-#293 := (+ #212 #289)
-#294 := (+ #211 #293)
-#292 := (>= #294 0::real)
-#295 := (= #294 0::real)
-#288 := (= #168 0::real)
-#312 := (not #288)
-#313 := (iff #12 #312)
-#310 := (iff #11 #288)
-#309 := [hypothesis]: #261
-#311 := [monotonicity #309]: #310
-#314 := [monotonicity #311]: #313
-#256 := [not-or-elim #255]: #12
-#315 := [mp #256 #314]: #312
-#316 := (or #288 #295)
-#317 := [th-lemma]: #316
-#318 := [unit-resolution #317 #315]: #295
-#319 := (not #295)
-#320 := (or #319 #292)
-#321 := [th-lemma]: #320
-#322 := [unit-resolution #321 #318]: #292
-#291 := (<= #294 0::real)
-#323 := (or #319 #291)
-#324 := [th-lemma]: #323
-#325 := [unit-resolution #324 #318]: #291
-#326 := [hypothesis]: #301
-#327 := [hypothesis]: #300
-#303 := (+ #9 #302)
-#305 := (>= #303 0::real)
-#329 := (or #328 #305)
-#330 := [th-lemma]: #329
-#331 := [unit-resolution #330 #309]: #305
-#304 := (<= #303 0::real)
-#332 := (or #328 #304)
-#333 := [th-lemma]: #332
-#334 := [unit-resolution #333 #309]: #304
-#335 := [th-lemma #334 #331 #327 #326 #325 #322 #308]: false
-#339 := [lemma #335]: #338
-#367 := [unit-resolution #339 #366 #363 #308]: #328
-#277 := (or #162 #261)
-#278 := [def-axiom]: #277
-#368 := [unit-resolution #278 #367]: #162
-#369 := [unit-resolution #280 #368]: #276
-#370 := [unit-resolution #354 #369]: #341
-#375 := [unit-resolution #374 #368 #370]: #371
-#357 := (or #319 #336 #337 #215)
-#343 := [hypothesis]: #295
-#344 := [unit-resolution #321 #343]: #292
-#345 := [unit-resolution #324 #343]: #291
-#342 := (>= #340 0::real)
-#346 := [unit-resolution #339 #327 #326 #308]: #328
-#347 := [unit-resolution #278 #346]: #162
-#348 := [unit-resolution #280 #347]: #276
-#350 := (or #349 #342)
-#351 := [th-lemma]: #350
-#352 := [unit-resolution #351 #348]: #342
-#355 := [unit-resolution #354 #348]: #341
-#356 := [th-lemma #355 #352 #327 #326 #345 #344 #308 #260 #257]: false
-#358 := [lemma #356]: #357
-#376 := [unit-resolution #358 #366 #363 #308]: #319
-#377 := [unit-resolution #317 #376]: #288
-#378 := (or #312 #306)
-#379 := [th-lemma]: #378
-#380 := [unit-resolution #379 #377 #375]: false
-#382 := [lemma #380]: #381
-#400 := [unit-resolution #382 #308]: #360
-#283 := (or #191 #281)
-#284 := [def-axiom]: #283
-#401 := [unit-resolution #284 #400]: #191
-#285 := (or #192 #282)
-#286 := [def-axiom]: #285
-#402 := [unit-resolution #286 #401]: #282
-#403 := (not #282)
-#404 := (or #403 #385)
-#405 := [th-lemma]: #404
-#406 := [unit-resolution #405 #402]: #385
-#384 := (<= #383 0::real)
-#407 := (or #403 #384)
-#408 := [th-lemma]: #407
-#409 := [unit-resolution #408 #402]: #384
-#386 := [hypothesis]: #288
-#387 := [unit-resolution #379 #386]: #306
-#392 := (iff #12 #328)
-#390 := (iff #11 #261)
-#388 := (iff #261 #11)
-#389 := [monotonicity #386]: #388
-#391 := [symm #389]: #390
-#393 := [monotonicity #391]: #392
-#394 := [mp #256 #393]: #328
-#395 := [unit-resolution #278 #394]: #162
-#396 := [unit-resolution #374 #395 #387]: #372
-#397 := [unit-resolution #280 #395]: #276
-#398 := [unit-resolution #354 #397 #396]: false
-#399 := [lemma #398]: #312
-#410 := [unit-resolution #317 #399]: #295
-#411 := [unit-resolution #321 #410]: #292
-#412 := [unit-resolution #324 #410]: #291
-#413 := [hypothesis]: #276
-#414 := [unit-resolution #351 #413]: #342
-#415 := [unit-resolution #354 #413]: #341
-#416 := [th-lemma #415 #414 #412 #411 #409 #406 #308]: false
-#418 := [lemma #416]: #417
-#423 := [unit-resolution #418 #420]: #215
-#273 := (or #179 #272)
-#258 := (not #220)
-#264 := (iff #258 #273)
-#274 := (not #273)
-#271 := (not #274)
-#266 := (iff #271 #273)
-#267 := [rewrite]: #266
-#268 := (iff #258 #271)
-#275 := (iff #220 #274)
-#270 := [rewrite]: #275
-#269 := [monotonicity #270]: #268
-#265 := [trans #269 #267]: #264
-#259 := [not-or-elim #255]: #258
-#263 := [mp #259 #265]: #273
-#424 := [unit-resolution #263 #423]: #179
-#425 := [th-lemma #412 #411 #424 #422 #260 #257]: false
-#426 := [lemma #425]: #161
-#435 := (or #432 #162)
-#433 := (or #11 #432 #162)
-#434 := [th-lemma]: #433
-#436 := [unit-resolution #434 #256]: #435
-#437 := [unit-resolution #436 #426]: #432
-#427 := [unit-resolution #278 #426]: #261
-#429 := [unit-resolution #333 #427]: #304
-#438 := (not #304)
-#439 := (or #371 #287 #438)
-#440 := [th-lemma]: #439
-#441 := [unit-resolution #440 #429 #437]: #371
-#428 := [unit-resolution #330 #427]: #305
-#430 := [th-lemma #429 #428 #412 #411 #409 #406 #308 #260 #257]: false
-#431 := [lemma #430]: #215
-#442 := [unit-resolution #263 #431]: #179
-[th-lemma #412 #411 #442 #441 #260 #257]: false
-unsat
-bae4db9bec568394a074211dd1bdf1addbc19bd3 401 0
-#2 := false
-#16 := 0::real
-decl f3 :: real
-#8 := f3
-#165 := (<= f3 0::real)
-#166 := (not #165)
-decl f5 :: real
-#10 := f5
-#54 := -1::real
-#55 := (* -1::real f5)
-decl f4 :: real
-#9 := f4
-#56 := (+ f4 #55)
-#237 := (<= #56 0::real)
-decl f6 :: (-> real real)
-#15 := (f6 f5)
-#82 := (* -1::real #15)
-#176 := (>= #15 0::real)
-#183 := (ite #176 #15 #82)
-#63 := (* f3 f5)
-#75 := -1/8::real
-#76 := (* -1/8::real #63)
-#62 := (* f3 f4)
-#73 := 1/8::real
-#74 := (* 1/8::real #62)
-#77 := (+ #74 #76)
-#188 := (/ #77 #183)
-#228 := (<= #188 0::real)
-#229 := (not #228)
-#191 := (* #15 #188)
-#203 := (* -1::real #191)
-#198 := (>= #191 0::real)
-#209 := (ite #198 #191 #203)
-#221 := (* -1::real #209)
-#222 := (+ #76 #221)
-#223 := (+ #74 #222)
-#219 := (>= #223 0::real)
-#234 := (and #219 #229)
-#248 := (not #219)
-#26 := (= #15 0::real)
-#263 := (or #26 #165 #248 #234 #237)
-#268 := (not #263)
-#13 := 8::real
-#11 := (- f4 f5)
-#12 := (* f3 #11)
-#14 := (/ #12 8::real)
-#18 := (- #15)
-#17 := (< #15 0::real)
-#19 := (ite #17 #18 #15)
-#20 := (/ #14 #19)
-#21 := (* #20 #15)
-#23 := (- #21)
-#22 := (< #21 0::real)
-#24 := (ite #22 #23 #21)
-#25 := (<= #24 #14)
-#30 := (< 0::real #20)
-#31 := (and #30 #25)
-#29 := (< 0::real f3)
-#32 := (implies #29 #31)
-#28 := (< f5 f4)
-#33 := (implies #28 #32)
-#27 := (not #26)
-#34 := (implies #27 #33)
-#35 := (implies #25 #34)
-#36 := (not #35)
-#271 := (iff #36 #268)
-#85 := (ite #17 #82 #15)
-#88 := (/ #77 #85)
-#116 := (< 0::real #88)
-#94 := (* #15 #88)
-#105 := (* -1::real #94)
-#99 := (< #94 0::real)
-#110 := (ite #99 #105 #94)
-#113 := (<= #110 #77)
-#122 := (and #113 #116)
-#130 := (not #29)
-#131 := (or #130 #122)
-#139 := (not #28)
-#140 := (or #139 #131)
-#148 := (or #26 #140)
-#156 := (not #113)
-#157 := (or #156 #148)
-#162 := (not #157)
-#269 := (iff #162 #268)
-#266 := (iff #157 #263)
-#251 := (or #165 #234)
-#254 := (or #237 #251)
-#257 := (or #26 #254)
-#260 := (or #248 #257)
-#264 := (iff #260 #263)
-#265 := [rewrite]: #264
-#261 := (iff #157 #260)
-#258 := (iff #148 #257)
-#255 := (iff #140 #254)
-#252 := (iff #131 #251)
-#235 := (iff #122 #234)
-#232 := (iff #116 #229)
-#225 := (< 0::real #188)
-#230 := (iff #225 #229)
-#231 := [rewrite]: #230
-#226 := (iff #116 #225)
-#189 := (= #88 #188)
-#186 := (= #85 #183)
-#177 := (not #176)
-#180 := (ite #177 #82 #15)
-#184 := (= #180 #183)
-#185 := [rewrite]: #184
-#181 := (= #85 #180)
-#178 := (iff #17 #177)
-#179 := [rewrite]: #178
-#182 := [monotonicity #179]: #181
-#187 := [trans #182 #185]: #186
-#190 := [monotonicity #187]: #189
-#227 := [monotonicity #190]: #226
-#233 := [trans #227 #231]: #232
-#220 := (iff #113 #219)
-#214 := (<= #209 #77)
-#218 := (iff #214 #219)
-#217 := [rewrite]: #218
-#215 := (iff #113 #214)
-#212 := (= #110 #209)
-#197 := (not #198)
-#206 := (ite #197 #203 #191)
-#210 := (= #206 #209)
-#211 := [rewrite]: #210
-#207 := (= #110 #206)
-#192 := (= #94 #191)
-#193 := [monotonicity #190]: #192
-#204 := (= #105 #203)
-#205 := [monotonicity #193]: #204
-#201 := (iff #99 #197)
-#194 := (< #191 0::real)
-#199 := (iff #194 #197)
-#200 := [rewrite]: #199
-#195 := (iff #99 #194)
-#196 := [monotonicity #193]: #195
-#202 := [trans #196 #200]: #201
-#208 := [monotonicity #202 #205 #193]: #207
-#213 := [trans #208 #211]: #212
-#216 := [monotonicity #213]: #215
-#224 := [trans #216 #217]: #220
-#236 := [monotonicity #224 #233]: #235
-#174 := (iff #130 #165)
-#169 := (not #166)
-#172 := (iff #169 #165)
-#173 := [rewrite]: #172
-#170 := (iff #130 #169)
-#167 := (iff #29 #166)
-#168 := [rewrite]: #167
-#171 := [monotonicity #168]: #170
-#175 := [trans #171 #173]: #174
-#253 := [monotonicity #175 #236]: #252
-#246 := (iff #139 #237)
-#238 := (not #237)
-#241 := (not #238)
-#244 := (iff #241 #237)
-#245 := [rewrite]: #244
-#242 := (iff #139 #241)
-#239 := (iff #28 #238)
-#240 := [rewrite]: #239
-#243 := [monotonicity #240]: #242
-#247 := [trans #243 #245]: #246
-#256 := [monotonicity #247 #253]: #255
-#259 := [monotonicity #256]: #258
-#249 := (iff #156 #248)
-#250 := [monotonicity #224]: #249
-#262 := [monotonicity #250 #259]: #261
-#267 := [trans #262 #265]: #266
-#270 := [monotonicity #267]: #269
-#163 := (iff #36 #162)
-#160 := (iff #35 #157)
-#153 := (implies #113 #148)
-#158 := (iff #153 #157)
-#159 := [rewrite]: #158
-#154 := (iff #35 #153)
-#151 := (iff #34 #148)
-#145 := (implies #27 #140)
-#149 := (iff #145 #148)
-#150 := [rewrite]: #149
-#146 := (iff #34 #145)
-#143 := (iff #33 #140)
-#136 := (implies #28 #131)
-#141 := (iff #136 #140)
-#142 := [rewrite]: #141
-#137 := (iff #33 #136)
-#134 := (iff #32 #131)
-#127 := (implies #29 #122)
-#132 := (iff #127 #131)
-#133 := [rewrite]: #132
-#128 := (iff #32 #127)
-#125 := (iff #31 #122)
-#119 := (and #116 #113)
-#123 := (iff #119 #122)
-#124 := [rewrite]: #123
-#120 := (iff #31 #119)
-#114 := (iff #25 #113)
-#80 := (= #14 #77)
-#64 := (* -1::real #63)
-#65 := (+ #62 #64)
-#70 := (/ #65 8::real)
-#78 := (= #70 #77)
-#79 := [rewrite]: #78
-#71 := (= #14 #70)
-#68 := (= #12 #65)
-#59 := (* f3 #56)
-#66 := (= #59 #65)
-#67 := [rewrite]: #66
-#60 := (= #12 #59)
-#57 := (= #11 #56)
-#58 := [rewrite]: #57
-#61 := [monotonicity #58]: #60
-#69 := [trans #61 #67]: #68
-#72 := [monotonicity #69]: #71
-#81 := [trans #72 #79]: #80
-#111 := (= #24 #110)
-#97 := (= #21 #94)
-#91 := (* #88 #15)
-#95 := (= #91 #94)
-#96 := [rewrite]: #95
-#92 := (= #21 #91)
-#89 := (= #20 #88)
-#86 := (= #19 #85)
-#83 := (= #18 #82)
-#84 := [rewrite]: #83
-#87 := [monotonicity #84]: #86
-#90 := [monotonicity #81 #87]: #89
-#93 := [monotonicity #90]: #92
-#98 := [trans #93 #96]: #97
-#108 := (= #23 #105)
-#102 := (- #94)
-#106 := (= #102 #105)
-#107 := [rewrite]: #106
-#103 := (= #23 #102)
-#104 := [monotonicity #98]: #103
-#109 := [trans #104 #107]: #108
-#100 := (iff #22 #99)
-#101 := [monotonicity #98]: #100
-#112 := [monotonicity #101 #109 #98]: #111
-#115 := [monotonicity #112 #81]: #114
-#117 := (iff #30 #116)
-#118 := [monotonicity #90]: #117
-#121 := [monotonicity #118 #115]: #120
-#126 := [trans #121 #124]: #125
-#129 := [monotonicity #126]: #128
-#135 := [trans #129 #133]: #134
-#138 := [monotonicity #135]: #137
-#144 := [trans #138 #142]: #143
-#147 := [monotonicity #144]: #146
-#152 := [trans #147 #150]: #151
-#155 := [monotonicity #115 #152]: #154
-#161 := [trans #155 #159]: #160
-#164 := [monotonicity #161]: #163
-#272 := [trans #164 #270]: #271
-#53 := [asserted]: #36
-#273 := [mp #53 #272]: #268
-#275 := [not-or-elim #273]: #166
-#279 := [not-or-elim #273]: #238
-#322 := (<= #183 0::real)
-#370 := (not #322)
-#318 := (<= #15 0::real)
-#404 := (not #318)
-#276 := [not-or-elim #273]: #219
-#352 := (+ #191 #221)
-#353 := (<= #352 0::real)
-#306 := (= #191 #209)
-#386 := [hypothesis]: #177
-#389 := (or #198 #176)
-#277 := (not #234)
-#301 := (iff #277 #228)
-#296 := (not #229)
-#299 := (iff #296 #228)
-#300 := [rewrite]: #299
-#297 := (iff #277 #296)
-#294 := (iff #234 #229)
-#1 := true
-#289 := (and true #229)
-#292 := (iff #289 #229)
-#293 := [rewrite]: #292
-#290 := (iff #234 #289)
-#287 := (iff #219 true)
-#288 := [iff-true #276]: #287
-#291 := [monotonicity #288]: #290
-#295 := [trans #291 #293]: #294
-#298 := [monotonicity #295]: #297
-#302 := [trans #298 #300]: #301
-#278 := [not-or-elim #273]: #277
-#303 := [mp #278 #302]: #228
-#387 := [hypothesis]: #197
-#388 := [th-lemma #387 #303 #386]: false
-#390 := [lemma #388]: #389
-#376 := [unit-resolution #390 #386]: #198
-#282 := (or #197 #306)
-#280 := [def-axiom]: #282
-#377 := [unit-resolution #280 #376]: #306
-#366 := (not #306)
-#367 := (or #366 #353)
-#368 := [th-lemma]: #367
-#391 := [unit-resolution #368 #377]: #353
-#324 := (* -1::real #183)
-#325 := (+ #82 #324)
-#326 := (<= #325 0::real)
-#305 := (= #82 #183)
-#283 := (or #176 #305)
-#284 := [def-axiom]: #283
-#392 := [unit-resolution #284 #386]: #305
-#342 := (not #305)
-#343 := (or #342 #326)
-#344 := [th-lemma]: #343
-#393 := [unit-resolution #344 #392]: #326
-#394 := (not #326)
-#395 := (or #370 #176 #394)
-#396 := [th-lemma]: #395
-#397 := [unit-resolution #396 #386 #393]: #370
-#311 := (* #183 #188)
-#319 := (* -1::real #311)
-#320 := (+ #76 #319)
-#321 := (+ #74 #320)
-#314 := (>= #321 0::real)
-#317 := (= #321 0::real)
-#310 := (= #183 0::real)
-#346 := (not #310)
-#304 := (= #15 #183)
-#336 := (not #304)
-#337 := (iff #27 #336)
-#334 := (iff #26 #304)
-#332 := (iff #304 #26)
-#331 := [hypothesis]: #310
-#333 := [monotonicity #331]: #332
-#335 := [symm #333]: #334
-#338 := [monotonicity #335]: #337
-#274 := [not-or-elim #273]: #27
-#339 := [mp #274 #338]: #336
-#285 := (or #177 #304)
-#286 := [def-axiom]: #285
-#340 := [unit-resolution #286 #339]: #177
-#341 := [unit-resolution #284 #340]: #305
-#345 := [unit-resolution #344 #341]: #326
-#347 := (or #346 #322)
-#348 := [th-lemma]: #347
-#349 := [unit-resolution #348 #331]: #322
-#350 := [th-lemma #340 #349 #345]: false
-#351 := [lemma #350]: #346
-#357 := (or #310 #317)
-#358 := [th-lemma]: #357
-#359 := [unit-resolution #358 #351]: #317
-#360 := (not #317)
-#398 := (or #360 #314)
-#399 := [th-lemma]: #398
-#400 := [unit-resolution #399 #359]: #314
-#313 := (<= #321 0::real)
-#361 := (or #360 #313)
-#362 := [th-lemma]: #361
-#363 := [unit-resolution #362 #359]: #313
-#401 := [th-lemma #363 #400 #303 #397 #376 #391 #276 #279 #275]: false
-#402 := [lemma #401]: #176
-#407 := (or #404 #177)
-#405 := (or #26 #404 #177)
-#406 := [th-lemma]: #405
-#408 := [unit-resolution #406 #274]: #407
-#409 := [unit-resolution #408 #402]: #404
-#328 := (+ #15 #324)
-#329 := (<= #328 0::real)
-#410 := [unit-resolution #286 #402]: #304
-#411 := (or #336 #329)
-#412 := [th-lemma]: #411
-#413 := [unit-resolution #412 #410]: #329
-#414 := (not #329)
-#415 := (or #370 #318 #414)
-#416 := [th-lemma]: #415
-#417 := [unit-resolution #416 #413 #409]: #370
-#327 := (+ #203 #221)
-#354 := (<= #327 0::real)
-#307 := (= #203 #209)
-#384 := (or #307 #322)
-#355 := (not #307)
-#356 := [hypothesis]: #355
-#308 := (or #198 #307)
-#309 := [def-axiom]: #308
-#364 := [unit-resolution #309 #356]: #198
-#365 := [unit-resolution #280 #364]: #306
-#380 := (= #203 #191)
-#378 := (= 0::real #191)
-#372 := (= #191 0::real)
-#369 := [unit-resolution #368 #365]: #353
-#371 := [hypothesis]: #370
-#373 := [th-lemma #364 #371 #364 #369 #276 #363 #303]: #372
-#379 := [symm #373]: #378
-#374 := (= #203 0::real)
-#375 := [th-lemma #364 #371 #364 #369 #276 #363 #303]: #374
-#381 := [trans #375 #379]: #380
-#382 := [trans #381 #365]: #307
-#383 := [unit-resolution #356 #382]: false
-#385 := [lemma #383]: #384
-#418 := [unit-resolution #385 #417]: #307
-#419 := (or #355 #354)
-#420 := [th-lemma]: #419
-#421 := [unit-resolution #420 #418]: #354
-#422 := [th-lemma #387 #421 #276 #363 #303 #417]: false
-#423 := [lemma #422]: #198
-[th-lemma #363 #400 #303 #409 #423 #279 #275]: false
-unsat
diff -r 7f58a9a843c2 -r a462d5207aa6 src/HOL/Multivariate_Analysis/Integration.thy
--- a/src/HOL/Multivariate_Analysis/Integration.thy	Tue Oct 26 11:45:12 2010 +0200
+++ b/src/HOL/Multivariate_Analysis/Integration.thy	Tue Oct 26 11:46:19 2010 +0200
@@ -8,8 +8,8 @@
 begin
 
 declare [[smt_certificates="~~/src/HOL/Multivariate_Analysis/Integration.certs"]]
-declare [[smt_fixed=false]]
-declare [[z3_proofs=true]]
+declare [[smt_fixed=true]]
+declare [[smt_oracle=false]]
 
 setup {* Arith_Data.add_tactic "Ferrante-Rackoff" (K FerranteRackoff.dlo_tac) *}
 
diff -r 7f58a9a843c2 -r a462d5207aa6 src/HOL/Probability/Euclidean_Lebesgue.thy
--- a/src/HOL/Probability/Euclidean_Lebesgue.thy	Tue Oct 26 11:45:12 2010 +0200
+++ b/src/HOL/Probability/Euclidean_Lebesgue.thy	Tue Oct 26 11:46:19 2010 +0200
@@ -122,7 +122,6 @@
   let ?u = "\<lambda>i x. real (u i x)" and ?f = "\<lambda>x. real (f x)"
   have u_simple:"\<And>k. lebesgue.simple_integral (u k) = lebesgue.positive_integral (u k)"
     apply(subst lebesgue.positive_integral_eq_simple_integral[THEN sym,OF u(1)]) ..
-    (*unfolding image_iff defer apply(rule) using u(2) by smt*)
   have int_u_le:"\<And>k. lebesgue.simple_integral (u k) \<le> lebesgue.positive_integral f"
     unfolding u_simple apply(rule lebesgue.positive_integral_mono)
     using isoton_Sup[OF u(3)] unfolding le_fun_def by auto
diff -r 7f58a9a843c2 -r a462d5207aa6 src/HOL/SMT_Examples/SMT_Examples.certs
--- a/src/HOL/SMT_Examples/SMT_Examples.certs	Tue Oct 26 11:45:12 2010 +0200
+++ b/src/HOL/SMT_Examples/SMT_Examples.certs	Tue Oct 26 11:46:19 2010 +0200
@@ -1,4 +1,4 @@
-ef3118b3c538f5cd123d726ccf13a3c2d3725bb0 8 0
+d4b1481d70f20d4d6280999633c905e21d180d13 8 0
 #2 := false
 #1 := true
 #8 := (not true)
@@ -7,7 +7,7 @@
 #25 := [asserted]: #8
 [mp #25 #27]: false
 unsat
-b59b2f429ffd47c407e4ef1af006540275b1a26c 33 0
+a38979487be0aafcf2d387180e92dfd3bd43e483 33 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -41,7 +41,7 @@
 #29 := [asserted]: #12
 [mp #29 #49]: false
 unsat
-2e7e9d422d65be29e15f02c69c60971cab2c6ff5 37 0
+fd75276ee28b486a6ea1b6b677d04008959d13f8 37 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -79,7 +79,7 @@
 #29 := [asserted]: #12
 [mp #29 #53]: false
 unsat
-c09f42a4df50b3429cb0f5ddbf56d93bf0b06b7b 66 0
+58aaefc3b25d8181c01a2139430686aeca861bf3 66 0
 #2 := false
 decl f4 :: S1
 #10 := f4
@@ -148,7 +148,7 @@
 unsat
 a3969d96ad7c1fdd20f7d69abeb13b18bac4be8d 1 0
 unsat
-8f1394900829ee257ef5682b19118d98b3c0c820 94 0
+694292afe609b4087c0435b347aed1c0c0b6b45b 94 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -243,7 +243,7 @@
 #39 := [asserted]: #22
 [mp #39 #108]: false
 unsat
-41b693f504b47ef3e9345eeec00c566a4d93af04 72 0
+fcb0f1f1909bdd097de1e485a000708289f9f1ed 72 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -316,7 +316,7 @@
 #36 := [asserted]: #19
 [mp #36 #88]: false
 unsat
-1bb9b155bb9b619999029c3bea6bb00c7c21cd3b 234 0
+36c95d1da5779fd86d36cb33e0f80e4f14e6c4f0 234 0
 #2 := false
 decl f6 :: S1
 #14 := f6
@@ -551,7 +551,7 @@
 #96 := [mp #69 #95]: #91
 [mp #96 #299]: false
 unsat
-c02efa254926732c7b107199403ddd23251d413c 52 0
+44ca45de077963316e54f5cdfef5cb8cd66ac906 52 0
 #2 := false
 decl f4 :: (-> S2 S2 S2)
 #16 := (:var 1 S2)
@@ -604,7 +604,7 @@
 #118 := [quant-inst]: #204
 [unit-resolution #118 #53 #541]: false
 unsat
-950f494f909b64c53d64f243647b66f8a05dd7f6 2578 0
+f79d03683394ca6e785cbd8e87f4249c3d42307a 2578 0
 #2 := false
 decl f35 :: S1
 #112 := f35
@@ -3183,7 +3183,7 @@
 #3638 := [unit-resolution #705 #3637 #3636 #3635]: #683
 [unit-resolution #1968 #3638 #3634]: false
 unsat
-d9089f92efb7cf3cd5f913b2fd8f4e6cc7fca01b 95 0
+3221f6bae508cb0c6bc508c2b8b4600cdb00669d 95 0
 #2 := false
 decl f3 :: (-> int S1)
 decl ?v0!0 :: int
@@ -3279,7 +3279,7 @@
 #102 := [and-elim #101]: #76
 [unit-resolution #102 #115]: false
 unsat
-c79d3e134c40dc60b6991210fa65efc043a31981 146 0
+517d7705593795e4a28f7687bc92edbaaad5e6a6 146 0
 #2 := false
 decl f3 :: (-> S1 S2 S1)
 #9 := (:var 0 S2)
@@ -3426,7 +3426,7 @@
 #261 := [quant-inst]: #256
 [unit-resolution #261 #584 #284]: false
 unsat
-90a02b978126d0cf254666f4e32434ce827e91f3 146 2
+f7796908cca3a39a93067ec7456dca4edfe09069 146 2
 #2 := false
 decl f3 :: (-> S1 S2 S1)
 #9 := (:var 0 S2)
@@ -3575,7 +3575,7 @@
 unsat
 WARNING: failed to find a pattern for quantifier (quantifier id: k!13)
 
-f01333d944f2f80d82a424a44d896dcad3d2ab6b 91 0
+3d560cfeafa07e8fb4e5aedbf244ed81193a1bdd 91 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl f4 :: S2
@@ -3667,7 +3667,7 @@
 #162 := [quant-inst]: #248
 [unit-resolution #162 #582 #79]: false
 unsat
-63e9e9c72f5ef2d46bc28af44941977dc976d3b5 17 0
+6f4135b5f443c9489ab6f839e6371eb6c05021a1 17 0
 #2 := false
 #8 := 3::int
 #9 := (= 3::int 3::int)
@@ -3685,7 +3685,7 @@
 #27 := [asserted]: #10
 [mp #27 #36]: false
 unsat
-711fabeeccec1b44c93a2cd4391df71f5fdafd74 17 0
+1fb88686c084cbd29d5379055cf31c165231f0d2 17 0
 #2 := false
 #8 := 3::real
 #9 := (= 3::real 3::real)
@@ -3703,7 +3703,7 @@
 #27 := [asserted]: #10
 [mp #27 #36]: false
 unsat
-eb7a82422e5eb210ae6e04c9f7170b09a67998d0 26 0
+4439cb9b553ba6a7d3d7adaf0bccb7b403389495 26 0
 #2 := false
 #11 := 4::int
 #9 := 1::int
@@ -3730,7 +3730,7 @@
 #30 := [asserted]: #13
 [mp #30 #45]: false
 unsat
-5764777c5ab04100aa6409067059f42abecddd25 41 0
+f4b4baf086c1953b46b6c8516c9a7e45f6c086ee 41 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -3772,7 +3772,7 @@
 #33 := [asserted]: #16
 [mp #33 #57]: false
 unsat
-f10e15cb480fc7147b50d697554b03e8d45998ff 35 0
+5926d4083f7d2a89c57531d8e87a5d554a39421a 35 0
 #2 := false
 #9 := 3::int
 #10 := 8::int
@@ -3808,7 +3808,7 @@
 #31 := [asserted]: #14
 [mp #31 #56]: false
 unsat
-85e154b43f9eaa0aee17c7df60f7b297367e646f 209 0
+53ebe62bcea7dc90158b3082dda2089fed123703 209 0
 #2 := false
 #11 := 0::real
 decl f4 :: real
@@ -4018,7 +4018,7 @@
 #231 := [unit-resolution #159 #230]: #150
 [th-lemma #125 #220 #227 #231]: false
 unsat
-c7afd26a7e4c735b3f9da1bcf41b42fb4f611502 42 0
+cbc9c5a04b9570a386fb97f8ff4491630835be54 42 0
 #2 := false
 decl f3 :: (-> S1 S2)
 decl f1 :: S1
@@ -4061,7 +4061,7 @@
 #32 := [asserted]: #15
 [mp #32 #58]: false
 unsat
-b1921561d90efa4396e2195f6befedbbc08c3f93 54 0
+732b399d3ae1d48d68db7a2b4fb14062c7ea7650 54 0
 #2 := false
 #13 := 1::int
 decl f3 :: int
@@ -4116,7 +4116,7 @@
 #33 := [asserted]: #16
 [mp #33 #72]: false
 unsat
-186b71f451f1ced8ef7a2af2f7333861c89cddbd 63 0
+a511ac5eff75bd85fb28de979615bdeb27073e2f 63 0
 #2 := false
 #15 := 0::int
 decl f4 :: int
@@ -4180,7 +4180,7 @@
 #81 := [mp #57 #80]: #68
 [mp #81 #93]: false
 unsat
-ed9f5b4ddb34caba3e930028ab3abbea1141767c 35 0
+5e99525435673f50d9e2cedb056a3eef3ca48d0f 35 0
 #2 := false
 #10 := 5::int
 #8 := 2::int
@@ -4216,7 +4216,7 @@
 #30 := [asserted]: #13
 [mp #30 #54]: false
 unsat
-e6971c89ab6428863738be19afcd7e6157397835 45 0
+cb1ff2dbd74d2844a905d03c2bb5dfdcef7b3703 45 0
 #2 := false
 #15 := 4::real
 decl f4 :: real
@@ -4262,7 +4262,7 @@
 #65 := [mp #41 #64]: #56
 [th-lemma #65 #52 #43]: false
 unsat
-4bafaa4fbebd6a7c5c47a5e807b07fb360f1fe97 59 0
+7357ea99a84507698d605d047a8912506786b005 59 0
 #2 := false
 #20 := (not false)
 decl f4 :: int
@@ -4322,7 +4322,7 @@
 #39 := [asserted]: #22
 [mp #39 #76]: false
 unsat
-c2be8bcf98f782ce6e39f901eead42a359d07f16 43 0
+a2e7fe792ce7e828740707e47e962b9013bfaa8c 43 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -4366,7 +4366,7 @@
 #31 := [asserted]: #14
 [mp #31 #62]: false
 unsat
-f13f6152ed2127a9ebc1d2b9377e88e7270d2645 86 0
+f746fa8e8060fa7d6624d49afb6c22d0c2467190 86 0
 #2 := false
 decl f3 :: int
 #9 := f3
@@ -4453,7 +4453,7 @@
 #104 := [unit-resolution #82 #103 #96 #87]: #65
 [unit-resolution #104 #117]: false
 unsat
-faa44c5ec66ed5260e47611608af7290f07ca77d 551 0
+96de0a1de3d9897dfb99656d5dd83bfdb80fa75e 551 0
 #2 := false
 #174 := 0::int
 decl f4 :: int
@@ -5005,7 +5005,7 @@
 #617 := [unit-resolution #411 #614]: #421
 [unit-resolution #601 #617 #593 #616]: false
 unsat
-4dd2cecd4113f0eaf15e733b006ad0e01202872f 2109 0
+be4350e057381018abf4a5df1b96e44aa5440970 2109 0
 #2 := false
 #10 := 0::int
 decl f3 :: int
@@ -7115,7 +7115,7 @@
 #2119 := [unit-resolution #2118 #2109 #2056 #2114 #2113 #2112 #2096 #2108]: #945
 [unit-resolution #1969 #2119 #2109 #2096 #2042 #2105 #2108]: false
 unsat
-91a72ccddaee78c8eef27b68b8a29a516e5fa812 52 0
+9371d51a82e0a1300620d46b4e7e3f2e34923066 52 0
 #2 := false
 #12 := 1::real
 decl f3 :: real
@@ -7168,7 +7168,7 @@
 #34 := [asserted]: #17
 [mp #34 #70]: false
 unsat
-fcbcf3a00f1d2be93e0056636348f79e12052409 348 0
+7d808a299ec3aa6543955e0b52da2db4f14e2ebc 348 0
 #2 := false
 #11 := 0::int
 decl f5 :: int
@@ -7517,7 +7517,7 @@
 #638 := [unit-resolution #642 #647]: #643
 [unit-resolution #638 #640 #637]: false
 unsat
-3ff5c7aca258ce7606adbaf5b380622b5f987775 354 0
+a58c3bad13ae6ef8848c31ae2ecb4d141ea9bdc6 354 0
 #2 := false
 #11 := 0::int
 decl f5 :: int
@@ -7872,7 +7872,7 @@
 #626 := [unit-resolution #621 #634]: #753
 [unit-resolution #626 #619 #508]: false
 unsat
-37b2210a0af8b22facfab20f06af5ae3c558113d 101 0
+cfd6420dc9709ceb6bf8be602fb4605c1ddb5222 101 0
 #2 := false
 #9 := 0::real
 decl f3 :: real
@@ -7974,7 +7974,7 @@
 #120 := [th-lemma]: #119
 [unit-resolution #120 #116 #109 #43]: false
 unsat
-70f2c00c05f2849d6805e35842428b4464a986bf 943 0
+957b603c67e0eb51df6576d5eeddcc6aa6ccd469 943 0
 #2 := false
 #49 := 1::int
 decl f4 :: (-> int int int)
@@ -8918,7 +8918,7 @@
 #1294 := [unit-resolution #1107 #1293 #1239]: #405
 [unit-resolution #1252 #1294 #1292]: false
 unsat
-659511229cba86eafd88b265af83c150a34ef866 24 0
+e0bd8674b0a8871e3484c1aaf5e9760d6cdde8fa 24 0
 #2 := false
 #8 := (exists (vars (?v0 int)) false)
 #9 := (not #8)
@@ -8943,7 +8943,7 @@
 #27 := [asserted]: #10
 [mp #27 #43]: false
 unsat
-9315f166813c097237f939d5bfec03336d48d6a9 24 0
+20e7b35733689b5c0fe416fc2b22bfe44b252442 24 0
 #2 := false
 #8 := (exists (vars (?v0 real)) false)
 #9 := (not #8)
@@ -8974,7 +8974,7 @@
 unsat
 0e0dcf19cd5b120a9f262cfa9c01b662a315ee94 1 0
 unsat
-2336c05cc0db64fbd723579d41aafc2ab55fbe93 67 0
+1781c1a480d6415ddb235a621259ce2092732ba5 67 0
 #2 := false
 #9 := 0::int
 #12 := 1::int
@@ -9042,7 +9042,7 @@
 #143 := [trans #141 #80]: #142
 [mp #143 #145]: false
 unsat
-5efd84778495b1b150aa0b9f4a0b4263b1687cbc 82 0
+cb54bc1c8221ce33a204ef4756c350ab3a9165fd 82 0
 #2 := false
 #9 := (:var 0 int)
 #11 := 0::int
@@ -9125,7 +9125,7 @@
 #35 := [asserted]: #18
 [mp #35 #101]: false
 unsat
-7f5cf2a606c1f6fc9684f5e78e16538004b7482b 78 0
+05e26467c63b2926bb1206f4d9498749ac8572cd 78 0
 #2 := false
 #9 := (:var 0 int)
 #11 := 2::int
@@ -9204,7 +9204,7 @@
 #36 := [asserted]: #19
 [mp #36 #97]: false
 unsat
-2a13654aa992c8bed90af2572886d27708a51b8d 61 0
+9a25b8cd095131859f14e6e15166f75f654f8b36 61 0
 #2 := false
 #13 := (:var 0 int)
 #8 := 2::int
@@ -9266,7 +9266,7 @@
 #35 := [asserted]: #18
 [mp #35 #80]: false
 unsat
-00a64958e6476c1107006d163ef1b97bd464c3ab 111 0
+b845be4ad91437fd7de4e1e43e09de89dff87060 111 0
 #2 := false
 #8 := 2::int
 decl ?v0!1 :: int
@@ -9378,7 +9378,7 @@
 #189 := [th-lemma]: #188
 [unit-resolution #189 #132 #130 #131]: false
 unsat
-3f82af9f48300cb861109298f1c808dfeedc27df 89 0
+d516d2245b3e1198319c778f5d87f60364d9480b 89 0
 #2 := false
 #8 := 0::int
 decl ?v0!0 :: int
@@ -9468,7 +9468,7 @@
 #172 := [unit-resolution #157 #95]: #171
 [unit-resolution #172 #170 #167]: false
 unsat
-acea26b9fcd9353bdce76a59fb81f2d230c19002 83 2
+16973ba3459b683ba763cfd9d1b131b50880d52b 83 2
 #2 := false
 #9 := 0::int
 #8 := (:var 0 int)
@@ -9554,7 +9554,7 @@
 unsat
 WARNING: failed to find a pattern for quantifier (quantifier id: k!9)
 
-baa910cd7ead809257c9ce1201462fe467c60aef 180 2
+6a2477ce7e396f5a6b8350494c34556e3187382b 180 2
 #2 := false
 #16 := 3::int
 #37 := -1::int
@@ -9737,7 +9737,7 @@
 unsat
 WARNING: failed to find a pattern for quantifier (quantifier id: k!9)
 
-7a877ca9edb4f2c73b1ef0625cc9c1f31c342b91 68 0
+2c2ba5876a1ae5b4aacba3ec088a92e8517d1db5 68 0
 #2 := false
 #16 := 1::int
 #13 := (:var 1 int)
@@ -9806,7 +9806,7 @@
 #37 := [asserted]: #20
 [mp #37 #88]: false
 unsat
-c8d9f4511ee6959de9f02b091245c0b85d6b9a13 107 0
+3bc68a4890101c78401460850d978a5b784ef891 107 0
 #2 := false
 #8 := 0::int
 decl ?v1!1 :: int
@@ -9914,7 +9914,7 @@
 #128 := [and-elim #106]: #93
 [th-lemma #128 #129 #130]: false
 unsat
-64c53f605d405ecd0170c0241c2194ef25f17257 117 0
+69398382e4236c1f3e9ea09ef96d5056d4f3fa6e 117 0
 #2 := false
 #8 := 0::int
 decl ?v1!1 :: int
@@ -10032,7 +10032,7 @@
 #193 := [unit-resolution #192 #115]: #103
 [unit-resolution #193 #135]: false
 unsat
-7bc9510644b978b75cac18b8fb186f89e0d2c0fd 148 0
+4e8319ba61c4c37d1677e9a262b47203f2bf5468 148 0
 #2 := false
 #149 := (not false)
 #11 := 0::int
@@ -10181,7 +10181,7 @@
 #163 := [mp #131 #162]: #158
 [mp #163 #186]: false
 unsat
-23471f6b1ed12f9477f5b746b57d0271e3fe26ad 67 0
+a21b19aa84de923d8a0d2dc0af8016cd64248558 67 0
 #2 := false
 #8 := (:var 0 int)
 #9 := (pattern #8)
@@ -10251,7 +10251,7 @@
 unsat
 53ac944328a76df2270bb4117390a226d92d4e8d 1 0
 unsat
-5645c40190078bc259023463ba288394a1ee2d31 75 0
+80d97536e18b652f6d95d83165f7e113fa8206dd 75 0
 #2 := false
 #10 := 1::int
 decl f5 :: int
@@ -10327,7 +10327,7 @@
 #37 := [asserted]: #20
 [mp #37 #91]: false
 unsat
-dfe5809b750cf5dfc5ba8d902ad5002b8123814d 62 0
+1290567b7974f50913459a9370404d1fb27c5c04 62 0
 #2 := false
 decl f4 :: real
 #10 := f4
@@ -10390,7 +10390,7 @@
 #37 := [asserted]: #20
 [mp #37 #79]: false
 unsat
-3845bb98c4dd099de3474412f61c35c8b79e798c 141 0
+539e99c284f7a3ed7bb350da08f51bfa73f9e832 141 0
 #2 := false
 decl f6 :: int
 #13 := f6
@@ -10532,7 +10532,7 @@
 #50 := [asserted]: #33
 [mp #50 #155]: false
 unsat
-522e7a274d393467135232ebd14a729963459539 252 0
+95f708529404688f5c32519f5db83b1972672eb0 252 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -10785,7 +10785,7 @@
 #544 := [unit-resolution #537 #456]: #562
 [th-lemma #460 #544 #542 #551]: false
 unsat
-4d15f891322a8916dc12e3586edb994e590a9767 227 0
+069a886d4e32ad09f893e803be1b967f3568fe31 227 0
 #2 := false
 #27 := 3::int
 decl f4 :: (-> S2 int)
@@ -11013,7 +11013,7 @@
 #607 := [unit-resolution #602 #605]: #632
 [th-lemma #161 #607 #160]: false
 unsat
-ee8d523b01e5668527c65aa2ae3489e22daf3c31 367 0
+dc0cfb9f55d790de5cad944289080b012df32109 367 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -11381,7 +11381,7 @@
 #461 := [th-lemma]: #460
 [unit-resolution #461 #469 #457]: false
 unsat
-fe0d866a3da682e02aab50789c1002badb2ec0c9 299 0
+1119baa29d78de9d8299759a1e2778fd64cb45ac 299 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -11681,7 +11681,7 @@
 #603 := [unit-resolution #617 #615]: #685
 [th-lemma #625 #190 #603 #630]: false
 unsat
-0be1401474e291c6d6933a302a6418a34a233b36 458 0
+bc26a0abfecc650600742f8182ea35bd8e9c0657 458 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -12140,7 +12140,7 @@
 #355 := [unit-resolution #374 #372]: #373
 [unit-resolution #355 #328]: false
 unsat
-75dd8d1e40b17d4d494dfbbca0b51228568d2c11 161 0
+d28cb53d0b19f6ffbd9f6906e69a9e4028ab5365 161 0
 #2 := false
 #13 := 0::int
 decl f5 :: int
@@ -12302,7 +12302,7 @@
 #366 := [unit-resolution #644 #660]: #652
 [th-lemma #661 #366 #266]: false
 unsat
-c37debf59e8d6c8b243d5aaa6c9491c65a29d492 604 0
+3bdd721710ce740508c48327f8e9174f1a8cdb9c 604 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -12907,7 +12907,7 @@
 #1005 := [unit-resolution #599 #859]: #455
 [unit-resolution #1005 #1004 #994]: false
 unsat
-8add4983d79a2879b8718ea3b1ded6de7ef7d64c 61 0
+9702672d0e4ef4f07fbabb8ea1413e6a7036c6b3 61 0
 #2 := false
 decl f7 :: S3
 #12 := f7
@@ -12969,7 +12969,7 @@
 #59 := [not-or-elim #58]: #57
 [unit-resolution #59 #251]: false
 unsat
-6a6cf93b65ddcaf1b125eb57f4a626298f29e47d 116 0
+eb96c266a8e3d434df367635dd7c28e36177b61a 116 0
 #2 := false
 decl f10 :: (-> S5 S3)
 decl f7 :: S5
@@ -13086,7 +13086,7 @@
 #81 := [not-or-elim #78]: #80
 [unit-resolution #81 #612]: false
 unsat
-c4ff195222fb458c30d04a5dbddcd6f66862822e 192 0
+9aa5c4fb11199431a576a38868b15130e8351add 192 0
 #2 := false
 decl f6 :: (-> S3 S2 S4)
 decl f3 :: S2
@@ -13279,7 +13279,7 @@
 #73 := [not-or-elim #70]: #72
 [unit-resolution #73 #505]: false
 unsat
-2dc4b9dba54c10e431adb8ebd743c805e8784c37 80 0
+25babfdee044def80821e354fcd8abca6147a0b0 80 0
 #2 := false
 decl f6 :: (-> S2 S3 S1)
 decl f5 :: S3
@@ -13360,7 +13360,7 @@
 #75 := [not-or-elim #69]: #74
 [mp #75 #96]: false
 unsat
-39345d35925f930054a812342385e19283e673d4 128 0
+608cd0071a67598a13af0858c9e1341886caf8cc 128 0
 #2 := false
 decl f3 :: (-> S2 S2)
 #15 := (:var 0 S2)
@@ -13489,7 +13489,7 @@
 #224 := [quant-inst]: #566
 [unit-resolution #224 #575 #583]: false
 unsat
-c66a2580a73c3d496a195fadc270ed658f997968 469 0
+737f3f173e29756f346a0a821d7647d108111546 469 0
 #2 := false
 decl f8 :: (-> S2 S4 S4)
 decl f9 :: S4
@@ -13959,7 +13959,7 @@
 #173 := [asserted]: #43
 [unit-resolution #173 #814]: false
 unsat
-4cc658eed58c39b67c9bb50c6dd977ba3d6d31a0 38 0
+5cfea173c08e120333c1dea606b9463cfcc6450a 38 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -13998,7 +13998,7 @@
 #31 := [asserted]: #14
 [mp #31 #54]: false
 unsat
-8134ded6ddb01de87deb72c99e279ab6f9bebab8 366 0
+9cf33fdca403c6c514f1cd0e17b6b0a250477095 366 0
 #2 := false
 decl f3 :: (-> int S2)
 #41 := 6::int
@@ -14365,7 +14365,7 @@
 #187 := [asserted]: #44
 [unit-resolution #187 #404]: false
 unsat
-2a228f77dfa0e1f9c335db511955697c625e5b3e 1271 0
+f72e33edaef326a0ed844a14ae54b706945ff4d5 1271 0
 #2 := false
 decl f6 :: (-> int int int)
 #12 := 2::int
@@ -15637,7 +15637,7 @@
 #615 := [unit-resolution #638 #1762]: #367
 [unit-resolution #615 #1764]: false
 unsat
-5234c113c47a34efd714baca9777f6d9bb4fe31e 76 0
+59b518b007738eb00dbca158af8db9e067af1dee 76 0
 #2 := false
 decl f3 :: (-> int S1)
 #12 := (:var 0 int)
@@ -15714,7 +15714,7 @@
 #689 := [quant-inst]: #688
 [unit-resolution #689 #158 #1022]: false
 unsat
-b9f47e2d664572f569f3105a25d0e77e894b5cdd 478 0
+997a0c6c7b0815f9412f3484edb90c328a2f5296 478 0
 #2 := false
 decl f7 :: (-> S4 S2)
 decl f8 :: (-> S1 S4)
diff -r 7f58a9a843c2 -r a462d5207aa6 src/HOL/SMT_Examples/SMT_Examples.thy
--- a/src/HOL/SMT_Examples/SMT_Examples.thy	Tue Oct 26 11:45:12 2010 +0200
+++ b/src/HOL/SMT_Examples/SMT_Examples.thy	Tue Oct 26 11:46:19 2010 +0200
@@ -8,7 +8,7 @@
 imports Complex_Main
 begin
 
-declare [[smt_solver=z3, z3_proofs=true]]
+declare [[smt_solver=z3, smt_oracle=false]]
 declare [[smt_certificates="~~/src/HOL/SMT_Examples/SMT_Examples.certs"]]
 declare [[smt_fixed=true]]
 
@@ -25,7 +25,7 @@
 lemma "(p \<or> q) \<and> \<not>p \<Longrightarrow> q" by smt
 
 lemma "(a \<and> b) \<or> (c \<and> d) \<Longrightarrow> (a \<and> b) \<or> (c \<and> d)"
-  using [[z3_proofs=false]] (* no Z3 proof *)
+  using [[smt_oracle=true]] (* no Z3 proof *)
   by smt
 
 lemma "(p1 \<and> p2) \<or> p3 \<longrightarrow> (p1 \<longrightarrow> (p3 \<and> p2) \<or> (p1 \<and> p3)) \<or> p1" by smt
@@ -358,15 +358,15 @@
 lemma "~ (\<exists>x::real. False)" by smt
 
 lemma "\<exists>x::int. 0 < x"
-  using [[z3_proofs=false]] (* no Z3 proof *)
+  using [[smt_oracle=true]] (* no Z3 proof *)
   by smt
 
 lemma "\<exists>x::real. 0 < x"
-  using [[z3_proofs=false]] (* no Z3 proof *)
+  using [[smt_oracle=true]] (* no Z3 proof *)
   by smt
 
 lemma "\<forall>x::int. \<exists>y. y > x"
-  using [[z3_proofs=false]] (* no Z3 proof *)
+  using [[smt_oracle=true]] (* no Z3 proof *)
   by smt
 
 lemma "\<forall>x y::int. (x = 0 \<and> y = 1) \<longrightarrow> x \<noteq> y" by smt
@@ -400,7 +400,7 @@
 subsection {* Non-linear arithmetic over integers and reals *}
 
 lemma "a > (0::int) \<Longrightarrow> a*b > 0 \<Longrightarrow> b > 0"
-  using [[z3_proofs=false]]  -- {* Isabelle's arithmetic decision procedures
+  using [[smt_oracle=true]]  -- {* Isabelle's arithmetic decision procedures
     are too weak to automatically prove @{thm zero_less_mult_pos}. *}
   by smt (* FIXME: use z3_rule *)
 
diff -r 7f58a9a843c2 -r a462d5207aa6 src/HOL/SMT_Examples/SMT_Tests.certs
--- a/src/HOL/SMT_Examples/SMT_Tests.certs	Tue Oct 26 11:45:12 2010 +0200
+++ b/src/HOL/SMT_Examples/SMT_Tests.certs	Tue Oct 26 11:46:19 2010 +0200
@@ -1,4 +1,4 @@
-ef3118b3c538f5cd123d726ccf13a3c2d3725bb0 8 0
+d4b1481d70f20d4d6280999633c905e21d180d13 8 0
 #2 := false
 #1 := true
 #8 := (not true)
@@ -7,7 +7,7 @@
 #25 := [asserted]: #8
 [mp #25 #27]: false
 unsat
-300ac981df663a0c38577b3d315e53c71dd0988e 16 0
+ac5b1925e47f9c59b180fdccd321c68a4a01a710 16 0
 #2 := false
 #8 := (not false)
 #9 := (not #8)
@@ -24,7 +24,7 @@
 #26 := [asserted]: #9
 [mp #26 #35]: false
 unsat
-0b184a84ce871fe108c2b5dce0e6482dd3c0450a 21 0
+b13645ce0b47b432b924b38e0bebde6cbcb236f9 21 0
 #2 := false
 #1 := true
 #8 := (not true)
@@ -46,7 +46,7 @@
 #27 := [asserted]: #10
 [mp #27 #40]: false
 unsat
-9acfa8385beeafd8546dddb4d92b4b4b9a1a0bd8 16 0
+8ec60d0baade8bddd39b6e00ec153f6bd8949184 16 0
 #2 := false
 #1 := true
 #8 := (and true true)
@@ -63,7 +63,7 @@
 #26 := [asserted]: #9
 [mp #26 #35]: false
 unsat
-d35ed39a7bb1024906bec1f4afa8168bb568efe7 16 0
+b448617db1567a507fc596f5b21ade645ca6e0f9 16 0
 #2 := false
 #1 := true
 #8 := (or true false)
@@ -80,7 +80,7 @@
 #26 := [asserted]: #9
 [mp #26 #35]: false
 unsat
-a3266a8f006b3750ff4748b6a1a76e7bde92780d 16 0
+bf545ecaa58049cbf454eac70ee3077f64564cca 16 0
 #2 := false
 #1 := true
 #8 := (implies false true)
@@ -97,7 +97,7 @@
 #26 := [asserted]: #9
 [mp #26 #35]: false
 unsat
-b59b2f429ffd47c407e4ef1af006540275b1a26c 33 0
+a38979487be0aafcf2d387180e92dfd3bd43e483 33 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -131,7 +131,7 @@
 #29 := [asserted]: #12
 [mp #29 #49]: false
 unsat
-3115e8e7b694b406a07c11043a6921a0dba8d5ea 41 0
+b2faf72eaa234b8ac1acedfef5768f99ca3da86b 41 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -173,157 +173,7 @@
 #30 := [asserted]: #13
 [mp #30 #57]: false
 unsat
-e3d163795277d672f4f54561a9fed7fa5b707b37 149 0
-#2 := false
-decl f5 :: S1
-#12 := f5
-decl f1 :: S1
-#4 := f1
-#44 := (= f1 f5)
-decl f4 :: S1
-#10 := f4
-#41 := (= f1 f4)
-decl f3 :: S1
-#8 := f3
-#38 := (= f1 f3)
-#47 := (ite #38 #41 #44)
-#53 := (not #38)
-#54 := (or #53 #41)
-#64 := (or #38 #44)
-#91 := (not #64)
-#90 := (not #54)
-#92 := (or #90 #91)
-#143 := [hypothesis]: #90
-#128 := (or #92 #54)
-#129 := [def-axiom]: #128
-#144 := [unit-resolution #129 #143]: #92
-#78 := (not #47)
-#116 := (or #54 #38)
-#117 := [def-axiom]: #116
-#145 := [unit-resolution #117 #143]: #38
-#110 := (not #41)
-#118 := (or #54 #110)
-#119 := [def-axiom]: #118
-#146 := [unit-resolution #119 #143]: #110
-#106 := (or #78 #53 #41)
-#107 := [def-axiom]: #106
-#147 := [unit-resolution #107 #146 #145]: #78
-#93 := (not #92)
-#137 := (or #47 #93)
-#100 := (iff #47 #92)
-#69 := (and #54 #64)
-#79 := (iff #69 #78)
-#103 := (iff #79 #100)
-#95 := (iff #92 #47)
-#101 := (iff #95 #100)
-#102 := [rewrite]: #101
-#98 := (iff #79 #95)
-#87 := (iff #93 #78)
-#96 := (iff #87 #95)
-#97 := [rewrite]: #96
-#84 := (iff #79 #87)
-#88 := (iff #69 #93)
-#89 := [rewrite]: #88
-#94 := [monotonicity #89]: #84
-#99 := [trans #94 #97]: #98
-#104 := [trans #99 #102]: #103
-#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)
-#82 := (iff #20 #79)
-#72 := (iff #47 #69)
-#75 := (not #72)
-#80 := (iff #75 #79)
-#81 := [rewrite]: #80
-#76 := (iff #20 #75)
-#73 := (iff #19 #72)
-#70 := (iff #18 #69)
-#67 := (iff #17 #64)
-#61 := (implies #53 #44)
-#65 := (iff #61 #64)
-#66 := [rewrite]: #65
-#62 := (iff #17 #61)
-#45 := (iff #13 #44)
-#46 := [rewrite]: #45
-#59 := (iff #16 #53)
-#39 := (iff #9 #38)
-#40 := [rewrite]: #39
-#60 := [monotonicity #40]: #59
-#63 := [monotonicity #60 #46]: #62
-#68 := [trans #63 #66]: #67
-#57 := (iff #15 #54)
-#50 := (implies #38 #41)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #15 #50)
-#42 := (iff #11 #41)
-#43 := [rewrite]: #42
-#52 := [monotonicity #40 #43]: #51
-#58 := [trans #52 #56]: #57
-#71 := [monotonicity #58 #68]: #70
-#48 := (iff #14 #47)
-#49 := [monotonicity #40 #43 #46]: #48
-#74 := [monotonicity #49 #71]: #73
-#77 := [monotonicity #74]: #76
-#83 := [trans #77 #81]: #82
-#37 := [asserted]: #20
-#86 := [mp #37 #83]: #79
-#105 := [mp #86 #104]: #100
-#134 := (not #100)
-#135 := (or #47 #93 #134)
-#136 := [def-axiom]: #135
-#138 := [unit-resolution #136 #105]: #137
-#148 := [unit-resolution #138 #147 #144]: false
-#149 := [lemma #148]: #54
-#150 := [hypothesis]: #78
-#156 := (or #38 #47)
-#151 := [unit-resolution #138 #150]: #93
-#130 := (or #92 #64)
-#131 := [def-axiom]: #130
-#152 := [unit-resolution #131 #151]: #64
-#153 := [hypothesis]: #53
-#113 := (not #44)
-#114 := (or #47 #38 #113)
-#115 := [def-axiom]: #114
-#154 := [unit-resolution #115 #153 #150]: #113
-#126 := (or #91 #38 #44)
-#127 := [def-axiom]: #126
-#155 := [unit-resolution #127 #154 #153 #152]: false
-#157 := [lemma #155]: #156
-#158 := [unit-resolution #157 #150]: #38
-#111 := (or #47 #53 #110)
-#112 := [def-axiom]: #111
-#159 := [unit-resolution #112 #158 #150]: #110
-#120 := (or #90 #53 #41)
-#121 := [def-axiom]: #120
-#160 := [unit-resolution #121 #159 #158 #149]: false
-#161 := [lemma #160]: #47
-#141 := (or #78 #92)
-#139 := (or #78 #92 #134)
-#140 := [def-axiom]: #139
-#142 := [unit-resolution #140 #105]: #141
-#162 := [unit-resolution #142 #161]: #92
-#132 := (or #93 #90 #91)
-#133 := [def-axiom]: #132
-#163 := [unit-resolution #133 #162 #149]: #91
-#122 := (or #64 #53)
-#123 := [def-axiom]: #122
-#164 := [unit-resolution #123 #163]: #53
-#124 := (or #64 #113)
-#125 := [def-axiom]: #124
-#165 := [unit-resolution #125 #163]: #113
-#108 := (or #78 #38 #44)
-#109 := [def-axiom]: #108
-[unit-resolution #109 #165 #164 #161]: false
-unsat
-293682654769f9a30e4727176ece5ebbfa2edbf9 65 0
+fa3a2c67c2833da196c4009cb283e94a9f22829b 65 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -389,74 +239,7 @@
 #33 := [asserted]: #16
 [mp #33 #81]: false
 unsat
-b7f1180181cd52aa741865e3ac17b4d97cf7408a 66 0
-#2 := false
-decl f3 :: S1
-#8 := f3
-decl f1 :: S1
-#4 := f1
-#33 := (= f1 f3)
-#51 := (not #33)
-#87 := [hypothesis]: #33
-decl f4 :: S1
-#10 := f4
-#36 := (= f1 f4)
-#42 := (not #36)
-#43 := (or #33 #42)
-#69 := (or #43 #51)
-#70 := [def-axiom]: #69
-#88 := [unit-resolution #70 #87]: #43
-#67 := (not #43)
-#89 := (or #51 #67)
-#52 := (or #51 #36)
-#57 := (ite #33 #43 #52)
-#60 := (not #57)
-#11 := (= f4 f1)
-#9 := (= f3 f1)
-#13 := (implies #9 #11)
-#12 := (implies #11 #9)
-#14 := (ite #9 #12 #13)
-#15 := (not #14)
-#61 := (iff #15 #60)
-#58 := (iff #14 #57)
-#55 := (iff #13 #52)
-#48 := (implies #33 #36)
-#53 := (iff #48 #52)
-#54 := [rewrite]: #53
-#49 := (iff #13 #48)
-#37 := (iff #11 #36)
-#38 := [rewrite]: #37
-#34 := (iff #9 #33)
-#35 := [rewrite]: #34
-#50 := [monotonicity #35 #38]: #49
-#56 := [trans #50 #54]: #55
-#46 := (iff #12 #43)
-#39 := (implies #36 #33)
-#44 := (iff #39 #43)
-#45 := [rewrite]: #44
-#40 := (iff #12 #39)
-#41 := [monotonicity #38 #35]: #40
-#47 := [trans #41 #45]: #46
-#59 := [monotonicity #35 #47 #56]: #58
-#62 := [monotonicity #59]: #61
-#32 := [asserted]: #15
-#65 := [mp #32 #62]: #60
-#83 := (or #57 #51 #67)
-#84 := [def-axiom]: #83
-#90 := [unit-resolution #84 #65]: #89
-#91 := [unit-resolution #90 #88 #87]: false
-#92 := [lemma #91]: #51
-#63 := (or #52 #33)
-#73 := [def-axiom]: #63
-#93 := [unit-resolution #73 #92]: #52
-#76 := (not #52)
-#94 := (or #33 #76)
-#85 := (or #57 #33 #76)
-#86 := [def-axiom]: #85
-#95 := [unit-resolution #86 #65]: #94
-[unit-resolution #95 #93 #92]: false
-unsat
-001f5ceb25bbdf443b66d76c2d62a655a1155fa7 29 0
+85a9b542a9c6d64e778f2449f892d6d55e153689 29 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -486,7 +269,7 @@
 #28 := [asserted]: #11
 [mp #28 #45]: false
 unsat
-140af760eaf1680b3107622d1bad9733191529ce 41 0
+a21434fdffa6243cc7410eb0aff669b84c5be474 41 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -528,75 +311,7 @@
 #30 := [asserted]: #13
 [mp #30 #57]: false
 unsat
-4ef549c8b4c07c939a8ccb4f819e8b3925600dc3 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)
-#79 := (iff #21 false)
-#1 := true
-#74 := (not true)
-#77 := (iff #74 false)
-#78 := [rewrite]: #77
-#75 := (iff #21 #74)
-#72 := (iff #20 true)
-#51 := (= f1 f6)
-#48 := (= f1 f5)
-#42 := (= f1 f4)
-#39 := (= f1 f3)
-#45 := (or #39 #42)
-#54 := (ite #45 #48 #51)
-#67 := (iff #54 #54)
-#70 := (iff #67 true)
-#71 := [rewrite]: #70
-#68 := (iff #20 #67)
-#65 := (iff #19 #54)
-#57 := (ite #42 #48 #51)
-#60 := (ite #39 #48 #57)
-#63 := (iff #60 #54)
-#64 := [rewrite]: #63
-#61 := (iff #19 #60)
-#58 := (iff #18 #57)
-#52 := (iff #16 #51)
-#53 := [rewrite]: #52
-#49 := (iff #14 #48)
-#50 := [rewrite]: #49
-#43 := (iff #11 #42)
-#44 := [rewrite]: #43
-#59 := [monotonicity #44 #50 #53]: #58
-#40 := (iff #9 #39)
-#41 := [rewrite]: #40
-#62 := [monotonicity #41 #50 #59]: #61
-#66 := [trans #62 #64]: #65
-#55 := (iff #17 #54)
-#46 := (iff #12 #45)
-#47 := [monotonicity #41 #44]: #46
-#56 := [monotonicity #47 #50 #53]: #55
-#69 := [monotonicity #56 #66]: #68
-#73 := [trans #69 #71]: #72
-#76 := [monotonicity #73]: #75
-#80 := [trans #76 #78]: #79
-#38 := [asserted]: #21
-[mp #38 #80]: false
-unsat
-6e4da81b8f15e2e0630be83dbec8d4ceab075fda 47 0
+a6a664cc4c3ff45fb3211b72c0f520208b902c9b 47 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -644,75 +359,7 @@
 #32 := [asserted]: #15
 [mp #32 #62]: false
 unsat
-00916919fe29a5b81ca835c8a92b8b60250f42f6 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)
-#79 := (iff #21 false)
-#1 := true
-#74 := (not true)
-#77 := (iff #74 false)
-#78 := [rewrite]: #77
-#75 := (iff #21 #74)
-#72 := (iff #20 true)
-#51 := (= f1 f6)
-#48 := (= f1 f5)
-#42 := (= f1 f4)
-#39 := (= f1 f3)
-#45 := (and #39 #42)
-#54 := (ite #45 #48 #51)
-#67 := (iff #54 #54)
-#70 := (iff #67 true)
-#71 := [rewrite]: #70
-#68 := (iff #20 #67)
-#65 := (iff #19 #54)
-#57 := (ite #42 #48 #51)
-#60 := (ite #39 #57 #51)
-#63 := (iff #60 #54)
-#64 := [rewrite]: #63
-#61 := (iff #19 #60)
-#52 := (iff #16 #51)
-#53 := [rewrite]: #52
-#58 := (iff #18 #57)
-#49 := (iff #14 #48)
-#50 := [rewrite]: #49
-#43 := (iff #11 #42)
-#44 := [rewrite]: #43
-#59 := [monotonicity #44 #50 #53]: #58
-#40 := (iff #9 #39)
-#41 := [rewrite]: #40
-#62 := [monotonicity #41 #59 #53]: #61
-#66 := [trans #62 #64]: #65
-#55 := (iff #17 #54)
-#46 := (iff #12 #45)
-#47 := [monotonicity #41 #44]: #46
-#56 := [monotonicity #47 #50 #53]: #55
-#69 := [monotonicity #56 #66]: #68
-#73 := [trans #69 #71]: #72
-#76 := [monotonicity #73]: #75
-#80 := [trans #76 #78]: #79
-#38 := [asserted]: #21
-[mp #38 #80]: false
-unsat
-d5bc9e39a4bb8116809502fbfd19f3ca0119f9c0 47 0
+d99e41f56c960ba88eb8ca95c5a49bd2181a7626 47 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -760,194 +407,7 @@
 #32 := [asserted]: #15
 [mp #32 #62]: false
 unsat
-7d731ec0802cbb5844eb34ccffb568c08f773a66 186 0
-#2 := false
-decl f5 :: S1
-#12 := f5
-decl f1 :: S1
-#4 := f1
-#47 := (= f1 f5)
-decl f3 :: S1
-#8 := f3
-#41 := (= f1 f3)
-#59 := (not #41)
-#76 := (or #59 #47)
-#119 := (not #76)
-decl f4 :: S1
-#10 := f4
-#44 := (= f1 f4)
-#68 := (or #59 #44)
-decl f6 :: S1
-#14 := f6
-#50 := (= f1 f6)
-#84 := (or #59 #50)
-#89 := (ite #68 #76 #84)
-#130 := (not #89)
-#53 := (ite #44 #47 #50)
-#60 := (or #59 #53)
-#112 := (not #44)
-#165 := [hypothesis]: #112
-#172 := (or #60 #44)
-#98 := (not #60)
-#163 := [hypothesis]: #98
-#148 := (or #60 #41)
-#149 := [def-axiom]: #148
-#164 := [unit-resolution #149 #163]: #41
-#124 := (not #50)
-#139 := (not #53)
-#150 := (or #60 #139)
-#151 := [def-axiom]: #150
-#166 := [unit-resolution #151 #163]: #139
-#146 := (or #53 #44 #124)
-#147 := [def-axiom]: #146
-#167 := [unit-resolution #147 #166 #165]: #124
-#157 := (or #89 #60)
-#99 := (iff #89 #98)
-#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)
-#102 := (iff #23 #99)
-#92 := (iff #60 #89)
-#95 := (not #92)
-#100 := (iff #95 #99)
-#101 := [rewrite]: #100
-#96 := (iff #23 #95)
-#93 := (iff #22 #92)
-#90 := (iff #21 #89)
-#87 := (iff #20 #84)
-#81 := (implies #41 #50)
-#85 := (iff #81 #84)
-#86 := [rewrite]: #85
-#82 := (iff #20 #81)
-#51 := (iff #15 #50)
-#52 := [rewrite]: #51
-#42 := (iff #9 #41)
-#43 := [rewrite]: #42
-#83 := [monotonicity #43 #52]: #82
-#88 := [trans #83 #86]: #87
-#79 := (iff #19 #76)
-#73 := (implies #41 #47)
-#77 := (iff #73 #76)
-#78 := [rewrite]: #77
-#74 := (iff #19 #73)
-#48 := (iff #13 #47)
-#49 := [rewrite]: #48
-#75 := [monotonicity #43 #49]: #74
-#80 := [trans #75 #78]: #79
-#71 := (iff #18 #68)
-#65 := (implies #41 #44)
-#69 := (iff #65 #68)
-#70 := [rewrite]: #69
-#66 := (iff #18 #65)
-#45 := (iff #11 #44)
-#46 := [rewrite]: #45
-#67 := [monotonicity #43 #46]: #66
-#72 := [trans #67 #70]: #71
-#91 := [monotonicity #72 #80 #88]: #90
-#63 := (iff #17 #60)
-#56 := (implies #41 #53)
-#61 := (iff #56 #60)
-#62 := [rewrite]: #61
-#57 := (iff #17 #56)
-#54 := (iff #16 #53)
-#55 := [monotonicity #46 #49 #52]: #54
-#58 := [monotonicity #43 #55]: #57
-#64 := [trans #58 #62]: #63
-#94 := [monotonicity #64 #91]: #93
-#97 := [monotonicity #94]: #96
-#103 := [trans #97 #101]: #102
-#40 := [asserted]: #23
-#106 := [mp #40 #103]: #99
-#154 := (not #99)
-#155 := (or #89 #60 #154)
-#156 := [def-axiom]: #155
-#158 := [unit-resolution #156 #106]: #157
-#168 := [unit-resolution #158 #163]: #89
-#109 := (not #68)
-#107 := (or #109 #59 #44)
-#104 := [def-axiom]: #107
-#169 := [unit-resolution #104 #164 #165]: #109
-#133 := (or #130 #68 #84)
-#134 := [def-axiom]: #133
-#170 := [unit-resolution #134 #169 #168]: #84
-#127 := (not #84)
-#128 := (or #127 #59 #50)
-#129 := [def-axiom]: #128
-#171 := [unit-resolution #129 #170 #167 #164]: false
-#173 := [lemma #171]: #172
-#176 := [unit-resolution #173 #165]: #60
-#161 := (or #130 #98)
-#159 := (or #130 #98 #154)
-#160 := [def-axiom]: #159
-#162 := [unit-resolution #160 #106]: #161
-#182 := [unit-resolution #162 #176]: #130
-#180 := (or #84 #44)
-#174 := [hypothesis]: #127
-#125 := (or #84 #124)
-#126 := [def-axiom]: #125
-#175 := [unit-resolution #126 #174]: #124
-#122 := (or #84 #41)
-#123 := [def-axiom]: #122
-#177 := [unit-resolution #123 #174]: #41
-#152 := (or #98 #59 #53)
-#153 := [def-axiom]: #152
-#178 := [unit-resolution #153 #177 #176]: #53
-#142 := (or #139 #44 #50)
-#143 := [def-axiom]: #142
-#179 := [unit-resolution #143 #178 #175 #165]: false
-#181 := [lemma #179]: #180
-#183 := [unit-resolution #181 #165]: #84
-#137 := (or #89 #68 #127)
-#138 := [def-axiom]: #137
-#184 := [unit-resolution #138 #183 #182]: #68
-#135 := (or #89 #109 #119)
-#136 := [def-axiom]: #135
-#185 := [unit-resolution #136 #184 #182]: #119
-#186 := [unit-resolution #104 #184 #165]: #59
-#114 := (or #76 #41)
-#115 := [def-axiom]: #114
-#187 := [unit-resolution #115 #186 #185]: false
-#188 := [lemma #187]: #44
-#113 := (or #68 #112)
-#108 := [def-axiom]: #113
-#191 := [unit-resolution #108 #188]: #68
-#189 := [hypothesis]: #59
-#190 := [unit-resolution #149 #189]: #60
-#192 := [unit-resolution #115 #189]: #76
-#193 := [unit-resolution #136 #192 #191]: #89
-#194 := [unit-resolution #162 #193 #190]: false
-#195 := [lemma #194]: #41
-#116 := (not #47)
-#144 := (or #53 #112 #116)
-#145 := [def-axiom]: #144
-#196 := [unit-resolution #145 #166 #188]: #116
-#131 := (or #130 #109 #76)
-#132 := [def-axiom]: #131
-#197 := [unit-resolution #132 #168 #191]: #76
-#120 := (or #119 #59 #47)
-#121 := [def-axiom]: #120
-#198 := [unit-resolution #121 #197 #196 #195]: false
-#199 := [lemma #198]: #60
-#200 := [unit-resolution #162 #199]: #130
-#201 := [unit-resolution #136 #200 #191]: #119
-#202 := [unit-resolution #153 #199 #195]: #53
-#140 := (or #139 #112 #47)
-#141 := [def-axiom]: #140
-#203 := [unit-resolution #141 #202 #188]: #47
-#117 := (or #76 #116)
-#118 := [def-axiom]: #117
-[unit-resolution #118 #203 #201]: false
-unsat
-8f2ba8a450b38e7bdf2f188b8cd61ae5399f3de8 55 0
+a8e5086b6e21c7bf961a22426cb7ae14847089d7 55 0
 #2 := false
 decl f3 :: S1
 #8 := f3
@@ -1003,41 +463,7 @@
 #71 := [and-elim #70]: #33
 [mp #71 #77]: false
 unsat
-4c5797ba6bf6e1b3bb6b8306b16e65642fb4c91c 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)
-#48 := (iff #12 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (iff #11 true)
-#30 := (= f1 f3)
-#33 := (not #30)
-#36 := (ite #30 #30 #33)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#34 := (iff #10 #33)
-#31 := (iff #9 #30)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#38 := [monotonicity #32 #32 #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#29 := [asserted]: #12
-[mp #29 #49]: false
-unsat
-97918cca48c9094bd5b3664f47e49327114322de 55 0
+e2d0843914ae918fb9bd06a2d6949232327217fa 55 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -1093,41 +519,7 @@
 #33 := [asserted]: #16
 [mp #33 #70]: false
 unsat
-9bd9eaea49f2e1ee09a5710de988a261a59b3161 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)
-#48 := (iff #12 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (iff #11 true)
-#30 := (= f1 f3)
-#33 := (not #30)
-#36 := (ite #33 #33 #30)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #11 #36)
-#31 := (iff #9 #30)
-#32 := [rewrite]: #31
-#34 := (iff #10 #33)
-#35 := [monotonicity #32]: #34
-#38 := [monotonicity #35 #35 #32]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#29 := [asserted]: #12
-[mp #29 #49]: false
-unsat
-54241528b45f8f4faa0c0db0443b55a0791bdebf 55 0
+00d9c16458cf2825e776c32505a513a412ede70f 55 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -1183,26 +575,7 @@
 #33 := [asserted]: #16
 [mp #33 #70]: false
 unsat
-7e9279650e1782ee3eacd8b5ddc9abff7cf3939f 18 0
-#2 := false
-decl f3 :: S2
-#8 := f3
-#9 := (= f3 f3)
-#10 := (not #9)
-#35 := (iff #10 false)
-#1 := true
-#30 := (not true)
-#33 := (iff #30 false)
-#34 := [rewrite]: #33
-#31 := (iff #10 #30)
-#28 := (iff #9 true)
-#29 := [rewrite]: #28
-#32 := [monotonicity #29]: #31
-#36 := [trans #32 #34]: #35
-#27 := [asserted]: #10
-[mp #27 #36]: false
-unsat
-fad369d322dc0c4cbd802fd43ac8e39269b90c24 49 0
+bca31cbd8bb6114896c32a11dfae7025f2fc07b1 49 0
 #2 := false
 decl f3 :: S1
 #8 := f3
@@ -1252,37 +625,7 @@
 #63 := [and-elim #61]: #34
 [mp #63 #69]: false
 unsat
-4f15136164606c4b4de495e81f7a15d214b1a16d 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)
-#45 := (iff #13 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #13 #40)
-#38 := (iff #12 true)
-#33 := (implies #10 #10)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #12 #33)
-#31 := (iff #11 #10)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#30 := [asserted]: #13
-[mp #30 #46]: false
-unsat
-b24d83f0e79204c7c5bc93564e0299d7be355898 54 0
+f5031e01f448cd128a3cce562b470d23d1a8bc59 54 0
 #2 := false
 decl f3 :: S1
 #8 := f3
@@ -1337,42 +680,7 @@
 #68 := [and-elim #66]: #34
 [mp #68 #74]: false
 unsat
-dc9c622e9c5a73b4906108c844d17870f8f467f3 34 0
-#2 := false
-decl f5 :: S2
-#11 := f5
-decl f3 :: S2
-#8 := f3
-#14 := (= f3 f5)
-decl f4 :: S2
-#9 := f4
-#12 := (= f4 f5)
-#58 := (iff #12 #14)
-#56 := (iff #14 #12)
-#10 := (= f3 f4)
-#13 := (and #10 #12)
-#34 := (not #13)
-#35 := (or #34 #14)
-#38 := (not #35)
-#15 := (implies #13 #14)
-#16 := (not #15)
-#39 := (iff #16 #38)
-#36 := (iff #15 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#33 := [asserted]: #16
-#43 := [mp #33 #40]: #38
-#41 := [not-or-elim #43]: #13
-#42 := [and-elim #41]: #10
-#57 := [monotonicity #42]: #56
-#59 := [symm #57]: #58
-#44 := [and-elim #41]: #12
-#54 := [mp #44 #59]: #14
-#45 := (not #14)
-#46 := [not-or-elim #43]: #45
-[unit-resolution #46 #54]: false
-unsat
-0f759d4f64321dbbf3a7fb1265c4748ce0ceab54 60 0
+38d7d5f12a8c933e456bba4a04c7645f4c87ea49 60 0
 #2 := false
 decl f4 :: S1
 #10 := f4
@@ -1433,35 +741,7 @@
 #70 := [mp #35 #67]: #64
 [mp #70 #68]: false
 unsat
-a8195f22c8d1b577a8f5ae2243196c5ebe015804 27 0
-#2 := false
-decl f5 :: (-> S2 S2)
-decl f4 :: S2
-#9 := f4
-#12 := (f5 f4)
-decl f3 :: S2
-#8 := f3
-#11 := (f5 f3)
-#13 := (= #11 #12)
-#10 := (= f3 f4)
-#33 := (not #10)
-#34 := (or #33 #13)
-#37 := (not #34)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#38 := (iff #15 #37)
-#35 := (iff #14 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#32 := [asserted]: #15
-#42 := [mp #32 #39]: #37
-#40 := [not-or-elim #42]: #10
-#51 := [monotonicity #40]: #13
-#41 := (not #13)
-#43 := [not-or-elim #42]: #41
-[unit-resolution #43 #51]: false
-unsat
-56fbd97995f4b7bc4d7561f89b146084e2ece4a4 79 0
+27121de8ceb5985c14cca2c4563e9cad4d2ebd3c 79 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -1541,39 +821,7 @@
 #36 := [asserted]: #19
 [mp #36 #93]: false
 unsat
-f0071ffac5f0293e3340ba2c318e33d4b7b540a9 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)
-#53 := (= #12 #11)
-#10 := (= f3 f4)
-#33 := (not #10)
-#34 := (or #33 #13)
-#37 := (not #34)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#38 := (iff #15 #37)
-#35 := (iff #14 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#32 := [asserted]: #15
-#42 := [mp #32 #39]: #37
-#40 := [not-or-elim #42]: #10
-#51 := (= f4 f3)
-#52 := [symm #40]: #51
-#54 := [monotonicity #52 #40]: #53
-#49 := [symm #54]: #13
-#41 := (not #13)
-#43 := [not-or-elim #42]: #41
-[unit-resolution #43 #49]: false
-unsat
-06f5c6a6bea9a2fa1b9f87412f4567c4e365964a 94 0
+dc14c19019afcaa63507e4b503184496ed6bfd2f 94 0
 #2 := false
 decl f5 :: S1
 #13 := f5
@@ -1668,71 +916,7 @@
 #96 := [not-or-elim #89]: #70
 [mp #96 #112]: false
 unsat
-16b0a3ece5062e22059e25c49e83e51c0b937a88 63 0
-#2 := false
-decl f3 :: (-> S2 S2)
-decl f4 :: S2
-#8 := f4
-#9 := (f3 f4)
-#46 := (= f4 #9)
-#10 := (f3 #9)
-#12 := (f3 #10)
-#78 := (= #12 #9)
-#76 := (= #9 #12)
-#37 := (= f4 #10)
-#13 := (f3 #12)
-#14 := (f3 #13)
-#40 := (= f4 #14)
-#43 := (and #37 #40)
-#52 := (not #43)
-#53 := (or #52 #46)
-#58 := (not #53)
-#17 := (= #9 f4)
-#15 := (= #14 f4)
-#11 := (= #10 f4)
-#16 := (and #11 #15)
-#18 := (implies #16 #17)
-#19 := (not #18)
-#59 := (iff #19 #58)
-#56 := (iff #18 #53)
-#49 := (implies #43 #46)
-#54 := (iff #49 #53)
-#55 := [rewrite]: #54
-#50 := (iff #18 #49)
-#47 := (iff #17 #46)
-#48 := [rewrite]: #47
-#44 := (iff #16 #43)
-#41 := (iff #15 #40)
-#42 := [rewrite]: #41
-#38 := (iff #11 #37)
-#39 := [rewrite]: #38
-#45 := [monotonicity #39 #42]: #44
-#51 := [monotonicity #45 #48]: #50
-#57 := [trans #51 #55]: #56
-#60 := [monotonicity #57]: #59
-#36 := [asserted]: #19
-#63 := [mp #36 #60]: #58
-#61 := [not-or-elim #63]: #43
-#62 := [and-elim #61]: #37
-#77 := [monotonicity #62]: #76
-#79 := [symm #77]: #78
-#81 := (= f4 #12)
-#67 := (= #14 #12)
-#70 := (= #12 #14)
-#72 := (= #10 #13)
-#74 := (= #13 #10)
-#75 := [monotonicity #79]: #74
-#73 := [symm #75]: #72
-#71 := [monotonicity #73]: #70
-#80 := [symm #71]: #67
-#64 := [and-elim #61]: #40
-#82 := [trans #64 #80]: #81
-#83 := [trans #82 #79]: #46
-#65 := (not #46)
-#66 := [not-or-elim #63]: #65
-[unit-resolution #66 #83]: false
-unsat
-f45903baa95c438d411754363ad5219754af16ca 114 0
+682b764e75beeea86518e9d265c22d014c6c1f1d 114 0
 #2 := false
 decl f5 :: S1
 #13 := f5
@@ -1847,203 +1031,7 @@
 #136 := [unit-resolution #109 #135]: #87
 [unit-resolution #93 #136 #134]: false
 unsat
-4b1d0031a7c5da8fe83e5d22bb3a19a4727fa881 195 0
-#2 := false
-decl f6 :: S2
-#13 := f6
-decl f4 :: S2
-#10 := f4
-#15 := (= f4 f6)
-decl f5 :: S2
-#11 := f5
-decl f3 :: S1
-#8 := f3
-decl f1 :: S1
-#4 := f1
-#40 := (= f1 f3)
-#43 := (ite #40 f4 f5)
-#49 := (= f6 #43)
-#200 := (iff #49 #15)
-#198 := (iff #15 #49)
-#46 := (= #43 f6)
-#50 := (iff #46 #49)
-#197 := [commutativity]: #50
-#195 := (iff #15 #46)
-#110 := (= f4 #43)
-#111 := (= f5 #43)
-#57 := (not #40)
-#180 := [hypothesis]: #57
-#114 := (or #40 #111)
-#115 := [def-axiom]: #114
-#184 := [unit-resolution #115 #180]: #111
-#185 := (= f6 f5)
-#18 := (= f5 f6)
-#174 := (iff #110 #15)
-#172 := (iff #15 #110)
-#68 := (or #18 #40)
-#95 := (not #68)
-#58 := (or #15 #57)
-#94 := (not #58)
-#96 := (or #94 #95)
-#123 := (not #18)
-#147 := [hypothesis]: #123
-#157 := (or #96 #18)
-#97 := (not #96)
-#145 := [hypothesis]: #97
-#132 := (or #96 #68)
-#133 := [def-axiom]: #132
-#148 := [unit-resolution #133 #145]: #68
-#128 := (or #95 #18 #40)
-#129 := [def-axiom]: #128
-#149 := [unit-resolution #129 #148 #147]: #40
-#112 := (or #57 #110)
-#113 := [def-axiom]: #112
-#150 := [unit-resolution #113 #149]: #110
-#153 := (= f6 f4)
-#130 := (or #96 #58)
-#131 := [def-axiom]: #130
-#151 := [unit-resolution #131 #145]: #58
-#121 := (or #94 #15 #57)
-#122 := [def-axiom]: #121
-#152 := [unit-resolution #122 #149 #151]: #15
-#154 := [symm #152]: #153
-#155 := [trans #154 #150]: #49
-#82 := (not #49)
-#143 := (or #82 #96)
-#104 := (iff #49 #96)
-#73 := (and #58 #68)
-#83 := (iff #73 #82)
-#107 := (iff #83 #104)
-#99 := (iff #96 #49)
-#105 := (iff #99 #104)
-#106 := [rewrite]: #105
-#102 := (iff #83 #99)
-#91 := (iff #97 #82)
-#100 := (iff #91 #99)
-#101 := [rewrite]: #100
-#88 := (iff #83 #91)
-#92 := (iff #73 #97)
-#93 := [rewrite]: #92
-#98 := [monotonicity #93]: #88
-#103 := [trans #98 #101]: #102
-#108 := [trans #103 #106]: #107
-#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)
-#22 := (not #21)
-#86 := (iff #22 #83)
-#76 := (iff #49 #73)
-#79 := (not #76)
-#84 := (iff #79 #83)
-#85 := [rewrite]: #84
-#80 := (iff #22 #79)
-#77 := (iff #21 #76)
-#74 := (iff #20 #73)
-#71 := (iff #19 #68)
-#65 := (implies #57 #18)
-#69 := (iff #65 #68)
-#70 := [rewrite]: #69
-#66 := (iff #19 #65)
-#63 := (iff #17 #57)
-#41 := (iff #9 #40)
-#42 := [rewrite]: #41
-#64 := [monotonicity #42]: #63
-#67 := [monotonicity #64]: #66
-#72 := [trans #67 #70]: #71
-#61 := (iff #16 #58)
-#54 := (implies #40 #15)
-#59 := (iff #54 #58)
-#60 := [rewrite]: #59
-#55 := (iff #16 #54)
-#56 := [monotonicity #42]: #55
-#62 := [trans #56 #60]: #61
-#75 := [monotonicity #62 #72]: #74
-#52 := (iff #14 #49)
-#51 := [rewrite]: #50
-#47 := (iff #14 #46)
-#44 := (= #12 #43)
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#53 := [trans #48 #51]: #52
-#78 := [monotonicity #53 #75]: #77
-#81 := [monotonicity #78]: #80
-#87 := [trans #81 #85]: #86
-#39 := [asserted]: #22
-#90 := [mp #39 #87]: #83
-#109 := [mp #90 #108]: #104
-#136 := (not #104)
-#141 := (or #82 #96 #136)
-#142 := [def-axiom]: #141
-#144 := [unit-resolution #142 #109]: #143
-#146 := [unit-resolution #144 #145]: #82
-#156 := [unit-resolution #146 #155]: false
-#158 := [lemma #156]: #157
-#159 := [unit-resolution #158 #147]: #96
-#139 := (or #49 #97)
-#137 := (or #49 #97 #136)
-#138 := [def-axiom]: #137
-#140 := [unit-resolution #138 #109]: #139
-#160 := [unit-resolution #140 #159]: #49
-#173 := [monotonicity #160]: #172
-#175 := [symm #173]: #174
-#163 := (not #111)
-#164 := (iff #123 #163)
-#161 := (iff #18 #111)
-#162 := [monotonicity #160]: #161
-#165 := [monotonicity #162]: #164
-#166 := [mp #147 #165]: #163
-#167 := [unit-resolution #115 #166]: #40
-#171 := [unit-resolution #113 #167]: #110
-#176 := [mp #171 #175]: #15
-#116 := (not #15)
-#126 := (or #68 #57)
-#127 := [def-axiom]: #126
-#168 := [unit-resolution #127 #167]: #68
-#134 := (or #97 #94 #95)
-#135 := [def-axiom]: #134
-#169 := [unit-resolution #135 #168 #159]: #94
-#117 := (or #58 #116)
-#118 := [def-axiom]: #117
-#170 := [unit-resolution #118 #169]: #116
-#177 := [unit-resolution #170 #176]: false
-#178 := [lemma #177]: #18
-#186 := [symm #178]: #185
-#187 := [trans #186 #184]: #49
-#124 := (or #68 #123)
-#125 := [def-axiom]: #124
-#179 := [unit-resolution #125 #178]: #68
-#119 := (or #58 #40)
-#120 := [def-axiom]: #119
-#181 := [unit-resolution #120 #180]: #58
-#182 := [unit-resolution #135 #181 #179]: #97
-#183 := [unit-resolution #144 #182]: #82
-#188 := [unit-resolution #183 #187]: false
-#189 := [lemma #188]: #40
-#194 := [unit-resolution #113 #189]: #110
-#196 := [monotonicity #194]: #195
-#199 := [trans #196 #197]: #198
-#201 := [symm #199]: #200
-#202 := (iff #82 #116)
-#203 := [monotonicity #201]: #202
-#190 := [hypothesis]: #82
-#204 := [mp #190 #203]: #116
-#191 := [unit-resolution #140 #190]: #97
-#192 := [unit-resolution #131 #191]: #58
-#193 := [unit-resolution #122 #192 #189]: #15
-#205 := [unit-resolution #193 #204]: false
-#206 := [lemma #205]: #49
-#210 := [mp #206 #201]: #15
-#207 := [unit-resolution #144 #206]: #96
-#208 := [unit-resolution #135 #207 #179]: #94
-#209 := [unit-resolution #118 #208]: #116
-[unit-resolution #209 #210]: false
-unsat
-d88d2fa5d625a6669d08e24799b598bc3243212b 121 0
+c134dad603b5004748b4c36796dfbdf41bc232cc 121 0
 #2 := false
 decl f5 :: S1
 #13 := f5
@@ -2165,44 +1153,7 @@
 #99 := [not-or-elim #92]: #98
 [mp #99 #138]: false
 unsat
-08da4c2954fa7e715a65caa44d6cfda212fd8151 36 0
-#2 := false
-decl f5 :: S2
-#10 := f5
-decl f3 :: S2
-#8 := f3
-#12 := (= f3 f5)
-#13 := (not #12)
-decl f4 :: S2
-#9 := f4
-#11 := (distinct f3 f4 f5)
-#33 := (not #11)
-#34 := (or #33 #13)
-#37 := (not #34)
-#14 := (implies #11 #13)
-#15 := (not #14)
-#38 := (iff #15 #37)
-#35 := (iff #14 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#32 := [asserted]: #15
-#42 := [mp #32 #39]: #37
-#41 := [not-or-elim #42]: #12
-#52 := (= f4 f5)
-#53 := (not #52)
-#50 := (= f3 f4)
-#51 := (not #50)
-#48 := (and #51 #13 #53)
-#40 := [not-or-elim #42]: #11
-#58 := (or #33 #48)
-#59 := [def-axiom]: #58
-#62 := [unit-resolution #59 #40]: #48
-#49 := (not #48)
-#45 := (or #49 #13)
-#43 := [def-axiom]: #45
-[unit-resolution #43 #62 #41]: false
-unsat
-bd50ed75e1a24fdaf488b7bfb75ceea321293722 110 0
+7afff0259006c1c4b6a802d510f1b96695b3e9ad 110 0
 #2 := false
 decl f4 :: S1
 #10 := f4
@@ -2313,85 +1264,7 @@
 #84 := [and-elim #83]: #44
 [mp #84 #129]: false
 unsat
-8dc240ee402eb47862312ada03d54f1453a80352 77 0
-#2 := false
-decl f4 :: S2
-#9 := f4
-decl f3 :: S2
-#8 := f3
-#81 := (= f3 f4)
-decl f6 :: S2
-#12 := f6
-#36 := (= f4 f6)
-#100 := (iff #36 #81)
-#98 := (iff #81 #36)
-#13 := (= f6 f4)
-#37 := (iff #13 #36)
-#97 := [commutativity]: #37
-#95 := (iff #81 #13)
-#14 := (= f3 f6)
-#42 := (not #36)
-#15 := (not #14)
-decl f5 :: S2
-#10 := f5
-#11 := (distinct f3 f4 f5)
-#51 := (not #11)
-#60 := (or #51 #15 #42)
-#63 := (not #60)
-#16 := (implies #13 #15)
-#17 := (implies #11 #16)
-#18 := (not #17)
-#66 := (iff #18 #63)
-#43 := (or #15 #42)
-#52 := (or #51 #43)
-#57 := (not #52)
-#64 := (iff #57 #63)
-#61 := (iff #52 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#58 := (iff #18 #57)
-#55 := (iff #17 #52)
-#48 := (implies #11 #43)
-#53 := (iff #48 #52)
-#54 := [rewrite]: #53
-#49 := (iff #17 #48)
-#46 := (iff #16 #43)
-#39 := (implies #36 #15)
-#44 := (iff #39 #43)
-#45 := [rewrite]: #44
-#40 := (iff #16 #39)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#47 := [trans #41 #45]: #46
-#50 := [monotonicity #47]: #49
-#56 := [trans #50 #54]: #55
-#59 := [monotonicity #56]: #58
-#67 := [trans #59 #65]: #66
-#35 := [asserted]: #18
-#68 := [mp #35 #67]: #63
-#70 := [not-or-elim #68]: #14
-#96 := [monotonicity #70]: #95
-#99 := [trans #96 #97]: #98
-#101 := [symm #99]: #100
-#71 := [not-or-elim #68]: #36
-#102 := [mp #71 #101]: #81
-#82 := (not #81)
-#79 := (= f4 f5)
-#80 := (not #79)
-#83 := (= f3 f5)
-#84 := (not #83)
-#77 := (and #82 #84 #80)
-#69 := [not-or-elim #68]: #11
-#89 := (or #51 #77)
-#90 := [def-axiom]: #89
-#93 := [unit-resolution #90 #69]: #77
-#78 := (not #77)
-#75 := (or #78 #82)
-#76 := [def-axiom]: #75
-#94 := [unit-resolution #76 #93]: #82
-[unit-resolution #94 #102]: false
-unsat
-82e8476a2b40c7b4ddf6aad1b870323c7e2adbfc 127 0
+83b90287eef3783de4d8fa4aad70d03dd0abddbf 127 0
 #2 := false
 decl f5 :: S1
 #13 := f5
@@ -2519,36 +1392,7 @@
 #149 := [unit-resolution #131 #147]: #97
 [unit-resolution #108 #149 #148]: false
 unsat
-3ec381e2388d16595dee423cb23410b8ee65f5be 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)
-#44 := (iff #12 false)
-#1 := true
-#39 := (not true)
-#42 := (iff #39 false)
-#43 := [rewrite]: #42
-#40 := (iff #12 #39)
-#37 := (iff #11 true)
-#32 := (not false)
-#35 := (iff #32 true)
-#36 := [rewrite]: #35
-#33 := (iff #11 #32)
-#30 := (iff #10 false)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31]: #33
-#38 := [trans #34 #36]: #37
-#41 := [monotonicity #38]: #40
-#45 := [trans #41 #43]: #44
-#29 := [asserted]: #12
-[mp #29 #45]: false
-unsat
-d88d10125d202994145262227e4bbc27de00325d 66 0
+a7f2c916e2192b153aaac29ea6f75d0842fd84d2 66 0
 #2 := false
 decl f3 :: S1
 #8 := f3
@@ -2615,38 +1459,7 @@
 #74 := [not-or-elim #84]: #33
 [unit-resolution #69 #74]: false
 unsat
-7978400bf5569e9c21731e843185e21f42a67667 30 0
-#2 := false
-decl f4 :: S2
-#9 := f4
-decl f3 :: S2
-#8 := f3
-#10 := (= f3 f4)
-#11 := (not #10)
-#12 := (not #11)
-#13 := (implies #10 #12)
-#14 := (not #13)
-#46 := (iff #14 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #14 #41)
-#39 := (iff #13 true)
-#34 := (implies #10 #10)
-#37 := (iff #34 true)
-#38 := [rewrite]: #37
-#35 := (iff #13 #34)
-#32 := (iff #12 #10)
-#33 := [rewrite]: #32
-#36 := [monotonicity #33]: #35
-#40 := [trans #36 #38]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#31 := [asserted]: #14
-[mp #31 #47]: false
-unsat
-123f558f9f3ffbb84aa29cf95bfa60a7fd8f9c53 156 0
+d398c106ccd0941d46bab8e5feda32347dd02740 156 0
 #2 := false
 decl f5 :: S1
 #13 := f5
@@ -2803,48 +1616,7 @@
 #114 := [def-axiom]: #113
 [unit-resolution #114 #172 #170]: false
 unsat
-10f35a88989b72a52fb3f98d7f7428c1e1b3e122 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)
-#35 := (not #13)
-#36 := (or #35 #15)
-#39 := (not #36)
-#16 := (implies #13 #15)
-#17 := (not #16)
-#40 := (iff #17 #39)
-#37 := (iff #16 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#34 := [asserted]: #17
-#44 := [mp #34 #41]: #39
-#46 := [not-or-elim #44]: #14
-#58 := (= f4 f5)
-#59 := (not #58)
-#57 := (not #12)
-#56 := (not #10)
-#54 := (and #56 #57 #59)
-#55 := (not #54)
-#42 := [not-or-elim #44]: #13
-#43 := [and-elim #42]: #10
-#52 := (or #55 #56)
-#53 := [def-axiom]: #52
-#66 := [unit-resolution #53 #43]: #55
-#62 := (or #15 #54)
-#63 := [def-axiom]: #62
-#67 := [unit-resolution #63 #66]: #15
-[unit-resolution #67 #46]: false
-unsat
-b3152f8558491ad9fde8dfd8e10a714b3e98cb57 114 0
+78ae843b278e5f0cc65999ee60776dec7c9f683f 114 0
 #2 := false
 decl f5 :: S1
 #13 := f5
@@ -2959,41 +1731,7 @@
 #101 := [mp #36 #100]: #94
 [mp #101 #130]: false
 unsat
-ed5b4a9da6fcf2483f2081f8e182d1c39bc7b1d0 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)
-#47 := (iff #15 false)
-#1 := true
-#42 := (not true)
-#45 := (iff #42 false)
-#46 := [rewrite]: #45
-#43 := (iff #15 #42)
-#40 := (iff #14 true)
-#35 := (implies #12 #12)
-#38 := (iff #35 true)
-#39 := [rewrite]: #38
-#36 := (iff #14 #35)
-#33 := (iff #13 #12)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#41 := [trans #37 #39]: #40
-#44 := [monotonicity #41]: #43
-#48 := [trans #44 #46]: #47
-#32 := [asserted]: #15
-[mp #32 #48]: false
-unsat
-710a09ff1423bdde95e9fb0541e56c839786cb31 198 0
+016fee2f7f490b7727a4579bedbeaa0a03271f5c 198 0
 #2 := false
 decl f5 :: S1
 #14 := f5
@@ -3192,99 +1930,7 @@
 #141 := [not-or-elim #136]: #93
 [mp #141 #215]: false
 unsat
-65f8a76a6f6a38a4bead0ee4b39d32d58aff533c 91 0
-#2 := false
-decl f5 :: S2
-#10 := f5
-decl f4 :: S2
-#9 := f4
-decl f3 :: S2
-#8 := f3
-#13 := (distinct f3 f4 f5)
-#67 := (= f4 f5)
-#68 := (not #67)
-#63 := (= f3 f5)
-#64 := (not #63)
-#61 := (= f3 f4)
-#62 := (not #61)
-#93 := (and #62 #64 #68)
-decl f6 :: S2
-#11 := f6
-#71 := (= f5 f6)
-#72 := (not #71)
-#69 := (= f4 f6)
-#70 := (not #69)
-#65 := (= f3 f6)
-#66 := (not #65)
-#73 := (and #62 #64 #66 #68 #70 #72)
-#12 := (distinct f3 f4 f5 f6)
-#14 := (distinct f4 f5 f6)
-#15 := (and #13 #14)
-#35 := (not #12)
-#36 := (or #35 #15)
-#39 := (not #36)
-#16 := (implies #12 #15)
-#17 := (not #16)
-#40 := (iff #17 #39)
-#37 := (iff #16 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#34 := [asserted]: #17
-#44 := [mp #34 #41]: #39
-#42 := [not-or-elim #44]: #12
-#89 := (or #35 #73)
-#90 := [def-axiom]: #89
-#121 := [unit-resolution #90 #42]: #73
-#74 := (not #73)
-#75 := (or #74 #62)
-#76 := [def-axiom]: #75
-#122 := [unit-resolution #76 #121]: #62
-#81 := (or #74 #68)
-#82 := [def-axiom]: #81
-#123 := [unit-resolution #82 #121]: #68
-#77 := (or #74 #64)
-#78 := [def-axiom]: #77
-#124 := [unit-resolution #78 #121]: #64
-#101 := (or #93 #61 #63 #67)
-#102 := [def-axiom]: #101
-#125 := [unit-resolution #102 #124 #123 #122]: #93
-#94 := (not #93)
-#105 := (or #13 #94)
-#106 := [def-axiom]: #105
-#126 := [unit-resolution #106 #125]: #13
-#107 := (and #68 #70 #72)
-#85 := (or #74 #72)
-#86 := [def-axiom]: #85
-#127 := [unit-resolution #86 #121]: #72
-#83 := (or #74 #70)
-#84 := [def-axiom]: #83
-#128 := [unit-resolution #84 #121]: #70
-#115 := (or #107 #67 #69 #71)
-#116 := [def-axiom]: #115
-#129 := [unit-resolution #116 #128 #127 #123]: #107
-#108 := (not #107)
-#119 := (or #14 #108)
-#120 := [def-axiom]: #119
-#130 := [unit-resolution #120 #129]: #14
-#54 := (not #14)
-#53 := (not #13)
-#55 := (or #53 #54)
-#43 := (not #15)
-#58 := (iff #43 #55)
-#56 := (not #55)
-#49 := (not #56)
-#46 := (iff #49 #55)
-#57 := [rewrite]: #46
-#50 := (iff #43 #49)
-#51 := (iff #15 #56)
-#52 := [rewrite]: #51
-#48 := [monotonicity #52]: #50
-#59 := [trans #48 #57]: #58
-#45 := [not-or-elim #44]: #43
-#60 := [mp #45 #59]: #55
-[unit-resolution #60 #130 #126]: false
-unsat
-c2ceb7f67b73bb3bdaed86d97f31bbabffade4ad 134 0
+3e0305075f83d65498b4a11b8ca72526b8e2d46d 134 0
 #2 := false
 decl f5 :: S1
 #14 := f5
@@ -3419,7 +2065,7 @@
 #121 := [not-or-elim #116]: #81
 [mp #121 #151]: false
 unsat
-77f105a2335d8f399aa84eb3f5b2c6fc18cb5cb0 162 0
+78ecef8a6265ee63380698aee66f7437c6eb9791 162 0
 #2 := false
 decl f5 :: S1
 #12 := f5
@@ -3582,7 +2228,7 @@
 #178 := [unit-resolution #128 #177]: #70
 [unit-resolution #136 #178 #176 #168]: false
 unsat
-f7a1358537b42b76857f25d2bb6dab6a65b957d3 54 0
+cbabdc011b8a302b61906c6191f0d7af27e25599 54 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -3637,7 +2283,7 @@
 #31 := [asserted]: #14
 [mp #31 #69]: false
 unsat
-cb5396a335ba3f235c4f126793b6452d8c22b8a0 144 0
+ae8651ca265765f3bb029935ca54bf350a439257 144 0
 #2 := false
 decl f5 :: S1
 #12 := f5
@@ -3782,33 +2428,7 @@
 #126 := [not-or-elim #121]: #102
 [mp #126 #161]: false
 unsat
-828c6cc5274797cbab0d66f9715797229aa86661 25 0
-#2 := false
-#8 := (:var 0 S2)
-#9 := (= #8 #8)
-#10 := (forall (vars (?v0 S2)) #9)
-#11 := (not #10)
-#43 := (iff #11 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #11 #38)
-#36 := (iff #10 true)
-#31 := (forall (vars (?v0 S2)) true)
-#34 := (iff #31 true)
-#35 := [elim-unused]: #34
-#32 := (iff #10 #31)
-#29 := (iff #9 true)
-#30 := [rewrite]: #29
-#33 := [quant-intro #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#28 := [asserted]: #11
-[mp #28 #44]: false
-unsat
-614eb9a555c5a60772dafc0939c267db1405600c 121 0
+f037e85f433fe4b6db0edebe38d7599d0d5f9a56 121 0
 #2 := false
 decl f5 :: S1
 #13 := f5
@@ -3930,42 +2550,7 @@
 #115 := [not-or-elim #109]: #90
 [mp #115 #138]: false
 unsat
-95dd35edf8ef21f4e7cf317ce58b9a2bec541f8f 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)
-#49 := (iff #13 false)
-#1 := true
-#44 := (not true)
-#47 := (iff #44 false)
-#48 := [rewrite]: #47
-#45 := (iff #13 #44)
-#42 := (iff #12 true)
-#31 := (= f1 #9)
-#34 := (forall (vars (?v0 S2)) #31)
-#37 := (iff #34 #34)
-#40 := (iff #37 true)
-#41 := [rewrite]: #40
-#38 := (iff #12 #37)
-#35 := (iff #11 #34)
-#32 := (iff #10 #31)
-#33 := [rewrite]: #32
-#36 := [quant-intro #33]: #35
-#39 := [monotonicity #36 #36]: #38
-#43 := [trans #39 #41]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#30 := [asserted]: #13
-[mp #30 #50]: false
-unsat
-93c5fb9808d8360640a347075369425791ec133b 123 0
+a79fa106ccc873005f00005d34ba1798389c2876 123 0
 #2 := false
 decl f4 :: S1
 #10 := f4
@@ -4089,7 +2674,1914 @@
 #92 := [not-or-elim #91]: #72
 [mp #92 #141]: false
 unsat
-b4400db85e456f9b3856673990716e60114a7552 95 0
+7e097d3ef4e0c4927519d96187a725503177b49b 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)
+#74 := (iff #17 false)
+#1 := true
+#69 := (not true)
+#72 := (iff #69 false)
+#73 := [rewrite]: #72
+#70 := (iff #17 #69)
+#67 := (iff #16 true)
+#38 := (= f1 f4)
+#35 := (= f1 f3)
+#44 := (not #35)
+#45 := (or #44 #38)
+#62 := (implies #45 #45)
+#65 := (iff #62 true)
+#66 := [rewrite]: #65
+#63 := (iff #16 #62)
+#60 := (iff #15 #45)
+#50 := (not #38)
+#55 := (implies #50 #44)
+#58 := (iff #55 #45)
+#59 := [rewrite]: #58
+#56 := (iff #15 #55)
+#53 := (iff #14 #44)
+#36 := (iff #9 #35)
+#37 := [rewrite]: #36
+#54 := [monotonicity #37]: #53
+#51 := (iff #13 #50)
+#39 := (iff #11 #38)
+#40 := [rewrite]: #39
+#52 := [monotonicity #40]: #51
+#57 := [monotonicity #52 #54]: #56
+#61 := [trans #57 #59]: #60
+#48 := (iff #12 #45)
+#41 := (implies #35 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #12 #41)
+#43 := [monotonicity #37 #40]: #42
+#49 := [trans #43 #47]: #48
+#64 := [monotonicity #49 #61]: #63
+#68 := [trans #64 #66]: #67
+#71 := [monotonicity #68]: #70
+#75 := [trans #71 #73]: #74
+#34 := [asserted]: #17
+[mp #34 #75]: false
+unsat
+cb74096d43b27b6df4bed4b142ce429518455d83 121 0
+#2 := false
+decl f5 :: S1
+#12 := f5
+decl f1 :: S1
+#4 := f1
+#44 := (= f1 f5)
+decl f4 :: S1
+#10 := f4
+#41 := (= f1 f4)
+decl f3 :: S1
+#8 := f3
+#38 := (= f1 f3)
+#53 := (not #38)
+#90 := (or #53 #41 #44)
+#137 := (iff #90 false)
+#132 := (or false false false)
+#135 := (iff #132 false)
+#136 := [rewrite]: #135
+#133 := (iff #90 #132)
+#123 := (iff #44 false)
+#113 := (not #44)
+#93 := (not #90)
+#99 := (or #53 #41 #44 #93)
+#104 := (not #99)
+#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)
+#107 := (iff #20 #104)
+#70 := (or #53 #44)
+#62 := (or #53 #41)
+#75 := (or #62 #70)
+#47 := (or #41 #44)
+#54 := (or #53 #47)
+#81 := (not #54)
+#82 := (or #81 #75)
+#87 := (not #82)
+#105 := (iff #87 #104)
+#102 := (iff #82 #99)
+#96 := (or #93 #75)
+#100 := (iff #96 #99)
+#101 := [rewrite]: #100
+#97 := (iff #82 #96)
+#94 := (iff #81 #93)
+#91 := (iff #54 #90)
+#92 := [rewrite]: #91
+#95 := [monotonicity #92]: #94
+#98 := [monotonicity #95]: #97
+#103 := [trans #98 #101]: #102
+#106 := [monotonicity #103]: #105
+#88 := (iff #20 #87)
+#85 := (iff #19 #82)
+#78 := (implies #54 #75)
+#83 := (iff #78 #82)
+#84 := [rewrite]: #83
+#79 := (iff #19 #78)
+#76 := (iff #18 #75)
+#73 := (iff #17 #70)
+#67 := (implies #38 #44)
+#71 := (iff #67 #70)
+#72 := [rewrite]: #71
+#68 := (iff #17 #67)
+#45 := (iff #13 #44)
+#46 := [rewrite]: #45
+#39 := (iff #9 #38)
+#40 := [rewrite]: #39
+#69 := [monotonicity #40 #46]: #68
+#74 := [trans #69 #72]: #73
+#65 := (iff #16 #62)
+#59 := (implies #38 #41)
+#63 := (iff #59 #62)
+#64 := [rewrite]: #63
+#60 := (iff #16 #59)
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#61 := [monotonicity #40 #43]: #60
+#66 := [trans #61 #64]: #65
+#77 := [monotonicity #66 #74]: #76
+#57 := (iff #15 #54)
+#50 := (implies #38 #47)
+#55 := (iff #50 #54)
+#56 := [rewrite]: #55
+#51 := (iff #15 #50)
+#48 := (iff #14 #47)
+#49 := [monotonicity #43 #46]: #48
+#52 := [monotonicity #40 #49]: #51
+#58 := [trans #52 #56]: #57
+#80 := [monotonicity #58 #77]: #79
+#86 := [trans #80 #84]: #85
+#89 := [monotonicity #86]: #88
+#108 := [trans #89 #106]: #107
+#37 := [asserted]: #20
+#109 := [mp #37 #108]: #104
+#114 := [not-or-elim #109]: #113
+#124 := [iff-false #114]: #123
+#121 := (iff #41 false)
+#111 := (not #41)
+#112 := [not-or-elim #109]: #111
+#122 := [iff-false #112]: #121
+#130 := (iff #53 false)
+#1 := true
+#125 := (not true)
+#128 := (iff #125 false)
+#129 := [rewrite]: #128
+#126 := (iff #53 #125)
+#119 := (iff #38 true)
+#110 := [not-or-elim #109]: #38
+#120 := [iff-true #110]: #119
+#127 := [monotonicity #120]: #126
+#131 := [trans #127 #129]: #130
+#134 := [monotonicity #131 #122 #124]: #133
+#138 := [trans #134 #136]: #137
+#115 := [not-or-elim #109]: #90
+[mp #115 #138]: false
+unsat
+f67715569c1aa586d3c8e9a94e103b17f1f34614 84 0
+#2 := false
+decl f4 :: S1
+#10 := f4
+decl f1 :: S1
+#4 := f1
+#38 := (= f1 f4)
+#53 := (not #38)
+#97 := [hypothesis]: #53
+decl f3 :: S1
+#8 := f3
+#35 := (= f1 f3)
+#44 := (not #35)
+#45 := (or #44 #38)
+#54 := (or #35 #53)
+#59 := (and #45 #54)
+#62 := (iff #35 #38)
+#68 := (not #59)
+#69 := (or #68 #62)
+#74 := (not #69)
+#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)
+#75 := (iff #17 #74)
+#72 := (iff #16 #69)
+#65 := (implies #59 #62)
+#70 := (iff #65 #69)
+#71 := [rewrite]: #70
+#66 := (iff #16 #65)
+#63 := (iff #15 #62)
+#39 := (iff #11 #38)
+#40 := [rewrite]: #39
+#36 := (iff #9 #35)
+#37 := [rewrite]: #36
+#64 := [monotonicity #37 #40]: #63
+#60 := (iff #14 #59)
+#57 := (iff #13 #54)
+#50 := (implies #38 #35)
+#55 := (iff #50 #54)
+#56 := [rewrite]: #55
+#51 := (iff #13 #50)
+#52 := [monotonicity #40 #37]: #51
+#58 := [trans #52 #56]: #57
+#48 := (iff #12 #45)
+#41 := (implies #35 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #12 #41)
+#43 := [monotonicity #37 #40]: #42
+#49 := [trans #43 #47]: #48
+#61 := [monotonicity #49 #58]: #60
+#67 := [monotonicity #61 #64]: #66
+#73 := [trans #67 #71]: #72
+#76 := [monotonicity #73]: #75
+#34 := [asserted]: #17
+#79 := [mp #34 #76]: #74
+#77 := [not-or-elim #79]: #59
+#78 := [and-elim #77]: #45
+#98 := [unit-resolution #78 #97]: #44
+#89 := (or #38 #35)
+#90 := (iff #38 #44)
+#81 := (not #62)
+#91 := (iff #81 #90)
+#92 := [rewrite]: #91
+#82 := [not-or-elim #79]: #81
+#93 := [mp #82 #92]: #90
+#94 := (not #90)
+#95 := (or #38 #35 #94)
+#88 := [def-axiom]: #95
+#86 := [unit-resolution #88 #93]: #89
+#99 := [unit-resolution #86 #98 #97]: false
+#100 := [lemma #99]: #38
+#80 := [and-elim #77]: #54
+#101 := [unit-resolution #80 #100]: #35
+#83 := (or #53 #44)
+#87 := (or #53 #44 #94)
+#85 := [def-axiom]: #87
+#96 := [unit-resolution #85 #93]: #83
+[unit-resolution #96 #101 #100]: false
+unsat
+8abc924327822787c2f5c4e6e7680303fbae57f8 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)
+#61 := (iff #15 false)
+#1 := true
+#56 := (not true)
+#59 := (iff #56 false)
+#60 := [rewrite]: #59
+#57 := (iff #15 #56)
+#54 := (iff #14 true)
+#36 := (= f1 f4)
+#33 := (= f1 f3)
+#39 := (iff #33 #36)
+#49 := (iff #39 #39)
+#52 := (iff #49 true)
+#53 := [rewrite]: #52
+#50 := (iff #14 #49)
+#47 := (iff #13 #39)
+#42 := (iff #36 #33)
+#45 := (iff #42 #39)
+#46 := [rewrite]: #45
+#43 := (iff #13 #42)
+#34 := (iff #9 #33)
+#35 := [rewrite]: #34
+#37 := (iff #11 #36)
+#38 := [rewrite]: #37
+#44 := [monotonicity #38 #35]: #43
+#48 := [trans #44 #46]: #47
+#40 := (iff #12 #39)
+#41 := [monotonicity #35 #38]: #40
+#51 := [monotonicity #41 #48]: #50
+#55 := [trans #51 #53]: #54
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#32 := [asserted]: #15
+[mp #32 #62]: false
+unsat
+3731fdf00230f94750072246058d6aec5d30ad57 41 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: S1
+#8 := f3
+#9 := (= f3 f1)
+#10 := (not #9)
+#11 := (iff #9 #10)
+#12 := (not #11)
+#13 := (not #12)
+#56 := (iff #13 false)
+#1 := true
+#51 := (not true)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #13 #51)
+#49 := (iff #12 true)
+#44 := (not false)
+#47 := (iff #44 true)
+#48 := [rewrite]: #47
+#45 := (iff #12 #44)
+#42 := (iff #11 false)
+#31 := (= f1 f3)
+#34 := (not #31)
+#37 := (iff #31 #34)
+#40 := (iff #37 false)
+#41 := [rewrite]: #40
+#38 := (iff #11 #37)
+#35 := (iff #10 #34)
+#32 := (iff #9 #31)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#39 := [monotonicity #33 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#30 := [asserted]: #13
+[mp #30 #57]: false
+unsat
+c4682bd721e64af9e51bd86d6d03d59662baa782 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)
+#74 := (iff #17 false)
+#1 := true
+#69 := (not true)
+#72 := (iff #69 false)
+#73 := [rewrite]: #72
+#70 := (iff #17 #69)
+#67 := (iff #16 true)
+#38 := (= f1 f4)
+#35 := (= f1 f3)
+#44 := (not #35)
+#45 := (or #44 #38)
+#62 := (iff #45 #45)
+#65 := (iff #62 true)
+#66 := [rewrite]: #65
+#63 := (iff #16 #62)
+#60 := (iff #15 #45)
+#50 := (not #38)
+#55 := (implies #50 #44)
+#58 := (iff #55 #45)
+#59 := [rewrite]: #58
+#56 := (iff #15 #55)
+#53 := (iff #14 #44)
+#36 := (iff #9 #35)
+#37 := [rewrite]: #36
+#54 := [monotonicity #37]: #53
+#51 := (iff #13 #50)
+#39 := (iff #11 #38)
+#40 := [rewrite]: #39
+#52 := [monotonicity #40]: #51
+#57 := [monotonicity #52 #54]: #56
+#61 := [trans #57 #59]: #60
+#48 := (iff #12 #45)
+#41 := (implies #35 #38)
+#46 := (iff #41 #45)
+#47 := [rewrite]: #46
+#42 := (iff #12 #41)
+#43 := [monotonicity #37 #40]: #42
+#49 := [trans #43 #47]: #48
+#64 := [monotonicity #49 #61]: #63
+#68 := [trans #64 #66]: #67
+#71 := [monotonicity #68]: #70
+#75 := [trans #71 #73]: #74
+#34 := [asserted]: #17
+[mp #34 #75]: false
+unsat
+36d1352b395221a431006c238d124165e2b745a3 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)
+#87 := (iff #19 false)
+#1 := true
+#82 := (not true)
+#85 := (iff #82 false)
+#86 := [rewrite]: #85
+#83 := (iff #19 #82)
+#80 := (iff #18 true)
+#37 := (= f1 f3)
+#40 := (iff #37 #37)
+#43 := (iff #40 true)
+#44 := [rewrite]: #43
+#78 := (iff #18 #40)
+#76 := (iff #17 #37)
+#47 := (iff #37 true)
+#50 := (iff #47 #37)
+#51 := [rewrite]: #50
+#74 := (iff #17 #47)
+#72 := (iff #16 true)
+#70 := (iff #16 #40)
+#68 := (iff #15 #37)
+#66 := (iff #15 #47)
+#64 := (iff #14 true)
+#62 := (iff #14 #40)
+#60 := (iff #13 #37)
+#58 := (iff #13 #47)
+#56 := (iff #12 true)
+#54 := (iff #12 #40)
+#52 := (iff #11 #37)
+#48 := (iff #11 #47)
+#45 := (iff #10 true)
+#41 := (iff #10 #40)
+#38 := (iff #9 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39 #39]: #41
+#46 := [trans #42 #44]: #45
+#49 := [monotonicity #39 #46]: #48
+#53 := [trans #49 #51]: #52
+#55 := [monotonicity #39 #53]: #54
+#57 := [trans #55 #44]: #56
+#59 := [monotonicity #39 #57]: #58
+#61 := [trans #59 #51]: #60
+#63 := [monotonicity #39 #61]: #62
+#65 := [trans #63 #44]: #64
+#67 := [monotonicity #39 #65]: #66
+#69 := [trans #67 #51]: #68
+#71 := [monotonicity #39 #69]: #70
+#73 := [trans #71 #44]: #72
+#75 := [monotonicity #39 #73]: #74
+#77 := [trans #75 #51]: #76
+#79 := [monotonicity #39 #77]: #78
+#81 := [trans #79 #44]: #80
+#84 := [monotonicity #81]: #83
+#88 := [trans #84 #86]: #87
+#36 := [asserted]: #19
+[mp #36 #88]: false
+unsat
+9a169ba4d23a9080465edad5616230c8b4e1ef98 149 0
+#2 := false
+decl f5 :: S1
+#12 := f5
+decl f1 :: S1
+#4 := f1
+#44 := (= f1 f5)
+decl f4 :: S1
+#10 := f4
+#41 := (= f1 f4)
+decl f3 :: S1
+#8 := f3
+#38 := (= f1 f3)
+#47 := (ite #38 #41 #44)
+#53 := (not #38)
+#54 := (or #53 #41)
+#64 := (or #38 #44)
+#91 := (not #64)
+#90 := (not #54)
+#92 := (or #90 #91)
+#143 := [hypothesis]: #90
+#128 := (or #92 #54)
+#129 := [def-axiom]: #128
+#144 := [unit-resolution #129 #143]: #92
+#78 := (not #47)
+#116 := (or #54 #38)
+#117 := [def-axiom]: #116
+#145 := [unit-resolution #117 #143]: #38
+#110 := (not #41)
+#118 := (or #54 #110)
+#119 := [def-axiom]: #118
+#146 := [unit-resolution #119 #143]: #110
+#106 := (or #78 #53 #41)
+#107 := [def-axiom]: #106
+#147 := [unit-resolution #107 #146 #145]: #78
+#93 := (not #92)
+#137 := (or #47 #93)
+#100 := (iff #47 #92)
+#69 := (and #54 #64)
+#79 := (iff #69 #78)
+#103 := (iff #79 #100)
+#95 := (iff #92 #47)
+#101 := (iff #95 #100)
+#102 := [rewrite]: #101
+#98 := (iff #79 #95)
+#87 := (iff #93 #78)
+#96 := (iff #87 #95)
+#97 := [rewrite]: #96
+#84 := (iff #79 #87)
+#88 := (iff #69 #93)
+#89 := [rewrite]: #88
+#94 := [monotonicity #89]: #84
+#99 := [trans #94 #97]: #98
+#104 := [trans #99 #102]: #103
+#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)
+#82 := (iff #20 #79)
+#72 := (iff #47 #69)
+#75 := (not #72)
+#80 := (iff #75 #79)
+#81 := [rewrite]: #80
+#76 := (iff #20 #75)
+#73 := (iff #19 #72)
+#70 := (iff #18 #69)
+#67 := (iff #17 #64)
+#61 := (implies #53 #44)
+#65 := (iff #61 #64)
+#66 := [rewrite]: #65
+#62 := (iff #17 #61)
+#45 := (iff #13 #44)
+#46 := [rewrite]: #45
+#59 := (iff #16 #53)
+#39 := (iff #9 #38)
+#40 := [rewrite]: #39
+#60 := [monotonicity #40]: #59
+#63 := [monotonicity #60 #46]: #62
+#68 := [trans #63 #66]: #67
+#57 := (iff #15 #54)
+#50 := (implies #38 #41)
+#55 := (iff #50 #54)
+#56 := [rewrite]: #55
+#51 := (iff #15 #50)
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#52 := [monotonicity #40 #43]: #51
+#58 := [trans #52 #56]: #57
+#71 := [monotonicity #58 #68]: #70
+#48 := (iff #14 #47)
+#49 := [monotonicity #40 #43 #46]: #48
+#74 := [monotonicity #49 #71]: #73
+#77 := [monotonicity #74]: #76
+#83 := [trans #77 #81]: #82
+#37 := [asserted]: #20
+#86 := [mp #37 #83]: #79
+#105 := [mp #86 #104]: #100
+#134 := (not #100)
+#135 := (or #47 #93 #134)
+#136 := [def-axiom]: #135
+#138 := [unit-resolution #136 #105]: #137
+#148 := [unit-resolution #138 #147 #144]: false
+#149 := [lemma #148]: #54
+#150 := [hypothesis]: #78
+#156 := (or #38 #47)
+#151 := [unit-resolution #138 #150]: #93
+#130 := (or #92 #64)
+#131 := [def-axiom]: #130
+#152 := [unit-resolution #131 #151]: #64
+#153 := [hypothesis]: #53
+#113 := (not #44)
+#114 := (or #47 #38 #113)
+#115 := [def-axiom]: #114
+#154 := [unit-resolution #115 #153 #150]: #113
+#126 := (or #91 #38 #44)
+#127 := [def-axiom]: #126
+#155 := [unit-resolution #127 #154 #153 #152]: false
+#157 := [lemma #155]: #156
+#158 := [unit-resolution #157 #150]: #38
+#111 := (or #47 #53 #110)
+#112 := [def-axiom]: #111
+#159 := [unit-resolution #112 #158 #150]: #110
+#120 := (or #90 #53 #41)
+#121 := [def-axiom]: #120
+#160 := [unit-resolution #121 #159 #158 #149]: false
+#161 := [lemma #160]: #47
+#141 := (or #78 #92)
+#139 := (or #78 #92 #134)
+#140 := [def-axiom]: #139
+#142 := [unit-resolution #140 #105]: #141
+#162 := [unit-resolution #142 #161]: #92
+#132 := (or #93 #90 #91)
+#133 := [def-axiom]: #132
+#163 := [unit-resolution #133 #162 #149]: #91
+#122 := (or #64 #53)
+#123 := [def-axiom]: #122
+#164 := [unit-resolution #123 #163]: #53
+#124 := (or #64 #113)
+#125 := [def-axiom]: #124
+#165 := [unit-resolution #125 #163]: #113
+#108 := (or #78 #38 #44)
+#109 := [def-axiom]: #108
+[unit-resolution #109 #165 #164 #161]: false
+unsat
+8d07b6d671ef5c9eedcaa35c22d5f1c7124504cb 66 0
+#2 := false
+decl f3 :: S1
+#8 := f3
+decl f1 :: S1
+#4 := f1
+#33 := (= f1 f3)
+#51 := (not #33)
+#87 := [hypothesis]: #33
+decl f4 :: S1
+#10 := f4
+#36 := (= f1 f4)
+#42 := (not #36)
+#43 := (or #33 #42)
+#69 := (or #43 #51)
+#70 := [def-axiom]: #69
+#88 := [unit-resolution #70 #87]: #43
+#67 := (not #43)
+#89 := (or #51 #67)
+#52 := (or #51 #36)
+#57 := (ite #33 #43 #52)
+#60 := (not #57)
+#11 := (= f4 f1)
+#9 := (= f3 f1)
+#13 := (implies #9 #11)
+#12 := (implies #11 #9)
+#14 := (ite #9 #12 #13)
+#15 := (not #14)
+#61 := (iff #15 #60)
+#58 := (iff #14 #57)
+#55 := (iff #13 #52)
+#48 := (implies #33 #36)
+#53 := (iff #48 #52)
+#54 := [rewrite]: #53
+#49 := (iff #13 #48)
+#37 := (iff #11 #36)
+#38 := [rewrite]: #37
+#34 := (iff #9 #33)
+#35 := [rewrite]: #34
+#50 := [monotonicity #35 #38]: #49
+#56 := [trans #50 #54]: #55
+#46 := (iff #12 #43)
+#39 := (implies #36 #33)
+#44 := (iff #39 #43)
+#45 := [rewrite]: #44
+#40 := (iff #12 #39)
+#41 := [monotonicity #38 #35]: #40
+#47 := [trans #41 #45]: #46
+#59 := [monotonicity #35 #47 #56]: #58
+#62 := [monotonicity #59]: #61
+#32 := [asserted]: #15
+#65 := [mp #32 #62]: #60
+#83 := (or #57 #51 #67)
+#84 := [def-axiom]: #83
+#90 := [unit-resolution #84 #65]: #89
+#91 := [unit-resolution #90 #88 #87]: false
+#92 := [lemma #91]: #51
+#63 := (or #52 #33)
+#73 := [def-axiom]: #63
+#93 := [unit-resolution #73 #92]: #52
+#76 := (not #52)
+#94 := (or #33 #76)
+#85 := (or #57 #33 #76)
+#86 := [def-axiom]: #85
+#95 := [unit-resolution #86 #65]: #94
+[unit-resolution #95 #93 #92]: false
+unsat
+415ad6a91bb75e131bb05d34f1965ab914825b25 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)
+#79 := (iff #21 false)
+#1 := true
+#74 := (not true)
+#77 := (iff #74 false)
+#78 := [rewrite]: #77
+#75 := (iff #21 #74)
+#72 := (iff #20 true)
+#51 := (= f1 f6)
+#48 := (= f1 f5)
+#42 := (= f1 f4)
+#39 := (= f1 f3)
+#45 := (or #39 #42)
+#54 := (ite #45 #48 #51)
+#67 := (iff #54 #54)
+#70 := (iff #67 true)
+#71 := [rewrite]: #70
+#68 := (iff #20 #67)
+#65 := (iff #19 #54)
+#57 := (ite #42 #48 #51)
+#60 := (ite #39 #48 #57)
+#63 := (iff #60 #54)
+#64 := [rewrite]: #63
+#61 := (iff #19 #60)
+#58 := (iff #18 #57)
+#52 := (iff #16 #51)
+#53 := [rewrite]: #52
+#49 := (iff #14 #48)
+#50 := [rewrite]: #49
+#43 := (iff #11 #42)
+#44 := [rewrite]: #43
+#59 := [monotonicity #44 #50 #53]: #58
+#40 := (iff #9 #39)
+#41 := [rewrite]: #40
+#62 := [monotonicity #41 #50 #59]: #61
+#66 := [trans #62 #64]: #65
+#55 := (iff #17 #54)
+#46 := (iff #12 #45)
+#47 := [monotonicity #41 #44]: #46
+#56 := [monotonicity #47 #50 #53]: #55
+#69 := [monotonicity #56 #66]: #68
+#73 := [trans #69 #71]: #72
+#76 := [monotonicity #73]: #75
+#80 := [trans #76 #78]: #79
+#38 := [asserted]: #21
+[mp #38 #80]: false
+unsat
+8b8741030ee2ece2c8d6b3906a1951bc56d9b885 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)
+#79 := (iff #21 false)
+#1 := true
+#74 := (not true)
+#77 := (iff #74 false)
+#78 := [rewrite]: #77
+#75 := (iff #21 #74)
+#72 := (iff #20 true)
+#51 := (= f1 f6)
+#48 := (= f1 f5)
+#42 := (= f1 f4)
+#39 := (= f1 f3)
+#45 := (and #39 #42)
+#54 := (ite #45 #48 #51)
+#67 := (iff #54 #54)
+#70 := (iff #67 true)
+#71 := [rewrite]: #70
+#68 := (iff #20 #67)
+#65 := (iff #19 #54)
+#57 := (ite #42 #48 #51)
+#60 := (ite #39 #57 #51)
+#63 := (iff #60 #54)
+#64 := [rewrite]: #63
+#61 := (iff #19 #60)
+#52 := (iff #16 #51)
+#53 := [rewrite]: #52
+#58 := (iff #18 #57)
+#49 := (iff #14 #48)
+#50 := [rewrite]: #49
+#43 := (iff #11 #42)
+#44 := [rewrite]: #43
+#59 := [monotonicity #44 #50 #53]: #58
+#40 := (iff #9 #39)
+#41 := [rewrite]: #40
+#62 := [monotonicity #41 #59 #53]: #61
+#66 := [trans #62 #64]: #65
+#55 := (iff #17 #54)
+#46 := (iff #12 #45)
+#47 := [monotonicity #41 #44]: #46
+#56 := [monotonicity #47 #50 #53]: #55
+#69 := [monotonicity #56 #66]: #68
+#73 := [trans #69 #71]: #72
+#76 := [monotonicity #73]: #75
+#80 := [trans #76 #78]: #79
+#38 := [asserted]: #21
+[mp #38 #80]: false
+unsat
+a0ca672c65c25c024851f833f39bfb2c705ec387 186 0
+#2 := false
+decl f5 :: S1
+#12 := f5
+decl f1 :: S1
+#4 := f1
+#47 := (= f1 f5)
+decl f3 :: S1
+#8 := f3
+#41 := (= f1 f3)
+#59 := (not #41)
+#76 := (or #59 #47)
+#119 := (not #76)
+decl f4 :: S1
+#10 := f4
+#44 := (= f1 f4)
+#68 := (or #59 #44)
+decl f6 :: S1
+#14 := f6
+#50 := (= f1 f6)
+#84 := (or #59 #50)
+#89 := (ite #68 #76 #84)
+#130 := (not #89)
+#53 := (ite #44 #47 #50)
+#60 := (or #59 #53)
+#112 := (not #44)
+#165 := [hypothesis]: #112
+#172 := (or #60 #44)
+#98 := (not #60)
+#163 := [hypothesis]: #98
+#148 := (or #60 #41)
+#149 := [def-axiom]: #148
+#164 := [unit-resolution #149 #163]: #41
+#124 := (not #50)
+#139 := (not #53)
+#150 := (or #60 #139)
+#151 := [def-axiom]: #150
+#166 := [unit-resolution #151 #163]: #139
+#146 := (or #53 #44 #124)
+#147 := [def-axiom]: #146
+#167 := [unit-resolution #147 #166 #165]: #124
+#157 := (or #89 #60)
+#99 := (iff #89 #98)
+#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)
+#102 := (iff #23 #99)
+#92 := (iff #60 #89)
+#95 := (not #92)
+#100 := (iff #95 #99)
+#101 := [rewrite]: #100
+#96 := (iff #23 #95)
+#93 := (iff #22 #92)
+#90 := (iff #21 #89)
+#87 := (iff #20 #84)
+#81 := (implies #41 #50)
+#85 := (iff #81 #84)
+#86 := [rewrite]: #85
+#82 := (iff #20 #81)
+#51 := (iff #15 #50)
+#52 := [rewrite]: #51
+#42 := (iff #9 #41)
+#43 := [rewrite]: #42
+#83 := [monotonicity #43 #52]: #82
+#88 := [trans #83 #86]: #87
+#79 := (iff #19 #76)
+#73 := (implies #41 #47)
+#77 := (iff #73 #76)
+#78 := [rewrite]: #77
+#74 := (iff #19 #73)
+#48 := (iff #13 #47)
+#49 := [rewrite]: #48
+#75 := [monotonicity #43 #49]: #74
+#80 := [trans #75 #78]: #79
+#71 := (iff #18 #68)
+#65 := (implies #41 #44)
+#69 := (iff #65 #68)
+#70 := [rewrite]: #69
+#66 := (iff #18 #65)
+#45 := (iff #11 #44)
+#46 := [rewrite]: #45
+#67 := [monotonicity #43 #46]: #66
+#72 := [trans #67 #70]: #71
+#91 := [monotonicity #72 #80 #88]: #90
+#63 := (iff #17 #60)
+#56 := (implies #41 #53)
+#61 := (iff #56 #60)
+#62 := [rewrite]: #61
+#57 := (iff #17 #56)
+#54 := (iff #16 #53)
+#55 := [monotonicity #46 #49 #52]: #54
+#58 := [monotonicity #43 #55]: #57
+#64 := [trans #58 #62]: #63
+#94 := [monotonicity #64 #91]: #93
+#97 := [monotonicity #94]: #96
+#103 := [trans #97 #101]: #102
+#40 := [asserted]: #23
+#106 := [mp #40 #103]: #99
+#154 := (not #99)
+#155 := (or #89 #60 #154)
+#156 := [def-axiom]: #155
+#158 := [unit-resolution #156 #106]: #157
+#168 := [unit-resolution #158 #163]: #89
+#109 := (not #68)
+#107 := (or #109 #59 #44)
+#104 := [def-axiom]: #107
+#169 := [unit-resolution #104 #164 #165]: #109
+#133 := (or #130 #68 #84)
+#134 := [def-axiom]: #133
+#170 := [unit-resolution #134 #169 #168]: #84
+#127 := (not #84)
+#128 := (or #127 #59 #50)
+#129 := [def-axiom]: #128
+#171 := [unit-resolution #129 #170 #167 #164]: false
+#173 := [lemma #171]: #172
+#176 := [unit-resolution #173 #165]: #60
+#161 := (or #130 #98)
+#159 := (or #130 #98 #154)
+#160 := [def-axiom]: #159
+#162 := [unit-resolution #160 #106]: #161
+#182 := [unit-resolution #162 #176]: #130
+#180 := (or #84 #44)
+#174 := [hypothesis]: #127
+#125 := (or #84 #124)
+#126 := [def-axiom]: #125
+#175 := [unit-resolution #126 #174]: #124
+#122 := (or #84 #41)
+#123 := [def-axiom]: #122
+#177 := [unit-resolution #123 #174]: #41
+#152 := (or #98 #59 #53)
+#153 := [def-axiom]: #152
+#178 := [unit-resolution #153 #177 #176]: #53
+#142 := (or #139 #44 #50)
+#143 := [def-axiom]: #142
+#179 := [unit-resolution #143 #178 #175 #165]: false
+#181 := [lemma #179]: #180
+#183 := [unit-resolution #181 #165]: #84
+#137 := (or #89 #68 #127)
+#138 := [def-axiom]: #137
+#184 := [unit-resolution #138 #183 #182]: #68
+#135 := (or #89 #109 #119)
+#136 := [def-axiom]: #135
+#185 := [unit-resolution #136 #184 #182]: #119
+#186 := [unit-resolution #104 #184 #165]: #59
+#114 := (or #76 #41)
+#115 := [def-axiom]: #114
+#187 := [unit-resolution #115 #186 #185]: false
+#188 := [lemma #187]: #44
+#113 := (or #68 #112)
+#108 := [def-axiom]: #113
+#191 := [unit-resolution #108 #188]: #68
+#189 := [hypothesis]: #59
+#190 := [unit-resolution #149 #189]: #60
+#192 := [unit-resolution #115 #189]: #76
+#193 := [unit-resolution #136 #192 #191]: #89
+#194 := [unit-resolution #162 #193 #190]: false
+#195 := [lemma #194]: #41
+#116 := (not #47)
+#144 := (or #53 #112 #116)
+#145 := [def-axiom]: #144
+#196 := [unit-resolution #145 #166 #188]: #116
+#131 := (or #130 #109 #76)
+#132 := [def-axiom]: #131
+#197 := [unit-resolution #132 #168 #191]: #76
+#120 := (or #119 #59 #47)
+#121 := [def-axiom]: #120
+#198 := [unit-resolution #121 #197 #196 #195]: false
+#199 := [lemma #198]: #60
+#200 := [unit-resolution #162 #199]: #130
+#201 := [unit-resolution #136 #200 #191]: #119
+#202 := [unit-resolution #153 #199 #195]: #53
+#140 := (or #139 #112 #47)
+#141 := [def-axiom]: #140
+#203 := [unit-resolution #141 #202 #188]: #47
+#117 := (or #76 #116)
+#118 := [def-axiom]: #117
+[unit-resolution #118 #203 #201]: false
+unsat
+6bcac7ed9b4a6f3af0933f64ee0cb316b51a44ed 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)
+#48 := (iff #12 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (iff #11 true)
+#30 := (= f1 f3)
+#33 := (not #30)
+#36 := (ite #30 #30 #33)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #11 #36)
+#34 := (iff #10 #33)
+#31 := (iff #9 #30)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#38 := [monotonicity #32 #32 #35]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#29 := [asserted]: #12
+[mp #29 #49]: false
+unsat
+be3ab8b5e09f8f942728ba1af0512891f56e0c5b 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)
+#48 := (iff #12 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (iff #11 true)
+#30 := (= f1 f3)
+#33 := (not #30)
+#36 := (ite #33 #33 #30)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #11 #36)
+#31 := (iff #9 #30)
+#32 := [rewrite]: #31
+#34 := (iff #10 #33)
+#35 := [monotonicity #32]: #34
+#38 := [monotonicity #35 #35 #32]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#29 := [asserted]: #12
+[mp #29 #49]: false
+unsat
+aa78c56be2c8312419ab25323cf112e3e8809e9f 18 0
+#2 := false
+decl f3 :: S2
+#8 := f3
+#9 := (= f3 f3)
+#10 := (not #9)
+#35 := (iff #10 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #10 #30)
+#28 := (iff #9 true)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#27 := [asserted]: #10
+[mp #27 #36]: false
+unsat
+8d3a435e96c2d773a90e94525d09aa8a352d27d6 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)
+#45 := (iff #13 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #13 #40)
+#38 := (iff #12 true)
+#33 := (implies #10 #10)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #12 #33)
+#31 := (iff #11 #10)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#30 := [asserted]: #13
+[mp #30 #46]: false
+unsat
+7d6e447cf6e1145f4f9a866bcc3cde4710e17c79 34 0
+#2 := false
+decl f5 :: S2
+#11 := f5
+decl f3 :: S2
+#8 := f3
+#14 := (= f3 f5)
+decl f4 :: S2
+#9 := f4
+#12 := (= f4 f5)
+#58 := (iff #12 #14)
+#56 := (iff #14 #12)
+#10 := (= f3 f4)
+#13 := (and #10 #12)
+#34 := (not #13)
+#35 := (or #34 #14)
+#38 := (not #35)
+#15 := (implies #13 #14)
+#16 := (not #15)
+#39 := (iff #16 #38)
+#36 := (iff #15 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#33 := [asserted]: #16
+#43 := [mp #33 #40]: #38
+#41 := [not-or-elim #43]: #13
+#42 := [and-elim #41]: #10
+#57 := [monotonicity #42]: #56
+#59 := [symm #57]: #58
+#44 := [and-elim #41]: #12
+#54 := [mp #44 #59]: #14
+#45 := (not #14)
+#46 := [not-or-elim #43]: #45
+[unit-resolution #46 #54]: false
+unsat
+810792c4ea80c0bc3287d99f969f1a65dc039da5 27 0
+#2 := false
+decl f5 :: (-> S2 S2)
+decl f4 :: S2
+#9 := f4
+#12 := (f5 f4)
+decl f3 :: S2
+#8 := f3
+#11 := (f5 f3)
+#13 := (= #11 #12)
+#10 := (= f3 f4)
+#33 := (not #10)
+#34 := (or #33 #13)
+#37 := (not #34)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#38 := (iff #15 #37)
+#35 := (iff #14 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#32 := [asserted]: #15
+#42 := [mp #32 #39]: #37
+#40 := [not-or-elim #42]: #10
+#51 := [monotonicity #40]: #13
+#41 := (not #13)
+#43 := [not-or-elim #42]: #41
+[unit-resolution #43 #51]: false
+unsat
+09e564f98c53b63bab667092b7072fa2b674fa08 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)
+#53 := (= #12 #11)
+#10 := (= f3 f4)
+#33 := (not #10)
+#34 := (or #33 #13)
+#37 := (not #34)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#38 := (iff #15 #37)
+#35 := (iff #14 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#32 := [asserted]: #15
+#42 := [mp #32 #39]: #37
+#40 := [not-or-elim #42]: #10
+#51 := (= f4 f3)
+#52 := [symm #40]: #51
+#54 := [monotonicity #52 #40]: #53
+#49 := [symm #54]: #13
+#41 := (not #13)
+#43 := [not-or-elim #42]: #41
+[unit-resolution #43 #49]: false
+unsat
+f97c055cc3b87ad54efe59b6c22e3e3633409f7e 63 0
+#2 := false
+decl f3 :: (-> S2 S2)
+decl f4 :: S2
+#8 := f4
+#9 := (f3 f4)
+#46 := (= f4 #9)
+#10 := (f3 #9)
+#12 := (f3 #10)
+#78 := (= #12 #9)
+#76 := (= #9 #12)
+#37 := (= f4 #10)
+#13 := (f3 #12)
+#14 := (f3 #13)
+#40 := (= f4 #14)
+#43 := (and #37 #40)
+#52 := (not #43)
+#53 := (or #52 #46)
+#58 := (not #53)
+#17 := (= #9 f4)
+#15 := (= #14 f4)
+#11 := (= #10 f4)
+#16 := (and #11 #15)
+#18 := (implies #16 #17)
+#19 := (not #18)
+#59 := (iff #19 #58)
+#56 := (iff #18 #53)
+#49 := (implies #43 #46)
+#54 := (iff #49 #53)
+#55 := [rewrite]: #54
+#50 := (iff #18 #49)
+#47 := (iff #17 #46)
+#48 := [rewrite]: #47
+#44 := (iff #16 #43)
+#41 := (iff #15 #40)
+#42 := [rewrite]: #41
+#38 := (iff #11 #37)
+#39 := [rewrite]: #38
+#45 := [monotonicity #39 #42]: #44
+#51 := [monotonicity #45 #48]: #50
+#57 := [trans #51 #55]: #56
+#60 := [monotonicity #57]: #59
+#36 := [asserted]: #19
+#63 := [mp #36 #60]: #58
+#61 := [not-or-elim #63]: #43
+#62 := [and-elim #61]: #37
+#77 := [monotonicity #62]: #76
+#79 := [symm #77]: #78
+#81 := (= f4 #12)
+#67 := (= #14 #12)
+#70 := (= #12 #14)
+#72 := (= #10 #13)
+#74 := (= #13 #10)
+#75 := [monotonicity #79]: #74
+#73 := [symm #75]: #72
+#71 := [monotonicity #73]: #70
+#80 := [symm #71]: #67
+#64 := [and-elim #61]: #40
+#82 := [trans #64 #80]: #81
+#83 := [trans #82 #79]: #46
+#65 := (not #46)
+#66 := [not-or-elim #63]: #65
+[unit-resolution #66 #83]: false
+unsat
+0b20a1cbaefe018fa6502d17013ec89dc657717b 195 0
+#2 := false
+decl f6 :: S2
+#13 := f6
+decl f4 :: S2
+#10 := f4
+#15 := (= f4 f6)
+decl f5 :: S2
+#11 := f5
+decl f3 :: S1
+#8 := f3
+decl f1 :: S1
+#4 := f1
+#40 := (= f1 f3)
+#43 := (ite #40 f4 f5)
+#49 := (= f6 #43)
+#200 := (iff #49 #15)
+#198 := (iff #15 #49)
+#46 := (= #43 f6)
+#50 := (iff #46 #49)
+#197 := [commutativity]: #50
+#195 := (iff #15 #46)
+#110 := (= f4 #43)
+#111 := (= f5 #43)
+#57 := (not #40)
+#180 := [hypothesis]: #57
+#114 := (or #40 #111)
+#115 := [def-axiom]: #114
+#184 := [unit-resolution #115 #180]: #111
+#185 := (= f6 f5)
+#18 := (= f5 f6)
+#174 := (iff #110 #15)
+#172 := (iff #15 #110)
+#68 := (or #18 #40)
+#95 := (not #68)
+#58 := (or #15 #57)
+#94 := (not #58)
+#96 := (or #94 #95)
+#123 := (not #18)
+#147 := [hypothesis]: #123
+#157 := (or #96 #18)
+#97 := (not #96)
+#145 := [hypothesis]: #97
+#132 := (or #96 #68)
+#133 := [def-axiom]: #132
+#148 := [unit-resolution #133 #145]: #68
+#128 := (or #95 #18 #40)
+#129 := [def-axiom]: #128
+#149 := [unit-resolution #129 #148 #147]: #40
+#112 := (or #57 #110)
+#113 := [def-axiom]: #112
+#150 := [unit-resolution #113 #149]: #110
+#153 := (= f6 f4)
+#130 := (or #96 #58)
+#131 := [def-axiom]: #130
+#151 := [unit-resolution #131 #145]: #58
+#121 := (or #94 #15 #57)
+#122 := [def-axiom]: #121
+#152 := [unit-resolution #122 #149 #151]: #15
+#154 := [symm #152]: #153
+#155 := [trans #154 #150]: #49
+#82 := (not #49)
+#143 := (or #82 #96)
+#104 := (iff #49 #96)
+#73 := (and #58 #68)
+#83 := (iff #73 #82)
+#107 := (iff #83 #104)
+#99 := (iff #96 #49)
+#105 := (iff #99 #104)
+#106 := [rewrite]: #105
+#102 := (iff #83 #99)
+#91 := (iff #97 #82)
+#100 := (iff #91 #99)
+#101 := [rewrite]: #100
+#88 := (iff #83 #91)
+#92 := (iff #73 #97)
+#93 := [rewrite]: #92
+#98 := [monotonicity #93]: #88
+#103 := [trans #98 #101]: #102
+#108 := [trans #103 #106]: #107
+#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)
+#22 := (not #21)
+#86 := (iff #22 #83)
+#76 := (iff #49 #73)
+#79 := (not #76)
+#84 := (iff #79 #83)
+#85 := [rewrite]: #84
+#80 := (iff #22 #79)
+#77 := (iff #21 #76)
+#74 := (iff #20 #73)
+#71 := (iff #19 #68)
+#65 := (implies #57 #18)
+#69 := (iff #65 #68)
+#70 := [rewrite]: #69
+#66 := (iff #19 #65)
+#63 := (iff #17 #57)
+#41 := (iff #9 #40)
+#42 := [rewrite]: #41
+#64 := [monotonicity #42]: #63
+#67 := [monotonicity #64]: #66
+#72 := [trans #67 #70]: #71
+#61 := (iff #16 #58)
+#54 := (implies #40 #15)
+#59 := (iff #54 #58)
+#60 := [rewrite]: #59
+#55 := (iff #16 #54)
+#56 := [monotonicity #42]: #55
+#62 := [trans #56 #60]: #61
+#75 := [monotonicity #62 #72]: #74
+#52 := (iff #14 #49)
+#51 := [rewrite]: #50
+#47 := (iff #14 #46)
+#44 := (= #12 #43)
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#53 := [trans #48 #51]: #52
+#78 := [monotonicity #53 #75]: #77
+#81 := [monotonicity #78]: #80
+#87 := [trans #81 #85]: #86
+#39 := [asserted]: #22
+#90 := [mp #39 #87]: #83
+#109 := [mp #90 #108]: #104
+#136 := (not #104)
+#141 := (or #82 #96 #136)
+#142 := [def-axiom]: #141
+#144 := [unit-resolution #142 #109]: #143
+#146 := [unit-resolution #144 #145]: #82
+#156 := [unit-resolution #146 #155]: false
+#158 := [lemma #156]: #157
+#159 := [unit-resolution #158 #147]: #96
+#139 := (or #49 #97)
+#137 := (or #49 #97 #136)
+#138 := [def-axiom]: #137
+#140 := [unit-resolution #138 #109]: #139
+#160 := [unit-resolution #140 #159]: #49
+#173 := [monotonicity #160]: #172
+#175 := [symm #173]: #174
+#163 := (not #111)
+#164 := (iff #123 #163)
+#161 := (iff #18 #111)
+#162 := [monotonicity #160]: #161
+#165 := [monotonicity #162]: #164
+#166 := [mp #147 #165]: #163
+#167 := [unit-resolution #115 #166]: #40
+#171 := [unit-resolution #113 #167]: #110
+#176 := [mp #171 #175]: #15
+#116 := (not #15)
+#126 := (or #68 #57)
+#127 := [def-axiom]: #126
+#168 := [unit-resolution #127 #167]: #68
+#134 := (or #97 #94 #95)
+#135 := [def-axiom]: #134
+#169 := [unit-resolution #135 #168 #159]: #94
+#117 := (or #58 #116)
+#118 := [def-axiom]: #117
+#170 := [unit-resolution #118 #169]: #116
+#177 := [unit-resolution #170 #176]: false
+#178 := [lemma #177]: #18
+#186 := [symm #178]: #185
+#187 := [trans #186 #184]: #49
+#124 := (or #68 #123)
+#125 := [def-axiom]: #124
+#179 := [unit-resolution #125 #178]: #68
+#119 := (or #58 #40)
+#120 := [def-axiom]: #119
+#181 := [unit-resolution #120 #180]: #58
+#182 := [unit-resolution #135 #181 #179]: #97
+#183 := [unit-resolution #144 #182]: #82
+#188 := [unit-resolution #183 #187]: false
+#189 := [lemma #188]: #40
+#194 := [unit-resolution #113 #189]: #110
+#196 := [monotonicity #194]: #195
+#199 := [trans #196 #197]: #198
+#201 := [symm #199]: #200
+#202 := (iff #82 #116)
+#203 := [monotonicity #201]: #202
+#190 := [hypothesis]: #82
+#204 := [mp #190 #203]: #116
+#191 := [unit-resolution #140 #190]: #97
+#192 := [unit-resolution #131 #191]: #58
+#193 := [unit-resolution #122 #192 #189]: #15
+#205 := [unit-resolution #193 #204]: false
+#206 := [lemma #205]: #49
+#210 := [mp #206 #201]: #15
+#207 := [unit-resolution #144 #206]: #96
+#208 := [unit-resolution #135 #207 #179]: #94
+#209 := [unit-resolution #118 #208]: #116
+[unit-resolution #209 #210]: false
+unsat
+ba53dbe39a10406601e0a359b3a1de14129ef1a1 36 0
+#2 := false
+decl f5 :: S2
+#10 := f5
+decl f3 :: S2
+#8 := f3
+#12 := (= f3 f5)
+#13 := (not #12)
+decl f4 :: S2
+#9 := f4
+#11 := (distinct f3 f4 f5)
+#33 := (not #11)
+#34 := (or #33 #13)
+#37 := (not #34)
+#14 := (implies #11 #13)
+#15 := (not #14)
+#38 := (iff #15 #37)
+#35 := (iff #14 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#32 := [asserted]: #15
+#42 := [mp #32 #39]: #37
+#41 := [not-or-elim #42]: #12
+#52 := (= f4 f5)
+#53 := (not #52)
+#50 := (= f3 f4)
+#51 := (not #50)
+#48 := (and #51 #13 #53)
+#40 := [not-or-elim #42]: #11
+#58 := (or #33 #48)
+#59 := [def-axiom]: #58
+#62 := [unit-resolution #59 #40]: #48
+#49 := (not #48)
+#45 := (or #49 #13)
+#43 := [def-axiom]: #45
+[unit-resolution #43 #62 #41]: false
+unsat
+08e0778705271e8f33e9bdf3c26b749a4c39eda2 77 0
+#2 := false
+decl f4 :: S2
+#9 := f4
+decl f3 :: S2
+#8 := f3
+#81 := (= f3 f4)
+decl f6 :: S2
+#12 := f6
+#36 := (= f4 f6)
+#100 := (iff #36 #81)
+#98 := (iff #81 #36)
+#13 := (= f6 f4)
+#37 := (iff #13 #36)
+#97 := [commutativity]: #37
+#95 := (iff #81 #13)
+#14 := (= f3 f6)
+#42 := (not #36)
+#15 := (not #14)
+decl f5 :: S2
+#10 := f5
+#11 := (distinct f3 f4 f5)
+#51 := (not #11)
+#60 := (or #51 #15 #42)
+#63 := (not #60)
+#16 := (implies #13 #15)
+#17 := (implies #11 #16)
+#18 := (not #17)
+#66 := (iff #18 #63)
+#43 := (or #15 #42)
+#52 := (or #51 #43)
+#57 := (not #52)
+#64 := (iff #57 #63)
+#61 := (iff #52 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#58 := (iff #18 #57)
+#55 := (iff #17 #52)
+#48 := (implies #11 #43)
+#53 := (iff #48 #52)
+#54 := [rewrite]: #53
+#49 := (iff #17 #48)
+#46 := (iff #16 #43)
+#39 := (implies #36 #15)
+#44 := (iff #39 #43)
+#45 := [rewrite]: #44
+#40 := (iff #16 #39)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#47 := [trans #41 #45]: #46
+#50 := [monotonicity #47]: #49
+#56 := [trans #50 #54]: #55
+#59 := [monotonicity #56]: #58
+#67 := [trans #59 #65]: #66
+#35 := [asserted]: #18
+#68 := [mp #35 #67]: #63
+#70 := [not-or-elim #68]: #14
+#96 := [monotonicity #70]: #95
+#99 := [trans #96 #97]: #98
+#101 := [symm #99]: #100
+#71 := [not-or-elim #68]: #36
+#102 := [mp #71 #101]: #81
+#82 := (not #81)
+#79 := (= f4 f5)
+#80 := (not #79)
+#83 := (= f3 f5)
+#84 := (not #83)
+#77 := (and #82 #84 #80)
+#69 := [not-or-elim #68]: #11
+#89 := (or #51 #77)
+#90 := [def-axiom]: #89
+#93 := [unit-resolution #90 #69]: #77
+#78 := (not #77)
+#75 := (or #78 #82)
+#76 := [def-axiom]: #75
+#94 := [unit-resolution #76 #93]: #82
+[unit-resolution #94 #102]: false
+unsat
+32fbe7827173348f5f83cc50b7e41574fd04dba5 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)
+#44 := (iff #12 false)
+#1 := true
+#39 := (not true)
+#42 := (iff #39 false)
+#43 := [rewrite]: #42
+#40 := (iff #12 #39)
+#37 := (iff #11 true)
+#32 := (not false)
+#35 := (iff #32 true)
+#36 := [rewrite]: #35
+#33 := (iff #11 #32)
+#30 := (iff #10 false)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31]: #33
+#38 := [trans #34 #36]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#29 := [asserted]: #12
+[mp #29 #45]: false
+unsat
+00d94d0af0e9abf6798a28ecb39a441c7c299833 30 0
+#2 := false
+decl f4 :: S2
+#9 := f4
+decl f3 :: S2
+#8 := f3
+#10 := (= f3 f4)
+#11 := (not #10)
+#12 := (not #11)
+#13 := (implies #10 #12)
+#14 := (not #13)
+#46 := (iff #14 false)
+#1 := true
+#41 := (not true)
+#44 := (iff #41 false)
+#45 := [rewrite]: #44
+#42 := (iff #14 #41)
+#39 := (iff #13 true)
+#34 := (implies #10 #10)
+#37 := (iff #34 true)
+#38 := [rewrite]: #37
+#35 := (iff #13 #34)
+#32 := (iff #12 #10)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#40 := [trans #36 #38]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#31 := [asserted]: #14
+[mp #31 #47]: false
+unsat
+11d1529c7a7d7cf3014e0031300d5be1524ea6df 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)
+#35 := (not #13)
+#36 := (or #35 #15)
+#39 := (not #36)
+#16 := (implies #13 #15)
+#17 := (not #16)
+#40 := (iff #17 #39)
+#37 := (iff #16 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#34 := [asserted]: #17
+#44 := [mp #34 #41]: #39
+#46 := [not-or-elim #44]: #14
+#58 := (= f4 f5)
+#59 := (not #58)
+#57 := (not #12)
+#56 := (not #10)
+#54 := (and #56 #57 #59)
+#55 := (not #54)
+#42 := [not-or-elim #44]: #13
+#43 := [and-elim #42]: #10
+#52 := (or #55 #56)
+#53 := [def-axiom]: #52
+#66 := [unit-resolution #53 #43]: #55
+#62 := (or #15 #54)
+#63 := [def-axiom]: #62
+#67 := [unit-resolution #63 #66]: #15
+[unit-resolution #67 #46]: false
+unsat
+8585364a9de57f2c76854513f54ec42d9a599f64 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)
+#47 := (iff #15 false)
+#1 := true
+#42 := (not true)
+#45 := (iff #42 false)
+#46 := [rewrite]: #45
+#43 := (iff #15 #42)
+#40 := (iff #14 true)
+#35 := (implies #12 #12)
+#38 := (iff #35 true)
+#39 := [rewrite]: #38
+#36 := (iff #14 #35)
+#33 := (iff #13 #12)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#41 := [trans #37 #39]: #40
+#44 := [monotonicity #41]: #43
+#48 := [trans #44 #46]: #47
+#32 := [asserted]: #15
+[mp #32 #48]: false
+unsat
+a785d8d462362aedcc845e3ec87cbb8d13b87ae7 91 0
+#2 := false
+decl f5 :: S2
+#10 := f5
+decl f4 :: S2
+#9 := f4
+decl f3 :: S2
+#8 := f3
+#13 := (distinct f3 f4 f5)
+#67 := (= f4 f5)
+#68 := (not #67)
+#63 := (= f3 f5)
+#64 := (not #63)
+#61 := (= f3 f4)
+#62 := (not #61)
+#93 := (and #62 #64 #68)
+decl f6 :: S2
+#11 := f6
+#71 := (= f5 f6)
+#72 := (not #71)
+#69 := (= f4 f6)
+#70 := (not #69)
+#65 := (= f3 f6)
+#66 := (not #65)
+#73 := (and #62 #64 #66 #68 #70 #72)
+#12 := (distinct f3 f4 f5 f6)
+#14 := (distinct f4 f5 f6)
+#15 := (and #13 #14)
+#35 := (not #12)
+#36 := (or #35 #15)
+#39 := (not #36)
+#16 := (implies #12 #15)
+#17 := (not #16)
+#40 := (iff #17 #39)
+#37 := (iff #16 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#34 := [asserted]: #17
+#44 := [mp #34 #41]: #39
+#42 := [not-or-elim #44]: #12
+#89 := (or #35 #73)
+#90 := [def-axiom]: #89
+#121 := [unit-resolution #90 #42]: #73
+#74 := (not #73)
+#75 := (or #74 #62)
+#76 := [def-axiom]: #75
+#122 := [unit-resolution #76 #121]: #62
+#81 := (or #74 #68)
+#82 := [def-axiom]: #81
+#123 := [unit-resolution #82 #121]: #68
+#77 := (or #74 #64)
+#78 := [def-axiom]: #77
+#124 := [unit-resolution #78 #121]: #64
+#101 := (or #93 #61 #63 #67)
+#102 := [def-axiom]: #101
+#125 := [unit-resolution #102 #124 #123 #122]: #93
+#94 := (not #93)
+#105 := (or #13 #94)
+#106 := [def-axiom]: #105
+#126 := [unit-resolution #106 #125]: #13
+#107 := (and #68 #70 #72)
+#85 := (or #74 #72)
+#86 := [def-axiom]: #85
+#127 := [unit-resolution #86 #121]: #72
+#83 := (or #74 #70)
+#84 := [def-axiom]: #83
+#128 := [unit-resolution #84 #121]: #70
+#115 := (or #107 #67 #69 #71)
+#116 := [def-axiom]: #115
+#129 := [unit-resolution #116 #128 #127 #123]: #107
+#108 := (not #107)
+#119 := (or #14 #108)
+#120 := [def-axiom]: #119
+#130 := [unit-resolution #120 #129]: #14
+#54 := (not #14)
+#53 := (not #13)
+#55 := (or #53 #54)
+#43 := (not #15)
+#58 := (iff #43 #55)
+#56 := (not #55)
+#49 := (not #56)
+#46 := (iff #49 #55)
+#57 := [rewrite]: #46
+#50 := (iff #43 #49)
+#51 := (iff #15 #56)
+#52 := [rewrite]: #51
+#48 := [monotonicity #52]: #50
+#59 := [trans #48 #57]: #58
+#45 := [not-or-elim #44]: #43
+#60 := [mp #45 #59]: #55
+[unit-resolution #60 #130 #126]: false
+unsat
+273a6dc6f10616be4347838d6cbb54a0b0ad5636 25 0
+#2 := false
+#8 := (:var 0 S2)
+#9 := (= #8 #8)
+#10 := (forall (vars (?v0 S2)) #9)
+#11 := (not #10)
+#43 := (iff #11 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #11 #38)
+#36 := (iff #10 true)
+#31 := (forall (vars (?v0 S2)) true)
+#34 := (iff #31 true)
+#35 := [elim-unused]: #34
+#32 := (iff #10 #31)
+#29 := (iff #9 true)
+#30 := [rewrite]: #29
+#33 := [quant-intro #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#28 := [asserted]: #11
+[mp #28 #44]: false
+unsat
+2b9ce0054ea55ee81c55715bd6d24aa6896b491c 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)
+#49 := (iff #13 false)
+#1 := true
+#44 := (not true)
+#47 := (iff #44 false)
+#48 := [rewrite]: #47
+#45 := (iff #13 #44)
+#42 := (iff #12 true)
+#31 := (= f1 #9)
+#34 := (forall (vars (?v0 S2)) #31)
+#37 := (iff #34 #34)
+#40 := (iff #37 true)
+#41 := [rewrite]: #40
+#38 := (iff #12 #37)
+#35 := (iff #11 #34)
+#32 := (iff #10 #31)
+#33 := [rewrite]: #32
+#36 := [quant-intro #33]: #35
+#39 := [monotonicity #36 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#30 := [asserted]: #13
+[mp #30 #50]: false
+unsat
+4905f6794c524726db3be755d752d3ea53fc4f9a 95 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl ?v0!0 :: S2
@@ -4185,68 +4677,7 @@
 #102 := [and-elim #101]: #76
 [unit-resolution #102 #115]: false
 unsat
-f23e61ff98637733b3412f875d5b578e0e8387fe 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)
-#74 := (iff #17 false)
-#1 := true
-#69 := (not true)
-#72 := (iff #69 false)
-#73 := [rewrite]: #72
-#70 := (iff #17 #69)
-#67 := (iff #16 true)
-#38 := (= f1 f4)
-#35 := (= f1 f3)
-#44 := (not #35)
-#45 := (or #44 #38)
-#62 := (implies #45 #45)
-#65 := (iff #62 true)
-#66 := [rewrite]: #65
-#63 := (iff #16 #62)
-#60 := (iff #15 #45)
-#50 := (not #38)
-#55 := (implies #50 #44)
-#58 := (iff #55 #45)
-#59 := [rewrite]: #58
-#56 := (iff #15 #55)
-#53 := (iff #14 #44)
-#36 := (iff #9 #35)
-#37 := [rewrite]: #36
-#54 := [monotonicity #37]: #53
-#51 := (iff #13 #50)
-#39 := (iff #11 #38)
-#40 := [rewrite]: #39
-#52 := [monotonicity #40]: #51
-#57 := [monotonicity #52 #54]: #56
-#61 := [trans #57 #59]: #60
-#48 := (iff #12 #45)
-#41 := (implies #35 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #12 #41)
-#43 := [monotonicity #37 #40]: #42
-#49 := [trans #43 #47]: #48
-#64 := [monotonicity #49 #61]: #63
-#68 := [trans #64 #66]: #67
-#71 := [monotonicity #68]: #70
-#75 := [trans #71 #73]: #74
-#34 := [asserted]: #17
-[mp #34 #75]: false
-unsat
-99ac0be7380191db43f2261910b85b072853ffc6 300 0
+48a51f989350a0e584db03a2950a272906be29b0 300 0
 #2 := false
 decl f4 :: (-> S2 S1)
 decl ?v0!1 :: S2
@@ -4547,129 +4978,7 @@
 #609 := [quant-inst]: #615
 [unit-resolution #609 #257 #603]: false
 unsat
-a8bd8ccd5c190cb3f1fa752363a309006c96634d 121 0
-#2 := false
-decl f5 :: S1
-#12 := f5
-decl f1 :: S1
-#4 := f1
-#44 := (= f1 f5)
-decl f4 :: S1
-#10 := f4
-#41 := (= f1 f4)
-decl f3 :: S1
-#8 := f3
-#38 := (= f1 f3)
-#53 := (not #38)
-#90 := (or #53 #41 #44)
-#137 := (iff #90 false)
-#132 := (or false false false)
-#135 := (iff #132 false)
-#136 := [rewrite]: #135
-#133 := (iff #90 #132)
-#123 := (iff #44 false)
-#113 := (not #44)
-#93 := (not #90)
-#99 := (or #53 #41 #44 #93)
-#104 := (not #99)
-#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)
-#107 := (iff #20 #104)
-#70 := (or #53 #44)
-#62 := (or #53 #41)
-#75 := (or #62 #70)
-#47 := (or #41 #44)
-#54 := (or #53 #47)
-#81 := (not #54)
-#82 := (or #81 #75)
-#87 := (not #82)
-#105 := (iff #87 #104)
-#102 := (iff #82 #99)
-#96 := (or #93 #75)
-#100 := (iff #96 #99)
-#101 := [rewrite]: #100
-#97 := (iff #82 #96)
-#94 := (iff #81 #93)
-#91 := (iff #54 #90)
-#92 := [rewrite]: #91
-#95 := [monotonicity #92]: #94
-#98 := [monotonicity #95]: #97
-#103 := [trans #98 #101]: #102
-#106 := [monotonicity #103]: #105
-#88 := (iff #20 #87)
-#85 := (iff #19 #82)
-#78 := (implies #54 #75)
-#83 := (iff #78 #82)
-#84 := [rewrite]: #83
-#79 := (iff #19 #78)
-#76 := (iff #18 #75)
-#73 := (iff #17 #70)
-#67 := (implies #38 #44)
-#71 := (iff #67 #70)
-#72 := [rewrite]: #71
-#68 := (iff #17 #67)
-#45 := (iff #13 #44)
-#46 := [rewrite]: #45
-#39 := (iff #9 #38)
-#40 := [rewrite]: #39
-#69 := [monotonicity #40 #46]: #68
-#74 := [trans #69 #72]: #73
-#65 := (iff #16 #62)
-#59 := (implies #38 #41)
-#63 := (iff #59 #62)
-#64 := [rewrite]: #63
-#60 := (iff #16 #59)
-#42 := (iff #11 #41)
-#43 := [rewrite]: #42
-#61 := [monotonicity #40 #43]: #60
-#66 := [trans #61 #64]: #65
-#77 := [monotonicity #66 #74]: #76
-#57 := (iff #15 #54)
-#50 := (implies #38 #47)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #15 #50)
-#48 := (iff #14 #47)
-#49 := [monotonicity #43 #46]: #48
-#52 := [monotonicity #40 #49]: #51
-#58 := [trans #52 #56]: #57
-#80 := [monotonicity #58 #77]: #79
-#86 := [trans #80 #84]: #85
-#89 := [monotonicity #86]: #88
-#108 := [trans #89 #106]: #107
-#37 := [asserted]: #20
-#109 := [mp #37 #108]: #104
-#114 := [not-or-elim #109]: #113
-#124 := [iff-false #114]: #123
-#121 := (iff #41 false)
-#111 := (not #41)
-#112 := [not-or-elim #109]: #111
-#122 := [iff-false #112]: #121
-#130 := (iff #53 false)
-#1 := true
-#125 := (not true)
-#128 := (iff #125 false)
-#129 := [rewrite]: #128
-#126 := (iff #53 #125)
-#119 := (iff #38 true)
-#110 := [not-or-elim #109]: #38
-#120 := [iff-true #110]: #119
-#127 := [monotonicity #120]: #126
-#131 := [trans #127 #129]: #130
-#134 := [monotonicity #131 #122 #124]: #133
-#138 := [trans #134 #136]: #137
-#115 := [not-or-elim #109]: #90
-[mp #115 #138]: false
-unsat
-cadcb33e2fa210fd60afd1f576e2a8b43f4a3cdf 201 0
+8d1c135b088bf498c079d2958e8764a8092679cf 201 0
 #2 := false
 decl f3 :: (-> S2 S1)
 #8 := (:var 0 S2)
@@ -4871,92 +5180,7 @@
 #211 := [quant-inst]: #320
 [unit-resolution #211 #595 #319]: false
 unsat
-49f39d63404aef857c81d69ce3ed08db1cf19a62 84 0
-#2 := false
-decl f4 :: S1
-#10 := f4
-decl f1 :: S1
-#4 := f1
-#38 := (= f1 f4)
-#53 := (not #38)
-#97 := [hypothesis]: #53
-decl f3 :: S1
-#8 := f3
-#35 := (= f1 f3)
-#44 := (not #35)
-#45 := (or #44 #38)
-#54 := (or #35 #53)
-#59 := (and #45 #54)
-#62 := (iff #35 #38)
-#68 := (not #59)
-#69 := (or #68 #62)
-#74 := (not #69)
-#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)
-#75 := (iff #17 #74)
-#72 := (iff #16 #69)
-#65 := (implies #59 #62)
-#70 := (iff #65 #69)
-#71 := [rewrite]: #70
-#66 := (iff #16 #65)
-#63 := (iff #15 #62)
-#39 := (iff #11 #38)
-#40 := [rewrite]: #39
-#36 := (iff #9 #35)
-#37 := [rewrite]: #36
-#64 := [monotonicity #37 #40]: #63
-#60 := (iff #14 #59)
-#57 := (iff #13 #54)
-#50 := (implies #38 #35)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #13 #50)
-#52 := [monotonicity #40 #37]: #51
-#58 := [trans #52 #56]: #57
-#48 := (iff #12 #45)
-#41 := (implies #35 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #12 #41)
-#43 := [monotonicity #37 #40]: #42
-#49 := [trans #43 #47]: #48
-#61 := [monotonicity #49 #58]: #60
-#67 := [monotonicity #61 #64]: #66
-#73 := [trans #67 #71]: #72
-#76 := [monotonicity #73]: #75
-#34 := [asserted]: #17
-#79 := [mp #34 #76]: #74
-#77 := [not-or-elim #79]: #59
-#78 := [and-elim #77]: #45
-#98 := [unit-resolution #78 #97]: #44
-#89 := (or #38 #35)
-#90 := (iff #38 #44)
-#81 := (not #62)
-#91 := (iff #81 #90)
-#92 := [rewrite]: #91
-#82 := [not-or-elim #79]: #81
-#93 := [mp #82 #92]: #90
-#94 := (not #90)
-#95 := (or #38 #35 #94)
-#88 := [def-axiom]: #95
-#86 := [unit-resolution #88 #93]: #89
-#99 := [unit-resolution #86 #98 #97]: false
-#100 := [lemma #99]: #38
-#80 := [and-elim #77]: #54
-#101 := [unit-resolution #80 #100]: #35
-#83 := (or #53 #44)
-#87 := (or #53 #44 #94)
-#85 := [def-axiom]: #87
-#96 := [unit-resolution #85 #93]: #83
-[unit-resolution #96 #101 #100]: false
-unsat
-275457b2bda52ffcdd4253789835ed95d90c1f17 244 0
+c2e19ee7461e4fbfe65c34d98111e3914f852baf 244 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl ?v0!0 :: S2
@@ -5201,55 +5425,7 @@
 #616 := [mp #343 #237]: #621
 [unit-resolution #616 #629 #330]: false
 unsat
-bbcd2845c0842c2c58bd699481f0fecfa298d8a7 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)
-#61 := (iff #15 false)
-#1 := true
-#56 := (not true)
-#59 := (iff #56 false)
-#60 := [rewrite]: #59
-#57 := (iff #15 #56)
-#54 := (iff #14 true)
-#36 := (= f1 f4)
-#33 := (= f1 f3)
-#39 := (iff #33 #36)
-#49 := (iff #39 #39)
-#52 := (iff #49 true)
-#53 := [rewrite]: #52
-#50 := (iff #14 #49)
-#47 := (iff #13 #39)
-#42 := (iff #36 #33)
-#45 := (iff #42 #39)
-#46 := [rewrite]: #45
-#43 := (iff #13 #42)
-#34 := (iff #9 #33)
-#35 := [rewrite]: #34
-#37 := (iff #11 #36)
-#38 := [rewrite]: #37
-#44 := [monotonicity #38 #35]: #43
-#48 := [trans #44 #46]: #47
-#40 := (iff #12 #39)
-#41 := [monotonicity #35 #38]: #40
-#51 := [monotonicity #41 #48]: #50
-#55 := [trans #51 #53]: #54
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#32 := [asserted]: #15
-[mp #32 #62]: false
-unsat
-b11d7db349f0b800b6d28726c33bbc51dfd5ec41 49 0
+35b6826e84c97e2db1e3cd91ad69abb16f131b93 49 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -5299,49 +5475,7 @@
 #35 := [asserted]: #18
 [mp #35 #65]: false
 unsat
-d6ad6bdc191dec543b99c99d75040cdba1ff04e8 41 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: S1
-#8 := f3
-#9 := (= f3 f1)
-#10 := (not #9)
-#11 := (iff #9 #10)
-#12 := (not #11)
-#13 := (not #12)
-#56 := (iff #13 false)
-#1 := true
-#51 := (not true)
-#54 := (iff #51 false)
-#55 := [rewrite]: #54
-#52 := (iff #13 #51)
-#49 := (iff #12 true)
-#44 := (not false)
-#47 := (iff #44 true)
-#48 := [rewrite]: #47
-#45 := (iff #12 #44)
-#42 := (iff #11 false)
-#31 := (= f1 f3)
-#34 := (not #31)
-#37 := (iff #31 #34)
-#40 := (iff #37 false)
-#41 := [rewrite]: #40
-#38 := (iff #11 #37)
-#35 := (iff #10 #34)
-#32 := (iff #9 #31)
-#33 := [rewrite]: #32
-#36 := [monotonicity #33]: #35
-#39 := [monotonicity #33 #36]: #38
-#43 := [trans #39 #41]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#30 := [asserted]: #13
-[mp #30 #57]: false
-unsat
-b5e5edf486660b04e5c2cc8e67825f081c9c49a9 136 0
+2e6f238fe51369f58bc6454a136532e4c6f3bd82 136 0
 #2 := false
 decl f3 :: (-> S2 S2 S1)
 decl f4 :: S2
@@ -5478,68 +5612,7 @@
 #593 := [quant-inst]: #592
 [unit-resolution #593 #610 #258]: false
 unsat
-81bf38fb0456bcb900ea52fab12378a5588effa7 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)
-#74 := (iff #17 false)
-#1 := true
-#69 := (not true)
-#72 := (iff #69 false)
-#73 := [rewrite]: #72
-#70 := (iff #17 #69)
-#67 := (iff #16 true)
-#38 := (= f1 f4)
-#35 := (= f1 f3)
-#44 := (not #35)
-#45 := (or #44 #38)
-#62 := (iff #45 #45)
-#65 := (iff #62 true)
-#66 := [rewrite]: #65
-#63 := (iff #16 #62)
-#60 := (iff #15 #45)
-#50 := (not #38)
-#55 := (implies #50 #44)
-#58 := (iff #55 #45)
-#59 := [rewrite]: #58
-#56 := (iff #15 #55)
-#53 := (iff #14 #44)
-#36 := (iff #9 #35)
-#37 := [rewrite]: #36
-#54 := [monotonicity #37]: #53
-#51 := (iff #13 #50)
-#39 := (iff #11 #38)
-#40 := [rewrite]: #39
-#52 := [monotonicity #40]: #51
-#57 := [monotonicity #52 #54]: #56
-#61 := [trans #57 #59]: #60
-#48 := (iff #12 #45)
-#41 := (implies #35 #38)
-#46 := (iff #41 #45)
-#47 := [rewrite]: #46
-#42 := (iff #12 #41)
-#43 := [monotonicity #37 #40]: #42
-#49 := [trans #43 #47]: #48
-#64 := [monotonicity #49 #61]: #63
-#68 := [trans #64 #66]: #67
-#71 := [monotonicity #68]: #70
-#75 := [trans #71 #73]: #74
-#34 := [asserted]: #17
-[mp #34 #75]: false
-unsat
-9d9671876c5da4fc5d4c634fb934bc459b3fb5e8 124 0
+a15d00efdb475e30bdd25ef3ed2227a8ea9c519f 124 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl f4 :: (-> S2 S2)
@@ -5664,80 +5737,7 @@
 #207 := [mp #217 #206]: #569
 [unit-resolution #207 #576 #88 #209]: false
 unsat
-7d3ca4c016c80378051605a2446d32cfa542aaf2 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)
-#87 := (iff #19 false)
-#1 := true
-#82 := (not true)
-#85 := (iff #82 false)
-#86 := [rewrite]: #85
-#83 := (iff #19 #82)
-#80 := (iff #18 true)
-#37 := (= f1 f3)
-#40 := (iff #37 #37)
-#43 := (iff #40 true)
-#44 := [rewrite]: #43
-#78 := (iff #18 #40)
-#76 := (iff #17 #37)
-#47 := (iff #37 true)
-#50 := (iff #47 #37)
-#51 := [rewrite]: #50
-#74 := (iff #17 #47)
-#72 := (iff #16 true)
-#70 := (iff #16 #40)
-#68 := (iff #15 #37)
-#66 := (iff #15 #47)
-#64 := (iff #14 true)
-#62 := (iff #14 #40)
-#60 := (iff #13 #37)
-#58 := (iff #13 #47)
-#56 := (iff #12 true)
-#54 := (iff #12 #40)
-#52 := (iff #11 #37)
-#48 := (iff #11 #47)
-#45 := (iff #10 true)
-#41 := (iff #10 #40)
-#38 := (iff #9 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39 #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #39 #46]: #48
-#53 := [trans #49 #51]: #52
-#55 := [monotonicity #39 #53]: #54
-#57 := [trans #55 #44]: #56
-#59 := [monotonicity #39 #57]: #58
-#61 := [trans #59 #51]: #60
-#63 := [monotonicity #39 #61]: #62
-#65 := [trans #63 #44]: #64
-#67 := [monotonicity #39 #65]: #66
-#69 := [trans #67 #51]: #68
-#71 := [monotonicity #39 #69]: #70
-#73 := [trans #71 #44]: #72
-#75 := [monotonicity #39 #73]: #74
-#77 := [trans #75 #51]: #76
-#79 := [monotonicity #39 #77]: #78
-#81 := [trans #79 #44]: #80
-#84 := [monotonicity #81]: #83
-#88 := [trans #84 #86]: #87
-#36 := [asserted]: #19
-[mp #36 #88]: false
-unsat
-6fba77c7ee170a1620030b502ad2db7a8a1aed9e 64 0
+0e7fa24f774b5d4840baee92f17adcdc6e36469d 64 0
 #2 := false
 decl f3 :: (-> S2 S2 S3)
 decl f4 :: S2
@@ -5802,33 +5802,7 @@
 #130 := [quant-inst]: #216
 [unit-resolution #130 #553 #64]: false
 unsat
-35917dcc4acd32693fbb42d1a381fa58c2e775dd 25 0
-#2 := false
-#8 := (:var 0 S2)
-#9 := (= #8 #8)
-#10 := (exists (vars (?v0 S2)) #9)
-#11 := (not #10)
-#43 := (iff #11 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #11 #38)
-#36 := (iff #10 true)
-#31 := (exists (vars (?v0 S2)) true)
-#34 := (iff #31 true)
-#35 := [elim-unused]: #34
-#32 := (iff #10 #31)
-#29 := (iff #9 true)
-#30 := [rewrite]: #29
-#33 := [quant-intro #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#28 := [asserted]: #11
-[mp #28 #44]: false
-unsat
-223d86a753fa4111a2efb19d2bcec167505d6a7e 250 0
+e97ea15e571d05d4542f0baceec935a45a20adf5 250 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl f7 :: S2
@@ -6079,7 +6053,33 @@
 #699 := [mp #350 #698]: #693
 [unit-resolution #699 #173 #714 #398]: false
 unsat
-48e86f3a23bbb7c517dedfe6660826ca25059fca 34 0
+150a137e969806c6900cabc66bb27970472c7ba1 25 0
+#2 := false
+#8 := (:var 0 S2)
+#9 := (= #8 #8)
+#10 := (exists (vars (?v0 S2)) #9)
+#11 := (not #10)
+#43 := (iff #11 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #11 #38)
+#36 := (iff #10 true)
+#31 := (exists (vars (?v0 S2)) true)
+#34 := (iff #31 true)
+#35 := [elim-unused]: #34
+#32 := (iff #10 #31)
+#29 := (iff #9 true)
+#30 := [rewrite]: #29
+#33 := [quant-intro #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#28 := [asserted]: #11
+[mp #28 #44]: false
+unsat
+b28b1c7eb24edf6acf5466ddd1304a6b881a60f9 34 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -6114,11 +6114,7 @@
 #30 := [asserted]: #13
 [mp #30 #50]: false
 unsat
-532713577ffc51767de4833038556b4e3293fda4 1 2
-unsat
-WARNING: failed to find a pattern for quantifier (quantifier id: k!9)
-
-fc7f88181fbb95ae1b43bd1ec021651eb1a6e29c 258 0
+043713d1f8d615cef2b57b8a8ae1162f9c51de61 258 0
 #2 := false
 decl f4 :: (-> S2 S1)
 decl ?v0!2 :: S2
@@ -6377,9 +6373,7 @@
 #579 := [quant-inst]: #578
 [unit-resolution #579 #432 #573]: false
 unsat
-b9a1dbc05a0fcdc4ae2c7e03b2b8a9ad6df98756 1 0
-unsat
-9db388838cd05c32098d6cee4786c7311602e951 222 0
+7fcf7ce1521f6f1599b2fe6f93ba5dee1cbd7b76 222 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl ?v0!0 :: S2
@@ -6602,9 +6596,7 @@
 #610 := [quant-inst]: #609
 [unit-resolution #610 #339 #320]: false
 unsat
-cbac2f7e87b549893b94e3792e09a58dadcc84e9 1 0
-unsat
-5815749abaa2e9d579422ebe3d14186ba8803728 49 0
+8031eb3bcd3fb97da7b874e36b0d4d2ae215ec7b 49 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -6654,9 +6646,7 @@
 #35 := [asserted]: #18
 [mp #35 #65]: false
 unsat
-1493ff264c0f89a95d188930a1476aec2a1aa1bb 1 0
-unsat
-e053e47f320825e5b9b67b9497406e00070abe43 122 0
+301a246cbbd414b8b75c6b801fee2f734cf2af47 122 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl ?v0!1 :: S2
@@ -6779,9 +6769,21 @@
 #287 := [quant-inst]: #200
 [unit-resolution #287 #620 #138]: false
 unsat
-1860fe1f45d9df9b729809ed662950c61f79f829 1 0
-unsat
-12d1461d1fa5477cb514ef80c18c85a012607364 105 0
+2317912b27971033dc831a6ce5ef74d0f20fbca2 1 2
+unsat
+WARNING: failed to find a pattern for quantifier (quantifier id: k!9)
+
+ee898f52c96d73444993788b39566855271caaec 1 0
+unsat
+f7daa562701d4999ed8a3f5ec133f08651bf6190 1 0
+unsat
+fdbe39cdd485517d8ec1964f2c4fb7b6646fe608 1 0
+unsat
+779c5fc38fd08b8484ec1da52f6a17e6b849eac4 1 0
+unsat
+b720bb30cc87882c3f660a5bf9c8737dde4c14c4 1 0
+unsat
+2acdf9e468d060988547fd7ad4c93238ed78a5bb 105 0
 #2 := false
 decl f3 :: (-> S1 S1)
 decl ?v0!1 :: S1
@@ -6887,9 +6889,7 @@
 #261 := [quant-inst]: #188
 [unit-resolution #261 #590 #259]: false
 unsat
-58aeee112e6b81dcd3353f63fc46ef0b0f3eb24c 1 0
-unsat
-ed0af7544f19477dc25f65a160752e70bd0bbf21 230 0
+ff2e1b7168f418022909b6d3ec628836562df57d 230 0
 #2 := false
 decl f3 :: (-> S1 S1)
 decl ?v0!0 :: S1
@@ -7120,7 +7120,7 @@
 #309 := [quant-inst]: #308
 [unit-resolution #309 #590 #312]: false
 unsat
-446f4f1e86496dc31d9127dadba175aab73fcdf4 156 0
+258fe7f9c05eff8e107778930f55bcfa407e2fde 156 0
 #2 := false
 decl f3 :: (-> S1 S2 S1)
 #9 := (:var 0 S2)
@@ -7277,7 +7277,7 @@
 #269 := [quant-inst]: #264
 [unit-resolution #269 #592 #292]: false
 unsat
-73417ccd5b8c2fb3c0c21a8c23809282ab12f8b8 74 0
+6c0f54222b59d5e628ff948749ac67e96364c6a1 74 0
 #2 := false
 decl f3 :: (-> S2 S3 S4)
 #9 := (:var 0 S3)
@@ -7352,7 +7352,7 @@
 #548 := [mp #55 #547]: #543
 [unit-resolution #548 #537]: false
 unsat
-e3e78e7b3355a0e12a6553b06865dbb99fa1ace5 108 0
+cba176f179e597e7b48393532028be8634e0c4f7 108 0
 #2 := false
 decl f3 :: (-> S1 S1)
 #11 := (:var 0 S1)
@@ -7461,13 +7461,7 @@
 #179 := [quant-inst]: #265
 [unit-resolution #179 #96 #599]: false
 unsat
-da85096b57c08af8febf5871c1333121a34c6d28 1 0
-unsat
-6c41d71d8ec4d73ffa088d938320c03ca09b9201 1 2
-unsat
-WARNING: failed to find a pattern for quantifier (quantifier id: k!12)
-
-12e3d2e5e3ee6fdfd1904d6ec3b7cee27863319e 183 2
+1f79e2aaf530f1cad27b8439c2a93a00022ad034 183 2
 #2 := false
 decl f3 :: (-> S1 S2 S1)
 #9 := (:var 0 S2)
@@ -7653,6 +7647,12 @@
 unsat
 WARNING: failed to find a pattern for quantifier (quantifier id: k!12)
 
+da85096b57c08af8febf5871c1333121a34c6d28 1 0
+unsat
+6c41d71d8ec4d73ffa088d938320c03ca09b9201 1 2
+unsat
+WARNING: failed to find a pattern for quantifier (quantifier id: k!12)
+
 5d15e0a34749300f4ce5f4c920d3ca259f7027cd 1 0
 unsat
 fa1639cb0c965ae73d4377750883cc09dbe87562 1 0
@@ -7663,7 +7663,7 @@
 unsat
 22c7d1d1136fafc0a09e243a12ede1ee4fee416f 1 0
 unsat
-92de3e43df292b3d7f698eeecd3084ad63385f52 107 0
+cfd9d2f647046e282a1080aae51b4b88be291157 107 0
 #2 := false
 decl f3 :: (-> S2 S1)
 #8 := (:var 0 S2)
@@ -7771,7 +7771,7 @@
 #279 := [quant-inst]: #193
 [unit-resolution #279 #102 #618]: false
 unsat
-ab595871a8f439823819ae39abbb09300ded5d4d 75 0
+9ea0d22c6270219f7cef6ee3d8f429562349b2a3 75 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -7847,7 +7847,7 @@
 #41 := [asserted]: #24
 [mp #41 #91]: false
 unsat
-66a02ca33e858454a913431cd41d1e5a58d7ca83 207 0
+51de51a0d85b126e271283f7eca5a0bb3a5a5bca 207 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl ?v1!0 :: (-> S2 S2)
@@ -8055,7 +8055,7 @@
 #622 := [mp #616 #257]: #277
 [unit-resolution #622 #645 #591 #596]: false
 unsat
-070caa247cea32871c723a813303329e9c48e89d 250 0
+628763241ae198f2ea4a54c641ca6e8df6d851ca 250 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl ?v1!1 :: (-> S2 S2)
@@ -8306,7 +8306,7 @@
 #616 := [mp #628 #615]: #622
 [unit-resolution #616 #128 #676 #607 #606]: false
 unsat
-ffccf343597d7c1ee1fd555056e55c0f14472255 238 0
+64bd43a9d49de65761e5220e25dbbe3dc269bf0e 238 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl ?v1!1 :: (-> S2 S2)
@@ -8545,7 +8545,215 @@
 #338 := [mp #643 #632]: #276
 [unit-resolution #338 #664 #617 #616]: false
 unsat
-8ce5d808d97d9f937477d79f321db3630294ec1d 43 0
+b8d80ad0d8c340491041b0c69d71b3944eaf90e6 93 0
+#2 := false
+decl f5 :: (-> S2 S1)
+decl f6 :: S2
+#16 := f6
+#20 := (f5 f6)
+decl f1 :: S1
+#4 := f1
+#65 := (= f1 #20)
+#84 := (not #65)
+decl f3 :: (-> S2 S3 S1)
+decl f4 :: S3
+#9 := f4
+#17 := (f3 f6 f4)
+#59 := (= f1 #17)
+#8 := (:var 0 S2)
+#12 := (f5 #8)
+#44 := (= f1 #12)
+#10 := (f3 #8 f4)
+#41 := (= f1 #10)
+#50 := (not #41)
+#51 := (or #50 #44)
+#56 := (forall (vars (?v0 S2)) #51)
+#62 := (and #56 #59)
+#71 := (not #62)
+#72 := (or #71 #65)
+#77 := (not #72)
+#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)
+#78 := (iff #23 #77)
+#75 := (iff #22 #72)
+#68 := (implies #62 #65)
+#73 := (iff #68 #72)
+#74 := [rewrite]: #73
+#69 := (iff #22 #68)
+#66 := (iff #21 #65)
+#67 := [rewrite]: #66
+#63 := (iff #19 #62)
+#60 := (iff #18 #59)
+#61 := [rewrite]: #60
+#57 := (iff #15 #56)
+#54 := (iff #14 #51)
+#47 := (implies #41 #44)
+#52 := (iff #47 #51)
+#53 := [rewrite]: #52
+#48 := (iff #14 #47)
+#45 := (iff #13 #44)
+#46 := [rewrite]: #45
+#42 := (iff #11 #41)
+#43 := [rewrite]: #42
+#49 := [monotonicity #43 #46]: #48
+#55 := [trans #49 #53]: #54
+#58 := [quant-intro #55]: #57
+#64 := [monotonicity #58 #61]: #63
+#70 := [monotonicity #64 #67]: #69
+#76 := [trans #70 #74]: #75
+#79 := [monotonicity #76]: #78
+#40 := [asserted]: #23
+#82 := [mp #40 #79]: #77
+#85 := [not-or-elim #82]: #84
+#80 := [not-or-elim #82]: #62
+#83 := [and-elim #80]: #59
+#572 := (pattern #12)
+#571 := (pattern #10)
+#573 := (forall (vars (?v0 S2)) (:pat #571 #572) #51)
+#576 := (iff #56 #573)
+#574 := (iff #51 #51)
+#575 := [refl]: #574
+#577 := [quant-intro #575]: #576
+#97 := (~ #56 #56)
+#95 := (~ #51 #51)
+#96 := [refl]: #95
+#98 := [nnf-pos #96]: #97
+#81 := [and-elim #80]: #56
+#88 := [mp~ #81 #98]: #56
+#578 := [mp #88 #577]: #573
+#155 := (not #59)
+#157 := (not #573)
+#244 := (or #157 #155 #65)
+#242 := (or #155 #65)
+#235 := (or #157 #242)
+#247 := (iff #235 #244)
+#175 := [rewrite]: #247
+#246 := [quant-inst]: #235
+#248 := [mp #246 #175]: #244
+[unit-resolution #248 #578 #83 #85]: false
+unsat
+0f8bf9d230b6b97c3b9a64ed4f1bb8757963fbc7 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
+#57 := (= f1 #19)
+decl f5 :: (-> S2 S1)
+#17 := (f5 f6)
+#54 := (= f1 #17)
+#60 := (and #54 #57)
+#63 := (not #60)
+#8 := (:var 0 S2)
+#12 := (f5 #8)
+#45 := (= f1 #12)
+#10 := (f3 #8 f4)
+#42 := (= f1 #10)
+#48 := (and #42 #45)
+#51 := (exists (vars (?v0 S2)) #48)
+#66 := (or #51 #63)
+#69 := (not #66)
+#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)
+#70 := (iff #24 #69)
+#67 := (iff #23 #66)
+#64 := (iff #22 #63)
+#61 := (iff #21 #60)
+#58 := (iff #20 #57)
+#59 := [rewrite]: #58
+#55 := (iff #18 #54)
+#56 := [rewrite]: #55
+#62 := [monotonicity #56 #59]: #61
+#65 := [monotonicity #62]: #64
+#52 := (iff #15 #51)
+#49 := (iff #14 #48)
+#46 := (iff #13 #45)
+#47 := [rewrite]: #46
+#43 := (iff #11 #42)
+#44 := [rewrite]: #43
+#50 := [monotonicity #44 #47]: #49
+#53 := [quant-intro #50]: #52
+#68 := [monotonicity #53 #65]: #67
+#71 := [monotonicity #68]: #70
+#41 := [asserted]: #24
+#74 := [mp #41 #71]: #69
+#75 := [not-or-elim #74]: #60
+#77 := [and-elim #75]: #57
+#76 := [and-elim #75]: #54
+#585 := (pattern #12)
+#584 := (pattern #10)
+#93 := (not #45)
+#92 := (not #42)
+#94 := (or #92 #93)
+#586 := (forall (vars (?v0 S2)) (:pat #584 #585) #94)
+#101 := (forall (vars (?v0 S2)) #94)
+#589 := (iff #101 #586)
+#587 := (iff #94 #94)
+#588 := [refl]: #587
+#590 := [quant-intro #588]: #589
+#87 := (not #48)
+#90 := (forall (vars (?v0 S2)) #87)
+#102 := (iff #90 #101)
+#99 := (iff #87 #94)
+#95 := (not #94)
+#83 := (not #95)
+#97 := (iff #83 #94)
+#98 := [rewrite]: #97
+#84 := (iff #87 #83)
+#85 := (iff #48 #95)
+#86 := [rewrite]: #85
+#96 := [monotonicity #86]: #84
+#100 := [trans #96 #98]: #99
+#103 := [quant-intro #100]: #102
+#72 := (not #51)
+#80 := (~ #72 #90)
+#88 := (~ #87 #87)
+#89 := [refl]: #88
+#78 := [nnf-neg #89]: #80
+#73 := [not-or-elim #74]: #72
+#91 := [mp~ #73 #78]: #90
+#104 := [mp #91 #103]: #101
+#591 := [mp #104 #590]: #586
+#255 := (not #57)
+#168 := (not #54)
+#248 := (not #586)
+#259 := (or #248 #168 #255)
+#169 := (or #255 #168)
+#260 := (or #248 #169)
+#578 := (iff #260 #259)
+#256 := (or #168 #255)
+#261 := (or #248 #256)
+#241 := (iff #261 #259)
+#576 := [rewrite]: #241
+#258 := (iff #260 #261)
+#170 := (iff #169 #256)
+#257 := [rewrite]: #170
+#262 := [monotonicity #257]: #258
+#235 := [trans #262 #576]: #578
+#188 := [quant-inst]: #260
+#365 := [mp #188 #235]: #259
+[unit-resolution #365 #591 #76 #77]: false
+unsat
+42f3c8af4c50150e11519c085a0ad69e107e1705 43 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -8589,7 +8797,7 @@
 #32 := [asserted]: #15
 [mp #32 #58]: false
 unsat
-ee1e5475ea11ff0f473b33b8c572488c1f039a0e 27 0
+e44a18e086890afdae37ccfa17aec44f2a634103 27 0
 #2 := false
 #1 := true
 #9 := (or false true)
@@ -8617,7 +8825,7 @@
 #28 := [asserted]: #11
 [mp #28 #46]: false
 unsat
-82c66294f6bc190a20d250a4062b09707f16aa4c 31 0
+48f0da3339d9c9f7707291c89458bdaf3e50c114 31 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -8649,7 +8857,7 @@
 #29 := [asserted]: #12
 [mp #29 #46]: false
 unsat
-f32b862e1d7121899074795ddf1c0725bc5cc874 33 0
+e7059fb5d2b001f75897ae16a2ace8ce919e02a1 33 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -8683,7 +8891,43 @@
 #30 := [asserted]: #13
 [mp #30 #47]: false
 unsat
-e070982f250a1ca780eab96adc6095281038c59d 38 0
+f5fef851c10f40408540848a3507970291adb3e5 35 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S2 S1)
+decl f4 :: S2
+#8 := f4
+#9 := (f3 f4)
+#10 := (= #9 f1)
+#11 := (not #10)
+#12 := (ite #10 #10 #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)
+#31 := (= f1 #9)
+#34 := (not #31)
+#37 := (ite #31 #31 #34)
+#40 := (iff #37 true)
+#41 := [rewrite]: #40
+#38 := (iff #12 #37)
+#35 := (iff #11 #34)
+#32 := (iff #10 #31)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#39 := [monotonicity #33 #33 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#30 := [asserted]: #13
+[mp #30 #50]: false
+unsat
+9facdecb47b87e40c25944deaa804ef85fc985e3 38 0
 #2 := false
 decl f3 :: (-> S2 S2)
 decl f4 :: S2
@@ -8722,43 +8966,7 @@
 #114 := [quant-inst]: #200
 [unit-resolution #114 #51 #50]: false
 unsat
-5566817723d9b0dab514cd1865ced56d8e166fe8 35 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f3 :: (-> S2 S1)
-decl f4 :: S2
-#8 := f4
-#9 := (f3 f4)
-#10 := (= #9 f1)
-#11 := (not #10)
-#12 := (ite #10 #10 #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)
-#31 := (= f1 #9)
-#34 := (not #31)
-#37 := (ite #31 #31 #34)
-#40 := (iff #37 true)
-#41 := [rewrite]: #40
-#38 := (iff #12 #37)
-#35 := (iff #11 #34)
-#32 := (iff #10 #31)
-#33 := [rewrite]: #32
-#36 := [monotonicity #33]: #35
-#39 := [monotonicity #33 #33 #36]: #38
-#43 := [trans #39 #41]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#30 := [asserted]: #13
-[mp #30 #50]: false
-unsat
-bc840300be3a9e2dc587394b4317175f8f11e65e 30 0
+ae9dfcc290bc6bcccab3cd3af533d10c7c03b3b8 30 0
 #2 := false
 decl f4 :: (-> S3 S4)
 decl f6 :: S3
@@ -8789,7 +8997,7 @@
 #104 := [quant-inst]: #190
 [unit-resolution #104 #41 #38]: false
 unsat
-4e0dadc89c97a124d33549e6d90d8c6fb94ffbbc 16 0
+90ce83a254a12d0f1bfd0c5eb5a99c36ab0fe295 16 0
 #2 := false
 #1 := true
 #8 := (implies true true)
@@ -8806,7 +9014,7 @@
 #26 := [asserted]: #9
 [mp #26 #35]: false
 unsat
-300f22ba0865fbc4bc611b5c5320b9fb475b953c 16 0
+9a0ddca6dee00a602bc428366efd931bcfcee94b 16 0
 #2 := false
 #8 := (implies false false)
 #9 := (not #8)
@@ -8823,7 +9031,7 @@
 #26 := [asserted]: #9
 [mp #26 #35]: false
 unsat
-5cdd14f812034153746401ccd7149e6a8e608edc 31 0
+cabaa8d0303be40a64e7064642dabce9e7bfcad7 31 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -8855,7 +9063,7 @@
 #29 := [asserted]: #12
 [mp #29 #46]: false
 unsat
-6c182dd23633c7853c1a91f152d7ab135330412d 48 0
+ac00789473bf074e49a8a6419c1f2a1042912d6a 48 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -8904,7 +9112,7 @@
 #31 := [asserted]: #14
 [mp #31 #63]: false
 unsat
-85c24c97e452e2742450de7a829a24bef0b7745e 53 0
+75052914158f379cd343f693f354895fa579a89c 53 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -8958,7 +9166,7 @@
 #31 := [asserted]: #14
 [mp #31 #68]: false
 unsat
-9c92a59e1b2801a69940e4a222a4ab6da3c64d26 56 0
+4bcd26d70bcaf24bb295031b732101a3dec2c643 56 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -9015,7 +9223,7 @@
 #32 := [asserted]: #15
 [mp #32 #71]: false
 unsat
-e45e8738077ad6b1be47d22a573712217695edc5 89 0
+7eeb56537bd13a6f6bc35096a4ddfb33dceb295f 89 0
 #2 := false
 decl f4 :: S1
 #10 := f4
@@ -9105,7 +9313,7 @@
 #86 := [not-or-elim #83]: #48
 [mp #86 #107]: false
 unsat
-54fa403d565ef2e106d2d33e4ac25062fa36ce4d 57 0
+38ce6b99e91d92d7feb75b7b5ff7006aee1a887f 57 0
 #2 := false
 decl f3 :: (-> S2 S1)
 decl f4 :: S2
@@ -9163,7 +9371,7 @@
 #59 := [not-or-elim #57]: #58
 [mp #59 #74]: false
 unsat
-65635b02b15ecbf13faf998b6e281ec4741d131a 50 0
+8e8baf35daf48781c204954ba8d7df5254aac6a8 50 0
 #2 := false
 decl f5 :: S2
 #11 := f5
@@ -9214,7 +9422,7 @@
 #62 := [not-or-elim #58]: #61
 [unit-resolution #62 #70]: false
 unsat
-317fa0f363a89944322628da895574f970f0290e 27 0
+7bbe1bf9e8878e3709a71589e39f12e31278f1b7 27 0
 #2 := false
 decl f5 :: (-> S2 S3)
 decl f4 :: S2
@@ -9242,7 +9450,7 @@
 #43 := [not-or-elim #42]: #41
 [unit-resolution #43 #51]: false
 unsat
-1d26941a5bb2830adb1f9668b97240fa88d0de2c 73 0
+a8014c2ba4ebe428717a3516d1900ca3b7591555 73 0
 #2 := false
 decl f3 :: (-> S1 S1)
 decl f4 :: S1
@@ -9316,7 +9524,7 @@
 #146 := [quant-inst]: #232
 [unit-resolution #146 #566 #74]: false
 unsat
-43323a2e96998bec6557b77d2200c04f63428dbf 106 0
+c0906c23e4b0650863a2ef0d68bafa4e06a9dd19 106 0
 #2 := false
 decl f3 :: (-> S2 S2 S1)
 decl ?v0!0 :: S2
@@ -9423,7 +9631,7 @@
 #239 := [mp #568 #238]: #254
 [unit-resolution #239 #583 #88]: false
 unsat
-c09f42a4df50b3429cb0f5ddbf56d93bf0b06b7b 66 0
+58aaefc3b25d8181c01a2139430686aeca861bf3 66 0
 #2 := false
 decl f4 :: S1
 #10 := f4
@@ -9490,7 +9698,7 @@
 #71 := [and-elim #69]: #40
 [mp #71 #85]: false
 unsat
-0e357e9971053d2577fa677046eba1d5718e4aa2 59 0
+d80d7bb97197c962c0b81d44c7a8cfd617b6ca33 59 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -9550,11 +9758,11 @@
 #37 := [asserted]: #20
 [mp #37 #72]: false
 unsat
-d654180cf0c8fb52012ec18288c7b9cba4237e00 3 0
+46acb4cd4b5353c32c529ffe509fc6f26ac2f2a1 3 0
 #2 := false
 [asserted]: false
 unsat
-499cbfe2406983d4607365f26173b22f6a49074a 18 0
+040123bf68e09d0b72cf990436bb29a623c102b8 18 0
 #2 := false
 #9 := 1::int
 #8 := 0::int
@@ -9573,7 +9781,7 @@
 #28 := [asserted]: #11
 [mp #28 #39]: false
 unsat
-7669ecc3fd6958d7a6535d8186e984760faa6558 18 0
+be1600749b493592f603ae3a7f9dcbc68d688187 18 0
 #2 := false
 #9 := 1::int
 #8 := 0::int
@@ -9592,7 +9800,7 @@
 #28 := [asserted]: #11
 [mp #28 #39]: false
 unsat
-399d7032965ae0b6a791d2007093e9c881b1b6df 18 0
+d6985ded37fcab252cac3fbb09a30e977c68973d 18 0
 #2 := false
 #9 := 2345678901::int
 #8 := 123456789::int
@@ -9611,7 +9819,7 @@
 #28 := [asserted]: #11
 [mp #28 #39]: false
 unsat
-27d5c260fdf33e6295946c76babe053e1d5624d6 30 0
+12f34f8245ed278a095c475d68eb5a5711d23981 30 0
 #2 := false
 decl f3 :: (-> int S2)
 #25 := 1::int
@@ -9642,7 +9850,7 @@
 #132 := [asserted]: #30
 [mp #132 #149]: false
 unsat
-8b231c32569080edc95ccdce9f961a9b49869ef0 225 0
+fb0035d341cb2e8ac6449dbe61b4ac5d9e12a151 225 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -9868,7 +10076,7 @@
 #616 := [unit-resolution #619 #618]: #347
 [th-lemma #617 #616 #166]: false
 unsat
-9c6198ccc440358afe5fbefeb129ea4a00cbbb0c 428 0
+f572500dcd49c30edfbceabc272b009fb11814d2 428 0
 #2 := false
 decl f4 :: (-> S2 int)
 decl f6 :: S2
@@ -10297,7 +10505,7 @@
 #393 := [unit-resolution #403 #411 #414]: #443
 [unit-resolution #393 #424]: false
 unsat
-206e819433d78c632645e8c99645a12ddf3b51c0 409 0
+1b539d34eedd00cd7cacdb9d650b014baeb31cd1 409 0
 #2 := false
 #181 := -1::int
 decl f4 :: (-> S2 int)
@@ -10707,7 +10915,7 @@
 #420 := [th-lemma]: #419
 [unit-resolution #420 #417 #412]: false
 unsat
-42b37d88064ab90bea2088cc1497480fb8953990 60 0
+b265c055659e0ea1b48e0304606789db36e05540 60 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -10768,7 +10976,7 @@
 #311 := [quant-inst]: #310
 [unit-resolution #311 #646 #151]: false
 unsat
-9798b09402a5018871b7e69145c530bf687b5055 60 0
+75c3bae150e305a0fc97df1a1e35cb97fdd88bd7 60 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -10829,7 +11037,7 @@
 #311 := [quant-inst]: #310
 [unit-resolution #311 #646 #151]: false
 unsat
-a870002129082499022465a324347d99a190812c 37 0
+c52f3166d15e1102a7ca505cd72ba484966ee318 37 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -10867,7 +11075,7 @@
 #136 := [asserted]: #34
 [mp #136 #154]: false
 unsat
-54e17ed584134deb7dd3985de3ff45b3769746ed 42 0
+b5b340366dfb8289e173cd594b95953e97e705ac 42 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -10910,68 +11118,7 @@
 #140 := [asserted]: #38
 [mp #140 #158]: false
 unsat
-6d74fb5fdf45d4b9f42d13b10663aa3e27c3c330 60 0
-#2 := false
-decl f3 :: (-> int S2)
-decl f4 :: (-> S2 int)
-decl f5 :: S2
-#25 := f5
-#26 := (f4 f5)
-#135 := (f3 #26)
-#141 := (= f5 #135)
-#146 := (not #141)
-#13 := 0::int
-#27 := (- #26 0::int)
-#28 := (f3 #27)
-#29 := (= #28 f5)
-#30 := (not #29)
-#147 := (iff #30 #146)
-#144 := (iff #29 #141)
-#138 := (= #135 f5)
-#142 := (iff #138 #141)
-#143 := [rewrite]: #142
-#139 := (iff #29 #138)
-#136 := (= #28 #135)
-#133 := (= #27 #26)
-#134 := [rewrite]: #133
-#137 := [monotonicity #134]: #136
-#140 := [monotonicity #137]: #139
-#145 := [trans #140 #143]: #144
-#148 := [monotonicity #145]: #147
-#132 := [asserted]: #30
-#151 := [mp #132 #148]: #146
-#8 := (:var 0 S2)
-#9 := (f4 #8)
-#639 := (pattern #9)
-#10 := (f3 #9)
-#48 := (= #8 #10)
-#640 := (forall (vars (?v0 S2)) (:pat #639) #48)
-#51 := (forall (vars (?v0 S2)) #48)
-#641 := (iff #51 #640)
-#643 := (iff #640 #640)
-#644 := [rewrite]: #643
-#642 := [rewrite]: #641
-#645 := [trans #642 #644]: #641
-#163 := (~ #51 #51)
-#161 := (~ #48 #48)
-#162 := [refl]: #161
-#164 := [nnf-pos #162]: #163
-#11 := (= #10 #8)
-#12 := (forall (vars (?v0 S2)) #11)
-#52 := (iff #12 #51)
-#49 := (iff #11 #48)
-#50 := [rewrite]: #49
-#53 := [quant-intro #50]: #52
-#47 := [asserted]: #12
-#56 := [mp #47 #53]: #51
-#152 := [mp~ #56 #164]: #51
-#646 := [mp #152 #645]: #640
-#224 := (not #640)
-#310 := (or #224 #141)
-#311 := [quant-inst]: #310
-[unit-resolution #311 #646 #151]: false
-unsat
-b9b9aa4c3f51dafeb0a0d1867b6ec055cde87e79 438 0
+3c1f7d30ea379c9ce2207a011fc3d11958eb42f1 438 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -11410,7 +11557,68 @@
 #404 := [unit-resolution #379 #434]: #485
 [unit-resolution #404 #396]: false
 unsat
-487dc506324bbdc4f045ceae0d9a8d2729196eb1 179 0
+b04995911f57617d06c9591edf349edadf325b74 60 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#135 := (f3 #26)
+#141 := (= f5 #135)
+#146 := (not #141)
+#13 := 0::int
+#27 := (- #26 0::int)
+#28 := (f3 #27)
+#29 := (= #28 f5)
+#30 := (not #29)
+#147 := (iff #30 #146)
+#144 := (iff #29 #141)
+#138 := (= #135 f5)
+#142 := (iff #138 #141)
+#143 := [rewrite]: #142
+#139 := (iff #29 #138)
+#136 := (= #28 #135)
+#133 := (= #27 #26)
+#134 := [rewrite]: #133
+#137 := [monotonicity #134]: #136
+#140 := [monotonicity #137]: #139
+#145 := [trans #140 #143]: #144
+#148 := [monotonicity #145]: #147
+#132 := [asserted]: #30
+#151 := [mp #132 #148]: #146
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#639 := (pattern #9)
+#10 := (f3 #9)
+#48 := (= #8 #10)
+#640 := (forall (vars (?v0 S2)) (:pat #639) #48)
+#51 := (forall (vars (?v0 S2)) #48)
+#641 := (iff #51 #640)
+#643 := (iff #640 #640)
+#644 := [rewrite]: #643
+#642 := [rewrite]: #641
+#645 := [trans #642 #644]: #641
+#163 := (~ #51 #51)
+#161 := (~ #48 #48)
+#162 := [refl]: #161
+#164 := [nnf-pos #162]: #163
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#52 := (iff #12 #51)
+#49 := (iff #11 #48)
+#50 := [rewrite]: #49
+#53 := [quant-intro #50]: #52
+#47 := [asserted]: #12
+#56 := [mp #47 #53]: #51
+#152 := [mp~ #56 #164]: #51
+#646 := [mp #152 #645]: #640
+#224 := (not #640)
+#310 := (or #224 #141)
+#311 := [quant-inst]: #310
+[unit-resolution #311 #646 #151]: false
+unsat
+2a686ca258d75e408aba2310eab7bfde718856c5 179 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -11590,7 +11798,7 @@
 #175 := [and-elim #174]: #154
 [unit-resolution #175 #587]: false
 unsat
-2f9c070703deaa5a8000b1eca828e079373a654c 321 0
+d2811f187a26b77cca78876fe4e7b2248df3c75e 321 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -11912,7 +12120,7 @@
 #181 := [and-elim #183]: #157
 [unit-resolution #181 #478]: false
 unsat
-d31a177ad3abcc23163a30e1d5b84f367c2764b8 329 0
+6750007dac6f87e186d233d8af85a2f566a05649 329 0
 #2 := false
 decl f6 :: S2
 #27 := f6
@@ -12242,41 +12450,7 @@
 #500 := [trans #499 #542]: #188
 [unit-resolution #198 #500]: false
 unsat
-2d9d46280589be884838dc154131e7cc5b93a904 33 0
-#2 := false
-decl f3 :: (-> int S2)
-#13 := 0::int
-#29 := (f3 0::int)
-decl f4 :: (-> S2 int)
-decl f5 :: S2
-#25 := f5
-#26 := (f4 f5)
-#27 := (* #26 0::int)
-#28 := (f3 #27)
-#30 := (= #28 #29)
-#31 := (not #30)
-#149 := (iff #31 false)
-#1 := true
-#144 := (not true)
-#147 := (iff #144 false)
-#148 := [rewrite]: #147
-#145 := (iff #31 #144)
-#142 := (iff #30 true)
-#137 := (= #29 #29)
-#140 := (iff #137 true)
-#141 := [rewrite]: #140
-#138 := (iff #30 #137)
-#134 := (= #27 0::int)
-#135 := [rewrite]: #134
-#136 := [monotonicity #135]: #30
-#139 := [monotonicity #136]: #138
-#143 := [trans #139 #141]: #142
-#146 := [monotonicity #143]: #145
-#150 := [trans #146 #148]: #149
-#133 := [asserted]: #31
-[mp #133 #150]: false
-unsat
-13fdb649a31033e319de9267921fa923a1c6b965 517 0
+38a43c830e9f2f628495aa4330122f2c2da981cd 517 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -12794,7 +12968,41 @@
 #282 := [unit-resolution #419 #286]: #319
 [unit-resolution #424 #282 #300]: false
 unsat
-24450ce0a41cb0a0348eb41438999f733a6e381f 33 0
+73fe8e8f8efc05a9592e80e471f1f73a8ea6b41e 33 0
+#2 := false
+decl f3 :: (-> int S2)
+#13 := 0::int
+#29 := (f3 0::int)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#27 := (* #26 0::int)
+#28 := (f3 #27)
+#30 := (= #28 #29)
+#31 := (not #30)
+#149 := (iff #31 false)
+#1 := true
+#144 := (not true)
+#147 := (iff #144 false)
+#148 := [rewrite]: #147
+#145 := (iff #31 #144)
+#142 := (iff #30 true)
+#137 := (= #29 #29)
+#140 := (iff #137 true)
+#141 := [rewrite]: #140
+#138 := (iff #30 #137)
+#134 := (= #27 0::int)
+#135 := [rewrite]: #134
+#136 := [monotonicity #135]: #30
+#139 := [monotonicity #136]: #138
+#143 := [trans #139 #141]: #142
+#146 := [monotonicity #143]: #145
+#150 := [trans #146 #148]: #149
+#133 := [asserted]: #31
+[mp #133 #150]: false
+unsat
+b8b27e6325657430dd1af6ebdf5787c6efe3284f 33 0
 #2 := false
 decl f3 :: (-> int S2)
 #13 := 0::int
@@ -12828,7 +13036,7 @@
 #133 := [asserted]: #31
 [mp #133 #150]: false
 unsat
-1e8972e2630fa2285c0c67ff5ba0a1263d55a492 60 0
+21ee0df98aa191c83f2b436328c15786df798f7a 60 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -12889,7 +13097,7 @@
 #311 := [quant-inst]: #310
 [unit-resolution #311 #646 #152]: false
 unsat
-e21662dbc702e0a68a796cfee66c613e7c9aa24d 60 0
+f2bd5534623dcef31ae5e3e9a7322f435fd34452 60 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -12950,7 +13158,7 @@
 #311 := [quant-inst]: #310
 [unit-resolution #311 #646 #152]: false
 unsat
-839b4d54676d59b13d32133c52ac13a6709c5d35 35 0
+563a522b2ffcab4b8b92a3674b4a7e71c6c68e79 35 0
 #2 := false
 decl f3 :: (-> int S2)
 #25 := 3::int
@@ -12986,7 +13194,7 @@
 #135 := [asserted]: #33
 [mp #135 #153]: false
 unsat
-68ef8375d310e3f53bec3a99bed61517fecbfd6b 250 0
+2f498bc61394e79ef8b8e82a20d5e6a57d031207 250 0
 #2 := false
 decl f5 :: (-> int S2)
 #11 := 0::int
@@ -13237,7 +13445,7 @@
 #269 := [asserted]: #57
 [unit-resolution #269 #746]: false
 unsat
-a3c5f7082796ba5aeb6ea604bf07f9672a32dbef 265 0
+344dd4c43f015bcb0632176ba256e3bea4a444a5 265 0
 #2 := false
 decl f5 :: (-> int S2)
 #11 := 0::int
@@ -13503,282 +13711,7 @@
 #271 := [asserted]: #59
 [unit-resolution #271 #738]: false
 unsat
-557fcb6227e5e97d879f09a9b899d2b5ad291311 274 0
-#2 := false
-decl f5 :: (-> int S2)
-#11 := 0::int
-#55 := (f5 0::int)
-decl f4 :: (-> int int int)
-#53 := (f4 0::int 0::int)
-#54 := (f5 #53)
-#56 := (= #54 #55)
-#831 := (= #53 0::int)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#850 := (pattern #29)
-#81 := -1::int
-#85 := (* -1::int #9)
-#82 := (* -1::int #8)
-#140 := (mod #82 #85)
-#361 := (+ #29 #140)
-#362 := (= #361 0::int)
-#30 := (mod #8 #9)
-#358 := (* -1::int #30)
-#359 := (+ #29 #358)
-#360 := (= #359 0::int)
-#107 := (<= #9 0::int)
-#103 := (<= #8 0::int)
-#300 := (or #103 #107)
-#301 := (not #300)
-#114 := (>= #8 0::int)
-#283 := (or #107 #114)
-#284 := (not #283)
-#307 := (or #284 #301)
-#363 := (ite #307 #360 #362)
-#357 := (= #29 0::int)
-#12 := (= #8 0::int)
-#364 := (ite #12 #357 #363)
-#356 := (= #8 #29)
-#13 := (= #9 0::int)
-#365 := (ite #13 #356 #364)
-#851 := (forall (vars (?v0 int) (?v1 int)) (:pat #850) #365)
-#368 := (forall (vars (?v0 int) (?v1 int)) #365)
-#854 := (iff #368 #851)
-#852 := (iff #365 #365)
-#853 := [refl]: #852
-#855 := [quant-intro #853]: #854
-#146 := (* -1::int #140)
-#325 := (ite #307 #30 #146)
-#328 := (ite #12 0::int #325)
-#331 := (ite #13 #8 #328)
-#334 := (= #29 #331)
-#337 := (forall (vars (?v0 int) (?v1 int)) #334)
-#369 := (iff #337 #368)
-#366 := (iff #334 #365)
-#367 := [rewrite]: #366
-#370 := [quant-intro #367]: #369
-#115 := (not #114)
-#108 := (not #107)
-#118 := (and #108 #115)
-#104 := (not #103)
-#111 := (and #104 #108)
-#121 := (or #111 #118)
-#166 := (ite #121 #30 #146)
-#169 := (ite #12 0::int #166)
-#172 := (ite #13 #8 #169)
-#175 := (= #29 #172)
-#178 := (forall (vars (?v0 int) (?v1 int)) #175)
-#338 := (iff #178 #337)
-#335 := (iff #175 #334)
-#332 := (= #172 #331)
-#329 := (= #169 #328)
-#326 := (= #166 #325)
-#310 := (iff #121 #307)
-#304 := (or #301 #284)
-#308 := (iff #304 #307)
-#309 := [rewrite]: #308
-#305 := (iff #121 #304)
-#302 := (iff #118 #284)
-#303 := [rewrite]: #302
-#281 := (iff #111 #301)
-#282 := [rewrite]: #281
-#306 := [monotonicity #282 #303]: #305
-#311 := [trans #306 #309]: #310
-#327 := [monotonicity #311]: #326
-#330 := [monotonicity #327]: #329
-#333 := [monotonicity #330]: #332
-#336 := [monotonicity #333]: #335
-#339 := [quant-intro #336]: #338
-#273 := (~ #178 #178)
-#270 := (~ #175 #175)
-#289 := [refl]: #270
-#274 := [nnf-pos #289]: #273
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#181 := (iff #37 #178)
-#75 := (and #16 #18)
-#78 := (or #17 #75)
-#151 := (ite #78 #30 #146)
-#154 := (ite #12 0::int #151)
-#157 := (ite #13 #8 #154)
-#160 := (= #29 #157)
-#163 := (forall (vars (?v0 int) (?v1 int)) #160)
-#179 := (iff #163 #178)
-#176 := (iff #160 #175)
-#173 := (= #157 #172)
-#170 := (= #154 #169)
-#167 := (= #151 #166)
-#122 := (iff #78 #121)
-#119 := (iff #75 #118)
-#116 := (iff #18 #115)
-#117 := [rewrite]: #116
-#109 := (iff #16 #108)
-#110 := [rewrite]: #109
-#120 := [monotonicity #110 #117]: #119
-#112 := (iff #17 #111)
-#105 := (iff #15 #104)
-#106 := [rewrite]: #105
-#113 := [monotonicity #106 #110]: #112
-#123 := [monotonicity #113 #120]: #122
-#168 := [monotonicity #123]: #167
-#171 := [monotonicity #168]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [quant-intro #177]: #179
-#164 := (iff #37 #163)
-#161 := (iff #36 #160)
-#158 := (= #35 #157)
-#155 := (= #34 #154)
-#152 := (= #33 #151)
-#149 := (= #32 #146)
-#143 := (- #140)
-#147 := (= #143 #146)
-#148 := [rewrite]: #147
-#144 := (= #32 #143)
-#141 := (= #31 #140)
-#86 := (= #23 #85)
-#87 := [rewrite]: #86
-#83 := (= #22 #82)
-#84 := [rewrite]: #83
-#142 := [monotonicity #84 #87]: #141
-#145 := [monotonicity #142]: #144
-#150 := [trans #145 #148]: #149
-#79 := (iff #20 #78)
-#76 := (iff #19 #75)
-#77 := [rewrite]: #76
-#80 := [monotonicity #77]: #79
-#153 := [monotonicity #80 #150]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#182 := [trans #165 #180]: #181
-#139 := [asserted]: #37
-#183 := [mp #139 #182]: #178
-#290 := [mp~ #183 #274]: #178
-#340 := [mp #290 #339]: #337
-#371 := [mp #340 #370]: #368
-#856 := [mp #371 #855]: #851
-#646 := (not #851)
-#788 := (or #646 #831)
-#429 := (* -1::int 0::int)
-#514 := (mod #429 #429)
-#515 := (+ #53 #514)
-#516 := (= #515 0::int)
-#507 := (mod 0::int 0::int)
-#518 := (* -1::int #507)
-#519 := (+ #53 #518)
-#447 := (= #519 0::int)
-#520 := (<= 0::int 0::int)
-#517 := (or #520 #520)
-#521 := (not #517)
-#500 := (>= 0::int 0::int)
-#835 := (or #520 #500)
-#837 := (not #835)
-#494 := (or #837 #521)
-#624 := (ite #494 #447 #516)
-#505 := (= 0::int 0::int)
-#506 := (ite #505 #831 #624)
-#838 := (= 0::int #53)
-#839 := (ite #505 #838 #506)
-#789 := (or #646 #839)
-#791 := (iff #789 #788)
-#786 := (iff #788 #788)
-#792 := [rewrite]: #786
-#644 := (iff #839 #831)
-#1 := true
-#796 := (ite true #831 #831)
-#797 := (iff #796 #831)
-#803 := [rewrite]: #797
-#801 := (iff #839 #796)
-#800 := (iff #506 #831)
-#536 := (+ #53 #507)
-#811 := (= #536 0::int)
-#808 := (ite true #831 #811)
-#798 := (iff #808 #831)
-#799 := [rewrite]: #798
-#805 := (iff #506 #808)
-#522 := (iff #624 #811)
-#526 := (ite false #447 #811)
-#806 := (iff #526 #811)
-#807 := [rewrite]: #806
-#527 := (iff #624 #526)
-#815 := (iff #516 #811)
-#810 := (= #515 #536)
-#813 := (= #514 #507)
-#435 := (= #429 0::int)
-#812 := [rewrite]: #435
-#535 := [monotonicity #812 #812]: #813
-#814 := [monotonicity #535]: #810
-#525 := [monotonicity #814]: #815
-#541 := (iff #494 false)
-#830 := (or false false)
-#539 := (iff #830 false)
-#540 := [rewrite]: #539
-#816 := (iff #494 #830)
-#829 := (iff #521 false)
-#484 := (not true)
-#822 := (iff #484 false)
-#823 := [rewrite]: #822
-#468 := (iff #521 #484)
-#826 := (iff #517 true)
-#493 := (or true true)
-#818 := (iff #493 true)
-#481 := [rewrite]: #818
-#825 := (iff #517 #493)
-#832 := (iff #520 true)
-#492 := [rewrite]: #832
-#463 := [monotonicity #492 #492]: #825
-#828 := [trans #463 #481]: #826
-#469 := [monotonicity #828]: #468
-#827 := [trans #469 #823]: #829
-#824 := (iff #837 false)
-#820 := (iff #837 #484)
-#482 := (iff #835 true)
-#834 := (iff #835 #493)
-#497 := (iff #500 true)
-#833 := [rewrite]: #497
-#477 := [monotonicity #492 #833]: #834
-#483 := [trans #477 #481]: #482
-#821 := [monotonicity #483]: #820
-#819 := [trans #821 #823]: #824
-#817 := [monotonicity #819 #827]: #816
-#542 := [trans #817 #540]: #541
-#528 := [monotonicity #542 #525]: #527
-#804 := [trans #528 #807]: #522
-#840 := (iff #505 true)
-#841 := [rewrite]: #840
-#809 := [monotonicity #841 #804]: #805
-#795 := [trans #809 #799]: #800
-#836 := (iff #838 #831)
-#842 := [rewrite]: #836
-#802 := [monotonicity #841 #842 #795]: #801
-#645 := [trans #802 #803]: #644
-#785 := [monotonicity #645]: #791
-#793 := [trans #785 #792]: #791
-#790 := [quant-inst]: #789
-#787 := [mp #790 #793]: #788
-#741 := [unit-resolution #787 #856]: #831
-#742 := [monotonicity #741]: #56
-#57 := (not #56)
-#269 := [asserted]: #57
-[unit-resolution #269 #742]: false
-unsat
-32d7b5a9ad9a19e13efcf9a11e88fc7fa8b6d32d 287 0
+426e56a2fa6cae689a233b52c380ff3e1f4c5d0f 287 0
 #2 := false
 decl f5 :: (-> int S2)
 #11 := 0::int
@@ -14066,329 +13999,7 @@
 #270 := [asserted]: #58
 [unit-resolution #270 #691]: false
 unsat
-c5c377ca97ceb2064a54831562497528f636353d 321 0
-#2 := false
-decl f5 :: (-> int S2)
-decl f4 :: (-> int int int)
-#11 := 0::int
-decl f6 :: (-> S2 int)
-decl f7 :: S2
-#53 := f7
-#54 := (f6 f7)
-#55 := (f4 #54 0::int)
-#56 := (f5 #55)
-#271 := (= f7 #56)
-#795 := (f5 #54)
-#772 := (= #795 #56)
-#771 := (= #56 #795)
-#768 := (= #55 #54)
-#848 := (= #54 #55)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#858 := (pattern #29)
-#82 := -1::int
-#86 := (* -1::int #9)
-#83 := (* -1::int #8)
-#141 := (mod #83 #86)
-#369 := (+ #29 #141)
-#370 := (= #369 0::int)
-#30 := (mod #8 #9)
-#366 := (* -1::int #30)
-#367 := (+ #29 #366)
-#368 := (= #367 0::int)
-#108 := (<= #9 0::int)
-#104 := (<= #8 0::int)
-#308 := (or #104 #108)
-#309 := (not #308)
-#115 := (>= #8 0::int)
-#291 := (or #108 #115)
-#292 := (not #291)
-#315 := (or #292 #309)
-#371 := (ite #315 #368 #370)
-#365 := (= #29 0::int)
-#12 := (= #8 0::int)
-#372 := (ite #12 #365 #371)
-#364 := (= #8 #29)
-#13 := (= #9 0::int)
-#373 := (ite #13 #364 #372)
-#859 := (forall (vars (?v0 int) (?v1 int)) (:pat #858) #373)
-#376 := (forall (vars (?v0 int) (?v1 int)) #373)
-#862 := (iff #376 #859)
-#860 := (iff #373 #373)
-#861 := [refl]: #860
-#863 := [quant-intro #861]: #862
-#147 := (* -1::int #141)
-#333 := (ite #315 #30 #147)
-#336 := (ite #12 0::int #333)
-#339 := (ite #13 #8 #336)
-#342 := (= #29 #339)
-#345 := (forall (vars (?v0 int) (?v1 int)) #342)
-#377 := (iff #345 #376)
-#374 := (iff #342 #373)
-#375 := [rewrite]: #374
-#378 := [quant-intro #375]: #377
-#116 := (not #115)
-#109 := (not #108)
-#119 := (and #109 #116)
-#105 := (not #104)
-#112 := (and #105 #109)
-#122 := (or #112 #119)
-#167 := (ite #122 #30 #147)
-#170 := (ite #12 0::int #167)
-#173 := (ite #13 #8 #170)
-#176 := (= #29 #173)
-#179 := (forall (vars (?v0 int) (?v1 int)) #176)
-#346 := (iff #179 #345)
-#343 := (iff #176 #342)
-#340 := (= #173 #339)
-#337 := (= #170 #336)
-#334 := (= #167 #333)
-#318 := (iff #122 #315)
-#312 := (or #309 #292)
-#316 := (iff #312 #315)
-#317 := [rewrite]: #316
-#313 := (iff #122 #312)
-#310 := (iff #119 #292)
-#311 := [rewrite]: #310
-#289 := (iff #112 #309)
-#290 := [rewrite]: #289
-#314 := [monotonicity #290 #311]: #313
-#319 := [trans #314 #317]: #318
-#335 := [monotonicity #319]: #334
-#338 := [monotonicity #335]: #337
-#341 := [monotonicity #338]: #340
-#344 := [monotonicity #341]: #343
-#347 := [quant-intro #344]: #346
-#281 := (~ #179 #179)
-#277 := (~ #176 #176)
-#297 := [refl]: #277
-#282 := [nnf-pos #297]: #281
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#182 := (iff #37 #179)
-#76 := (and #16 #18)
-#79 := (or #17 #76)
-#152 := (ite #79 #30 #147)
-#155 := (ite #12 0::int #152)
-#158 := (ite #13 #8 #155)
-#161 := (= #29 #158)
-#164 := (forall (vars (?v0 int) (?v1 int)) #161)
-#180 := (iff #164 #179)
-#177 := (iff #161 #176)
-#174 := (= #158 #173)
-#171 := (= #155 #170)
-#168 := (= #152 #167)
-#123 := (iff #79 #122)
-#120 := (iff #76 #119)
-#117 := (iff #18 #116)
-#118 := [rewrite]: #117
-#110 := (iff #16 #109)
-#111 := [rewrite]: #110
-#121 := [monotonicity #111 #118]: #120
-#113 := (iff #17 #112)
-#106 := (iff #15 #105)
-#107 := [rewrite]: #106
-#114 := [monotonicity #107 #111]: #113
-#124 := [monotonicity #114 #121]: #123
-#169 := [monotonicity #124]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [quant-intro #178]: #180
-#165 := (iff #37 #164)
-#162 := (iff #36 #161)
-#159 := (= #35 #158)
-#156 := (= #34 #155)
-#153 := (= #33 #152)
-#150 := (= #32 #147)
-#144 := (- #141)
-#148 := (= #144 #147)
-#149 := [rewrite]: #148
-#145 := (= #32 #144)
-#142 := (= #31 #141)
-#87 := (= #23 #86)
-#88 := [rewrite]: #87
-#84 := (= #22 #83)
-#85 := [rewrite]: #84
-#143 := [monotonicity #85 #88]: #142
-#146 := [monotonicity #143]: #145
-#151 := [trans #146 #149]: #150
-#80 := (iff #20 #79)
-#77 := (iff #19 #76)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#154 := [monotonicity #81 #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#183 := [trans #166 #181]: #182
-#140 := [asserted]: #37
-#184 := [mp #140 #183]: #179
-#298 := [mp~ #184 #282]: #179
-#348 := [mp #298 #347]: #345
-#379 := [mp #348 #378]: #376
-#864 := [mp #379 #863]: #859
-#653 := (not #859)
-#654 := (or #653 #848)
-#437 := (* -1::int 0::int)
-#522 := (* -1::int #54)
-#523 := (mod #522 #437)
-#524 := (+ #55 #523)
-#515 := (= #524 0::int)
-#526 := (mod #54 0::int)
-#527 := (* -1::int #526)
-#455 := (+ #55 #527)
-#528 := (= #455 0::int)
-#525 := (<= 0::int 0::int)
-#529 := (<= #54 0::int)
-#508 := (or #529 #525)
-#843 := (not #508)
-#845 := (>= #54 0::int)
-#502 := (or #525 #845)
-#632 := (not #502)
-#839 := (or #632 #843)
-#513 := (ite #839 #528 #515)
-#514 := (= #55 0::int)
-#846 := (= #54 0::int)
-#847 := (ite #846 #514 #513)
-#849 := (= 0::int 0::int)
-#844 := (ite #849 #848 #847)
-#796 := (or #653 #844)
-#798 := (iff #796 #654)
-#793 := (iff #654 #654)
-#794 := [rewrite]: #793
-#811 := (iff #844 #848)
-#544 := (mod #522 0::int)
-#819 := (+ #55 #544)
-#534 := (= #819 0::int)
-#806 := (ite #846 #514 #534)
-#1 := true
-#803 := (ite true #848 #806)
-#810 := (iff #803 #848)
-#805 := [rewrite]: #810
-#804 := (iff #844 #803)
-#807 := (iff #847 #806)
-#813 := (iff #513 #534)
-#814 := (ite false #528 #534)
-#812 := (iff #814 #534)
-#816 := [rewrite]: #812
-#815 := (iff #513 #814)
-#535 := (iff #515 #534)
-#823 := (= #524 #819)
-#818 := (= #523 #544)
-#821 := (= #437 0::int)
-#543 := [rewrite]: #821
-#822 := [monotonicity #543]: #818
-#533 := [monotonicity #822]: #823
-#536 := [monotonicity #533]: #535
-#443 := (iff #839 false)
-#825 := (or false false)
-#549 := (iff #825 false)
-#550 := [rewrite]: #549
-#547 := (iff #839 #825)
-#838 := (iff #843 false)
-#491 := (not true)
-#829 := (iff #491 false)
-#830 := [rewrite]: #829
-#837 := (iff #843 #491)
-#476 := (iff #508 true)
-#827 := (or #529 true)
-#834 := (iff #827 true)
-#836 := [rewrite]: #834
-#833 := (iff #508 #827)
-#500 := (iff #525 true)
-#505 := [rewrite]: #500
-#471 := [monotonicity #505]: #833
-#477 := [trans #471 #836]: #476
-#835 := [monotonicity #477]: #837
-#824 := [trans #835 #830]: #838
-#831 := (iff #632 false)
-#492 := (iff #632 #491)
-#489 := (iff #502 true)
-#841 := (or true #845)
-#485 := (iff #841 true)
-#826 := [rewrite]: #485
-#501 := (iff #502 #841)
-#842 := [monotonicity #505]: #501
-#490 := [trans #842 #826]: #489
-#828 := [monotonicity #490]: #492
-#832 := [trans #828 #830]: #831
-#548 := [monotonicity #832 #824]: #547
-#820 := [trans #548 #550]: #443
-#530 := [monotonicity #820 #536]: #815
-#817 := [trans #530 #816]: #813
-#808 := [monotonicity #817]: #807
-#850 := (iff #849 true)
-#840 := [rewrite]: #850
-#809 := [monotonicity #840 #808]: #804
-#652 := [trans #809 #805]: #811
-#799 := [monotonicity #652]: #798
-#800 := [trans #799 #794]: #798
-#797 := [quant-inst]: #796
-#801 := [mp #797 #800]: #654
-#779 := [unit-resolution #801 #864]: #848
-#769 := [symm #779]: #768
-#765 := [monotonicity #769]: #771
-#756 := [symm #765]: #772
-#802 := (= f7 #795)
-#38 := (:var 0 S2)
-#39 := (f6 #38)
-#865 := (pattern #39)
-#40 := (f5 #39)
-#186 := (= #38 #40)
-#866 := (forall (vars (?v0 S2)) (:pat #865) #186)
-#189 := (forall (vars (?v0 S2)) #186)
-#867 := (iff #189 #866)
-#869 := (iff #866 #866)
-#870 := [rewrite]: #869
-#868 := [rewrite]: #867
-#871 := [trans #868 #870]: #867
-#283 := (~ #189 #189)
-#299 := (~ #186 #186)
-#300 := [refl]: #299
-#284 := [nnf-pos #300]: #283
-#41 := (= #40 #38)
-#42 := (forall (vars (?v0 S2)) #41)
-#190 := (iff #42 #189)
-#187 := (iff #41 #186)
-#188 := [rewrite]: #187
-#191 := [quant-intro #188]: #190
-#185 := [asserted]: #42
-#194 := [mp #185 #191]: #189
-#301 := [mp~ #194 #284]: #189
-#872 := [mp #301 #871]: #866
-#634 := (not #866)
-#787 := (or #634 #802)
-#788 := [quant-inst]: #787
-#770 := [unit-resolution #788 #872]: #802
-#757 := [trans #770 #756]: #271
-#274 := (not #271)
-#57 := (= #56 f7)
-#58 := (not #57)
-#275 := (iff #58 #274)
-#272 := (iff #57 #271)
-#273 := [rewrite]: #272
-#276 := [monotonicity #273]: #275
-#270 := [asserted]: #58
-#279 := [mp #270 #276]: #274
-[unit-resolution #279 #757]: false
-unsat
-b75d0d31bfc8b1838bed57a3059c21b7ee56aaf6 287 0
+f595f2976198bb59087cfc3afdc24567f743886b 287 0
 #2 := false
 decl f5 :: (-> int S2)
 #53 := 1::int
@@ -14676,7 +14287,7 @@
 #270 := [asserted]: #58
 [unit-resolution #270 #692]: false
 unsat
-192147dde9bbf2d1457462417b1b13f9cf65afdf 298 0
+69a73700cfd90edae90cc37e225595659ec32fc1 298 0
 #2 := false
 decl f5 :: (-> int S2)
 #53 := 3::int
@@ -14975,312 +14586,7 @@
 #271 := [asserted]: #59
 [unit-resolution #271 #706]: false
 unsat
-64092e43f0b1d98a4db3438cb496ffa4c38dbe0d 304 0
-#2 := false
-decl f5 :: (-> int S2)
-#11 := 0::int
-#56 := (f5 0::int)
-decl f4 :: (-> int int int)
-#53 := 1::int
-#54 := (f4 0::int 1::int)
-#55 := (f5 #54)
-#57 := (= #55 #56)
-#838 := (= #54 0::int)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#850 := (pattern #29)
-#82 := -1::int
-#86 := (* -1::int #9)
-#83 := (* -1::int #8)
-#141 := (mod #83 #86)
-#362 := (+ #29 #141)
-#363 := (= #362 0::int)
-#30 := (mod #8 #9)
-#359 := (* -1::int #30)
-#360 := (+ #29 #359)
-#361 := (= #360 0::int)
-#108 := (<= #9 0::int)
-#104 := (<= #8 0::int)
-#301 := (or #104 #108)
-#302 := (not #301)
-#115 := (>= #8 0::int)
-#284 := (or #108 #115)
-#285 := (not #284)
-#308 := (or #285 #302)
-#364 := (ite #308 #361 #363)
-#358 := (= #29 0::int)
-#12 := (= #8 0::int)
-#365 := (ite #12 #358 #364)
-#357 := (= #8 #29)
-#13 := (= #9 0::int)
-#366 := (ite #13 #357 #365)
-#851 := (forall (vars (?v0 int) (?v1 int)) (:pat #850) #366)
-#369 := (forall (vars (?v0 int) (?v1 int)) #366)
-#854 := (iff #369 #851)
-#852 := (iff #366 #366)
-#853 := [refl]: #852
-#855 := [quant-intro #853]: #854
-#147 := (* -1::int #141)
-#326 := (ite #308 #30 #147)
-#329 := (ite #12 0::int #326)
-#332 := (ite #13 #8 #329)
-#335 := (= #29 #332)
-#338 := (forall (vars (?v0 int) (?v1 int)) #335)
-#370 := (iff #338 #369)
-#367 := (iff #335 #366)
-#368 := [rewrite]: #367
-#371 := [quant-intro #368]: #370
-#116 := (not #115)
-#109 := (not #108)
-#119 := (and #109 #116)
-#105 := (not #104)
-#112 := (and #105 #109)
-#122 := (or #112 #119)
-#167 := (ite #122 #30 #147)
-#170 := (ite #12 0::int #167)
-#173 := (ite #13 #8 #170)
-#176 := (= #29 #173)
-#179 := (forall (vars (?v0 int) (?v1 int)) #176)
-#339 := (iff #179 #338)
-#336 := (iff #176 #335)
-#333 := (= #173 #332)
-#330 := (= #170 #329)
-#327 := (= #167 #326)
-#311 := (iff #122 #308)
-#305 := (or #302 #285)
-#309 := (iff #305 #308)
-#310 := [rewrite]: #309
-#306 := (iff #122 #305)
-#303 := (iff #119 #285)
-#304 := [rewrite]: #303
-#282 := (iff #112 #302)
-#283 := [rewrite]: #282
-#307 := [monotonicity #283 #304]: #306
-#312 := [trans #307 #310]: #311
-#328 := [monotonicity #312]: #327
-#331 := [monotonicity #328]: #330
-#334 := [monotonicity #331]: #333
-#337 := [monotonicity #334]: #336
-#340 := [quant-intro #337]: #339
-#274 := (~ #179 #179)
-#271 := (~ #176 #176)
-#290 := [refl]: #271
-#275 := [nnf-pos #290]: #274
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#182 := (iff #37 #179)
-#76 := (and #16 #18)
-#79 := (or #17 #76)
-#152 := (ite #79 #30 #147)
-#155 := (ite #12 0::int #152)
-#158 := (ite #13 #8 #155)
-#161 := (= #29 #158)
-#164 := (forall (vars (?v0 int) (?v1 int)) #161)
-#180 := (iff #164 #179)
-#177 := (iff #161 #176)
-#174 := (= #158 #173)
-#171 := (= #155 #170)
-#168 := (= #152 #167)
-#123 := (iff #79 #122)
-#120 := (iff #76 #119)
-#117 := (iff #18 #116)
-#118 := [rewrite]: #117
-#110 := (iff #16 #109)
-#111 := [rewrite]: #110
-#121 := [monotonicity #111 #118]: #120
-#113 := (iff #17 #112)
-#106 := (iff #15 #105)
-#107 := [rewrite]: #106
-#114 := [monotonicity #107 #111]: #113
-#124 := [monotonicity #114 #121]: #123
-#169 := [monotonicity #124]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [quant-intro #178]: #180
-#165 := (iff #37 #164)
-#162 := (iff #36 #161)
-#159 := (= #35 #158)
-#156 := (= #34 #155)
-#153 := (= #33 #152)
-#150 := (= #32 #147)
-#144 := (- #141)
-#148 := (= #144 #147)
-#149 := [rewrite]: #148
-#145 := (= #32 #144)
-#142 := (= #31 #141)
-#87 := (= #23 #86)
-#88 := [rewrite]: #87
-#84 := (= #22 #83)
-#85 := [rewrite]: #84
-#143 := [monotonicity #85 #88]: #142
-#146 := [monotonicity #143]: #145
-#151 := [trans #146 #149]: #150
-#80 := (iff #20 #79)
-#77 := (iff #19 #76)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#154 := [monotonicity #81 #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#183 := [trans #166 #181]: #182
-#140 := [asserted]: #37
-#184 := [mp #140 #183]: #179
-#291 := [mp~ #184 #275]: #179
-#341 := [mp #291 #340]: #338
-#372 := [mp #341 #371]: #369
-#856 := [mp #372 #855]: #851
-#676 := (not #851)
-#678 := (or #676 #838)
-#430 := (* -1::int 1::int)
-#514 := (* -1::int 0::int)
-#515 := (mod #514 #430)
-#516 := (+ #54 #515)
-#507 := (= #516 0::int)
-#518 := (mod 0::int 1::int)
-#519 := (* -1::int #518)
-#520 := (+ #54 #519)
-#517 := (= #520 0::int)
-#521 := (<= 1::int 0::int)
-#500 := (<= 0::int 0::int)
-#835 := (or #500 #521)
-#837 := (not #835)
-#494 := (>= 0::int 0::int)
-#624 := (or #521 #494)
-#831 := (not #624)
-#505 := (or #831 #837)
-#506 := (ite #505 #517 #507)
-#839 := (= 0::int 0::int)
-#840 := (ite #839 #838 #506)
-#841 := (= 0::int #54)
-#836 := (= 1::int 0::int)
-#842 := (ite #836 #841 #840)
-#679 := (or #676 #842)
-#680 := (iff #679 #678)
-#682 := (iff #678 #678)
-#683 := [rewrite]: #682
-#776 := (iff #842 #838)
-#625 := (ite false #838 #838)
-#780 := (iff #625 #838)
-#782 := [rewrite]: #780
-#772 := (iff #842 #625)
-#775 := (iff #840 #838)
-#1 := true
-#784 := (ite true #838 #838)
-#668 := (iff #784 #838)
-#627 := [rewrite]: #668
-#666 := (iff #840 #784)
-#783 := (iff #506 #838)
-#626 := (iff #506 #625)
-#794 := (iff #507 #838)
-#793 := (= #516 #54)
-#809 := (+ #54 0::int)
-#800 := (= #809 #54)
-#795 := [rewrite]: #800
-#786 := (= #516 #809)
-#791 := (= #515 0::int)
-#645 := (mod 0::int -1::int)
-#789 := (= #645 0::int)
-#790 := [rewrite]: #789
-#646 := (= #515 #645)
-#803 := (= #430 -1::int)
-#644 := [rewrite]: #803
-#522 := (= #514 0::int)
-#804 := [rewrite]: #522
-#788 := [monotonicity #804 #644]: #646
-#785 := [trans #788 #790]: #791
-#792 := [monotonicity #785]: #786
-#787 := [trans #792 #795]: #793
-#623 := [monotonicity #787]: #794
-#802 := (iff #517 #838)
-#796 := (= #520 #54)
-#798 := (= #520 #809)
-#808 := (= #519 0::int)
-#806 := (= #519 #514)
-#527 := (= #518 0::int)
-#528 := [rewrite]: #527
-#807 := [monotonicity #528]: #806
-#805 := [trans #807 #804]: #808
-#799 := [monotonicity #805]: #798
-#801 := [trans #799 #795]: #796
-#797 := [monotonicity #801]: #802
-#525 := (iff #505 false)
-#536 := (or false false)
-#811 := (iff #536 false)
-#815 := [rewrite]: #811
-#810 := (iff #505 #536)
-#813 := (iff #837 false)
-#819 := (not true)
-#826 := (iff #819 false)
-#828 := [rewrite]: #826
-#436 := (iff #837 #819)
-#541 := (iff #835 true)
-#830 := (or true false)
-#539 := (iff #830 true)
-#540 := [rewrite]: #539
-#816 := (iff #835 #830)
-#477 := (iff #521 false)
-#818 := [rewrite]: #477
-#829 := (iff #500 true)
-#827 := [rewrite]: #829
-#817 := [monotonicity #827 #818]: #816
-#542 := [trans #817 #540]: #541
-#812 := [monotonicity #542]: #436
-#535 := [trans #812 #828]: #813
-#468 := (iff #831 false)
-#825 := (iff #831 #819)
-#823 := (iff #624 true)
-#483 := (or false true)
-#821 := (iff #483 true)
-#822 := [rewrite]: #821
-#484 := (iff #624 #483)
-#481 := (iff #494 true)
-#482 := [rewrite]: #481
-#820 := [monotonicity #818 #482]: #484
-#824 := [trans #820 #822]: #823
-#463 := [monotonicity #824]: #825
-#469 := [trans #463 #828]: #468
-#814 := [monotonicity #469 #535]: #810
-#526 := [trans #814 #815]: #525
-#779 := [monotonicity #526 #797 #623]: #626
-#781 := [trans #779 #782]: #783
-#493 := (iff #839 true)
-#834 := [rewrite]: #493
-#667 := [monotonicity #834 #781]: #666
-#677 := [trans #667 #627]: #775
-#497 := (iff #841 #838)
-#833 := [rewrite]: #497
-#832 := (iff #836 false)
-#492 := [rewrite]: #832
-#773 := [monotonicity #492 #833 #677]: #772
-#661 := [trans #773 #782]: #776
-#681 := [monotonicity #661]: #680
-#684 := [trans #681 #683]: #680
-#672 := [quant-inst]: #679
-#777 := [mp #672 #684]: #678
-#712 := [unit-resolution #777 #856]: #838
-#708 := [monotonicity #712]: #57
-#58 := (not #57)
-#270 := [asserted]: #58
-[unit-resolution #270 #708]: false
-unsat
-9ffddad65860c13b15f4fc36ad26084e810a67ad 360 0
+4183c3ff4a9f3923626099be345775dc19db2d14 360 0
 #2 := false
 decl f5 :: (-> int S2)
 decl f3 :: (-> int int int)
@@ -15641,310 +14947,7 @@
 #557 := [trans #620 #572]: #272
 [unit-resolution #280 #557]: false
 unsat
-d5a593ec8919de39ee6c16ac3310bcb1eb62e0ae 302 0
-#2 := false
-decl f5 :: (-> int S2)
-#11 := 0::int
-#56 := (f5 0::int)
-decl f4 :: (-> int int int)
-#53 := 1::int
-#54 := (f4 1::int 1::int)
-#55 := (f5 #54)
-#57 := (= #55 #56)
-#505 := (= #54 0::int)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#850 := (pattern #29)
-#82 := -1::int
-#86 := (* -1::int #9)
-#83 := (* -1::int #8)
-#141 := (mod #83 #86)
-#362 := (+ #29 #141)
-#363 := (= #362 0::int)
-#30 := (mod #8 #9)
-#359 := (* -1::int #30)
-#360 := (+ #29 #359)
-#361 := (= #360 0::int)
-#108 := (<= #9 0::int)
-#104 := (<= #8 0::int)
-#301 := (or #104 #108)
-#302 := (not #301)
-#115 := (>= #8 0::int)
-#284 := (or #108 #115)
-#285 := (not #284)
-#308 := (or #285 #302)
-#364 := (ite #308 #361 #363)
-#358 := (= #29 0::int)
-#12 := (= #8 0::int)
-#365 := (ite #12 #358 #364)
-#357 := (= #8 #29)
-#13 := (= #9 0::int)
-#366 := (ite #13 #357 #365)
-#851 := (forall (vars (?v0 int) (?v1 int)) (:pat #850) #366)
-#369 := (forall (vars (?v0 int) (?v1 int)) #366)
-#854 := (iff #369 #851)
-#852 := (iff #366 #366)
-#853 := [refl]: #852
-#855 := [quant-intro #853]: #854
-#147 := (* -1::int #141)
-#326 := (ite #308 #30 #147)
-#329 := (ite #12 0::int #326)
-#332 := (ite #13 #8 #329)
-#335 := (= #29 #332)
-#338 := (forall (vars (?v0 int) (?v1 int)) #335)
-#370 := (iff #338 #369)
-#367 := (iff #335 #366)
-#368 := [rewrite]: #367
-#371 := [quant-intro #368]: #370
-#116 := (not #115)
-#109 := (not #108)
-#119 := (and #109 #116)
-#105 := (not #104)
-#112 := (and #105 #109)
-#122 := (or #112 #119)
-#167 := (ite #122 #30 #147)
-#170 := (ite #12 0::int #167)
-#173 := (ite #13 #8 #170)
-#176 := (= #29 #173)
-#179 := (forall (vars (?v0 int) (?v1 int)) #176)
-#339 := (iff #179 #338)
-#336 := (iff #176 #335)
-#333 := (= #173 #332)
-#330 := (= #170 #329)
-#327 := (= #167 #326)
-#311 := (iff #122 #308)
-#305 := (or #302 #285)
-#309 := (iff #305 #308)
-#310 := [rewrite]: #309
-#306 := (iff #122 #305)
-#303 := (iff #119 #285)
-#304 := [rewrite]: #303
-#282 := (iff #112 #302)
-#283 := [rewrite]: #282
-#307 := [monotonicity #283 #304]: #306
-#312 := [trans #307 #310]: #311
-#328 := [monotonicity #312]: #327
-#331 := [monotonicity #328]: #330
-#334 := [monotonicity #331]: #333
-#337 := [monotonicity #334]: #336
-#340 := [quant-intro #337]: #339
-#274 := (~ #179 #179)
-#271 := (~ #176 #176)
-#290 := [refl]: #271
-#275 := [nnf-pos #290]: #274
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#182 := (iff #37 #179)
-#76 := (and #16 #18)
-#79 := (or #17 #76)
-#152 := (ite #79 #30 #147)
-#155 := (ite #12 0::int #152)
-#158 := (ite #13 #8 #155)
-#161 := (= #29 #158)
-#164 := (forall (vars (?v0 int) (?v1 int)) #161)
-#180 := (iff #164 #179)
-#177 := (iff #161 #176)
-#174 := (= #158 #173)
-#171 := (= #155 #170)
-#168 := (= #152 #167)
-#123 := (iff #79 #122)
-#120 := (iff #76 #119)
-#117 := (iff #18 #116)
-#118 := [rewrite]: #117
-#110 := (iff #16 #109)
-#111 := [rewrite]: #110
-#121 := [monotonicity #111 #118]: #120
-#113 := (iff #17 #112)
-#106 := (iff #15 #105)
-#107 := [rewrite]: #106
-#114 := [monotonicity #107 #111]: #113
-#124 := [monotonicity #114 #121]: #123
-#169 := [monotonicity #124]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [quant-intro #178]: #180
-#165 := (iff #37 #164)
-#162 := (iff #36 #161)
-#159 := (= #35 #158)
-#156 := (= #34 #155)
-#153 := (= #33 #152)
-#150 := (= #32 #147)
-#144 := (- #141)
-#148 := (= #144 #147)
-#149 := [rewrite]: #148
-#145 := (= #32 #144)
-#142 := (= #31 #141)
-#87 := (= #23 #86)
-#88 := [rewrite]: #87
-#84 := (= #22 #83)
-#85 := [rewrite]: #84
-#143 := [monotonicity #85 #88]: #142
-#146 := [monotonicity #143]: #145
-#151 := [trans #146 #149]: #150
-#80 := (iff #20 #79)
-#77 := (iff #19 #76)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#154 := [monotonicity #81 #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#183 := [trans #166 #181]: #182
-#140 := [asserted]: #37
-#184 := [mp #140 #183]: #179
-#291 := [mp~ #184 #275]: #179
-#341 := [mp #291 #340]: #338
-#372 := [mp #341 #371]: #369
-#856 := [mp #372 #855]: #851
-#776 := (not #851)
-#661 := (or #776 #505)
-#430 := (* -1::int 1::int)
-#514 := (mod #430 #430)
-#515 := (+ #54 #514)
-#516 := (= #515 0::int)
-#507 := (mod 1::int 1::int)
-#518 := (* -1::int #507)
-#519 := (+ #54 #518)
-#520 := (= #519 0::int)
-#517 := (<= 1::int 0::int)
-#521 := (or #517 #517)
-#500 := (not #521)
-#835 := (>= 1::int 0::int)
-#837 := (or #517 #835)
-#494 := (not #837)
-#624 := (or #494 #500)
-#831 := (ite #624 #520 #516)
-#506 := (= 1::int 0::int)
-#838 := (ite #506 #505 #831)
-#839 := (= 1::int #54)
-#840 := (ite #506 #839 #838)
-#676 := (or #776 #840)
-#679 := (iff #676 #661)
-#680 := (iff #661 #661)
-#681 := [rewrite]: #680
-#772 := (iff #840 #505)
-#832 := (= #54 1::int)
-#667 := (ite false #832 #505)
-#775 := (iff #667 #505)
-#677 := [rewrite]: #775
-#668 := (iff #840 #667)
-#784 := (iff #838 #505)
-#779 := (ite false #505 #505)
-#783 := (iff #779 #505)
-#781 := [rewrite]: #783
-#780 := (iff #838 #779)
-#625 := (iff #831 #505)
-#1 := true
-#792 := (ite true #505 #505)
-#794 := (iff #792 #505)
-#623 := [rewrite]: #794
-#793 := (iff #831 #792)
-#785 := (iff #516 #505)
-#790 := (= #515 #54)
-#807 := (+ #54 0::int)
-#808 := (= #807 #54)
-#805 := [rewrite]: #808
-#788 := (= #515 #807)
-#645 := (= #514 0::int)
-#801 := (mod -1::int -1::int)
-#803 := (= #801 0::int)
-#644 := [rewrite]: #803
-#802 := (= #514 #801)
-#795 := (= #430 -1::int)
-#796 := [rewrite]: #795
-#797 := [monotonicity #796 #796]: #802
-#646 := [trans #797 #644]: #645
-#789 := [monotonicity #646]: #788
-#791 := [trans #789 #805]: #790
-#786 := [monotonicity #791]: #785
-#799 := (iff #520 #505)
-#809 := (= #519 #54)
-#522 := (= #519 #807)
-#528 := (= #518 0::int)
-#811 := (* -1::int 0::int)
-#526 := (= #811 0::int)
-#527 := [rewrite]: #526
-#815 := (= #518 #811)
-#810 := (= #507 0::int)
-#814 := [rewrite]: #810
-#525 := [monotonicity #814]: #815
-#806 := [trans #525 #527]: #528
-#804 := [monotonicity #806]: #522
-#798 := [trans #804 #805]: #809
-#800 := [monotonicity #798]: #799
-#535 := (iff #624 true)
-#477 := (or false true)
-#482 := (iff #477 true)
-#483 := [rewrite]: #482
-#812 := (iff #624 #477)
-#542 := (iff #500 true)
-#816 := (not false)
-#540 := (iff #816 true)
-#541 := [rewrite]: #540
-#817 := (iff #500 #816)
-#827 := (iff #521 false)
-#826 := (or false false)
-#469 := (iff #826 false)
-#829 := [rewrite]: #469
-#828 := (iff #521 #826)
-#497 := (iff #517 false)
-#833 := [rewrite]: #497
-#468 := [monotonicity #833 #833]: #828
-#830 := [trans #468 #829]: #827
-#539 := [monotonicity #830]: #817
-#436 := [trans #539 #541]: #542
-#825 := (iff #494 false)
-#821 := (not true)
-#824 := (iff #821 false)
-#819 := [rewrite]: #824
-#822 := (iff #494 #821)
-#484 := (iff #837 true)
-#818 := (iff #837 #477)
-#493 := (iff #835 true)
-#834 := [rewrite]: #493
-#481 := [monotonicity #833 #834]: #818
-#820 := [trans #481 #483]: #484
-#823 := [monotonicity #820]: #822
-#463 := [trans #823 #819]: #825
-#813 := [monotonicity #463 #436]: #812
-#536 := [trans #813 #483]: #535
-#787 := [monotonicity #536 #800 #786]: #793
-#626 := [trans #787 #623]: #625
-#841 := (iff #506 false)
-#836 := [rewrite]: #841
-#782 := [monotonicity #836 #626]: #780
-#666 := [trans #782 #781]: #784
-#842 := (iff #839 #832)
-#492 := [rewrite]: #842
-#627 := [monotonicity #836 #492 #666]: #668
-#773 := [trans #627 #677]: #772
-#672 := [monotonicity #773]: #679
-#682 := [trans #672 #681]: #679
-#678 := [quant-inst]: #676
-#683 := [mp #678 #682]: #661
-#703 := [unit-resolution #683 #856]: #505
-#699 := [monotonicity #703]: #57
-#58 := (not #57)
-#270 := [asserted]: #58
-[unit-resolution #270 #699]: false
-unsat
-bc318995e409f6e5340f5c18fb5eab5001ed9343 288 0
+f2f039ccfb9f8bb6046ed67b2d5f9e4965b93c1c 288 0
 #2 := false
 decl f5 :: (-> int S2)
 #11 := 0::int
@@ -16233,321 +15236,7 @@
 #270 := [asserted]: #58
 [unit-resolution #270 #692]: false
 unsat
-6860ddff5f419fe559575a6c298a4b8f50cb8ee7 313 0
-#2 := false
-decl f5 :: (-> int S2)
-#11 := 0::int
-#57 := (f5 0::int)
-decl f4 :: (-> int int int)
-#54 := 1::int
-#53 := 3::int
-#55 := (f4 3::int 1::int)
-#56 := (f5 #55)
-#58 := (= #56 #57)
-#839 := (= #55 0::int)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#851 := (pattern #29)
-#83 := -1::int
-#87 := (* -1::int #9)
-#84 := (* -1::int #8)
-#142 := (mod #84 #87)
-#363 := (+ #29 #142)
-#364 := (= #363 0::int)
-#30 := (mod #8 #9)
-#360 := (* -1::int #30)
-#361 := (+ #29 #360)
-#362 := (= #361 0::int)
-#109 := (<= #9 0::int)
-#105 := (<= #8 0::int)
-#302 := (or #105 #109)
-#303 := (not #302)
-#116 := (>= #8 0::int)
-#285 := (or #109 #116)
-#286 := (not #285)
-#309 := (or #286 #303)
-#365 := (ite #309 #362 #364)
-#359 := (= #29 0::int)
-#12 := (= #8 0::int)
-#366 := (ite #12 #359 #365)
-#358 := (= #8 #29)
-#13 := (= #9 0::int)
-#367 := (ite #13 #358 #366)
-#852 := (forall (vars (?v0 int) (?v1 int)) (:pat #851) #367)
-#370 := (forall (vars (?v0 int) (?v1 int)) #367)
-#855 := (iff #370 #852)
-#853 := (iff #367 #367)
-#854 := [refl]: #853
-#856 := [quant-intro #854]: #855
-#148 := (* -1::int #142)
-#327 := (ite #309 #30 #148)
-#330 := (ite #12 0::int #327)
-#333 := (ite #13 #8 #330)
-#336 := (= #29 #333)
-#339 := (forall (vars (?v0 int) (?v1 int)) #336)
-#371 := (iff #339 #370)
-#368 := (iff #336 #367)
-#369 := [rewrite]: #368
-#372 := [quant-intro #369]: #371
-#117 := (not #116)
-#110 := (not #109)
-#120 := (and #110 #117)
-#106 := (not #105)
-#113 := (and #106 #110)
-#123 := (or #113 #120)
-#168 := (ite #123 #30 #148)
-#171 := (ite #12 0::int #168)
-#174 := (ite #13 #8 #171)
-#177 := (= #29 #174)
-#180 := (forall (vars (?v0 int) (?v1 int)) #177)
-#340 := (iff #180 #339)
-#337 := (iff #177 #336)
-#334 := (= #174 #333)
-#331 := (= #171 #330)
-#328 := (= #168 #327)
-#312 := (iff #123 #309)
-#306 := (or #303 #286)
-#310 := (iff #306 #309)
-#311 := [rewrite]: #310
-#307 := (iff #123 #306)
-#304 := (iff #120 #286)
-#305 := [rewrite]: #304
-#283 := (iff #113 #303)
-#284 := [rewrite]: #283
-#308 := [monotonicity #284 #305]: #307
-#313 := [trans #308 #311]: #312
-#329 := [monotonicity #313]: #328
-#332 := [monotonicity #329]: #331
-#335 := [monotonicity #332]: #334
-#338 := [monotonicity #335]: #337
-#341 := [quant-intro #338]: #340
-#275 := (~ #180 #180)
-#272 := (~ #177 #177)
-#291 := [refl]: #272
-#276 := [nnf-pos #291]: #275
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#183 := (iff #37 #180)
-#77 := (and #16 #18)
-#80 := (or #17 #77)
-#153 := (ite #80 #30 #148)
-#156 := (ite #12 0::int #153)
-#159 := (ite #13 #8 #156)
-#162 := (= #29 #159)
-#165 := (forall (vars (?v0 int) (?v1 int)) #162)
-#181 := (iff #165 #180)
-#178 := (iff #162 #177)
-#175 := (= #159 #174)
-#172 := (= #156 #171)
-#169 := (= #153 #168)
-#124 := (iff #80 #123)
-#121 := (iff #77 #120)
-#118 := (iff #18 #117)
-#119 := [rewrite]: #118
-#111 := (iff #16 #110)
-#112 := [rewrite]: #111
-#122 := [monotonicity #112 #119]: #121
-#114 := (iff #17 #113)
-#107 := (iff #15 #106)
-#108 := [rewrite]: #107
-#115 := [monotonicity #108 #112]: #114
-#125 := [monotonicity #115 #122]: #124
-#170 := [monotonicity #125]: #169
-#173 := [monotonicity #170]: #172
-#176 := [monotonicity #173]: #175
-#179 := [monotonicity #176]: #178
-#182 := [quant-intro #179]: #181
-#166 := (iff #37 #165)
-#163 := (iff #36 #162)
-#160 := (= #35 #159)
-#157 := (= #34 #156)
-#154 := (= #33 #153)
-#151 := (= #32 #148)
-#145 := (- #142)
-#149 := (= #145 #148)
-#150 := [rewrite]: #149
-#146 := (= #32 #145)
-#143 := (= #31 #142)
-#88 := (= #23 #87)
-#89 := [rewrite]: #88
-#85 := (= #22 #84)
-#86 := [rewrite]: #85
-#144 := [monotonicity #86 #89]: #143
-#147 := [monotonicity #144]: #146
-#152 := [trans #147 #150]: #151
-#81 := (iff #20 #80)
-#78 := (iff #19 #77)
-#79 := [rewrite]: #78
-#82 := [monotonicity #79]: #81
-#155 := [monotonicity #82 #152]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [quant-intro #164]: #166
-#184 := [trans #167 #182]: #183
-#141 := [asserted]: #37
-#185 := [mp #141 #184]: #180
-#292 := [mp~ #185 #276]: #180
-#342 := [mp #292 #341]: #339
-#373 := [mp #342 #372]: #370
-#857 := [mp #373 #856]: #852
-#685 := (not #852)
-#778 := (or #685 #839)
-#431 := (* -1::int 1::int)
-#515 := (* -1::int 3::int)
-#516 := (mod #515 #431)
-#517 := (+ #55 #516)
-#508 := (= #517 0::int)
-#519 := (mod 3::int 1::int)
-#520 := (* -1::int #519)
-#521 := (+ #55 #520)
-#518 := (= #521 0::int)
-#522 := (<= 1::int 0::int)
-#501 := (<= 3::int 0::int)
-#836 := (or #501 #522)
-#838 := (not #836)
-#495 := (>= 3::int 0::int)
-#625 := (or #522 #495)
-#832 := (not #625)
-#506 := (or #832 #838)
-#507 := (ite #506 #518 #508)
-#840 := (= 3::int 0::int)
-#841 := (ite #840 #839 #507)
-#842 := (= 3::int #55)
-#837 := (= 1::int 0::int)
-#843 := (ite #837 #842 #841)
-#775 := (or #685 #843)
-#766 := (iff #775 #778)
-#760 := (iff #778 #778)
-#757 := [rewrite]: #760
-#683 := (iff #843 #839)
-#834 := (= #55 3::int)
-#679 := (ite false #834 #839)
-#681 := (iff #679 #839)
-#682 := [rewrite]: #681
-#680 := (iff #843 #679)
-#662 := (iff #841 #839)
-#776 := (ite false #839 #839)
-#774 := (iff #776 #839)
-#777 := [rewrite]: #774
-#678 := (iff #841 #776)
-#669 := (iff #507 #839)
-#1 := true
-#784 := (ite true #839 #839)
-#667 := (iff #784 #839)
-#668 := [rewrite]: #667
-#782 := (iff #507 #784)
-#781 := (iff #508 #839)
-#627 := (= #517 #55)
-#800 := (+ #55 0::int)
-#797 := (= #800 #55)
-#802 := [rewrite]: #797
-#624 := (= #517 #800)
-#788 := (= #516 0::int)
-#646 := -3::int
-#792 := (mod -3::int -1::int)
-#793 := (= #792 0::int)
-#794 := [rewrite]: #793
-#786 := (= #516 #792)
-#790 := (= #431 -1::int)
-#791 := [rewrite]: #790
-#647 := (= #515 -3::int)
-#789 := [rewrite]: #647
-#787 := [monotonicity #789 #791]: #786
-#795 := [trans #787 #794]: #788
-#626 := [monotonicity #795]: #624
-#780 := [trans #626 #802]: #627
-#783 := [monotonicity #780]: #781
-#804 := (iff #518 #839)
-#803 := (= #521 #55)
-#801 := (= #521 #800)
-#810 := (= #520 0::int)
-#808 := (* -1::int 0::int)
-#809 := (= #808 0::int)
-#806 := [rewrite]: #809
-#523 := (= #520 #808)
-#529 := (= #519 0::int)
-#807 := [rewrite]: #529
-#805 := [monotonicity #807]: #523
-#799 := [trans #805 #806]: #810
-#796 := [monotonicity #799]: #801
-#798 := [trans #796 #802]: #803
-#645 := [monotonicity #798]: #804
-#527 := (iff #506 true)
-#485 := (or false true)
-#823 := (iff #485 true)
-#824 := [rewrite]: #823
-#816 := (iff #506 #485)
-#815 := (iff #838 true)
-#813 := (not false)
-#537 := (iff #813 true)
-#811 := [rewrite]: #537
-#814 := (iff #838 #813)
-#543 := (iff #836 false)
-#817 := (or false false)
-#541 := (iff #817 false)
-#542 := [rewrite]: #541
-#818 := (iff #836 #817)
-#819 := (iff #522 false)
-#482 := [rewrite]: #819
-#828 := (iff #501 false)
-#831 := [rewrite]: #828
-#540 := [monotonicity #831 #482]: #818
-#437 := [trans #540 #542]: #543
-#536 := [monotonicity #437]: #814
-#812 := [trans #536 #811]: #815
-#470 := (iff #832 false)
-#826 := (not true)
-#829 := (iff #826 false)
-#469 := [rewrite]: #829
-#464 := (iff #832 #826)
-#825 := (iff #625 true)
-#821 := (iff #625 #485)
-#483 := (iff #495 true)
-#484 := [rewrite]: #483
-#822 := [monotonicity #482 #484]: #821
-#820 := [trans #822 #824]: #825
-#827 := [monotonicity #820]: #464
-#830 := [trans #827 #469]: #470
-#526 := [monotonicity #830 #812]: #816
-#528 := [trans #526 #824]: #527
-#785 := [monotonicity #528 #645 #783]: #782
-#628 := [trans #785 #668]: #669
-#835 := (iff #840 false)
-#478 := [rewrite]: #835
-#773 := [monotonicity #478 #628]: #678
-#677 := [trans #773 #777]: #662
-#498 := (iff #842 #834)
-#494 := [rewrite]: #498
-#833 := (iff #837 false)
-#493 := [rewrite]: #833
-#673 := [monotonicity #493 #494 #677]: #680
-#684 := [trans #673 #682]: #683
-#768 := [monotonicity #684]: #766
-#759 := [trans #768 #757]: #766
-#779 := [quant-inst]: #775
-#769 := [mp #779 #759]: #778
-#701 := [unit-resolution #769 #857]: #839
-#702 := [monotonicity #701]: #58
-#59 := (not #58)
-#271 := [asserted]: #59
-[unit-resolution #271 #702]: false
-unsat
-55de26cad67b2fd694b0a728f5c662e01cc56f2a 302 0
+ed1dcbda8b48a8192bb34e0311b0082775d33ed7 302 0
 #2 := false
 decl f5 :: (-> int S2)
 #11 := 0::int
@@ -16850,455 +15539,7 @@
 #271 := [asserted]: #59
 [unit-resolution #271 #702]: false
 unsat
-921cbc00d40a6ed7847a6fd4ceb1178d690d0926 447 0
-#2 := false
-#11 := 0::int
-decl f6 :: (-> S2 int)
-decl f7 :: S2
-#53 := f7
-#54 := (f6 f7)
-#496 := (>= #54 0::int)
-decl f5 :: (-> int S2)
-#762 := (f5 #54)
-#708 := (f6 #762)
-#704 := (= #708 0::int)
-#655 := (not #704)
-#841 := (= #54 0::int)
-#674 := (not #841)
-#656 := (iff #674 #655)
-#653 := (iff #841 #704)
-#651 := (iff #704 #841)
-#649 := (= #708 #54)
-#643 := (= #762 f7)
-#763 := (= f7 #762)
-#38 := (:var 0 S2)
-#39 := (f6 #38)
-#859 := (pattern #39)
-#40 := (f5 #39)
-#188 := (= #38 #40)
-#860 := (forall (vars (?v0 S2)) (:pat #859) #188)
-#191 := (forall (vars (?v0 S2)) #188)
-#861 := (iff #191 #860)
-#863 := (iff #860 #860)
-#864 := [rewrite]: #863
-#862 := [rewrite]: #861
-#865 := [trans #862 #864]: #861
-#278 := (~ #191 #191)
-#294 := (~ #188 #188)
-#295 := [refl]: #294
-#279 := [nnf-pos #295]: #278
-#41 := (= #40 #38)
-#42 := (forall (vars (?v0 S2)) #41)
-#192 := (iff #42 #191)
-#189 := (iff #41 #188)
-#190 := [rewrite]: #189
-#193 := [quant-intro #190]: #192
-#187 := [asserted]: #42
-#196 := [mp #187 #193]: #191
-#296 := [mp~ #196 #279]: #191
-#866 := [mp #296 #865]: #860
-#759 := (not #860)
-#766 := (or #759 #763)
-#750 := [quant-inst]: #766
-#688 := [unit-resolution #750 #866]: #763
-#644 := [symm #688]: #643
-#650 := [monotonicity #644]: #649
-#652 := [monotonicity #650]: #651
-#654 := [symm #652]: #653
-#657 := [monotonicity #654]: #656
-#486 := (not #496)
-#673 := [hypothesis]: #486
-#677 := (or #674 #496)
-#687 := [th-lemma]: #677
-#667 := [unit-resolution #687 #673]: #674
-#658 := [mp #667 #657]: #655
-#689 := (or #496 #704)
-#9 := (:var 0 int)
-#44 := (f5 #9)
-#867 := (pattern #44)
-#211 := (>= #9 0::int)
-#45 := (f6 #44)
-#50 := (= #45 0::int)
-#261 := (or #50 #211)
-#874 := (forall (vars (?v0 int)) (:pat #867) #261)
-#266 := (forall (vars (?v0 int)) #261)
-#877 := (iff #266 #874)
-#875 := (iff #261 #261)
-#876 := [refl]: #875
-#878 := [quant-intro #876]: #877
-#282 := (~ #266 #266)
-#300 := (~ #261 #261)
-#301 := [refl]: #300
-#283 := [nnf-pos #301]: #282
-#49 := (< #9 0::int)
-#51 := (implies #49 #50)
-#52 := (forall (vars (?v0 int)) #51)
-#269 := (iff #52 #266)
-#232 := (= 0::int #45)
-#238 := (not #49)
-#239 := (or #238 #232)
-#244 := (forall (vars (?v0 int)) #239)
-#267 := (iff #244 #266)
-#264 := (iff #239 #261)
-#258 := (or #211 #50)
-#262 := (iff #258 #261)
-#263 := [rewrite]: #262
-#259 := (iff #239 #258)
-#256 := (iff #232 #50)
-#257 := [rewrite]: #256
-#254 := (iff #238 #211)
-#214 := (not #211)
-#249 := (not #214)
-#252 := (iff #249 #211)
-#253 := [rewrite]: #252
-#250 := (iff #238 #249)
-#247 := (iff #49 #214)
-#248 := [rewrite]: #247
-#251 := [monotonicity #248]: #250
-#255 := [trans #251 #253]: #254
-#260 := [monotonicity #255 #257]: #259
-#265 := [trans #260 #263]: #264
-#268 := [quant-intro #265]: #267
-#245 := (iff #52 #244)
-#242 := (iff #51 #239)
-#235 := (implies #49 #232)
-#240 := (iff #235 #239)
-#241 := [rewrite]: #240
-#236 := (iff #51 #235)
-#233 := (iff #50 #232)
-#234 := [rewrite]: #233
-#237 := [monotonicity #234]: #236
-#243 := [trans #237 #241]: #242
-#246 := [quant-intro #243]: #245
-#270 := [trans #246 #268]: #269
-#231 := [asserted]: #52
-#271 := [mp #231 #270]: #266
-#302 := [mp~ #271 #283]: #266
-#879 := [mp #302 #878]: #874
-#729 := (not #874)
-#671 := (or #729 #496 #704)
-#709 := (or #704 #496)
-#695 := (or #729 #709)
-#662 := (iff #695 #671)
-#691 := (or #729 #689)
-#672 := (iff #691 #671)
-#631 := [rewrite]: #672
-#697 := (iff #695 #691)
-#635 := (iff #709 #689)
-#690 := [rewrite]: #635
-#665 := [monotonicity #690]: #697
-#664 := [trans #665 #631]: #662
-#696 := [quant-inst]: #695
-#666 := [mp #696 #664]: #671
-#675 := [unit-resolution #666 #879]: #689
-#676 := [unit-resolution #675 #673]: #704
-#659 := [unit-resolution #676 #658]: false
-#660 := [lemma #659]: #496
-#502 := (<= #54 0::int)
-#830 := (not #502)
-#625 := (or #486 #830 #841)
-#684 := (not #625)
-decl f4 :: (-> int int int)
-#55 := 1::int
-#56 := (f4 #54 1::int)
-#840 := (= #56 0::int)
-#760 := (not #840)
-#58 := (f5 0::int)
-#57 := (f5 #56)
-#59 := (= #57 #58)
-#645 := [hypothesis]: #840
-#661 := [monotonicity #645]: #59
-#60 := (not #59)
-#272 := [asserted]: #60
-#622 := [unit-resolution #272 #661]: false
-#623 := [lemma #622]: #760
-#632 := (or #684 #840)
-#84 := -1::int
-#516 := (* -1::int #54)
-#809 := (mod #516 -1::int)
-#810 := (+ #56 #809)
-#800 := (= #810 0::int)
-#781 := (ite #625 #840 #800)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#852 := (pattern #29)
-#88 := (* -1::int #9)
-#85 := (* -1::int #8)
-#143 := (mod #85 #88)
-#364 := (+ #29 #143)
-#365 := (= #364 0::int)
-#30 := (mod #8 #9)
-#361 := (* -1::int #30)
-#362 := (+ #29 #361)
-#363 := (= #362 0::int)
-#110 := (<= #9 0::int)
-#106 := (<= #8 0::int)
-#303 := (or #106 #110)
-#304 := (not #303)
-#117 := (>= #8 0::int)
-#286 := (or #110 #117)
-#287 := (not #286)
-#310 := (or #287 #304)
-#366 := (ite #310 #363 #365)
-#360 := (= #29 0::int)
-#12 := (= #8 0::int)
-#367 := (ite #12 #360 #366)
-#359 := (= #8 #29)
-#13 := (= #9 0::int)
-#368 := (ite #13 #359 #367)
-#853 := (forall (vars (?v0 int) (?v1 int)) (:pat #852) #368)
-#371 := (forall (vars (?v0 int) (?v1 int)) #368)
-#856 := (iff #371 #853)
-#854 := (iff #368 #368)
-#855 := [refl]: #854
-#857 := [quant-intro #855]: #856
-#149 := (* -1::int #143)
-#328 := (ite #310 #30 #149)
-#331 := (ite #12 0::int #328)
-#334 := (ite #13 #8 #331)
-#337 := (= #29 #334)
-#340 := (forall (vars (?v0 int) (?v1 int)) #337)
-#372 := (iff #340 #371)
-#369 := (iff #337 #368)
-#370 := [rewrite]: #369
-#373 := [quant-intro #370]: #372
-#118 := (not #117)
-#111 := (not #110)
-#121 := (and #111 #118)
-#107 := (not #106)
-#114 := (and #107 #111)
-#124 := (or #114 #121)
-#169 := (ite #124 #30 #149)
-#172 := (ite #12 0::int #169)
-#175 := (ite #13 #8 #172)
-#178 := (= #29 #175)
-#181 := (forall (vars (?v0 int) (?v1 int)) #178)
-#341 := (iff #181 #340)
-#338 := (iff #178 #337)
-#335 := (= #175 #334)
-#332 := (= #172 #331)
-#329 := (= #169 #328)
-#313 := (iff #124 #310)
-#307 := (or #304 #287)
-#311 := (iff #307 #310)
-#312 := [rewrite]: #311
-#308 := (iff #124 #307)
-#305 := (iff #121 #287)
-#306 := [rewrite]: #305
-#284 := (iff #114 #304)
-#285 := [rewrite]: #284
-#309 := [monotonicity #285 #306]: #308
-#314 := [trans #309 #312]: #313
-#330 := [monotonicity #314]: #329
-#333 := [monotonicity #330]: #332
-#336 := [monotonicity #333]: #335
-#339 := [monotonicity #336]: #338
-#342 := [quant-intro #339]: #341
-#276 := (~ #181 #181)
-#273 := (~ #178 #178)
-#292 := [refl]: #273
-#277 := [nnf-pos #292]: #276
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#184 := (iff #37 #181)
-#78 := (and #16 #18)
-#81 := (or #17 #78)
-#154 := (ite #81 #30 #149)
-#157 := (ite #12 0::int #154)
-#160 := (ite #13 #8 #157)
-#163 := (= #29 #160)
-#166 := (forall (vars (?v0 int) (?v1 int)) #163)
-#182 := (iff #166 #181)
-#179 := (iff #163 #178)
-#176 := (= #160 #175)
-#173 := (= #157 #172)
-#170 := (= #154 #169)
-#125 := (iff #81 #124)
-#122 := (iff #78 #121)
-#119 := (iff #18 #118)
-#120 := [rewrite]: #119
-#112 := (iff #16 #111)
-#113 := [rewrite]: #112
-#123 := [monotonicity #113 #120]: #122
-#115 := (iff #17 #114)
-#108 := (iff #15 #107)
-#109 := [rewrite]: #108
-#116 := [monotonicity #109 #113]: #115
-#126 := [monotonicity #116 #123]: #125
-#171 := [monotonicity #126]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [quant-intro #180]: #182
-#167 := (iff #37 #166)
-#164 := (iff #36 #163)
-#161 := (= #35 #160)
-#158 := (= #34 #157)
-#155 := (= #33 #154)
-#152 := (= #32 #149)
-#146 := (- #143)
-#150 := (= #146 #149)
-#151 := [rewrite]: #150
-#147 := (= #32 #146)
-#144 := (= #31 #143)
-#89 := (= #23 #88)
-#90 := [rewrite]: #89
-#86 := (= #22 #85)
-#87 := [rewrite]: #86
-#145 := [monotonicity #87 #90]: #144
-#148 := [monotonicity #145]: #147
-#153 := [trans #148 #151]: #152
-#82 := (iff #20 #81)
-#79 := (iff #19 #78)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#156 := [monotonicity #83 #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [monotonicity #162]: #164
-#168 := [quant-intro #165]: #167
-#185 := [trans #168 #183]: #184
-#142 := [asserted]: #37
-#186 := [mp #142 #185]: #181
-#293 := [mp~ #186 #277]: #181
-#343 := [mp #293 #342]: #340
-#374 := [mp #343 #373]: #371
-#858 := [mp #374 #857]: #853
-#786 := (not #853)
-#668 := (or #786 #781)
-#432 := (* -1::int 1::int)
-#517 := (mod #516 #432)
-#518 := (+ #56 #517)
-#509 := (= #518 0::int)
-#520 := (mod #54 1::int)
-#521 := (* -1::int #520)
-#522 := (+ #56 #521)
-#519 := (= #522 0::int)
-#523 := (<= 1::int 0::int)
-#837 := (or #502 #523)
-#839 := (not #837)
-#626 := (or #523 #496)
-#833 := (not #626)
-#507 := (or #833 #839)
-#508 := (ite #507 #519 #509)
-#842 := (ite #841 #840 #508)
-#843 := (= #54 #56)
-#838 := (= 1::int 0::int)
-#844 := (ite #838 #843 #842)
-#669 := (or #786 #844)
-#629 := (iff #669 #668)
-#679 := (iff #668 #668)
-#774 := [rewrite]: #679
-#785 := (iff #844 #781)
-#831 := (or #486 #830)
-#646 := (or #831 #841)
-#647 := (ite #646 #840 #800)
-#782 := (iff #647 #781)
-#627 := (iff #646 #625)
-#628 := [rewrite]: #627
-#784 := [monotonicity #628]: #782
-#789 := (iff #844 #647)
-#793 := (ite false #843 #647)
-#794 := (iff #793 #647)
-#795 := [rewrite]: #794
-#787 := (iff #844 #793)
-#791 := (iff #842 #647)
-#797 := (ite #831 #840 #800)
-#804 := (ite #841 #840 #797)
-#648 := (iff #804 #647)
-#790 := [rewrite]: #648
-#799 := (iff #842 #804)
-#798 := (iff #508 #797)
-#801 := (iff #509 #800)
-#807 := (= #518 #810)
-#524 := (= #517 #809)
-#530 := (= #432 -1::int)
-#808 := [rewrite]: #530
-#806 := [monotonicity #808]: #524
-#811 := [monotonicity #806]: #807
-#802 := [monotonicity #811]: #801
-#528 := (iff #519 #840)
-#817 := (= #522 #56)
-#537 := (+ #56 0::int)
-#816 := (= #537 #56)
-#813 := [rewrite]: #816
-#538 := (= #522 #537)
-#814 := (= #521 0::int)
-#541 := (* -1::int 0::int)
-#544 := (= #541 0::int)
-#438 := [rewrite]: #544
-#542 := (= #521 #541)
-#818 := (= #520 0::int)
-#819 := [rewrite]: #818
-#543 := [monotonicity #819]: #542
-#815 := [trans #543 #438]: #814
-#812 := [monotonicity #815]: #538
-#527 := [trans #812 #813]: #817
-#529 := [monotonicity #527]: #528
-#829 := (iff #507 #831)
-#470 := (iff #839 #830)
-#465 := (iff #837 #502)
-#824 := (or #502 false)
-#821 := (iff #824 #502)
-#827 := [rewrite]: #821
-#825 := (iff #837 #824)
-#499 := (iff #523 false)
-#835 := [rewrite]: #499
-#826 := [monotonicity #835]: #825
-#828 := [trans #826 #827]: #465
-#471 := [monotonicity #828]: #470
-#822 := (iff #833 #486)
-#484 := (iff #626 #496)
-#495 := (or false #496)
-#820 := (iff #495 #496)
-#483 := [rewrite]: #820
-#836 := (iff #626 #495)
-#479 := [monotonicity #835]: #836
-#485 := [trans #479 #483]: #484
-#823 := [monotonicity #485]: #822
-#832 := [monotonicity #823 #471]: #829
-#803 := [monotonicity #832 #529 #802]: #798
-#805 := [monotonicity #803]: #799
-#792 := [trans #805 #790]: #791
-#834 := (iff #838 false)
-#494 := [rewrite]: #834
-#788 := [monotonicity #494 #792]: #787
-#796 := [trans #788 #795]: #789
-#783 := [trans #796 #784]: #785
-#777 := [monotonicity #783]: #629
-#775 := [trans #777 #774]: #629
-#670 := [quant-inst]: #669
-#778 := [mp #670 #775]: #668
-#630 := [unit-resolution #778 #858]: #781
-#780 := (not #781)
-#767 := (or #780 #684 #840)
-#769 := [def-axiom]: #767
-#633 := [unit-resolution #769 #630]: #632
-#634 := [unit-resolution #633 #623]: #684
-#680 := (or #625 #502)
-#681 := [def-axiom]: #680
-#636 := [unit-resolution #681 #634]: #502
-#682 := (or #625 #674)
-#683 := [def-axiom]: #682
-#637 := [unit-resolution #683 #634]: #674
-#638 := (or #841 #830 #486)
-#639 := [th-lemma]: #638
-[unit-resolution #639 #637 #636 #660]: false
-unsat
-b39f51f6b3dc27b329777d3e0b54f2354e076c4d 292 0
+8f1427496ff61632aac173e792df93e6d2f8fec2 292 0
 #2 := false
 decl f5 :: (-> int S2)
 #56 := 1::int
@@ -17591,7 +15832,7 @@
 #271 := [asserted]: #59
 [unit-resolution #271 #701]: false
 unsat
-8abb85a64c00016f8d51c89dca4f66482ca1b3ed 538 0
+d3447cf6898d788767aea97d325e514adc5f9e24 538 0
 #2 := false
 #11 := 0::int
 decl f6 :: (-> S2 int)
@@ -18130,313 +16371,7 @@
 #593 := [trans #591 #608]: #781
 [unit-resolution #661 #593]: false
 unsat
-ab86a54cb616e2b66ccbd5c4b16ac320b8b6bebe 305 0
-#2 := false
-decl f5 :: (-> int S2)
-#11 := 0::int
-#56 := (f5 0::int)
-decl f4 :: (-> int int int)
-#53 := 3::int
-#54 := (f4 0::int 3::int)
-#55 := (f5 #54)
-#57 := (= #55 #56)
-#507 := (= #54 0::int)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#851 := (pattern #29)
-#82 := -1::int
-#86 := (* -1::int #9)
-#83 := (* -1::int #8)
-#141 := (mod #83 #86)
-#362 := (+ #29 #141)
-#363 := (= #362 0::int)
-#30 := (mod #8 #9)
-#359 := (* -1::int #30)
-#360 := (+ #29 #359)
-#361 := (= #360 0::int)
-#108 := (<= #9 0::int)
-#104 := (<= #8 0::int)
-#301 := (or #104 #108)
-#302 := (not #301)
-#115 := (>= #8 0::int)
-#284 := (or #108 #115)
-#285 := (not #284)
-#308 := (or #285 #302)
-#364 := (ite #308 #361 #363)
-#358 := (= #29 0::int)
-#12 := (= #8 0::int)
-#365 := (ite #12 #358 #364)
-#357 := (= #8 #29)
-#13 := (= #9 0::int)
-#366 := (ite #13 #357 #365)
-#852 := (forall (vars (?v0 int) (?v1 int)) (:pat #851) #366)
-#369 := (forall (vars (?v0 int) (?v1 int)) #366)
-#855 := (iff #369 #852)
-#853 := (iff #366 #366)
-#854 := [refl]: #853
-#856 := [quant-intro #854]: #855
-#147 := (* -1::int #141)
-#326 := (ite #308 #30 #147)
-#329 := (ite #12 0::int #326)
-#332 := (ite #13 #8 #329)
-#335 := (= #29 #332)
-#338 := (forall (vars (?v0 int) (?v1 int)) #335)
-#370 := (iff #338 #369)
-#367 := (iff #335 #366)
-#368 := [rewrite]: #367
-#371 := [quant-intro #368]: #370
-#116 := (not #115)
-#109 := (not #108)
-#119 := (and #109 #116)
-#105 := (not #104)
-#112 := (and #105 #109)
-#122 := (or #112 #119)
-#167 := (ite #122 #30 #147)
-#170 := (ite #12 0::int #167)
-#173 := (ite #13 #8 #170)
-#176 := (= #29 #173)
-#179 := (forall (vars (?v0 int) (?v1 int)) #176)
-#339 := (iff #179 #338)
-#336 := (iff #176 #335)
-#333 := (= #173 #332)
-#330 := (= #170 #329)
-#327 := (= #167 #326)
-#311 := (iff #122 #308)
-#305 := (or #302 #285)
-#309 := (iff #305 #308)
-#310 := [rewrite]: #309
-#306 := (iff #122 #305)
-#303 := (iff #119 #285)
-#304 := [rewrite]: #303
-#282 := (iff #112 #302)
-#283 := [rewrite]: #282
-#307 := [monotonicity #283 #304]: #306
-#312 := [trans #307 #310]: #311
-#328 := [monotonicity #312]: #327
-#331 := [monotonicity #328]: #330
-#334 := [monotonicity #331]: #333
-#337 := [monotonicity #334]: #336
-#340 := [quant-intro #337]: #339
-#274 := (~ #179 #179)
-#271 := (~ #176 #176)
-#290 := [refl]: #271
-#275 := [nnf-pos #290]: #274
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#182 := (iff #37 #179)
-#76 := (and #16 #18)
-#79 := (or #17 #76)
-#152 := (ite #79 #30 #147)
-#155 := (ite #12 0::int #152)
-#158 := (ite #13 #8 #155)
-#161 := (= #29 #158)
-#164 := (forall (vars (?v0 int) (?v1 int)) #161)
-#180 := (iff #164 #179)
-#177 := (iff #161 #176)
-#174 := (= #158 #173)
-#171 := (= #155 #170)
-#168 := (= #152 #167)
-#123 := (iff #79 #122)
-#120 := (iff #76 #119)
-#117 := (iff #18 #116)
-#118 := [rewrite]: #117
-#110 := (iff #16 #109)
-#111 := [rewrite]: #110
-#121 := [monotonicity #111 #118]: #120
-#113 := (iff #17 #112)
-#106 := (iff #15 #105)
-#107 := [rewrite]: #106
-#114 := [monotonicity #107 #111]: #113
-#124 := [monotonicity #114 #121]: #123
-#169 := [monotonicity #124]: #168
-#172 := [monotonicity #169]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [quant-intro #178]: #180
-#165 := (iff #37 #164)
-#162 := (iff #36 #161)
-#159 := (= #35 #158)
-#156 := (= #34 #155)
-#153 := (= #33 #152)
-#150 := (= #32 #147)
-#144 := (- #141)
-#148 := (= #144 #147)
-#149 := [rewrite]: #148
-#145 := (= #32 #144)
-#142 := (= #31 #141)
-#87 := (= #23 #86)
-#88 := [rewrite]: #87
-#84 := (= #22 #83)
-#85 := [rewrite]: #84
-#143 := [monotonicity #85 #88]: #142
-#146 := [monotonicity #143]: #145
-#151 := [trans #146 #149]: #150
-#80 := (iff #20 #79)
-#77 := (iff #19 #76)
-#78 := [rewrite]: #77
-#81 := [monotonicity #78]: #80
-#154 := [monotonicity #81 #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [quant-intro #163]: #165
-#183 := [trans #166 #181]: #182
-#140 := [asserted]: #37
-#184 := [mp #140 #183]: #179
-#291 := [mp~ #184 #275]: #179
-#341 := [mp #291 #340]: #338
-#372 := [mp #341 #371]: #369
-#857 := [mp #372 #856]: #852
-#677 := (not #852)
-#679 := (or #677 #507)
-#430 := (* -1::int 3::int)
-#515 := (* -1::int 0::int)
-#516 := (mod #515 #430)
-#517 := (+ #54 #516)
-#508 := (= #517 0::int)
-#519 := (mod 0::int 3::int)
-#520 := (* -1::int #519)
-#448 := (+ #54 #520)
-#521 := (= #448 0::int)
-#518 := (<= 3::int 0::int)
-#522 := (<= 0::int 0::int)
-#501 := (or #522 #518)
-#836 := (not #501)
-#838 := (>= 0::int 0::int)
-#495 := (or #518 #838)
-#625 := (not #495)
-#832 := (or #625 #836)
-#506 := (ite #832 #521 #508)
-#839 := (= 0::int 0::int)
-#840 := (ite #839 #507 #506)
-#841 := (= 0::int #54)
-#842 := (= 3::int 0::int)
-#837 := (ite #842 #841 #840)
-#680 := (or #677 #837)
-#681 := (iff #680 #679)
-#683 := (iff #679 #679)
-#684 := [rewrite]: #683
-#777 := (iff #837 #507)
-#626 := (ite false #507 #507)
-#781 := (iff #626 #507)
-#783 := [rewrite]: #781
-#773 := (iff #837 #626)
-#776 := (iff #840 #507)
-#1 := true
-#785 := (ite true #507 #507)
-#669 := (iff #785 #507)
-#628 := [rewrite]: #669
-#667 := (iff #840 #785)
-#784 := (iff #506 #507)
-#627 := (iff #506 #626)
-#795 := (iff #508 #507)
-#794 := (= #517 #54)
-#806 := (+ #54 0::int)
-#800 := (= #806 #54)
-#801 := [rewrite]: #800
-#787 := (= #517 #806)
-#792 := (= #516 0::int)
-#798 := -3::int
-#646 := (mod 0::int -3::int)
-#790 := (= #646 0::int)
-#791 := [rewrite]: #790
-#647 := (= #516 #646)
-#804 := (= #430 -3::int)
-#645 := [rewrite]: #804
-#808 := (= #515 0::int)
-#523 := [rewrite]: #808
-#789 := [monotonicity #523 #645]: #647
-#786 := [trans #789 #791]: #792
-#793 := [monotonicity #786]: #787
-#788 := [trans #793 #801]: #794
-#624 := [monotonicity #788]: #795
-#802 := (iff #521 #507)
-#796 := (= #448 #54)
-#810 := (= #448 #806)
-#805 := (= #520 0::int)
-#529 := (= #520 #515)
-#527 := (= #519 0::int)
-#528 := [rewrite]: #527
-#807 := [monotonicity #528]: #529
-#809 := [trans #807 #523]: #805
-#799 := [monotonicity #809]: #810
-#797 := [trans #799 #801]: #796
-#803 := [monotonicity #797]: #802
-#816 := (iff #832 false)
-#536 := (or false false)
-#815 := (iff #536 false)
-#812 := [rewrite]: #815
-#537 := (iff #832 #536)
-#813 := (iff #836 false)
-#825 := (not true)
-#464 := (iff #825 false)
-#827 := [rewrite]: #464
-#543 := (iff #836 #825)
-#541 := (iff #501 true)
-#828 := (or true false)
-#818 := (iff #828 true)
-#540 := [rewrite]: #818
-#831 := (iff #501 #828)
-#835 := (iff #518 false)
-#478 := [rewrite]: #835
-#470 := (iff #522 true)
-#830 := [rewrite]: #470
-#817 := [monotonicity #830 #478]: #831
-#542 := [trans #817 #540]: #541
-#436 := [monotonicity #542]: #543
-#814 := [trans #436 #827]: #813
-#829 := (iff #625 false)
-#820 := (iff #625 #825)
-#823 := (iff #495 true)
-#483 := (or false true)
-#821 := (iff #483 true)
-#822 := [rewrite]: #821
-#484 := (iff #495 #483)
-#819 := (iff #838 true)
-#482 := [rewrite]: #819
-#485 := [monotonicity #478 #482]: #484
-#824 := [trans #485 #822]: #823
-#826 := [monotonicity #824]: #820
-#469 := [trans #826 #827]: #829
-#811 := [monotonicity #469 #814]: #537
-#526 := [trans #811 #812]: #816
-#780 := [monotonicity #526 #803 #624]: #627
-#782 := [trans #780 #783]: #784
-#834 := (iff #839 true)
-#494 := [rewrite]: #834
-#668 := [monotonicity #494 #782]: #667
-#678 := [trans #668 #628]: #776
-#493 := (iff #841 #507)
-#498 := [rewrite]: #493
-#843 := (iff #842 false)
-#833 := [rewrite]: #843
-#774 := [monotonicity #833 #498 #678]: #773
-#662 := [trans #774 #783]: #777
-#682 := [monotonicity #662]: #681
-#685 := [trans #682 #684]: #681
-#673 := [quant-inst]: #680
-#778 := [mp #673 #685]: #679
-#713 := [unit-resolution #778 #857]: #507
-#709 := [monotonicity #713]: #57
-#58 := (not #57)
-#270 := [asserted]: #58
-[unit-resolution #270 #709]: false
-unsat
-b9b522deb0a9246b7d18bd07eb8550de7aa969f7 605 0
+b68469389563a7c2adfa58d6c3a299893ac9030d 605 0
 #2 := false
 decl f5 :: (-> int S2)
 #11 := 0::int
@@ -19042,7 +16977,2280 @@
 #603 := [unit-resolution #535 #671]: #61
 [unit-resolution #603 #596]: false
 unsat
-a249032926dbefc0badb62f9f4f23768776070bc 328 0
+548d39bc73378ffff45c17ea9af834838e4f2aed 274 0
+#2 := false
+decl f5 :: (-> int S2)
+#11 := 0::int
+#55 := (f5 0::int)
+decl f4 :: (-> int int int)
+#53 := (f4 0::int 0::int)
+#54 := (f5 #53)
+#56 := (= #54 #55)
+#831 := (= #53 0::int)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#850 := (pattern #29)
+#81 := -1::int
+#85 := (* -1::int #9)
+#82 := (* -1::int #8)
+#140 := (mod #82 #85)
+#361 := (+ #29 #140)
+#362 := (= #361 0::int)
+#30 := (mod #8 #9)
+#358 := (* -1::int #30)
+#359 := (+ #29 #358)
+#360 := (= #359 0::int)
+#107 := (<= #9 0::int)
+#103 := (<= #8 0::int)
+#300 := (or #103 #107)
+#301 := (not #300)
+#114 := (>= #8 0::int)
+#283 := (or #107 #114)
+#284 := (not #283)
+#307 := (or #284 #301)
+#363 := (ite #307 #360 #362)
+#357 := (= #29 0::int)
+#12 := (= #8 0::int)
+#364 := (ite #12 #357 #363)
+#356 := (= #8 #29)
+#13 := (= #9 0::int)
+#365 := (ite #13 #356 #364)
+#851 := (forall (vars (?v0 int) (?v1 int)) (:pat #850) #365)
+#368 := (forall (vars (?v0 int) (?v1 int)) #365)
+#854 := (iff #368 #851)
+#852 := (iff #365 #365)
+#853 := [refl]: #852
+#855 := [quant-intro #853]: #854
+#146 := (* -1::int #140)
+#325 := (ite #307 #30 #146)
+#328 := (ite #12 0::int #325)
+#331 := (ite #13 #8 #328)
+#334 := (= #29 #331)
+#337 := (forall (vars (?v0 int) (?v1 int)) #334)
+#369 := (iff #337 #368)
+#366 := (iff #334 #365)
+#367 := [rewrite]: #366
+#370 := [quant-intro #367]: #369
+#115 := (not #114)
+#108 := (not #107)
+#118 := (and #108 #115)
+#104 := (not #103)
+#111 := (and #104 #108)
+#121 := (or #111 #118)
+#166 := (ite #121 #30 #146)
+#169 := (ite #12 0::int #166)
+#172 := (ite #13 #8 #169)
+#175 := (= #29 #172)
+#178 := (forall (vars (?v0 int) (?v1 int)) #175)
+#338 := (iff #178 #337)
+#335 := (iff #175 #334)
+#332 := (= #172 #331)
+#329 := (= #169 #328)
+#326 := (= #166 #325)
+#310 := (iff #121 #307)
+#304 := (or #301 #284)
+#308 := (iff #304 #307)
+#309 := [rewrite]: #308
+#305 := (iff #121 #304)
+#302 := (iff #118 #284)
+#303 := [rewrite]: #302
+#281 := (iff #111 #301)
+#282 := [rewrite]: #281
+#306 := [monotonicity #282 #303]: #305
+#311 := [trans #306 #309]: #310
+#327 := [monotonicity #311]: #326
+#330 := [monotonicity #327]: #329
+#333 := [monotonicity #330]: #332
+#336 := [monotonicity #333]: #335
+#339 := [quant-intro #336]: #338
+#273 := (~ #178 #178)
+#270 := (~ #175 #175)
+#289 := [refl]: #270
+#274 := [nnf-pos #289]: #273
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#181 := (iff #37 #178)
+#75 := (and #16 #18)
+#78 := (or #17 #75)
+#151 := (ite #78 #30 #146)
+#154 := (ite #12 0::int #151)
+#157 := (ite #13 #8 #154)
+#160 := (= #29 #157)
+#163 := (forall (vars (?v0 int) (?v1 int)) #160)
+#179 := (iff #163 #178)
+#176 := (iff #160 #175)
+#173 := (= #157 #172)
+#170 := (= #154 #169)
+#167 := (= #151 #166)
+#122 := (iff #78 #121)
+#119 := (iff #75 #118)
+#116 := (iff #18 #115)
+#117 := [rewrite]: #116
+#109 := (iff #16 #108)
+#110 := [rewrite]: #109
+#120 := [monotonicity #110 #117]: #119
+#112 := (iff #17 #111)
+#105 := (iff #15 #104)
+#106 := [rewrite]: #105
+#113 := [monotonicity #106 #110]: #112
+#123 := [monotonicity #113 #120]: #122
+#168 := [monotonicity #123]: #167
+#171 := [monotonicity #168]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#180 := [quant-intro #177]: #179
+#164 := (iff #37 #163)
+#161 := (iff #36 #160)
+#158 := (= #35 #157)
+#155 := (= #34 #154)
+#152 := (= #33 #151)
+#149 := (= #32 #146)
+#143 := (- #140)
+#147 := (= #143 #146)
+#148 := [rewrite]: #147
+#144 := (= #32 #143)
+#141 := (= #31 #140)
+#86 := (= #23 #85)
+#87 := [rewrite]: #86
+#83 := (= #22 #82)
+#84 := [rewrite]: #83
+#142 := [monotonicity #84 #87]: #141
+#145 := [monotonicity #142]: #144
+#150 := [trans #145 #148]: #149
+#79 := (iff #20 #78)
+#76 := (iff #19 #75)
+#77 := [rewrite]: #76
+#80 := [monotonicity #77]: #79
+#153 := [monotonicity #80 #150]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [quant-intro #162]: #164
+#182 := [trans #165 #180]: #181
+#139 := [asserted]: #37
+#183 := [mp #139 #182]: #178
+#290 := [mp~ #183 #274]: #178
+#340 := [mp #290 #339]: #337
+#371 := [mp #340 #370]: #368
+#856 := [mp #371 #855]: #851
+#646 := (not #851)
+#788 := (or #646 #831)
+#429 := (* -1::int 0::int)
+#514 := (mod #429 #429)
+#515 := (+ #53 #514)
+#516 := (= #515 0::int)
+#507 := (mod 0::int 0::int)
+#518 := (* -1::int #507)
+#519 := (+ #53 #518)
+#447 := (= #519 0::int)
+#520 := (<= 0::int 0::int)
+#517 := (or #520 #520)
+#521 := (not #517)
+#500 := (>= 0::int 0::int)
+#835 := (or #520 #500)
+#837 := (not #835)
+#494 := (or #837 #521)
+#624 := (ite #494 #447 #516)
+#505 := (= 0::int 0::int)
+#506 := (ite #505 #831 #624)
+#838 := (= 0::int #53)
+#839 := (ite #505 #838 #506)
+#789 := (or #646 #839)
+#791 := (iff #789 #788)
+#786 := (iff #788 #788)
+#792 := [rewrite]: #786
+#644 := (iff #839 #831)
+#1 := true
+#796 := (ite true #831 #831)
+#797 := (iff #796 #831)
+#803 := [rewrite]: #797
+#801 := (iff #839 #796)
+#800 := (iff #506 #831)
+#536 := (+ #53 #507)
+#811 := (= #536 0::int)
+#808 := (ite true #831 #811)
+#798 := (iff #808 #831)
+#799 := [rewrite]: #798
+#805 := (iff #506 #808)
+#522 := (iff #624 #811)
+#526 := (ite false #447 #811)
+#806 := (iff #526 #811)
+#807 := [rewrite]: #806
+#527 := (iff #624 #526)
+#815 := (iff #516 #811)
+#810 := (= #515 #536)
+#813 := (= #514 #507)
+#435 := (= #429 0::int)
+#812 := [rewrite]: #435
+#535 := [monotonicity #812 #812]: #813
+#814 := [monotonicity #535]: #810
+#525 := [monotonicity #814]: #815
+#541 := (iff #494 false)
+#830 := (or false false)
+#539 := (iff #830 false)
+#540 := [rewrite]: #539
+#816 := (iff #494 #830)
+#829 := (iff #521 false)
+#484 := (not true)
+#822 := (iff #484 false)
+#823 := [rewrite]: #822
+#468 := (iff #521 #484)
+#826 := (iff #517 true)
+#493 := (or true true)
+#818 := (iff #493 true)
+#481 := [rewrite]: #818
+#825 := (iff #517 #493)
+#832 := (iff #520 true)
+#492 := [rewrite]: #832
+#463 := [monotonicity #492 #492]: #825
+#828 := [trans #463 #481]: #826
+#469 := [monotonicity #828]: #468
+#827 := [trans #469 #823]: #829
+#824 := (iff #837 false)
+#820 := (iff #837 #484)
+#482 := (iff #835 true)
+#834 := (iff #835 #493)
+#497 := (iff #500 true)
+#833 := [rewrite]: #497
+#477 := [monotonicity #492 #833]: #834
+#483 := [trans #477 #481]: #482
+#821 := [monotonicity #483]: #820
+#819 := [trans #821 #823]: #824
+#817 := [monotonicity #819 #827]: #816
+#542 := [trans #817 #540]: #541
+#528 := [monotonicity #542 #525]: #527
+#804 := [trans #528 #807]: #522
+#840 := (iff #505 true)
+#841 := [rewrite]: #840
+#809 := [monotonicity #841 #804]: #805
+#795 := [trans #809 #799]: #800
+#836 := (iff #838 #831)
+#842 := [rewrite]: #836
+#802 := [monotonicity #841 #842 #795]: #801
+#645 := [trans #802 #803]: #644
+#785 := [monotonicity #645]: #791
+#793 := [trans #785 #792]: #791
+#790 := [quant-inst]: #789
+#787 := [mp #790 #793]: #788
+#741 := [unit-resolution #787 #856]: #831
+#742 := [monotonicity #741]: #56
+#57 := (not #56)
+#269 := [asserted]: #57
+[unit-resolution #269 #742]: false
+unsat
+2a856348a2d0d12d43659d3f8fbd60f2f395959a 321 0
+#2 := false
+decl f5 :: (-> int S2)
+decl f4 :: (-> int int int)
+#11 := 0::int
+decl f6 :: (-> S2 int)
+decl f7 :: S2
+#53 := f7
+#54 := (f6 f7)
+#55 := (f4 #54 0::int)
+#56 := (f5 #55)
+#271 := (= f7 #56)
+#795 := (f5 #54)
+#772 := (= #795 #56)
+#771 := (= #56 #795)
+#768 := (= #55 #54)
+#848 := (= #54 #55)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#858 := (pattern #29)
+#82 := -1::int
+#86 := (* -1::int #9)
+#83 := (* -1::int #8)
+#141 := (mod #83 #86)
+#369 := (+ #29 #141)
+#370 := (= #369 0::int)
+#30 := (mod #8 #9)
+#366 := (* -1::int #30)
+#367 := (+ #29 #366)
+#368 := (= #367 0::int)
+#108 := (<= #9 0::int)
+#104 := (<= #8 0::int)
+#308 := (or #104 #108)
+#309 := (not #308)
+#115 := (>= #8 0::int)
+#291 := (or #108 #115)
+#292 := (not #291)
+#315 := (or #292 #309)
+#371 := (ite #315 #368 #370)
+#365 := (= #29 0::int)
+#12 := (= #8 0::int)
+#372 := (ite #12 #365 #371)
+#364 := (= #8 #29)
+#13 := (= #9 0::int)
+#373 := (ite #13 #364 #372)
+#859 := (forall (vars (?v0 int) (?v1 int)) (:pat #858) #373)
+#376 := (forall (vars (?v0 int) (?v1 int)) #373)
+#862 := (iff #376 #859)
+#860 := (iff #373 #373)
+#861 := [refl]: #860
+#863 := [quant-intro #861]: #862
+#147 := (* -1::int #141)
+#333 := (ite #315 #30 #147)
+#336 := (ite #12 0::int #333)
+#339 := (ite #13 #8 #336)
+#342 := (= #29 #339)
+#345 := (forall (vars (?v0 int) (?v1 int)) #342)
+#377 := (iff #345 #376)
+#374 := (iff #342 #373)
+#375 := [rewrite]: #374
+#378 := [quant-intro #375]: #377
+#116 := (not #115)
+#109 := (not #108)
+#119 := (and #109 #116)
+#105 := (not #104)
+#112 := (and #105 #109)
+#122 := (or #112 #119)
+#167 := (ite #122 #30 #147)
+#170 := (ite #12 0::int #167)
+#173 := (ite #13 #8 #170)
+#176 := (= #29 #173)
+#179 := (forall (vars (?v0 int) (?v1 int)) #176)
+#346 := (iff #179 #345)
+#343 := (iff #176 #342)
+#340 := (= #173 #339)
+#337 := (= #170 #336)
+#334 := (= #167 #333)
+#318 := (iff #122 #315)
+#312 := (or #309 #292)
+#316 := (iff #312 #315)
+#317 := [rewrite]: #316
+#313 := (iff #122 #312)
+#310 := (iff #119 #292)
+#311 := [rewrite]: #310
+#289 := (iff #112 #309)
+#290 := [rewrite]: #289
+#314 := [monotonicity #290 #311]: #313
+#319 := [trans #314 #317]: #318
+#335 := [monotonicity #319]: #334
+#338 := [monotonicity #335]: #337
+#341 := [monotonicity #338]: #340
+#344 := [monotonicity #341]: #343
+#347 := [quant-intro #344]: #346
+#281 := (~ #179 #179)
+#277 := (~ #176 #176)
+#297 := [refl]: #277
+#282 := [nnf-pos #297]: #281
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#182 := (iff #37 #179)
+#76 := (and #16 #18)
+#79 := (or #17 #76)
+#152 := (ite #79 #30 #147)
+#155 := (ite #12 0::int #152)
+#158 := (ite #13 #8 #155)
+#161 := (= #29 #158)
+#164 := (forall (vars (?v0 int) (?v1 int)) #161)
+#180 := (iff #164 #179)
+#177 := (iff #161 #176)
+#174 := (= #158 #173)
+#171 := (= #155 #170)
+#168 := (= #152 #167)
+#123 := (iff #79 #122)
+#120 := (iff #76 #119)
+#117 := (iff #18 #116)
+#118 := [rewrite]: #117
+#110 := (iff #16 #109)
+#111 := [rewrite]: #110
+#121 := [monotonicity #111 #118]: #120
+#113 := (iff #17 #112)
+#106 := (iff #15 #105)
+#107 := [rewrite]: #106
+#114 := [monotonicity #107 #111]: #113
+#124 := [monotonicity #114 #121]: #123
+#169 := [monotonicity #124]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [quant-intro #178]: #180
+#165 := (iff #37 #164)
+#162 := (iff #36 #161)
+#159 := (= #35 #158)
+#156 := (= #34 #155)
+#153 := (= #33 #152)
+#150 := (= #32 #147)
+#144 := (- #141)
+#148 := (= #144 #147)
+#149 := [rewrite]: #148
+#145 := (= #32 #144)
+#142 := (= #31 #141)
+#87 := (= #23 #86)
+#88 := [rewrite]: #87
+#84 := (= #22 #83)
+#85 := [rewrite]: #84
+#143 := [monotonicity #85 #88]: #142
+#146 := [monotonicity #143]: #145
+#151 := [trans #146 #149]: #150
+#80 := (iff #20 #79)
+#77 := (iff #19 #76)
+#78 := [rewrite]: #77
+#81 := [monotonicity #78]: #80
+#154 := [monotonicity #81 #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [quant-intro #163]: #165
+#183 := [trans #166 #181]: #182
+#140 := [asserted]: #37
+#184 := [mp #140 #183]: #179
+#298 := [mp~ #184 #282]: #179
+#348 := [mp #298 #347]: #345
+#379 := [mp #348 #378]: #376
+#864 := [mp #379 #863]: #859
+#653 := (not #859)
+#654 := (or #653 #848)
+#437 := (* -1::int 0::int)
+#522 := (* -1::int #54)
+#523 := (mod #522 #437)
+#524 := (+ #55 #523)
+#515 := (= #524 0::int)
+#526 := (mod #54 0::int)
+#527 := (* -1::int #526)
+#455 := (+ #55 #527)
+#528 := (= #455 0::int)
+#525 := (<= 0::int 0::int)
+#529 := (<= #54 0::int)
+#508 := (or #529 #525)
+#843 := (not #508)
+#845 := (>= #54 0::int)
+#502 := (or #525 #845)
+#632 := (not #502)
+#839 := (or #632 #843)
+#513 := (ite #839 #528 #515)
+#514 := (= #55 0::int)
+#846 := (= #54 0::int)
+#847 := (ite #846 #514 #513)
+#849 := (= 0::int 0::int)
+#844 := (ite #849 #848 #847)
+#796 := (or #653 #844)
+#798 := (iff #796 #654)
+#793 := (iff #654 #654)
+#794 := [rewrite]: #793
+#811 := (iff #844 #848)
+#544 := (mod #522 0::int)
+#819 := (+ #55 #544)
+#534 := (= #819 0::int)
+#806 := (ite #846 #514 #534)
+#1 := true
+#803 := (ite true #848 #806)
+#810 := (iff #803 #848)
+#805 := [rewrite]: #810
+#804 := (iff #844 #803)
+#807 := (iff #847 #806)
+#813 := (iff #513 #534)
+#814 := (ite false #528 #534)
+#812 := (iff #814 #534)
+#816 := [rewrite]: #812
+#815 := (iff #513 #814)
+#535 := (iff #515 #534)
+#823 := (= #524 #819)
+#818 := (= #523 #544)
+#821 := (= #437 0::int)
+#543 := [rewrite]: #821
+#822 := [monotonicity #543]: #818
+#533 := [monotonicity #822]: #823
+#536 := [monotonicity #533]: #535
+#443 := (iff #839 false)
+#825 := (or false false)
+#549 := (iff #825 false)
+#550 := [rewrite]: #549
+#547 := (iff #839 #825)
+#838 := (iff #843 false)
+#491 := (not true)
+#829 := (iff #491 false)
+#830 := [rewrite]: #829
+#837 := (iff #843 #491)
+#476 := (iff #508 true)
+#827 := (or #529 true)
+#834 := (iff #827 true)
+#836 := [rewrite]: #834
+#833 := (iff #508 #827)
+#500 := (iff #525 true)
+#505 := [rewrite]: #500
+#471 := [monotonicity #505]: #833
+#477 := [trans #471 #836]: #476
+#835 := [monotonicity #477]: #837
+#824 := [trans #835 #830]: #838
+#831 := (iff #632 false)
+#492 := (iff #632 #491)
+#489 := (iff #502 true)
+#841 := (or true #845)
+#485 := (iff #841 true)
+#826 := [rewrite]: #485
+#501 := (iff #502 #841)
+#842 := [monotonicity #505]: #501
+#490 := [trans #842 #826]: #489
+#828 := [monotonicity #490]: #492
+#832 := [trans #828 #830]: #831
+#548 := [monotonicity #832 #824]: #547
+#820 := [trans #548 #550]: #443
+#530 := [monotonicity #820 #536]: #815
+#817 := [trans #530 #816]: #813
+#808 := [monotonicity #817]: #807
+#850 := (iff #849 true)
+#840 := [rewrite]: #850
+#809 := [monotonicity #840 #808]: #804
+#652 := [trans #809 #805]: #811
+#799 := [monotonicity #652]: #798
+#800 := [trans #799 #794]: #798
+#797 := [quant-inst]: #796
+#801 := [mp #797 #800]: #654
+#779 := [unit-resolution #801 #864]: #848
+#769 := [symm #779]: #768
+#765 := [monotonicity #769]: #771
+#756 := [symm #765]: #772
+#802 := (= f7 #795)
+#38 := (:var 0 S2)
+#39 := (f6 #38)
+#865 := (pattern #39)
+#40 := (f5 #39)
+#186 := (= #38 #40)
+#866 := (forall (vars (?v0 S2)) (:pat #865) #186)
+#189 := (forall (vars (?v0 S2)) #186)
+#867 := (iff #189 #866)
+#869 := (iff #866 #866)
+#870 := [rewrite]: #869
+#868 := [rewrite]: #867
+#871 := [trans #868 #870]: #867
+#283 := (~ #189 #189)
+#299 := (~ #186 #186)
+#300 := [refl]: #299
+#284 := [nnf-pos #300]: #283
+#41 := (= #40 #38)
+#42 := (forall (vars (?v0 S2)) #41)
+#190 := (iff #42 #189)
+#187 := (iff #41 #186)
+#188 := [rewrite]: #187
+#191 := [quant-intro #188]: #190
+#185 := [asserted]: #42
+#194 := [mp #185 #191]: #189
+#301 := [mp~ #194 #284]: #189
+#872 := [mp #301 #871]: #866
+#634 := (not #866)
+#787 := (or #634 #802)
+#788 := [quant-inst]: #787
+#770 := [unit-resolution #788 #872]: #802
+#757 := [trans #770 #756]: #271
+#274 := (not #271)
+#57 := (= #56 f7)
+#58 := (not #57)
+#275 := (iff #58 #274)
+#272 := (iff #57 #271)
+#273 := [rewrite]: #272
+#276 := [monotonicity #273]: #275
+#270 := [asserted]: #58
+#279 := [mp #270 #276]: #274
+[unit-resolution #279 #757]: false
+unsat
+42cd145e516d85b450559c9cc1b54c1ed7265de3 304 0
+#2 := false
+decl f5 :: (-> int S2)
+#11 := 0::int
+#56 := (f5 0::int)
+decl f4 :: (-> int int int)
+#53 := 1::int
+#54 := (f4 0::int 1::int)
+#55 := (f5 #54)
+#57 := (= #55 #56)
+#838 := (= #54 0::int)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#850 := (pattern #29)
+#82 := -1::int
+#86 := (* -1::int #9)
+#83 := (* -1::int #8)
+#141 := (mod #83 #86)
+#362 := (+ #29 #141)
+#363 := (= #362 0::int)
+#30 := (mod #8 #9)
+#359 := (* -1::int #30)
+#360 := (+ #29 #359)
+#361 := (= #360 0::int)
+#108 := (<= #9 0::int)
+#104 := (<= #8 0::int)
+#301 := (or #104 #108)
+#302 := (not #301)
+#115 := (>= #8 0::int)
+#284 := (or #108 #115)
+#285 := (not #284)
+#308 := (or #285 #302)
+#364 := (ite #308 #361 #363)
+#358 := (= #29 0::int)
+#12 := (= #8 0::int)
+#365 := (ite #12 #358 #364)
+#357 := (= #8 #29)
+#13 := (= #9 0::int)
+#366 := (ite #13 #357 #365)
+#851 := (forall (vars (?v0 int) (?v1 int)) (:pat #850) #366)
+#369 := (forall (vars (?v0 int) (?v1 int)) #366)
+#854 := (iff #369 #851)
+#852 := (iff #366 #366)
+#853 := [refl]: #852
+#855 := [quant-intro #853]: #854
+#147 := (* -1::int #141)
+#326 := (ite #308 #30 #147)
+#329 := (ite #12 0::int #326)
+#332 := (ite #13 #8 #329)
+#335 := (= #29 #332)
+#338 := (forall (vars (?v0 int) (?v1 int)) #335)
+#370 := (iff #338 #369)
+#367 := (iff #335 #366)
+#368 := [rewrite]: #367
+#371 := [quant-intro #368]: #370
+#116 := (not #115)
+#109 := (not #108)
+#119 := (and #109 #116)
+#105 := (not #104)
+#112 := (and #105 #109)
+#122 := (or #112 #119)
+#167 := (ite #122 #30 #147)
+#170 := (ite #12 0::int #167)
+#173 := (ite #13 #8 #170)
+#176 := (= #29 #173)
+#179 := (forall (vars (?v0 int) (?v1 int)) #176)
+#339 := (iff #179 #338)
+#336 := (iff #176 #335)
+#333 := (= #173 #332)
+#330 := (= #170 #329)
+#327 := (= #167 #326)
+#311 := (iff #122 #308)
+#305 := (or #302 #285)
+#309 := (iff #305 #308)
+#310 := [rewrite]: #309
+#306 := (iff #122 #305)
+#303 := (iff #119 #285)
+#304 := [rewrite]: #303
+#282 := (iff #112 #302)
+#283 := [rewrite]: #282
+#307 := [monotonicity #283 #304]: #306
+#312 := [trans #307 #310]: #311
+#328 := [monotonicity #312]: #327
+#331 := [monotonicity #328]: #330
+#334 := [monotonicity #331]: #333
+#337 := [monotonicity #334]: #336
+#340 := [quant-intro #337]: #339
+#274 := (~ #179 #179)
+#271 := (~ #176 #176)
+#290 := [refl]: #271
+#275 := [nnf-pos #290]: #274
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#182 := (iff #37 #179)
+#76 := (and #16 #18)
+#79 := (or #17 #76)
+#152 := (ite #79 #30 #147)
+#155 := (ite #12 0::int #152)
+#158 := (ite #13 #8 #155)
+#161 := (= #29 #158)
+#164 := (forall (vars (?v0 int) (?v1 int)) #161)
+#180 := (iff #164 #179)
+#177 := (iff #161 #176)
+#174 := (= #158 #173)
+#171 := (= #155 #170)
+#168 := (= #152 #167)
+#123 := (iff #79 #122)
+#120 := (iff #76 #119)
+#117 := (iff #18 #116)
+#118 := [rewrite]: #117
+#110 := (iff #16 #109)
+#111 := [rewrite]: #110
+#121 := [monotonicity #111 #118]: #120
+#113 := (iff #17 #112)
+#106 := (iff #15 #105)
+#107 := [rewrite]: #106
+#114 := [monotonicity #107 #111]: #113
+#124 := [monotonicity #114 #121]: #123
+#169 := [monotonicity #124]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [quant-intro #178]: #180
+#165 := (iff #37 #164)
+#162 := (iff #36 #161)
+#159 := (= #35 #158)
+#156 := (= #34 #155)
+#153 := (= #33 #152)
+#150 := (= #32 #147)
+#144 := (- #141)
+#148 := (= #144 #147)
+#149 := [rewrite]: #148
+#145 := (= #32 #144)
+#142 := (= #31 #141)
+#87 := (= #23 #86)
+#88 := [rewrite]: #87
+#84 := (= #22 #83)
+#85 := [rewrite]: #84
+#143 := [monotonicity #85 #88]: #142
+#146 := [monotonicity #143]: #145
+#151 := [trans #146 #149]: #150
+#80 := (iff #20 #79)
+#77 := (iff #19 #76)
+#78 := [rewrite]: #77
+#81 := [monotonicity #78]: #80
+#154 := [monotonicity #81 #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [quant-intro #163]: #165
+#183 := [trans #166 #181]: #182
+#140 := [asserted]: #37
+#184 := [mp #140 #183]: #179
+#291 := [mp~ #184 #275]: #179
+#341 := [mp #291 #340]: #338
+#372 := [mp #341 #371]: #369
+#856 := [mp #372 #855]: #851
+#676 := (not #851)
+#678 := (or #676 #838)
+#430 := (* -1::int 1::int)
+#514 := (* -1::int 0::int)
+#515 := (mod #514 #430)
+#516 := (+ #54 #515)
+#507 := (= #516 0::int)
+#518 := (mod 0::int 1::int)
+#519 := (* -1::int #518)
+#520 := (+ #54 #519)
+#517 := (= #520 0::int)
+#521 := (<= 1::int 0::int)
+#500 := (<= 0::int 0::int)
+#835 := (or #500 #521)
+#837 := (not #835)
+#494 := (>= 0::int 0::int)
+#624 := (or #521 #494)
+#831 := (not #624)
+#505 := (or #831 #837)
+#506 := (ite #505 #517 #507)
+#839 := (= 0::int 0::int)
+#840 := (ite #839 #838 #506)
+#841 := (= 0::int #54)
+#836 := (= 1::int 0::int)
+#842 := (ite #836 #841 #840)
+#679 := (or #676 #842)
+#680 := (iff #679 #678)
+#682 := (iff #678 #678)
+#683 := [rewrite]: #682
+#776 := (iff #842 #838)
+#625 := (ite false #838 #838)
+#780 := (iff #625 #838)
+#782 := [rewrite]: #780
+#772 := (iff #842 #625)
+#775 := (iff #840 #838)
+#1 := true
+#784 := (ite true #838 #838)
+#668 := (iff #784 #838)
+#627 := [rewrite]: #668
+#666 := (iff #840 #784)
+#783 := (iff #506 #838)
+#626 := (iff #506 #625)
+#794 := (iff #507 #838)
+#793 := (= #516 #54)
+#809 := (+ #54 0::int)
+#800 := (= #809 #54)
+#795 := [rewrite]: #800
+#786 := (= #516 #809)
+#791 := (= #515 0::int)
+#645 := (mod 0::int -1::int)
+#789 := (= #645 0::int)
+#790 := [rewrite]: #789
+#646 := (= #515 #645)
+#803 := (= #430 -1::int)
+#644 := [rewrite]: #803
+#522 := (= #514 0::int)
+#804 := [rewrite]: #522
+#788 := [monotonicity #804 #644]: #646
+#785 := [trans #788 #790]: #791
+#792 := [monotonicity #785]: #786
+#787 := [trans #792 #795]: #793
+#623 := [monotonicity #787]: #794
+#802 := (iff #517 #838)
+#796 := (= #520 #54)
+#798 := (= #520 #809)
+#808 := (= #519 0::int)
+#806 := (= #519 #514)
+#527 := (= #518 0::int)
+#528 := [rewrite]: #527
+#807 := [monotonicity #528]: #806
+#805 := [trans #807 #804]: #808
+#799 := [monotonicity #805]: #798
+#801 := [trans #799 #795]: #796
+#797 := [monotonicity #801]: #802
+#525 := (iff #505 false)
+#536 := (or false false)
+#811 := (iff #536 false)
+#815 := [rewrite]: #811
+#810 := (iff #505 #536)
+#813 := (iff #837 false)
+#819 := (not true)
+#826 := (iff #819 false)
+#828 := [rewrite]: #826
+#436 := (iff #837 #819)
+#541 := (iff #835 true)
+#830 := (or true false)
+#539 := (iff #830 true)
+#540 := [rewrite]: #539
+#816 := (iff #835 #830)
+#477 := (iff #521 false)
+#818 := [rewrite]: #477
+#829 := (iff #500 true)
+#827 := [rewrite]: #829
+#817 := [monotonicity #827 #818]: #816
+#542 := [trans #817 #540]: #541
+#812 := [monotonicity #542]: #436
+#535 := [trans #812 #828]: #813
+#468 := (iff #831 false)
+#825 := (iff #831 #819)
+#823 := (iff #624 true)
+#483 := (or false true)
+#821 := (iff #483 true)
+#822 := [rewrite]: #821
+#484 := (iff #624 #483)
+#481 := (iff #494 true)
+#482 := [rewrite]: #481
+#820 := [monotonicity #818 #482]: #484
+#824 := [trans #820 #822]: #823
+#463 := [monotonicity #824]: #825
+#469 := [trans #463 #828]: #468
+#814 := [monotonicity #469 #535]: #810
+#526 := [trans #814 #815]: #525
+#779 := [monotonicity #526 #797 #623]: #626
+#781 := [trans #779 #782]: #783
+#493 := (iff #839 true)
+#834 := [rewrite]: #493
+#667 := [monotonicity #834 #781]: #666
+#677 := [trans #667 #627]: #775
+#497 := (iff #841 #838)
+#833 := [rewrite]: #497
+#832 := (iff #836 false)
+#492 := [rewrite]: #832
+#773 := [monotonicity #492 #833 #677]: #772
+#661 := [trans #773 #782]: #776
+#681 := [monotonicity #661]: #680
+#684 := [trans #681 #683]: #680
+#672 := [quant-inst]: #679
+#777 := [mp #672 #684]: #678
+#712 := [unit-resolution #777 #856]: #838
+#708 := [monotonicity #712]: #57
+#58 := (not #57)
+#270 := [asserted]: #58
+[unit-resolution #270 #708]: false
+unsat
+121357a49f554c92c48529c5e8845192f6c0a8a5 302 0
+#2 := false
+decl f5 :: (-> int S2)
+#11 := 0::int
+#56 := (f5 0::int)
+decl f4 :: (-> int int int)
+#53 := 1::int
+#54 := (f4 1::int 1::int)
+#55 := (f5 #54)
+#57 := (= #55 #56)
+#505 := (= #54 0::int)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#850 := (pattern #29)
+#82 := -1::int
+#86 := (* -1::int #9)
+#83 := (* -1::int #8)
+#141 := (mod #83 #86)
+#362 := (+ #29 #141)
+#363 := (= #362 0::int)
+#30 := (mod #8 #9)
+#359 := (* -1::int #30)
+#360 := (+ #29 #359)
+#361 := (= #360 0::int)
+#108 := (<= #9 0::int)
+#104 := (<= #8 0::int)
+#301 := (or #104 #108)
+#302 := (not #301)
+#115 := (>= #8 0::int)
+#284 := (or #108 #115)
+#285 := (not #284)
+#308 := (or #285 #302)
+#364 := (ite #308 #361 #363)
+#358 := (= #29 0::int)
+#12 := (= #8 0::int)
+#365 := (ite #12 #358 #364)
+#357 := (= #8 #29)
+#13 := (= #9 0::int)
+#366 := (ite #13 #357 #365)
+#851 := (forall (vars (?v0 int) (?v1 int)) (:pat #850) #366)
+#369 := (forall (vars (?v0 int) (?v1 int)) #366)
+#854 := (iff #369 #851)
+#852 := (iff #366 #366)
+#853 := [refl]: #852
+#855 := [quant-intro #853]: #854
+#147 := (* -1::int #141)
+#326 := (ite #308 #30 #147)
+#329 := (ite #12 0::int #326)
+#332 := (ite #13 #8 #329)
+#335 := (= #29 #332)
+#338 := (forall (vars (?v0 int) (?v1 int)) #335)
+#370 := (iff #338 #369)
+#367 := (iff #335 #366)
+#368 := [rewrite]: #367
+#371 := [quant-intro #368]: #370
+#116 := (not #115)
+#109 := (not #108)
+#119 := (and #109 #116)
+#105 := (not #104)
+#112 := (and #105 #109)
+#122 := (or #112 #119)
+#167 := (ite #122 #30 #147)
+#170 := (ite #12 0::int #167)
+#173 := (ite #13 #8 #170)
+#176 := (= #29 #173)
+#179 := (forall (vars (?v0 int) (?v1 int)) #176)
+#339 := (iff #179 #338)
+#336 := (iff #176 #335)
+#333 := (= #173 #332)
+#330 := (= #170 #329)
+#327 := (= #167 #326)
+#311 := (iff #122 #308)
+#305 := (or #302 #285)
+#309 := (iff #305 #308)
+#310 := [rewrite]: #309
+#306 := (iff #122 #305)
+#303 := (iff #119 #285)
+#304 := [rewrite]: #303
+#282 := (iff #112 #302)
+#283 := [rewrite]: #282
+#307 := [monotonicity #283 #304]: #306
+#312 := [trans #307 #310]: #311
+#328 := [monotonicity #312]: #327
+#331 := [monotonicity #328]: #330
+#334 := [monotonicity #331]: #333
+#337 := [monotonicity #334]: #336
+#340 := [quant-intro #337]: #339
+#274 := (~ #179 #179)
+#271 := (~ #176 #176)
+#290 := [refl]: #271
+#275 := [nnf-pos #290]: #274
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#182 := (iff #37 #179)
+#76 := (and #16 #18)
+#79 := (or #17 #76)
+#152 := (ite #79 #30 #147)
+#155 := (ite #12 0::int #152)
+#158 := (ite #13 #8 #155)
+#161 := (= #29 #158)
+#164 := (forall (vars (?v0 int) (?v1 int)) #161)
+#180 := (iff #164 #179)
+#177 := (iff #161 #176)
+#174 := (= #158 #173)
+#171 := (= #155 #170)
+#168 := (= #152 #167)
+#123 := (iff #79 #122)
+#120 := (iff #76 #119)
+#117 := (iff #18 #116)
+#118 := [rewrite]: #117
+#110 := (iff #16 #109)
+#111 := [rewrite]: #110
+#121 := [monotonicity #111 #118]: #120
+#113 := (iff #17 #112)
+#106 := (iff #15 #105)
+#107 := [rewrite]: #106
+#114 := [monotonicity #107 #111]: #113
+#124 := [monotonicity #114 #121]: #123
+#169 := [monotonicity #124]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [quant-intro #178]: #180
+#165 := (iff #37 #164)
+#162 := (iff #36 #161)
+#159 := (= #35 #158)
+#156 := (= #34 #155)
+#153 := (= #33 #152)
+#150 := (= #32 #147)
+#144 := (- #141)
+#148 := (= #144 #147)
+#149 := [rewrite]: #148
+#145 := (= #32 #144)
+#142 := (= #31 #141)
+#87 := (= #23 #86)
+#88 := [rewrite]: #87
+#84 := (= #22 #83)
+#85 := [rewrite]: #84
+#143 := [monotonicity #85 #88]: #142
+#146 := [monotonicity #143]: #145
+#151 := [trans #146 #149]: #150
+#80 := (iff #20 #79)
+#77 := (iff #19 #76)
+#78 := [rewrite]: #77
+#81 := [monotonicity #78]: #80
+#154 := [monotonicity #81 #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [quant-intro #163]: #165
+#183 := [trans #166 #181]: #182
+#140 := [asserted]: #37
+#184 := [mp #140 #183]: #179
+#291 := [mp~ #184 #275]: #179
+#341 := [mp #291 #340]: #338
+#372 := [mp #341 #371]: #369
+#856 := [mp #372 #855]: #851
+#776 := (not #851)
+#661 := (or #776 #505)
+#430 := (* -1::int 1::int)
+#514 := (mod #430 #430)
+#515 := (+ #54 #514)
+#516 := (= #515 0::int)
+#507 := (mod 1::int 1::int)
+#518 := (* -1::int #507)
+#519 := (+ #54 #518)
+#520 := (= #519 0::int)
+#517 := (<= 1::int 0::int)
+#521 := (or #517 #517)
+#500 := (not #521)
+#835 := (>= 1::int 0::int)
+#837 := (or #517 #835)
+#494 := (not #837)
+#624 := (or #494 #500)
+#831 := (ite #624 #520 #516)
+#506 := (= 1::int 0::int)
+#838 := (ite #506 #505 #831)
+#839 := (= 1::int #54)
+#840 := (ite #506 #839 #838)
+#676 := (or #776 #840)
+#679 := (iff #676 #661)
+#680 := (iff #661 #661)
+#681 := [rewrite]: #680
+#772 := (iff #840 #505)
+#832 := (= #54 1::int)
+#667 := (ite false #832 #505)
+#775 := (iff #667 #505)
+#677 := [rewrite]: #775
+#668 := (iff #840 #667)
+#784 := (iff #838 #505)
+#779 := (ite false #505 #505)
+#783 := (iff #779 #505)
+#781 := [rewrite]: #783
+#780 := (iff #838 #779)
+#625 := (iff #831 #505)
+#1 := true
+#792 := (ite true #505 #505)
+#794 := (iff #792 #505)
+#623 := [rewrite]: #794
+#793 := (iff #831 #792)
+#785 := (iff #516 #505)
+#790 := (= #515 #54)
+#807 := (+ #54 0::int)
+#808 := (= #807 #54)
+#805 := [rewrite]: #808
+#788 := (= #515 #807)
+#645 := (= #514 0::int)
+#801 := (mod -1::int -1::int)
+#803 := (= #801 0::int)
+#644 := [rewrite]: #803
+#802 := (= #514 #801)
+#795 := (= #430 -1::int)
+#796 := [rewrite]: #795
+#797 := [monotonicity #796 #796]: #802
+#646 := [trans #797 #644]: #645
+#789 := [monotonicity #646]: #788
+#791 := [trans #789 #805]: #790
+#786 := [monotonicity #791]: #785
+#799 := (iff #520 #505)
+#809 := (= #519 #54)
+#522 := (= #519 #807)
+#528 := (= #518 0::int)
+#811 := (* -1::int 0::int)
+#526 := (= #811 0::int)
+#527 := [rewrite]: #526
+#815 := (= #518 #811)
+#810 := (= #507 0::int)
+#814 := [rewrite]: #810
+#525 := [monotonicity #814]: #815
+#806 := [trans #525 #527]: #528
+#804 := [monotonicity #806]: #522
+#798 := [trans #804 #805]: #809
+#800 := [monotonicity #798]: #799
+#535 := (iff #624 true)
+#477 := (or false true)
+#482 := (iff #477 true)
+#483 := [rewrite]: #482
+#812 := (iff #624 #477)
+#542 := (iff #500 true)
+#816 := (not false)
+#540 := (iff #816 true)
+#541 := [rewrite]: #540
+#817 := (iff #500 #816)
+#827 := (iff #521 false)
+#826 := (or false false)
+#469 := (iff #826 false)
+#829 := [rewrite]: #469
+#828 := (iff #521 #826)
+#497 := (iff #517 false)
+#833 := [rewrite]: #497
+#468 := [monotonicity #833 #833]: #828
+#830 := [trans #468 #829]: #827
+#539 := [monotonicity #830]: #817
+#436 := [trans #539 #541]: #542
+#825 := (iff #494 false)
+#821 := (not true)
+#824 := (iff #821 false)
+#819 := [rewrite]: #824
+#822 := (iff #494 #821)
+#484 := (iff #837 true)
+#818 := (iff #837 #477)
+#493 := (iff #835 true)
+#834 := [rewrite]: #493
+#481 := [monotonicity #833 #834]: #818
+#820 := [trans #481 #483]: #484
+#823 := [monotonicity #820]: #822
+#463 := [trans #823 #819]: #825
+#813 := [monotonicity #463 #436]: #812
+#536 := [trans #813 #483]: #535
+#787 := [monotonicity #536 #800 #786]: #793
+#626 := [trans #787 #623]: #625
+#841 := (iff #506 false)
+#836 := [rewrite]: #841
+#782 := [monotonicity #836 #626]: #780
+#666 := [trans #782 #781]: #784
+#842 := (iff #839 #832)
+#492 := [rewrite]: #842
+#627 := [monotonicity #836 #492 #666]: #668
+#773 := [trans #627 #677]: #772
+#672 := [monotonicity #773]: #679
+#682 := [trans #672 #681]: #679
+#678 := [quant-inst]: #676
+#683 := [mp #678 #682]: #661
+#703 := [unit-resolution #683 #856]: #505
+#699 := [monotonicity #703]: #57
+#58 := (not #57)
+#270 := [asserted]: #58
+[unit-resolution #270 #699]: false
+unsat
+2c035401970833955895c9fd35464fade49dcbf1 313 0
+#2 := false
+decl f5 :: (-> int S2)
+#11 := 0::int
+#57 := (f5 0::int)
+decl f4 :: (-> int int int)
+#54 := 1::int
+#53 := 3::int
+#55 := (f4 3::int 1::int)
+#56 := (f5 #55)
+#58 := (= #56 #57)
+#839 := (= #55 0::int)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#851 := (pattern #29)
+#83 := -1::int
+#87 := (* -1::int #9)
+#84 := (* -1::int #8)
+#142 := (mod #84 #87)
+#363 := (+ #29 #142)
+#364 := (= #363 0::int)
+#30 := (mod #8 #9)
+#360 := (* -1::int #30)
+#361 := (+ #29 #360)
+#362 := (= #361 0::int)
+#109 := (<= #9 0::int)
+#105 := (<= #8 0::int)
+#302 := (or #105 #109)
+#303 := (not #302)
+#116 := (>= #8 0::int)
+#285 := (or #109 #116)
+#286 := (not #285)
+#309 := (or #286 #303)
+#365 := (ite #309 #362 #364)
+#359 := (= #29 0::int)
+#12 := (= #8 0::int)
+#366 := (ite #12 #359 #365)
+#358 := (= #8 #29)
+#13 := (= #9 0::int)
+#367 := (ite #13 #358 #366)
+#852 := (forall (vars (?v0 int) (?v1 int)) (:pat #851) #367)
+#370 := (forall (vars (?v0 int) (?v1 int)) #367)
+#855 := (iff #370 #852)
+#853 := (iff #367 #367)
+#854 := [refl]: #853
+#856 := [quant-intro #854]: #855
+#148 := (* -1::int #142)
+#327 := (ite #309 #30 #148)
+#330 := (ite #12 0::int #327)
+#333 := (ite #13 #8 #330)
+#336 := (= #29 #333)
+#339 := (forall (vars (?v0 int) (?v1 int)) #336)
+#371 := (iff #339 #370)
+#368 := (iff #336 #367)
+#369 := [rewrite]: #368
+#372 := [quant-intro #369]: #371
+#117 := (not #116)
+#110 := (not #109)
+#120 := (and #110 #117)
+#106 := (not #105)
+#113 := (and #106 #110)
+#123 := (or #113 #120)
+#168 := (ite #123 #30 #148)
+#171 := (ite #12 0::int #168)
+#174 := (ite #13 #8 #171)
+#177 := (= #29 #174)
+#180 := (forall (vars (?v0 int) (?v1 int)) #177)
+#340 := (iff #180 #339)
+#337 := (iff #177 #336)
+#334 := (= #174 #333)
+#331 := (= #171 #330)
+#328 := (= #168 #327)
+#312 := (iff #123 #309)
+#306 := (or #303 #286)
+#310 := (iff #306 #309)
+#311 := [rewrite]: #310
+#307 := (iff #123 #306)
+#304 := (iff #120 #286)
+#305 := [rewrite]: #304
+#283 := (iff #113 #303)
+#284 := [rewrite]: #283
+#308 := [monotonicity #284 #305]: #307
+#313 := [trans #308 #311]: #312
+#329 := [monotonicity #313]: #328
+#332 := [monotonicity #329]: #331
+#335 := [monotonicity #332]: #334
+#338 := [monotonicity #335]: #337
+#341 := [quant-intro #338]: #340
+#275 := (~ #180 #180)
+#272 := (~ #177 #177)
+#291 := [refl]: #272
+#276 := [nnf-pos #291]: #275
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#183 := (iff #37 #180)
+#77 := (and #16 #18)
+#80 := (or #17 #77)
+#153 := (ite #80 #30 #148)
+#156 := (ite #12 0::int #153)
+#159 := (ite #13 #8 #156)
+#162 := (= #29 #159)
+#165 := (forall (vars (?v0 int) (?v1 int)) #162)
+#181 := (iff #165 #180)
+#178 := (iff #162 #177)
+#175 := (= #159 #174)
+#172 := (= #156 #171)
+#169 := (= #153 #168)
+#124 := (iff #80 #123)
+#121 := (iff #77 #120)
+#118 := (iff #18 #117)
+#119 := [rewrite]: #118
+#111 := (iff #16 #110)
+#112 := [rewrite]: #111
+#122 := [monotonicity #112 #119]: #121
+#114 := (iff #17 #113)
+#107 := (iff #15 #106)
+#108 := [rewrite]: #107
+#115 := [monotonicity #108 #112]: #114
+#125 := [monotonicity #115 #122]: #124
+#170 := [monotonicity #125]: #169
+#173 := [monotonicity #170]: #172
+#176 := [monotonicity #173]: #175
+#179 := [monotonicity #176]: #178
+#182 := [quant-intro #179]: #181
+#166 := (iff #37 #165)
+#163 := (iff #36 #162)
+#160 := (= #35 #159)
+#157 := (= #34 #156)
+#154 := (= #33 #153)
+#151 := (= #32 #148)
+#145 := (- #142)
+#149 := (= #145 #148)
+#150 := [rewrite]: #149
+#146 := (= #32 #145)
+#143 := (= #31 #142)
+#88 := (= #23 #87)
+#89 := [rewrite]: #88
+#85 := (= #22 #84)
+#86 := [rewrite]: #85
+#144 := [monotonicity #86 #89]: #143
+#147 := [monotonicity #144]: #146
+#152 := [trans #147 #150]: #151
+#81 := (iff #20 #80)
+#78 := (iff #19 #77)
+#79 := [rewrite]: #78
+#82 := [monotonicity #79]: #81
+#155 := [monotonicity #82 #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [quant-intro #164]: #166
+#184 := [trans #167 #182]: #183
+#141 := [asserted]: #37
+#185 := [mp #141 #184]: #180
+#292 := [mp~ #185 #276]: #180
+#342 := [mp #292 #341]: #339
+#373 := [mp #342 #372]: #370
+#857 := [mp #373 #856]: #852
+#685 := (not #852)
+#778 := (or #685 #839)
+#431 := (* -1::int 1::int)
+#515 := (* -1::int 3::int)
+#516 := (mod #515 #431)
+#517 := (+ #55 #516)
+#508 := (= #517 0::int)
+#519 := (mod 3::int 1::int)
+#520 := (* -1::int #519)
+#521 := (+ #55 #520)
+#518 := (= #521 0::int)
+#522 := (<= 1::int 0::int)
+#501 := (<= 3::int 0::int)
+#836 := (or #501 #522)
+#838 := (not #836)
+#495 := (>= 3::int 0::int)
+#625 := (or #522 #495)
+#832 := (not #625)
+#506 := (or #832 #838)
+#507 := (ite #506 #518 #508)
+#840 := (= 3::int 0::int)
+#841 := (ite #840 #839 #507)
+#842 := (= 3::int #55)
+#837 := (= 1::int 0::int)
+#843 := (ite #837 #842 #841)
+#775 := (or #685 #843)
+#766 := (iff #775 #778)
+#760 := (iff #778 #778)
+#757 := [rewrite]: #760
+#683 := (iff #843 #839)
+#834 := (= #55 3::int)
+#679 := (ite false #834 #839)
+#681 := (iff #679 #839)
+#682 := [rewrite]: #681
+#680 := (iff #843 #679)
+#662 := (iff #841 #839)
+#776 := (ite false #839 #839)
+#774 := (iff #776 #839)
+#777 := [rewrite]: #774
+#678 := (iff #841 #776)
+#669 := (iff #507 #839)
+#1 := true
+#784 := (ite true #839 #839)
+#667 := (iff #784 #839)
+#668 := [rewrite]: #667
+#782 := (iff #507 #784)
+#781 := (iff #508 #839)
+#627 := (= #517 #55)
+#800 := (+ #55 0::int)
+#797 := (= #800 #55)
+#802 := [rewrite]: #797
+#624 := (= #517 #800)
+#788 := (= #516 0::int)
+#646 := -3::int
+#792 := (mod -3::int -1::int)
+#793 := (= #792 0::int)
+#794 := [rewrite]: #793
+#786 := (= #516 #792)
+#790 := (= #431 -1::int)
+#791 := [rewrite]: #790
+#647 := (= #515 -3::int)
+#789 := [rewrite]: #647
+#787 := [monotonicity #789 #791]: #786
+#795 := [trans #787 #794]: #788
+#626 := [monotonicity #795]: #624
+#780 := [trans #626 #802]: #627
+#783 := [monotonicity #780]: #781
+#804 := (iff #518 #839)
+#803 := (= #521 #55)
+#801 := (= #521 #800)
+#810 := (= #520 0::int)
+#808 := (* -1::int 0::int)
+#809 := (= #808 0::int)
+#806 := [rewrite]: #809
+#523 := (= #520 #808)
+#529 := (= #519 0::int)
+#807 := [rewrite]: #529
+#805 := [monotonicity #807]: #523
+#799 := [trans #805 #806]: #810
+#796 := [monotonicity #799]: #801
+#798 := [trans #796 #802]: #803
+#645 := [monotonicity #798]: #804
+#527 := (iff #506 true)
+#485 := (or false true)
+#823 := (iff #485 true)
+#824 := [rewrite]: #823
+#816 := (iff #506 #485)
+#815 := (iff #838 true)
+#813 := (not false)
+#537 := (iff #813 true)
+#811 := [rewrite]: #537
+#814 := (iff #838 #813)
+#543 := (iff #836 false)
+#817 := (or false false)
+#541 := (iff #817 false)
+#542 := [rewrite]: #541
+#818 := (iff #836 #817)
+#819 := (iff #522 false)
+#482 := [rewrite]: #819
+#828 := (iff #501 false)
+#831 := [rewrite]: #828
+#540 := [monotonicity #831 #482]: #818
+#437 := [trans #540 #542]: #543
+#536 := [monotonicity #437]: #814
+#812 := [trans #536 #811]: #815
+#470 := (iff #832 false)
+#826 := (not true)
+#829 := (iff #826 false)
+#469 := [rewrite]: #829
+#464 := (iff #832 #826)
+#825 := (iff #625 true)
+#821 := (iff #625 #485)
+#483 := (iff #495 true)
+#484 := [rewrite]: #483
+#822 := [monotonicity #482 #484]: #821
+#820 := [trans #822 #824]: #825
+#827 := [monotonicity #820]: #464
+#830 := [trans #827 #469]: #470
+#526 := [monotonicity #830 #812]: #816
+#528 := [trans #526 #824]: #527
+#785 := [monotonicity #528 #645 #783]: #782
+#628 := [trans #785 #668]: #669
+#835 := (iff #840 false)
+#478 := [rewrite]: #835
+#773 := [monotonicity #478 #628]: #678
+#677 := [trans #773 #777]: #662
+#498 := (iff #842 #834)
+#494 := [rewrite]: #498
+#833 := (iff #837 false)
+#493 := [rewrite]: #833
+#673 := [monotonicity #493 #494 #677]: #680
+#684 := [trans #673 #682]: #683
+#768 := [monotonicity #684]: #766
+#759 := [trans #768 #757]: #766
+#779 := [quant-inst]: #775
+#769 := [mp #779 #759]: #778
+#701 := [unit-resolution #769 #857]: #839
+#702 := [monotonicity #701]: #58
+#59 := (not #58)
+#271 := [asserted]: #59
+[unit-resolution #271 #702]: false
+unsat
+80ae46a7e9c57ab25c6d7a036d7583b3c508d2eb 447 0
+#2 := false
+#11 := 0::int
+decl f6 :: (-> S2 int)
+decl f7 :: S2
+#53 := f7
+#54 := (f6 f7)
+#496 := (>= #54 0::int)
+decl f5 :: (-> int S2)
+#762 := (f5 #54)
+#708 := (f6 #762)
+#704 := (= #708 0::int)
+#655 := (not #704)
+#841 := (= #54 0::int)
+#674 := (not #841)
+#656 := (iff #674 #655)
+#653 := (iff #841 #704)
+#651 := (iff #704 #841)
+#649 := (= #708 #54)
+#643 := (= #762 f7)
+#763 := (= f7 #762)
+#38 := (:var 0 S2)
+#39 := (f6 #38)
+#859 := (pattern #39)
+#40 := (f5 #39)
+#188 := (= #38 #40)
+#860 := (forall (vars (?v0 S2)) (:pat #859) #188)
+#191 := (forall (vars (?v0 S2)) #188)
+#861 := (iff #191 #860)
+#863 := (iff #860 #860)
+#864 := [rewrite]: #863
+#862 := [rewrite]: #861
+#865 := [trans #862 #864]: #861
+#278 := (~ #191 #191)
+#294 := (~ #188 #188)
+#295 := [refl]: #294
+#279 := [nnf-pos #295]: #278
+#41 := (= #40 #38)
+#42 := (forall (vars (?v0 S2)) #41)
+#192 := (iff #42 #191)
+#189 := (iff #41 #188)
+#190 := [rewrite]: #189
+#193 := [quant-intro #190]: #192
+#187 := [asserted]: #42
+#196 := [mp #187 #193]: #191
+#296 := [mp~ #196 #279]: #191
+#866 := [mp #296 #865]: #860
+#759 := (not #860)
+#766 := (or #759 #763)
+#750 := [quant-inst]: #766
+#688 := [unit-resolution #750 #866]: #763
+#644 := [symm #688]: #643
+#650 := [monotonicity #644]: #649
+#652 := [monotonicity #650]: #651
+#654 := [symm #652]: #653
+#657 := [monotonicity #654]: #656
+#486 := (not #496)
+#673 := [hypothesis]: #486
+#677 := (or #674 #496)
+#687 := [th-lemma]: #677
+#667 := [unit-resolution #687 #673]: #674
+#658 := [mp #667 #657]: #655
+#689 := (or #496 #704)
+#9 := (:var 0 int)
+#44 := (f5 #9)
+#867 := (pattern #44)
+#211 := (>= #9 0::int)
+#45 := (f6 #44)
+#50 := (= #45 0::int)
+#261 := (or #50 #211)
+#874 := (forall (vars (?v0 int)) (:pat #867) #261)
+#266 := (forall (vars (?v0 int)) #261)
+#877 := (iff #266 #874)
+#875 := (iff #261 #261)
+#876 := [refl]: #875
+#878 := [quant-intro #876]: #877
+#282 := (~ #266 #266)
+#300 := (~ #261 #261)
+#301 := [refl]: #300
+#283 := [nnf-pos #301]: #282
+#49 := (< #9 0::int)
+#51 := (implies #49 #50)
+#52 := (forall (vars (?v0 int)) #51)
+#269 := (iff #52 #266)
+#232 := (= 0::int #45)
+#238 := (not #49)
+#239 := (or #238 #232)
+#244 := (forall (vars (?v0 int)) #239)
+#267 := (iff #244 #266)
+#264 := (iff #239 #261)
+#258 := (or #211 #50)
+#262 := (iff #258 #261)
+#263 := [rewrite]: #262
+#259 := (iff #239 #258)
+#256 := (iff #232 #50)
+#257 := [rewrite]: #256
+#254 := (iff #238 #211)
+#214 := (not #211)
+#249 := (not #214)
+#252 := (iff #249 #211)
+#253 := [rewrite]: #252
+#250 := (iff #238 #249)
+#247 := (iff #49 #214)
+#248 := [rewrite]: #247
+#251 := [monotonicity #248]: #250
+#255 := [trans #251 #253]: #254
+#260 := [monotonicity #255 #257]: #259
+#265 := [trans #260 #263]: #264
+#268 := [quant-intro #265]: #267
+#245 := (iff #52 #244)
+#242 := (iff #51 #239)
+#235 := (implies #49 #232)
+#240 := (iff #235 #239)
+#241 := [rewrite]: #240
+#236 := (iff #51 #235)
+#233 := (iff #50 #232)
+#234 := [rewrite]: #233
+#237 := [monotonicity #234]: #236
+#243 := [trans #237 #241]: #242
+#246 := [quant-intro #243]: #245
+#270 := [trans #246 #268]: #269
+#231 := [asserted]: #52
+#271 := [mp #231 #270]: #266
+#302 := [mp~ #271 #283]: #266
+#879 := [mp #302 #878]: #874
+#729 := (not #874)
+#671 := (or #729 #496 #704)
+#709 := (or #704 #496)
+#695 := (or #729 #709)
+#662 := (iff #695 #671)
+#691 := (or #729 #689)
+#672 := (iff #691 #671)
+#631 := [rewrite]: #672
+#697 := (iff #695 #691)
+#635 := (iff #709 #689)
+#690 := [rewrite]: #635
+#665 := [monotonicity #690]: #697
+#664 := [trans #665 #631]: #662
+#696 := [quant-inst]: #695
+#666 := [mp #696 #664]: #671
+#675 := [unit-resolution #666 #879]: #689
+#676 := [unit-resolution #675 #673]: #704
+#659 := [unit-resolution #676 #658]: false
+#660 := [lemma #659]: #496
+#502 := (<= #54 0::int)
+#830 := (not #502)
+#625 := (or #486 #830 #841)
+#684 := (not #625)
+decl f4 :: (-> int int int)
+#55 := 1::int
+#56 := (f4 #54 1::int)
+#840 := (= #56 0::int)
+#760 := (not #840)
+#58 := (f5 0::int)
+#57 := (f5 #56)
+#59 := (= #57 #58)
+#645 := [hypothesis]: #840
+#661 := [monotonicity #645]: #59
+#60 := (not #59)
+#272 := [asserted]: #60
+#622 := [unit-resolution #272 #661]: false
+#623 := [lemma #622]: #760
+#632 := (or #684 #840)
+#84 := -1::int
+#516 := (* -1::int #54)
+#809 := (mod #516 -1::int)
+#810 := (+ #56 #809)
+#800 := (= #810 0::int)
+#781 := (ite #625 #840 #800)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#852 := (pattern #29)
+#88 := (* -1::int #9)
+#85 := (* -1::int #8)
+#143 := (mod #85 #88)
+#364 := (+ #29 #143)
+#365 := (= #364 0::int)
+#30 := (mod #8 #9)
+#361 := (* -1::int #30)
+#362 := (+ #29 #361)
+#363 := (= #362 0::int)
+#110 := (<= #9 0::int)
+#106 := (<= #8 0::int)
+#303 := (or #106 #110)
+#304 := (not #303)
+#117 := (>= #8 0::int)
+#286 := (or #110 #117)
+#287 := (not #286)
+#310 := (or #287 #304)
+#366 := (ite #310 #363 #365)
+#360 := (= #29 0::int)
+#12 := (= #8 0::int)
+#367 := (ite #12 #360 #366)
+#359 := (= #8 #29)
+#13 := (= #9 0::int)
+#368 := (ite #13 #359 #367)
+#853 := (forall (vars (?v0 int) (?v1 int)) (:pat #852) #368)
+#371 := (forall (vars (?v0 int) (?v1 int)) #368)
+#856 := (iff #371 #853)
+#854 := (iff #368 #368)
+#855 := [refl]: #854
+#857 := [quant-intro #855]: #856
+#149 := (* -1::int #143)
+#328 := (ite #310 #30 #149)
+#331 := (ite #12 0::int #328)
+#334 := (ite #13 #8 #331)
+#337 := (= #29 #334)
+#340 := (forall (vars (?v0 int) (?v1 int)) #337)
+#372 := (iff #340 #371)
+#369 := (iff #337 #368)
+#370 := [rewrite]: #369
+#373 := [quant-intro #370]: #372
+#118 := (not #117)
+#111 := (not #110)
+#121 := (and #111 #118)
+#107 := (not #106)
+#114 := (and #107 #111)
+#124 := (or #114 #121)
+#169 := (ite #124 #30 #149)
+#172 := (ite #12 0::int #169)
+#175 := (ite #13 #8 #172)
+#178 := (= #29 #175)
+#181 := (forall (vars (?v0 int) (?v1 int)) #178)
+#341 := (iff #181 #340)
+#338 := (iff #178 #337)
+#335 := (= #175 #334)
+#332 := (= #172 #331)
+#329 := (= #169 #328)
+#313 := (iff #124 #310)
+#307 := (or #304 #287)
+#311 := (iff #307 #310)
+#312 := [rewrite]: #311
+#308 := (iff #124 #307)
+#305 := (iff #121 #287)
+#306 := [rewrite]: #305
+#284 := (iff #114 #304)
+#285 := [rewrite]: #284
+#309 := [monotonicity #285 #306]: #308
+#314 := [trans #309 #312]: #313
+#330 := [monotonicity #314]: #329
+#333 := [monotonicity #330]: #332
+#336 := [monotonicity #333]: #335
+#339 := [monotonicity #336]: #338
+#342 := [quant-intro #339]: #341
+#276 := (~ #181 #181)
+#273 := (~ #178 #178)
+#292 := [refl]: #273
+#277 := [nnf-pos #292]: #276
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#184 := (iff #37 #181)
+#78 := (and #16 #18)
+#81 := (or #17 #78)
+#154 := (ite #81 #30 #149)
+#157 := (ite #12 0::int #154)
+#160 := (ite #13 #8 #157)
+#163 := (= #29 #160)
+#166 := (forall (vars (?v0 int) (?v1 int)) #163)
+#182 := (iff #166 #181)
+#179 := (iff #163 #178)
+#176 := (= #160 #175)
+#173 := (= #157 #172)
+#170 := (= #154 #169)
+#125 := (iff #81 #124)
+#122 := (iff #78 #121)
+#119 := (iff #18 #118)
+#120 := [rewrite]: #119
+#112 := (iff #16 #111)
+#113 := [rewrite]: #112
+#123 := [monotonicity #113 #120]: #122
+#115 := (iff #17 #114)
+#108 := (iff #15 #107)
+#109 := [rewrite]: #108
+#116 := [monotonicity #109 #113]: #115
+#126 := [monotonicity #116 #123]: #125
+#171 := [monotonicity #126]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#180 := [monotonicity #177]: #179
+#183 := [quant-intro #180]: #182
+#167 := (iff #37 #166)
+#164 := (iff #36 #163)
+#161 := (= #35 #160)
+#158 := (= #34 #157)
+#155 := (= #33 #154)
+#152 := (= #32 #149)
+#146 := (- #143)
+#150 := (= #146 #149)
+#151 := [rewrite]: #150
+#147 := (= #32 #146)
+#144 := (= #31 #143)
+#89 := (= #23 #88)
+#90 := [rewrite]: #89
+#86 := (= #22 #85)
+#87 := [rewrite]: #86
+#145 := [monotonicity #87 #90]: #144
+#148 := [monotonicity #145]: #147
+#153 := [trans #148 #151]: #152
+#82 := (iff #20 #81)
+#79 := (iff #19 #78)
+#80 := [rewrite]: #79
+#83 := [monotonicity #80]: #82
+#156 := [monotonicity #83 #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [monotonicity #162]: #164
+#168 := [quant-intro #165]: #167
+#185 := [trans #168 #183]: #184
+#142 := [asserted]: #37
+#186 := [mp #142 #185]: #181
+#293 := [mp~ #186 #277]: #181
+#343 := [mp #293 #342]: #340
+#374 := [mp #343 #373]: #371
+#858 := [mp #374 #857]: #853
+#786 := (not #853)
+#668 := (or #786 #781)
+#432 := (* -1::int 1::int)
+#517 := (mod #516 #432)
+#518 := (+ #56 #517)
+#509 := (= #518 0::int)
+#520 := (mod #54 1::int)
+#521 := (* -1::int #520)
+#522 := (+ #56 #521)
+#519 := (= #522 0::int)
+#523 := (<= 1::int 0::int)
+#837 := (or #502 #523)
+#839 := (not #837)
+#626 := (or #523 #496)
+#833 := (not #626)
+#507 := (or #833 #839)
+#508 := (ite #507 #519 #509)
+#842 := (ite #841 #840 #508)
+#843 := (= #54 #56)
+#838 := (= 1::int 0::int)
+#844 := (ite #838 #843 #842)
+#669 := (or #786 #844)
+#629 := (iff #669 #668)
+#679 := (iff #668 #668)
+#774 := [rewrite]: #679
+#785 := (iff #844 #781)
+#831 := (or #486 #830)
+#646 := (or #831 #841)
+#647 := (ite #646 #840 #800)
+#782 := (iff #647 #781)
+#627 := (iff #646 #625)
+#628 := [rewrite]: #627
+#784 := [monotonicity #628]: #782
+#789 := (iff #844 #647)
+#793 := (ite false #843 #647)
+#794 := (iff #793 #647)
+#795 := [rewrite]: #794
+#787 := (iff #844 #793)
+#791 := (iff #842 #647)
+#797 := (ite #831 #840 #800)
+#804 := (ite #841 #840 #797)
+#648 := (iff #804 #647)
+#790 := [rewrite]: #648
+#799 := (iff #842 #804)
+#798 := (iff #508 #797)
+#801 := (iff #509 #800)
+#807 := (= #518 #810)
+#524 := (= #517 #809)
+#530 := (= #432 -1::int)
+#808 := [rewrite]: #530
+#806 := [monotonicity #808]: #524
+#811 := [monotonicity #806]: #807
+#802 := [monotonicity #811]: #801
+#528 := (iff #519 #840)
+#817 := (= #522 #56)
+#537 := (+ #56 0::int)
+#816 := (= #537 #56)
+#813 := [rewrite]: #816
+#538 := (= #522 #537)
+#814 := (= #521 0::int)
+#541 := (* -1::int 0::int)
+#544 := (= #541 0::int)
+#438 := [rewrite]: #544
+#542 := (= #521 #541)
+#818 := (= #520 0::int)
+#819 := [rewrite]: #818
+#543 := [monotonicity #819]: #542
+#815 := [trans #543 #438]: #814
+#812 := [monotonicity #815]: #538
+#527 := [trans #812 #813]: #817
+#529 := [monotonicity #527]: #528
+#829 := (iff #507 #831)
+#470 := (iff #839 #830)
+#465 := (iff #837 #502)
+#824 := (or #502 false)
+#821 := (iff #824 #502)
+#827 := [rewrite]: #821
+#825 := (iff #837 #824)
+#499 := (iff #523 false)
+#835 := [rewrite]: #499
+#826 := [monotonicity #835]: #825
+#828 := [trans #826 #827]: #465
+#471 := [monotonicity #828]: #470
+#822 := (iff #833 #486)
+#484 := (iff #626 #496)
+#495 := (or false #496)
+#820 := (iff #495 #496)
+#483 := [rewrite]: #820
+#836 := (iff #626 #495)
+#479 := [monotonicity #835]: #836
+#485 := [trans #479 #483]: #484
+#823 := [monotonicity #485]: #822
+#832 := [monotonicity #823 #471]: #829
+#803 := [monotonicity #832 #529 #802]: #798
+#805 := [monotonicity #803]: #799
+#792 := [trans #805 #790]: #791
+#834 := (iff #838 false)
+#494 := [rewrite]: #834
+#788 := [monotonicity #494 #792]: #787
+#796 := [trans #788 #795]: #789
+#783 := [trans #796 #784]: #785
+#777 := [monotonicity #783]: #629
+#775 := [trans #777 #774]: #629
+#670 := [quant-inst]: #669
+#778 := [mp #670 #775]: #668
+#630 := [unit-resolution #778 #858]: #781
+#780 := (not #781)
+#767 := (or #780 #684 #840)
+#769 := [def-axiom]: #767
+#633 := [unit-resolution #769 #630]: #632
+#634 := [unit-resolution #633 #623]: #684
+#680 := (or #625 #502)
+#681 := [def-axiom]: #680
+#636 := [unit-resolution #681 #634]: #502
+#682 := (or #625 #674)
+#683 := [def-axiom]: #682
+#637 := [unit-resolution #683 #634]: #674
+#638 := (or #841 #830 #486)
+#639 := [th-lemma]: #638
+[unit-resolution #639 #637 #636 #660]: false
+unsat
+124e92a80da0b0c9c6ea2fb487ed064cc0c65420 305 0
+#2 := false
+decl f5 :: (-> int S2)
+#11 := 0::int
+#56 := (f5 0::int)
+decl f4 :: (-> int int int)
+#53 := 3::int
+#54 := (f4 0::int 3::int)
+#55 := (f5 #54)
+#57 := (= #55 #56)
+#507 := (= #54 0::int)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#851 := (pattern #29)
+#82 := -1::int
+#86 := (* -1::int #9)
+#83 := (* -1::int #8)
+#141 := (mod #83 #86)
+#362 := (+ #29 #141)
+#363 := (= #362 0::int)
+#30 := (mod #8 #9)
+#359 := (* -1::int #30)
+#360 := (+ #29 #359)
+#361 := (= #360 0::int)
+#108 := (<= #9 0::int)
+#104 := (<= #8 0::int)
+#301 := (or #104 #108)
+#302 := (not #301)
+#115 := (>= #8 0::int)
+#284 := (or #108 #115)
+#285 := (not #284)
+#308 := (or #285 #302)
+#364 := (ite #308 #361 #363)
+#358 := (= #29 0::int)
+#12 := (= #8 0::int)
+#365 := (ite #12 #358 #364)
+#357 := (= #8 #29)
+#13 := (= #9 0::int)
+#366 := (ite #13 #357 #365)
+#852 := (forall (vars (?v0 int) (?v1 int)) (:pat #851) #366)
+#369 := (forall (vars (?v0 int) (?v1 int)) #366)
+#855 := (iff #369 #852)
+#853 := (iff #366 #366)
+#854 := [refl]: #853
+#856 := [quant-intro #854]: #855
+#147 := (* -1::int #141)
+#326 := (ite #308 #30 #147)
+#329 := (ite #12 0::int #326)
+#332 := (ite #13 #8 #329)
+#335 := (= #29 #332)
+#338 := (forall (vars (?v0 int) (?v1 int)) #335)
+#370 := (iff #338 #369)
+#367 := (iff #335 #366)
+#368 := [rewrite]: #367
+#371 := [quant-intro #368]: #370
+#116 := (not #115)
+#109 := (not #108)
+#119 := (and #109 #116)
+#105 := (not #104)
+#112 := (and #105 #109)
+#122 := (or #112 #119)
+#167 := (ite #122 #30 #147)
+#170 := (ite #12 0::int #167)
+#173 := (ite #13 #8 #170)
+#176 := (= #29 #173)
+#179 := (forall (vars (?v0 int) (?v1 int)) #176)
+#339 := (iff #179 #338)
+#336 := (iff #176 #335)
+#333 := (= #173 #332)
+#330 := (= #170 #329)
+#327 := (= #167 #326)
+#311 := (iff #122 #308)
+#305 := (or #302 #285)
+#309 := (iff #305 #308)
+#310 := [rewrite]: #309
+#306 := (iff #122 #305)
+#303 := (iff #119 #285)
+#304 := [rewrite]: #303
+#282 := (iff #112 #302)
+#283 := [rewrite]: #282
+#307 := [monotonicity #283 #304]: #306
+#312 := [trans #307 #310]: #311
+#328 := [monotonicity #312]: #327
+#331 := [monotonicity #328]: #330
+#334 := [monotonicity #331]: #333
+#337 := [monotonicity #334]: #336
+#340 := [quant-intro #337]: #339
+#274 := (~ #179 #179)
+#271 := (~ #176 #176)
+#290 := [refl]: #271
+#275 := [nnf-pos #290]: #274
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#182 := (iff #37 #179)
+#76 := (and #16 #18)
+#79 := (or #17 #76)
+#152 := (ite #79 #30 #147)
+#155 := (ite #12 0::int #152)
+#158 := (ite #13 #8 #155)
+#161 := (= #29 #158)
+#164 := (forall (vars (?v0 int) (?v1 int)) #161)
+#180 := (iff #164 #179)
+#177 := (iff #161 #176)
+#174 := (= #158 #173)
+#171 := (= #155 #170)
+#168 := (= #152 #167)
+#123 := (iff #79 #122)
+#120 := (iff #76 #119)
+#117 := (iff #18 #116)
+#118 := [rewrite]: #117
+#110 := (iff #16 #109)
+#111 := [rewrite]: #110
+#121 := [monotonicity #111 #118]: #120
+#113 := (iff #17 #112)
+#106 := (iff #15 #105)
+#107 := [rewrite]: #106
+#114 := [monotonicity #107 #111]: #113
+#124 := [monotonicity #114 #121]: #123
+#169 := [monotonicity #124]: #168
+#172 := [monotonicity #169]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [quant-intro #178]: #180
+#165 := (iff #37 #164)
+#162 := (iff #36 #161)
+#159 := (= #35 #158)
+#156 := (= #34 #155)
+#153 := (= #33 #152)
+#150 := (= #32 #147)
+#144 := (- #141)
+#148 := (= #144 #147)
+#149 := [rewrite]: #148
+#145 := (= #32 #144)
+#142 := (= #31 #141)
+#87 := (= #23 #86)
+#88 := [rewrite]: #87
+#84 := (= #22 #83)
+#85 := [rewrite]: #84
+#143 := [monotonicity #85 #88]: #142
+#146 := [monotonicity #143]: #145
+#151 := [trans #146 #149]: #150
+#80 := (iff #20 #79)
+#77 := (iff #19 #76)
+#78 := [rewrite]: #77
+#81 := [monotonicity #78]: #80
+#154 := [monotonicity #81 #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [quant-intro #163]: #165
+#183 := [trans #166 #181]: #182
+#140 := [asserted]: #37
+#184 := [mp #140 #183]: #179
+#291 := [mp~ #184 #275]: #179
+#341 := [mp #291 #340]: #338
+#372 := [mp #341 #371]: #369
+#857 := [mp #372 #856]: #852
+#677 := (not #852)
+#679 := (or #677 #507)
+#430 := (* -1::int 3::int)
+#515 := (* -1::int 0::int)
+#516 := (mod #515 #430)
+#517 := (+ #54 #516)
+#508 := (= #517 0::int)
+#519 := (mod 0::int 3::int)
+#520 := (* -1::int #519)
+#448 := (+ #54 #520)
+#521 := (= #448 0::int)
+#518 := (<= 3::int 0::int)
+#522 := (<= 0::int 0::int)
+#501 := (or #522 #518)
+#836 := (not #501)
+#838 := (>= 0::int 0::int)
+#495 := (or #518 #838)
+#625 := (not #495)
+#832 := (or #625 #836)
+#506 := (ite #832 #521 #508)
+#839 := (= 0::int 0::int)
+#840 := (ite #839 #507 #506)
+#841 := (= 0::int #54)
+#842 := (= 3::int 0::int)
+#837 := (ite #842 #841 #840)
+#680 := (or #677 #837)
+#681 := (iff #680 #679)
+#683 := (iff #679 #679)
+#684 := [rewrite]: #683
+#777 := (iff #837 #507)
+#626 := (ite false #507 #507)
+#781 := (iff #626 #507)
+#783 := [rewrite]: #781
+#773 := (iff #837 #626)
+#776 := (iff #840 #507)
+#1 := true
+#785 := (ite true #507 #507)
+#669 := (iff #785 #507)
+#628 := [rewrite]: #669
+#667 := (iff #840 #785)
+#784 := (iff #506 #507)
+#627 := (iff #506 #626)
+#795 := (iff #508 #507)
+#794 := (= #517 #54)
+#806 := (+ #54 0::int)
+#800 := (= #806 #54)
+#801 := [rewrite]: #800
+#787 := (= #517 #806)
+#792 := (= #516 0::int)
+#798 := -3::int
+#646 := (mod 0::int -3::int)
+#790 := (= #646 0::int)
+#791 := [rewrite]: #790
+#647 := (= #516 #646)
+#804 := (= #430 -3::int)
+#645 := [rewrite]: #804
+#808 := (= #515 0::int)
+#523 := [rewrite]: #808
+#789 := [monotonicity #523 #645]: #647
+#786 := [trans #789 #791]: #792
+#793 := [monotonicity #786]: #787
+#788 := [trans #793 #801]: #794
+#624 := [monotonicity #788]: #795
+#802 := (iff #521 #507)
+#796 := (= #448 #54)
+#810 := (= #448 #806)
+#805 := (= #520 0::int)
+#529 := (= #520 #515)
+#527 := (= #519 0::int)
+#528 := [rewrite]: #527
+#807 := [monotonicity #528]: #529
+#809 := [trans #807 #523]: #805
+#799 := [monotonicity #809]: #810
+#797 := [trans #799 #801]: #796
+#803 := [monotonicity #797]: #802
+#816 := (iff #832 false)
+#536 := (or false false)
+#815 := (iff #536 false)
+#812 := [rewrite]: #815
+#537 := (iff #832 #536)
+#813 := (iff #836 false)
+#825 := (not true)
+#464 := (iff #825 false)
+#827 := [rewrite]: #464
+#543 := (iff #836 #825)
+#541 := (iff #501 true)
+#828 := (or true false)
+#818 := (iff #828 true)
+#540 := [rewrite]: #818
+#831 := (iff #501 #828)
+#835 := (iff #518 false)
+#478 := [rewrite]: #835
+#470 := (iff #522 true)
+#830 := [rewrite]: #470
+#817 := [monotonicity #830 #478]: #831
+#542 := [trans #817 #540]: #541
+#436 := [monotonicity #542]: #543
+#814 := [trans #436 #827]: #813
+#829 := (iff #625 false)
+#820 := (iff #625 #825)
+#823 := (iff #495 true)
+#483 := (or false true)
+#821 := (iff #483 true)
+#822 := [rewrite]: #821
+#484 := (iff #495 #483)
+#819 := (iff #838 true)
+#482 := [rewrite]: #819
+#485 := [monotonicity #478 #482]: #484
+#824 := [trans #485 #822]: #823
+#826 := [monotonicity #824]: #820
+#469 := [trans #826 #827]: #829
+#811 := [monotonicity #469 #814]: #537
+#526 := [trans #811 #812]: #816
+#780 := [monotonicity #526 #803 #624]: #627
+#782 := [trans #780 #783]: #784
+#834 := (iff #839 true)
+#494 := [rewrite]: #834
+#668 := [monotonicity #494 #782]: #667
+#678 := [trans #668 #628]: #776
+#493 := (iff #841 #507)
+#498 := [rewrite]: #493
+#843 := (iff #842 false)
+#833 := [rewrite]: #843
+#774 := [monotonicity #833 #498 #678]: #773
+#662 := [trans #774 #783]: #777
+#682 := [monotonicity #662]: #681
+#685 := [trans #682 #684]: #681
+#673 := [quant-inst]: #680
+#778 := [mp #673 #685]: #679
+#713 := [unit-resolution #778 #857]: #507
+#709 := [monotonicity #713]: #57
+#58 := (not #57)
+#270 := [asserted]: #58
+[unit-resolution #270 #709]: false
+unsat
+48fbc21a65dea108392ceeedb3a0cbae0d536aab 328 0
 #2 := false
 decl f5 :: (-> int S2)
 #53 := 1::int
@@ -19371,7 +19579,7 @@
 #271 := [asserted]: #59
 [unit-resolution #271 #708]: false
 unsat
-165a0539a08e682081735200b8ab8b693d5da15d 303 0
+30266f09c986583d8c5407f4e044da694063d38f 303 0
 #2 := false
 decl f5 :: (-> int S2)
 #11 := 0::int
@@ -19675,7 +19883,1213 @@
 #270 := [asserted]: #58
 [unit-resolution #270 #700]: false
 unsat
-1ea3fbc0fb4cdf962c25032ebbea931c454f09b7 848 0
+29a274d82d7dfcc17be98231a7a95a9ec14cd706 533 0
+#2 := false
+#55 := 3::int
+decl f6 :: (-> S2 int)
+decl f7 :: S2
+#53 := f7
+#54 := (f6 f7)
+#533 := (mod #54 3::int)
+#664 := (>= #533 3::int)
+#665 := (not #664)
+#1 := true
+#75 := [true-axiom]: true
+#674 := (or false #665)
+#635 := [th-lemma]: #674
+#636 := [unit-resolution #635 #75]: #665
+#11 := 0::int
+decl f5 :: (-> int S2)
+decl f4 :: (-> int int int)
+#56 := (f4 #54 3::int)
+#57 := (f5 #56)
+#58 := (f6 #57)
+#84 := -1::int
+#779 := (* -1::int #58)
+#763 := (+ #56 #779)
+#766 := (>= #763 0::int)
+#773 := (= #56 #58)
+#780 := (>= #56 0::int)
+#784 := (= #58 0::int)
+#649 := (not #784)
+#746 := (<= #58 0::int)
+#643 := (not #746)
+#276 := (>= #58 3::int)
+#59 := (< #58 3::int)
+#60 := (not #59)
+#284 := (iff #60 #276)
+#275 := (not #276)
+#279 := (not #275)
+#282 := (iff #279 #276)
+#283 := [rewrite]: #282
+#280 := (iff #60 #279)
+#277 := (iff #59 #275)
+#278 := [rewrite]: #277
+#281 := [monotonicity #278]: #280
+#285 := [trans #281 #283]: #284
+#272 := [asserted]: #60
+#286 := [mp #272 #285]: #276
+#645 := (or #643 #275)
+#646 := [th-lemma]: #645
+#647 := [unit-resolution #646 #286]: #643
+#650 := (or #649 #746)
+#651 := [th-lemma]: #650
+#652 := [unit-resolution #651 #647]: #649
+#9 := (:var 0 int)
+#44 := (f5 #9)
+#880 := (pattern #44)
+#211 := (>= #9 0::int)
+#45 := (f6 #44)
+#50 := (= #45 0::int)
+#261 := (or #50 #211)
+#887 := (forall (vars (?v0 int)) (:pat #880) #261)
+#266 := (forall (vars (?v0 int)) #261)
+#890 := (iff #266 #887)
+#888 := (iff #261 #261)
+#889 := [refl]: #888
+#891 := [quant-intro #889]: #890
+#294 := (~ #266 #266)
+#312 := (~ #261 #261)
+#313 := [refl]: #312
+#295 := [nnf-pos #313]: #294
+#49 := (< #9 0::int)
+#51 := (implies #49 #50)
+#52 := (forall (vars (?v0 int)) #51)
+#269 := (iff #52 #266)
+#232 := (= 0::int #45)
+#238 := (not #49)
+#239 := (or #238 #232)
+#244 := (forall (vars (?v0 int)) #239)
+#267 := (iff #244 #266)
+#264 := (iff #239 #261)
+#258 := (or #211 #50)
+#262 := (iff #258 #261)
+#263 := [rewrite]: #262
+#259 := (iff #239 #258)
+#256 := (iff #232 #50)
+#257 := [rewrite]: #256
+#254 := (iff #238 #211)
+#214 := (not #211)
+#249 := (not #214)
+#252 := (iff #249 #211)
+#253 := [rewrite]: #252
+#250 := (iff #238 #249)
+#247 := (iff #49 #214)
+#248 := [rewrite]: #247
+#251 := [monotonicity #248]: #250
+#255 := [trans #251 #253]: #254
+#260 := [monotonicity #255 #257]: #259
+#265 := [trans #260 #263]: #264
+#268 := [quant-intro #265]: #267
+#245 := (iff #52 #244)
+#242 := (iff #51 #239)
+#235 := (implies #49 #232)
+#240 := (iff #235 #239)
+#241 := [rewrite]: #240
+#236 := (iff #51 #235)
+#233 := (iff #50 #232)
+#234 := [rewrite]: #233
+#237 := [monotonicity #234]: #236
+#243 := [trans #237 #241]: #242
+#246 := [quant-intro #243]: #245
+#270 := [trans #246 #268]: #269
+#231 := [asserted]: #52
+#271 := [mp #231 #270]: #266
+#314 := [mp~ #271 #295]: #266
+#892 := [mp #314 #891]: #887
+#765 := (not #887)
+#770 := (or #765 #780 #784)
+#785 := (or #784 #780)
+#756 := (or #765 #785)
+#742 := (iff #756 #770)
+#767 := (or #780 #784)
+#759 := (or #765 #767)
+#758 := (iff #759 #770)
+#762 := [rewrite]: #758
+#760 := (iff #756 #759)
+#768 := (iff #785 #767)
+#769 := [rewrite]: #768
+#761 := [monotonicity #769]: #760
+#743 := [trans #761 #762]: #742
+#757 := [quant-inst]: #756
+#745 := [mp #757 #743]: #770
+#653 := [unit-resolution #745 #892 #652]: #780
+#782 := (not #780)
+#783 := (or #773 #782)
+#195 := (= #9 #45)
+#220 := (or #195 #214)
+#881 := (forall (vars (?v0 int)) (:pat #880) #220)
+#225 := (forall (vars (?v0 int)) #220)
+#884 := (iff #225 #881)
+#882 := (iff #220 #220)
+#883 := [refl]: #882
+#885 := [quant-intro #883]: #884
+#292 := (~ #225 #225)
+#309 := (~ #220 #220)
+#310 := [refl]: #309
+#293 := [nnf-pos #310]: #292
+#46 := (= #45 #9)
+#43 := (<= 0::int #9)
+#47 := (implies #43 #46)
+#48 := (forall (vars (?v0 int)) #47)
+#228 := (iff #48 #225)
+#202 := (not #43)
+#203 := (or #202 #195)
+#208 := (forall (vars (?v0 int)) #203)
+#226 := (iff #208 #225)
+#223 := (iff #203 #220)
+#217 := (or #214 #195)
+#221 := (iff #217 #220)
+#222 := [rewrite]: #221
+#218 := (iff #203 #217)
+#215 := (iff #202 #214)
+#212 := (iff #43 #211)
+#213 := [rewrite]: #212
+#216 := [monotonicity #213]: #215
+#219 := [monotonicity #216]: #218
+#224 := [trans #219 #222]: #223
+#227 := [quant-intro #224]: #226
+#209 := (iff #48 #208)
+#206 := (iff #47 #203)
+#199 := (implies #43 #195)
+#204 := (iff #199 #203)
+#205 := [rewrite]: #204
+#200 := (iff #47 #199)
+#197 := (iff #46 #195)
+#198 := [rewrite]: #197
+#201 := [monotonicity #198]: #200
+#207 := [trans #201 #205]: #206
+#210 := [quant-intro #207]: #209
+#229 := [trans #210 #227]: #228
+#194 := [asserted]: #48
+#230 := [mp #194 #229]: #225
+#311 := [mp~ #230 #293]: #225
+#886 := [mp #311 #885]: #881
+#781 := (not #881)
+#786 := (or #781 #773 #782)
+#775 := (or #781 #783)
+#777 := (iff #775 #786)
+#778 := [rewrite]: #777
+#776 := [quant-inst]: #775
+#772 := [mp #776 #778]: #786
+#654 := [unit-resolution #772 #886]: #783
+#637 := [unit-resolution #654 #653]: #773
+#655 := (not #773)
+#625 := (or #655 #766)
+#626 := [th-lemma]: #625
+#627 := [unit-resolution #626 #637]: #766
+#534 := (* -1::int #533)
+#462 := (+ #56 #534)
+#802 := (<= #462 0::int)
+#535 := (= #462 0::int)
+#556 := -3::int
+#529 := (* -1::int #54)
+#827 := (mod #529 -3::int)
+#551 := (+ #56 #827)
+#826 := (= #551 0::int)
+#852 := (>= #54 0::int)
+#498 := (not #852)
+#536 := (<= #54 0::int)
+#841 := (not #536)
+#845 := (or #841 #498)
+#541 := (ite #845 #535 #826)
+#521 := (= #56 0::int)
+#853 := (= #54 0::int)
+#821 := (ite #853 #521 #541)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#865 := (pattern #29)
+#88 := (* -1::int #9)
+#85 := (* -1::int #8)
+#143 := (mod #85 #88)
+#376 := (+ #29 #143)
+#377 := (= #376 0::int)
+#30 := (mod #8 #9)
+#373 := (* -1::int #30)
+#374 := (+ #29 #373)
+#375 := (= #374 0::int)
+#110 := (<= #9 0::int)
+#106 := (<= #8 0::int)
+#315 := (or #106 #110)
+#316 := (not #315)
+#117 := (>= #8 0::int)
+#298 := (or #110 #117)
+#299 := (not #298)
+#322 := (or #299 #316)
+#378 := (ite #322 #375 #377)
+#372 := (= #29 0::int)
+#12 := (= #8 0::int)
+#379 := (ite #12 #372 #378)
+#371 := (= #8 #29)
+#13 := (= #9 0::int)
+#380 := (ite #13 #371 #379)
+#866 := (forall (vars (?v0 int) (?v1 int)) (:pat #865) #380)
+#383 := (forall (vars (?v0 int) (?v1 int)) #380)
+#869 := (iff #383 #866)
+#867 := (iff #380 #380)
+#868 := [refl]: #867
+#870 := [quant-intro #868]: #869
+#149 := (* -1::int #143)
+#340 := (ite #322 #30 #149)
+#343 := (ite #12 0::int #340)
+#346 := (ite #13 #8 #343)
+#349 := (= #29 #346)
+#352 := (forall (vars (?v0 int) (?v1 int)) #349)
+#384 := (iff #352 #383)
+#381 := (iff #349 #380)
+#382 := [rewrite]: #381
+#385 := [quant-intro #382]: #384
+#118 := (not #117)
+#111 := (not #110)
+#121 := (and #111 #118)
+#107 := (not #106)
+#114 := (and #107 #111)
+#124 := (or #114 #121)
+#169 := (ite #124 #30 #149)
+#172 := (ite #12 0::int #169)
+#175 := (ite #13 #8 #172)
+#178 := (= #29 #175)
+#181 := (forall (vars (?v0 int) (?v1 int)) #178)
+#353 := (iff #181 #352)
+#350 := (iff #178 #349)
+#347 := (= #175 #346)
+#344 := (= #172 #343)
+#341 := (= #169 #340)
+#325 := (iff #124 #322)
+#319 := (or #316 #299)
+#323 := (iff #319 #322)
+#324 := [rewrite]: #323
+#320 := (iff #124 #319)
+#317 := (iff #121 #299)
+#318 := [rewrite]: #317
+#296 := (iff #114 #316)
+#297 := [rewrite]: #296
+#321 := [monotonicity #297 #318]: #320
+#326 := [trans #321 #324]: #325
+#342 := [monotonicity #326]: #341
+#345 := [monotonicity #342]: #344
+#348 := [monotonicity #345]: #347
+#351 := [monotonicity #348]: #350
+#354 := [quant-intro #351]: #353
+#288 := (~ #181 #181)
+#273 := (~ #178 #178)
+#304 := [refl]: #273
+#289 := [nnf-pos #304]: #288
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#184 := (iff #37 #181)
+#78 := (and #16 #18)
+#81 := (or #17 #78)
+#154 := (ite #81 #30 #149)
+#157 := (ite #12 0::int #154)
+#160 := (ite #13 #8 #157)
+#163 := (= #29 #160)
+#166 := (forall (vars (?v0 int) (?v1 int)) #163)
+#182 := (iff #166 #181)
+#179 := (iff #163 #178)
+#176 := (= #160 #175)
+#173 := (= #157 #172)
+#170 := (= #154 #169)
+#125 := (iff #81 #124)
+#122 := (iff #78 #121)
+#119 := (iff #18 #118)
+#120 := [rewrite]: #119
+#112 := (iff #16 #111)
+#113 := [rewrite]: #112
+#123 := [monotonicity #113 #120]: #122
+#115 := (iff #17 #114)
+#108 := (iff #15 #107)
+#109 := [rewrite]: #108
+#116 := [monotonicity #109 #113]: #115
+#126 := [monotonicity #116 #123]: #125
+#171 := [monotonicity #126]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#180 := [monotonicity #177]: #179
+#183 := [quant-intro #180]: #182
+#167 := (iff #37 #166)
+#164 := (iff #36 #163)
+#161 := (= #35 #160)
+#158 := (= #34 #157)
+#155 := (= #33 #154)
+#152 := (= #32 #149)
+#146 := (- #143)
+#150 := (= #146 #149)
+#151 := [rewrite]: #150
+#147 := (= #32 #146)
+#144 := (= #31 #143)
+#89 := (= #23 #88)
+#90 := [rewrite]: #89
+#86 := (= #22 #85)
+#87 := [rewrite]: #86
+#145 := [monotonicity #87 #90]: #144
+#148 := [monotonicity #145]: #147
+#153 := [trans #148 #151]: #152
+#82 := (iff #20 #81)
+#79 := (iff #19 #78)
+#80 := [rewrite]: #79
+#83 := [monotonicity #80]: #82
+#156 := [monotonicity #83 #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [monotonicity #162]: #164
+#168 := [quant-intro #165]: #167
+#185 := [trans #168 #183]: #184
+#142 := [asserted]: #37
+#186 := [mp #142 #185]: #181
+#305 := [mp~ #186 #289]: #181
+#355 := [mp #305 #354]: #352
+#386 := [mp #355 #385]: #383
+#871 := [mp #386 #870]: #866
+#810 := (not #866)
+#811 := (or #810 #821)
+#444 := (* -1::int 3::int)
+#530 := (mod #529 #444)
+#531 := (+ #56 #530)
+#522 := (= #531 0::int)
+#532 := (<= 3::int 0::int)
+#515 := (or #536 #532)
+#850 := (not #515)
+#509 := (or #532 #852)
+#639 := (not #509)
+#846 := (or #639 #850)
+#520 := (ite #846 #535 #522)
+#854 := (ite #853 #521 #520)
+#855 := (= #54 #56)
+#856 := (= 3::int 0::int)
+#851 := (ite #856 #855 #854)
+#816 := (or #810 #851)
+#812 := (iff #816 #811)
+#659 := (iff #811 #811)
+#660 := [rewrite]: #659
+#814 := (iff #851 #821)
+#819 := (ite false #855 #821)
+#824 := (iff #819 #821)
+#813 := [rewrite]: #824
+#823 := (iff #851 #819)
+#822 := (iff #854 #821)
+#542 := (iff #520 #541)
+#830 := (iff #522 #826)
+#825 := (= #531 #551)
+#828 := (= #530 #827)
+#557 := (= #444 -3::int)
+#450 := [rewrite]: #557
+#550 := [monotonicity #450]: #828
+#829 := [monotonicity #550]: #825
+#540 := [monotonicity #829]: #830
+#554 := (iff #846 #845)
+#484 := (or #498 #841)
+#831 := (iff #484 #845)
+#832 := [rewrite]: #831
+#844 := (iff #846 #484)
+#843 := (iff #850 #841)
+#840 := (iff #515 #536)
+#836 := (or #536 false)
+#839 := (iff #836 #536)
+#834 := [rewrite]: #839
+#837 := (iff #515 #836)
+#507 := (iff #532 false)
+#512 := [rewrite]: #507
+#838 := [monotonicity #512]: #837
+#478 := [trans #838 #834]: #840
+#483 := [monotonicity #478]: #843
+#499 := (iff #639 #498)
+#496 := (iff #509 #852)
+#848 := (or false #852)
+#492 := (iff #848 #852)
+#833 := [rewrite]: #492
+#508 := (iff #509 #848)
+#849 := [monotonicity #512]: #508
+#497 := [trans #849 #833]: #496
+#835 := [monotonicity #497]: #499
+#842 := [monotonicity #835 #483]: #844
+#555 := [trans #842 #832]: #554
+#543 := [monotonicity #555 #540]: #542
+#537 := [monotonicity #543]: #822
+#857 := (iff #856 false)
+#847 := [rewrite]: #857
+#820 := [monotonicity #847 #537]: #823
+#815 := [trans #820 #813]: #814
+#818 := [monotonicity #815]: #812
+#661 := [trans #818 #660]: #812
+#817 := [quant-inst]: #816
+#803 := [mp #817 #661]: #811
+#628 := [unit-resolution #803 #871]: #821
+#692 := (not #853)
+#691 := (not #521)
+#633 := (iff #649 #691)
+#632 := (iff #784 #521)
+#630 := (iff #521 #784)
+#631 := [monotonicity #637]: #630
+#475 := [symm #631]: #632
+#629 := [monotonicity #475]: #633
+#634 := [mp #652 #629]: #691
+#790 := (not #821)
+#787 := (or #790 #692 #521)
+#788 := [def-axiom]: #787
+#613 := [unit-resolution #788 #634 #628]: #692
+#791 := (or #790 #853 #541)
+#676 := [def-axiom]: #791
+#616 := [unit-resolution #676 #613 #628]: #541
+#696 := (f5 #54)
+#748 := (f6 #696)
+#749 := (= #748 0::int)
+#614 := (not #749)
+#619 := (iff #692 #614)
+#617 := (iff #853 #749)
+#612 := (iff #749 #853)
+#621 := (= #748 #54)
+#622 := (= #696 f7)
+#697 := (= f7 #696)
+#38 := (:var 0 S2)
+#39 := (f6 #38)
+#872 := (pattern #39)
+#40 := (f5 #39)
+#188 := (= #38 #40)
+#873 := (forall (vars (?v0 S2)) (:pat #872) #188)
+#191 := (forall (vars (?v0 S2)) #188)
+#874 := (iff #191 #873)
+#876 := (iff #873 #873)
+#877 := [rewrite]: #876
+#875 := [rewrite]: #874
+#878 := [trans #875 #877]: #874
+#290 := (~ #191 #191)
+#306 := (~ #188 #188)
+#307 := [refl]: #306
+#291 := [nnf-pos #307]: #290
+#41 := (= #40 #38)
+#42 := (forall (vars (?v0 S2)) #41)
+#192 := (iff #42 #191)
+#189 := (iff #41 #188)
+#190 := [rewrite]: #189
+#193 := [quant-intro #190]: #192
+#187 := [asserted]: #42
+#196 := [mp #187 #193]: #191
+#308 := [mp~ #196 #291]: #191
+#879 := [mp #308 #878]: #873
+#792 := (not #873)
+#789 := (or #792 #697)
+#793 := [quant-inst]: #789
+#620 := [unit-resolution #793 #879]: #697
+#623 := [symm #620]: #622
+#624 := [monotonicity #623]: #621
+#615 := [monotonicity #624]: #612
+#618 := [symm #615]: #617
+#609 := [monotonicity #618]: #619
+#599 := [mp #613 #609]: #614
+#750 := (or #749 #852)
+#753 := (or #765 #749 #852)
+#754 := (or #765 #750)
+#755 := (iff #754 #753)
+#733 := [rewrite]: #755
+#744 := [quant-inst]: #754
+#734 := [mp #744 #733]: #753
+#601 := [unit-resolution #734 #892]: #750
+#602 := [unit-resolution #601 #599]: #852
+#605 := (or #853 #841 #498)
+#606 := [th-lemma]: #605
+#610 := [unit-resolution #606 #613]: #845
+#603 := [unit-resolution #610 #602]: #841
+#804 := (or #845 #536)
+#805 := [def-axiom]: #804
+#611 := [unit-resolution #805 #603]: #845
+#801 := (not #845)
+#641 := (not #541)
+#794 := (or #641 #801 #535)
+#795 := [def-axiom]: #794
+#604 := [unit-resolution #795 #611 #616]: #535
+#796 := (not #535)
+#607 := (or #796 #802)
+#608 := [th-lemma]: #607
+#594 := [unit-resolution #608 #604]: #802
+[th-lemma #594 #286 #627 #636]: false
+unsat
+914ab31d83892bfaa2a8848c9049be9e1ce2cb06 671 0
+#2 := false
+decl f6 :: (-> S2 int)
+decl f5 :: (-> int S2)
+decl f4 :: (-> int int int)
+#55 := 3::int
+decl f7 :: S2
+#53 := f7
+#54 := (f6 f7)
+#56 := (f4 #54 3::int)
+#57 := (f5 #56)
+#805 := (f6 #57)
+#806 := (= #56 #805)
+#476 := (not #806)
+#514 := (= #54 #56)
+#692 := (not #514)
+#473 := (iff #692 #476)
+#483 := (iff #514 #806)
+#490 := (iff #806 #514)
+#679 := (= #56 #54)
+#486 := (iff #679 #514)
+#489 := [commutativity]: #486
+#481 := (iff #806 #679)
+#494 := (= #805 #54)
+#58 := (= #57 f7)
+#274 := (= f7 #57)
+#286 := (>= #54 3::int)
+#11 := 0::int
+#870 := (= #56 0::int)
+#549 := (iff #870 #514)
+#547 := (iff #514 #870)
+#702 := (= 0::int #56)
+#545 := (iff #702 #870)
+#546 := [commutativity]: #545
+#541 := (iff #514 #702)
+#530 := (= #54 0::int)
+#285 := (not #286)
+#632 := [hypothesis]: #285
+#538 := (or #530 #286)
+#708 := 1::int
+#769 := (div #54 3::int)
+#628 := -2::int
+#618 := (* -2::int #769)
+#661 := (mod #54 3::int)
+#85 := -1::int
+#868 := (* -1::int #661)
+#619 := (+ #868 #618)
+#617 := (+ #54 #619)
+#620 := (>= #617 1::int)
+#627 := (not #620)
+#802 := (>= #56 0::int)
+#729 := (>= #661 0::int)
+#1 := true
+#76 := [true-axiom]: true
+#630 := (or false #729)
+#616 := [th-lemma]: #630
+#602 := [unit-resolution #616 #76]: #729
+#542 := (+ #56 #868)
+#817 := (>= #542 0::int)
+#543 := (= #542 0::int)
+#572 := -3::int
+#537 := (* -1::int #54)
+#851 := (mod #537 -3::int)
+#562 := (+ #56 #851)
+#565 := (= #562 0::int)
+#876 := (<= #54 0::int)
+#577 := (not #876)
+#873 := (>= #54 0::int)
+#863 := (not #873)
+#472 := (or #863 #577)
+#559 := (ite #472 #543 #565)
+#713 := (not #530)
+#604 := [hypothesis]: #713
+#606 := (or #530 #559)
+#842 := (ite #530 #870 #559)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#887 := (pattern #29)
+#89 := (* -1::int #9)
+#86 := (* -1::int #8)
+#144 := (mod #86 #89)
+#398 := (+ #29 #144)
+#399 := (= #398 0::int)
+#30 := (mod #8 #9)
+#395 := (* -1::int #30)
+#396 := (+ #29 #395)
+#397 := (= #396 0::int)
+#111 := (<= #9 0::int)
+#107 := (<= #8 0::int)
+#337 := (or #107 #111)
+#338 := (not #337)
+#118 := (>= #8 0::int)
+#320 := (or #111 #118)
+#321 := (not #320)
+#344 := (or #321 #338)
+#400 := (ite #344 #397 #399)
+#394 := (= #29 0::int)
+#12 := (= #8 0::int)
+#401 := (ite #12 #394 #400)
+#393 := (= #8 #29)
+#13 := (= #9 0::int)
+#402 := (ite #13 #393 #401)
+#888 := (forall (vars (?v0 int) (?v1 int)) (:pat #887) #402)
+#405 := (forall (vars (?v0 int) (?v1 int)) #402)
+#891 := (iff #405 #888)
+#889 := (iff #402 #402)
+#890 := [refl]: #889
+#892 := [quant-intro #890]: #891
+#150 := (* -1::int #144)
+#362 := (ite #344 #30 #150)
+#365 := (ite #12 0::int #362)
+#368 := (ite #13 #8 #365)
+#371 := (= #29 #368)
+#374 := (forall (vars (?v0 int) (?v1 int)) #371)
+#406 := (iff #374 #405)
+#403 := (iff #371 #402)
+#404 := [rewrite]: #403
+#407 := [quant-intro #404]: #406
+#119 := (not #118)
+#112 := (not #111)
+#122 := (and #112 #119)
+#108 := (not #107)
+#115 := (and #108 #112)
+#125 := (or #115 #122)
+#170 := (ite #125 #30 #150)
+#173 := (ite #12 0::int #170)
+#176 := (ite #13 #8 #173)
+#179 := (= #29 #176)
+#182 := (forall (vars (?v0 int) (?v1 int)) #179)
+#375 := (iff #182 #374)
+#372 := (iff #179 #371)
+#369 := (= #176 #368)
+#366 := (= #173 #365)
+#363 := (= #170 #362)
+#347 := (iff #125 #344)
+#341 := (or #338 #321)
+#345 := (iff #341 #344)
+#346 := [rewrite]: #345
+#342 := (iff #125 #341)
+#339 := (iff #122 #321)
+#340 := [rewrite]: #339
+#318 := (iff #115 #338)
+#319 := [rewrite]: #318
+#343 := [monotonicity #319 #340]: #342
+#348 := [trans #343 #346]: #347
+#364 := [monotonicity #348]: #363
+#367 := [monotonicity #364]: #366
+#370 := [monotonicity #367]: #369
+#373 := [monotonicity #370]: #372
+#376 := [quant-intro #373]: #375
+#310 := (~ #182 #182)
+#307 := (~ #179 #179)
+#326 := [refl]: #307
+#311 := [nnf-pos #326]: #310
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#185 := (iff #37 #182)
+#79 := (and #16 #18)
+#82 := (or #17 #79)
+#155 := (ite #82 #30 #150)
+#158 := (ite #12 0::int #155)
+#161 := (ite #13 #8 #158)
+#164 := (= #29 #161)
+#167 := (forall (vars (?v0 int) (?v1 int)) #164)
+#183 := (iff #167 #182)
+#180 := (iff #164 #179)
+#177 := (= #161 #176)
+#174 := (= #158 #173)
+#171 := (= #155 #170)
+#126 := (iff #82 #125)
+#123 := (iff #79 #122)
+#120 := (iff #18 #119)
+#121 := [rewrite]: #120
+#113 := (iff #16 #112)
+#114 := [rewrite]: #113
+#124 := [monotonicity #114 #121]: #123
+#116 := (iff #17 #115)
+#109 := (iff #15 #108)
+#110 := [rewrite]: #109
+#117 := [monotonicity #110 #114]: #116
+#127 := [monotonicity #117 #124]: #126
+#172 := [monotonicity #127]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#181 := [monotonicity #178]: #180
+#184 := [quant-intro #181]: #183
+#168 := (iff #37 #167)
+#165 := (iff #36 #164)
+#162 := (= #35 #161)
+#159 := (= #34 #158)
+#156 := (= #33 #155)
+#153 := (= #32 #150)
+#147 := (- #144)
+#151 := (= #147 #150)
+#152 := [rewrite]: #151
+#148 := (= #32 #147)
+#145 := (= #31 #144)
+#90 := (= #23 #89)
+#91 := [rewrite]: #90
+#87 := (= #22 #86)
+#88 := [rewrite]: #87
+#146 := [monotonicity #88 #91]: #145
+#149 := [monotonicity #146]: #148
+#154 := [trans #149 #152]: #153
+#83 := (iff #20 #82)
+#80 := (iff #19 #79)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#157 := [monotonicity #84 #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [monotonicity #163]: #165
+#169 := [quant-intro #166]: #168
+#186 := [trans #169 #184]: #185
+#143 := [asserted]: #37
+#187 := [mp #143 #186]: #182
+#327 := [mp~ #187 #311]: #182
+#377 := [mp #327 #376]: #374
+#408 := [mp #377 #407]: #405
+#893 := [mp #408 #892]: #888
+#840 := (not #888)
+#681 := (or #840 #842)
+#558 := (* -1::int 3::int)
+#872 := (mod #537 #558)
+#874 := (+ #56 #872)
+#531 := (= #874 0::int)
+#875 := (<= 3::int 0::int)
+#877 := (or #876 #875)
+#878 := (not #877)
+#879 := (or #875 #873)
+#869 := (not #879)
+#529 := (or #869 #878)
+#534 := (ite #529 #543 #531)
+#871 := (ite #530 #870 #534)
+#855 := (= 3::int 0::int)
+#518 := (ite #855 #514 #871)
+#682 := (or #840 #518)
+#825 := (iff #682 #681)
+#827 := (iff #681 #681)
+#828 := [rewrite]: #827
+#839 := (iff #518 #842)
+#836 := (ite false #514 #842)
+#833 := (iff #836 #842)
+#838 := [rewrite]: #833
+#837 := (iff #518 #836)
+#846 := (iff #871 #842)
+#841 := (iff #534 #559)
+#843 := (iff #531 #565)
+#563 := (= #874 #562)
+#848 := (= #872 #851)
+#573 := (= #558 -3::int)
+#847 := [rewrite]: #573
+#852 := [monotonicity #847]: #848
+#564 := [monotonicity #852]: #563
+#844 := [monotonicity #564]: #843
+#849 := (iff #529 #472)
+#578 := (iff #878 #577)
+#854 := (iff #877 #876)
+#506 := (or #876 false)
+#867 := (iff #506 #876)
+#853 := [rewrite]: #867
+#866 := (iff #877 #506)
+#521 := (iff #875 false)
+#857 := [rewrite]: #521
+#864 := [monotonicity #857]: #866
+#576 := [trans #864 #853]: #854
+#579 := [monotonicity #576]: #578
+#865 := (iff #869 #863)
+#862 := (iff #879 #873)
+#858 := (or false #873)
+#861 := (iff #858 #873)
+#856 := [rewrite]: #861
+#859 := (iff #879 #858)
+#860 := [monotonicity #857]: #859
+#500 := [trans #860 #856]: #862
+#505 := [monotonicity #500]: #865
+#850 := [monotonicity #505 #579]: #849
+#845 := [monotonicity #850 #844]: #841
+#835 := [monotonicity #845]: #846
+#519 := (iff #855 false)
+#520 := [rewrite]: #519
+#832 := [monotonicity #520 #835]: #837
+#834 := [trans #832 #838]: #839
+#826 := [monotonicity #834]: #825
+#822 := [trans #826 #828]: #825
+#683 := [quant-inst]: #682
+#823 := [mp #683 #822]: #681
+#605 := [unit-resolution #823 #893]: #842
+#698 := (not #842)
+#709 := (or #698 #530 #559)
+#717 := [def-axiom]: #709
+#607 := [unit-resolution #717 #605]: #606
+#608 := [unit-resolution #607 #604]: #559
+#811 := (f5 #54)
+#779 := (f6 #811)
+#781 := (= #779 0::int)
+#592 := (not #781)
+#594 := (iff #713 #592)
+#603 := (iff #530 #781)
+#613 := (iff #781 #530)
+#611 := (= #779 #54)
+#609 := (= #811 f7)
+#815 := (= f7 #811)
+#38 := (:var 0 S2)
+#39 := (f6 #38)
+#894 := (pattern #39)
+#40 := (f5 #39)
+#189 := (= #38 #40)
+#895 := (forall (vars (?v0 S2)) (:pat #894) #189)
+#192 := (forall (vars (?v0 S2)) #189)
+#896 := (iff #192 #895)
+#898 := (iff #895 #895)
+#899 := [rewrite]: #898
+#897 := [rewrite]: #896
+#900 := [trans #897 #899]: #896
+#312 := (~ #192 #192)
+#328 := (~ #189 #189)
+#329 := [refl]: #328
+#313 := [nnf-pos #329]: #312
+#41 := (= #40 #38)
+#42 := (forall (vars (?v0 S2)) #41)
+#193 := (iff #42 #192)
+#190 := (iff #41 #189)
+#191 := [rewrite]: #190
+#194 := [quant-intro #191]: #193
+#188 := [asserted]: #42
+#197 := [mp #188 #194]: #192
+#330 := [mp~ #197 #313]: #192
+#901 := [mp #330 #900]: #895
+#796 := (not #895)
+#793 := (or #796 #815)
+#795 := [quant-inst]: #793
+#685 := [unit-resolution #795 #901]: #815
+#610 := [symm #685]: #609
+#612 := [monotonicity #610]: #611
+#614 := [monotonicity #612]: #613
+#615 := [symm #614]: #603
+#595 := [monotonicity #615]: #594
+#596 := [mp #604 #595]: #592
+#768 := (or #781 #873)
+#44 := (f5 #9)
+#902 := (pattern #44)
+#212 := (>= #9 0::int)
+#45 := (f6 #44)
+#50 := (= #45 0::int)
+#262 := (or #50 #212)
+#909 := (forall (vars (?v0 int)) (:pat #902) #262)
+#267 := (forall (vars (?v0 int)) #262)
+#912 := (iff #267 #909)
+#910 := (iff #262 #262)
+#911 := [refl]: #910
+#913 := [quant-intro #911]: #912
+#316 := (~ #267 #267)
+#334 := (~ #262 #262)
+#335 := [refl]: #334
+#317 := [nnf-pos #335]: #316
+#49 := (< #9 0::int)
+#51 := (implies #49 #50)
+#52 := (forall (vars (?v0 int)) #51)
+#270 := (iff #52 #267)
+#233 := (= 0::int #45)
+#239 := (not #49)
+#240 := (or #239 #233)
+#245 := (forall (vars (?v0 int)) #240)
+#268 := (iff #245 #267)
+#265 := (iff #240 #262)
+#259 := (or #212 #50)
+#263 := (iff #259 #262)
+#264 := [rewrite]: #263
+#260 := (iff #240 #259)
+#257 := (iff #233 #50)
+#258 := [rewrite]: #257
+#255 := (iff #239 #212)
+#215 := (not #212)
+#250 := (not #215)
+#253 := (iff #250 #212)
+#254 := [rewrite]: #253
+#251 := (iff #239 #250)
+#248 := (iff #49 #215)
+#249 := [rewrite]: #248
+#252 := [monotonicity #249]: #251
+#256 := [trans #252 #254]: #255
+#261 := [monotonicity #256 #258]: #260
+#266 := [trans #261 #264]: #265
+#269 := [quant-intro #266]: #268
+#246 := (iff #52 #245)
+#243 := (iff #51 #240)
+#236 := (implies #49 #233)
+#241 := (iff #236 #240)
+#242 := [rewrite]: #241
+#237 := (iff #51 #236)
+#234 := (iff #50 #233)
+#235 := [rewrite]: #234
+#238 := [monotonicity #235]: #237
+#244 := [trans #238 #242]: #243
+#247 := [quant-intro #244]: #246
+#271 := [trans #247 #269]: #270
+#232 := [asserted]: #52
+#272 := [mp #232 #271]: #267
+#336 := [mp~ #272 #317]: #267
+#914 := [mp #336 #913]: #909
+#782 := (not #909)
+#771 := (or #782 #781 #873)
+#772 := (or #782 #768)
+#774 := (iff #772 #771)
+#775 := [rewrite]: #774
+#773 := [quant-inst]: #772
+#776 := [mp #773 #775]: #771
+#597 := [unit-resolution #776 #914]: #768
+#598 := [unit-resolution #597 #596]: #873
+#599 := (or #530 #577 #863)
+#600 := [th-lemma]: #599
+#593 := [unit-resolution #600 #598 #604]: #577
+#824 := (or #472 #876)
+#831 := [def-axiom]: #824
+#601 := [unit-resolution #831 #593]: #472
+#660 := (not #472)
+#818 := (not #559)
+#821 := (or #818 #660 #543)
+#703 := [def-axiom]: #821
+#586 := [unit-resolution #703 #601 #608]: #543
+#664 := (not #543)
+#587 := (or #664 #817)
+#588 := [th-lemma]: #587
+#590 := [unit-resolution #588 #586]: #817
+#591 := (not #729)
+#589 := (not #817)
+#580 := (or #802 #589 #591)
+#581 := [th-lemma]: #580
+#582 := [unit-resolution #581 #590 #602]: #802
+#816 := (<= #542 0::int)
+#574 := (or #664 #816)
+#583 := [th-lemma]: #574
+#584 := [unit-resolution #583 #586]: #816
+#804 := (not #802)
+#649 := (not #816)
+#626 := (or #627 #286 #649 #804)
+#625 := [hypothesis]: #802
+#747 := (* -3::int #769)
+#750 := (+ #868 #747)
+#751 := (+ #54 #750)
+#727 := (<= #751 0::int)
+#746 := (= #751 0::int)
+#657 := (or false #746)
+#695 := [th-lemma]: #657
+#680 := [unit-resolution #695 #76]: #746
+#658 := (not #746)
+#665 := (or #658 #727)
+#667 := [th-lemma]: #665
+#668 := [unit-resolution #667 #680]: #727
+#677 := [hypothesis]: #816
+#633 := [hypothesis]: #620
+#624 := [th-lemma #632 #633 #677 #668 #625]: false
+#629 := [lemma #624]: #626
+#575 := [unit-resolution #629 #584 #632 #582]: #627
+#666 := (>= #751 0::int)
+#640 := (or #658 #666)
+#636 := [th-lemma]: #640
+#641 := [unit-resolution #636 #680]: #666
+#711 := (* -1::int #56)
+#712 := (+ #54 #711)
+#722 := (<= #712 0::int)
+#560 := (not #722)
+#555 := (not #274)
+#557 := (or #555 #286)
+#299 := (iff #274 #286)
+#59 := (< #54 3::int)
+#60 := (not #59)
+#61 := (iff #58 #60)
+#304 := (iff #61 #299)
+#280 := (iff #60 #274)
+#302 := (iff #280 #299)
+#296 := (iff #286 #274)
+#300 := (iff #296 #299)
+#301 := [rewrite]: #300
+#297 := (iff #280 #296)
+#294 := (iff #60 #286)
+#289 := (not #285)
+#292 := (iff #289 #286)
+#293 := [rewrite]: #292
+#290 := (iff #60 #289)
+#287 := (iff #59 #285)
+#288 := [rewrite]: #287
+#291 := [monotonicity #288]: #290
+#295 := [trans #291 #293]: #294
+#298 := [monotonicity #295]: #297
+#303 := [trans #298 #301]: #302
+#283 := (iff #61 #280)
+#277 := (iff #274 #60)
+#281 := (iff #277 #280)
+#282 := [rewrite]: #281
+#278 := (iff #61 #277)
+#275 := (iff #58 #274)
+#276 := [rewrite]: #275
+#279 := [monotonicity #276]: #278
+#284 := [trans #279 #282]: #283
+#305 := [trans #284 #303]: #304
+#273 := [asserted]: #61
+#306 := [mp #273 #305]: #299
+#466 := (not #299)
+#556 := (or #555 #286 #466)
+#484 := [def-axiom]: #556
+#554 := [unit-resolution #484 #306]: #557
+#585 := [unit-resolution #554 #632]: #555
+#693 := (or #692 #274)
+#688 := (= #811 #57)
+#686 := (= #57 #811)
+#678 := [hypothesis]: #514
+#684 := [symm #678]: #679
+#687 := [monotonicity #684]: #686
+#689 := [symm #687]: #688
+#690 := [trans #685 #689]: #274
+#723 := [hypothesis]: #555
+#691 := [unit-resolution #723 #690]: false
+#694 := [lemma #691]: #693
+#566 := [unit-resolution #694 #585]: #692
+#707 := (>= #712 0::int)
+#669 := (* -1::int #769)
+#671 := (+ #868 #669)
+#637 := (+ #54 #671)
+#639 := (>= #637 0::int)
+#621 := (or #639 #876)
+#645 := (not #639)
+#634 := [hypothesis]: #645
+#706 := (>= #661 3::int)
+#730 := (not #706)
+#675 := (or false #730)
+#676 := [th-lemma]: #675
+#659 := [unit-resolution #676 #76]: #730
+#696 := [hypothesis]: #577
+#631 := [th-lemma #696 #659 #641 #634]: false
+#623 := [lemma #631]: #621
+#567 := [unit-resolution #623 #593]: #639
+#643 := (or #645 #649 #707)
+#642 := (not #707)
+#644 := [hypothesis]: #642
+#635 := [hypothesis]: #639
+#638 := [th-lemma #677 #635 #668 #644]: false
+#646 := [lemma #638]: #643
+#568 := [unit-resolution #646 #567 #584]: #707
+#569 := (or #514 #560 #642)
+#570 := [th-lemma]: #569
+#561 := [unit-resolution #570 #568 #566]: #560
+#571 := [th-lemma #590 #561 #641 #575]: false
+#540 := [lemma #571]: #538
+#697 := [unit-resolution #540 #632]: #530
+#532 := [monotonicity #697]: #541
+#548 := [trans #532 #546]: #547
+#539 := [symm #548]: #549
+#699 := (or #713 #870)
+#715 := (or #698 #713 #870)
+#716 := [def-axiom]: #715
+#701 := [unit-resolution #716 #605]: #699
+#728 := [unit-resolution #701 #697]: #870
+#550 := [mp #728 #539]: #514
+#533 := [unit-resolution #566 #550]: false
+#535 := [lemma #533]: #286
+#553 := (or #274 #285)
+#551 := (or #274 #285 #466)
+#552 := [def-axiom]: #551
+#544 := [unit-resolution #552 #306]: #553
+#496 := [unit-resolution #544 #535]: #274
+#498 := [symm #496]: #58
+#499 := [monotonicity #498]: #494
+#485 := [monotonicity #499]: #481
+#491 := [trans #485 #489]: #490
+#492 := [symm #491]: #483
+#474 := [monotonicity #492]: #473
+#524 := (or #577 #285)
+#525 := [th-lemma]: #524
+#526 := [unit-resolution #525 #535]: #577
+#527 := (or #713 #876)
+#516 := [th-lemma]: #527
+#528 := [unit-resolution #516 #526]: #713
+#509 := [unit-resolution #607 #528]: #559
+#511 := [unit-resolution #831 #526]: #472
+#512 := [unit-resolution #703 #511 #509]: #543
+#502 := [unit-resolution #583 #512]: #816
+#508 := (or #560 #285 #706 #649)
+#482 := [th-lemma]: #508
+#487 := [unit-resolution #482 #502 #535 #659]: #560
+#488 := (or #692 #722)
+#493 := [th-lemma]: #488
+#495 := [unit-resolution #493 #487]: #692
+#477 := [mp #495 #474]: #476
+#510 := [unit-resolution #588 #512]: #817
+#513 := (or #802 #591 #589)
+#501 := [th-lemma]: #513
+#503 := [unit-resolution #501 #510 #602]: #802
+#803 := (or #804 #806)
+#196 := (= #9 #45)
+#221 := (or #196 #215)
+#903 := (forall (vars (?v0 int)) (:pat #902) #221)
+#226 := (forall (vars (?v0 int)) #221)
+#906 := (iff #226 #903)
+#904 := (iff #221 #221)
+#905 := [refl]: #904
+#907 := [quant-intro #905]: #906
+#314 := (~ #226 #226)
+#331 := (~ #221 #221)
+#332 := [refl]: #331
+#315 := [nnf-pos #332]: #314
+#46 := (= #45 #9)
+#43 := (<= 0::int #9)
+#47 := (implies #43 #46)
+#48 := (forall (vars (?v0 int)) #47)
+#229 := (iff #48 #226)
+#203 := (not #43)
+#204 := (or #203 #196)
+#209 := (forall (vars (?v0 int)) #204)
+#227 := (iff #209 #226)
+#224 := (iff #204 #221)
+#218 := (or #215 #196)
+#222 := (iff #218 #221)
+#223 := [rewrite]: #222
+#219 := (iff #204 #218)
+#216 := (iff #203 #215)
+#213 := (iff #43 #212)
+#214 := [rewrite]: #213
+#217 := [monotonicity #214]: #216
+#220 := [monotonicity #217]: #219
+#225 := [trans #220 #223]: #224
+#228 := [quant-intro #225]: #227
+#210 := (iff #48 #209)
+#207 := (iff #47 #204)
+#200 := (implies #43 #196)
+#205 := (iff #200 #204)
+#206 := [rewrite]: #205
+#201 := (iff #47 #200)
+#198 := (iff #46 #196)
+#199 := [rewrite]: #198
+#202 := [monotonicity #199]: #201
+#208 := [trans #202 #206]: #207
+#211 := [quant-intro #208]: #210
+#230 := [trans #211 #228]: #229
+#195 := [asserted]: #48
+#231 := [mp #195 #230]: #226
+#333 := [mp~ #231 #315]: #226
+#908 := [mp #333 #907]: #903
+#798 := (not #903)
+#799 := (or #798 #804 #806)
+#807 := (or #806 #804)
+#800 := (or #798 #807)
+#790 := (iff #800 #799)
+#801 := (or #798 #803)
+#788 := (iff #801 #799)
+#789 := [rewrite]: #788
+#785 := (iff #800 #801)
+#808 := (iff #807 #803)
+#797 := [rewrite]: #808
+#786 := [monotonicity #797]: #785
+#791 := [trans #786 #789]: #790
+#794 := [quant-inst]: #800
+#787 := [mp #794 #791]: #799
+#504 := [unit-resolution #787 #908]: #803
+#507 := [unit-resolution #504 #503]: #806
+[unit-resolution #507 #477]: false
+unsat
+d5d2986a8efaefb5e38f30bc14afaad18d3334c6 848 0
 #2 := false
 decl f5 :: (-> int S2)
 decl f6 :: (-> S2 int)
@@ -20524,541 +21938,7 @@
 #1103 := [trans #935 #1102]: #300
 [unit-resolution #308 #1103]: false
 unsat
-c6db48e3ca2ab6d6ca0cc08571bd32ed207dc08a 533 0
-#2 := false
-#55 := 3::int
-decl f6 :: (-> S2 int)
-decl f7 :: S2
-#53 := f7
-#54 := (f6 f7)
-#533 := (mod #54 3::int)
-#664 := (>= #533 3::int)
-#665 := (not #664)
-#1 := true
-#75 := [true-axiom]: true
-#674 := (or false #665)
-#635 := [th-lemma]: #674
-#636 := [unit-resolution #635 #75]: #665
-#11 := 0::int
-decl f5 :: (-> int S2)
-decl f4 :: (-> int int int)
-#56 := (f4 #54 3::int)
-#57 := (f5 #56)
-#58 := (f6 #57)
-#84 := -1::int
-#779 := (* -1::int #58)
-#763 := (+ #56 #779)
-#766 := (>= #763 0::int)
-#773 := (= #56 #58)
-#780 := (>= #56 0::int)
-#784 := (= #58 0::int)
-#649 := (not #784)
-#746 := (<= #58 0::int)
-#643 := (not #746)
-#276 := (>= #58 3::int)
-#59 := (< #58 3::int)
-#60 := (not #59)
-#284 := (iff #60 #276)
-#275 := (not #276)
-#279 := (not #275)
-#282 := (iff #279 #276)
-#283 := [rewrite]: #282
-#280 := (iff #60 #279)
-#277 := (iff #59 #275)
-#278 := [rewrite]: #277
-#281 := [monotonicity #278]: #280
-#285 := [trans #281 #283]: #284
-#272 := [asserted]: #60
-#286 := [mp #272 #285]: #276
-#645 := (or #643 #275)
-#646 := [th-lemma]: #645
-#647 := [unit-resolution #646 #286]: #643
-#650 := (or #649 #746)
-#651 := [th-lemma]: #650
-#652 := [unit-resolution #651 #647]: #649
-#9 := (:var 0 int)
-#44 := (f5 #9)
-#880 := (pattern #44)
-#211 := (>= #9 0::int)
-#45 := (f6 #44)
-#50 := (= #45 0::int)
-#261 := (or #50 #211)
-#887 := (forall (vars (?v0 int)) (:pat #880) #261)
-#266 := (forall (vars (?v0 int)) #261)
-#890 := (iff #266 #887)
-#888 := (iff #261 #261)
-#889 := [refl]: #888
-#891 := [quant-intro #889]: #890
-#294 := (~ #266 #266)
-#312 := (~ #261 #261)
-#313 := [refl]: #312
-#295 := [nnf-pos #313]: #294
-#49 := (< #9 0::int)
-#51 := (implies #49 #50)
-#52 := (forall (vars (?v0 int)) #51)
-#269 := (iff #52 #266)
-#232 := (= 0::int #45)
-#238 := (not #49)
-#239 := (or #238 #232)
-#244 := (forall (vars (?v0 int)) #239)
-#267 := (iff #244 #266)
-#264 := (iff #239 #261)
-#258 := (or #211 #50)
-#262 := (iff #258 #261)
-#263 := [rewrite]: #262
-#259 := (iff #239 #258)
-#256 := (iff #232 #50)
-#257 := [rewrite]: #256
-#254 := (iff #238 #211)
-#214 := (not #211)
-#249 := (not #214)
-#252 := (iff #249 #211)
-#253 := [rewrite]: #252
-#250 := (iff #238 #249)
-#247 := (iff #49 #214)
-#248 := [rewrite]: #247
-#251 := [monotonicity #248]: #250
-#255 := [trans #251 #253]: #254
-#260 := [monotonicity #255 #257]: #259
-#265 := [trans #260 #263]: #264
-#268 := [quant-intro #265]: #267
-#245 := (iff #52 #244)
-#242 := (iff #51 #239)
-#235 := (implies #49 #232)
-#240 := (iff #235 #239)
-#241 := [rewrite]: #240
-#236 := (iff #51 #235)
-#233 := (iff #50 #232)
-#234 := [rewrite]: #233
-#237 := [monotonicity #234]: #236
-#243 := [trans #237 #241]: #242
-#246 := [quant-intro #243]: #245
-#270 := [trans #246 #268]: #269
-#231 := [asserted]: #52
-#271 := [mp #231 #270]: #266
-#314 := [mp~ #271 #295]: #266
-#892 := [mp #314 #891]: #887
-#765 := (not #887)
-#770 := (or #765 #780 #784)
-#785 := (or #784 #780)
-#756 := (or #765 #785)
-#742 := (iff #756 #770)
-#767 := (or #780 #784)
-#759 := (or #765 #767)
-#758 := (iff #759 #770)
-#762 := [rewrite]: #758
-#760 := (iff #756 #759)
-#768 := (iff #785 #767)
-#769 := [rewrite]: #768
-#761 := [monotonicity #769]: #760
-#743 := [trans #761 #762]: #742
-#757 := [quant-inst]: #756
-#745 := [mp #757 #743]: #770
-#653 := [unit-resolution #745 #892 #652]: #780
-#782 := (not #780)
-#783 := (or #773 #782)
-#195 := (= #9 #45)
-#220 := (or #195 #214)
-#881 := (forall (vars (?v0 int)) (:pat #880) #220)
-#225 := (forall (vars (?v0 int)) #220)
-#884 := (iff #225 #881)
-#882 := (iff #220 #220)
-#883 := [refl]: #882
-#885 := [quant-intro #883]: #884
-#292 := (~ #225 #225)
-#309 := (~ #220 #220)
-#310 := [refl]: #309
-#293 := [nnf-pos #310]: #292
-#46 := (= #45 #9)
-#43 := (<= 0::int #9)
-#47 := (implies #43 #46)
-#48 := (forall (vars (?v0 int)) #47)
-#228 := (iff #48 #225)
-#202 := (not #43)
-#203 := (or #202 #195)
-#208 := (forall (vars (?v0 int)) #203)
-#226 := (iff #208 #225)
-#223 := (iff #203 #220)
-#217 := (or #214 #195)
-#221 := (iff #217 #220)
-#222 := [rewrite]: #221
-#218 := (iff #203 #217)
-#215 := (iff #202 #214)
-#212 := (iff #43 #211)
-#213 := [rewrite]: #212
-#216 := [monotonicity #213]: #215
-#219 := [monotonicity #216]: #218
-#224 := [trans #219 #222]: #223
-#227 := [quant-intro #224]: #226
-#209 := (iff #48 #208)
-#206 := (iff #47 #203)
-#199 := (implies #43 #195)
-#204 := (iff #199 #203)
-#205 := [rewrite]: #204
-#200 := (iff #47 #199)
-#197 := (iff #46 #195)
-#198 := [rewrite]: #197
-#201 := [monotonicity #198]: #200
-#207 := [trans #201 #205]: #206
-#210 := [quant-intro #207]: #209
-#229 := [trans #210 #227]: #228
-#194 := [asserted]: #48
-#230 := [mp #194 #229]: #225
-#311 := [mp~ #230 #293]: #225
-#886 := [mp #311 #885]: #881
-#781 := (not #881)
-#786 := (or #781 #773 #782)
-#775 := (or #781 #783)
-#777 := (iff #775 #786)
-#778 := [rewrite]: #777
-#776 := [quant-inst]: #775
-#772 := [mp #776 #778]: #786
-#654 := [unit-resolution #772 #886]: #783
-#637 := [unit-resolution #654 #653]: #773
-#655 := (not #773)
-#625 := (or #655 #766)
-#626 := [th-lemma]: #625
-#627 := [unit-resolution #626 #637]: #766
-#534 := (* -1::int #533)
-#462 := (+ #56 #534)
-#802 := (<= #462 0::int)
-#535 := (= #462 0::int)
-#556 := -3::int
-#529 := (* -1::int #54)
-#827 := (mod #529 -3::int)
-#551 := (+ #56 #827)
-#826 := (= #551 0::int)
-#852 := (>= #54 0::int)
-#498 := (not #852)
-#536 := (<= #54 0::int)
-#841 := (not #536)
-#845 := (or #841 #498)
-#541 := (ite #845 #535 #826)
-#521 := (= #56 0::int)
-#853 := (= #54 0::int)
-#821 := (ite #853 #521 #541)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#865 := (pattern #29)
-#88 := (* -1::int #9)
-#85 := (* -1::int #8)
-#143 := (mod #85 #88)
-#376 := (+ #29 #143)
-#377 := (= #376 0::int)
-#30 := (mod #8 #9)
-#373 := (* -1::int #30)
-#374 := (+ #29 #373)
-#375 := (= #374 0::int)
-#110 := (<= #9 0::int)
-#106 := (<= #8 0::int)
-#315 := (or #106 #110)
-#316 := (not #315)
-#117 := (>= #8 0::int)
-#298 := (or #110 #117)
-#299 := (not #298)
-#322 := (or #299 #316)
-#378 := (ite #322 #375 #377)
-#372 := (= #29 0::int)
-#12 := (= #8 0::int)
-#379 := (ite #12 #372 #378)
-#371 := (= #8 #29)
-#13 := (= #9 0::int)
-#380 := (ite #13 #371 #379)
-#866 := (forall (vars (?v0 int) (?v1 int)) (:pat #865) #380)
-#383 := (forall (vars (?v0 int) (?v1 int)) #380)
-#869 := (iff #383 #866)
-#867 := (iff #380 #380)
-#868 := [refl]: #867
-#870 := [quant-intro #868]: #869
-#149 := (* -1::int #143)
-#340 := (ite #322 #30 #149)
-#343 := (ite #12 0::int #340)
-#346 := (ite #13 #8 #343)
-#349 := (= #29 #346)
-#352 := (forall (vars (?v0 int) (?v1 int)) #349)
-#384 := (iff #352 #383)
-#381 := (iff #349 #380)
-#382 := [rewrite]: #381
-#385 := [quant-intro #382]: #384
-#118 := (not #117)
-#111 := (not #110)
-#121 := (and #111 #118)
-#107 := (not #106)
-#114 := (and #107 #111)
-#124 := (or #114 #121)
-#169 := (ite #124 #30 #149)
-#172 := (ite #12 0::int #169)
-#175 := (ite #13 #8 #172)
-#178 := (= #29 #175)
-#181 := (forall (vars (?v0 int) (?v1 int)) #178)
-#353 := (iff #181 #352)
-#350 := (iff #178 #349)
-#347 := (= #175 #346)
-#344 := (= #172 #343)
-#341 := (= #169 #340)
-#325 := (iff #124 #322)
-#319 := (or #316 #299)
-#323 := (iff #319 #322)
-#324 := [rewrite]: #323
-#320 := (iff #124 #319)
-#317 := (iff #121 #299)
-#318 := [rewrite]: #317
-#296 := (iff #114 #316)
-#297 := [rewrite]: #296
-#321 := [monotonicity #297 #318]: #320
-#326 := [trans #321 #324]: #325
-#342 := [monotonicity #326]: #341
-#345 := [monotonicity #342]: #344
-#348 := [monotonicity #345]: #347
-#351 := [monotonicity #348]: #350
-#354 := [quant-intro #351]: #353
-#288 := (~ #181 #181)
-#273 := (~ #178 #178)
-#304 := [refl]: #273
-#289 := [nnf-pos #304]: #288
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#184 := (iff #37 #181)
-#78 := (and #16 #18)
-#81 := (or #17 #78)
-#154 := (ite #81 #30 #149)
-#157 := (ite #12 0::int #154)
-#160 := (ite #13 #8 #157)
-#163 := (= #29 #160)
-#166 := (forall (vars (?v0 int) (?v1 int)) #163)
-#182 := (iff #166 #181)
-#179 := (iff #163 #178)
-#176 := (= #160 #175)
-#173 := (= #157 #172)
-#170 := (= #154 #169)
-#125 := (iff #81 #124)
-#122 := (iff #78 #121)
-#119 := (iff #18 #118)
-#120 := [rewrite]: #119
-#112 := (iff #16 #111)
-#113 := [rewrite]: #112
-#123 := [monotonicity #113 #120]: #122
-#115 := (iff #17 #114)
-#108 := (iff #15 #107)
-#109 := [rewrite]: #108
-#116 := [monotonicity #109 #113]: #115
-#126 := [monotonicity #116 #123]: #125
-#171 := [monotonicity #126]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#180 := [monotonicity #177]: #179
-#183 := [quant-intro #180]: #182
-#167 := (iff #37 #166)
-#164 := (iff #36 #163)
-#161 := (= #35 #160)
-#158 := (= #34 #157)
-#155 := (= #33 #154)
-#152 := (= #32 #149)
-#146 := (- #143)
-#150 := (= #146 #149)
-#151 := [rewrite]: #150
-#147 := (= #32 #146)
-#144 := (= #31 #143)
-#89 := (= #23 #88)
-#90 := [rewrite]: #89
-#86 := (= #22 #85)
-#87 := [rewrite]: #86
-#145 := [monotonicity #87 #90]: #144
-#148 := [monotonicity #145]: #147
-#153 := [trans #148 #151]: #152
-#82 := (iff #20 #81)
-#79 := (iff #19 #78)
-#80 := [rewrite]: #79
-#83 := [monotonicity #80]: #82
-#156 := [monotonicity #83 #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [monotonicity #162]: #164
-#168 := [quant-intro #165]: #167
-#185 := [trans #168 #183]: #184
-#142 := [asserted]: #37
-#186 := [mp #142 #185]: #181
-#305 := [mp~ #186 #289]: #181
-#355 := [mp #305 #354]: #352
-#386 := [mp #355 #385]: #383
-#871 := [mp #386 #870]: #866
-#810 := (not #866)
-#811 := (or #810 #821)
-#444 := (* -1::int 3::int)
-#530 := (mod #529 #444)
-#531 := (+ #56 #530)
-#522 := (= #531 0::int)
-#532 := (<= 3::int 0::int)
-#515 := (or #536 #532)
-#850 := (not #515)
-#509 := (or #532 #852)
-#639 := (not #509)
-#846 := (or #639 #850)
-#520 := (ite #846 #535 #522)
-#854 := (ite #853 #521 #520)
-#855 := (= #54 #56)
-#856 := (= 3::int 0::int)
-#851 := (ite #856 #855 #854)
-#816 := (or #810 #851)
-#812 := (iff #816 #811)
-#659 := (iff #811 #811)
-#660 := [rewrite]: #659
-#814 := (iff #851 #821)
-#819 := (ite false #855 #821)
-#824 := (iff #819 #821)
-#813 := [rewrite]: #824
-#823 := (iff #851 #819)
-#822 := (iff #854 #821)
-#542 := (iff #520 #541)
-#830 := (iff #522 #826)
-#825 := (= #531 #551)
-#828 := (= #530 #827)
-#557 := (= #444 -3::int)
-#450 := [rewrite]: #557
-#550 := [monotonicity #450]: #828
-#829 := [monotonicity #550]: #825
-#540 := [monotonicity #829]: #830
-#554 := (iff #846 #845)
-#484 := (or #498 #841)
-#831 := (iff #484 #845)
-#832 := [rewrite]: #831
-#844 := (iff #846 #484)
-#843 := (iff #850 #841)
-#840 := (iff #515 #536)
-#836 := (or #536 false)
-#839 := (iff #836 #536)
-#834 := [rewrite]: #839
-#837 := (iff #515 #836)
-#507 := (iff #532 false)
-#512 := [rewrite]: #507
-#838 := [monotonicity #512]: #837
-#478 := [trans #838 #834]: #840
-#483 := [monotonicity #478]: #843
-#499 := (iff #639 #498)
-#496 := (iff #509 #852)
-#848 := (or false #852)
-#492 := (iff #848 #852)
-#833 := [rewrite]: #492
-#508 := (iff #509 #848)
-#849 := [monotonicity #512]: #508
-#497 := [trans #849 #833]: #496
-#835 := [monotonicity #497]: #499
-#842 := [monotonicity #835 #483]: #844
-#555 := [trans #842 #832]: #554
-#543 := [monotonicity #555 #540]: #542
-#537 := [monotonicity #543]: #822
-#857 := (iff #856 false)
-#847 := [rewrite]: #857
-#820 := [monotonicity #847 #537]: #823
-#815 := [trans #820 #813]: #814
-#818 := [monotonicity #815]: #812
-#661 := [trans #818 #660]: #812
-#817 := [quant-inst]: #816
-#803 := [mp #817 #661]: #811
-#628 := [unit-resolution #803 #871]: #821
-#692 := (not #853)
-#691 := (not #521)
-#633 := (iff #649 #691)
-#632 := (iff #784 #521)
-#630 := (iff #521 #784)
-#631 := [monotonicity #637]: #630
-#475 := [symm #631]: #632
-#629 := [monotonicity #475]: #633
-#634 := [mp #652 #629]: #691
-#790 := (not #821)
-#787 := (or #790 #692 #521)
-#788 := [def-axiom]: #787
-#613 := [unit-resolution #788 #634 #628]: #692
-#791 := (or #790 #853 #541)
-#676 := [def-axiom]: #791
-#616 := [unit-resolution #676 #613 #628]: #541
-#696 := (f5 #54)
-#748 := (f6 #696)
-#749 := (= #748 0::int)
-#614 := (not #749)
-#619 := (iff #692 #614)
-#617 := (iff #853 #749)
-#612 := (iff #749 #853)
-#621 := (= #748 #54)
-#622 := (= #696 f7)
-#697 := (= f7 #696)
-#38 := (:var 0 S2)
-#39 := (f6 #38)
-#872 := (pattern #39)
-#40 := (f5 #39)
-#188 := (= #38 #40)
-#873 := (forall (vars (?v0 S2)) (:pat #872) #188)
-#191 := (forall (vars (?v0 S2)) #188)
-#874 := (iff #191 #873)
-#876 := (iff #873 #873)
-#877 := [rewrite]: #876
-#875 := [rewrite]: #874
-#878 := [trans #875 #877]: #874
-#290 := (~ #191 #191)
-#306 := (~ #188 #188)
-#307 := [refl]: #306
-#291 := [nnf-pos #307]: #290
-#41 := (= #40 #38)
-#42 := (forall (vars (?v0 S2)) #41)
-#192 := (iff #42 #191)
-#189 := (iff #41 #188)
-#190 := [rewrite]: #189
-#193 := [quant-intro #190]: #192
-#187 := [asserted]: #42
-#196 := [mp #187 #193]: #191
-#308 := [mp~ #196 #291]: #191
-#879 := [mp #308 #878]: #873
-#792 := (not #873)
-#789 := (or #792 #697)
-#793 := [quant-inst]: #789
-#620 := [unit-resolution #793 #879]: #697
-#623 := [symm #620]: #622
-#624 := [monotonicity #623]: #621
-#615 := [monotonicity #624]: #612
-#618 := [symm #615]: #617
-#609 := [monotonicity #618]: #619
-#599 := [mp #613 #609]: #614
-#750 := (or #749 #852)
-#753 := (or #765 #749 #852)
-#754 := (or #765 #750)
-#755 := (iff #754 #753)
-#733 := [rewrite]: #755
-#744 := [quant-inst]: #754
-#734 := [mp #744 #733]: #753
-#601 := [unit-resolution #734 #892]: #750
-#602 := [unit-resolution #601 #599]: #852
-#605 := (or #853 #841 #498)
-#606 := [th-lemma]: #605
-#610 := [unit-resolution #606 #613]: #845
-#603 := [unit-resolution #610 #602]: #841
-#804 := (or #845 #536)
-#805 := [def-axiom]: #804
-#611 := [unit-resolution #805 #603]: #845
-#801 := (not #845)
-#641 := (not #541)
-#794 := (or #641 #801 #535)
-#795 := [def-axiom]: #794
-#604 := [unit-resolution #795 #611 #616]: #535
-#796 := (not #535)
-#607 := (or #796 #802)
-#608 := [th-lemma]: #607
-#594 := [unit-resolution #608 #604]: #802
-[th-lemma #594 #286 #627 #636]: false
-unsat
-8342168df0506311d150a31ce587a3d2d101af50 961 0
+7c27e22543c792c36da02bc4168bcd3f7ce7432d 961 0
 #2 := false
 decl f5 :: (-> int S2)
 decl f6 :: (-> S2 int)
@@ -22020,679 +22900,7 @@
 #1225 := [trans #1224 #1218]: #301
 [unit-resolution #309 #1225]: false
 unsat
-c2c50da38f700cf1e41aeaaa2ecd24baa852fd7f 671 0
-#2 := false
-decl f6 :: (-> S2 int)
-decl f5 :: (-> int S2)
-decl f4 :: (-> int int int)
-#55 := 3::int
-decl f7 :: S2
-#53 := f7
-#54 := (f6 f7)
-#56 := (f4 #54 3::int)
-#57 := (f5 #56)
-#805 := (f6 #57)
-#806 := (= #56 #805)
-#476 := (not #806)
-#514 := (= #54 #56)
-#692 := (not #514)
-#473 := (iff #692 #476)
-#483 := (iff #514 #806)
-#490 := (iff #806 #514)
-#679 := (= #56 #54)
-#486 := (iff #679 #514)
-#489 := [commutativity]: #486
-#481 := (iff #806 #679)
-#494 := (= #805 #54)
-#58 := (= #57 f7)
-#274 := (= f7 #57)
-#286 := (>= #54 3::int)
-#11 := 0::int
-#870 := (= #56 0::int)
-#549 := (iff #870 #514)
-#547 := (iff #514 #870)
-#702 := (= 0::int #56)
-#545 := (iff #702 #870)
-#546 := [commutativity]: #545
-#541 := (iff #514 #702)
-#530 := (= #54 0::int)
-#285 := (not #286)
-#632 := [hypothesis]: #285
-#538 := (or #530 #286)
-#708 := 1::int
-#769 := (div #54 3::int)
-#628 := -2::int
-#618 := (* -2::int #769)
-#661 := (mod #54 3::int)
-#85 := -1::int
-#868 := (* -1::int #661)
-#619 := (+ #868 #618)
-#617 := (+ #54 #619)
-#620 := (>= #617 1::int)
-#627 := (not #620)
-#802 := (>= #56 0::int)
-#729 := (>= #661 0::int)
-#1 := true
-#76 := [true-axiom]: true
-#630 := (or false #729)
-#616 := [th-lemma]: #630
-#602 := [unit-resolution #616 #76]: #729
-#542 := (+ #56 #868)
-#817 := (>= #542 0::int)
-#543 := (= #542 0::int)
-#572 := -3::int
-#537 := (* -1::int #54)
-#851 := (mod #537 -3::int)
-#562 := (+ #56 #851)
-#565 := (= #562 0::int)
-#876 := (<= #54 0::int)
-#577 := (not #876)
-#873 := (>= #54 0::int)
-#863 := (not #873)
-#472 := (or #863 #577)
-#559 := (ite #472 #543 #565)
-#713 := (not #530)
-#604 := [hypothesis]: #713
-#606 := (or #530 #559)
-#842 := (ite #530 #870 #559)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#887 := (pattern #29)
-#89 := (* -1::int #9)
-#86 := (* -1::int #8)
-#144 := (mod #86 #89)
-#398 := (+ #29 #144)
-#399 := (= #398 0::int)
-#30 := (mod #8 #9)
-#395 := (* -1::int #30)
-#396 := (+ #29 #395)
-#397 := (= #396 0::int)
-#111 := (<= #9 0::int)
-#107 := (<= #8 0::int)
-#337 := (or #107 #111)
-#338 := (not #337)
-#118 := (>= #8 0::int)
-#320 := (or #111 #118)
-#321 := (not #320)
-#344 := (or #321 #338)
-#400 := (ite #344 #397 #399)
-#394 := (= #29 0::int)
-#12 := (= #8 0::int)
-#401 := (ite #12 #394 #400)
-#393 := (= #8 #29)
-#13 := (= #9 0::int)
-#402 := (ite #13 #393 #401)
-#888 := (forall (vars (?v0 int) (?v1 int)) (:pat #887) #402)
-#405 := (forall (vars (?v0 int) (?v1 int)) #402)
-#891 := (iff #405 #888)
-#889 := (iff #402 #402)
-#890 := [refl]: #889
-#892 := [quant-intro #890]: #891
-#150 := (* -1::int #144)
-#362 := (ite #344 #30 #150)
-#365 := (ite #12 0::int #362)
-#368 := (ite #13 #8 #365)
-#371 := (= #29 #368)
-#374 := (forall (vars (?v0 int) (?v1 int)) #371)
-#406 := (iff #374 #405)
-#403 := (iff #371 #402)
-#404 := [rewrite]: #403
-#407 := [quant-intro #404]: #406
-#119 := (not #118)
-#112 := (not #111)
-#122 := (and #112 #119)
-#108 := (not #107)
-#115 := (and #108 #112)
-#125 := (or #115 #122)
-#170 := (ite #125 #30 #150)
-#173 := (ite #12 0::int #170)
-#176 := (ite #13 #8 #173)
-#179 := (= #29 #176)
-#182 := (forall (vars (?v0 int) (?v1 int)) #179)
-#375 := (iff #182 #374)
-#372 := (iff #179 #371)
-#369 := (= #176 #368)
-#366 := (= #173 #365)
-#363 := (= #170 #362)
-#347 := (iff #125 #344)
-#341 := (or #338 #321)
-#345 := (iff #341 #344)
-#346 := [rewrite]: #345
-#342 := (iff #125 #341)
-#339 := (iff #122 #321)
-#340 := [rewrite]: #339
-#318 := (iff #115 #338)
-#319 := [rewrite]: #318
-#343 := [monotonicity #319 #340]: #342
-#348 := [trans #343 #346]: #347
-#364 := [monotonicity #348]: #363
-#367 := [monotonicity #364]: #366
-#370 := [monotonicity #367]: #369
-#373 := [monotonicity #370]: #372
-#376 := [quant-intro #373]: #375
-#310 := (~ #182 #182)
-#307 := (~ #179 #179)
-#326 := [refl]: #307
-#311 := [nnf-pos #326]: #310
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#185 := (iff #37 #182)
-#79 := (and #16 #18)
-#82 := (or #17 #79)
-#155 := (ite #82 #30 #150)
-#158 := (ite #12 0::int #155)
-#161 := (ite #13 #8 #158)
-#164 := (= #29 #161)
-#167 := (forall (vars (?v0 int) (?v1 int)) #164)
-#183 := (iff #167 #182)
-#180 := (iff #164 #179)
-#177 := (= #161 #176)
-#174 := (= #158 #173)
-#171 := (= #155 #170)
-#126 := (iff #82 #125)
-#123 := (iff #79 #122)
-#120 := (iff #18 #119)
-#121 := [rewrite]: #120
-#113 := (iff #16 #112)
-#114 := [rewrite]: #113
-#124 := [monotonicity #114 #121]: #123
-#116 := (iff #17 #115)
-#109 := (iff #15 #108)
-#110 := [rewrite]: #109
-#117 := [monotonicity #110 #114]: #116
-#127 := [monotonicity #117 #124]: #126
-#172 := [monotonicity #127]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#181 := [monotonicity #178]: #180
-#184 := [quant-intro #181]: #183
-#168 := (iff #37 #167)
-#165 := (iff #36 #164)
-#162 := (= #35 #161)
-#159 := (= #34 #158)
-#156 := (= #33 #155)
-#153 := (= #32 #150)
-#147 := (- #144)
-#151 := (= #147 #150)
-#152 := [rewrite]: #151
-#148 := (= #32 #147)
-#145 := (= #31 #144)
-#90 := (= #23 #89)
-#91 := [rewrite]: #90
-#87 := (= #22 #86)
-#88 := [rewrite]: #87
-#146 := [monotonicity #88 #91]: #145
-#149 := [monotonicity #146]: #148
-#154 := [trans #149 #152]: #153
-#83 := (iff #20 #82)
-#80 := (iff #19 #79)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#157 := [monotonicity #84 #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [monotonicity #163]: #165
-#169 := [quant-intro #166]: #168
-#186 := [trans #169 #184]: #185
-#143 := [asserted]: #37
-#187 := [mp #143 #186]: #182
-#327 := [mp~ #187 #311]: #182
-#377 := [mp #327 #376]: #374
-#408 := [mp #377 #407]: #405
-#893 := [mp #408 #892]: #888
-#840 := (not #888)
-#681 := (or #840 #842)
-#558 := (* -1::int 3::int)
-#872 := (mod #537 #558)
-#874 := (+ #56 #872)
-#531 := (= #874 0::int)
-#875 := (<= 3::int 0::int)
-#877 := (or #876 #875)
-#878 := (not #877)
-#879 := (or #875 #873)
-#869 := (not #879)
-#529 := (or #869 #878)
-#534 := (ite #529 #543 #531)
-#871 := (ite #530 #870 #534)
-#855 := (= 3::int 0::int)
-#518 := (ite #855 #514 #871)
-#682 := (or #840 #518)
-#825 := (iff #682 #681)
-#827 := (iff #681 #681)
-#828 := [rewrite]: #827
-#839 := (iff #518 #842)
-#836 := (ite false #514 #842)
-#833 := (iff #836 #842)
-#838 := [rewrite]: #833
-#837 := (iff #518 #836)
-#846 := (iff #871 #842)
-#841 := (iff #534 #559)
-#843 := (iff #531 #565)
-#563 := (= #874 #562)
-#848 := (= #872 #851)
-#573 := (= #558 -3::int)
-#847 := [rewrite]: #573
-#852 := [monotonicity #847]: #848
-#564 := [monotonicity #852]: #563
-#844 := [monotonicity #564]: #843
-#849 := (iff #529 #472)
-#578 := (iff #878 #577)
-#854 := (iff #877 #876)
-#506 := (or #876 false)
-#867 := (iff #506 #876)
-#853 := [rewrite]: #867
-#866 := (iff #877 #506)
-#521 := (iff #875 false)
-#857 := [rewrite]: #521
-#864 := [monotonicity #857]: #866
-#576 := [trans #864 #853]: #854
-#579 := [monotonicity #576]: #578
-#865 := (iff #869 #863)
-#862 := (iff #879 #873)
-#858 := (or false #873)
-#861 := (iff #858 #873)
-#856 := [rewrite]: #861
-#859 := (iff #879 #858)
-#860 := [monotonicity #857]: #859
-#500 := [trans #860 #856]: #862
-#505 := [monotonicity #500]: #865
-#850 := [monotonicity #505 #579]: #849
-#845 := [monotonicity #850 #844]: #841
-#835 := [monotonicity #845]: #846
-#519 := (iff #855 false)
-#520 := [rewrite]: #519
-#832 := [monotonicity #520 #835]: #837
-#834 := [trans #832 #838]: #839
-#826 := [monotonicity #834]: #825
-#822 := [trans #826 #828]: #825
-#683 := [quant-inst]: #682
-#823 := [mp #683 #822]: #681
-#605 := [unit-resolution #823 #893]: #842
-#698 := (not #842)
-#709 := (or #698 #530 #559)
-#717 := [def-axiom]: #709
-#607 := [unit-resolution #717 #605]: #606
-#608 := [unit-resolution #607 #604]: #559
-#811 := (f5 #54)
-#779 := (f6 #811)
-#781 := (= #779 0::int)
-#592 := (not #781)
-#594 := (iff #713 #592)
-#603 := (iff #530 #781)
-#613 := (iff #781 #530)
-#611 := (= #779 #54)
-#609 := (= #811 f7)
-#815 := (= f7 #811)
-#38 := (:var 0 S2)
-#39 := (f6 #38)
-#894 := (pattern #39)
-#40 := (f5 #39)
-#189 := (= #38 #40)
-#895 := (forall (vars (?v0 S2)) (:pat #894) #189)
-#192 := (forall (vars (?v0 S2)) #189)
-#896 := (iff #192 #895)
-#898 := (iff #895 #895)
-#899 := [rewrite]: #898
-#897 := [rewrite]: #896
-#900 := [trans #897 #899]: #896
-#312 := (~ #192 #192)
-#328 := (~ #189 #189)
-#329 := [refl]: #328
-#313 := [nnf-pos #329]: #312
-#41 := (= #40 #38)
-#42 := (forall (vars (?v0 S2)) #41)
-#193 := (iff #42 #192)
-#190 := (iff #41 #189)
-#191 := [rewrite]: #190
-#194 := [quant-intro #191]: #193
-#188 := [asserted]: #42
-#197 := [mp #188 #194]: #192
-#330 := [mp~ #197 #313]: #192
-#901 := [mp #330 #900]: #895
-#796 := (not #895)
-#793 := (or #796 #815)
-#795 := [quant-inst]: #793
-#685 := [unit-resolution #795 #901]: #815
-#610 := [symm #685]: #609
-#612 := [monotonicity #610]: #611
-#614 := [monotonicity #612]: #613
-#615 := [symm #614]: #603
-#595 := [monotonicity #615]: #594
-#596 := [mp #604 #595]: #592
-#768 := (or #781 #873)
-#44 := (f5 #9)
-#902 := (pattern #44)
-#212 := (>= #9 0::int)
-#45 := (f6 #44)
-#50 := (= #45 0::int)
-#262 := (or #50 #212)
-#909 := (forall (vars (?v0 int)) (:pat #902) #262)
-#267 := (forall (vars (?v0 int)) #262)
-#912 := (iff #267 #909)
-#910 := (iff #262 #262)
-#911 := [refl]: #910
-#913 := [quant-intro #911]: #912
-#316 := (~ #267 #267)
-#334 := (~ #262 #262)
-#335 := [refl]: #334
-#317 := [nnf-pos #335]: #316
-#49 := (< #9 0::int)
-#51 := (implies #49 #50)
-#52 := (forall (vars (?v0 int)) #51)
-#270 := (iff #52 #267)
-#233 := (= 0::int #45)
-#239 := (not #49)
-#240 := (or #239 #233)
-#245 := (forall (vars (?v0 int)) #240)
-#268 := (iff #245 #267)
-#265 := (iff #240 #262)
-#259 := (or #212 #50)
-#263 := (iff #259 #262)
-#264 := [rewrite]: #263
-#260 := (iff #240 #259)
-#257 := (iff #233 #50)
-#258 := [rewrite]: #257
-#255 := (iff #239 #212)
-#215 := (not #212)
-#250 := (not #215)
-#253 := (iff #250 #212)
-#254 := [rewrite]: #253
-#251 := (iff #239 #250)
-#248 := (iff #49 #215)
-#249 := [rewrite]: #248
-#252 := [monotonicity #249]: #251
-#256 := [trans #252 #254]: #255
-#261 := [monotonicity #256 #258]: #260
-#266 := [trans #261 #264]: #265
-#269 := [quant-intro #266]: #268
-#246 := (iff #52 #245)
-#243 := (iff #51 #240)
-#236 := (implies #49 #233)
-#241 := (iff #236 #240)
-#242 := [rewrite]: #241
-#237 := (iff #51 #236)
-#234 := (iff #50 #233)
-#235 := [rewrite]: #234
-#238 := [monotonicity #235]: #237
-#244 := [trans #238 #242]: #243
-#247 := [quant-intro #244]: #246
-#271 := [trans #247 #269]: #270
-#232 := [asserted]: #52
-#272 := [mp #232 #271]: #267
-#336 := [mp~ #272 #317]: #267
-#914 := [mp #336 #913]: #909
-#782 := (not #909)
-#771 := (or #782 #781 #873)
-#772 := (or #782 #768)
-#774 := (iff #772 #771)
-#775 := [rewrite]: #774
-#773 := [quant-inst]: #772
-#776 := [mp #773 #775]: #771
-#597 := [unit-resolution #776 #914]: #768
-#598 := [unit-resolution #597 #596]: #873
-#599 := (or #530 #577 #863)
-#600 := [th-lemma]: #599
-#593 := [unit-resolution #600 #598 #604]: #577
-#824 := (or #472 #876)
-#831 := [def-axiom]: #824
-#601 := [unit-resolution #831 #593]: #472
-#660 := (not #472)
-#818 := (not #559)
-#821 := (or #818 #660 #543)
-#703 := [def-axiom]: #821
-#586 := [unit-resolution #703 #601 #608]: #543
-#664 := (not #543)
-#587 := (or #664 #817)
-#588 := [th-lemma]: #587
-#590 := [unit-resolution #588 #586]: #817
-#591 := (not #729)
-#589 := (not #817)
-#580 := (or #802 #589 #591)
-#581 := [th-lemma]: #580
-#582 := [unit-resolution #581 #590 #602]: #802
-#816 := (<= #542 0::int)
-#574 := (or #664 #816)
-#583 := [th-lemma]: #574
-#584 := [unit-resolution #583 #586]: #816
-#804 := (not #802)
-#649 := (not #816)
-#626 := (or #627 #286 #649 #804)
-#625 := [hypothesis]: #802
-#747 := (* -3::int #769)
-#750 := (+ #868 #747)
-#751 := (+ #54 #750)
-#727 := (<= #751 0::int)
-#746 := (= #751 0::int)
-#657 := (or false #746)
-#695 := [th-lemma]: #657
-#680 := [unit-resolution #695 #76]: #746
-#658 := (not #746)
-#665 := (or #658 #727)
-#667 := [th-lemma]: #665
-#668 := [unit-resolution #667 #680]: #727
-#677 := [hypothesis]: #816
-#633 := [hypothesis]: #620
-#624 := [th-lemma #632 #633 #677 #668 #625]: false
-#629 := [lemma #624]: #626
-#575 := [unit-resolution #629 #584 #632 #582]: #627
-#666 := (>= #751 0::int)
-#640 := (or #658 #666)
-#636 := [th-lemma]: #640
-#641 := [unit-resolution #636 #680]: #666
-#711 := (* -1::int #56)
-#712 := (+ #54 #711)
-#722 := (<= #712 0::int)
-#560 := (not #722)
-#555 := (not #274)
-#557 := (or #555 #286)
-#299 := (iff #274 #286)
-#59 := (< #54 3::int)
-#60 := (not #59)
-#61 := (iff #58 #60)
-#304 := (iff #61 #299)
-#280 := (iff #60 #274)
-#302 := (iff #280 #299)
-#296 := (iff #286 #274)
-#300 := (iff #296 #299)
-#301 := [rewrite]: #300
-#297 := (iff #280 #296)
-#294 := (iff #60 #286)
-#289 := (not #285)
-#292 := (iff #289 #286)
-#293 := [rewrite]: #292
-#290 := (iff #60 #289)
-#287 := (iff #59 #285)
-#288 := [rewrite]: #287
-#291 := [monotonicity #288]: #290
-#295 := [trans #291 #293]: #294
-#298 := [monotonicity #295]: #297
-#303 := [trans #298 #301]: #302
-#283 := (iff #61 #280)
-#277 := (iff #274 #60)
-#281 := (iff #277 #280)
-#282 := [rewrite]: #281
-#278 := (iff #61 #277)
-#275 := (iff #58 #274)
-#276 := [rewrite]: #275
-#279 := [monotonicity #276]: #278
-#284 := [trans #279 #282]: #283
-#305 := [trans #284 #303]: #304
-#273 := [asserted]: #61
-#306 := [mp #273 #305]: #299
-#466 := (not #299)
-#556 := (or #555 #286 #466)
-#484 := [def-axiom]: #556
-#554 := [unit-resolution #484 #306]: #557
-#585 := [unit-resolution #554 #632]: #555
-#693 := (or #692 #274)
-#688 := (= #811 #57)
-#686 := (= #57 #811)
-#678 := [hypothesis]: #514
-#684 := [symm #678]: #679
-#687 := [monotonicity #684]: #686
-#689 := [symm #687]: #688
-#690 := [trans #685 #689]: #274
-#723 := [hypothesis]: #555
-#691 := [unit-resolution #723 #690]: false
-#694 := [lemma #691]: #693
-#566 := [unit-resolution #694 #585]: #692
-#707 := (>= #712 0::int)
-#669 := (* -1::int #769)
-#671 := (+ #868 #669)
-#637 := (+ #54 #671)
-#639 := (>= #637 0::int)
-#621 := (or #639 #876)
-#645 := (not #639)
-#634 := [hypothesis]: #645
-#706 := (>= #661 3::int)
-#730 := (not #706)
-#675 := (or false #730)
-#676 := [th-lemma]: #675
-#659 := [unit-resolution #676 #76]: #730
-#696 := [hypothesis]: #577
-#631 := [th-lemma #696 #659 #641 #634]: false
-#623 := [lemma #631]: #621
-#567 := [unit-resolution #623 #593]: #639
-#643 := (or #645 #649 #707)
-#642 := (not #707)
-#644 := [hypothesis]: #642
-#635 := [hypothesis]: #639
-#638 := [th-lemma #677 #635 #668 #644]: false
-#646 := [lemma #638]: #643
-#568 := [unit-resolution #646 #567 #584]: #707
-#569 := (or #514 #560 #642)
-#570 := [th-lemma]: #569
-#561 := [unit-resolution #570 #568 #566]: #560
-#571 := [th-lemma #590 #561 #641 #575]: false
-#540 := [lemma #571]: #538
-#697 := [unit-resolution #540 #632]: #530
-#532 := [monotonicity #697]: #541
-#548 := [trans #532 #546]: #547
-#539 := [symm #548]: #549
-#699 := (or #713 #870)
-#715 := (or #698 #713 #870)
-#716 := [def-axiom]: #715
-#701 := [unit-resolution #716 #605]: #699
-#728 := [unit-resolution #701 #697]: #870
-#550 := [mp #728 #539]: #514
-#533 := [unit-resolution #566 #550]: false
-#535 := [lemma #533]: #286
-#553 := (or #274 #285)
-#551 := (or #274 #285 #466)
-#552 := [def-axiom]: #551
-#544 := [unit-resolution #552 #306]: #553
-#496 := [unit-resolution #544 #535]: #274
-#498 := [symm #496]: #58
-#499 := [monotonicity #498]: #494
-#485 := [monotonicity #499]: #481
-#491 := [trans #485 #489]: #490
-#492 := [symm #491]: #483
-#474 := [monotonicity #492]: #473
-#524 := (or #577 #285)
-#525 := [th-lemma]: #524
-#526 := [unit-resolution #525 #535]: #577
-#527 := (or #713 #876)
-#516 := [th-lemma]: #527
-#528 := [unit-resolution #516 #526]: #713
-#509 := [unit-resolution #607 #528]: #559
-#511 := [unit-resolution #831 #526]: #472
-#512 := [unit-resolution #703 #511 #509]: #543
-#502 := [unit-resolution #583 #512]: #816
-#508 := (or #560 #285 #706 #649)
-#482 := [th-lemma]: #508
-#487 := [unit-resolution #482 #502 #535 #659]: #560
-#488 := (or #692 #722)
-#493 := [th-lemma]: #488
-#495 := [unit-resolution #493 #487]: #692
-#477 := [mp #495 #474]: #476
-#510 := [unit-resolution #588 #512]: #817
-#513 := (or #802 #591 #589)
-#501 := [th-lemma]: #513
-#503 := [unit-resolution #501 #510 #602]: #802
-#803 := (or #804 #806)
-#196 := (= #9 #45)
-#221 := (or #196 #215)
-#903 := (forall (vars (?v0 int)) (:pat #902) #221)
-#226 := (forall (vars (?v0 int)) #221)
-#906 := (iff #226 #903)
-#904 := (iff #221 #221)
-#905 := [refl]: #904
-#907 := [quant-intro #905]: #906
-#314 := (~ #226 #226)
-#331 := (~ #221 #221)
-#332 := [refl]: #331
-#315 := [nnf-pos #332]: #314
-#46 := (= #45 #9)
-#43 := (<= 0::int #9)
-#47 := (implies #43 #46)
-#48 := (forall (vars (?v0 int)) #47)
-#229 := (iff #48 #226)
-#203 := (not #43)
-#204 := (or #203 #196)
-#209 := (forall (vars (?v0 int)) #204)
-#227 := (iff #209 #226)
-#224 := (iff #204 #221)
-#218 := (or #215 #196)
-#222 := (iff #218 #221)
-#223 := [rewrite]: #222
-#219 := (iff #204 #218)
-#216 := (iff #203 #215)
-#213 := (iff #43 #212)
-#214 := [rewrite]: #213
-#217 := [monotonicity #214]: #216
-#220 := [monotonicity #217]: #219
-#225 := [trans #220 #223]: #224
-#228 := [quant-intro #225]: #227
-#210 := (iff #48 #209)
-#207 := (iff #47 #204)
-#200 := (implies #43 #196)
-#205 := (iff #200 #204)
-#206 := [rewrite]: #205
-#201 := (iff #47 #200)
-#198 := (iff #46 #196)
-#199 := [rewrite]: #198
-#202 := [monotonicity #199]: #201
-#208 := [trans #202 #206]: #207
-#211 := [quant-intro #208]: #210
-#230 := [trans #211 #228]: #229
-#195 := [asserted]: #48
-#231 := [mp #195 #230]: #226
-#333 := [mp~ #231 #315]: #226
-#908 := [mp #333 #907]: #903
-#798 := (not #903)
-#799 := (or #798 #804 #806)
-#807 := (or #806 #804)
-#800 := (or #798 #807)
-#790 := (iff #800 #799)
-#801 := (or #798 #803)
-#788 := (iff #801 #799)
-#789 := [rewrite]: #788
-#785 := (iff #800 #801)
-#808 := (iff #807 #803)
-#797 := [rewrite]: #808
-#786 := [monotonicity #797]: #785
-#791 := [trans #786 #789]: #790
-#794 := [quant-inst]: #800
-#787 := [mp #794 #791]: #799
-#504 := [unit-resolution #787 #908]: #803
-#507 := [unit-resolution #504 #503]: #806
-[unit-resolution #507 #477]: false
-unsat
-0acf022ca28d30081e73fadc3fdcfea21e99a21c 60 0
+85ac6a29deaf91400dbfbdf638baba5914d49e18 60 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -22753,7 +22961,7 @@
 #630 := [unit-resolution #632 #631]: #266
 [th-lemma #159 #629 #630]: false
 unsat
-aa7ead3dd8b4a36efac1c966a70956175fb7e15a 60 0
+ec431e8216f1d8b2f670cdb0885c1e07fa83e950 60 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -22814,7 +23022,7 @@
 #630 := [th-lemma]: #632
 [unit-resolution #630 #271 #159]: false
 unsat
-4da37f686a90a43bb4bcf93c60d1755d615df6ac 253 0
+db10b3baed96f5ad894a70d823fdba86b4614481 253 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -23068,129 +23276,7 @@
 #473 := [lemma #472]: #233
 [unit-resolution #631 #473 #487]: false
 unsat
-5536a80305cbc5c1c65da302174d985517f94ac4 60 0
-#2 := false
-#13 := 0::int
-decl f4 :: (-> S2 int)
-decl f5 :: S2
-#25 := f5
-#26 := (f4 f5)
-decl f6 :: S2
-#27 := f6
-#28 := (f4 f6)
-#137 := -1::int
-#138 := (* -1::int #28)
-#139 := (+ #26 #138)
-#140 := (<= #139 0::int)
-#143 := (ite #140 #28 #26)
-#149 := (* -1::int #143)
-#150 := (+ #26 #149)
-#151 := (<= #150 0::int)
-#156 := (not #151)
-#29 := (<= #26 #28)
-#30 := (ite #29 #28 #26)
-#31 := (<= #26 #30)
-#32 := (not #31)
-#157 := (iff #32 #156)
-#154 := (iff #31 #151)
-#146 := (<= #26 #143)
-#152 := (iff #146 #151)
-#153 := [rewrite]: #152
-#147 := (iff #31 #146)
-#144 := (= #30 #143)
-#141 := (iff #29 #140)
-#142 := [rewrite]: #141
-#145 := [monotonicity #142]: #144
-#148 := [monotonicity #145]: #147
-#155 := [trans #148 #153]: #154
-#158 := [monotonicity #155]: #157
-#134 := [asserted]: #32
-#159 := [mp #134 #158]: #156
-#317 := (= #26 #143)
-#232 := (not #140)
-#625 := [hypothesis]: #140
-#637 := (+ #28 #149)
-#280 := (<= #637 0::int)
-#231 := (= #28 #143)
-#318 := (or #232 #231)
-#319 := [def-axiom]: #318
-#626 := [unit-resolution #319 #625]: #231
-#627 := (not #231)
-#622 := (or #627 #280)
-#628 := [th-lemma]: #622
-#266 := [unit-resolution #628 #626]: #280
-#629 := [th-lemma #266 #159 #625]: false
-#631 := [lemma #629]: #232
-#310 := (or #140 #317)
-#321 := [def-axiom]: #310
-#271 := [unit-resolution #321 #631]: #317
-#272 := (not #317)
-#632 := (or #272 #151)
-#630 := [th-lemma]: #632
-[unit-resolution #630 #271 #159]: false
-unsat
-1f939e5dc55e38d665a6a7ffafbec37b57ae831f 60 0
-#2 := false
-#13 := 0::int
-decl f4 :: (-> S2 int)
-decl f6 :: S2
-#27 := f6
-#28 := (f4 f6)
-decl f5 :: S2
-#25 := f5
-#26 := (f4 f5)
-#137 := -1::int
-#140 := (* -1::int #28)
-#141 := (+ #26 #140)
-#139 := (>= #141 0::int)
-#143 := (ite #139 #26 #28)
-#149 := (* -1::int #143)
-#637 := (+ #28 #149)
-#628 := (<= #637 0::int)
-#317 := (= #28 #143)
-#232 := (not #139)
-#231 := (= #26 #143)
-#624 := (not #231)
-#150 := (+ #26 #149)
-#151 := (<= #150 0::int)
-#156 := (not #151)
-#29 := (<= #28 #26)
-#30 := (ite #29 #26 #28)
-#31 := (<= #26 #30)
-#32 := (not #31)
-#157 := (iff #32 #156)
-#154 := (iff #31 #151)
-#146 := (<= #26 #143)
-#152 := (iff #146 #151)
-#153 := [rewrite]: #152
-#147 := (iff #31 #146)
-#144 := (= #30 #143)
-#138 := (iff #29 #139)
-#142 := [rewrite]: #138
-#145 := [monotonicity #142]: #144
-#148 := [monotonicity #145]: #147
-#155 := [trans #148 #153]: #154
-#158 := [monotonicity #155]: #157
-#134 := [asserted]: #32
-#159 := [mp #134 #158]: #156
-#280 := [hypothesis]: #231
-#625 := (or #624 #151)
-#626 := [th-lemma]: #625
-#627 := [unit-resolution #626 #280 #159]: false
-#622 := [lemma #627]: #624
-#318 := (or #232 #231)
-#319 := [def-axiom]: #318
-#629 := [unit-resolution #319 #622]: #232
-#310 := (or #139 #317)
-#321 := [def-axiom]: #310
-#631 := [unit-resolution #321 #629]: #317
-#271 := (not #317)
-#272 := (or #271 #628)
-#632 := [th-lemma]: #272
-#630 := [unit-resolution #632 #631]: #628
-[th-lemma #159 #629 #630]: false
-unsat
-d3e83d573ed30cf5c8453245f4134046eb5c6487 103 0
+89bc3a6333da51700f7daac14eb84da9abc113a1 103 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -23294,7 +23380,404 @@
 #642 := [unit-resolution #636 #635]: #638
 [th-lemma #642 #193 #194]: false
 unsat
-e8bb28c85cd05d1e4eb92c6e0ebb5900ad2217ca 437 0
+c39739842d64e1dca61912be5a777a90f01e28fd 117 0
+#2 := false
+decl f3 :: (-> int S2)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#13 := 0::int
+#141 := -1::int
+#142 := (* -1::int #28)
+#143 := (+ #26 #142)
+#154 := (>= #143 0::int)
+#156 := (ite #154 #28 #26)
+#159 := (f3 #156)
+#144 := (<= #143 0::int)
+#147 := (ite #144 #26 #28)
+#150 := (f3 #147)
+#162 := (= #150 #159)
+#649 := (f3 #26)
+#558 := (= #649 #159)
+#556 := (= #159 #649)
+#564 := (= #156 #26)
+#259 := (= #26 #156)
+#436 := (f3 #28)
+#577 := (= #436 #159)
+#586 := (= #159 #436)
+#479 := (= #156 #28)
+#331 := (= #28 #156)
+#489 := (not #259)
+#584 := [hypothesis]: #489
+#312 := (or #154 #259)
+#647 := [def-axiom]: #312
+#588 := [unit-resolution #647 #584]: #154
+#332 := (not #154)
+#329 := (or #332 #331)
+#333 := [def-axiom]: #329
+#490 := [unit-resolution #333 #588]: #331
+#480 := [symm #490]: #479
+#590 := [monotonicity #480]: #586
+#579 := [symm #590]: #577
+#491 := (= #150 #436)
+#492 := (= #147 #28)
+#326 := (= #28 #147)
+#241 := (not #144)
+#496 := (or #241 #259)
+#473 := (= #26 #28)
+#585 := [hypothesis]: #144
+#488 := [th-lemma #588 #585]: #473
+#494 := [trans #488 #490]: #259
+#495 := [unit-resolution #584 #494]: false
+#589 := [lemma #495]: #496
+#439 := [unit-resolution #589 #584]: #241
+#319 := (or #144 #326)
+#330 := [def-axiom]: #319
+#587 := [unit-resolution #330 #439]: #326
+#493 := [symm #587]: #492
+#484 := [monotonicity #493]: #491
+#571 := [trans #484 #579]: #162
+#165 := (not #162)
+#32 := (<= #28 #26)
+#33 := (ite #32 #28 #26)
+#34 := (f3 #33)
+#29 := (<= #26 #28)
+#30 := (ite #29 #26 #28)
+#31 := (f3 #30)
+#35 := (= #31 #34)
+#36 := (not #35)
+#166 := (iff #36 #165)
+#163 := (iff #35 #162)
+#160 := (= #34 #159)
+#157 := (= #33 #156)
+#153 := (iff #32 #154)
+#155 := [rewrite]: #153
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#151 := (= #31 #150)
+#148 := (= #30 #147)
+#145 := (iff #29 #144)
+#146 := [rewrite]: #145
+#149 := [monotonicity #146]: #148
+#152 := [monotonicity #149]: #151
+#164 := [monotonicity #152 #161]: #163
+#167 := [monotonicity #164]: #166
+#138 := [asserted]: #36
+#168 := [mp #138 #167]: #165
+#568 := [unit-resolution #168 #571]: false
+#570 := [lemma #568]: #259
+#565 := [symm #570]: #564
+#557 := [monotonicity #565]: #556
+#555 := [symm #557]: #558
+#553 := (= #150 #649)
+#562 := (= #147 #26)
+#240 := (= #26 #147)
+#435 := [hypothesis]: #241
+#437 := (or #154 #144)
+#596 := [th-lemma]: #437
+#478 := [unit-resolution #596 #435]: #154
+#580 := [unit-resolution #333 #478]: #331
+#581 := [symm #580]: #479
+#572 := [monotonicity #581]: #586
+#573 := [symm #572]: #577
+#582 := [unit-resolution #330 #435]: #326
+#578 := [symm #582]: #492
+#583 := [monotonicity #578]: #491
+#574 := [trans #583 #573]: #162
+#575 := [unit-resolution #168 #574]: false
+#569 := [lemma #575]: #144
+#327 := (or #241 #240)
+#328 := [def-axiom]: #327
+#566 := [unit-resolution #328 #569]: #240
+#567 := [symm #566]: #562
+#554 := [monotonicity #567]: #553
+#559 := [trans #554 #555]: #162
+[unit-resolution #168 #559]: false
+unsat
+c3edc6cce39c9c380e8b07a4426540e2db018197 156 0
+#2 := false
+decl f3 :: (-> int S2)
+#13 := 0::int
+#30 := (f3 0::int)
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#27 := (<= #26 0::int)
+#28 := (ite #27 #26 0::int)
+#29 := (f3 #28)
+#31 := (= #29 #30)
+#294 := (= #28 0::int)
+#299 := (f3 #26)
+#576 := (f4 #299)
+#577 := (= #576 0::int)
+#442 := (= #26 0::int)
+#567 := (not #294)
+#573 := [hypothesis]: #567
+#287 := (or #27 #294)
+#298 := [def-axiom]: #287
+#404 := [unit-resolution #298 #573]: #27
+#581 := (>= #26 0::int)
+#408 := (not #577)
+#556 := (iff #567 #408)
+#448 := (iff #294 #577)
+#565 := (= #28 #576)
+#564 := (= #26 #576)
+#561 := (= #576 #26)
+#568 := (= #299 f5)
+#227 := (= f5 #299)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#624 := (pattern #9)
+#10 := (f3 #9)
+#50 := (= #8 #10)
+#625 := (forall (vars (?v0 S2)) (:pat #624) #50)
+#53 := (forall (vars (?v0 S2)) #50)
+#626 := (iff #53 #625)
+#628 := (iff #625 #625)
+#629 := [rewrite]: #628
+#627 := [rewrite]: #626
+#630 := [trans #627 #629]: #626
+#148 := (~ #53 #53)
+#146 := (~ #50 #50)
+#147 := [refl]: #146
+#149 := [nnf-pos #147]: #148
+#11 := (= #10 #8)
+#12 := (forall (vars (?v0 S2)) #11)
+#54 := (iff #12 #53)
+#51 := (iff #11 #50)
+#52 := [rewrite]: #51
+#55 := [quant-intro #52]: #54
+#49 := [asserted]: #12
+#58 := [mp #49 #55]: #53
+#137 := [mp~ #58 #149]: #53
+#631 := [mp #137 #630]: #625
+#301 := (not #625)
+#280 := (or #301 #227)
+#616 := [quant-inst]: #280
+#574 := [unit-resolution #616 #631]: #227
+#575 := [symm #574]: #568
+#563 := [monotonicity #575]: #561
+#562 := [symm #563]: #564
+#407 := (= #28 #26)
+#208 := (= #26 #28)
+#209 := (not #27)
+#295 := (or #209 #208)
+#296 := [def-axiom]: #295
+#406 := [unit-resolution #296 #404]: #208
+#560 := [symm #406]: #407
+#447 := [trans #560 #562]: #565
+#449 := [monotonicity #447]: #448
+#458 := [monotonicity #449]: #556
+#553 := [mp #573 #458]: #408
+#582 := (or #577 #581)
+#14 := (:var 0 int)
+#16 := (f3 #14)
+#632 := (pattern #16)
+#75 := (>= #14 0::int)
+#17 := (f4 #16)
+#22 := (= #17 0::int)
+#123 := (or #22 #75)
+#639 := (forall (vars (?v0 int)) (:pat #632) #123)
+#128 := (forall (vars (?v0 int)) #123)
+#642 := (iff #128 #639)
+#640 := (iff #123 #123)
+#641 := [refl]: #640
+#643 := [quant-intro #641]: #642
+#140 := (~ #128 #128)
+#152 := (~ #123 #123)
+#153 := [refl]: #152
+#141 := [nnf-pos #153]: #140
+#21 := (< #14 0::int)
+#23 := (implies #21 #22)
+#24 := (forall (vars (?v0 int)) #23)
+#131 := (iff #24 #128)
+#94 := (= 0::int #17)
+#100 := (not #21)
+#101 := (or #100 #94)
+#106 := (forall (vars (?v0 int)) #101)
+#129 := (iff #106 #128)
+#126 := (iff #101 #123)
+#120 := (or #75 #22)
+#124 := (iff #120 #123)
+#125 := [rewrite]: #124
+#121 := (iff #101 #120)
+#118 := (iff #94 #22)
+#119 := [rewrite]: #118
+#116 := (iff #100 #75)
+#76 := (not #75)
+#111 := (not #76)
+#114 := (iff #111 #75)
+#115 := [rewrite]: #114
+#112 := (iff #100 #111)
+#109 := (iff #21 #76)
+#110 := [rewrite]: #109
+#113 := [monotonicity #110]: #112
+#117 := [trans #113 #115]: #116
+#122 := [monotonicity #117 #119]: #121
+#127 := [trans #122 #125]: #126
+#130 := [quant-intro #127]: #129
+#107 := (iff #24 #106)
+#104 := (iff #23 #101)
+#97 := (implies #21 #94)
+#102 := (iff #97 #101)
+#103 := [rewrite]: #102
+#98 := (iff #23 #97)
+#95 := (iff #22 #94)
+#96 := [rewrite]: #95
+#99 := [monotonicity #96]: #98
+#105 := [trans #99 #103]: #104
+#108 := [quant-intro #105]: #107
+#132 := [trans #108 #130]: #131
+#93 := [asserted]: #24
+#133 := [mp #93 #132]: #128
+#154 := [mp~ #133 #141]: #128
+#644 := [mp #154 #643]: #639
+#614 := (not #639)
+#584 := (or #614 #577 #581)
+#425 := (or #614 #582)
+#427 := (iff #425 #584)
+#569 := [rewrite]: #427
+#426 := [quant-inst]: #425
+#570 := [mp #426 #569]: #584
+#554 := [unit-resolution #570 #644]: #582
+#557 := [unit-resolution #554 #553]: #581
+#457 := [th-lemma #557 #404]: #442
+#459 := [trans #563 #457]: #577
+#460 := [unit-resolution #553 #459]: false
+#453 := [lemma #460]: #294
+#583 := [monotonicity #453]: #31
+#32 := (not #31)
+#134 := [asserted]: #32
+[unit-resolution #134 #583]: false
+unsat
+d84df414dbdb37289879fadf547b4a4bc9c68951 60 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+#137 := -1::int
+#138 := (* -1::int #28)
+#139 := (+ #26 #138)
+#140 := (<= #139 0::int)
+#143 := (ite #140 #28 #26)
+#149 := (* -1::int #143)
+#150 := (+ #26 #149)
+#151 := (<= #150 0::int)
+#156 := (not #151)
+#29 := (<= #26 #28)
+#30 := (ite #29 #28 #26)
+#31 := (<= #26 #30)
+#32 := (not #31)
+#157 := (iff #32 #156)
+#154 := (iff #31 #151)
+#146 := (<= #26 #143)
+#152 := (iff #146 #151)
+#153 := [rewrite]: #152
+#147 := (iff #31 #146)
+#144 := (= #30 #143)
+#141 := (iff #29 #140)
+#142 := [rewrite]: #141
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#155 := [trans #148 #153]: #154
+#158 := [monotonicity #155]: #157
+#134 := [asserted]: #32
+#159 := [mp #134 #158]: #156
+#317 := (= #26 #143)
+#232 := (not #140)
+#625 := [hypothesis]: #140
+#637 := (+ #28 #149)
+#280 := (<= #637 0::int)
+#231 := (= #28 #143)
+#318 := (or #232 #231)
+#319 := [def-axiom]: #318
+#626 := [unit-resolution #319 #625]: #231
+#627 := (not #231)
+#622 := (or #627 #280)
+#628 := [th-lemma]: #622
+#266 := [unit-resolution #628 #626]: #280
+#629 := [th-lemma #266 #159 #625]: false
+#631 := [lemma #629]: #232
+#310 := (or #140 #317)
+#321 := [def-axiom]: #310
+#271 := [unit-resolution #321 #631]: #317
+#272 := (not #317)
+#632 := (or #272 #151)
+#630 := [th-lemma]: #632
+[unit-resolution #630 #271 #159]: false
+unsat
+2abc216904909a8ab09db7d8ddd5116874c405b2 60 0
+#2 := false
+#13 := 0::int
+decl f4 :: (-> S2 int)
+decl f6 :: S2
+#27 := f6
+#28 := (f4 f6)
+decl f5 :: S2
+#25 := f5
+#26 := (f4 f5)
+#137 := -1::int
+#140 := (* -1::int #28)
+#141 := (+ #26 #140)
+#139 := (>= #141 0::int)
+#143 := (ite #139 #26 #28)
+#149 := (* -1::int #143)
+#637 := (+ #28 #149)
+#628 := (<= #637 0::int)
+#317 := (= #28 #143)
+#232 := (not #139)
+#231 := (= #26 #143)
+#624 := (not #231)
+#150 := (+ #26 #149)
+#151 := (<= #150 0::int)
+#156 := (not #151)
+#29 := (<= #28 #26)
+#30 := (ite #29 #26 #28)
+#31 := (<= #26 #30)
+#32 := (not #31)
+#157 := (iff #32 #156)
+#154 := (iff #31 #151)
+#146 := (<= #26 #143)
+#152 := (iff #146 #151)
+#153 := [rewrite]: #152
+#147 := (iff #31 #146)
+#144 := (= #30 #143)
+#138 := (iff #29 #139)
+#142 := [rewrite]: #138
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#155 := [trans #148 #153]: #154
+#158 := [monotonicity #155]: #157
+#134 := [asserted]: #32
+#159 := [mp #134 #158]: #156
+#280 := [hypothesis]: #231
+#625 := (or #624 #151)
+#626 := [th-lemma]: #625
+#627 := [unit-resolution #626 #280 #159]: false
+#622 := [lemma #627]: #624
+#318 := (or #232 #231)
+#319 := [def-axiom]: #318
+#629 := [unit-resolution #319 #622]: #232
+#310 := (or #139 #317)
+#321 := [def-axiom]: #310
+#631 := [unit-resolution #321 #629]: #317
+#271 := (not #317)
+#272 := (or #271 #628)
+#632 := [th-lemma]: #272
+#630 := [unit-resolution #632 #631]: #628
+[th-lemma #159 #629 #630]: false
+unsat
+14969492cac173e86b554790b2b1280f30825e8b 437 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -23732,282 +24215,7 @@
 #462 := [unit-resolution #492 #479]: #669
 [th-lemma #462 #528 #194 #475 #461]: false
 unsat
-ddf4ee3ffc7523dd708ffeab45ca4db621550c07 117 0
-#2 := false
-decl f3 :: (-> int S2)
-decl f4 :: (-> S2 int)
-decl f5 :: S2
-#25 := f5
-#26 := (f4 f5)
-decl f6 :: S2
-#27 := f6
-#28 := (f4 f6)
-#13 := 0::int
-#141 := -1::int
-#142 := (* -1::int #28)
-#143 := (+ #26 #142)
-#154 := (>= #143 0::int)
-#156 := (ite #154 #28 #26)
-#159 := (f3 #156)
-#144 := (<= #143 0::int)
-#147 := (ite #144 #26 #28)
-#150 := (f3 #147)
-#162 := (= #150 #159)
-#649 := (f3 #26)
-#558 := (= #649 #159)
-#556 := (= #159 #649)
-#564 := (= #156 #26)
-#259 := (= #26 #156)
-#436 := (f3 #28)
-#577 := (= #436 #159)
-#586 := (= #159 #436)
-#479 := (= #156 #28)
-#331 := (= #28 #156)
-#489 := (not #259)
-#584 := [hypothesis]: #489
-#312 := (or #154 #259)
-#647 := [def-axiom]: #312
-#588 := [unit-resolution #647 #584]: #154
-#332 := (not #154)
-#329 := (or #332 #331)
-#333 := [def-axiom]: #329
-#490 := [unit-resolution #333 #588]: #331
-#480 := [symm #490]: #479
-#590 := [monotonicity #480]: #586
-#579 := [symm #590]: #577
-#491 := (= #150 #436)
-#492 := (= #147 #28)
-#326 := (= #28 #147)
-#241 := (not #144)
-#496 := (or #241 #259)
-#473 := (= #26 #28)
-#585 := [hypothesis]: #144
-#488 := [th-lemma #588 #585]: #473
-#494 := [trans #488 #490]: #259
-#495 := [unit-resolution #584 #494]: false
-#589 := [lemma #495]: #496
-#439 := [unit-resolution #589 #584]: #241
-#319 := (or #144 #326)
-#330 := [def-axiom]: #319
-#587 := [unit-resolution #330 #439]: #326
-#493 := [symm #587]: #492
-#484 := [monotonicity #493]: #491
-#571 := [trans #484 #579]: #162
-#165 := (not #162)
-#32 := (<= #28 #26)
-#33 := (ite #32 #28 #26)
-#34 := (f3 #33)
-#29 := (<= #26 #28)
-#30 := (ite #29 #26 #28)
-#31 := (f3 #30)
-#35 := (= #31 #34)
-#36 := (not #35)
-#166 := (iff #36 #165)
-#163 := (iff #35 #162)
-#160 := (= #34 #159)
-#157 := (= #33 #156)
-#153 := (iff #32 #154)
-#155 := [rewrite]: #153
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#151 := (= #31 #150)
-#148 := (= #30 #147)
-#145 := (iff #29 #144)
-#146 := [rewrite]: #145
-#149 := [monotonicity #146]: #148
-#152 := [monotonicity #149]: #151
-#164 := [monotonicity #152 #161]: #163
-#167 := [monotonicity #164]: #166
-#138 := [asserted]: #36
-#168 := [mp #138 #167]: #165
-#568 := [unit-resolution #168 #571]: false
-#570 := [lemma #568]: #259
-#565 := [symm #570]: #564
-#557 := [monotonicity #565]: #556
-#555 := [symm #557]: #558
-#553 := (= #150 #649)
-#562 := (= #147 #26)
-#240 := (= #26 #147)
-#435 := [hypothesis]: #241
-#437 := (or #154 #144)
-#596 := [th-lemma]: #437
-#478 := [unit-resolution #596 #435]: #154
-#580 := [unit-resolution #333 #478]: #331
-#581 := [symm #580]: #479
-#572 := [monotonicity #581]: #586
-#573 := [symm #572]: #577
-#582 := [unit-resolution #330 #435]: #326
-#578 := [symm #582]: #492
-#583 := [monotonicity #578]: #491
-#574 := [trans #583 #573]: #162
-#575 := [unit-resolution #168 #574]: false
-#569 := [lemma #575]: #144
-#327 := (or #241 #240)
-#328 := [def-axiom]: #327
-#566 := [unit-resolution #328 #569]: #240
-#567 := [symm #566]: #562
-#554 := [monotonicity #567]: #553
-#559 := [trans #554 #555]: #162
-[unit-resolution #168 #559]: false
-unsat
-12109499f925774016387c1f6f51980ab6ede03b 156 0
-#2 := false
-decl f3 :: (-> int S2)
-#13 := 0::int
-#30 := (f3 0::int)
-decl f4 :: (-> S2 int)
-decl f5 :: S2
-#25 := f5
-#26 := (f4 f5)
-#27 := (<= #26 0::int)
-#28 := (ite #27 #26 0::int)
-#29 := (f3 #28)
-#31 := (= #29 #30)
-#294 := (= #28 0::int)
-#299 := (f3 #26)
-#576 := (f4 #299)
-#577 := (= #576 0::int)
-#442 := (= #26 0::int)
-#567 := (not #294)
-#573 := [hypothesis]: #567
-#287 := (or #27 #294)
-#298 := [def-axiom]: #287
-#404 := [unit-resolution #298 #573]: #27
-#581 := (>= #26 0::int)
-#408 := (not #577)
-#556 := (iff #567 #408)
-#448 := (iff #294 #577)
-#565 := (= #28 #576)
-#564 := (= #26 #576)
-#561 := (= #576 #26)
-#568 := (= #299 f5)
-#227 := (= f5 #299)
-#8 := (:var 0 S2)
-#9 := (f4 #8)
-#624 := (pattern #9)
-#10 := (f3 #9)
-#50 := (= #8 #10)
-#625 := (forall (vars (?v0 S2)) (:pat #624) #50)
-#53 := (forall (vars (?v0 S2)) #50)
-#626 := (iff #53 #625)
-#628 := (iff #625 #625)
-#629 := [rewrite]: #628
-#627 := [rewrite]: #626
-#630 := [trans #627 #629]: #626
-#148 := (~ #53 #53)
-#146 := (~ #50 #50)
-#147 := [refl]: #146
-#149 := [nnf-pos #147]: #148
-#11 := (= #10 #8)
-#12 := (forall (vars (?v0 S2)) #11)
-#54 := (iff #12 #53)
-#51 := (iff #11 #50)
-#52 := [rewrite]: #51
-#55 := [quant-intro #52]: #54
-#49 := [asserted]: #12
-#58 := [mp #49 #55]: #53
-#137 := [mp~ #58 #149]: #53
-#631 := [mp #137 #630]: #625
-#301 := (not #625)
-#280 := (or #301 #227)
-#616 := [quant-inst]: #280
-#574 := [unit-resolution #616 #631]: #227
-#575 := [symm #574]: #568
-#563 := [monotonicity #575]: #561
-#562 := [symm #563]: #564
-#407 := (= #28 #26)
-#208 := (= #26 #28)
-#209 := (not #27)
-#295 := (or #209 #208)
-#296 := [def-axiom]: #295
-#406 := [unit-resolution #296 #404]: #208
-#560 := [symm #406]: #407
-#447 := [trans #560 #562]: #565
-#449 := [monotonicity #447]: #448
-#458 := [monotonicity #449]: #556
-#553 := [mp #573 #458]: #408
-#582 := (or #577 #581)
-#14 := (:var 0 int)
-#16 := (f3 #14)
-#632 := (pattern #16)
-#75 := (>= #14 0::int)
-#17 := (f4 #16)
-#22 := (= #17 0::int)
-#123 := (or #22 #75)
-#639 := (forall (vars (?v0 int)) (:pat #632) #123)
-#128 := (forall (vars (?v0 int)) #123)
-#642 := (iff #128 #639)
-#640 := (iff #123 #123)
-#641 := [refl]: #640
-#643 := [quant-intro #641]: #642
-#140 := (~ #128 #128)
-#152 := (~ #123 #123)
-#153 := [refl]: #152
-#141 := [nnf-pos #153]: #140
-#21 := (< #14 0::int)
-#23 := (implies #21 #22)
-#24 := (forall (vars (?v0 int)) #23)
-#131 := (iff #24 #128)
-#94 := (= 0::int #17)
-#100 := (not #21)
-#101 := (or #100 #94)
-#106 := (forall (vars (?v0 int)) #101)
-#129 := (iff #106 #128)
-#126 := (iff #101 #123)
-#120 := (or #75 #22)
-#124 := (iff #120 #123)
-#125 := [rewrite]: #124
-#121 := (iff #101 #120)
-#118 := (iff #94 #22)
-#119 := [rewrite]: #118
-#116 := (iff #100 #75)
-#76 := (not #75)
-#111 := (not #76)
-#114 := (iff #111 #75)
-#115 := [rewrite]: #114
-#112 := (iff #100 #111)
-#109 := (iff #21 #76)
-#110 := [rewrite]: #109
-#113 := [monotonicity #110]: #112
-#117 := [trans #113 #115]: #116
-#122 := [monotonicity #117 #119]: #121
-#127 := [trans #122 #125]: #126
-#130 := [quant-intro #127]: #129
-#107 := (iff #24 #106)
-#104 := (iff #23 #101)
-#97 := (implies #21 #94)
-#102 := (iff #97 #101)
-#103 := [rewrite]: #102
-#98 := (iff #23 #97)
-#95 := (iff #22 #94)
-#96 := [rewrite]: #95
-#99 := [monotonicity #96]: #98
-#105 := [trans #99 #103]: #104
-#108 := [quant-intro #105]: #107
-#132 := [trans #108 #130]: #131
-#93 := [asserted]: #24
-#133 := [mp #93 #132]: #128
-#154 := [mp~ #133 #141]: #128
-#644 := [mp #154 #643]: #639
-#614 := (not #639)
-#584 := (or #614 #577 #581)
-#425 := (or #614 #582)
-#427 := (iff #425 #584)
-#569 := [rewrite]: #427
-#426 := [quant-inst]: #425
-#570 := [mp #426 #569]: #584
-#554 := [unit-resolution #570 #644]: #582
-#557 := [unit-resolution #554 #553]: #581
-#457 := [th-lemma #557 #404]: #442
-#459 := [trans #563 #457]: #577
-#460 := [unit-resolution #553 #459]: false
-#453 := [lemma #460]: #294
-#583 := [monotonicity #453]: #31
-#32 := (not #31)
-#134 := [asserted]: #32
-[unit-resolution #134 #583]: false
-unsat
-1a0992c511947512c28712c25329faef3db2a506 103 0
+452992a55139d640bc8969517cd3166d0f13bb37 103 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -24111,7 +24319,7 @@
 #642 := [unit-resolution #636 #635]: #639
 [th-lemma #642 #195 #194]: false
 unsat
-2cff16037fa28fd9b7fe01fda3fea3217a638862 119 0
+c2cc039657273f4c31549e108b87c8f33092d45f 119 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -24231,7 +24439,7 @@
 #540 := [trans #557 #539]: #162
 [unit-resolution #168 #540]: false
 unsat
-9e66dd3e51867d9c417bdcc6c8dae7bdcbe15ce9 164 0
+a6a23143d2240b5fcacf31f97f0b436ce20b01cf 164 0
 #2 := false
 decl f3 :: (-> int S2)
 decl f4 :: (-> S2 int)
@@ -24396,7 +24604,7 @@
 #142 := [mp #133 #139]: #137
 [unit-resolution #142 #586]: false
 unsat
-b26c16020695ec5cb482a06eafc452bf48579bac 139 0
+f5e2e20fb8c501f38b6d2f15c9fef9418df3a3f5 139 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -24536,7 +24744,7 @@
 #260 := [th-lemma]: #618
 [unit-resolution #260 #139 #617]: false
 unsat
-cc925ce2d7fa7e6045f376fe0b86848bf9965e04 75 0
+3413e63e105cab337755fe6950808ba664d2597a 75 0
 #2 := false
 decl f3 :: (-> int S2)
 #28 := 1::int
@@ -24612,7 +24820,7 @@
 #153 := [and-elim #151]: #32
 [unit-resolution #153 #339]: false
 unsat
-258c4ff3957e31cbdc91a889a36ababa8b18bb74 20 0
+7c99e4c706a5bfe7c4bac45e274e4bb5f5ba171b 20 0
 #2 := false
 decl f4 :: (-> S2 int)
 decl f5 :: S2
@@ -24633,7 +24841,7 @@
 #130 := [asserted]: #28
 [mp #130 #141]: false
 unsat
-b707e36223641f43f77b1aee28addc35f2bcee4b 319 0
+2c1b55c23f4e7de8da8d5f6f9bfa461e094d5fdc 319 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -24953,25 +25161,7 @@
 #507 := [unit-resolution #506 #504]: #623
 [th-lemma #507 #516 #163 #162]: false
 unsat
-631bb5c1eda2ba4c09e88b58a78c4ca019a52bd5 17 0
-#2 := false
-#8 := 0::int
-#9 := (= 0::int 0::int)
-#10 := (not #9)
-#35 := (iff #10 false)
-#1 := true
-#30 := (not true)
-#33 := (iff #30 false)
-#34 := [rewrite]: #33
-#31 := (iff #10 #30)
-#28 := (iff #9 true)
-#29 := [rewrite]: #28
-#32 := [monotonicity #29]: #31
-#36 := [trans #32 #34]: #35
-#27 := [asserted]: #10
-[mp #27 #36]: false
-unsat
-333d9adb9c916d1ff36a4481fd80329786125ad5 325 0
+b1d5ad1c199444dbf6fe73759c2c90d7c60b146e 325 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -25297,51 +25487,7 @@
 #515 := [th-lemma]: #519
 [unit-resolution #515 #510 #517]: false
 unsat
-28a49ab9e1e8afe831840a9d1d70432378c40524 25 0
-#2 := false
-#8 := 0::int
-#9 := (- 0::int)
-#10 := (= 0::int #9)
-#11 := (not #10)
-#43 := (iff #11 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #11 #38)
-#36 := (iff #10 true)
-#31 := (= 0::int 0::int)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #10 #31)
-#29 := (= #9 0::int)
-#30 := [rewrite]: #29
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#28 := [asserted]: #11
-[mp #28 #44]: false
-unsat
-faf90dd136ed7151b245f7421706b221be33e497 17 0
-#2 := false
-#8 := 1::int
-#9 := (= 1::int 1::int)
-#10 := (not #9)
-#35 := (iff #10 false)
-#1 := true
-#30 := (not true)
-#33 := (iff #30 false)
-#34 := [rewrite]: #33
-#31 := (iff #10 #30)
-#28 := (iff #9 true)
-#29 := [rewrite]: #28
-#32 := [monotonicity #29]: #31
-#36 := [trans #32 #34]: #35
-#27 := [asserted]: #10
-[mp #27 #36]: false
-unsat
-00947a900acc4b06198fe82553f699a3348499ea 38 0
+a489de1c5d2012bec455302dfb4702c1a1df77d2 38 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -25380,42 +25526,7 @@
 #228 := [unit-resolution #313 #154]: #144
 [unit-resolution #228 #155]: false
 unsat
-7392687761c667823aab65a1bcb19e1202861610 34 0
-#2 := false
-#8 := 1::int
-#9 := (- 1::int)
-#10 := (= #9 1::int)
-#11 := (not #10)
-#12 := (not #11)
-#52 := (iff #12 false)
-#1 := true
-#47 := (not true)
-#50 := (iff #47 false)
-#51 := [rewrite]: #50
-#48 := (iff #12 #47)
-#45 := (iff #11 true)
-#40 := (not false)
-#43 := (iff #40 true)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 false)
-#30 := -1::int
-#33 := (= -1::int 1::int)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#31 := (= #9 -1::int)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#29 := [asserted]: #12
-[mp #29 #53]: false
-unsat
-01e7532e7ea90063f4d8028d82907a60219f0691 292 0
+08e6db4ea57a4ed26d47431f93a880d0e622c6f9 292 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -25708,79 +25819,7 @@
 #583 := [unit-resolution #586 #503]: #657
 [th-lemma #583 #605 #592]: false
 unsat
-e368f2011d2d745eea4e08822ed13634e5b6be4e 40 0
-#2 := false
-#12 := 567::int
-#10 := 345::int
-#8 := 123::int
-#9 := (- 123::int)
-#11 := (+ #9 345::int)
-#13 := (< #11 567::int)
-#14 := (not #13)
-#58 := (iff #14 false)
-#38 := 222::int
-#43 := (< 222::int 567::int)
-#46 := (not #43)
-#56 := (iff #46 false)
-#1 := true
-#51 := (not true)
-#54 := (iff #51 false)
-#55 := [rewrite]: #54
-#52 := (iff #46 #51)
-#49 := (iff #43 true)
-#50 := [rewrite]: #49
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#47 := (iff #14 #46)
-#44 := (iff #13 #43)
-#41 := (= #11 222::int)
-#32 := -123::int
-#35 := (+ -123::int 345::int)
-#39 := (= #35 222::int)
-#40 := [rewrite]: #39
-#36 := (= #11 #35)
-#33 := (= #9 -123::int)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#42 := [trans #37 #40]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#59 := [trans #48 #57]: #58
-#31 := [asserted]: #14
-[mp #31 #59]: false
-unsat
-6856ce5c38958c154c5630f30070f1299de0a73a 30 0
-#2 := false
-#10 := 2345678901::int
-#8 := 123456789::int
-#9 := (- 123456789::int)
-#11 := (< #9 2345678901::int)
-#12 := (not #11)
-#48 := (iff #12 false)
-#30 := -123456789::int
-#33 := (< -123456789::int 2345678901::int)
-#36 := (not #33)
-#46 := (iff #36 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #36 #41)
-#39 := (iff #33 true)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#37 := (iff #12 #36)
-#34 := (iff #11 #33)
-#31 := (= #9 -123456789::int)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#38 := [monotonicity #35]: #37
-#49 := [trans #38 #47]: #48
-#29 := [asserted]: #12
-[mp #29 #49]: false
-unsat
-9af62203be53f0918acd3e5a19c29adeb325e821 11 0
+7a80c4532f5787abddc50ad2e7bc9838390acb73 11 0
 #2 := false
 decl f4 :: (-> S2 int)
 decl f5 :: S2
@@ -25792,34 +25831,7 @@
 #129 := [asserted]: #27
 [mp #129 #133]: false
 unsat
-5beff0398ac80bd4310abe8d1006f828914d1ddd 26 0
-#2 := false
-decl f3 :: int
-#8 := f3
-#9 := 0::int
-#10 := (+ f3 0::int)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-ecbbc277377c6ea59671702660167f70e18bac2b 54 0
+a5e0b28483c053128bc0be113d20a82250433b74 54 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -25874,64 +25886,7 @@
 #171 := [and-elim #170]: #144
 [th-lemma #171 #172 #173]: false
 unsat
-89946d5d67b763e42f800ede863ab8bce34f2003 26 0
-#2 := false
-decl f3 :: int
-#9 := f3
-#8 := 0::int
-#10 := (+ 0::int f3)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-bb5d039a38eba1786eb72150674dd17c7a6eed7e 29 0
-#2 := false
-decl f3 :: int
-#8 := f3
-decl f4 :: int
-#9 := f4
-#11 := (+ f4 f3)
-#10 := (+ f3 f4)
-#12 := (= #10 #11)
-#13 := (not #12)
-#45 := (iff #13 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #13 #40)
-#38 := (iff #12 true)
-#33 := (= #10 #10)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #12 #33)
-#31 := (= #11 #10)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#30 := [asserted]: #13
-[mp #30 #46]: false
-unsat
-e761c0b6a7ce21273c17c2e2c5540ab035d56e47 55 0
+4d82a9a048129e417a9e0a1825ce1ac4532cabd0 55 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -25987,41 +25942,7 @@
 #172 := [and-elim #171]: #144
 [th-lemma #172 #173 #174]: false
 unsat
-6be423993ea88d7bfa5dfa04d4fc58ccd8bf39d4 33 0
-#2 := false
-decl f5 :: int
-#10 := f5
-decl f4 :: int
-#9 := f4
-decl f3 :: int
-#8 := f3
-#13 := (+ f3 f4)
-#14 := (+ #13 f5)
-#11 := (+ f4 f5)
-#12 := (+ f3 #11)
-#15 := (= #12 #14)
-#16 := (not #15)
-#48 := (iff #16 false)
-#1 := true
-#43 := (not true)
-#46 := (iff #43 false)
-#47 := [rewrite]: #46
-#44 := (iff #16 #43)
-#41 := (iff #15 true)
-#36 := (= #12 #12)
-#39 := (iff #36 true)
-#40 := [rewrite]: #39
-#37 := (iff #15 #36)
-#34 := (= #14 #12)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#42 := [trans #38 #40]: #41
-#45 := [monotonicity #42]: #44
-#49 := [trans #45 #47]: #48
-#33 := [asserted]: #16
-[mp #33 #49]: false
-unsat
-8ef23587881ccafe5fb8b0c94a42df18ed62c340 55 0
+839ca15e4db302dc5cd29e9aa43868c766ec1b81 55 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -26077,53 +25998,7 @@
 #173 := [and-elim #171]: #152
 [th-lemma #173 #172 #174]: false
 unsat
-f34f9158033293bcd8d531d1fd221cc3340dd1d4 45 0
-#2 := false
-decl f4 :: int
-#9 := f4
-#13 := (- f4)
-decl f3 :: int
-#8 := f3
-#14 := (= f3 #13)
-#11 := 0::int
-#10 := (+ f3 f4)
-#12 := (= #10 0::int)
-#15 := (iff #12 #14)
-#16 := (not #15)
-#62 := (iff #16 false)
-#47 := (not #12)
-#34 := -1::int
-#35 := (* -1::int f4)
-#38 := (= f3 #35)
-#48 := (iff #38 #47)
-#60 := (iff #48 false)
-#55 := (iff #12 #47)
-#58 := (iff #55 false)
-#59 := [rewrite]: #58
-#56 := (iff #48 #55)
-#53 := (iff #38 #12)
-#54 := [rewrite]: #53
-#57 := [monotonicity #54]: #56
-#61 := [trans #57 #59]: #60
-#51 := (iff #16 #48)
-#41 := (iff #12 #38)
-#44 := (not #41)
-#49 := (iff #44 #48)
-#50 := [rewrite]: #49
-#45 := (iff #16 #44)
-#42 := (iff #15 #41)
-#39 := (iff #14 #38)
-#36 := (= #13 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#43 := [monotonicity #40]: #42
-#46 := [monotonicity #43]: #45
-#52 := [trans #46 #50]: #51
-#63 := [trans #52 #61]: #62
-#33 := [asserted]: #16
-[mp #33 #63]: false
-unsat
-3c933bbec35e3b1947f865f102b1cc06b618d6d5 61 0
+2fa07586f302aa9750784686f2cfa4df7ec4584e 61 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -26185,61 +26060,7 @@
 #179 := [and-elim #177]: #149
 [th-lemma #179 #178 #180]: false
 unsat
-581098ef0bfed59ccd21b34aa98652ee0c38c97c 26 0
-#2 := false
-#8 := 1::int
-#9 := (- 1::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)
-#29 := -1::int
-#32 := (= -1::int -1::int)
-#35 := (iff #32 true)
-#36 := [rewrite]: #35
-#33 := (iff #10 #32)
-#30 := (= #9 -1::int)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31 #31]: #33
-#38 := [trans #34 #36]: #37
-#41 := [monotonicity #38]: #40
-#45 := [trans #41 #43]: #44
-#28 := [asserted]: #11
-[mp #28 #45]: false
-unsat
-627b9649fe4139aa10844958a49f92fc2ed56e6b 26 0
-#2 := false
-#8 := 3::int
-#9 := (- 3::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)
-#29 := -3::int
-#32 := (= -3::int -3::int)
-#35 := (iff #32 true)
-#36 := [rewrite]: #35
-#33 := (iff #10 #32)
-#30 := (= #9 -3::int)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31 #31]: #33
-#38 := [trans #34 #36]: #37
-#41 := [monotonicity #38]: #40
-#45 := [trans #41 #43]: #44
-#28 := [asserted]: #11
-[mp #28 #45]: false
-unsat
-6f0da92e2f84bd612985ca7ec2cf4ab63063d3d9 53 0
+fe16712a1fa51f4a62675a12f177489494d4ff85 53 0
 #2 := false
 #13 := 0::int
 decl f4 :: (-> S2 int)
@@ -26293,7 +26114,394 @@
 #171 := [and-elim #169]: #149
 [th-lemma #171 #170 #172]: false
 unsat
-38476cf6298acd443b7e96455508697d68d94894 58 0
+88db0d3335480a81cfc5f118ecaef1678c52c57c 17 0
+#2 := false
+#8 := 0::int
+#9 := (= 0::int 0::int)
+#10 := (not #9)
+#35 := (iff #10 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #10 #30)
+#28 := (iff #9 true)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#27 := [asserted]: #10
+[mp #27 #36]: false
+unsat
+3bd4cf5a7808f0310fbc231a810dbf418d0f69cc 25 0
+#2 := false
+#8 := 0::int
+#9 := (- 0::int)
+#10 := (= 0::int #9)
+#11 := (not #10)
+#43 := (iff #11 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #11 #38)
+#36 := (iff #10 true)
+#31 := (= 0::int 0::int)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #10 #31)
+#29 := (= #9 0::int)
+#30 := [rewrite]: #29
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#28 := [asserted]: #11
+[mp #28 #44]: false
+unsat
+575466500975f7b2e0bdbc552a0711af0164ab2f 17 0
+#2 := false
+#8 := 1::int
+#9 := (= 1::int 1::int)
+#10 := (not #9)
+#35 := (iff #10 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #10 #30)
+#28 := (iff #9 true)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#27 := [asserted]: #10
+[mp #27 #36]: false
+unsat
+a2fa5e02114a58b8161c5f17b5db7f1bd8de21cc 34 0
+#2 := false
+#8 := 1::int
+#9 := (- 1::int)
+#10 := (= #9 1::int)
+#11 := (not #10)
+#12 := (not #11)
+#52 := (iff #12 false)
+#1 := true
+#47 := (not true)
+#50 := (iff #47 false)
+#51 := [rewrite]: #50
+#48 := (iff #12 #47)
+#45 := (iff #11 true)
+#40 := (not false)
+#43 := (iff #40 true)
+#44 := [rewrite]: #43
+#41 := (iff #11 #40)
+#38 := (iff #10 false)
+#30 := -1::int
+#33 := (= -1::int 1::int)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #10 #33)
+#31 := (= #9 -1::int)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#49 := [monotonicity #46]: #48
+#53 := [trans #49 #51]: #52
+#29 := [asserted]: #12
+[mp #29 #53]: false
+unsat
+833da25c34dad32196cafeb37ee24e9c4b09f5e6 40 0
+#2 := false
+#12 := 567::int
+#10 := 345::int
+#8 := 123::int
+#9 := (- 123::int)
+#11 := (+ #9 345::int)
+#13 := (< #11 567::int)
+#14 := (not #13)
+#58 := (iff #14 false)
+#38 := 222::int
+#43 := (< 222::int 567::int)
+#46 := (not #43)
+#56 := (iff #46 false)
+#1 := true
+#51 := (not true)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #46 #51)
+#49 := (iff #43 true)
+#50 := [rewrite]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#47 := (iff #14 #46)
+#44 := (iff #13 #43)
+#41 := (= #11 222::int)
+#32 := -123::int
+#35 := (+ -123::int 345::int)
+#39 := (= #35 222::int)
+#40 := [rewrite]: #39
+#36 := (= #11 #35)
+#33 := (= #9 -123::int)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#42 := [trans #37 #40]: #41
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#59 := [trans #48 #57]: #58
+#31 := [asserted]: #14
+[mp #31 #59]: false
+unsat
+94a3c69e40ab8834fda1414aac36766b6e6d0448 30 0
+#2 := false
+#10 := 2345678901::int
+#8 := 123456789::int
+#9 := (- 123456789::int)
+#11 := (< #9 2345678901::int)
+#12 := (not #11)
+#48 := (iff #12 false)
+#30 := -123456789::int
+#33 := (< -123456789::int 2345678901::int)
+#36 := (not #33)
+#46 := (iff #36 false)
+#1 := true
+#41 := (not true)
+#44 := (iff #41 false)
+#45 := [rewrite]: #44
+#42 := (iff #36 #41)
+#39 := (iff #33 true)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#37 := (iff #12 #36)
+#34 := (iff #11 #33)
+#31 := (= #9 -123456789::int)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#38 := [monotonicity #35]: #37
+#49 := [trans #38 #47]: #48
+#29 := [asserted]: #12
+[mp #29 #49]: false
+unsat
+44da310bca35772c7c4ab7b6f9468b0cf95baf9e 26 0
+#2 := false
+decl f3 :: int
+#8 := f3
+#9 := 0::int
+#10 := (+ f3 0::int)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+fed373ed1a62868b78e70bd0d9a3428669ee5457 26 0
+#2 := false
+decl f3 :: int
+#9 := f3
+#8 := 0::int
+#10 := (+ 0::int f3)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+bb9d75a7a3abc7f60dd441b4f982645b6039e03e 29 0
+#2 := false
+decl f3 :: int
+#8 := f3
+decl f4 :: int
+#9 := f4
+#11 := (+ f4 f3)
+#10 := (+ f3 f4)
+#12 := (= #10 #11)
+#13 := (not #12)
+#45 := (iff #13 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #13 #40)
+#38 := (iff #12 true)
+#33 := (= #10 #10)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #12 #33)
+#31 := (= #11 #10)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#30 := [asserted]: #13
+[mp #30 #46]: false
+unsat
+698ca3e8d5433877845f98d57033a6d63af62497 33 0
+#2 := false
+decl f5 :: int
+#10 := f5
+decl f4 :: int
+#9 := f4
+decl f3 :: int
+#8 := f3
+#13 := (+ f3 f4)
+#14 := (+ #13 f5)
+#11 := (+ f4 f5)
+#12 := (+ f3 #11)
+#15 := (= #12 #14)
+#16 := (not #15)
+#48 := (iff #16 false)
+#1 := true
+#43 := (not true)
+#46 := (iff #43 false)
+#47 := [rewrite]: #46
+#44 := (iff #16 #43)
+#41 := (iff #15 true)
+#36 := (= #12 #12)
+#39 := (iff #36 true)
+#40 := [rewrite]: #39
+#37 := (iff #15 #36)
+#34 := (= #14 #12)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#42 := [trans #38 #40]: #41
+#45 := [monotonicity #42]: #44
+#49 := [trans #45 #47]: #48
+#33 := [asserted]: #16
+[mp #33 #49]: false
+unsat
+41dc588e082dd0bed2354a8e37e9f3c6c05151c1 45 0
+#2 := false
+decl f4 :: int
+#9 := f4
+#13 := (- f4)
+decl f3 :: int
+#8 := f3
+#14 := (= f3 #13)
+#11 := 0::int
+#10 := (+ f3 f4)
+#12 := (= #10 0::int)
+#15 := (iff #12 #14)
+#16 := (not #15)
+#62 := (iff #16 false)
+#47 := (not #12)
+#34 := -1::int
+#35 := (* -1::int f4)
+#38 := (= f3 #35)
+#48 := (iff #38 #47)
+#60 := (iff #48 false)
+#55 := (iff #12 #47)
+#58 := (iff #55 false)
+#59 := [rewrite]: #58
+#56 := (iff #48 #55)
+#53 := (iff #38 #12)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#51 := (iff #16 #48)
+#41 := (iff #12 #38)
+#44 := (not #41)
+#49 := (iff #44 #48)
+#50 := [rewrite]: #49
+#45 := (iff #16 #44)
+#42 := (iff #15 #41)
+#39 := (iff #14 #38)
+#36 := (= #13 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#43 := [monotonicity #40]: #42
+#46 := [monotonicity #43]: #45
+#52 := [trans #46 #50]: #51
+#63 := [trans #52 #61]: #62
+#33 := [asserted]: #16
+[mp #33 #63]: false
+unsat
+d7837998c869430b9e700142d2b377bead7796dc 26 0
+#2 := false
+#8 := 1::int
+#9 := (- 1::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)
+#29 := -1::int
+#32 := (= -1::int -1::int)
+#35 := (iff #32 true)
+#36 := [rewrite]: #35
+#33 := (iff #10 #32)
+#30 := (= #9 -1::int)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31 #31]: #33
+#38 := [trans #34 #36]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#28 := [asserted]: #11
+[mp #28 #45]: false
+unsat
+70a72eb40efd415a7fc201441ac2d390324dc85f 26 0
+#2 := false
+#8 := 3::int
+#9 := (- 3::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)
+#29 := -3::int
+#32 := (= -3::int -3::int)
+#35 := (iff #32 true)
+#36 := [rewrite]: #35
+#33 := (iff #10 #32)
+#30 := (= #9 -3::int)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31 #31]: #33
+#38 := [trans #34 #36]: #37
+#41 := [monotonicity #38]: #40
+#45 := [trans #41 #43]: #44
+#28 := [asserted]: #11
+[mp #28 #45]: false
+unsat
+c4720018b6df523588840d966fa6b5f79e529106 58 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -26352,7 +26560,7 @@
 #31 := [asserted]: #14
 [mp #31 #77]: false
 unsat
-792b4b3859919262c72016c9acfe8ea3843e85d7 61 0
+c156df2cdcaafc0712bbd7f760cf7c1135b2a278 61 0
 #2 := false
 #8 := 0::int
 decl f3 :: int
@@ -26414,67 +26622,7 @@
 #31 := [asserted]: #14
 [mp #31 #79]: false
 unsat
-e55670f249d7d5f46be920cd9d904dea4e4fc39f 26 0
-#2 := false
-decl f3 :: int
-#8 := f3
-#9 := 0::int
-#10 := (- f3 0::int)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-a90b5df92ad9a6706799b2ce3864229806b976dc 32 0
-#2 := false
-decl f3 :: int
-#9 := f3
-#11 := (- f3)
-#8 := 0::int
-#10 := (- 0::int f3)
-#12 := (= #10 #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)
-#31 := -1::int
-#32 := (* -1::int f3)
-#37 := (= #32 #32)
-#40 := (iff #37 true)
-#41 := [rewrite]: #40
-#38 := (iff #12 #37)
-#35 := (= #11 #32)
-#36 := [rewrite]: #35
-#33 := (= #10 #32)
-#34 := [rewrite]: #33
-#39 := [monotonicity #34 #36]: #38
-#43 := [trans #39 #41]: #42
-#46 := [monotonicity #43]: #45
-#50 := [trans #46 #48]: #49
-#30 := [asserted]: #13
-[mp #30 #50]: false
-unsat
-ad72886d0079cf60e87d335a960f64cba8248b20 61 0
+1c28009871674ce12da75bf1dced4812d4d59e07 61 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -26536,7 +26684,67 @@
 #31 := [asserted]: #14
 [mp #31 #79]: false
 unsat
-d08f4e145bad8aa6777f75810df1459ec9077380 64 0
+fc81f629d09c01783c65b3ee17baad49669d55bf 26 0
+#2 := false
+decl f3 :: int
+#8 := f3
+#9 := 0::int
+#10 := (- f3 0::int)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+aec51136d021a387f2d6872e725f19b898f18ef5 32 0
+#2 := false
+decl f3 :: int
+#9 := f3
+#11 := (- f3)
+#8 := 0::int
+#10 := (- 0::int f3)
+#12 := (= #10 #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)
+#31 := -1::int
+#32 := (* -1::int f3)
+#37 := (= #32 #32)
+#40 := (iff #37 true)
+#41 := [rewrite]: #40
+#38 := (iff #12 #37)
+#35 := (= #11 #32)
+#36 := [rewrite]: #35
+#33 := (= #10 #32)
+#34 := [rewrite]: #33
+#39 := [monotonicity #34 #36]: #38
+#43 := [trans #39 #41]: #42
+#46 := [monotonicity #43]: #45
+#50 := [trans #46 #48]: #49
+#30 := [asserted]: #13
+[mp #30 #50]: false
+unsat
+31fc2c351446233f2061fde4a4592b401c54f862 64 0
 #2 := false
 #12 := 0::int
 decl f4 :: int
@@ -26601,7 +26809,7 @@
 #32 := [asserted]: #15
 [mp #32 #81]: false
 unsat
-b835fac148452954f8fe0754df04f54bf681e269 44 0
+7e5077e88974e2fa3da11f2fc124b2fc85a4f520 44 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -26646,7 +26854,7 @@
 #31 := [asserted]: #14
 [mp #31 #61]: false
 unsat
-988b478ff3b6a0c8396fcbd4c2a01d93e477e7a6 42 0
+891b65b932309e97c69155ee809ef85f6496b3c5 42 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -26689,34 +26897,7 @@
 #31 := [asserted]: #14
 [mp #31 #59]: false
 unsat
-8d27e1414f3d037da5784d95941af1a199886e3b 26 0
-#2 := false
-#9 := 0::int
-decl f3 :: int
-#8 := f3
-#10 := (* f3 0::int)
-#11 := (= #10 0::int)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= 0::int 0::int)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-49a025166be07b22ecb69da498e85645cad3436d 48 0
+e90209aecaafc9e5a8d65cc3bfe9923d664d1180 48 0
 #2 := false
 decl f5 :: int
 #11 := f5
@@ -26765,7 +26946,34 @@
 #33 := [asserted]: #16
 [mp #33 #64]: false
 unsat
-7a9044897deb1d6290b6a90dcd09885d5511c7e4 26 0
+65a9f6762bf7c73e050776f2f97205392ade9eb8 26 0
+#2 := false
+#9 := 0::int
+decl f3 :: int
+#8 := f3
+#10 := (* f3 0::int)
+#11 := (= #10 0::int)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= 0::int 0::int)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+592736b964503a2e2a8b3d310866adf35fdeb70d 26 0
 #2 := false
 #8 := 0::int
 decl f3 :: int
@@ -26792,7 +27000,7 @@
 #29 := [asserted]: #12
 [mp #29 #44]: false
 unsat
-5eb0c3df4e96042f330237e1b919e90ecdb74f83 26 0
+89e44e496d1c9e19d85ee56ab3fb92079351f1b0 26 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -26819,7 +27027,7 @@
 #29 := [asserted]: #12
 [mp #29 #44]: false
 unsat
-330d57794eed4517ab10b237d85c8054ec6a5ea1 26 0
+38200cf17f447eb7490b14a7927d61babf42be2c 26 0
 #2 := false
 decl f3 :: int
 #9 := f3
@@ -26846,7 +27054,7 @@
 #29 := [asserted]: #12
 [mp #29 #44]: false
 unsat
-118cf0819162003a4a6b17d8f67a00e396d7fe91 40 0
+f1f03cdf8e0332171bfb331e70236cd578ef1b1a 40 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -26887,7 +27095,7 @@
 #31 := [asserted]: #14
 [mp #31 #58]: false
 unsat
-4971035b314acd7eb08bbed7d6905e357c5d571c 35 0
+dcb91b564372ef4df7bba10a66d7a6eecfdd1891 35 0
 #2 := false
 decl f3 :: int
 #10 := f3
@@ -26923,7 +27131,7 @@
 #31 := [asserted]: #14
 [mp #31 #53]: false
 unsat
-d8009fc7f359356bf7ea607592f41aaeaef5cced 28 0
+e58e9441ca33f62ea126f129a1302457840ee037 28 0
 #2 := false
 #8 := 3::int
 decl f3 :: int
@@ -26952,7 +27160,7 @@
 #30 := [asserted]: #13
 [mp #30 #46]: false
 unsat
-5f6da7a3c4fe819b8be2bc640a3f6427ec98f801 244 0
+dc9c4895f383c2bc2209a55e4f8478193dad358d 244 0
 #2 := false
 #11 := 0::int
 decl f3 :: (-> int int int)
@@ -27197,276 +27405,7 @@
 #683 := [mp #696 #682]: #695
 [unit-resolution #683 #742 #167]: false
 unsat
-c874d9a87d8800bf1a614a4635e058f59b457075 268 0
-#2 := false
-#11 := 0::int
-decl f4 :: (-> int int int)
-#38 := (f4 0::int 0::int)
-#39 := (= #38 0::int)
-#40 := (not #39)
-#167 := [asserted]: #40
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#743 := (pattern #29)
-#64 := -1::int
-#68 := (* -1::int #9)
-#65 := (* -1::int #8)
-#123 := (mod #65 #68)
-#254 := (+ #29 #123)
-#255 := (= #254 0::int)
-#30 := (mod #8 #9)
-#251 := (* -1::int #30)
-#252 := (+ #29 #251)
-#253 := (= #252 0::int)
-#90 := (<= #9 0::int)
-#86 := (<= #8 0::int)
-#193 := (or #86 #90)
-#194 := (not #193)
-#97 := (>= #8 0::int)
-#185 := (or #90 #97)
-#186 := (not #185)
-#200 := (or #186 #194)
-#256 := (ite #200 #253 #255)
-#250 := (= #29 0::int)
-#12 := (= #8 0::int)
-#257 := (ite #12 #250 #256)
-#249 := (= #8 #29)
-#13 := (= #9 0::int)
-#258 := (ite #13 #249 #257)
-#744 := (forall (vars (?v0 int) (?v1 int)) (:pat #743) #258)
-#261 := (forall (vars (?v0 int) (?v1 int)) #258)
-#747 := (iff #261 #744)
-#745 := (iff #258 #258)
-#746 := [refl]: #745
-#748 := [quant-intro #746]: #747
-#129 := (* -1::int #123)
-#218 := (ite #200 #30 #129)
-#221 := (ite #12 0::int #218)
-#224 := (ite #13 #8 #221)
-#227 := (= #29 #224)
-#230 := (forall (vars (?v0 int) (?v1 int)) #227)
-#262 := (iff #230 #261)
-#259 := (iff #227 #258)
-#260 := [rewrite]: #259
-#263 := [quant-intro #260]: #262
-#98 := (not #97)
-#91 := (not #90)
-#101 := (and #91 #98)
-#87 := (not #86)
-#94 := (and #87 #91)
-#104 := (or #94 #101)
-#149 := (ite #104 #30 #129)
-#152 := (ite #12 0::int #149)
-#155 := (ite #13 #8 #152)
-#158 := (= #29 #155)
-#161 := (forall (vars (?v0 int) (?v1 int)) #158)
-#231 := (iff #161 #230)
-#228 := (iff #158 #227)
-#225 := (= #155 #224)
-#222 := (= #152 #221)
-#219 := (= #149 #218)
-#203 := (iff #104 #200)
-#197 := (or #194 #186)
-#201 := (iff #197 #200)
-#202 := [rewrite]: #201
-#198 := (iff #104 #197)
-#195 := (iff #101 #186)
-#196 := [rewrite]: #195
-#183 := (iff #94 #194)
-#184 := [rewrite]: #183
-#199 := [monotonicity #184 #196]: #198
-#204 := [trans #199 #202]: #203
-#220 := [monotonicity #204]: #219
-#223 := [monotonicity #220]: #222
-#226 := [monotonicity #223]: #225
-#229 := [monotonicity #226]: #228
-#232 := [quant-intro #229]: #231
-#181 := (~ #161 #161)
-#178 := (~ #158 #158)
-#191 := [refl]: #178
-#182 := [nnf-pos #191]: #181
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#164 := (iff #37 #161)
-#58 := (and #16 #18)
-#61 := (or #17 #58)
-#134 := (ite #61 #30 #129)
-#137 := (ite #12 0::int #134)
-#140 := (ite #13 #8 #137)
-#143 := (= #29 #140)
-#146 := (forall (vars (?v0 int) (?v1 int)) #143)
-#162 := (iff #146 #161)
-#159 := (iff #143 #158)
-#156 := (= #140 #155)
-#153 := (= #137 #152)
-#150 := (= #134 #149)
-#105 := (iff #61 #104)
-#102 := (iff #58 #101)
-#99 := (iff #18 #98)
-#100 := [rewrite]: #99
-#92 := (iff #16 #91)
-#93 := [rewrite]: #92
-#103 := [monotonicity #93 #100]: #102
-#95 := (iff #17 #94)
-#88 := (iff #15 #87)
-#89 := [rewrite]: #88
-#96 := [monotonicity #89 #93]: #95
-#106 := [monotonicity #96 #103]: #105
-#151 := [monotonicity #106]: #150
-#154 := [monotonicity #151]: #153
-#157 := [monotonicity #154]: #156
-#160 := [monotonicity #157]: #159
-#163 := [quant-intro #160]: #162
-#147 := (iff #37 #146)
-#144 := (iff #36 #143)
-#141 := (= #35 #140)
-#138 := (= #34 #137)
-#135 := (= #33 #134)
-#132 := (= #32 #129)
-#126 := (- #123)
-#130 := (= #126 #129)
-#131 := [rewrite]: #130
-#127 := (= #32 #126)
-#124 := (= #31 #123)
-#69 := (= #23 #68)
-#70 := [rewrite]: #69
-#66 := (= #22 #65)
-#67 := [rewrite]: #66
-#125 := [monotonicity #67 #70]: #124
-#128 := [monotonicity #125]: #127
-#133 := [trans #128 #131]: #132
-#62 := (iff #20 #61)
-#59 := (iff #19 #58)
-#60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#136 := [monotonicity #63 #133]: #135
-#139 := [monotonicity #136]: #138
-#142 := [monotonicity #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [quant-intro #145]: #147
-#165 := [trans #148 #163]: #164
-#122 := [asserted]: #37
-#166 := [mp #122 #165]: #161
-#192 := [mp~ #166 #182]: #161
-#233 := [mp #192 #232]: #230
-#264 := [mp #233 #263]: #261
-#749 := [mp #264 #748]: #744
-#690 := (not #744)
-#696 := (or #690 #39)
-#322 := (* -1::int 0::int)
-#407 := (mod #322 #322)
-#408 := (+ #38 #407)
-#409 := (= #408 0::int)
-#400 := (mod 0::int 0::int)
-#411 := (* -1::int #400)
-#412 := (+ #38 #411)
-#340 := (= #412 0::int)
-#413 := (<= 0::int 0::int)
-#410 := (or #413 #413)
-#414 := (not #410)
-#393 := (>= 0::int 0::int)
-#728 := (or #413 #393)
-#730 := (not #728)
-#387 := (or #730 #414)
-#517 := (ite #387 #340 #409)
-#724 := (= 0::int 0::int)
-#398 := (ite #724 #39 #517)
-#168 := (= 0::int #38)
-#399 := (ite #724 #168 #398)
-#537 := (or #690 #399)
-#539 := (iff #537 #696)
-#682 := (iff #696 #696)
-#683 := [rewrite]: #682
-#694 := (iff #399 #39)
-#1 := true
-#691 := (ite true #39 #39)
-#688 := (iff #691 #39)
-#689 := [rewrite]: #688
-#692 := (iff #399 #691)
-#698 := (iff #398 #39)
-#328 := (+ #38 #400)
-#428 := (= #328 0::int)
-#699 := (ite true #39 #428)
-#697 := (iff #699 #39)
-#701 := [rewrite]: #697
-#700 := (iff #398 #699)
-#420 := (iff #517 #428)
-#707 := (ite false #340 #428)
-#418 := (iff #707 #428)
-#419 := [rewrite]: #418
-#704 := (iff #517 #707)
-#429 := (iff #409 #428)
-#705 := (= #408 #328)
-#434 := (= #407 #400)
-#432 := (= #322 0::int)
-#433 := [rewrite]: #432
-#435 := [monotonicity #433 #433]: #434
-#706 := [monotonicity #435]: #705
-#703 := [monotonicity #706]: #429
-#709 := (iff #387 false)
-#361 := (or false false)
-#720 := (iff #361 false)
-#723 := [rewrite]: #720
-#362 := (iff #387 #361)
-#719 := (iff #414 false)
-#711 := (not true)
-#376 := (iff #711 false)
-#377 := [rewrite]: #376
-#718 := (iff #414 #711)
-#717 := (iff #410 true)
-#725 := (or true true)
-#726 := (iff #725 true)
-#386 := [rewrite]: #726
-#715 := (iff #410 #725)
-#733 := (iff #413 true)
-#734 := [rewrite]: #733
-#716 := [monotonicity #734 #734]: #715
-#712 := [trans #716 #386]: #717
-#356 := [monotonicity #712]: #718
-#721 := [trans #356 #377]: #719
-#713 := (iff #730 false)
-#374 := (iff #730 #711)
-#727 := (iff #728 true)
-#385 := (iff #728 #725)
-#729 := (iff #393 true)
-#735 := [rewrite]: #729
-#390 := [monotonicity #734 #735]: #385
-#370 := [trans #390 #386]: #727
-#375 := [monotonicity #370]: #374
-#714 := [trans #375 #377]: #713
-#722 := [monotonicity #714 #721]: #362
-#710 := [trans #722 #723]: #709
-#708 := [monotonicity #710 #703]: #704
-#421 := [trans #708 #419]: #420
-#731 := (iff #724 true)
-#732 := [rewrite]: #731
-#415 := [monotonicity #732 #421]: #700
-#702 := [trans #415 #701]: #698
-#174 := (iff #168 #39)
-#175 := [rewrite]: #174
-#693 := [monotonicity #732 #175 #702]: #692
-#695 := [trans #693 #689]: #694
-#681 := [monotonicity #695]: #539
-#684 := [trans #681 #683]: #539
-#538 := [quant-inst]: #537
-#678 := [mp #538 #684]: #696
-[unit-resolution #678 #749 #167]: false
-unsat
-3f2a64334c06cd9085e37e04663f0058aaac8b80 257 0
+6b27a316bc3cb1671937528bbb2aa4c5f16dd00c 257 0
 #2 := false
 #11 := 0::int
 decl f3 :: (-> int int int)
@@ -27724,7 +27663,7 @@
 #673 := [mp #687 #520]: #680
 [unit-resolution #673 #743 #168]: false
 unsat
-2feb38075fe02eeb2836b76bf8c76e21fff33262 281 0
+ac9468ec7d34e56bdf0ee161b89fe3a4afadc438 281 0
 #2 := false
 #11 := 0::int
 decl f3 :: (-> int int int)
@@ -28006,284 +27945,7 @@
 #667 := [mp #573 #670]: #572
 [unit-resolution #667 #742 #168]: false
 unsat
-6b83c7688301a86c79fbfd8522bd1686332a1eaf 276 0
-#2 := false
-decl f4 :: (-> int int int)
-#11 := 0::int
-decl f5 :: int
-#38 := f5
-#39 := (f4 f5 0::int)
-#169 := (= f5 #39)
-#172 := (not #169)
-#40 := (= #39 f5)
-#41 := (not #40)
-#173 := (iff #41 #172)
-#170 := (iff #40 #169)
-#171 := [rewrite]: #170
-#174 := [monotonicity #171]: #173
-#168 := [asserted]: #41
-#177 := [mp #168 #174]: #172
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#741 := (pattern #29)
-#65 := -1::int
-#69 := (* -1::int #9)
-#66 := (* -1::int #8)
-#124 := (mod #66 #69)
-#252 := (+ #29 #124)
-#253 := (= #252 0::int)
-#30 := (mod #8 #9)
-#249 := (* -1::int #30)
-#250 := (+ #29 #249)
-#251 := (= #250 0::int)
-#91 := (<= #9 0::int)
-#87 := (<= #8 0::int)
-#191 := (or #87 #91)
-#192 := (not #191)
-#98 := (>= #8 0::int)
-#183 := (or #91 #98)
-#184 := (not #183)
-#198 := (or #184 #192)
-#254 := (ite #198 #251 #253)
-#248 := (= #29 0::int)
-#12 := (= #8 0::int)
-#255 := (ite #12 #248 #254)
-#247 := (= #8 #29)
-#13 := (= #9 0::int)
-#256 := (ite #13 #247 #255)
-#742 := (forall (vars (?v0 int) (?v1 int)) (:pat #741) #256)
-#259 := (forall (vars (?v0 int) (?v1 int)) #256)
-#745 := (iff #259 #742)
-#743 := (iff #256 #256)
-#744 := [refl]: #743
-#746 := [quant-intro #744]: #745
-#130 := (* -1::int #124)
-#216 := (ite #198 #30 #130)
-#219 := (ite #12 0::int #216)
-#222 := (ite #13 #8 #219)
-#225 := (= #29 #222)
-#228 := (forall (vars (?v0 int) (?v1 int)) #225)
-#260 := (iff #228 #259)
-#257 := (iff #225 #256)
-#258 := [rewrite]: #257
-#261 := [quant-intro #258]: #260
-#99 := (not #98)
-#92 := (not #91)
-#102 := (and #92 #99)
-#88 := (not #87)
-#95 := (and #88 #92)
-#105 := (or #95 #102)
-#150 := (ite #105 #30 #130)
-#153 := (ite #12 0::int #150)
-#156 := (ite #13 #8 #153)
-#159 := (= #29 #156)
-#162 := (forall (vars (?v0 int) (?v1 int)) #159)
-#229 := (iff #162 #228)
-#226 := (iff #159 #225)
-#223 := (= #156 #222)
-#220 := (= #153 #219)
-#217 := (= #150 #216)
-#201 := (iff #105 #198)
-#195 := (or #192 #184)
-#199 := (iff #195 #198)
-#200 := [rewrite]: #199
-#196 := (iff #105 #195)
-#193 := (iff #102 #184)
-#194 := [rewrite]: #193
-#181 := (iff #95 #192)
-#182 := [rewrite]: #181
-#197 := [monotonicity #182 #194]: #196
-#202 := [trans #197 #200]: #201
-#218 := [monotonicity #202]: #217
-#221 := [monotonicity #218]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [quant-intro #227]: #229
-#179 := (~ #162 #162)
-#175 := (~ #159 #159)
-#189 := [refl]: #175
-#180 := [nnf-pos #189]: #179
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#165 := (iff #37 #162)
-#59 := (and #16 #18)
-#62 := (or #17 #59)
-#135 := (ite #62 #30 #130)
-#138 := (ite #12 0::int #135)
-#141 := (ite #13 #8 #138)
-#144 := (= #29 #141)
-#147 := (forall (vars (?v0 int) (?v1 int)) #144)
-#163 := (iff #147 #162)
-#160 := (iff #144 #159)
-#157 := (= #141 #156)
-#154 := (= #138 #153)
-#151 := (= #135 #150)
-#106 := (iff #62 #105)
-#103 := (iff #59 #102)
-#100 := (iff #18 #99)
-#101 := [rewrite]: #100
-#93 := (iff #16 #92)
-#94 := [rewrite]: #93
-#104 := [monotonicity #94 #101]: #103
-#96 := (iff #17 #95)
-#89 := (iff #15 #88)
-#90 := [rewrite]: #89
-#97 := [monotonicity #90 #94]: #96
-#107 := [monotonicity #97 #104]: #106
-#152 := [monotonicity #107]: #151
-#155 := [monotonicity #152]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [quant-intro #161]: #163
-#148 := (iff #37 #147)
-#145 := (iff #36 #144)
-#142 := (= #35 #141)
-#139 := (= #34 #138)
-#136 := (= #33 #135)
-#133 := (= #32 #130)
-#127 := (- #124)
-#131 := (= #127 #130)
-#132 := [rewrite]: #131
-#128 := (= #32 #127)
-#125 := (= #31 #124)
-#70 := (= #23 #69)
-#71 := [rewrite]: #70
-#67 := (= #22 #66)
-#68 := [rewrite]: #67
-#126 := [monotonicity #68 #71]: #125
-#129 := [monotonicity #126]: #128
-#134 := [trans #129 #132]: #133
-#63 := (iff #20 #62)
-#60 := (iff #19 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#137 := [monotonicity #64 #134]: #136
-#140 := [monotonicity #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [quant-intro #146]: #148
-#166 := [trans #149 #164]: #165
-#123 := [asserted]: #37
-#167 := [mp #123 #166]: #162
-#190 := [mp~ #167 #180]: #162
-#231 := [mp #190 #230]: #228
-#262 := [mp #231 #261]: #259
-#747 := [mp #262 #746]: #742
-#535 := (not #742)
-#536 := (or #535 #169)
-#320 := (* -1::int 0::int)
-#405 := (* -1::int f5)
-#406 := (mod #405 #320)
-#407 := (+ #39 #406)
-#398 := (= #407 0::int)
-#409 := (mod f5 0::int)
-#410 := (* -1::int #409)
-#338 := (+ #39 #410)
-#411 := (= #338 0::int)
-#408 := (<= 0::int 0::int)
-#412 := (<= f5 0::int)
-#391 := (or #412 #408)
-#726 := (not #391)
-#728 := (>= f5 0::int)
-#385 := (or #408 #728)
-#515 := (not #385)
-#722 := (or #515 #726)
-#396 := (ite #722 #411 #398)
-#397 := (= #39 0::int)
-#729 := (= f5 0::int)
-#730 := (ite #729 #397 #396)
-#731 := (= 0::int 0::int)
-#732 := (ite #731 #169 #730)
-#537 := (or #535 #732)
-#680 := (iff #537 #536)
-#682 := (iff #536 #536)
-#676 := [rewrite]: #682
-#688 := (iff #732 #169)
-#426 := (mod #405 0::int)
-#705 := (+ #39 #426)
-#416 := (= #705 0::int)
-#700 := (ite #729 #397 #416)
-#1 := true
-#691 := (ite true #169 #700)
-#692 := (iff #691 #169)
-#693 := [rewrite]: #692
-#686 := (iff #732 #691)
-#689 := (iff #730 #700)
-#699 := (iff #396 #416)
-#419 := (ite false #411 #416)
-#413 := (iff #419 #416)
-#695 := [rewrite]: #413
-#697 := (iff #396 #419)
-#417 := (iff #398 #416)
-#702 := (= #407 #705)
-#427 := (= #406 #426)
-#703 := (= #320 0::int)
-#704 := [rewrite]: #703
-#701 := [monotonicity #704]: #427
-#706 := [monotonicity #701]: #702
-#418 := [monotonicity #706]: #417
-#433 := (iff #722 false)
-#707 := (or false false)
-#431 := (iff #707 false)
-#432 := [rewrite]: #431
-#708 := (iff #722 #707)
-#718 := (iff #726 false)
-#373 := (not true)
-#711 := (iff #373 false)
-#712 := [rewrite]: #711
-#360 := (iff #726 #373)
-#719 := (iff #391 true)
-#715 := (or #412 true)
-#354 := (iff #715 true)
-#717 := [rewrite]: #354
-#710 := (iff #391 #715)
-#723 := (iff #408 true)
-#383 := [rewrite]: #723
-#716 := [monotonicity #383]: #710
-#359 := [trans #716 #717]: #719
-#720 := [monotonicity #359]: #360
-#721 := [trans #720 #712]: #718
-#713 := (iff #515 false)
-#374 := (iff #515 #373)
-#709 := (iff #385 true)
-#388 := (or true #728)
-#725 := (iff #388 true)
-#368 := [rewrite]: #725
-#724 := (iff #385 #388)
-#384 := [monotonicity #383]: #724
-#372 := [trans #384 #368]: #709
-#375 := [monotonicity #372]: #374
-#714 := [trans #375 #712]: #713
-#430 := [monotonicity #714 #721]: #708
-#326 := [trans #430 #432]: #433
-#698 := [monotonicity #326 #418]: #697
-#696 := [trans #698 #695]: #699
-#690 := [monotonicity #696]: #689
-#727 := (iff #731 true)
-#733 := [rewrite]: #727
-#687 := [monotonicity #733 #690]: #686
-#694 := [trans #687 #693]: #688
-#681 := [monotonicity #694]: #680
-#677 := [trans #681 #676]: #680
-#679 := [quant-inst]: #537
-#683 := [mp #679 #677]: #536
-[unit-resolution #683 #747 #177]: false
-unsat
-a0dd84d240eccf81ab65033fdd888802845765bd 281 0
+9c82ae76cec416fd404b909bc700a14311ef9064 281 0
 #2 := false
 #38 := 1::int
 decl f3 :: (-> int int int)
@@ -28565,306 +28227,7 @@
 #667 := [mp #573 #670]: #572
 [unit-resolution #667 #742 #168]: false
 unsat
-1028cda2400990738320cbc2fe031f4833efde19 298 0
-#2 := false
-#11 := 0::int
-decl f4 :: (-> int int int)
-#38 := 1::int
-#39 := (f4 0::int 1::int)
-#40 := (= #39 0::int)
-#41 := (not #40)
-#168 := [asserted]: #41
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#743 := (pattern #29)
-#65 := -1::int
-#69 := (* -1::int #9)
-#66 := (* -1::int #8)
-#124 := (mod #66 #69)
-#255 := (+ #29 #124)
-#256 := (= #255 0::int)
-#30 := (mod #8 #9)
-#252 := (* -1::int #30)
-#253 := (+ #29 #252)
-#254 := (= #253 0::int)
-#91 := (<= #9 0::int)
-#87 := (<= #8 0::int)
-#194 := (or #87 #91)
-#195 := (not #194)
-#98 := (>= #8 0::int)
-#186 := (or #91 #98)
-#187 := (not #186)
-#201 := (or #187 #195)
-#257 := (ite #201 #254 #256)
-#251 := (= #29 0::int)
-#12 := (= #8 0::int)
-#258 := (ite #12 #251 #257)
-#250 := (= #8 #29)
-#13 := (= #9 0::int)
-#259 := (ite #13 #250 #258)
-#744 := (forall (vars (?v0 int) (?v1 int)) (:pat #743) #259)
-#262 := (forall (vars (?v0 int) (?v1 int)) #259)
-#747 := (iff #262 #744)
-#745 := (iff #259 #259)
-#746 := [refl]: #745
-#748 := [quant-intro #746]: #747
-#130 := (* -1::int #124)
-#219 := (ite #201 #30 #130)
-#222 := (ite #12 0::int #219)
-#225 := (ite #13 #8 #222)
-#228 := (= #29 #225)
-#231 := (forall (vars (?v0 int) (?v1 int)) #228)
-#263 := (iff #231 #262)
-#260 := (iff #228 #259)
-#261 := [rewrite]: #260
-#264 := [quant-intro #261]: #263
-#99 := (not #98)
-#92 := (not #91)
-#102 := (and #92 #99)
-#88 := (not #87)
-#95 := (and #88 #92)
-#105 := (or #95 #102)
-#150 := (ite #105 #30 #130)
-#153 := (ite #12 0::int #150)
-#156 := (ite #13 #8 #153)
-#159 := (= #29 #156)
-#162 := (forall (vars (?v0 int) (?v1 int)) #159)
-#232 := (iff #162 #231)
-#229 := (iff #159 #228)
-#226 := (= #156 #225)
-#223 := (= #153 #222)
-#220 := (= #150 #219)
-#204 := (iff #105 #201)
-#198 := (or #195 #187)
-#202 := (iff #198 #201)
-#203 := [rewrite]: #202
-#199 := (iff #105 #198)
-#196 := (iff #102 #187)
-#197 := [rewrite]: #196
-#184 := (iff #95 #195)
-#185 := [rewrite]: #184
-#200 := [monotonicity #185 #197]: #199
-#205 := [trans #200 #203]: #204
-#221 := [monotonicity #205]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [quant-intro #230]: #232
-#182 := (~ #162 #162)
-#179 := (~ #159 #159)
-#192 := [refl]: #179
-#183 := [nnf-pos #192]: #182
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#165 := (iff #37 #162)
-#59 := (and #16 #18)
-#62 := (or #17 #59)
-#135 := (ite #62 #30 #130)
-#138 := (ite #12 0::int #135)
-#141 := (ite #13 #8 #138)
-#144 := (= #29 #141)
-#147 := (forall (vars (?v0 int) (?v1 int)) #144)
-#163 := (iff #147 #162)
-#160 := (iff #144 #159)
-#157 := (= #141 #156)
-#154 := (= #138 #153)
-#151 := (= #135 #150)
-#106 := (iff #62 #105)
-#103 := (iff #59 #102)
-#100 := (iff #18 #99)
-#101 := [rewrite]: #100
-#93 := (iff #16 #92)
-#94 := [rewrite]: #93
-#104 := [monotonicity #94 #101]: #103
-#96 := (iff #17 #95)
-#89 := (iff #15 #88)
-#90 := [rewrite]: #89
-#97 := [monotonicity #90 #94]: #96
-#107 := [monotonicity #97 #104]: #106
-#152 := [monotonicity #107]: #151
-#155 := [monotonicity #152]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [quant-intro #161]: #163
-#148 := (iff #37 #147)
-#145 := (iff #36 #144)
-#142 := (= #35 #141)
-#139 := (= #34 #138)
-#136 := (= #33 #135)
-#133 := (= #32 #130)
-#127 := (- #124)
-#131 := (= #127 #130)
-#132 := [rewrite]: #131
-#128 := (= #32 #127)
-#125 := (= #31 #124)
-#70 := (= #23 #69)
-#71 := [rewrite]: #70
-#67 := (= #22 #66)
-#68 := [rewrite]: #67
-#126 := [monotonicity #68 #71]: #125
-#129 := [monotonicity #126]: #128
-#134 := [trans #129 #132]: #133
-#63 := (iff #20 #62)
-#60 := (iff #19 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#137 := [monotonicity #64 #134]: #136
-#140 := [monotonicity #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [quant-intro #146]: #148
-#166 := [trans #149 #164]: #165
-#123 := [asserted]: #37
-#167 := [mp #123 #166]: #162
-#193 := [mp~ #167 #183]: #162
-#234 := [mp #193 #233]: #231
-#265 := [mp #234 #264]: #262
-#749 := [mp #265 #748]: #744
-#665 := (not #744)
-#666 := (or #665 #40)
-#323 := (* -1::int 1::int)
-#407 := (* -1::int 0::int)
-#408 := (mod #407 #323)
-#409 := (+ #39 #408)
-#400 := (= #409 0::int)
-#411 := (mod 0::int 1::int)
-#412 := (* -1::int #411)
-#413 := (+ #39 #412)
-#410 := (= #413 0::int)
-#414 := (<= 1::int 0::int)
-#393 := (<= 0::int 0::int)
-#728 := (or #393 #414)
-#730 := (not #728)
-#387 := (>= 0::int 0::int)
-#517 := (or #414 #387)
-#724 := (not #517)
-#398 := (or #724 #730)
-#399 := (ite #398 #410 #400)
-#731 := (= 0::int 0::int)
-#732 := (ite #731 #40 #399)
-#169 := (= 0::int #39)
-#733 := (= 1::int 0::int)
-#734 := (ite #733 #169 #732)
-#669 := (or #665 #734)
-#569 := (iff #669 #666)
-#572 := (iff #666 #666)
-#565 := [rewrite]: #572
-#668 := (iff #734 #40)
-#686 := (ite false #40 #40)
-#516 := (iff #686 #40)
-#518 := [rewrite]: #516
-#561 := (iff #734 #686)
-#559 := (iff #732 #40)
-#1 := true
-#673 := (ite true #40 #40)
-#674 := (iff #673 #40)
-#677 := [rewrite]: #674
-#675 := (iff #732 #673)
-#519 := (iff #399 #40)
-#680 := (iff #399 #686)
-#679 := (iff #400 #40)
-#684 := (= #409 #39)
-#415 := (+ #39 0::int)
-#698 := (= #415 #39)
-#702 := [rewrite]: #698
-#682 := (= #409 #415)
-#539 := (= #408 0::int)
-#695 := (mod 0::int -1::int)
-#537 := (= #695 0::int)
-#538 := [rewrite]: #537
-#690 := (= #408 #695)
-#689 := (= #323 -1::int)
-#694 := [rewrite]: #689
-#420 := (= #407 0::int)
-#421 := [rewrite]: #420
-#696 := [monotonicity #421 #694]: #690
-#681 := [trans #696 #538]: #539
-#683 := [monotonicity #681]: #682
-#678 := [trans #683 #702]: #684
-#685 := [monotonicity #678]: #679
-#693 := (iff #410 #40)
-#691 := (= #413 #39)
-#697 := (= #413 #415)
-#699 := (= #412 0::int)
-#418 := (= #412 #407)
-#704 := (= #411 0::int)
-#708 := [rewrite]: #704
-#419 := [monotonicity #708]: #418
-#700 := [trans #419 #421]: #699
-#701 := [monotonicity #700]: #697
-#692 := [trans #701 #702]: #691
-#688 := [monotonicity #692]: #693
-#703 := (iff #398 false)
-#329 := (or false false)
-#428 := (iff #329 false)
-#429 := [rewrite]: #428
-#705 := (iff #398 #329)
-#434 := (iff #730 false)
-#714 := (not true)
-#717 := (iff #714 false)
-#712 := [rewrite]: #717
-#432 := (iff #730 #714)
-#709 := (iff #728 true)
-#361 := (or true false)
-#720 := (iff #361 true)
-#723 := [rewrite]: #720
-#362 := (iff #728 #361)
-#390 := (iff #414 false)
-#726 := [rewrite]: #390
-#719 := (iff #393 true)
-#721 := [rewrite]: #719
-#722 := [monotonicity #721 #726]: #362
-#710 := [trans #722 #723]: #709
-#433 := [monotonicity #710]: #432
-#435 := [trans #433 #712]: #434
-#718 := (iff #724 false)
-#715 := (iff #724 #714)
-#377 := (iff #517 true)
-#370 := (or false true)
-#375 := (iff #370 true)
-#376 := [rewrite]: #375
-#711 := (iff #517 #370)
-#386 := (iff #387 true)
-#727 := [rewrite]: #386
-#374 := [monotonicity #726 #727]: #711
-#713 := [trans #374 #376]: #377
-#716 := [monotonicity #713]: #715
-#356 := [trans #716 #712]: #718
-#706 := [monotonicity #356 #435]: #705
-#707 := [trans #706 #429]: #703
-#687 := [monotonicity #707 #688 #685]: #680
-#672 := [trans #687 #518]: #519
-#725 := (iff #731 true)
-#385 := [rewrite]: #725
-#676 := [monotonicity #385 #672]: #675
-#560 := [trans #676 #677]: #559
-#175 := (iff #169 #40)
-#176 := [rewrite]: #175
-#729 := (iff #733 false)
-#735 := [rewrite]: #729
-#520 := [monotonicity #735 #176 #560]: #561
-#570 := [trans #520 #518]: #668
-#571 := [monotonicity #570]: #569
-#573 := [trans #571 #565]: #569
-#554 := [quant-inst]: #669
-#574 := [mp #554 #573]: #666
-[unit-resolution #574 #749 #168]: false
-unsat
-517d94dcf477960e98fa3a6ad1a7d3b1e41941d9 292 0
+892e25c8bdf423f86a8231d77f83b5c173fd91c0 292 0
 #2 := false
 #38 := 3::int
 decl f3 :: (-> int int int)
@@ -29157,304 +28520,7 @@
 #660 := [mp #653 #664]: #659
 [unit-resolution #660 #743 #169]: false
 unsat
-4c32c3169bc41583f37f35faf2502f1708b05bd0 296 0
-#2 := false
-#11 := 0::int
-decl f4 :: (-> int int int)
-#38 := 1::int
-#39 := (f4 1::int 1::int)
-#40 := (= #39 0::int)
-#41 := (not #40)
-#168 := [asserted]: #41
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#743 := (pattern #29)
-#65 := -1::int
-#69 := (* -1::int #9)
-#66 := (* -1::int #8)
-#124 := (mod #66 #69)
-#255 := (+ #29 #124)
-#256 := (= #255 0::int)
-#30 := (mod #8 #9)
-#252 := (* -1::int #30)
-#253 := (+ #29 #252)
-#254 := (= #253 0::int)
-#91 := (<= #9 0::int)
-#87 := (<= #8 0::int)
-#194 := (or #87 #91)
-#195 := (not #194)
-#98 := (>= #8 0::int)
-#186 := (or #91 #98)
-#187 := (not #186)
-#201 := (or #187 #195)
-#257 := (ite #201 #254 #256)
-#251 := (= #29 0::int)
-#12 := (= #8 0::int)
-#258 := (ite #12 #251 #257)
-#250 := (= #8 #29)
-#13 := (= #9 0::int)
-#259 := (ite #13 #250 #258)
-#744 := (forall (vars (?v0 int) (?v1 int)) (:pat #743) #259)
-#262 := (forall (vars (?v0 int) (?v1 int)) #259)
-#747 := (iff #262 #744)
-#745 := (iff #259 #259)
-#746 := [refl]: #745
-#748 := [quant-intro #746]: #747
-#130 := (* -1::int #124)
-#219 := (ite #201 #30 #130)
-#222 := (ite #12 0::int #219)
-#225 := (ite #13 #8 #222)
-#228 := (= #29 #225)
-#231 := (forall (vars (?v0 int) (?v1 int)) #228)
-#263 := (iff #231 #262)
-#260 := (iff #228 #259)
-#261 := [rewrite]: #260
-#264 := [quant-intro #261]: #263
-#99 := (not #98)
-#92 := (not #91)
-#102 := (and #92 #99)
-#88 := (not #87)
-#95 := (and #88 #92)
-#105 := (or #95 #102)
-#150 := (ite #105 #30 #130)
-#153 := (ite #12 0::int #150)
-#156 := (ite #13 #8 #153)
-#159 := (= #29 #156)
-#162 := (forall (vars (?v0 int) (?v1 int)) #159)
-#232 := (iff #162 #231)
-#229 := (iff #159 #228)
-#226 := (= #156 #225)
-#223 := (= #153 #222)
-#220 := (= #150 #219)
-#204 := (iff #105 #201)
-#198 := (or #195 #187)
-#202 := (iff #198 #201)
-#203 := [rewrite]: #202
-#199 := (iff #105 #198)
-#196 := (iff #102 #187)
-#197 := [rewrite]: #196
-#184 := (iff #95 #195)
-#185 := [rewrite]: #184
-#200 := [monotonicity #185 #197]: #199
-#205 := [trans #200 #203]: #204
-#221 := [monotonicity #205]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [quant-intro #230]: #232
-#182 := (~ #162 #162)
-#179 := (~ #159 #159)
-#192 := [refl]: #179
-#183 := [nnf-pos #192]: #182
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#165 := (iff #37 #162)
-#59 := (and #16 #18)
-#62 := (or #17 #59)
-#135 := (ite #62 #30 #130)
-#138 := (ite #12 0::int #135)
-#141 := (ite #13 #8 #138)
-#144 := (= #29 #141)
-#147 := (forall (vars (?v0 int) (?v1 int)) #144)
-#163 := (iff #147 #162)
-#160 := (iff #144 #159)
-#157 := (= #141 #156)
-#154 := (= #138 #153)
-#151 := (= #135 #150)
-#106 := (iff #62 #105)
-#103 := (iff #59 #102)
-#100 := (iff #18 #99)
-#101 := [rewrite]: #100
-#93 := (iff #16 #92)
-#94 := [rewrite]: #93
-#104 := [monotonicity #94 #101]: #103
-#96 := (iff #17 #95)
-#89 := (iff #15 #88)
-#90 := [rewrite]: #89
-#97 := [monotonicity #90 #94]: #96
-#107 := [monotonicity #97 #104]: #106
-#152 := [monotonicity #107]: #151
-#155 := [monotonicity #152]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [quant-intro #161]: #163
-#148 := (iff #37 #147)
-#145 := (iff #36 #144)
-#142 := (= #35 #141)
-#139 := (= #34 #138)
-#136 := (= #33 #135)
-#133 := (= #32 #130)
-#127 := (- #124)
-#131 := (= #127 #130)
-#132 := [rewrite]: #131
-#128 := (= #32 #127)
-#125 := (= #31 #124)
-#70 := (= #23 #69)
-#71 := [rewrite]: #70
-#67 := (= #22 #66)
-#68 := [rewrite]: #67
-#126 := [monotonicity #68 #71]: #125
-#129 := [monotonicity #126]: #128
-#134 := [trans #129 #132]: #133
-#63 := (iff #20 #62)
-#60 := (iff #19 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#137 := [monotonicity #64 #134]: #136
-#140 := [monotonicity #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [quant-intro #146]: #148
-#166 := [trans #149 #164]: #165
-#123 := [asserted]: #37
-#167 := [mp #123 #166]: #162
-#193 := [mp~ #167 #183]: #162
-#234 := [mp #193 #233]: #231
-#265 := [mp #234 #264]: #262
-#749 := [mp #265 #748]: #744
-#666 := (not #744)
-#669 := (or #666 #40)
-#323 := (* -1::int 1::int)
-#407 := (mod #323 #323)
-#408 := (+ #39 #407)
-#409 := (= #408 0::int)
-#400 := (mod 1::int 1::int)
-#411 := (* -1::int #400)
-#412 := (+ #39 #411)
-#413 := (= #412 0::int)
-#410 := (<= 1::int 0::int)
-#414 := (or #410 #410)
-#393 := (not #414)
-#728 := (>= 1::int 0::int)
-#730 := (or #410 #728)
-#387 := (not #730)
-#517 := (or #387 #393)
-#724 := (ite #517 #413 #409)
-#398 := (= 1::int 0::int)
-#399 := (ite #398 #40 #724)
-#731 := (= 1::int #39)
-#732 := (ite #398 #731 #399)
-#554 := (or #666 #732)
-#571 := (iff #554 #669)
-#565 := (iff #669 #669)
-#573 := [rewrite]: #565
-#570 := (iff #732 #40)
-#735 := (= #39 1::int)
-#559 := (ite false #735 #40)
-#520 := (iff #559 #40)
-#668 := [rewrite]: #520
-#560 := (iff #732 #559)
-#674 := (iff #399 #40)
-#519 := (ite false #40 #40)
-#675 := (iff #519 #40)
-#676 := [rewrite]: #675
-#672 := (iff #399 #519)
-#516 := (iff #724 #40)
-#1 := true
-#679 := (ite true #40 #40)
-#680 := (iff #679 #40)
-#687 := [rewrite]: #680
-#685 := (iff #724 #679)
-#684 := (iff #409 #40)
-#682 := (= #408 #39)
-#699 := (+ #39 0::int)
-#697 := (= #699 #39)
-#701 := [rewrite]: #697
-#539 := (= #408 #699)
-#537 := (= #407 0::int)
-#689 := (mod -1::int -1::int)
-#690 := (= #689 0::int)
-#696 := [rewrite]: #690
-#694 := (= #407 #689)
-#693 := (= #323 -1::int)
-#688 := [rewrite]: #693
-#695 := [monotonicity #688 #688]: #694
-#538 := [trans #695 #696]: #537
-#681 := [monotonicity #538]: #539
-#683 := [trans #681 #701]: #682
-#678 := [monotonicity #683]: #684
-#691 := (iff #413 #40)
-#698 := (= #412 #39)
-#700 := (= #412 #699)
-#420 := (= #411 0::int)
-#707 := (* -1::int 0::int)
-#418 := (= #707 0::int)
-#419 := [rewrite]: #418
-#704 := (= #411 #707)
-#429 := (= #400 0::int)
-#703 := [rewrite]: #429
-#708 := [monotonicity #703]: #704
-#421 := [trans #708 #419]: #420
-#415 := [monotonicity #421]: #700
-#702 := [trans #415 #701]: #698
-#692 := [monotonicity #702]: #691
-#706 := (iff #517 true)
-#727 := (or false true)
-#374 := (iff #727 true)
-#375 := [rewrite]: #374
-#329 := (iff #517 #727)
-#434 := (iff #393 true)
-#723 := (not false)
-#432 := (iff #723 true)
-#433 := [rewrite]: #432
-#709 := (iff #393 #723)
-#722 := (iff #414 false)
-#356 := (or false false)
-#361 := (iff #356 false)
-#362 := [rewrite]: #361
-#719 := (iff #414 #356)
-#385 := (iff #410 false)
-#390 := [rewrite]: #385
-#721 := [monotonicity #390 #390]: #719
-#720 := [trans #721 #362]: #722
-#710 := [monotonicity #720]: #709
-#435 := [trans #710 #433]: #434
-#712 := (iff #387 false)
-#713 := (not true)
-#716 := (iff #713 false)
-#717 := [rewrite]: #716
-#714 := (iff #387 #713)
-#376 := (iff #730 true)
-#370 := (iff #730 #727)
-#726 := (iff #728 true)
-#386 := [rewrite]: #726
-#711 := [monotonicity #390 #386]: #370
-#377 := [trans #711 #375]: #376
-#715 := [monotonicity #377]: #714
-#718 := [trans #715 #717]: #712
-#705 := [monotonicity #718 #435]: #329
-#428 := [trans #705 #375]: #706
-#686 := [monotonicity #428 #692 #678]: #685
-#518 := [trans #686 #687]: #516
-#733 := (iff #398 false)
-#734 := [rewrite]: #733
-#673 := [monotonicity #734 #518]: #672
-#677 := [trans #673 #676]: #674
-#729 := (iff #731 #735)
-#725 := [rewrite]: #729
-#561 := [monotonicity #734 #725 #677]: #560
-#665 := [trans #561 #668]: #570
-#572 := [monotonicity #665]: #571
-#574 := [trans #572 #573]: #571
-#569 := [quant-inst]: #554
-#575 := [mp #569 #574]: #669
-[unit-resolution #575 #749 #168]: false
-unsat
-7f4e87626d8d9f850815ab9f11ca7ece76ac9405 335 0
+dcc2c3c66de3e673b0cfeb392eb7d2e8ec04caf3 335 0
 #2 := false
 decl f3 :: (-> int int int)
 #39 := 1::int
@@ -29790,7 +28856,7 @@
 #500 := [mp #530 #497]: #170
 [unit-resolution #178 #500]: false
 unsat
-3dd3e5e067f99d1c90bd9e0ee3fa61701d0112dd 306 0
+2a60c54232ee9900c0a7254451730bed52200c08 306 0
 #2 := false
 #11 := 0::int
 decl f3 :: (-> int int int)
@@ -30097,315 +29163,7 @@
 #682 := [mp #588 #685]: #587
 [unit-resolution #682 #757 #193]: false
 unsat
-8c6b824970f94cadce3aa1f861ee0fe83c8cdcae 307 0
-#2 := false
-#11 := 0::int
-decl f4 :: (-> int int int)
-#39 := 1::int
-#38 := 3::int
-#40 := (f4 3::int 1::int)
-#41 := (= #40 0::int)
-#42 := (not #41)
-#169 := [asserted]: #42
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#744 := (pattern #29)
-#66 := -1::int
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#125 := (mod #67 #70)
-#256 := (+ #29 #125)
-#257 := (= #256 0::int)
-#30 := (mod #8 #9)
-#253 := (* -1::int #30)
-#254 := (+ #29 #253)
-#255 := (= #254 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#195 := (or #88 #92)
-#196 := (not #195)
-#99 := (>= #8 0::int)
-#187 := (or #92 #99)
-#188 := (not #187)
-#202 := (or #188 #196)
-#258 := (ite #202 #255 #257)
-#252 := (= #29 0::int)
-#12 := (= #8 0::int)
-#259 := (ite #12 #252 #258)
-#251 := (= #8 #29)
-#13 := (= #9 0::int)
-#260 := (ite #13 #251 #259)
-#745 := (forall (vars (?v0 int) (?v1 int)) (:pat #744) #260)
-#263 := (forall (vars (?v0 int) (?v1 int)) #260)
-#748 := (iff #263 #745)
-#746 := (iff #260 #260)
-#747 := [refl]: #746
-#749 := [quant-intro #747]: #748
-#131 := (* -1::int #125)
-#220 := (ite #202 #30 #131)
-#223 := (ite #12 0::int #220)
-#226 := (ite #13 #8 #223)
-#229 := (= #29 #226)
-#232 := (forall (vars (?v0 int) (?v1 int)) #229)
-#264 := (iff #232 #263)
-#261 := (iff #229 #260)
-#262 := [rewrite]: #261
-#265 := [quant-intro #262]: #264
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#151 := (ite #106 #30 #131)
-#154 := (ite #12 0::int #151)
-#157 := (ite #13 #8 #154)
-#160 := (= #29 #157)
-#163 := (forall (vars (?v0 int) (?v1 int)) #160)
-#233 := (iff #163 #232)
-#230 := (iff #160 #229)
-#227 := (= #157 #226)
-#224 := (= #154 #223)
-#221 := (= #151 #220)
-#205 := (iff #106 #202)
-#199 := (or #196 #188)
-#203 := (iff #199 #202)
-#204 := [rewrite]: #203
-#200 := (iff #106 #199)
-#197 := (iff #103 #188)
-#198 := [rewrite]: #197
-#185 := (iff #96 #196)
-#186 := [rewrite]: #185
-#201 := [monotonicity #186 #198]: #200
-#206 := [trans #201 #204]: #205
-#222 := [monotonicity #206]: #221
-#225 := [monotonicity #222]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [quant-intro #231]: #233
-#183 := (~ #163 #163)
-#180 := (~ #160 #160)
-#193 := [refl]: #180
-#184 := [nnf-pos #193]: #183
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#166 := (iff #37 #163)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#136 := (ite #63 #30 #131)
-#139 := (ite #12 0::int #136)
-#142 := (ite #13 #8 #139)
-#145 := (= #29 #142)
-#148 := (forall (vars (?v0 int) (?v1 int)) #145)
-#164 := (iff #148 #163)
-#161 := (iff #145 #160)
-#158 := (= #142 #157)
-#155 := (= #139 #154)
-#152 := (= #136 #151)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#153 := [monotonicity #108]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#149 := (iff #37 #148)
-#146 := (iff #36 #145)
-#143 := (= #35 #142)
-#140 := (= #34 #139)
-#137 := (= #33 #136)
-#134 := (= #32 #131)
-#128 := (- #125)
-#132 := (= #128 #131)
-#133 := [rewrite]: #132
-#129 := (= #32 #128)
-#126 := (= #31 #125)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#127 := [monotonicity #69 #72]: #126
-#130 := [monotonicity #127]: #129
-#135 := [trans #130 #133]: #134
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#138 := [monotonicity #65 #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [quant-intro #147]: #149
-#167 := [trans #150 #165]: #166
-#124 := [asserted]: #37
-#168 := [mp #124 #167]: #163
-#194 := [mp~ #168 #184]: #163
-#235 := [mp #194 #234]: #232
-#266 := [mp #235 #265]: #263
-#750 := [mp #266 #749]: #745
-#577 := (not #745)
-#578 := (or #577 #41)
-#324 := (* -1::int 1::int)
-#408 := (* -1::int 3::int)
-#409 := (mod #408 #324)
-#410 := (+ #40 #409)
-#401 := (= #410 0::int)
-#412 := (mod 3::int 1::int)
-#413 := (* -1::int #412)
-#414 := (+ #40 #413)
-#411 := (= #414 0::int)
-#415 := (<= 1::int 0::int)
-#394 := (<= 3::int 0::int)
-#729 := (or #394 #415)
-#731 := (not #729)
-#388 := (>= 3::int 0::int)
-#518 := (or #415 #388)
-#725 := (not #518)
-#399 := (or #725 #731)
-#400 := (ite #399 #411 #401)
-#732 := (= 3::int 0::int)
-#733 := (ite #732 #41 #400)
-#734 := (= 3::int #40)
-#735 := (= 1::int 0::int)
-#730 := (ite #735 #734 #733)
-#671 := (or #577 #730)
-#672 := (iff #671 #578)
-#661 := (iff #578 #578)
-#653 := [rewrite]: #661
-#575 := (iff #730 #41)
-#391 := (= #40 3::int)
-#570 := (ite false #391 #41)
-#566 := (iff #570 #41)
-#574 := [rewrite]: #566
-#572 := (iff #730 #570)
-#670 := (iff #733 #41)
-#521 := (ite false #41 #41)
-#666 := (iff #521 #41)
-#667 := [rewrite]: #666
-#669 := (iff #733 #521)
-#561 := (iff #400 #41)
-#1 := true
-#676 := (ite true #41 #41)
-#678 := (iff #676 #41)
-#560 := [rewrite]: #678
-#677 := (iff #400 #676)
-#673 := (iff #401 #41)
-#519 := (= #410 #40)
-#692 := (+ #40 0::int)
-#689 := (= #692 #40)
-#690 := [rewrite]: #689
-#688 := (= #410 #692)
-#687 := (= #409 0::int)
-#538 := -3::int
-#684 := (mod -3::int -1::int)
-#680 := (= #684 0::int)
-#686 := [rewrite]: #680
-#685 := (= #409 #684)
-#682 := (= #324 -1::int)
-#683 := [rewrite]: #682
-#539 := (= #408 -3::int)
-#540 := [rewrite]: #539
-#679 := [monotonicity #540 #683]: #685
-#681 := [trans #679 #686]: #687
-#517 := [monotonicity #681]: #688
-#520 := [trans #517 #690]: #519
-#674 := [monotonicity #520]: #673
-#691 := (iff #411 #41)
-#695 := (= #414 #40)
-#693 := (= #414 #692)
-#699 := (= #413 0::int)
-#700 := (* -1::int 0::int)
-#698 := (= #700 0::int)
-#702 := [rewrite]: #698
-#701 := (= #413 #700)
-#421 := (= #412 0::int)
-#422 := [rewrite]: #421
-#416 := [monotonicity #422]: #701
-#703 := [trans #416 #702]: #699
-#694 := [monotonicity #703]: #693
-#696 := [trans #694 #690]: #695
-#697 := [monotonicity #696]: #691
-#419 := (iff #399 true)
-#377 := (or false true)
-#715 := (iff #377 true)
-#716 := [rewrite]: #715
-#705 := (iff #399 #377)
-#704 := (iff #731 true)
-#330 := (not false)
-#429 := (iff #330 true)
-#430 := [rewrite]: #429
-#706 := (iff #731 #330)
-#435 := (iff #729 false)
-#724 := (or false false)
-#433 := (iff #724 false)
-#434 := [rewrite]: #433
-#710 := (iff #729 #724)
-#371 := (iff #415 false)
-#712 := [rewrite]: #371
-#723 := (iff #394 false)
-#721 := [rewrite]: #723
-#711 := [monotonicity #721 #712]: #710
-#436 := [trans #711 #434]: #435
-#707 := [monotonicity #436]: #706
-#708 := [trans #707 #430]: #704
-#362 := (iff #725 false)
-#713 := (not true)
-#720 := (iff #713 false)
-#722 := [rewrite]: #720
-#719 := (iff #725 #713)
-#717 := (iff #518 true)
-#378 := (iff #518 #377)
-#375 := (iff #388 true)
-#376 := [rewrite]: #375
-#714 := [monotonicity #712 #376]: #378
-#718 := [trans #714 #716]: #717
-#357 := [monotonicity #718]: #719
-#363 := [trans #357 #722]: #362
-#709 := [monotonicity #363 #708]: #705
-#420 := [trans #709 #716]: #419
-#675 := [monotonicity #420 #697 #674]: #677
-#562 := [trans #675 #560]: #561
-#387 := (iff #732 false)
-#728 := [rewrite]: #387
-#571 := [monotonicity #728 #562]: #669
-#555 := [trans #571 #667]: #670
-#386 := (iff #734 #391)
-#727 := [rewrite]: #386
-#736 := (iff #735 false)
-#726 := [rewrite]: #736
-#573 := [monotonicity #726 #727 #555]: #572
-#576 := [trans #573 #574]: #575
-#659 := [monotonicity #576]: #672
-#650 := [trans #659 #653]: #672
-#668 := [quant-inst]: #671
-#652 := [mp #668 #650]: #578
-[unit-resolution #652 #750 #169]: false
-unsat
-7415b61df67d0382c7c8726284760c97b73cdf04 315 0
+923c4bec65f1ce0be6fa5d4ec7cf2b004a307f06 315 0
 #2 := false
 #66 := -1::int
 decl f3 :: (-> int int int)
@@ -30721,316 +29479,7 @@
 #678 := [mp #675 #677]: #686
 [unit-resolution #678 #757 #193]: false
 unsat
-b8e3350e9ffae8bc4261f75ecb8e0cef6e684921 308 0
-#2 := false
-#11 := 0::int
-decl f5 :: int
-#38 := f5
-#732 := (= f5 0::int)
-#573 := (not #732)
-#394 := (<= f5 0::int)
-#720 := (not #394)
-#388 := (>= f5 0::int)
-#377 := (not #388)
-#688 := (or #377 #720 #732)
-#575 := (not #688)
-#66 := -1::int
-#408 := (* -1::int f5)
-#700 := (mod #408 -1::int)
-decl f4 :: (-> int int int)
-#39 := 1::int
-#40 := (f4 f5 1::int)
-#698 := (+ #40 #700)
-#703 := (= #698 0::int)
-#41 := (= #40 0::int)
-#520 := (ite #688 #41 #703)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#744 := (pattern #29)
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#125 := (mod #67 #70)
-#256 := (+ #29 #125)
-#257 := (= #256 0::int)
-#30 := (mod #8 #9)
-#253 := (* -1::int #30)
-#254 := (+ #29 #253)
-#255 := (= #254 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#195 := (or #88 #92)
-#196 := (not #195)
-#99 := (>= #8 0::int)
-#187 := (or #92 #99)
-#188 := (not #187)
-#202 := (or #188 #196)
-#258 := (ite #202 #255 #257)
-#252 := (= #29 0::int)
-#12 := (= #8 0::int)
-#259 := (ite #12 #252 #258)
-#251 := (= #8 #29)
-#13 := (= #9 0::int)
-#260 := (ite #13 #251 #259)
-#745 := (forall (vars (?v0 int) (?v1 int)) (:pat #744) #260)
-#263 := (forall (vars (?v0 int) (?v1 int)) #260)
-#748 := (iff #263 #745)
-#746 := (iff #260 #260)
-#747 := [refl]: #746
-#749 := [quant-intro #747]: #748
-#131 := (* -1::int #125)
-#220 := (ite #202 #30 #131)
-#223 := (ite #12 0::int #220)
-#226 := (ite #13 #8 #223)
-#229 := (= #29 #226)
-#232 := (forall (vars (?v0 int) (?v1 int)) #229)
-#264 := (iff #232 #263)
-#261 := (iff #229 #260)
-#262 := [rewrite]: #261
-#265 := [quant-intro #262]: #264
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#151 := (ite #106 #30 #131)
-#154 := (ite #12 0::int #151)
-#157 := (ite #13 #8 #154)
-#160 := (= #29 #157)
-#163 := (forall (vars (?v0 int) (?v1 int)) #160)
-#233 := (iff #163 #232)
-#230 := (iff #160 #229)
-#227 := (= #157 #226)
-#224 := (= #154 #223)
-#221 := (= #151 #220)
-#205 := (iff #106 #202)
-#199 := (or #196 #188)
-#203 := (iff #199 #202)
-#204 := [rewrite]: #203
-#200 := (iff #106 #199)
-#197 := (iff #103 #188)
-#198 := [rewrite]: #197
-#185 := (iff #96 #196)
-#186 := [rewrite]: #185
-#201 := [monotonicity #186 #198]: #200
-#206 := [trans #201 #204]: #205
-#222 := [monotonicity #206]: #221
-#225 := [monotonicity #222]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [quant-intro #231]: #233
-#183 := (~ #163 #163)
-#180 := (~ #160 #160)
-#193 := [refl]: #180
-#184 := [nnf-pos #193]: #183
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#166 := (iff #37 #163)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#136 := (ite #63 #30 #131)
-#139 := (ite #12 0::int #136)
-#142 := (ite #13 #8 #139)
-#145 := (= #29 #142)
-#148 := (forall (vars (?v0 int) (?v1 int)) #145)
-#164 := (iff #148 #163)
-#161 := (iff #145 #160)
-#158 := (= #142 #157)
-#155 := (= #139 #154)
-#152 := (= #136 #151)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#153 := [monotonicity #108]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#149 := (iff #37 #148)
-#146 := (iff #36 #145)
-#143 := (= #35 #142)
-#140 := (= #34 #139)
-#137 := (= #33 #136)
-#134 := (= #32 #131)
-#128 := (- #125)
-#132 := (= #128 #131)
-#133 := [rewrite]: #132
-#129 := (= #32 #128)
-#126 := (= #31 #125)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#127 := [monotonicity #69 #72]: #126
-#130 := [monotonicity #127]: #129
-#135 := [trans #130 #133]: #134
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#138 := [monotonicity #65 #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [quant-intro #147]: #149
-#167 := [trans #150 #165]: #166
-#124 := [asserted]: #37
-#168 := [mp #124 #167]: #163
-#194 := [mp~ #168 #184]: #163
-#235 := [mp #194 #234]: #232
-#266 := [mp #235 #265]: #263
-#750 := [mp #266 #749]: #745
-#675 := (not #745)
-#678 := (or #675 #520)
-#324 := (* -1::int 1::int)
-#409 := (mod #408 #324)
-#410 := (+ #40 #409)
-#401 := (= #410 0::int)
-#412 := (mod f5 1::int)
-#413 := (* -1::int #412)
-#414 := (+ #40 #413)
-#411 := (= #414 0::int)
-#415 := (<= 1::int 0::int)
-#729 := (or #394 #415)
-#731 := (not #729)
-#518 := (or #415 #388)
-#725 := (not #518)
-#399 := (or #725 #731)
-#400 := (ite #399 #411 #401)
-#733 := (ite #732 #41 #400)
-#734 := (= f5 #40)
-#735 := (= 1::int 0::int)
-#730 := (ite #735 #734 #733)
-#560 := (or #675 #730)
-#562 := (iff #560 #678)
-#669 := (iff #678 #678)
-#571 := [rewrite]: #669
-#676 := (iff #730 #520)
-#363 := (or #377 #720)
-#697 := (or #363 #732)
-#538 := (ite #697 #41 #703)
-#673 := (iff #538 #520)
-#517 := (iff #697 #688)
-#519 := [rewrite]: #517
-#674 := [monotonicity #519]: #673
-#687 := (iff #730 #538)
-#684 := (ite false #734 #538)
-#680 := (iff #684 #538)
-#686 := [rewrite]: #680
-#685 := (iff #730 #684)
-#682 := (iff #733 #538)
-#694 := (ite #363 #41 #703)
-#695 := (ite #732 #41 #694)
-#539 := (iff #695 #538)
-#540 := [rewrite]: #539
-#696 := (iff #733 #695)
-#689 := (iff #400 #694)
-#692 := (iff #401 #703)
-#702 := (= #410 #698)
-#701 := (= #409 #700)
-#421 := (= #324 -1::int)
-#422 := [rewrite]: #421
-#416 := [monotonicity #422]: #701
-#699 := [monotonicity #416]: #702
-#693 := [monotonicity #699]: #692
-#419 := (iff #411 #41)
-#705 := (= #414 #40)
-#707 := (+ #40 0::int)
-#704 := (= #707 #40)
-#708 := [rewrite]: #704
-#429 := (= #414 #707)
-#330 := (= #413 0::int)
-#711 := (* -1::int 0::int)
-#435 := (= #711 0::int)
-#436 := [rewrite]: #435
-#433 := (= #413 #711)
-#724 := (= #412 0::int)
-#710 := [rewrite]: #724
-#434 := [monotonicity #710]: #433
-#706 := [trans #434 #436]: #330
-#430 := [monotonicity #706]: #429
-#709 := [trans #430 #708]: #705
-#420 := [monotonicity #709]: #419
-#723 := (iff #399 #363)
-#722 := (iff #731 #720)
-#719 := (iff #729 #394)
-#715 := (or #394 false)
-#718 := (iff #715 #394)
-#713 := [rewrite]: #718
-#716 := (iff #729 #715)
-#386 := (iff #415 false)
-#391 := [rewrite]: #386
-#717 := [monotonicity #391]: #716
-#357 := [trans #717 #713]: #719
-#362 := [monotonicity #357]: #722
-#378 := (iff #725 #377)
-#375 := (iff #518 #388)
-#727 := (or false #388)
-#371 := (iff #727 #388)
-#712 := [rewrite]: #371
-#387 := (iff #518 #727)
-#728 := [monotonicity #391]: #387
-#376 := [trans #728 #712]: #375
-#714 := [monotonicity #376]: #378
-#721 := [monotonicity #714 #362]: #723
-#690 := [monotonicity #721 #420 #693]: #689
-#691 := [monotonicity #690]: #696
-#683 := [trans #691 #540]: #682
-#736 := (iff #735 false)
-#726 := [rewrite]: #736
-#679 := [monotonicity #726 #683]: #685
-#681 := [trans #679 #686]: #687
-#677 := [trans #681 #674]: #676
-#521 := [monotonicity #677]: #562
-#666 := [trans #521 #571]: #562
-#561 := [quant-inst]: #560
-#667 := [mp #561 #666]: #678
-#660 := [unit-resolution #667 #750]: #520
-#668 := (not #520)
-#665 := (or #668 #575)
-#42 := (not #41)
-#169 := [asserted]: #42
-#672 := (or #668 #575 #41)
-#659 := [def-axiom]: #672
-#654 := [unit-resolution #659 #169]: #665
-#655 := [unit-resolution #654 #660]: #575
-#566 := (or #688 #573)
-#574 := [def-axiom]: #566
-#656 := [unit-resolution #574 #655]: #573
-#670 := (or #688 #388)
-#555 := [def-axiom]: #670
-#657 := [unit-resolution #555 #655]: #388
-#570 := (or #688 #394)
-#572 := [def-axiom]: #570
-#651 := [unit-resolution #572 #655]: #394
-#658 := (or #732 #720 #377)
-#642 := [th-lemma]: #658
-[unit-resolution #642 #651 #657 #656]: false
-unsat
-8385e60ed3af381853b64133bc38d95658f35f76 311 0
+f6b6632f2c5a6045abfce98be6bbc967a6c8ca72 311 0
 #2 := false
 #177 := -3::int
 decl f3 :: (-> int int int)
@@ -31342,325 +29791,7 @@
 #661 := [mp #659 #672]: #660
 [unit-resolution #661 #750 #188]: false
 unsat
-62cbad5f8230a32f1b29d792652e1e27f6a3a147 317 0
-#2 := false
-#11 := 0::int
-decl f4 :: (-> int int int)
-#66 := -1::int
-#172 := (f4 0::int -1::int)
-#175 := (= #172 0::int)
-#188 := (not #175)
-#38 := 1::int
-#39 := (- 1::int)
-#40 := (f4 0::int #39)
-#41 := (= #40 0::int)
-#42 := (not #41)
-#191 := (iff #42 #188)
-#178 := (= 0::int #172)
-#183 := (not #178)
-#189 := (iff #183 #188)
-#186 := (iff #178 #175)
-#187 := [rewrite]: #186
-#190 := [monotonicity #187]: #189
-#184 := (iff #42 #183)
-#181 := (iff #41 #178)
-#179 := (iff #175 #178)
-#180 := [rewrite]: #179
-#176 := (iff #41 #175)
-#173 := (= #40 #172)
-#170 := (= #39 -1::int)
-#171 := [rewrite]: #170
-#174 := [monotonicity #171]: #173
-#177 := [monotonicity #174]: #176
-#182 := [trans #177 #180]: #181
-#185 := [monotonicity #182]: #184
-#192 := [trans #185 #190]: #191
-#169 := [asserted]: #42
-#193 := [mp #169 #192]: #188
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#758 := (pattern #29)
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#125 := (mod #67 #70)
-#270 := (+ #29 #125)
-#271 := (= #270 0::int)
-#30 := (mod #8 #9)
-#267 := (* -1::int #30)
-#268 := (+ #29 #267)
-#269 := (= #268 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#209 := (or #88 #92)
-#210 := (not #209)
-#99 := (>= #8 0::int)
-#201 := (or #92 #99)
-#202 := (not #201)
-#216 := (or #202 #210)
-#272 := (ite #216 #269 #271)
-#266 := (= #29 0::int)
-#12 := (= #8 0::int)
-#273 := (ite #12 #266 #272)
-#265 := (= #8 #29)
-#13 := (= #9 0::int)
-#274 := (ite #13 #265 #273)
-#759 := (forall (vars (?v0 int) (?v1 int)) (:pat #758) #274)
-#277 := (forall (vars (?v0 int) (?v1 int)) #274)
-#762 := (iff #277 #759)
-#760 := (iff #274 #274)
-#761 := [refl]: #760
-#763 := [quant-intro #761]: #762
-#131 := (* -1::int #125)
-#234 := (ite #216 #30 #131)
-#237 := (ite #12 0::int #234)
-#240 := (ite #13 #8 #237)
-#243 := (= #29 #240)
-#246 := (forall (vars (?v0 int) (?v1 int)) #243)
-#278 := (iff #246 #277)
-#275 := (iff #243 #274)
-#276 := [rewrite]: #275
-#279 := [quant-intro #276]: #278
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#151 := (ite #106 #30 #131)
-#154 := (ite #12 0::int #151)
-#157 := (ite #13 #8 #154)
-#160 := (= #29 #157)
-#163 := (forall (vars (?v0 int) (?v1 int)) #160)
-#247 := (iff #163 #246)
-#244 := (iff #160 #243)
-#241 := (= #157 #240)
-#238 := (= #154 #237)
-#235 := (= #151 #234)
-#219 := (iff #106 #216)
-#213 := (or #210 #202)
-#217 := (iff #213 #216)
-#218 := [rewrite]: #217
-#214 := (iff #106 #213)
-#211 := (iff #103 #202)
-#212 := [rewrite]: #211
-#199 := (iff #96 #210)
-#200 := [rewrite]: #199
-#215 := [monotonicity #200 #212]: #214
-#220 := [trans #215 #218]: #219
-#236 := [monotonicity #220]: #235
-#239 := [monotonicity #236]: #238
-#242 := [monotonicity #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [quant-intro #245]: #247
-#197 := (~ #163 #163)
-#194 := (~ #160 #160)
-#207 := [refl]: #194
-#198 := [nnf-pos #207]: #197
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#166 := (iff #37 #163)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#136 := (ite #63 #30 #131)
-#139 := (ite #12 0::int #136)
-#142 := (ite #13 #8 #139)
-#145 := (= #29 #142)
-#148 := (forall (vars (?v0 int) (?v1 int)) #145)
-#164 := (iff #148 #163)
-#161 := (iff #145 #160)
-#158 := (= #142 #157)
-#155 := (= #139 #154)
-#152 := (= #136 #151)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#153 := [monotonicity #108]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#149 := (iff #37 #148)
-#146 := (iff #36 #145)
-#143 := (= #35 #142)
-#140 := (= #34 #139)
-#137 := (= #33 #136)
-#134 := (= #32 #131)
-#128 := (- #125)
-#132 := (= #128 #131)
-#133 := [rewrite]: #132
-#129 := (= #32 #128)
-#126 := (= #31 #125)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#127 := [monotonicity #69 #72]: #126
-#130 := [monotonicity #127]: #129
-#135 := [trans #130 #133]: #134
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#138 := [monotonicity #65 #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [quant-intro #147]: #149
-#167 := [trans #150 #165]: #166
-#124 := [asserted]: #37
-#168 := [mp #124 #167]: #163
-#208 := [mp~ #168 #198]: #163
-#249 := [mp #208 #248]: #246
-#280 := [mp #249 #279]: #277
-#764 := [mp #280 #763]: #759
-#535 := (not #759)
-#683 := (or #535 #175)
-#338 := (* -1::int -1::int)
-#422 := (* -1::int 0::int)
-#423 := (mod #422 #338)
-#424 := (+ #172 #423)
-#415 := (= #424 0::int)
-#426 := (mod 0::int -1::int)
-#427 := (* -1::int #426)
-#428 := (+ #172 #427)
-#425 := (= #428 0::int)
-#429 := (<= -1::int 0::int)
-#408 := (<= 0::int 0::int)
-#743 := (or #408 #429)
-#745 := (not #743)
-#402 := (>= 0::int 0::int)
-#532 := (or #429 #402)
-#739 := (not #532)
-#413 := (or #739 #745)
-#414 := (ite #413 #425 #415)
-#746 := (= 0::int 0::int)
-#747 := (ite #746 #175 #414)
-#748 := (= -1::int 0::int)
-#749 := (ite #748 #178 #747)
-#585 := (or #535 #749)
-#681 := (iff #585 #683)
-#569 := (iff #683 #683)
-#584 := [rewrite]: #569
-#575 := (iff #749 #175)
-#693 := (ite false #175 #175)
-#701 := (iff #693 #175)
-#695 := [rewrite]: #701
-#692 := (iff #749 #693)
-#691 := (iff #747 #175)
-#1 := true
-#533 := (ite true #175 #175)
-#688 := (iff #533 #175)
-#690 := [rewrite]: #688
-#534 := (iff #747 #533)
-#702 := (iff #414 #175)
-#694 := (iff #414 #693)
-#698 := (iff #415 #175)
-#696 := (= #424 #172)
-#436 := (+ #172 0::int)
-#430 := (= #436 #172)
-#712 := [rewrite]: #430
-#553 := (= #424 #436)
-#711 := (= #423 0::int)
-#703 := (mod 0::int 1::int)
-#710 := (= #703 0::int)
-#705 := [rewrite]: #710
-#704 := (= #423 #703)
-#707 := (= #338 1::int)
-#708 := [rewrite]: #707
-#723 := (= #422 0::int)
-#433 := [rewrite]: #723
-#709 := [monotonicity #433 #708]: #704
-#552 := [trans #709 #705]: #711
-#554 := [monotonicity #552]: #553
-#697 := [trans #554 #712]: #696
-#699 := [monotonicity #697]: #698
-#717 := (iff #425 #175)
-#716 := (= #428 #172)
-#714 := (= #428 #436)
-#434 := (= #427 0::int)
-#722 := (= #427 #422)
-#444 := (= #426 0::int)
-#718 := [rewrite]: #444
-#719 := [monotonicity #718]: #722
-#435 := [trans #719 #433]: #434
-#715 := [monotonicity #435]: #714
-#713 := [trans #715 #712]: #716
-#706 := [monotonicity #713]: #717
-#721 := (iff #413 false)
-#448 := (or false false)
-#344 := (iff #448 false)
-#720 := [rewrite]: #344
-#449 := (iff #413 #448)
-#725 := (iff #745 false)
-#729 := (not true)
-#732 := (iff #729 false)
-#727 := [rewrite]: #732
-#738 := (iff #745 #729)
-#737 := (iff #743 true)
-#385 := (or true true)
-#390 := (iff #385 true)
-#391 := [rewrite]: #390
-#376 := (iff #743 #385)
-#405 := (iff #429 true)
-#741 := [rewrite]: #405
-#734 := (iff #408 true)
-#736 := [rewrite]: #734
-#377 := [monotonicity #736 #741]: #376
-#735 := [trans #377 #391]: #737
-#724 := [monotonicity #735]: #738
-#447 := [trans #724 #727]: #725
-#733 := (iff #739 false)
-#730 := (iff #739 #729)
-#392 := (iff #532 true)
-#726 := (iff #532 #385)
-#401 := (iff #402 true)
-#742 := [rewrite]: #401
-#389 := [monotonicity #741 #742]: #726
-#728 := [trans #389 #391]: #392
-#731 := [monotonicity #728]: #730
-#371 := [trans #731 #727]: #733
-#450 := [monotonicity #371 #447]: #449
-#443 := [trans #450 #720]: #721
-#700 := [monotonicity #443 #706 #699]: #694
-#531 := [trans #700 #695]: #702
-#740 := (iff #746 true)
-#400 := [rewrite]: #740
-#687 := [monotonicity #400 #531]: #534
-#689 := [trans #687 #690]: #691
-#744 := (iff #748 false)
-#750 := [rewrite]: #744
-#574 := [monotonicity #750 #187 #689]: #692
-#576 := [trans #574 #695]: #575
-#684 := [monotonicity #576]: #681
-#586 := [trans #684 #584]: #681
-#680 := [quant-inst]: #585
-#587 := [mp #680 #586]: #683
-[unit-resolution #587 #764 #193]: false
-unsat
-9598c0d2e42a8240df571681abaece65536e1221 362 0
+ef319beaaae1961d7e0fb146b0bd21608ccf741d 362 0
 #2 := false
 #11 := 0::int
 #39 := 1::int
@@ -32023,7 +30154,6498 @@
 #563 := [th-lemma]: #562
 [unit-resolution #563 #561 #633]: false
 unsat
-79ab94d82443340b024a2e044bfbebeb9d8e374b 327 0
+24bbfda15529f2b078998e7a57a330dfd637cef3 282 0
+#2 := false
+#11 := 0::int
+decl f3 :: (-> int int int)
+#38 := 3::int
+#39 := (f3 0::int 3::int)
+#40 := (= #39 0::int)
+#41 := (not #40)
+#168 := [asserted]: #41
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#737 := (pattern #10)
+#65 := -1::int
+#69 := (* -1::int #9)
+#66 := (* -1::int #8)
+#72 := (div #66 #69)
+#239 := (* -1::int #72)
+#240 := (+ #10 #239)
+#241 := (= #240 0::int)
+#21 := (div #8 #9)
+#236 := (* -1::int #21)
+#237 := (+ #10 #236)
+#238 := (= #237 0::int)
+#91 := (<= #9 0::int)
+#87 := (<= #8 0::int)
+#194 := (or #87 #91)
+#195 := (not #194)
+#98 := (>= #8 0::int)
+#186 := (or #91 #98)
+#187 := (not #186)
+#201 := (or #187 #195)
+#242 := (ite #201 #238 #241)
+#235 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#243 := (ite #14 #235 #242)
+#738 := (forall (vars (?v0 int) (?v1 int)) (:pat #737) #243)
+#246 := (forall (vars (?v0 int) (?v1 int)) #243)
+#741 := (iff #246 #738)
+#739 := (iff #243 #243)
+#740 := [refl]: #739
+#742 := [quant-intro #740]: #741
+#206 := (ite #201 #21 #72)
+#209 := (ite #14 0::int #206)
+#212 := (= #10 #209)
+#215 := (forall (vars (?v0 int) (?v1 int)) #212)
+#247 := (iff #215 #246)
+#244 := (iff #212 #243)
+#245 := [rewrite]: #244
+#248 := [quant-intro #245]: #247
+#99 := (not #98)
+#92 := (not #91)
+#102 := (and #92 #99)
+#88 := (not #87)
+#95 := (and #88 #92)
+#105 := (or #95 #102)
+#108 := (ite #105 #21 #72)
+#111 := (ite #14 0::int #108)
+#114 := (= #10 #111)
+#117 := (forall (vars (?v0 int) (?v1 int)) #114)
+#216 := (iff #117 #215)
+#213 := (iff #114 #212)
+#210 := (= #111 #209)
+#207 := (= #108 #206)
+#204 := (iff #105 #201)
+#198 := (or #195 #187)
+#202 := (iff #198 #201)
+#203 := [rewrite]: #202
+#199 := (iff #105 #198)
+#196 := (iff #102 #187)
+#197 := [rewrite]: #196
+#184 := (iff #95 #195)
+#185 := [rewrite]: #184
+#200 := [monotonicity #185 #197]: #199
+#205 := [trans #200 #203]: #204
+#208 := [monotonicity #205]: #207
+#211 := [monotonicity #208]: #210
+#214 := [monotonicity #211]: #213
+#217 := [quant-intro #214]: #216
+#190 := (~ #117 #117)
+#188 := (~ #114 #114)
+#189 := [refl]: #188
+#191 := [nnf-pos #189]: #190
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#120 := (iff #28 #117)
+#59 := (and #16 #18)
+#62 := (or #17 #59)
+#75 := (ite #62 #21 #72)
+#78 := (ite #14 0::int #75)
+#81 := (= #10 #78)
+#84 := (forall (vars (?v0 int) (?v1 int)) #81)
+#118 := (iff #84 #117)
+#115 := (iff #81 #114)
+#112 := (= #78 #111)
+#109 := (= #75 #108)
+#106 := (iff #62 #105)
+#103 := (iff #59 #102)
+#100 := (iff #18 #99)
+#101 := [rewrite]: #100
+#93 := (iff #16 #92)
+#94 := [rewrite]: #93
+#104 := [monotonicity #94 #101]: #103
+#96 := (iff #17 #95)
+#89 := (iff #15 #88)
+#90 := [rewrite]: #89
+#97 := [monotonicity #90 #94]: #96
+#107 := [monotonicity #97 #104]: #106
+#110 := [monotonicity #107]: #109
+#113 := [monotonicity #110]: #112
+#116 := [monotonicity #113]: #115
+#119 := [quant-intro #116]: #118
+#85 := (iff #28 #84)
+#82 := (iff #27 #81)
+#79 := (= #26 #78)
+#76 := (= #25 #75)
+#73 := (= #24 #72)
+#70 := (= #23 #69)
+#71 := [rewrite]: #70
+#67 := (= #22 #66)
+#68 := [rewrite]: #67
+#74 := [monotonicity #68 #71]: #73
+#63 := (iff #20 #62)
+#60 := (iff #19 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#77 := [monotonicity #64 #74]: #76
+#80 := [monotonicity #77]: #79
+#83 := [monotonicity #80]: #82
+#86 := [quant-intro #83]: #85
+#121 := [trans #86 #119]: #120
+#58 := [asserted]: #28
+#122 := [mp #58 #121]: #117
+#181 := [mp~ #122 #191]: #117
+#218 := [mp #181 #217]: #215
+#249 := [mp #218 #248]: #246
+#743 := [mp #249 #742]: #738
+#572 := (not #738)
+#573 := (or #572 #40)
+#323 := (* -1::int 3::int)
+#408 := (* -1::int 0::int)
+#409 := (div #408 #323)
+#410 := (* -1::int #409)
+#401 := (+ #39 #410)
+#412 := (= #401 0::int)
+#413 := (div 0::int 3::int)
+#341 := (* -1::int #413)
+#414 := (+ #39 #341)
+#411 := (= #414 0::int)
+#415 := (<= 3::int 0::int)
+#394 := (<= 0::int 0::int)
+#729 := (or #394 #415)
+#731 := (not #729)
+#388 := (>= 0::int 0::int)
+#518 := (or #415 #388)
+#725 := (not #518)
+#399 := (or #725 #731)
+#400 := (ite #399 #411 #412)
+#732 := (= 3::int 0::int)
+#733 := (= 0::int 0::int)
+#734 := (or #733 #732)
+#735 := (ite #734 #40 #400)
+#566 := (or #572 #735)
+#575 := (iff #566 #573)
+#577 := (iff #573 #573)
+#578 := [rewrite]: #577
+#555 := (iff #735 #40)
+#1 := true
+#669 := (ite true #40 #40)
+#667 := (iff #669 #40)
+#670 := [rewrite]: #667
+#571 := (iff #735 #669)
+#562 := (iff #400 #40)
+#677 := (ite false #40 #40)
+#560 := (iff #677 #40)
+#561 := [rewrite]: #560
+#675 := (iff #400 #677)
+#674 := (iff #412 #40)
+#520 := (= #401 #39)
+#703 := (+ #39 0::int)
+#694 := (= #703 #39)
+#689 := [rewrite]: #694
+#517 := (= #401 #703)
+#681 := (= #410 0::int)
+#416 := (= #408 0::int)
+#698 := [rewrite]: #416
+#686 := (= #410 #408)
+#679 := (= #409 0::int)
+#697 := -3::int
+#540 := (div 0::int -3::int)
+#684 := (= #540 0::int)
+#685 := [rewrite]: #684
+#682 := (= #409 #540)
+#538 := (= #323 -3::int)
+#539 := [rewrite]: #538
+#683 := [monotonicity #698 #539]: #682
+#680 := [trans #683 #685]: #679
+#687 := [monotonicity #680]: #686
+#688 := [trans #687 #698]: #681
+#519 := [monotonicity #688]: #517
+#673 := [trans #519 #689]: #520
+#676 := [monotonicity #673]: #674
+#696 := (iff #411 #40)
+#690 := (= #414 #39)
+#692 := (= #414 #703)
+#702 := (= #341 0::int)
+#700 := (= #341 #408)
+#421 := (= #413 0::int)
+#422 := [rewrite]: #421
+#701 := [monotonicity #422]: #700
+#699 := [trans #701 #698]: #702
+#693 := [monotonicity #699]: #692
+#695 := [trans #693 #689]: #690
+#691 := [monotonicity #695]: #696
+#419 := (iff #399 false)
+#430 := (or false false)
+#705 := (iff #430 false)
+#709 := [rewrite]: #705
+#704 := (iff #399 #430)
+#707 := (iff #731 false)
+#720 := (not true)
+#363 := (iff #720 false)
+#723 := [rewrite]: #363
+#329 := (iff #731 #720)
+#435 := (iff #729 true)
+#391 := (or true false)
+#728 := (iff #391 true)
+#371 := [rewrite]: #728
+#433 := (iff #729 #391)
+#376 := (iff #415 false)
+#377 := [rewrite]: #376
+#710 := (iff #394 true)
+#711 := [rewrite]: #710
+#434 := [monotonicity #711 #377]: #433
+#436 := [trans #434 #371]: #435
+#706 := [monotonicity #436]: #329
+#429 := [trans #706 #723]: #707
+#721 := (iff #725 false)
+#722 := (iff #725 #720)
+#719 := (iff #518 true)
+#715 := (or false true)
+#718 := (iff #715 true)
+#713 := [rewrite]: #718
+#716 := (iff #518 #715)
+#378 := (iff #388 true)
+#714 := [rewrite]: #378
+#717 := [monotonicity #377 #714]: #716
+#357 := [trans #717 #713]: #719
+#362 := [monotonicity #357]: #722
+#724 := [trans #362 #723]: #721
+#708 := [monotonicity #724 #429]: #704
+#420 := [trans #708 #709]: #419
+#678 := [monotonicity #420 #691 #676]: #675
+#521 := [trans #678 #561]: #562
+#712 := (iff #734 true)
+#727 := (iff #734 #391)
+#726 := (iff #732 false)
+#386 := [rewrite]: #726
+#730 := (iff #733 true)
+#736 := [rewrite]: #730
+#387 := [monotonicity #736 #386]: #727
+#375 := [trans #387 #371]: #712
+#666 := [monotonicity #375 #521]: #571
+#570 := [trans #666 #670]: #555
+#576 := [monotonicity #570]: #575
+#671 := [trans #576 #578]: #575
+#574 := [quant-inst]: #566
+#668 := [mp #574 #671]: #573
+[unit-resolution #668 #743 #168]: false
+unsat
+12ef6b4ae9675610f423327a4c22119f401927ad 307 0
+#2 := false
+#11 := 0::int
+decl f3 :: (-> int int int)
+#170 := -3::int
+#173 := (f3 0::int -3::int)
+#176 := (= #173 0::int)
+#189 := (not #176)
+#38 := 3::int
+#39 := (- 3::int)
+#40 := (f3 0::int #39)
+#41 := (= #40 0::int)
+#42 := (not #41)
+#192 := (iff #42 #189)
+#179 := (= 0::int #173)
+#184 := (not #179)
+#190 := (iff #184 #189)
+#187 := (iff #179 #176)
+#188 := [rewrite]: #187
+#191 := [monotonicity #188]: #190
+#185 := (iff #42 #184)
+#182 := (iff #41 #179)
+#180 := (iff #176 #179)
+#181 := [rewrite]: #180
+#177 := (iff #41 #176)
+#174 := (= #40 #173)
+#171 := (= #39 -3::int)
+#172 := [rewrite]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#183 := [trans #178 #181]: #182
+#186 := [monotonicity #183]: #185
+#193 := [trans #186 #191]: #192
+#169 := [asserted]: #42
+#194 := [mp #169 #193]: #189
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#753 := (pattern #10)
+#66 := -1::int
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#73 := (div #67 #70)
+#255 := (* -1::int #73)
+#256 := (+ #10 #255)
+#257 := (= #256 0::int)
+#21 := (div #8 #9)
+#252 := (* -1::int #21)
+#253 := (+ #10 #252)
+#254 := (= #253 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#210 := (or #88 #92)
+#211 := (not #210)
+#99 := (>= #8 0::int)
+#202 := (or #92 #99)
+#203 := (not #202)
+#217 := (or #203 #211)
+#258 := (ite #217 #254 #257)
+#251 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#259 := (ite #14 #251 #258)
+#754 := (forall (vars (?v0 int) (?v1 int)) (:pat #753) #259)
+#262 := (forall (vars (?v0 int) (?v1 int)) #259)
+#757 := (iff #262 #754)
+#755 := (iff #259 #259)
+#756 := [refl]: #755
+#758 := [quant-intro #756]: #757
+#222 := (ite #217 #21 #73)
+#225 := (ite #14 0::int #222)
+#228 := (= #10 #225)
+#231 := (forall (vars (?v0 int) (?v1 int)) #228)
+#263 := (iff #231 #262)
+#260 := (iff #228 #259)
+#261 := [rewrite]: #260
+#264 := [quant-intro #261]: #263
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#109 := (ite #106 #21 #73)
+#112 := (ite #14 0::int #109)
+#115 := (= #10 #112)
+#118 := (forall (vars (?v0 int) (?v1 int)) #115)
+#232 := (iff #118 #231)
+#229 := (iff #115 #228)
+#226 := (= #112 #225)
+#223 := (= #109 #222)
+#220 := (iff #106 #217)
+#214 := (or #211 #203)
+#218 := (iff #214 #217)
+#219 := [rewrite]: #218
+#215 := (iff #106 #214)
+#212 := (iff #103 #203)
+#213 := [rewrite]: #212
+#200 := (iff #96 #211)
+#201 := [rewrite]: #200
+#216 := [monotonicity #201 #213]: #215
+#221 := [trans #216 #219]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [quant-intro #230]: #232
+#206 := (~ #118 #118)
+#204 := (~ #115 #115)
+#205 := [refl]: #204
+#207 := [nnf-pos #205]: #206
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#121 := (iff #28 #118)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#76 := (ite #63 #21 #73)
+#79 := (ite #14 0::int #76)
+#82 := (= #10 #79)
+#85 := (forall (vars (?v0 int) (?v1 int)) #82)
+#119 := (iff #85 #118)
+#116 := (iff #82 #115)
+#113 := (= #79 #112)
+#110 := (= #76 #109)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#111 := [monotonicity #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [quant-intro #117]: #119
+#86 := (iff #28 #85)
+#83 := (iff #27 #82)
+#80 := (= #26 #79)
+#77 := (= #25 #76)
+#74 := (= #24 #73)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#75 := [monotonicity #69 #72]: #74
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#78 := [monotonicity #65 #75]: #77
+#81 := [monotonicity #78]: #80
+#84 := [monotonicity #81]: #83
+#87 := [quant-intro #84]: #86
+#122 := [trans #87 #120]: #121
+#59 := [asserted]: #28
+#123 := [mp #59 #122]: #118
+#197 := [mp~ #123 #207]: #118
+#234 := [mp #197 #233]: #231
+#265 := [mp #234 #264]: #262
+#759 := [mp #265 #758]: #754
+#586 := (not #754)
+#588 := (or #586 #176)
+#339 := (* -1::int -3::int)
+#424 := (* -1::int 0::int)
+#425 := (div #424 #339)
+#426 := (* -1::int #425)
+#417 := (+ #173 #426)
+#428 := (= #417 0::int)
+#429 := (div 0::int -3::int)
+#357 := (* -1::int #429)
+#430 := (+ #173 #357)
+#427 := (= #430 0::int)
+#431 := (<= -3::int 0::int)
+#410 := (<= 0::int 0::int)
+#745 := (or #410 #431)
+#747 := (not #745)
+#404 := (>= 0::int 0::int)
+#534 := (or #431 #404)
+#741 := (not #534)
+#415 := (or #741 #747)
+#416 := (ite #415 #427 #428)
+#748 := (= -3::int 0::int)
+#749 := (= 0::int 0::int)
+#750 := (or #749 #748)
+#751 := (ite #750 #176 #416)
+#589 := (or #586 #751)
+#590 := (iff #589 #588)
+#592 := (iff #588 #588)
+#593 := [rewrite]: #592
+#686 := (iff #751 #176)
+#1 := true
+#537 := (ite true #176 #176)
+#682 := (iff #537 #176)
+#683 := [rewrite]: #682
+#685 := (iff #751 #537)
+#577 := (iff #416 #176)
+#692 := (ite false #176 #176)
+#694 := (iff #692 #176)
+#576 := [rewrite]: #694
+#693 := (iff #416 #692)
+#689 := (iff #428 #176)
+#535 := (= #417 #173)
+#719 := (+ #173 0::int)
+#710 := (= #719 #173)
+#705 := [rewrite]: #710
+#704 := (= #417 #719)
+#703 := (= #426 0::int)
+#432 := (= #424 0::int)
+#714 := [rewrite]: #432
+#696 := (= #426 #424)
+#701 := (= #425 0::int)
+#555 := (div 0::int 3::int)
+#699 := (= #555 0::int)
+#700 := [rewrite]: #699
+#556 := (= #425 #555)
+#713 := (= #339 3::int)
+#554 := [rewrite]: #713
+#698 := [monotonicity #714 #554]: #556
+#695 := [trans #698 #700]: #701
+#702 := [monotonicity #695]: #696
+#697 := [trans #702 #714]: #703
+#533 := [monotonicity #697]: #704
+#536 := [trans #533 #705]: #535
+#690 := [monotonicity #536]: #689
+#712 := (iff #427 #176)
+#706 := (= #430 #173)
+#708 := (= #430 #719)
+#718 := (= #357 0::int)
+#716 := (= #357 #424)
+#437 := (= #429 0::int)
+#438 := [rewrite]: #437
+#717 := [monotonicity #438]: #716
+#715 := [trans #717 #714]: #718
+#709 := [monotonicity #715]: #708
+#711 := [trans #709 #705]: #706
+#707 := [monotonicity #711]: #712
+#435 := (iff #415 false)
+#446 := (or false false)
+#721 := (iff #446 false)
+#725 := [rewrite]: #721
+#720 := (iff #415 #446)
+#723 := (iff #747 false)
+#736 := (not true)
+#379 := (iff #736 false)
+#739 := [rewrite]: #379
+#345 := (iff #747 #736)
+#451 := (iff #745 true)
+#731 := (or true true)
+#734 := (iff #731 true)
+#729 := [rewrite]: #734
+#449 := (iff #745 #731)
+#392 := (iff #431 true)
+#393 := [rewrite]: #392
+#726 := (iff #410 true)
+#727 := [rewrite]: #726
+#450 := [monotonicity #727 #393]: #449
+#452 := [trans #450 #729]: #451
+#722 := [monotonicity #452]: #345
+#445 := [trans #722 #739]: #723
+#737 := (iff #741 false)
+#738 := (iff #741 #736)
+#735 := (iff #534 true)
+#732 := (iff #534 #731)
+#394 := (iff #404 true)
+#730 := [rewrite]: #394
+#733 := [monotonicity #393 #730]: #732
+#373 := [trans #733 #729]: #735
+#378 := [monotonicity #373]: #738
+#740 := [trans #378 #739]: #737
+#724 := [monotonicity #740 #445]: #720
+#436 := [trans #724 #725]: #435
+#691 := [monotonicity #436 #707 #690]: #693
+#578 := [trans #691 #576]: #577
+#728 := (iff #750 true)
+#407 := (or true false)
+#744 := (iff #407 true)
+#387 := [rewrite]: #744
+#743 := (iff #750 #407)
+#742 := (iff #748 false)
+#402 := [rewrite]: #742
+#746 := (iff #749 true)
+#752 := [rewrite]: #746
+#403 := [monotonicity #752 #402]: #743
+#391 := [trans #403 #387]: #728
+#587 := [monotonicity #391 #578]: #685
+#571 := [trans #587 #683]: #686
+#591 := [monotonicity #571]: #590
+#594 := [trans #591 #593]: #590
+#582 := [quant-inst]: #589
+#687 := [mp #582 #594]: #588
+[unit-resolution #687 #759 #194]: false
+unsat
+35df6ca3b9d8297d2ae93fc18a5a2fbecd67e27f 296 0
+#2 := false
+#11 := 0::int
+decl f3 :: (-> int int int)
+#39 := 3::int
+#38 := 1::int
+#40 := (f3 1::int 3::int)
+#41 := (= #40 0::int)
+#42 := (not #41)
+#169 := [asserted]: #42
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#737 := (pattern #10)
+#66 := -1::int
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#73 := (div #67 #70)
+#240 := (* -1::int #73)
+#241 := (+ #10 #240)
+#242 := (= #241 0::int)
+#21 := (div #8 #9)
+#237 := (* -1::int #21)
+#238 := (+ #10 #237)
+#239 := (= #238 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#195 := (or #88 #92)
+#196 := (not #195)
+#99 := (>= #8 0::int)
+#187 := (or #92 #99)
+#188 := (not #187)
+#202 := (or #188 #196)
+#243 := (ite #202 #239 #242)
+#236 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#244 := (ite #14 #236 #243)
+#738 := (forall (vars (?v0 int) (?v1 int)) (:pat #737) #244)
+#247 := (forall (vars (?v0 int) (?v1 int)) #244)
+#741 := (iff #247 #738)
+#739 := (iff #244 #244)
+#740 := [refl]: #739
+#742 := [quant-intro #740]: #741
+#207 := (ite #202 #21 #73)
+#210 := (ite #14 0::int #207)
+#213 := (= #10 #210)
+#216 := (forall (vars (?v0 int) (?v1 int)) #213)
+#248 := (iff #216 #247)
+#245 := (iff #213 #244)
+#246 := [rewrite]: #245
+#249 := [quant-intro #246]: #248
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#109 := (ite #106 #21 #73)
+#112 := (ite #14 0::int #109)
+#115 := (= #10 #112)
+#118 := (forall (vars (?v0 int) (?v1 int)) #115)
+#217 := (iff #118 #216)
+#214 := (iff #115 #213)
+#211 := (= #112 #210)
+#208 := (= #109 #207)
+#205 := (iff #106 #202)
+#199 := (or #196 #188)
+#203 := (iff #199 #202)
+#204 := [rewrite]: #203
+#200 := (iff #106 #199)
+#197 := (iff #103 #188)
+#198 := [rewrite]: #197
+#185 := (iff #96 #196)
+#186 := [rewrite]: #185
+#201 := [monotonicity #186 #198]: #200
+#206 := [trans #201 #204]: #205
+#209 := [monotonicity #206]: #208
+#212 := [monotonicity #209]: #211
+#215 := [monotonicity #212]: #214
+#218 := [quant-intro #215]: #217
+#191 := (~ #118 #118)
+#189 := (~ #115 #115)
+#190 := [refl]: #189
+#192 := [nnf-pos #190]: #191
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#121 := (iff #28 #118)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#76 := (ite #63 #21 #73)
+#79 := (ite #14 0::int #76)
+#82 := (= #10 #79)
+#85 := (forall (vars (?v0 int) (?v1 int)) #82)
+#119 := (iff #85 #118)
+#116 := (iff #82 #115)
+#113 := (= #79 #112)
+#110 := (= #76 #109)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#111 := [monotonicity #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [quant-intro #117]: #119
+#86 := (iff #28 #85)
+#83 := (iff #27 #82)
+#80 := (= #26 #79)
+#77 := (= #25 #76)
+#74 := (= #24 #73)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#75 := [monotonicity #69 #72]: #74
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#78 := [monotonicity #65 #75]: #77
+#81 := [monotonicity #78]: #80
+#84 := [monotonicity #81]: #83
+#87 := [quant-intro #84]: #86
+#122 := [trans #87 #120]: #121
+#59 := [asserted]: #28
+#123 := [mp #59 #122]: #118
+#182 := [mp~ #123 #192]: #118
+#219 := [mp #182 #218]: #216
+#250 := [mp #219 #249]: #247
+#743 := [mp #250 #742]: #738
+#650 := (not #738)
+#652 := (or #650 #41)
+#324 := (* -1::int 3::int)
+#408 := (* -1::int 1::int)
+#409 := (div #408 #324)
+#410 := (* -1::int #409)
+#401 := (+ #40 #410)
+#412 := (= #401 0::int)
+#413 := (div 1::int 3::int)
+#414 := (* -1::int #413)
+#411 := (+ #40 #414)
+#415 := (= #411 0::int)
+#394 := (<= 3::int 0::int)
+#729 := (<= 1::int 0::int)
+#731 := (or #729 #394)
+#388 := (not #731)
+#518 := (>= 1::int 0::int)
+#725 := (or #394 #518)
+#399 := (not #725)
+#400 := (or #399 #388)
+#732 := (ite #400 #415 #412)
+#733 := (= 3::int 0::int)
+#734 := (= 1::int 0::int)
+#735 := (or #734 #733)
+#730 := (ite #735 #41 #732)
+#662 := (or #650 #730)
+#664 := (iff #662 #652)
+#665 := (iff #652 #652)
+#654 := [rewrite]: #665
+#661 := (iff #730 #41)
+#578 := (ite false #41 #41)
+#672 := (iff #578 #41)
+#659 := [rewrite]: #672
+#671 := (iff #730 #578)
+#576 := (iff #732 #41)
+#666 := (= #40 1::int)
+#1 := true
+#572 := (ite true #41 #666)
+#574 := (iff #572 #41)
+#575 := [rewrite]: #574
+#573 := (iff #732 #572)
+#555 := (iff #412 #666)
+#675 := (+ -1::int #40)
+#521 := (= #675 0::int)
+#667 := (iff #521 #666)
+#670 := [rewrite]: #667
+#669 := (iff #412 #521)
+#561 := (= #401 #675)
+#674 := (+ #40 -1::int)
+#678 := (= #674 #675)
+#560 := [rewrite]: #678
+#676 := (= #401 #674)
+#520 := (= #410 -1::int)
+#539 := (= #408 -1::int)
+#540 := [rewrite]: #539
+#517 := (= #410 #408)
+#681 := (= #409 1::int)
+#682 := -3::int
+#685 := (div -1::int -3::int)
+#686 := (= #685 1::int)
+#687 := [rewrite]: #686
+#679 := (= #409 #685)
+#683 := (= #324 -3::int)
+#684 := [rewrite]: #683
+#680 := [monotonicity #540 #684]: #679
+#688 := [trans #680 #687]: #681
+#519 := [monotonicity #688]: #517
+#673 := [trans #519 #540]: #520
+#677 := [monotonicity #673]: #676
+#562 := [trans #677 #560]: #561
+#571 := [monotonicity #562]: #669
+#570 := [trans #571 #670]: #555
+#697 := (iff #415 #41)
+#696 := (= #411 #40)
+#693 := (+ #40 0::int)
+#690 := (= #693 #40)
+#695 := [rewrite]: #690
+#694 := (= #411 #693)
+#703 := (= #414 0::int)
+#701 := (* -1::int 0::int)
+#702 := (= #701 0::int)
+#699 := [rewrite]: #702
+#416 := (= #414 #701)
+#422 := (= #413 0::int)
+#700 := [rewrite]: #422
+#698 := [monotonicity #700]: #416
+#692 := [trans #698 #699]: #703
+#689 := [monotonicity #692]: #694
+#691 := [trans #689 #695]: #696
+#538 := [monotonicity #691]: #697
+#420 := (iff #400 true)
+#716 := (or false true)
+#713 := (iff #716 true)
+#719 := [rewrite]: #713
+#709 := (iff #400 #716)
+#708 := (iff #388 true)
+#706 := (not false)
+#430 := (iff #706 true)
+#704 := [rewrite]: #430
+#707 := (iff #388 #706)
+#436 := (iff #731 false)
+#727 := (or false false)
+#371 := (iff #727 false)
+#712 := [rewrite]: #371
+#434 := (iff #731 #727)
+#377 := (iff #394 false)
+#378 := [rewrite]: #377
+#711 := (iff #729 false)
+#433 := [rewrite]: #711
+#435 := [monotonicity #433 #378]: #434
+#330 := [trans #435 #712]: #436
+#429 := [monotonicity #330]: #707
+#705 := [trans #429 #704]: #708
+#724 := (iff #399 false)
+#722 := (not true)
+#723 := (iff #722 false)
+#721 := [rewrite]: #723
+#362 := (iff #399 #722)
+#357 := (iff #725 true)
+#717 := (iff #725 #716)
+#714 := (iff #518 true)
+#715 := [rewrite]: #714
+#718 := [monotonicity #378 #715]: #717
+#720 := [trans #718 #719]: #357
+#363 := [monotonicity #720]: #362
+#710 := [trans #363 #721]: #724
+#419 := [monotonicity #710 #705]: #709
+#421 := [trans #419 #719]: #420
+#566 := [monotonicity #421 #538 #570]: #573
+#577 := [trans #566 #575]: #576
+#375 := (iff #735 false)
+#387 := (iff #735 #727)
+#386 := (iff #733 false)
+#391 := [rewrite]: #386
+#736 := (iff #734 false)
+#726 := [rewrite]: #736
+#728 := [monotonicity #726 #391]: #387
+#376 := [trans #728 #712]: #375
+#668 := [monotonicity #376 #577]: #671
+#653 := [trans #668 #659]: #661
+#660 := [monotonicity #653]: #664
+#655 := [trans #660 #654]: #664
+#663 := [quant-inst]: #662
+#656 := [mp #663 #655]: #652
+[unit-resolution #656 #743 #169]: false
+unsat
+d02187cb7fcefe99851febe02397cc4a2e6fdbff 286 0
+#2 := false
+#40 := 1::int
+decl f3 :: (-> int int int)
+#38 := 3::int
+#39 := (f3 3::int 3::int)
+#41 := (= #39 1::int)
+#42 := (not #41)
+#169 := [asserted]: #42
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#727 := (pattern #10)
+#11 := 0::int
+#66 := -1::int
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#73 := (div #67 #70)
+#230 := (* -1::int #73)
+#231 := (+ #10 #230)
+#232 := (= #231 0::int)
+#21 := (div #8 #9)
+#227 := (* -1::int #21)
+#228 := (+ #10 #227)
+#229 := (= #228 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#185 := (or #88 #92)
+#186 := (not #185)
+#99 := (>= #8 0::int)
+#177 := (or #92 #99)
+#178 := (not #177)
+#192 := (or #178 #186)
+#233 := (ite #192 #229 #232)
+#226 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#234 := (ite #14 #226 #233)
+#728 := (forall (vars (?v0 int) (?v1 int)) (:pat #727) #234)
+#237 := (forall (vars (?v0 int) (?v1 int)) #234)
+#731 := (iff #237 #728)
+#729 := (iff #234 #234)
+#730 := [refl]: #729
+#732 := [quant-intro #730]: #731
+#197 := (ite #192 #21 #73)
+#200 := (ite #14 0::int #197)
+#203 := (= #10 #200)
+#206 := (forall (vars (?v0 int) (?v1 int)) #203)
+#238 := (iff #206 #237)
+#235 := (iff #203 #234)
+#236 := [rewrite]: #235
+#239 := [quant-intro #236]: #238
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#109 := (ite #106 #21 #73)
+#112 := (ite #14 0::int #109)
+#115 := (= #10 #112)
+#118 := (forall (vars (?v0 int) (?v1 int)) #115)
+#207 := (iff #118 #206)
+#204 := (iff #115 #203)
+#201 := (= #112 #200)
+#198 := (= #109 #197)
+#195 := (iff #106 #192)
+#189 := (or #186 #178)
+#193 := (iff #189 #192)
+#194 := [rewrite]: #193
+#190 := (iff #106 #189)
+#187 := (iff #103 #178)
+#188 := [rewrite]: #187
+#175 := (iff #96 #186)
+#176 := [rewrite]: #175
+#191 := [monotonicity #176 #188]: #190
+#196 := [trans #191 #194]: #195
+#199 := [monotonicity #196]: #198
+#202 := [monotonicity #199]: #201
+#205 := [monotonicity #202]: #204
+#208 := [quant-intro #205]: #207
+#181 := (~ #118 #118)
+#179 := (~ #115 #115)
+#180 := [refl]: #179
+#182 := [nnf-pos #180]: #181
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#121 := (iff #28 #118)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#76 := (ite #63 #21 #73)
+#79 := (ite #14 0::int #76)
+#82 := (= #10 #79)
+#85 := (forall (vars (?v0 int) (?v1 int)) #82)
+#119 := (iff #85 #118)
+#116 := (iff #82 #115)
+#113 := (= #79 #112)
+#110 := (= #76 #109)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#111 := [monotonicity #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [quant-intro #117]: #119
+#86 := (iff #28 #85)
+#83 := (iff #27 #82)
+#80 := (= #26 #79)
+#77 := (= #25 #76)
+#74 := (= #24 #73)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#75 := [monotonicity #69 #72]: #74
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#78 := [monotonicity #65 #75]: #77
+#81 := [monotonicity #78]: #80
+#84 := [monotonicity #81]: #83
+#87 := [quant-intro #84]: #86
+#122 := [trans #87 #120]: #121
+#59 := [asserted]: #28
+#123 := [mp #59 #122]: #118
+#172 := [mp~ #123 #182]: #118
+#209 := [mp #172 #208]: #206
+#240 := [mp #209 #239]: #237
+#733 := [mp #240 #732]: #728
+#565 := (not #728)
+#566 := (or #565 #41)
+#314 := (* -1::int 3::int)
+#398 := (div #314 #314)
+#399 := (* -1::int #398)
+#400 := (+ #39 #399)
+#391 := (= #400 0::int)
+#402 := (div 3::int 3::int)
+#403 := (* -1::int #402)
+#404 := (+ #39 #403)
+#401 := (= #404 0::int)
+#405 := (<= 3::int 0::int)
+#384 := (or #405 #405)
+#719 := (not #384)
+#721 := (>= 3::int 0::int)
+#378 := (or #405 #721)
+#508 := (not #378)
+#715 := (or #508 #719)
+#389 := (ite #715 #401 #391)
+#390 := (= #39 0::int)
+#722 := (= 3::int 0::int)
+#723 := (or #722 #722)
+#724 := (ite #723 #390 #389)
+#567 := (or #565 #724)
+#661 := (iff #567 #566)
+#662 := (iff #566 #566)
+#649 := [rewrite]: #662
+#556 := (iff #724 #41)
+#660 := (ite false #390 #41)
+#562 := (iff #660 #41)
+#563 := [rewrite]: #562
+#545 := (iff #724 #660)
+#656 := (iff #389 #41)
+#1 := true
+#551 := (ite true #41 #41)
+#659 := (iff #551 #41)
+#561 := [rewrite]: #659
+#552 := (iff #389 #551)
+#668 := (iff #391 #41)
+#689 := (+ -1::int #39)
+#679 := (= #689 0::int)
+#686 := (iff #679 #41)
+#681 := [rewrite]: #686
+#667 := (iff #391 #679)
+#664 := (= #400 #689)
+#406 := (+ #39 -1::int)
+#693 := (= #406 #689)
+#682 := [rewrite]: #693
+#510 := (= #400 #406)
+#507 := (= #399 -1::int)
+#699 := (* -1::int 1::int)
+#411 := (= #699 -1::int)
+#412 := [rewrite]: #411
+#671 := (= #399 #699)
+#676 := (= #398 1::int)
+#529 := -3::int
+#673 := (div -3::int -3::int)
+#669 := (= #673 1::int)
+#670 := [rewrite]: #669
+#674 := (= #398 #673)
+#530 := (= #314 -3::int)
+#672 := [rewrite]: #530
+#675 := [monotonicity #672 #672]: #674
+#677 := [trans #675 #670]: #676
+#678 := [monotonicity #677]: #671
+#509 := [trans #678 #412]: #507
+#663 := [monotonicity #509]: #510
+#666 := [trans #663 #682]: #664
+#665 := [monotonicity #666]: #667
+#550 := [trans #665 #681]: #668
+#687 := (iff #401 #41)
+#680 := (iff #401 #679)
+#683 := (= #404 #689)
+#688 := (= #404 #406)
+#690 := (= #403 -1::int)
+#409 := (= #403 #699)
+#698 := (= #402 1::int)
+#695 := [rewrite]: #698
+#410 := [monotonicity #695]: #409
+#691 := [trans #410 #412]: #690
+#692 := [monotonicity #691]: #688
+#684 := [trans #692 #682]: #683
+#685 := [monotonicity #684]: #680
+#528 := [trans #685 #681]: #687
+#420 := (iff #715 true)
+#367 := (or false true)
+#705 := (iff #367 true)
+#706 := [rewrite]: #705
+#697 := (iff #715 #367)
+#320 := (iff #719 true)
+#701 := (not false)
+#425 := (iff #701 true)
+#426 := [rewrite]: #425
+#423 := (iff #719 #701)
+#714 := (iff #384 false)
+#726 := (or false false)
+#381 := (iff #726 false)
+#717 := [rewrite]: #381
+#713 := (iff #384 #726)
+#361 := (iff #405 false)
+#702 := [rewrite]: #361
+#711 := [monotonicity #702 #702]: #713
+#700 := [trans #711 #717]: #714
+#424 := [monotonicity #700]: #423
+#696 := [trans #424 #426]: #320
+#352 := (iff #508 false)
+#703 := (not true)
+#710 := (iff #703 false)
+#712 := [rewrite]: #710
+#709 := (iff #508 #703)
+#707 := (iff #378 true)
+#368 := (iff #378 #367)
+#365 := (iff #721 true)
+#366 := [rewrite]: #365
+#704 := [monotonicity #702 #366]: #368
+#708 := [trans #704 #706]: #707
+#347 := [monotonicity #708]: #709
+#353 := [trans #347 #712]: #352
+#419 := [monotonicity #353 #696]: #697
+#694 := [trans #419 #706]: #420
+#511 := [monotonicity #694 #528 #550]: #552
+#657 := [trans #511 #561]: #656
+#377 := (iff #723 false)
+#716 := (iff #723 #726)
+#725 := (iff #722 false)
+#720 := [rewrite]: #725
+#376 := [monotonicity #720 #720]: #716
+#718 := [trans #376 #717]: #377
+#560 := [monotonicity #718 #657]: #545
+#564 := [trans #560 #563]: #556
+#658 := [monotonicity #564]: #661
+#651 := [trans #658 #649]: #661
+#568 := [quant-inst]: #567
+#643 := [mp #568 #651]: #566
+[unit-resolution #643 #733 #169]: false
+unsat
+fc9ffeceefa2f1854d4c8adb404766a307c30ad9 310 0
+#2 := false
+#41 := 1::int
+decl f3 :: (-> int int int)
+#39 := 3::int
+#38 := 5::int
+#40 := (f3 5::int 3::int)
+#42 := (= #40 1::int)
+#43 := (not #42)
+#170 := [asserted]: #43
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#728 := (pattern #10)
+#11 := 0::int
+#67 := -1::int
+#71 := (* -1::int #9)
+#68 := (* -1::int #8)
+#74 := (div #68 #71)
+#231 := (* -1::int #74)
+#232 := (+ #10 #231)
+#233 := (= #232 0::int)
+#21 := (div #8 #9)
+#228 := (* -1::int #21)
+#229 := (+ #10 #228)
+#230 := (= #229 0::int)
+#93 := (<= #9 0::int)
+#89 := (<= #8 0::int)
+#186 := (or #89 #93)
+#187 := (not #186)
+#100 := (>= #8 0::int)
+#178 := (or #93 #100)
+#179 := (not #178)
+#193 := (or #179 #187)
+#234 := (ite #193 #230 #233)
+#227 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#235 := (ite #14 #227 #234)
+#729 := (forall (vars (?v0 int) (?v1 int)) (:pat #728) #235)
+#238 := (forall (vars (?v0 int) (?v1 int)) #235)
+#732 := (iff #238 #729)
+#730 := (iff #235 #235)
+#731 := [refl]: #730
+#733 := [quant-intro #731]: #732
+#198 := (ite #193 #21 #74)
+#201 := (ite #14 0::int #198)
+#204 := (= #10 #201)
+#207 := (forall (vars (?v0 int) (?v1 int)) #204)
+#239 := (iff #207 #238)
+#236 := (iff #204 #235)
+#237 := [rewrite]: #236
+#240 := [quant-intro #237]: #239
+#101 := (not #100)
+#94 := (not #93)
+#104 := (and #94 #101)
+#90 := (not #89)
+#97 := (and #90 #94)
+#107 := (or #97 #104)
+#110 := (ite #107 #21 #74)
+#113 := (ite #14 0::int #110)
+#116 := (= #10 #113)
+#119 := (forall (vars (?v0 int) (?v1 int)) #116)
+#208 := (iff #119 #207)
+#205 := (iff #116 #204)
+#202 := (= #113 #201)
+#199 := (= #110 #198)
+#196 := (iff #107 #193)
+#190 := (or #187 #179)
+#194 := (iff #190 #193)
+#195 := [rewrite]: #194
+#191 := (iff #107 #190)
+#188 := (iff #104 #179)
+#189 := [rewrite]: #188
+#176 := (iff #97 #187)
+#177 := [rewrite]: #176
+#192 := [monotonicity #177 #189]: #191
+#197 := [trans #192 #195]: #196
+#200 := [monotonicity #197]: #199
+#203 := [monotonicity #200]: #202
+#206 := [monotonicity #203]: #205
+#209 := [quant-intro #206]: #208
+#182 := (~ #119 #119)
+#180 := (~ #116 #116)
+#181 := [refl]: #180
+#183 := [nnf-pos #181]: #182
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#122 := (iff #28 #119)
+#61 := (and #16 #18)
+#64 := (or #17 #61)
+#77 := (ite #64 #21 #74)
+#80 := (ite #14 0::int #77)
+#83 := (= #10 #80)
+#86 := (forall (vars (?v0 int) (?v1 int)) #83)
+#120 := (iff #86 #119)
+#117 := (iff #83 #116)
+#114 := (= #80 #113)
+#111 := (= #77 #110)
+#108 := (iff #64 #107)
+#105 := (iff #61 #104)
+#102 := (iff #18 #101)
+#103 := [rewrite]: #102
+#95 := (iff #16 #94)
+#96 := [rewrite]: #95
+#106 := [monotonicity #96 #103]: #105
+#98 := (iff #17 #97)
+#91 := (iff #15 #90)
+#92 := [rewrite]: #91
+#99 := [monotonicity #92 #96]: #98
+#109 := [monotonicity #99 #106]: #108
+#112 := [monotonicity #109]: #111
+#115 := [monotonicity #112]: #114
+#118 := [monotonicity #115]: #117
+#121 := [quant-intro #118]: #120
+#87 := (iff #28 #86)
+#84 := (iff #27 #83)
+#81 := (= #26 #80)
+#78 := (= #25 #77)
+#75 := (= #24 #74)
+#72 := (= #23 #71)
+#73 := [rewrite]: #72
+#69 := (= #22 #68)
+#70 := [rewrite]: #69
+#76 := [monotonicity #70 #73]: #75
+#65 := (iff #20 #64)
+#62 := (iff #19 #61)
+#63 := [rewrite]: #62
+#66 := [monotonicity #63]: #65
+#79 := [monotonicity #66 #76]: #78
+#82 := [monotonicity #79]: #81
+#85 := [monotonicity #82]: #84
+#88 := [quant-intro #85]: #87
+#123 := [trans #88 #121]: #122
+#60 := [asserted]: #28
+#124 := [mp #60 #123]: #119
+#173 := [mp~ #124 #183]: #119
+#210 := [mp #173 #209]: #207
+#241 := [mp #210 #240]: #238
+#734 := [mp #241 #733]: #729
+#633 := (not #729)
+#634 := (or #633 #42)
+#315 := (* -1::int 3::int)
+#399 := (* -1::int 5::int)
+#400 := (div #399 #315)
+#401 := (* -1::int #400)
+#392 := (+ #40 #401)
+#403 := (= #392 0::int)
+#404 := (div 5::int 3::int)
+#405 := (* -1::int #404)
+#402 := (+ #40 #405)
+#406 := (= #402 0::int)
+#385 := (<= 3::int 0::int)
+#720 := (<= 5::int 0::int)
+#722 := (or #720 #385)
+#379 := (not #722)
+#509 := (>= 5::int 0::int)
+#716 := (or #385 #509)
+#390 := (not #716)
+#391 := (or #390 #379)
+#723 := (ite #391 #406 #403)
+#724 := (= #40 0::int)
+#725 := (= 3::int 0::int)
+#726 := (= 5::int 0::int)
+#721 := (or #726 #725)
+#727 := (ite #721 #724 #723)
+#636 := (or #633 #727)
+#638 := (iff #636 #634)
+#635 := (iff #634 #634)
+#640 := [rewrite]: #635
+#642 := (iff #727 #42)
+#656 := (ite false #724 #42)
+#647 := (iff #656 #42)
+#648 := [rewrite]: #647
+#645 := (iff #727 #656)
+#655 := (iff #723 #42)
+#665 := 2::int
+#662 := (= #40 2::int)
+#1 := true
+#644 := (ite true #42 #662)
+#653 := (iff #644 #42)
+#654 := [rewrite]: #653
+#641 := (iff #723 #644)
+#650 := (iff #403 #662)
+#512 := -2::int
+#563 := (+ -2::int #40)
+#567 := (= #563 0::int)
+#659 := (iff #567 #662)
+#663 := [rewrite]: #659
+#568 := (iff #403 #567)
+#565 := (= #392 #563)
+#661 := (+ #40 -2::int)
+#564 := (= #661 #563)
+#557 := [rewrite]: #564
+#546 := (= #392 #661)
+#657 := (= #401 -2::int)
+#551 := (* -1::int 2::int)
+#660 := (= #551 -2::int)
+#562 := [rewrite]: #660
+#552 := (= #401 #551)
+#666 := (= #400 2::int)
+#672 := -3::int
+#671 := -5::int
+#510 := (div -5::int -3::int)
+#667 := (= #510 2::int)
+#668 := [rewrite]: #667
+#511 := (= #400 #510)
+#679 := (= #315 -3::int)
+#508 := [rewrite]: #679
+#677 := (= #399 -5::int)
+#678 := [rewrite]: #677
+#664 := [monotonicity #678 #508]: #511
+#669 := [trans #664 #668]: #666
+#553 := [monotonicity #669]: #552
+#658 := [trans #553 #562]: #657
+#561 := [monotonicity #658]: #546
+#566 := [trans #561 #557]: #565
+#569 := [monotonicity #566]: #568
+#652 := [trans #569 #663]: #650
+#676 := (iff #406 #42)
+#686 := (+ -1::int #40)
+#530 := (= #686 0::int)
+#674 := (iff #530 #42)
+#675 := [rewrite]: #674
+#531 := (iff #406 #530)
+#688 := (= #402 #686)
+#685 := (+ #40 -1::int)
+#687 := (= #685 #686)
+#682 := [rewrite]: #687
+#680 := (= #402 #685)
+#683 := (= #405 -1::int)
+#407 := (* -1::int 1::int)
+#690 := (= #407 -1::int)
+#694 := [rewrite]: #690
+#689 := (= #405 #407)
+#691 := (= #404 1::int)
+#692 := [rewrite]: #691
+#693 := [monotonicity #692]: #689
+#684 := [trans #693 #694]: #683
+#681 := [monotonicity #684]: #680
+#529 := [trans #681 #682]: #688
+#673 := [monotonicity #529]: #531
+#670 := [trans #673 #675]: #676
+#412 := (iff #391 true)
+#708 := (or false true)
+#710 := (iff #708 true)
+#348 := [rewrite]: #710
+#410 := (iff #391 #708)
+#696 := (iff #379 true)
+#698 := (not false)
+#695 := (iff #698 true)
+#699 := [rewrite]: #695
+#420 := (iff #379 #698)
+#321 := (iff #722 false)
+#378 := (or false false)
+#703 := (iff #378 false)
+#366 := [rewrite]: #703
+#426 := (iff #722 #378)
+#369 := (iff #385 false)
+#705 := [rewrite]: #369
+#424 := (iff #720 false)
+#425 := [rewrite]: #424
+#427 := [monotonicity #425 #705]: #426
+#697 := [trans #427 #366]: #321
+#421 := [monotonicity #697]: #420
+#700 := [trans #421 #699]: #696
+#701 := (iff #390 false)
+#353 := (not true)
+#712 := (iff #353 false)
+#715 := [rewrite]: #712
+#354 := (iff #390 #353)
+#711 := (iff #716 true)
+#709 := (iff #716 #708)
+#706 := (iff #509 true)
+#707 := [rewrite]: #706
+#704 := [monotonicity #705 #707]: #709
+#713 := [trans #704 #348]: #711
+#714 := [monotonicity #713]: #354
+#702 := [trans #714 #715]: #701
+#411 := [monotonicity #702 #700]: #410
+#413 := [trans #411 #348]: #412
+#643 := [monotonicity #413 #670 #652]: #641
+#651 := [trans #643 #654]: #655
+#367 := (iff #721 false)
+#719 := (iff #721 #378)
+#382 := (iff #725 false)
+#718 := [rewrite]: #382
+#717 := (iff #726 false)
+#377 := [rewrite]: #717
+#362 := [monotonicity #377 #718]: #719
+#368 := [trans #362 #366]: #367
+#646 := [monotonicity #368 #651]: #645
+#649 := [trans #646 #648]: #642
+#639 := [monotonicity #649]: #638
+#626 := [trans #639 #640]: #638
+#637 := [quant-inst]: #636
+#627 := [mp #637 #626]: #634
+[unit-resolution #627 #734 #170]: false
+unsat
+334231bac1c10cb79d865cb2c86779cf7dd19631 324 0
+#2 := false
+#68 := -1::int
+decl f3 :: (-> int int int)
+#172 := -3::int
+#38 := 1::int
+#175 := (f3 1::int -3::int)
+#180 := (= #175 -1::int)
+#193 := (not #180)
+#42 := (- 1::int)
+#39 := 3::int
+#40 := (- 3::int)
+#41 := (f3 1::int #40)
+#43 := (= #41 #42)
+#44 := (not #43)
+#196 := (iff #44 #193)
+#183 := (= -1::int #175)
+#188 := (not #183)
+#194 := (iff #188 #193)
+#191 := (iff #183 #180)
+#192 := [rewrite]: #191
+#195 := [monotonicity #192]: #194
+#189 := (iff #44 #188)
+#186 := (iff #43 #183)
+#184 := (iff #180 #183)
+#185 := [rewrite]: #184
+#181 := (iff #43 #180)
+#178 := (= #42 -1::int)
+#179 := [rewrite]: #178
+#176 := (= #41 #175)
+#173 := (= #40 -3::int)
+#174 := [rewrite]: #173
+#177 := [monotonicity #174]: #176
+#182 := [monotonicity #177 #179]: #181
+#187 := [trans #182 #185]: #186
+#190 := [monotonicity #187]: #189
+#197 := [trans #190 #195]: #196
+#171 := [asserted]: #44
+#198 := [mp #171 #197]: #193
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#756 := (pattern #10)
+#11 := 0::int
+#72 := (* -1::int #9)
+#69 := (* -1::int #8)
+#75 := (div #69 #72)
+#259 := (* -1::int #75)
+#260 := (+ #10 #259)
+#261 := (= #260 0::int)
+#21 := (div #8 #9)
+#256 := (* -1::int #21)
+#257 := (+ #10 #256)
+#258 := (= #257 0::int)
+#94 := (<= #9 0::int)
+#90 := (<= #8 0::int)
+#214 := (or #90 #94)
+#215 := (not #214)
+#101 := (>= #8 0::int)
+#206 := (or #94 #101)
+#207 := (not #206)
+#221 := (or #207 #215)
+#262 := (ite #221 #258 #261)
+#255 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#263 := (ite #14 #255 #262)
+#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
+#266 := (forall (vars (?v0 int) (?v1 int)) #263)
+#760 := (iff #266 #757)
+#758 := (iff #263 #263)
+#759 := [refl]: #758
+#761 := [quant-intro #759]: #760
+#226 := (ite #221 #21 #75)
+#229 := (ite #14 0::int #226)
+#232 := (= #10 #229)
+#235 := (forall (vars (?v0 int) (?v1 int)) #232)
+#267 := (iff #235 #266)
+#264 := (iff #232 #263)
+#265 := [rewrite]: #264
+#268 := [quant-intro #265]: #267
+#102 := (not #101)
+#95 := (not #94)
+#105 := (and #95 #102)
+#91 := (not #90)
+#98 := (and #91 #95)
+#108 := (or #98 #105)
+#111 := (ite #108 #21 #75)
+#114 := (ite #14 0::int #111)
+#117 := (= #10 #114)
+#120 := (forall (vars (?v0 int) (?v1 int)) #117)
+#236 := (iff #120 #235)
+#233 := (iff #117 #232)
+#230 := (= #114 #229)
+#227 := (= #111 #226)
+#224 := (iff #108 #221)
+#218 := (or #215 #207)
+#222 := (iff #218 #221)
+#223 := [rewrite]: #222
+#219 := (iff #108 #218)
+#216 := (iff #105 #207)
+#217 := [rewrite]: #216
+#204 := (iff #98 #215)
+#205 := [rewrite]: #204
+#220 := [monotonicity #205 #217]: #219
+#225 := [trans #220 #223]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [quant-intro #234]: #236
+#210 := (~ #120 #120)
+#208 := (~ #117 #117)
+#209 := [refl]: #208
+#211 := [nnf-pos #209]: #210
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#123 := (iff #28 #120)
+#62 := (and #16 #18)
+#65 := (or #17 #62)
+#78 := (ite #65 #21 #75)
+#81 := (ite #14 0::int #78)
+#84 := (= #10 #81)
+#87 := (forall (vars (?v0 int) (?v1 int)) #84)
+#121 := (iff #87 #120)
+#118 := (iff #84 #117)
+#115 := (= #81 #114)
+#112 := (= #78 #111)
+#109 := (iff #65 #108)
+#106 := (iff #62 #105)
+#103 := (iff #18 #102)
+#104 := [rewrite]: #103
+#96 := (iff #16 #95)
+#97 := [rewrite]: #96
+#107 := [monotonicity #97 #104]: #106
+#99 := (iff #17 #98)
+#92 := (iff #15 #91)
+#93 := [rewrite]: #92
+#100 := [monotonicity #93 #97]: #99
+#110 := [monotonicity #100 #107]: #109
+#113 := [monotonicity #110]: #112
+#116 := [monotonicity #113]: #115
+#119 := [monotonicity #116]: #118
+#122 := [quant-intro #119]: #121
+#88 := (iff #28 #87)
+#85 := (iff #27 #84)
+#82 := (= #26 #81)
+#79 := (= #25 #78)
+#76 := (= #24 #75)
+#73 := (= #23 #72)
+#74 := [rewrite]: #73
+#70 := (= #22 #69)
+#71 := [rewrite]: #70
+#77 := [monotonicity #71 #74]: #76
+#66 := (iff #20 #65)
+#63 := (iff #19 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#80 := [monotonicity #67 #77]: #79
+#83 := [monotonicity #80]: #82
+#86 := [monotonicity #83]: #85
+#89 := [quant-intro #86]: #88
+#124 := [trans #89 #122]: #123
+#61 := [asserted]: #28
+#125 := [mp #61 #124]: #120
+#201 := [mp~ #125 #211]: #120
+#238 := [mp #201 #237]: #235
+#269 := [mp #238 #268]: #266
+#762 := [mp #269 #761]: #757
+#672 := (not #757)
+#669 := (or #672 #180)
+#343 := (* -1::int -3::int)
+#427 := (* -1::int 1::int)
+#428 := (div #427 #343)
+#429 := (* -1::int #428)
+#420 := (+ #175 #429)
+#431 := (= #420 0::int)
+#432 := (div 1::int -3::int)
+#433 := (* -1::int #432)
+#430 := (+ #175 #433)
+#434 := (= #430 0::int)
+#413 := (<= -3::int 0::int)
+#748 := (<= 1::int 0::int)
+#750 := (or #748 #413)
+#407 := (not #750)
+#537 := (>= 1::int 0::int)
+#744 := (or #413 #537)
+#418 := (not #744)
+#419 := (or #418 #407)
+#751 := (ite #419 #434 #431)
+#752 := (= #175 0::int)
+#753 := (= -3::int 0::int)
+#754 := (= 1::int 0::int)
+#749 := (or #754 #753)
+#755 := (ite #749 #752 #751)
+#671 := (or #672 #755)
+#682 := (iff #671 #669)
+#679 := (iff #669 #669)
+#684 := [rewrite]: #679
+#678 := (iff #755 #180)
+#585 := (ite false #752 #180)
+#595 := (iff #585 #180)
+#596 := [rewrite]: #595
+#687 := (iff #755 #585)
+#597 := (iff #751 #180)
+#593 := (iff #751 #585)
+#591 := (iff #431 #180)
+#580 := (+ 1::int #175)
+#685 := (= #580 0::int)
+#574 := (iff #685 #180)
+#589 := [rewrite]: #574
+#686 := (iff #431 #685)
+#688 := (= #420 #580)
+#694 := (+ #175 1::int)
+#581 := (= #694 #580)
+#540 := [rewrite]: #581
+#697 := (= #420 #694)
+#695 := (= #429 1::int)
+#536 := (* -1::int -1::int)
+#692 := (= #536 1::int)
+#693 := [rewrite]: #692
+#538 := (= #429 #536)
+#700 := (= #428 -1::int)
+#704 := (div -1::int 3::int)
+#705 := (= #704 -1::int)
+#706 := [rewrite]: #705
+#698 := (= #428 #704)
+#702 := (= #343 3::int)
+#703 := [rewrite]: #702
+#559 := (= #427 -1::int)
+#701 := [rewrite]: #559
+#699 := [monotonicity #701 #703]: #698
+#707 := [trans #699 #706]: #700
+#539 := [monotonicity #707]: #538
+#696 := [trans #539 #693]: #695
+#579 := [monotonicity #696]: #697
+#590 := [trans #579 #540]: #688
+#689 := [monotonicity #590]: #686
+#592 := [trans #689 #589]: #591
+#557 := (iff #434 #752)
+#710 := (= #430 #175)
+#713 := (+ #175 0::int)
+#714 := (= #713 #175)
+#715 := [rewrite]: #714
+#708 := (= #430 #713)
+#711 := (= #433 0::int)
+#435 := (* -1::int 0::int)
+#718 := (= #435 0::int)
+#722 := [rewrite]: #718
+#717 := (= #433 #435)
+#719 := (= #432 0::int)
+#720 := [rewrite]: #719
+#721 := [monotonicity #720]: #717
+#712 := [trans #721 #722]: #711
+#709 := [monotonicity #712]: #708
+#716 := [trans #709 #715]: #710
+#558 := [monotonicity #716]: #557
+#440 := (iff #419 false)
+#406 := (or false false)
+#731 := (iff #406 false)
+#394 := [rewrite]: #731
+#438 := (iff #419 #406)
+#724 := (iff #407 false)
+#1 := true
+#381 := (not true)
+#740 := (iff #381 false)
+#743 := [rewrite]: #740
+#723 := (iff #407 #381)
+#448 := (iff #750 true)
+#454 := (or false true)
+#725 := (iff #454 true)
+#726 := [rewrite]: #725
+#455 := (iff #750 #454)
+#397 := (iff #413 true)
+#733 := [rewrite]: #397
+#452 := (iff #748 false)
+#453 := [rewrite]: #452
+#349 := [monotonicity #453 #733]: #455
+#449 := [trans #349 #726]: #448
+#727 := [monotonicity #449]: #723
+#728 := [trans #727 #743]: #724
+#729 := (iff #418 false)
+#382 := (iff #418 #381)
+#739 := (iff #744 true)
+#736 := (or true true)
+#738 := (iff #736 true)
+#376 := [rewrite]: #738
+#737 := (iff #744 #736)
+#734 := (iff #537 true)
+#735 := [rewrite]: #734
+#732 := [monotonicity #733 #735]: #737
+#741 := [trans #732 #376]: #739
+#742 := [monotonicity #741]: #382
+#730 := [trans #742 #743]: #729
+#439 := [monotonicity #730 #728]: #438
+#441 := [trans #439 #394]: #440
+#594 := [monotonicity #441 #558 #592]: #593
+#690 := [trans #594 #596]: #597
+#395 := (iff #749 false)
+#747 := (iff #749 #406)
+#410 := (iff #753 false)
+#746 := [rewrite]: #410
+#745 := (iff #754 false)
+#405 := [rewrite]: #745
+#390 := [monotonicity #405 #746]: #747
+#396 := [trans #390 #394]: #395
+#691 := [monotonicity #396 #690]: #687
+#680 := [trans #691 #596]: #678
+#683 := [monotonicity #680]: #682
+#673 := [trans #683 #684]: #682
+#681 := [quant-inst]: #671
+#674 := [mp #681 #673]: #669
+[unit-resolution #674 #762 #198]: false
+unsat
+60a3e615568433502bc15c7d472c0ece644ee329 323 0
+#2 := false
+#68 := -1::int
+decl f3 :: (-> int int int)
+#172 := -3::int
+#38 := 3::int
+#175 := (f3 3::int -3::int)
+#180 := (= #175 -1::int)
+#193 := (not #180)
+#41 := 1::int
+#42 := (- 1::int)
+#39 := (- 3::int)
+#40 := (f3 3::int #39)
+#43 := (= #40 #42)
+#44 := (not #43)
+#196 := (iff #44 #193)
+#183 := (= -1::int #175)
+#188 := (not #183)
+#194 := (iff #188 #193)
+#191 := (iff #183 #180)
+#192 := [rewrite]: #191
+#195 := [monotonicity #192]: #194
+#189 := (iff #44 #188)
+#186 := (iff #43 #183)
+#184 := (iff #180 #183)
+#185 := [rewrite]: #184
+#181 := (iff #43 #180)
+#178 := (= #42 -1::int)
+#179 := [rewrite]: #178
+#176 := (= #40 #175)
+#173 := (= #39 -3::int)
+#174 := [rewrite]: #173
+#177 := [monotonicity #174]: #176
+#182 := [monotonicity #177 #179]: #181
+#187 := [trans #182 #185]: #186
+#190 := [monotonicity #187]: #189
+#197 := [trans #190 #195]: #196
+#171 := [asserted]: #44
+#198 := [mp #171 #197]: #193
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#756 := (pattern #10)
+#11 := 0::int
+#72 := (* -1::int #9)
+#69 := (* -1::int #8)
+#75 := (div #69 #72)
+#259 := (* -1::int #75)
+#260 := (+ #10 #259)
+#261 := (= #260 0::int)
+#21 := (div #8 #9)
+#256 := (* -1::int #21)
+#257 := (+ #10 #256)
+#258 := (= #257 0::int)
+#94 := (<= #9 0::int)
+#90 := (<= #8 0::int)
+#214 := (or #90 #94)
+#215 := (not #214)
+#101 := (>= #8 0::int)
+#206 := (or #94 #101)
+#207 := (not #206)
+#221 := (or #207 #215)
+#262 := (ite #221 #258 #261)
+#255 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#263 := (ite #14 #255 #262)
+#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
+#266 := (forall (vars (?v0 int) (?v1 int)) #263)
+#760 := (iff #266 #757)
+#758 := (iff #263 #263)
+#759 := [refl]: #758
+#761 := [quant-intro #759]: #760
+#226 := (ite #221 #21 #75)
+#229 := (ite #14 0::int #226)
+#232 := (= #10 #229)
+#235 := (forall (vars (?v0 int) (?v1 int)) #232)
+#267 := (iff #235 #266)
+#264 := (iff #232 #263)
+#265 := [rewrite]: #264
+#268 := [quant-intro #265]: #267
+#102 := (not #101)
+#95 := (not #94)
+#105 := (and #95 #102)
+#91 := (not #90)
+#98 := (and #91 #95)
+#108 := (or #98 #105)
+#111 := (ite #108 #21 #75)
+#114 := (ite #14 0::int #111)
+#117 := (= #10 #114)
+#120 := (forall (vars (?v0 int) (?v1 int)) #117)
+#236 := (iff #120 #235)
+#233 := (iff #117 #232)
+#230 := (= #114 #229)
+#227 := (= #111 #226)
+#224 := (iff #108 #221)
+#218 := (or #215 #207)
+#222 := (iff #218 #221)
+#223 := [rewrite]: #222
+#219 := (iff #108 #218)
+#216 := (iff #105 #207)
+#217 := [rewrite]: #216
+#204 := (iff #98 #215)
+#205 := [rewrite]: #204
+#220 := [monotonicity #205 #217]: #219
+#225 := [trans #220 #223]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [quant-intro #234]: #236
+#210 := (~ #120 #120)
+#208 := (~ #117 #117)
+#209 := [refl]: #208
+#211 := [nnf-pos #209]: #210
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#123 := (iff #28 #120)
+#62 := (and #16 #18)
+#65 := (or #17 #62)
+#78 := (ite #65 #21 #75)
+#81 := (ite #14 0::int #78)
+#84 := (= #10 #81)
+#87 := (forall (vars (?v0 int) (?v1 int)) #84)
+#121 := (iff #87 #120)
+#118 := (iff #84 #117)
+#115 := (= #81 #114)
+#112 := (= #78 #111)
+#109 := (iff #65 #108)
+#106 := (iff #62 #105)
+#103 := (iff #18 #102)
+#104 := [rewrite]: #103
+#96 := (iff #16 #95)
+#97 := [rewrite]: #96
+#107 := [monotonicity #97 #104]: #106
+#99 := (iff #17 #98)
+#92 := (iff #15 #91)
+#93 := [rewrite]: #92
+#100 := [monotonicity #93 #97]: #99
+#110 := [monotonicity #100 #107]: #109
+#113 := [monotonicity #110]: #112
+#116 := [monotonicity #113]: #115
+#119 := [monotonicity #116]: #118
+#122 := [quant-intro #119]: #121
+#88 := (iff #28 #87)
+#85 := (iff #27 #84)
+#82 := (= #26 #81)
+#79 := (= #25 #78)
+#76 := (= #24 #75)
+#73 := (= #23 #72)
+#74 := [rewrite]: #73
+#70 := (= #22 #69)
+#71 := [rewrite]: #70
+#77 := [monotonicity #71 #74]: #76
+#66 := (iff #20 #65)
+#63 := (iff #19 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#80 := [monotonicity #67 #77]: #79
+#83 := [monotonicity #80]: #82
+#86 := [monotonicity #83]: #85
+#89 := [quant-intro #86]: #88
+#124 := [trans #89 #122]: #123
+#61 := [asserted]: #28
+#125 := [mp #61 #124]: #120
+#201 := [mp~ #125 #211]: #120
+#238 := [mp #201 #237]: #235
+#269 := [mp #238 #268]: #266
+#762 := [mp #269 #761]: #757
+#680 := (not #757)
+#672 := (or #680 #180)
+#343 := (* -1::int -3::int)
+#427 := (* -1::int 3::int)
+#428 := (div #427 #343)
+#429 := (* -1::int #428)
+#420 := (+ #175 #429)
+#431 := (= #420 0::int)
+#432 := (div 3::int -3::int)
+#433 := (* -1::int #432)
+#430 := (+ #175 #433)
+#434 := (= #430 0::int)
+#413 := (<= -3::int 0::int)
+#748 := (<= 3::int 0::int)
+#750 := (or #748 #413)
+#407 := (not #750)
+#537 := (>= 3::int 0::int)
+#744 := (or #413 #537)
+#418 := (not #744)
+#419 := (or #418 #407)
+#751 := (ite #419 #434 #431)
+#752 := (= #175 0::int)
+#753 := (= -3::int 0::int)
+#754 := (= 3::int 0::int)
+#749 := (or #754 #753)
+#755 := (ite #749 #752 #751)
+#669 := (or #680 #755)
+#681 := (iff #669 #672)
+#683 := (iff #672 #672)
+#679 := [rewrite]: #683
+#691 := (iff #755 #180)
+#595 := (ite false #752 #180)
+#690 := (iff #595 #180)
+#687 := [rewrite]: #690
+#596 := (iff #755 #595)
+#593 := (iff #751 #180)
+#574 := (ite false #180 #180)
+#592 := (iff #574 #180)
+#585 := [rewrite]: #592
+#589 := (iff #751 #574)
+#686 := (iff #431 #180)
+#714 := (+ 1::int #175)
+#558 := (= #714 0::int)
+#702 := (iff #558 #180)
+#703 := [rewrite]: #702
+#590 := (iff #431 #558)
+#540 := (= #420 #714)
+#713 := (+ #175 1::int)
+#715 := (= #713 #714)
+#710 := [rewrite]: #715
+#580 := (= #420 #713)
+#697 := (= #429 1::int)
+#435 := (* -1::int -1::int)
+#718 := (= #435 1::int)
+#722 := [rewrite]: #718
+#696 := (= #429 #435)
+#693 := (= #428 -1::int)
+#707 := (div -3::int 3::int)
+#539 := (= #707 -1::int)
+#692 := [rewrite]: #539
+#536 := (= #428 #707)
+#706 := (= #343 3::int)
+#700 := [rewrite]: #706
+#699 := (= #427 -3::int)
+#705 := [rewrite]: #699
+#538 := [monotonicity #705 #700]: #536
+#695 := [trans #538 #692]: #693
+#694 := [monotonicity #695]: #696
+#579 := [trans #694 #722]: #697
+#581 := [monotonicity #579]: #580
+#688 := [trans #581 #710]: #540
+#685 := [monotonicity #688]: #590
+#689 := [trans #685 #703]: #686
+#704 := (iff #434 #180)
+#559 := (iff #434 #558)
+#716 := (= #430 #714)
+#708 := (= #430 #713)
+#711 := (= #433 1::int)
+#717 := (= #433 #435)
+#719 := (= #432 -1::int)
+#720 := [rewrite]: #719
+#721 := [monotonicity #720]: #717
+#712 := [trans #721 #722]: #711
+#709 := [monotonicity #712]: #708
+#557 := [trans #709 #710]: #716
+#701 := [monotonicity #557]: #559
+#698 := [trans #701 #703]: #704
+#440 := (iff #419 false)
+#406 := (or false false)
+#731 := (iff #406 false)
+#394 := [rewrite]: #731
+#438 := (iff #419 #406)
+#724 := (iff #407 false)
+#1 := true
+#381 := (not true)
+#740 := (iff #381 false)
+#743 := [rewrite]: #740
+#723 := (iff #407 #381)
+#448 := (iff #750 true)
+#454 := (or false true)
+#725 := (iff #454 true)
+#726 := [rewrite]: #725
+#455 := (iff #750 #454)
+#397 := (iff #413 true)
+#733 := [rewrite]: #397
+#452 := (iff #748 false)
+#453 := [rewrite]: #452
+#349 := [monotonicity #453 #733]: #455
+#449 := [trans #349 #726]: #448
+#727 := [monotonicity #449]: #723
+#728 := [trans #727 #743]: #724
+#729 := (iff #418 false)
+#382 := (iff #418 #381)
+#739 := (iff #744 true)
+#736 := (or true true)
+#738 := (iff #736 true)
+#376 := [rewrite]: #738
+#737 := (iff #744 #736)
+#734 := (iff #537 true)
+#735 := [rewrite]: #734
+#732 := [monotonicity #733 #735]: #737
+#741 := [trans #732 #376]: #739
+#742 := [monotonicity #741]: #382
+#730 := [trans #742 #743]: #729
+#439 := [monotonicity #730 #728]: #438
+#441 := [trans #439 #394]: #440
+#591 := [monotonicity #441 #698 #689]: #589
+#594 := [trans #591 #585]: #593
+#395 := (iff #749 false)
+#747 := (iff #749 #406)
+#410 := (iff #753 false)
+#746 := [rewrite]: #410
+#745 := (iff #754 false)
+#405 := [rewrite]: #745
+#390 := [monotonicity #405 #746]: #747
+#396 := [trans #390 #394]: #395
+#597 := [monotonicity #396 #594]: #596
+#678 := [trans #597 #687]: #691
+#682 := [monotonicity #678]: #681
+#684 := [trans #682 #679]: #681
+#671 := [quant-inst]: #669
+#673 := [mp #671 #684]: #672
+[unit-resolution #673 #762 #198]: false
+unsat
+0217fb3975a8ed7626e13b93029371f1151b43e4 326 0
+#2 := false
+#179 := -2::int
+decl f3 :: (-> int int int)
+#173 := -3::int
+#38 := 5::int
+#176 := (f3 5::int -3::int)
+#182 := (= #176 -2::int)
+#185 := (not #182)
+#42 := 2::int
+#43 := (- 2::int)
+#39 := 3::int
+#40 := (- 3::int)
+#41 := (f3 5::int #40)
+#44 := (= #41 #43)
+#45 := (not #44)
+#186 := (iff #45 #185)
+#183 := (iff #44 #182)
+#180 := (= #43 -2::int)
+#181 := [rewrite]: #180
+#177 := (= #41 #176)
+#174 := (= #40 -3::int)
+#175 := [rewrite]: #174
+#178 := [monotonicity #175]: #177
+#184 := [monotonicity #178 #181]: #183
+#187 := [monotonicity #184]: #186
+#172 := [asserted]: #45
+#190 := [mp #172 #187]: #185
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#747 := (pattern #10)
+#11 := 0::int
+#69 := -1::int
+#73 := (* -1::int #9)
+#70 := (* -1::int #8)
+#76 := (div #70 #73)
+#249 := (* -1::int #76)
+#250 := (+ #10 #249)
+#251 := (= #250 0::int)
+#21 := (div #8 #9)
+#246 := (* -1::int #21)
+#247 := (+ #10 #246)
+#248 := (= #247 0::int)
+#95 := (<= #9 0::int)
+#91 := (<= #8 0::int)
+#204 := (or #91 #95)
+#205 := (not #204)
+#102 := (>= #8 0::int)
+#196 := (or #95 #102)
+#197 := (not #196)
+#211 := (or #197 #205)
+#252 := (ite #211 #248 #251)
+#245 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#253 := (ite #14 #245 #252)
+#748 := (forall (vars (?v0 int) (?v1 int)) (:pat #747) #253)
+#256 := (forall (vars (?v0 int) (?v1 int)) #253)
+#751 := (iff #256 #748)
+#749 := (iff #253 #253)
+#750 := [refl]: #749
+#752 := [quant-intro #750]: #751
+#216 := (ite #211 #21 #76)
+#219 := (ite #14 0::int #216)
+#222 := (= #10 #219)
+#225 := (forall (vars (?v0 int) (?v1 int)) #222)
+#257 := (iff #225 #256)
+#254 := (iff #222 #253)
+#255 := [rewrite]: #254
+#258 := [quant-intro #255]: #257
+#103 := (not #102)
+#96 := (not #95)
+#106 := (and #96 #103)
+#92 := (not #91)
+#99 := (and #92 #96)
+#109 := (or #99 #106)
+#112 := (ite #109 #21 #76)
+#115 := (ite #14 0::int #112)
+#118 := (= #10 #115)
+#121 := (forall (vars (?v0 int) (?v1 int)) #118)
+#226 := (iff #121 #225)
+#223 := (iff #118 #222)
+#220 := (= #115 #219)
+#217 := (= #112 #216)
+#214 := (iff #109 #211)
+#208 := (or #205 #197)
+#212 := (iff #208 #211)
+#213 := [rewrite]: #212
+#209 := (iff #109 #208)
+#206 := (iff #106 #197)
+#207 := [rewrite]: #206
+#194 := (iff #99 #205)
+#195 := [rewrite]: #194
+#210 := [monotonicity #195 #207]: #209
+#215 := [trans #210 #213]: #214
+#218 := [monotonicity #215]: #217
+#221 := [monotonicity #218]: #220
+#224 := [monotonicity #221]: #223
+#227 := [quant-intro #224]: #226
+#200 := (~ #121 #121)
+#198 := (~ #118 #118)
+#199 := [refl]: #198
+#201 := [nnf-pos #199]: #200
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#124 := (iff #28 #121)
+#63 := (and #16 #18)
+#66 := (or #17 #63)
+#79 := (ite #66 #21 #76)
+#82 := (ite #14 0::int #79)
+#85 := (= #10 #82)
+#88 := (forall (vars (?v0 int) (?v1 int)) #85)
+#122 := (iff #88 #121)
+#119 := (iff #85 #118)
+#116 := (= #82 #115)
+#113 := (= #79 #112)
+#110 := (iff #66 #109)
+#107 := (iff #63 #106)
+#104 := (iff #18 #103)
+#105 := [rewrite]: #104
+#97 := (iff #16 #96)
+#98 := [rewrite]: #97
+#108 := [monotonicity #98 #105]: #107
+#100 := (iff #17 #99)
+#93 := (iff #15 #92)
+#94 := [rewrite]: #93
+#101 := [monotonicity #94 #98]: #100
+#111 := [monotonicity #101 #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [monotonicity #117]: #119
+#123 := [quant-intro #120]: #122
+#89 := (iff #28 #88)
+#86 := (iff #27 #85)
+#83 := (= #26 #82)
+#80 := (= #25 #79)
+#77 := (= #24 #76)
+#74 := (= #23 #73)
+#75 := [rewrite]: #74
+#71 := (= #22 #70)
+#72 := [rewrite]: #71
+#78 := [monotonicity #72 #75]: #77
+#67 := (iff #20 #66)
+#64 := (iff #19 #63)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#81 := [monotonicity #68 #78]: #80
+#84 := [monotonicity #81]: #83
+#87 := [monotonicity #84]: #86
+#90 := [quant-intro #87]: #89
+#125 := [trans #90 #123]: #124
+#62 := [asserted]: #28
+#126 := [mp #62 #125]: #121
+#191 := [mp~ #126 #201]: #121
+#228 := [mp #191 #227]: #225
+#259 := [mp #228 #258]: #256
+#753 := [mp #259 #752]: #748
+#667 := (not #748)
+#661 := (or #667 #182)
+#333 := (* -1::int -3::int)
+#418 := (* -1::int 5::int)
+#419 := (div #418 #333)
+#420 := (* -1::int #419)
+#411 := (+ #176 #420)
+#422 := (= #411 0::int)
+#423 := (div 5::int -3::int)
+#351 := (* -1::int #423)
+#424 := (+ #176 #351)
+#421 := (= #424 0::int)
+#425 := (<= -3::int 0::int)
+#404 := (<= 5::int 0::int)
+#739 := (or #404 #425)
+#741 := (not #739)
+#398 := (>= 5::int 0::int)
+#528 := (or #425 #398)
+#735 := (not #528)
+#409 := (or #735 #741)
+#410 := (ite #409 #421 #422)
+#742 := (= #176 0::int)
+#743 := (= -3::int 0::int)
+#744 := (= 5::int 0::int)
+#745 := (or #744 #743)
+#740 := (ite #745 #742 #410)
+#668 := (or #667 #740)
+#653 := (iff #668 #661)
+#656 := (iff #661 #661)
+#657 := [rewrite]: #656
+#665 := (iff #740 #182)
+#673 := (ite false #742 #182)
+#675 := (iff #673 #182)
+#664 := [rewrite]: #675
+#674 := (iff #740 #673)
+#662 := (iff #410 #182)
+#693 := (= #176 -1::int)
+#682 := (ite false #693 #182)
+#663 := (iff #682 #182)
+#660 := [rewrite]: #663
+#669 := (iff #410 #682)
+#681 := (iff #422 #182)
+#565 := (+ 2::int #176)
+#584 := (= #565 0::int)
+#587 := (iff #584 #182)
+#588 := [rewrite]: #587
+#585 := (iff #422 #584)
+#583 := (= #411 #565)
+#676 := (+ #176 2::int)
+#580 := (= #676 #565)
+#582 := [rewrite]: #580
+#677 := (= #411 #676)
+#679 := (= #420 2::int)
+#688 := (* -1::int -2::int)
+#572 := (= #688 2::int)
+#531 := [rewrite]: #572
+#570 := (= #420 #688)
+#687 := (= #419 -2::int)
+#696 := -5::int
+#529 := (div -5::int 3::int)
+#684 := (= #529 -2::int)
+#686 := [rewrite]: #684
+#530 := (= #419 #529)
+#698 := (= #333 3::int)
+#527 := [rewrite]: #698
+#697 := (= #418 -5::int)
+#691 := [rewrite]: #697
+#683 := [monotonicity #691 #527]: #530
+#685 := [trans #683 #686]: #687
+#571 := [monotonicity #685]: #570
+#581 := [trans #571 #531]: #679
+#680 := [monotonicity #581]: #677
+#576 := [trans #680 #582]: #583
+#586 := [monotonicity #576]: #585
+#678 := [trans #586 #588]: #681
+#689 := (iff #421 #693)
+#712 := 1::int
+#705 := (+ 1::int #176)
+#549 := (= #705 0::int)
+#694 := (iff #549 #693)
+#695 := [rewrite]: #694
+#550 := (iff #421 #549)
+#707 := (= #424 #705)
+#704 := (+ #176 1::int)
+#706 := (= #704 #705)
+#701 := [rewrite]: #706
+#699 := (= #424 #704)
+#702 := (= #351 1::int)
+#711 := (* -1::int -1::int)
+#709 := (= #711 1::int)
+#713 := [rewrite]: #709
+#426 := (= #351 #711)
+#432 := (= #423 -1::int)
+#710 := [rewrite]: #432
+#708 := [monotonicity #710]: #426
+#703 := [trans #708 #713]: #702
+#700 := [monotonicity #703]: #699
+#548 := [trans #700 #701]: #707
+#692 := [monotonicity #548]: #550
+#690 := [trans #692 #695]: #689
+#430 := (iff #409 false)
+#737 := (or false false)
+#381 := (iff #737 false)
+#722 := [rewrite]: #381
+#719 := (iff #409 #737)
+#718 := (iff #741 false)
+#1 := true
+#732 := (not true)
+#733 := (iff #732 false)
+#731 := [rewrite]: #733
+#440 := (iff #741 #732)
+#717 := (iff #739 true)
+#444 := (or false true)
+#339 := (iff #444 true)
+#716 := [rewrite]: #339
+#445 := (iff #739 #444)
+#387 := (iff #425 true)
+#388 := [rewrite]: #387
+#721 := (iff #404 false)
+#443 := [rewrite]: #721
+#446 := [monotonicity #443 #388]: #445
+#439 := [trans #446 #716]: #717
+#714 := [monotonicity #439]: #440
+#715 := [trans #714 #731]: #718
+#734 := (iff #735 false)
+#372 := (iff #735 #732)
+#367 := (iff #528 true)
+#726 := (or true true)
+#723 := (iff #726 true)
+#729 := [rewrite]: #723
+#727 := (iff #528 #726)
+#724 := (iff #398 true)
+#725 := [rewrite]: #724
+#728 := [monotonicity #388 #725]: #727
+#730 := [trans #728 #729]: #367
+#373 := [monotonicity #730]: #372
+#720 := [trans #373 #731]: #734
+#429 := [monotonicity #720 #715]: #719
+#431 := [trans #429 #722]: #430
+#671 := [monotonicity #431 #690 #678]: #669
+#672 := [trans #671 #660]: #662
+#385 := (iff #745 false)
+#397 := (iff #745 #737)
+#396 := (iff #743 false)
+#401 := [rewrite]: #396
+#746 := (iff #744 false)
+#736 := [rewrite]: #746
+#738 := [monotonicity #736 #401]: #397
+#386 := [trans #738 #722]: #385
+#670 := [monotonicity #386 #672]: #674
+#666 := [trans #670 #664]: #665
+#655 := [monotonicity #666]: #653
+#658 := [trans #655 #657]: #653
+#652 := [quant-inst]: #668
+#654 := [mp #652 #658]: #661
+[unit-resolution #654 #753 #190]: false
+unsat
+a5e7ca3a1a908b3cfa96261b62a5e5f564ff08b5 321 0
+#2 := false
+#67 := -1::int
+decl f3 :: (-> int int int)
+#40 := 3::int
+#173 := (f3 -1::int 3::int)
+#176 := (= #173 -1::int)
+#189 := (not #176)
+#38 := 1::int
+#39 := (- 1::int)
+#41 := (f3 #39 3::int)
+#42 := (= #41 #39)
+#43 := (not #42)
+#192 := (iff #43 #189)
+#179 := (= -1::int #173)
+#184 := (not #179)
+#190 := (iff #184 #189)
+#187 := (iff #179 #176)
+#188 := [rewrite]: #187
+#191 := [monotonicity #188]: #190
+#185 := (iff #43 #184)
+#182 := (iff #42 #179)
+#180 := (iff #176 #179)
+#181 := [rewrite]: #180
+#177 := (iff #42 #176)
+#171 := (= #39 -1::int)
+#172 := [rewrite]: #171
+#174 := (= #41 #173)
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175 #172]: #177
+#183 := [trans #178 #181]: #182
+#186 := [monotonicity #183]: #185
+#193 := [trans #186 #191]: #192
+#170 := [asserted]: #43
+#194 := [mp #170 #193]: #189
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#752 := (pattern #10)
+#11 := 0::int
+#71 := (* -1::int #9)
+#68 := (* -1::int #8)
+#74 := (div #68 #71)
+#255 := (* -1::int #74)
+#256 := (+ #10 #255)
+#257 := (= #256 0::int)
+#21 := (div #8 #9)
+#252 := (* -1::int #21)
+#253 := (+ #10 #252)
+#254 := (= #253 0::int)
+#93 := (<= #9 0::int)
+#89 := (<= #8 0::int)
+#210 := (or #89 #93)
+#211 := (not #210)
+#100 := (>= #8 0::int)
+#202 := (or #93 #100)
+#203 := (not #202)
+#217 := (or #203 #211)
+#258 := (ite #217 #254 #257)
+#251 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#259 := (ite #14 #251 #258)
+#753 := (forall (vars (?v0 int) (?v1 int)) (:pat #752) #259)
+#262 := (forall (vars (?v0 int) (?v1 int)) #259)
+#756 := (iff #262 #753)
+#754 := (iff #259 #259)
+#755 := [refl]: #754
+#757 := [quant-intro #755]: #756
+#222 := (ite #217 #21 #74)
+#225 := (ite #14 0::int #222)
+#228 := (= #10 #225)
+#231 := (forall (vars (?v0 int) (?v1 int)) #228)
+#263 := (iff #231 #262)
+#260 := (iff #228 #259)
+#261 := [rewrite]: #260
+#264 := [quant-intro #261]: #263
+#101 := (not #100)
+#94 := (not #93)
+#104 := (and #94 #101)
+#90 := (not #89)
+#97 := (and #90 #94)
+#107 := (or #97 #104)
+#110 := (ite #107 #21 #74)
+#113 := (ite #14 0::int #110)
+#116 := (= #10 #113)
+#119 := (forall (vars (?v0 int) (?v1 int)) #116)
+#232 := (iff #119 #231)
+#229 := (iff #116 #228)
+#226 := (= #113 #225)
+#223 := (= #110 #222)
+#220 := (iff #107 #217)
+#214 := (or #211 #203)
+#218 := (iff #214 #217)
+#219 := [rewrite]: #218
+#215 := (iff #107 #214)
+#212 := (iff #104 #203)
+#213 := [rewrite]: #212
+#200 := (iff #97 #211)
+#201 := [rewrite]: #200
+#216 := [monotonicity #201 #213]: #215
+#221 := [trans #216 #219]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [quant-intro #230]: #232
+#206 := (~ #119 #119)
+#204 := (~ #116 #116)
+#205 := [refl]: #204
+#207 := [nnf-pos #205]: #206
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#122 := (iff #28 #119)
+#61 := (and #16 #18)
+#64 := (or #17 #61)
+#77 := (ite #64 #21 #74)
+#80 := (ite #14 0::int #77)
+#83 := (= #10 #80)
+#86 := (forall (vars (?v0 int) (?v1 int)) #83)
+#120 := (iff #86 #119)
+#117 := (iff #83 #116)
+#114 := (= #80 #113)
+#111 := (= #77 #110)
+#108 := (iff #64 #107)
+#105 := (iff #61 #104)
+#102 := (iff #18 #101)
+#103 := [rewrite]: #102
+#95 := (iff #16 #94)
+#96 := [rewrite]: #95
+#106 := [monotonicity #96 #103]: #105
+#98 := (iff #17 #97)
+#91 := (iff #15 #90)
+#92 := [rewrite]: #91
+#99 := [monotonicity #92 #96]: #98
+#109 := [monotonicity #99 #106]: #108
+#112 := [monotonicity #109]: #111
+#115 := [monotonicity #112]: #114
+#118 := [monotonicity #115]: #117
+#121 := [quant-intro #118]: #120
+#87 := (iff #28 #86)
+#84 := (iff #27 #83)
+#81 := (= #26 #80)
+#78 := (= #25 #77)
+#75 := (= #24 #74)
+#72 := (= #23 #71)
+#73 := [rewrite]: #72
+#69 := (= #22 #68)
+#70 := [rewrite]: #69
+#76 := [monotonicity #70 #73]: #75
+#65 := (iff #20 #64)
+#62 := (iff #19 #61)
+#63 := [rewrite]: #62
+#66 := [monotonicity #63]: #65
+#79 := [monotonicity #66 #76]: #78
+#82 := [monotonicity #79]: #81
+#85 := [monotonicity #82]: #84
+#88 := [quant-intro #85]: #87
+#123 := [trans #88 #121]: #122
+#60 := [asserted]: #28
+#124 := [mp #60 #123]: #119
+#197 := [mp~ #124 #207]: #119
+#234 := [mp #197 #233]: #231
+#265 := [mp #234 #264]: #262
+#758 := [mp #265 #757]: #753
+#665 := (not #753)
+#667 := (or #665 #176)
+#339 := (* -1::int 3::int)
+#423 := (* -1::int -1::int)
+#424 := (div #423 #339)
+#425 := (* -1::int #424)
+#416 := (+ #173 #425)
+#427 := (= #416 0::int)
+#428 := (div -1::int 3::int)
+#429 := (* -1::int #428)
+#426 := (+ #173 #429)
+#430 := (= #426 0::int)
+#409 := (<= 3::int 0::int)
+#744 := (<= -1::int 0::int)
+#746 := (or #744 #409)
+#403 := (not #746)
+#533 := (>= -1::int 0::int)
+#740 := (or #409 #533)
+#414 := (not #740)
+#415 := (or #414 #403)
+#747 := (ite #415 #430 #427)
+#748 := (= #173 0::int)
+#749 := (= 3::int 0::int)
+#750 := (= -1::int 0::int)
+#745 := (or #750 #749)
+#751 := (ite #745 #748 #747)
+#677 := (or #665 #751)
+#679 := (iff #677 #667)
+#680 := (iff #667 #667)
+#669 := [rewrite]: #680
+#676 := (iff #751 #176)
+#593 := (ite false #748 #176)
+#687 := (iff #593 #176)
+#674 := [rewrite]: #687
+#686 := (iff #751 #593)
+#591 := (iff #747 #176)
+#1 := true
+#587 := (ite true #176 #748)
+#589 := (iff #587 #176)
+#590 := [rewrite]: #589
+#588 := (iff #747 #587)
+#570 := (iff #427 #748)
+#682 := (= #416 #173)
+#577 := (+ #173 0::int)
+#586 := (= #577 #173)
+#681 := [rewrite]: #586
+#536 := (= #416 #577)
+#575 := (= #425 0::int)
+#689 := (* -1::int 0::int)
+#690 := (= #689 0::int)
+#693 := [rewrite]: #690
+#691 := (= #425 #689)
+#535 := (= #424 0::int)
+#694 := -3::int
+#702 := (div 1::int -3::int)
+#532 := (= #702 0::int)
+#534 := [rewrite]: #532
+#696 := (= #424 #702)
+#695 := (= #339 -3::int)
+#701 := [rewrite]: #695
+#717 := (= #423 1::int)
+#714 := [rewrite]: #717
+#703 := [monotonicity #714 #701]: #696
+#688 := [trans #703 #534]: #535
+#692 := [monotonicity #688]: #691
+#576 := [trans #692 #693]: #575
+#684 := [monotonicity #576]: #536
+#685 := [trans #684 #681]: #682
+#585 := [monotonicity #685]: #570
+#699 := (iff #430 #176)
+#705 := (+ 1::int #173)
+#553 := (= #705 0::int)
+#697 := (iff #553 #176)
+#698 := [rewrite]: #697
+#554 := (iff #430 #553)
+#706 := (= #426 #705)
+#708 := (+ #173 1::int)
+#710 := (= #708 #705)
+#711 := [rewrite]: #710
+#709 := (= #426 #708)
+#718 := (= #429 1::int)
+#431 := (= #429 #423)
+#715 := (= #428 -1::int)
+#716 := [rewrite]: #715
+#713 := [monotonicity #716]: #431
+#707 := [trans #713 #714]: #718
+#704 := [monotonicity #707]: #709
+#712 := [trans #704 #711]: #706
+#555 := [monotonicity #712]: #554
+#700 := [trans #555 #698]: #699
+#436 := (iff #415 true)
+#726 := (or true false)
+#450 := (iff #726 true)
+#451 := [rewrite]: #450
+#434 := (iff #415 #726)
+#720 := (iff #403 false)
+#722 := (not true)
+#719 := (iff #722 false)
+#723 := [rewrite]: #719
+#444 := (iff #403 #722)
+#345 := (iff #746 true)
+#448 := (iff #746 #726)
+#393 := (iff #409 false)
+#729 := [rewrite]: #393
+#739 := (iff #744 true)
+#725 := [rewrite]: #739
+#449 := [monotonicity #725 #729]: #448
+#721 := [trans #449 #451]: #345
+#445 := [monotonicity #721]: #444
+#724 := [trans #445 #723]: #720
+#738 := (iff #414 true)
+#372 := (not false)
+#377 := (iff #372 true)
+#378 := [rewrite]: #377
+#735 := (iff #414 #372)
+#728 := (iff #740 false)
+#402 := (or false false)
+#727 := (iff #402 false)
+#390 := [rewrite]: #727
+#732 := (iff #740 #402)
+#730 := (iff #533 false)
+#731 := [rewrite]: #730
+#733 := [monotonicity #729 #731]: #732
+#734 := [trans #733 #390]: #728
+#737 := [monotonicity #734]: #735
+#736 := [trans #737 #378]: #738
+#435 := [monotonicity #736 #724]: #434
+#437 := [trans #435 #451]: #436
+#581 := [monotonicity #437 #700 #585]: #588
+#592 := [trans #581 #590]: #591
+#391 := (iff #745 false)
+#743 := (iff #745 #402)
+#406 := (iff #749 false)
+#742 := [rewrite]: #406
+#741 := (iff #750 false)
+#401 := [rewrite]: #741
+#386 := [monotonicity #401 #742]: #743
+#392 := [trans #386 #390]: #391
+#683 := [monotonicity #392 #592]: #686
+#668 := [trans #683 #674]: #676
+#675 := [monotonicity #668]: #679
+#670 := [trans #675 #669]: #679
+#678 := [quant-inst]: #677
+#671 := [mp #678 #670]: #667
+[unit-resolution #671 #758 #194]: false
+unsat
+4a26f9179dc065943e8b39f87c50b753014abca8 323 0
+#2 := false
+#68 := -1::int
+decl f3 :: (-> int int int)
+#38 := 3::int
+#172 := -3::int
+#175 := (f3 -3::int 3::int)
+#180 := (= #175 -1::int)
+#193 := (not #180)
+#41 := 1::int
+#42 := (- 1::int)
+#39 := (- 3::int)
+#40 := (f3 #39 3::int)
+#43 := (= #40 #42)
+#44 := (not #43)
+#196 := (iff #44 #193)
+#183 := (= -1::int #175)
+#188 := (not #183)
+#194 := (iff #188 #193)
+#191 := (iff #183 #180)
+#192 := [rewrite]: #191
+#195 := [monotonicity #192]: #194
+#189 := (iff #44 #188)
+#186 := (iff #43 #183)
+#184 := (iff #180 #183)
+#185 := [rewrite]: #184
+#181 := (iff #43 #180)
+#178 := (= #42 -1::int)
+#179 := [rewrite]: #178
+#176 := (= #40 #175)
+#173 := (= #39 -3::int)
+#174 := [rewrite]: #173
+#177 := [monotonicity #174]: #176
+#182 := [monotonicity #177 #179]: #181
+#187 := [trans #182 #185]: #186
+#190 := [monotonicity #187]: #189
+#197 := [trans #190 #195]: #196
+#171 := [asserted]: #44
+#198 := [mp #171 #197]: #193
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#756 := (pattern #10)
+#11 := 0::int
+#72 := (* -1::int #9)
+#69 := (* -1::int #8)
+#75 := (div #69 #72)
+#259 := (* -1::int #75)
+#260 := (+ #10 #259)
+#261 := (= #260 0::int)
+#21 := (div #8 #9)
+#256 := (* -1::int #21)
+#257 := (+ #10 #256)
+#258 := (= #257 0::int)
+#94 := (<= #9 0::int)
+#90 := (<= #8 0::int)
+#214 := (or #90 #94)
+#215 := (not #214)
+#101 := (>= #8 0::int)
+#206 := (or #94 #101)
+#207 := (not #206)
+#221 := (or #207 #215)
+#262 := (ite #221 #258 #261)
+#255 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#263 := (ite #14 #255 #262)
+#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
+#266 := (forall (vars (?v0 int) (?v1 int)) #263)
+#760 := (iff #266 #757)
+#758 := (iff #263 #263)
+#759 := [refl]: #758
+#761 := [quant-intro #759]: #760
+#226 := (ite #221 #21 #75)
+#229 := (ite #14 0::int #226)
+#232 := (= #10 #229)
+#235 := (forall (vars (?v0 int) (?v1 int)) #232)
+#267 := (iff #235 #266)
+#264 := (iff #232 #263)
+#265 := [rewrite]: #264
+#268 := [quant-intro #265]: #267
+#102 := (not #101)
+#95 := (not #94)
+#105 := (and #95 #102)
+#91 := (not #90)
+#98 := (and #91 #95)
+#108 := (or #98 #105)
+#111 := (ite #108 #21 #75)
+#114 := (ite #14 0::int #111)
+#117 := (= #10 #114)
+#120 := (forall (vars (?v0 int) (?v1 int)) #117)
+#236 := (iff #120 #235)
+#233 := (iff #117 #232)
+#230 := (= #114 #229)
+#227 := (= #111 #226)
+#224 := (iff #108 #221)
+#218 := (or #215 #207)
+#222 := (iff #218 #221)
+#223 := [rewrite]: #222
+#219 := (iff #108 #218)
+#216 := (iff #105 #207)
+#217 := [rewrite]: #216
+#204 := (iff #98 #215)
+#205 := [rewrite]: #204
+#220 := [monotonicity #205 #217]: #219
+#225 := [trans #220 #223]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [quant-intro #234]: #236
+#210 := (~ #120 #120)
+#208 := (~ #117 #117)
+#209 := [refl]: #208
+#211 := [nnf-pos #209]: #210
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#123 := (iff #28 #120)
+#62 := (and #16 #18)
+#65 := (or #17 #62)
+#78 := (ite #65 #21 #75)
+#81 := (ite #14 0::int #78)
+#84 := (= #10 #81)
+#87 := (forall (vars (?v0 int) (?v1 int)) #84)
+#121 := (iff #87 #120)
+#118 := (iff #84 #117)
+#115 := (= #81 #114)
+#112 := (= #78 #111)
+#109 := (iff #65 #108)
+#106 := (iff #62 #105)
+#103 := (iff #18 #102)
+#104 := [rewrite]: #103
+#96 := (iff #16 #95)
+#97 := [rewrite]: #96
+#107 := [monotonicity #97 #104]: #106
+#99 := (iff #17 #98)
+#92 := (iff #15 #91)
+#93 := [rewrite]: #92
+#100 := [monotonicity #93 #97]: #99
+#110 := [monotonicity #100 #107]: #109
+#113 := [monotonicity #110]: #112
+#116 := [monotonicity #113]: #115
+#119 := [monotonicity #116]: #118
+#122 := [quant-intro #119]: #121
+#88 := (iff #28 #87)
+#85 := (iff #27 #84)
+#82 := (= #26 #81)
+#79 := (= #25 #78)
+#76 := (= #24 #75)
+#73 := (= #23 #72)
+#74 := [rewrite]: #73
+#70 := (= #22 #69)
+#71 := [rewrite]: #70
+#77 := [monotonicity #71 #74]: #76
+#66 := (iff #20 #65)
+#63 := (iff #19 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#80 := [monotonicity #67 #77]: #79
+#83 := [monotonicity #80]: #82
+#86 := [monotonicity #83]: #85
+#89 := [quant-intro #86]: #88
+#124 := [trans #89 #122]: #123
+#61 := [asserted]: #28
+#125 := [mp #61 #124]: #120
+#201 := [mp~ #125 #211]: #120
+#238 := [mp #201 #237]: #235
+#269 := [mp #238 #268]: #266
+#762 := [mp #269 #761]: #757
+#680 := (not #757)
+#672 := (or #680 #180)
+#343 := (* -1::int 3::int)
+#427 := (* -1::int -3::int)
+#428 := (div #427 #343)
+#429 := (* -1::int #428)
+#420 := (+ #175 #429)
+#431 := (= #420 0::int)
+#432 := (div -3::int 3::int)
+#433 := (* -1::int #432)
+#430 := (+ #175 #433)
+#434 := (= #430 0::int)
+#413 := (<= 3::int 0::int)
+#748 := (<= -3::int 0::int)
+#750 := (or #748 #413)
+#407 := (not #750)
+#537 := (>= -3::int 0::int)
+#744 := (or #413 #537)
+#418 := (not #744)
+#419 := (or #418 #407)
+#751 := (ite #419 #434 #431)
+#752 := (= #175 0::int)
+#753 := (= 3::int 0::int)
+#754 := (= -3::int 0::int)
+#749 := (or #754 #753)
+#755 := (ite #749 #752 #751)
+#669 := (or #680 #755)
+#681 := (iff #669 #672)
+#683 := (iff #672 #672)
+#679 := [rewrite]: #683
+#691 := (iff #755 #180)
+#595 := (ite false #752 #180)
+#690 := (iff #595 #180)
+#687 := [rewrite]: #690
+#596 := (iff #755 #595)
+#593 := (iff #751 #180)
+#1 := true
+#574 := (ite true #180 #180)
+#592 := (iff #574 #180)
+#585 := [rewrite]: #592
+#589 := (iff #751 #574)
+#686 := (iff #431 #180)
+#714 := (+ 1::int #175)
+#558 := (= #714 0::int)
+#702 := (iff #558 #180)
+#703 := [rewrite]: #702
+#590 := (iff #431 #558)
+#540 := (= #420 #714)
+#713 := (+ #175 1::int)
+#715 := (= #713 #714)
+#710 := [rewrite]: #715
+#580 := (= #420 #713)
+#697 := (= #429 1::int)
+#435 := (* -1::int -1::int)
+#718 := (= #435 1::int)
+#722 := [rewrite]: #718
+#696 := (= #429 #435)
+#693 := (= #428 -1::int)
+#707 := (div 3::int -3::int)
+#539 := (= #707 -1::int)
+#692 := [rewrite]: #539
+#536 := (= #428 #707)
+#706 := (= #343 -3::int)
+#700 := [rewrite]: #706
+#699 := (= #427 3::int)
+#705 := [rewrite]: #699
+#538 := [monotonicity #705 #700]: #536
+#695 := [trans #538 #692]: #693
+#694 := [monotonicity #695]: #696
+#579 := [trans #694 #722]: #697
+#581 := [monotonicity #579]: #580
+#688 := [trans #581 #710]: #540
+#685 := [monotonicity #688]: #590
+#689 := [trans #685 #703]: #686
+#704 := (iff #434 #180)
+#559 := (iff #434 #558)
+#716 := (= #430 #714)
+#708 := (= #430 #713)
+#711 := (= #433 1::int)
+#717 := (= #433 #435)
+#719 := (= #432 -1::int)
+#720 := [rewrite]: #719
+#721 := [monotonicity #720]: #717
+#712 := [trans #721 #722]: #711
+#709 := [monotonicity #712]: #708
+#557 := [trans #709 #710]: #716
+#701 := [monotonicity #557]: #559
+#698 := [trans #701 #703]: #704
+#440 := (iff #419 true)
+#730 := (or true false)
+#454 := (iff #730 true)
+#455 := [rewrite]: #454
+#438 := (iff #419 #730)
+#724 := (iff #407 false)
+#726 := (not true)
+#723 := (iff #726 false)
+#727 := [rewrite]: #723
+#448 := (iff #407 #726)
+#349 := (iff #750 true)
+#452 := (iff #750 #730)
+#397 := (iff #413 false)
+#733 := [rewrite]: #397
+#743 := (iff #748 true)
+#729 := [rewrite]: #743
+#453 := [monotonicity #729 #733]: #452
+#725 := [trans #453 #455]: #349
+#449 := [monotonicity #725]: #448
+#728 := [trans #449 #727]: #724
+#742 := (iff #418 true)
+#376 := (not false)
+#381 := (iff #376 true)
+#382 := [rewrite]: #381
+#739 := (iff #418 #376)
+#732 := (iff #744 false)
+#406 := (or false false)
+#731 := (iff #406 false)
+#394 := [rewrite]: #731
+#736 := (iff #744 #406)
+#734 := (iff #537 false)
+#735 := [rewrite]: #734
+#737 := [monotonicity #733 #735]: #736
+#738 := [trans #737 #394]: #732
+#741 := [monotonicity #738]: #739
+#740 := [trans #741 #382]: #742
+#439 := [monotonicity #740 #728]: #438
+#441 := [trans #439 #455]: #440
+#591 := [monotonicity #441 #698 #689]: #589
+#594 := [trans #591 #585]: #593
+#395 := (iff #749 false)
+#747 := (iff #749 #406)
+#410 := (iff #753 false)
+#746 := [rewrite]: #410
+#745 := (iff #754 false)
+#405 := [rewrite]: #745
+#390 := [monotonicity #405 #746]: #747
+#396 := [trans #390 #394]: #395
+#597 := [monotonicity #396 #594]: #596
+#678 := [trans #597 #687]: #691
+#682 := [monotonicity #678]: #681
+#684 := [trans #682 #679]: #681
+#671 := [quant-inst]: #669
+#673 := [mp #671 #684]: #672
+[unit-resolution #673 #762 #198]: false
+unsat
+aa5c848d75f817ce17fcfbcc43fdae3201eb9151 326 0
+#2 := false
+#179 := -2::int
+decl f3 :: (-> int int int)
+#40 := 3::int
+#173 := -5::int
+#176 := (f3 -5::int 3::int)
+#182 := (= #176 -2::int)
+#185 := (not #182)
+#42 := 2::int
+#43 := (- 2::int)
+#38 := 5::int
+#39 := (- 5::int)
+#41 := (f3 #39 3::int)
+#44 := (= #41 #43)
+#45 := (not #44)
+#186 := (iff #45 #185)
+#183 := (iff #44 #182)
+#180 := (= #43 -2::int)
+#181 := [rewrite]: #180
+#177 := (= #41 #176)
+#174 := (= #39 -5::int)
+#175 := [rewrite]: #174
+#178 := [monotonicity #175]: #177
+#184 := [monotonicity #178 #181]: #183
+#187 := [monotonicity #184]: #186
+#172 := [asserted]: #45
+#190 := [mp #172 #187]: #185
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#747 := (pattern #10)
+#11 := 0::int
+#69 := -1::int
+#73 := (* -1::int #9)
+#70 := (* -1::int #8)
+#76 := (div #70 #73)
+#249 := (* -1::int #76)
+#250 := (+ #10 #249)
+#251 := (= #250 0::int)
+#21 := (div #8 #9)
+#246 := (* -1::int #21)
+#247 := (+ #10 #246)
+#248 := (= #247 0::int)
+#95 := (<= #9 0::int)
+#91 := (<= #8 0::int)
+#204 := (or #91 #95)
+#205 := (not #204)
+#102 := (>= #8 0::int)
+#196 := (or #95 #102)
+#197 := (not #196)
+#211 := (or #197 #205)
+#252 := (ite #211 #248 #251)
+#245 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#253 := (ite #14 #245 #252)
+#748 := (forall (vars (?v0 int) (?v1 int)) (:pat #747) #253)
+#256 := (forall (vars (?v0 int) (?v1 int)) #253)
+#751 := (iff #256 #748)
+#749 := (iff #253 #253)
+#750 := [refl]: #749
+#752 := [quant-intro #750]: #751
+#216 := (ite #211 #21 #76)
+#219 := (ite #14 0::int #216)
+#222 := (= #10 #219)
+#225 := (forall (vars (?v0 int) (?v1 int)) #222)
+#257 := (iff #225 #256)
+#254 := (iff #222 #253)
+#255 := [rewrite]: #254
+#258 := [quant-intro #255]: #257
+#103 := (not #102)
+#96 := (not #95)
+#106 := (and #96 #103)
+#92 := (not #91)
+#99 := (and #92 #96)
+#109 := (or #99 #106)
+#112 := (ite #109 #21 #76)
+#115 := (ite #14 0::int #112)
+#118 := (= #10 #115)
+#121 := (forall (vars (?v0 int) (?v1 int)) #118)
+#226 := (iff #121 #225)
+#223 := (iff #118 #222)
+#220 := (= #115 #219)
+#217 := (= #112 #216)
+#214 := (iff #109 #211)
+#208 := (or #205 #197)
+#212 := (iff #208 #211)
+#213 := [rewrite]: #212
+#209 := (iff #109 #208)
+#206 := (iff #106 #197)
+#207 := [rewrite]: #206
+#194 := (iff #99 #205)
+#195 := [rewrite]: #194
+#210 := [monotonicity #195 #207]: #209
+#215 := [trans #210 #213]: #214
+#218 := [monotonicity #215]: #217
+#221 := [monotonicity #218]: #220
+#224 := [monotonicity #221]: #223
+#227 := [quant-intro #224]: #226
+#200 := (~ #121 #121)
+#198 := (~ #118 #118)
+#199 := [refl]: #198
+#201 := [nnf-pos #199]: #200
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#124 := (iff #28 #121)
+#63 := (and #16 #18)
+#66 := (or #17 #63)
+#79 := (ite #66 #21 #76)
+#82 := (ite #14 0::int #79)
+#85 := (= #10 #82)
+#88 := (forall (vars (?v0 int) (?v1 int)) #85)
+#122 := (iff #88 #121)
+#119 := (iff #85 #118)
+#116 := (= #82 #115)
+#113 := (= #79 #112)
+#110 := (iff #66 #109)
+#107 := (iff #63 #106)
+#104 := (iff #18 #103)
+#105 := [rewrite]: #104
+#97 := (iff #16 #96)
+#98 := [rewrite]: #97
+#108 := [monotonicity #98 #105]: #107
+#100 := (iff #17 #99)
+#93 := (iff #15 #92)
+#94 := [rewrite]: #93
+#101 := [monotonicity #94 #98]: #100
+#111 := [monotonicity #101 #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [monotonicity #117]: #119
+#123 := [quant-intro #120]: #122
+#89 := (iff #28 #88)
+#86 := (iff #27 #85)
+#83 := (= #26 #82)
+#80 := (= #25 #79)
+#77 := (= #24 #76)
+#74 := (= #23 #73)
+#75 := [rewrite]: #74
+#71 := (= #22 #70)
+#72 := [rewrite]: #71
+#78 := [monotonicity #72 #75]: #77
+#67 := (iff #20 #66)
+#64 := (iff #19 #63)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#81 := [monotonicity #68 #78]: #80
+#84 := [monotonicity #81]: #83
+#87 := [monotonicity #84]: #86
+#90 := [quant-intro #87]: #89
+#125 := [trans #90 #123]: #124
+#62 := [asserted]: #28
+#126 := [mp #62 #125]: #121
+#191 := [mp~ #126 #201]: #121
+#228 := [mp #191 #227]: #225
+#259 := [mp #228 #258]: #256
+#753 := [mp #259 #752]: #748
+#667 := (not #748)
+#661 := (or #667 #182)
+#333 := (* -1::int 3::int)
+#418 := (* -1::int -5::int)
+#419 := (div #418 #333)
+#420 := (* -1::int #419)
+#411 := (+ #176 #420)
+#422 := (= #411 0::int)
+#423 := (div -5::int 3::int)
+#351 := (* -1::int #423)
+#424 := (+ #176 #351)
+#421 := (= #424 0::int)
+#425 := (<= 3::int 0::int)
+#404 := (<= -5::int 0::int)
+#739 := (or #404 #425)
+#741 := (not #739)
+#398 := (>= -5::int 0::int)
+#528 := (or #425 #398)
+#735 := (not #528)
+#409 := (or #735 #741)
+#410 := (ite #409 #421 #422)
+#742 := (= #176 0::int)
+#743 := (= 3::int 0::int)
+#744 := (= -5::int 0::int)
+#745 := (or #744 #743)
+#740 := (ite #745 #742 #410)
+#668 := (or #667 #740)
+#653 := (iff #668 #661)
+#656 := (iff #661 #661)
+#657 := [rewrite]: #656
+#665 := (iff #740 #182)
+#673 := (ite false #742 #182)
+#675 := (iff #673 #182)
+#664 := [rewrite]: #675
+#674 := (iff #740 #673)
+#662 := (iff #410 #182)
+#586 := (= #176 -1::int)
+#1 := true
+#682 := (ite true #182 #586)
+#663 := (iff #682 #182)
+#660 := [rewrite]: #663
+#669 := (iff #410 #682)
+#681 := (iff #422 #586)
+#570 := 1::int
+#680 := (+ 1::int #176)
+#576 := (= #680 0::int)
+#587 := (iff #576 #586)
+#588 := [rewrite]: #587
+#584 := (iff #422 #576)
+#582 := (= #411 #680)
+#581 := (+ #176 1::int)
+#565 := (= #581 #680)
+#580 := [rewrite]: #565
+#676 := (= #411 #581)
+#531 := (= #420 1::int)
+#687 := (* -1::int -1::int)
+#571 := (= #687 1::int)
+#572 := [rewrite]: #571
+#685 := (= #420 #687)
+#684 := (= #419 -1::int)
+#696 := -3::int
+#698 := (div 5::int -3::int)
+#530 := (= #698 -1::int)
+#683 := [rewrite]: #530
+#527 := (= #419 #698)
+#697 := (= #333 -3::int)
+#691 := [rewrite]: #697
+#689 := (= #418 5::int)
+#690 := [rewrite]: #689
+#529 := [monotonicity #690 #691]: #527
+#686 := [trans #529 #683]: #684
+#688 := [monotonicity #686]: #685
+#679 := [trans #688 #572]: #531
+#677 := [monotonicity #679]: #676
+#583 := [trans #677 #580]: #582
+#585 := [monotonicity #583]: #584
+#678 := [trans #585 #588]: #681
+#694 := (iff #421 #182)
+#700 := (+ 2::int #176)
+#548 := (= #700 0::int)
+#692 := (iff #548 #182)
+#693 := [rewrite]: #692
+#549 := (iff #421 #548)
+#701 := (= #424 #700)
+#703 := (+ #176 2::int)
+#705 := (= #703 #700)
+#706 := [rewrite]: #705
+#704 := (= #424 #703)
+#713 := (= #351 2::int)
+#711 := (* -1::int -2::int)
+#712 := (= #711 2::int)
+#709 := [rewrite]: #712
+#426 := (= #351 #711)
+#432 := (= #423 -2::int)
+#710 := [rewrite]: #432
+#708 := [monotonicity #710]: #426
+#702 := [trans #708 #709]: #713
+#699 := [monotonicity #702]: #704
+#707 := [trans #699 #706]: #701
+#550 := [monotonicity #707]: #549
+#695 := [trans #550 #693]: #694
+#430 := (iff #409 true)
+#720 := (or true false)
+#444 := (iff #720 true)
+#445 := [rewrite]: #444
+#719 := (iff #409 #720)
+#718 := (iff #741 false)
+#716 := (not true)
+#440 := (iff #716 false)
+#714 := [rewrite]: #440
+#717 := (iff #741 #716)
+#446 := (iff #739 true)
+#721 := (iff #739 #720)
+#387 := (iff #425 false)
+#388 := [rewrite]: #387
+#731 := (iff #404 true)
+#734 := [rewrite]: #731
+#443 := [monotonicity #734 #388]: #721
+#339 := [trans #443 #445]: #446
+#439 := [monotonicity #339]: #717
+#715 := [trans #439 #714]: #718
+#373 := (iff #735 true)
+#729 := (not false)
+#732 := (iff #729 true)
+#372 := [rewrite]: #732
+#367 := (iff #735 #729)
+#728 := (iff #528 false)
+#737 := (or false false)
+#381 := (iff #737 false)
+#722 := [rewrite]: #381
+#726 := (iff #528 #737)
+#724 := (iff #398 false)
+#725 := [rewrite]: #724
+#727 := [monotonicity #388 #725]: #726
+#723 := [trans #727 #722]: #728
+#730 := [monotonicity #723]: #367
+#733 := [trans #730 #372]: #373
+#429 := [monotonicity #733 #715]: #719
+#431 := [trans #429 #445]: #430
+#671 := [monotonicity #431 #695 #678]: #669
+#672 := [trans #671 #660]: #662
+#385 := (iff #745 false)
+#397 := (iff #745 #737)
+#396 := (iff #743 false)
+#401 := [rewrite]: #396
+#746 := (iff #744 false)
+#736 := [rewrite]: #746
+#738 := [monotonicity #736 #401]: #397
+#386 := [trans #738 #722]: #385
+#670 := [monotonicity #386 #672]: #674
+#666 := [trans #670 #664]: #665
+#655 := [monotonicity #666]: #653
+#658 := [trans #655 #657]: #653
+#652 := [quant-inst]: #668
+#654 := [mp #652 #658]: #661
+[unit-resolution #654 #753 #190]: false
+unsat
+4ca477e5a43a16dacbb90f983ac5a8510c16d464 327 0
+#2 := false
+#11 := 0::int
+decl f3 :: (-> int int int)
+#174 := -3::int
+#68 := -1::int
+#177 := (f3 -1::int -3::int)
+#180 := (= #177 0::int)
+#193 := (not #180)
+#40 := 3::int
+#41 := (- 3::int)
+#38 := 1::int
+#39 := (- 1::int)
+#42 := (f3 #39 #41)
+#43 := (= #42 0::int)
+#44 := (not #43)
+#196 := (iff #44 #193)
+#183 := (= 0::int #177)
+#188 := (not #183)
+#194 := (iff #188 #193)
+#191 := (iff #183 #180)
+#192 := [rewrite]: #191
+#195 := [monotonicity #192]: #194
+#189 := (iff #44 #188)
+#186 := (iff #43 #183)
+#184 := (iff #180 #183)
+#185 := [rewrite]: #184
+#181 := (iff #43 #180)
+#178 := (= #42 #177)
+#175 := (= #41 -3::int)
+#176 := [rewrite]: #175
+#172 := (= #39 -1::int)
+#173 := [rewrite]: #172
+#179 := [monotonicity #173 #176]: #178
+#182 := [monotonicity #179]: #181
+#187 := [trans #182 #185]: #186
+#190 := [monotonicity #187]: #189
+#197 := [trans #190 #195]: #196
+#171 := [asserted]: #44
+#198 := [mp #171 #197]: #193
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#756 := (pattern #10)
+#72 := (* -1::int #9)
+#69 := (* -1::int #8)
+#75 := (div #69 #72)
+#259 := (* -1::int #75)
+#260 := (+ #10 #259)
+#261 := (= #260 0::int)
+#21 := (div #8 #9)
+#256 := (* -1::int #21)
+#257 := (+ #10 #256)
+#258 := (= #257 0::int)
+#94 := (<= #9 0::int)
+#90 := (<= #8 0::int)
+#214 := (or #90 #94)
+#215 := (not #214)
+#101 := (>= #8 0::int)
+#206 := (or #94 #101)
+#207 := (not #206)
+#221 := (or #207 #215)
+#262 := (ite #221 #258 #261)
+#255 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#263 := (ite #14 #255 #262)
+#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
+#266 := (forall (vars (?v0 int) (?v1 int)) #263)
+#760 := (iff #266 #757)
+#758 := (iff #263 #263)
+#759 := [refl]: #758
+#761 := [quant-intro #759]: #760
+#226 := (ite #221 #21 #75)
+#229 := (ite #14 0::int #226)
+#232 := (= #10 #229)
+#235 := (forall (vars (?v0 int) (?v1 int)) #232)
+#267 := (iff #235 #266)
+#264 := (iff #232 #263)
+#265 := [rewrite]: #264
+#268 := [quant-intro #265]: #267
+#102 := (not #101)
+#95 := (not #94)
+#105 := (and #95 #102)
+#91 := (not #90)
+#98 := (and #91 #95)
+#108 := (or #98 #105)
+#111 := (ite #108 #21 #75)
+#114 := (ite #14 0::int #111)
+#117 := (= #10 #114)
+#120 := (forall (vars (?v0 int) (?v1 int)) #117)
+#236 := (iff #120 #235)
+#233 := (iff #117 #232)
+#230 := (= #114 #229)
+#227 := (= #111 #226)
+#224 := (iff #108 #221)
+#218 := (or #215 #207)
+#222 := (iff #218 #221)
+#223 := [rewrite]: #222
+#219 := (iff #108 #218)
+#216 := (iff #105 #207)
+#217 := [rewrite]: #216
+#204 := (iff #98 #215)
+#205 := [rewrite]: #204
+#220 := [monotonicity #205 #217]: #219
+#225 := [trans #220 #223]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [monotonicity #231]: #233
+#237 := [quant-intro #234]: #236
+#210 := (~ #120 #120)
+#208 := (~ #117 #117)
+#209 := [refl]: #208
+#211 := [nnf-pos #209]: #210
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#123 := (iff #28 #120)
+#62 := (and #16 #18)
+#65 := (or #17 #62)
+#78 := (ite #65 #21 #75)
+#81 := (ite #14 0::int #78)
+#84 := (= #10 #81)
+#87 := (forall (vars (?v0 int) (?v1 int)) #84)
+#121 := (iff #87 #120)
+#118 := (iff #84 #117)
+#115 := (= #81 #114)
+#112 := (= #78 #111)
+#109 := (iff #65 #108)
+#106 := (iff #62 #105)
+#103 := (iff #18 #102)
+#104 := [rewrite]: #103
+#96 := (iff #16 #95)
+#97 := [rewrite]: #96
+#107 := [monotonicity #97 #104]: #106
+#99 := (iff #17 #98)
+#92 := (iff #15 #91)
+#93 := [rewrite]: #92
+#100 := [monotonicity #93 #97]: #99
+#110 := [monotonicity #100 #107]: #109
+#113 := [monotonicity #110]: #112
+#116 := [monotonicity #113]: #115
+#119 := [monotonicity #116]: #118
+#122 := [quant-intro #119]: #121
+#88 := (iff #28 #87)
+#85 := (iff #27 #84)
+#82 := (= #26 #81)
+#79 := (= #25 #78)
+#76 := (= #24 #75)
+#73 := (= #23 #72)
+#74 := [rewrite]: #73
+#70 := (= #22 #69)
+#71 := [rewrite]: #70
+#77 := [monotonicity #71 #74]: #76
+#66 := (iff #20 #65)
+#63 := (iff #19 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#80 := [monotonicity #67 #77]: #79
+#83 := [monotonicity #80]: #82
+#86 := [monotonicity #83]: #85
+#89 := [quant-intro #86]: #88
+#124 := [trans #89 #122]: #123
+#61 := [asserted]: #28
+#125 := [mp #61 #124]: #120
+#201 := [mp~ #125 #211]: #120
+#238 := [mp #201 #237]: #235
+#269 := [mp #238 #268]: #266
+#762 := [mp #269 #761]: #757
+#681 := (not #757)
+#682 := (or #681 #180)
+#343 := (* -1::int -3::int)
+#427 := (* -1::int -1::int)
+#428 := (div #427 #343)
+#429 := (* -1::int #428)
+#420 := (+ #177 #429)
+#431 := (= #420 0::int)
+#432 := (div -1::int -3::int)
+#433 := (* -1::int #432)
+#430 := (+ #177 #433)
+#434 := (= #430 0::int)
+#413 := (<= -3::int 0::int)
+#748 := (<= -1::int 0::int)
+#750 := (or #748 #413)
+#407 := (not #750)
+#537 := (>= -1::int 0::int)
+#744 := (or #413 #537)
+#418 := (not #744)
+#419 := (or #418 #407)
+#751 := (ite #419 #434 #431)
+#752 := (= -3::int 0::int)
+#753 := (= -1::int 0::int)
+#754 := (or #753 #752)
+#749 := (ite #754 #180 #751)
+#683 := (or #681 #749)
+#684 := (iff #683 #682)
+#674 := (iff #682 #682)
+#675 := [rewrite]: #674
+#669 := (iff #749 #180)
+#687 := (ite false #180 #180)
+#680 := (iff #687 #180)
+#672 := [rewrite]: #680
+#691 := (iff #749 #687)
+#597 := (iff #751 #180)
+#701 := (= #177 1::int)
+#585 := (ite false #701 #180)
+#595 := (iff #585 #180)
+#596 := [rewrite]: #595
+#593 := (iff #751 #585)
+#591 := (iff #431 #180)
+#574 := (= #420 #177)
+#688 := (+ #177 0::int)
+#686 := (= #688 #177)
+#689 := [rewrite]: #686
+#590 := (= #420 #688)
+#581 := (= #429 0::int)
+#696 := (* -1::int 0::int)
+#579 := (= #696 0::int)
+#580 := [rewrite]: #579
+#694 := (= #429 #696)
+#693 := (= #428 0::int)
+#707 := (div 1::int 3::int)
+#539 := (= #707 0::int)
+#692 := [rewrite]: #539
+#536 := (= #428 #707)
+#706 := (= #343 3::int)
+#700 := [rewrite]: #706
+#699 := (= #427 1::int)
+#705 := [rewrite]: #699
+#538 := [monotonicity #705 #700]: #536
+#695 := [trans #538 #692]: #693
+#697 := [monotonicity #695]: #694
+#540 := [trans #697 #580]: #581
+#685 := [monotonicity #540]: #590
+#589 := [trans #685 #689]: #574
+#592 := [monotonicity #589]: #591
+#704 := (iff #434 #701)
+#709 := (+ -1::int #177)
+#557 := (= #709 0::int)
+#702 := (iff #557 #701)
+#703 := [rewrite]: #702
+#558 := (iff #434 #557)
+#710 := (= #430 #709)
+#712 := (+ #177 -1::int)
+#714 := (= #712 #709)
+#715 := [rewrite]: #714
+#713 := (= #430 #712)
+#722 := (= #433 -1::int)
+#720 := (* -1::int 1::int)
+#721 := (= #720 -1::int)
+#718 := [rewrite]: #721
+#435 := (= #433 #720)
+#441 := (= #432 1::int)
+#719 := [rewrite]: #441
+#717 := [monotonicity #719]: #435
+#711 := [trans #717 #718]: #722
+#708 := [monotonicity #711]: #713
+#716 := [trans #708 #715]: #710
+#559 := [monotonicity #716]: #558
+#698 := [trans #559 #703]: #704
+#439 := (iff #419 false)
+#746 := (or false false)
+#390 := (iff #746 false)
+#731 := [rewrite]: #390
+#728 := (iff #419 #746)
+#727 := (iff #407 false)
+#1 := true
+#741 := (not true)
+#742 := (iff #741 false)
+#740 := [rewrite]: #742
+#449 := (iff #407 #741)
+#726 := (iff #750 true)
+#453 := (or true true)
+#349 := (iff #453 true)
+#725 := [rewrite]: #349
+#454 := (iff #750 #453)
+#396 := (iff #413 true)
+#397 := [rewrite]: #396
+#730 := (iff #748 true)
+#452 := [rewrite]: #730
+#455 := [monotonicity #452 #397]: #454
+#448 := [trans #455 #725]: #726
+#723 := [monotonicity #448]: #449
+#724 := [trans #723 #740]: #727
+#743 := (iff #418 false)
+#381 := (iff #418 #741)
+#376 := (iff #744 true)
+#735 := (or true false)
+#732 := (iff #735 true)
+#738 := [rewrite]: #732
+#736 := (iff #744 #735)
+#733 := (iff #537 false)
+#734 := [rewrite]: #733
+#737 := [monotonicity #397 #734]: #736
+#739 := [trans #737 #738]: #376
+#382 := [monotonicity #739]: #381
+#729 := [trans #382 #740]: #743
+#438 := [monotonicity #729 #724]: #728
+#440 := [trans #438 #731]: #439
+#594 := [monotonicity #440 #698 #592]: #593
+#690 := [trans #594 #596]: #597
+#394 := (iff #754 false)
+#406 := (iff #754 #746)
+#405 := (iff #752 false)
+#410 := [rewrite]: #405
+#755 := (iff #753 false)
+#745 := [rewrite]: #755
+#747 := [monotonicity #745 #410]: #406
+#395 := [trans #747 #731]: #394
+#678 := [monotonicity #395 #690]: #691
+#671 := [trans #678 #672]: #669
+#673 := [monotonicity #671]: #684
+#676 := [trans #673 #675]: #684
+#679 := [quant-inst]: #683
+#670 := [mp #679 #676]: #682
+[unit-resolution #670 #762 #198]: false
+unsat
+ddc5a6b304650a08be4d46afd02b8b25ea1c25a2 311 0
+#2 := false
+#41 := 1::int
+decl f3 :: (-> int int int)
+#171 := -3::int
+#174 := (f3 -3::int -3::int)
+#177 := (= #174 1::int)
+#190 := (not #177)
+#38 := 3::int
+#39 := (- 3::int)
+#40 := (f3 #39 #39)
+#42 := (= #40 1::int)
+#43 := (not #42)
+#193 := (iff #43 #190)
+#180 := (= 1::int #174)
+#185 := (not #180)
+#191 := (iff #185 #190)
+#188 := (iff #180 #177)
+#189 := [rewrite]: #188
+#192 := [monotonicity #189]: #191
+#186 := (iff #43 #185)
+#183 := (iff #42 #180)
+#181 := (iff #177 #180)
+#182 := [rewrite]: #181
+#178 := (iff #42 #177)
+#175 := (= #40 #174)
+#172 := (= #39 -3::int)
+#173 := [rewrite]: #172
+#176 := [monotonicity #173 #173]: #175
+#179 := [monotonicity #176]: #178
+#184 := [trans #179 #182]: #183
+#187 := [monotonicity #184]: #186
+#194 := [trans #187 #192]: #193
+#170 := [asserted]: #43
+#195 := [mp #170 #194]: #190
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#753 := (pattern #10)
+#11 := 0::int
+#67 := -1::int
+#71 := (* -1::int #9)
+#68 := (* -1::int #8)
+#74 := (div #68 #71)
+#256 := (* -1::int #74)
+#257 := (+ #10 #256)
+#258 := (= #257 0::int)
+#21 := (div #8 #9)
+#253 := (* -1::int #21)
+#254 := (+ #10 #253)
+#255 := (= #254 0::int)
+#93 := (<= #9 0::int)
+#89 := (<= #8 0::int)
+#211 := (or #89 #93)
+#212 := (not #211)
+#100 := (>= #8 0::int)
+#203 := (or #93 #100)
+#204 := (not #203)
+#218 := (or #204 #212)
+#259 := (ite #218 #255 #258)
+#252 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#260 := (ite #14 #252 #259)
+#754 := (forall (vars (?v0 int) (?v1 int)) (:pat #753) #260)
+#263 := (forall (vars (?v0 int) (?v1 int)) #260)
+#757 := (iff #263 #754)
+#755 := (iff #260 #260)
+#756 := [refl]: #755
+#758 := [quant-intro #756]: #757
+#223 := (ite #218 #21 #74)
+#226 := (ite #14 0::int #223)
+#229 := (= #10 #226)
+#232 := (forall (vars (?v0 int) (?v1 int)) #229)
+#264 := (iff #232 #263)
+#261 := (iff #229 #260)
+#262 := [rewrite]: #261
+#265 := [quant-intro #262]: #264
+#101 := (not #100)
+#94 := (not #93)
+#104 := (and #94 #101)
+#90 := (not #89)
+#97 := (and #90 #94)
+#107 := (or #97 #104)
+#110 := (ite #107 #21 #74)
+#113 := (ite #14 0::int #110)
+#116 := (= #10 #113)
+#119 := (forall (vars (?v0 int) (?v1 int)) #116)
+#233 := (iff #119 #232)
+#230 := (iff #116 #229)
+#227 := (= #113 #226)
+#224 := (= #110 #223)
+#221 := (iff #107 #218)
+#215 := (or #212 #204)
+#219 := (iff #215 #218)
+#220 := [rewrite]: #219
+#216 := (iff #107 #215)
+#213 := (iff #104 #204)
+#214 := [rewrite]: #213
+#201 := (iff #97 #212)
+#202 := [rewrite]: #201
+#217 := [monotonicity #202 #214]: #216
+#222 := [trans #217 #220]: #221
+#225 := [monotonicity #222]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [quant-intro #231]: #233
+#207 := (~ #119 #119)
+#205 := (~ #116 #116)
+#206 := [refl]: #205
+#208 := [nnf-pos #206]: #207
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#122 := (iff #28 #119)
+#61 := (and #16 #18)
+#64 := (or #17 #61)
+#77 := (ite #64 #21 #74)
+#80 := (ite #14 0::int #77)
+#83 := (= #10 #80)
+#86 := (forall (vars (?v0 int) (?v1 int)) #83)
+#120 := (iff #86 #119)
+#117 := (iff #83 #116)
+#114 := (= #80 #113)
+#111 := (= #77 #110)
+#108 := (iff #64 #107)
+#105 := (iff #61 #104)
+#102 := (iff #18 #101)
+#103 := [rewrite]: #102
+#95 := (iff #16 #94)
+#96 := [rewrite]: #95
+#106 := [monotonicity #96 #103]: #105
+#98 := (iff #17 #97)
+#91 := (iff #15 #90)
+#92 := [rewrite]: #91
+#99 := [monotonicity #92 #96]: #98
+#109 := [monotonicity #99 #106]: #108
+#112 := [monotonicity #109]: #111
+#115 := [monotonicity #112]: #114
+#118 := [monotonicity #115]: #117
+#121 := [quant-intro #118]: #120
+#87 := (iff #28 #86)
+#84 := (iff #27 #83)
+#81 := (= #26 #80)
+#78 := (= #25 #77)
+#75 := (= #24 #74)
+#72 := (= #23 #71)
+#73 := [rewrite]: #72
+#69 := (= #22 #68)
+#70 := [rewrite]: #69
+#76 := [monotonicity #70 #73]: #75
+#65 := (iff #20 #64)
+#62 := (iff #19 #61)
+#63 := [rewrite]: #62
+#66 := [monotonicity #63]: #65
+#79 := [monotonicity #66 #76]: #78
+#82 := [monotonicity #79]: #81
+#85 := [monotonicity #82]: #84
+#88 := [quant-intro #85]: #87
+#123 := [trans #88 #121]: #122
+#60 := [asserted]: #28
+#124 := [mp #60 #123]: #119
+#198 := [mp~ #124 #208]: #119
+#235 := [mp #198 #234]: #232
+#266 := [mp #235 #265]: #263
+#759 := [mp #266 #758]: #754
+#590 := (not #754)
+#591 := (or #590 #177)
+#340 := (* -1::int -3::int)
+#424 := (div #340 #340)
+#425 := (* -1::int #424)
+#426 := (+ #174 #425)
+#417 := (= #426 0::int)
+#428 := (div -3::int -3::int)
+#429 := (* -1::int #428)
+#430 := (+ #174 #429)
+#427 := (= #430 0::int)
+#431 := (<= -3::int 0::int)
+#410 := (or #431 #431)
+#745 := (not #410)
+#747 := (>= -3::int 0::int)
+#404 := (or #431 #747)
+#534 := (not #404)
+#741 := (or #534 #745)
+#415 := (ite #741 #427 #417)
+#416 := (= #174 0::int)
+#748 := (= -3::int 0::int)
+#749 := (or #748 #748)
+#750 := (ite #749 #416 #415)
+#592 := (or #590 #750)
+#594 := (iff #592 #591)
+#684 := (iff #591 #591)
+#688 := [rewrite]: #684
+#589 := (iff #750 #177)
+#683 := (ite false #416 #177)
+#586 := (iff #683 #177)
+#588 := [rewrite]: #586
+#686 := (iff #750 #683)
+#587 := (iff #415 #177)
+#576 := (ite false #177 #177)
+#537 := (iff #576 #177)
+#685 := [rewrite]: #537
+#577 := (iff #415 #576)
+#691 := (iff #417 #177)
+#715 := (+ -1::int #174)
+#705 := (= #715 0::int)
+#712 := (iff #705 #177)
+#707 := [rewrite]: #712
+#692 := (iff #417 #705)
+#689 := (= #426 #715)
+#432 := (+ #174 -1::int)
+#719 := (= #432 #715)
+#708 := [rewrite]: #719
+#535 := (= #426 #432)
+#704 := (= #425 -1::int)
+#725 := (* -1::int 1::int)
+#437 := (= #725 -1::int)
+#438 := [rewrite]: #437
+#703 := (= #425 #725)
+#696 := (= #424 1::int)
+#698 := (div 3::int 3::int)
+#701 := (= #698 1::int)
+#695 := [rewrite]: #701
+#699 := (= #424 #698)
+#555 := (= #340 3::int)
+#556 := [rewrite]: #555
+#700 := [monotonicity #556 #556]: #699
+#702 := [trans #700 #695]: #696
+#697 := [monotonicity #702]: #703
+#533 := [trans #697 #438]: #704
+#536 := [monotonicity #533]: #535
+#690 := [trans #536 #708]: #689
+#693 := [monotonicity #690]: #692
+#694 := [trans #693 #707]: #691
+#713 := (iff #427 #177)
+#706 := (iff #427 #705)
+#709 := (= #430 #715)
+#714 := (= #430 #432)
+#716 := (= #429 -1::int)
+#435 := (= #429 #725)
+#724 := (= #428 1::int)
+#721 := [rewrite]: #724
+#436 := [monotonicity #721]: #435
+#717 := [trans #436 #438]: #716
+#718 := [monotonicity #717]: #714
+#710 := [trans #718 #708]: #709
+#711 := [monotonicity #710]: #706
+#554 := [trans #711 #707]: #713
+#446 := (iff #741 false)
+#752 := (or false false)
+#407 := (iff #752 false)
+#743 := [rewrite]: #407
+#723 := (iff #741 #752)
+#346 := (iff #745 false)
+#1 := true
+#729 := (not true)
+#736 := (iff #729 false)
+#738 := [rewrite]: #736
+#451 := (iff #745 #729)
+#449 := (iff #410 true)
+#739 := (or true true)
+#726 := (iff #739 true)
+#727 := [rewrite]: #726
+#737 := (iff #410 #739)
+#387 := (iff #431 true)
+#728 := [rewrite]: #387
+#740 := [monotonicity #728 #728]: #737
+#450 := [trans #740 #727]: #449
+#452 := [monotonicity #450]: #451
+#722 := [trans #452 #738]: #346
+#378 := (iff #534 false)
+#735 := (iff #534 #729)
+#733 := (iff #404 true)
+#393 := (or true false)
+#731 := (iff #393 true)
+#732 := [rewrite]: #731
+#394 := (iff #404 #393)
+#391 := (iff #747 false)
+#392 := [rewrite]: #391
+#730 := [monotonicity #728 #392]: #394
+#734 := [trans #730 #732]: #733
+#373 := [monotonicity #734]: #735
+#379 := [trans #373 #738]: #378
+#445 := [monotonicity #379 #722]: #723
+#720 := [trans #445 #743]: #446
+#578 := [monotonicity #720 #554 #694]: #577
+#682 := [trans #578 #685]: #587
+#403 := (iff #749 false)
+#742 := (iff #749 #752)
+#751 := (iff #748 false)
+#746 := [rewrite]: #751
+#402 := [monotonicity #746 #746]: #742
+#744 := [trans #402 #743]: #403
+#571 := [monotonicity #744 #682]: #686
+#582 := [trans #571 #588]: #589
+#687 := [monotonicity #582]: #594
+#675 := [trans #687 #688]: #594
+#593 := [quant-inst]: #592
+#677 := [mp #593 #675]: #591
+[unit-resolution #677 #759 #195]: false
+unsat
+081d17418769caf8ceb0841229da368f6008d179 338 0
+#2 := false
+#43 := 1::int
+decl f3 :: (-> int int int)
+#176 := -3::int
+#173 := -5::int
+#179 := (f3 -5::int -3::int)
+#182 := (= #179 1::int)
+#195 := (not #182)
+#40 := 3::int
+#41 := (- 3::int)
+#38 := 5::int
+#39 := (- 5::int)
+#42 := (f3 #39 #41)
+#44 := (= #42 1::int)
+#45 := (not #44)
+#198 := (iff #45 #195)
+#185 := (= 1::int #179)
+#190 := (not #185)
+#196 := (iff #190 #195)
+#193 := (iff #185 #182)
+#194 := [rewrite]: #193
+#197 := [monotonicity #194]: #196
+#191 := (iff #45 #190)
+#188 := (iff #44 #185)
+#186 := (iff #182 #185)
+#187 := [rewrite]: #186
+#183 := (iff #44 #182)
+#180 := (= #42 #179)
+#177 := (= #41 -3::int)
+#178 := [rewrite]: #177
+#174 := (= #39 -5::int)
+#175 := [rewrite]: #174
+#181 := [monotonicity #175 #178]: #180
+#184 := [monotonicity #181]: #183
+#189 := [trans #184 #187]: #188
+#192 := [monotonicity #189]: #191
+#199 := [trans #192 #197]: #198
+#172 := [asserted]: #45
+#200 := [mp #172 #199]: #195
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#10 := (f3 #8 #9)
+#758 := (pattern #10)
+#11 := 0::int
+#69 := -1::int
+#73 := (* -1::int #9)
+#70 := (* -1::int #8)
+#76 := (div #70 #73)
+#261 := (* -1::int #76)
+#262 := (+ #10 #261)
+#263 := (= #262 0::int)
+#21 := (div #8 #9)
+#258 := (* -1::int #21)
+#259 := (+ #10 #258)
+#260 := (= #259 0::int)
+#95 := (<= #9 0::int)
+#91 := (<= #8 0::int)
+#216 := (or #91 #95)
+#217 := (not #216)
+#102 := (>= #8 0::int)
+#208 := (or #95 #102)
+#209 := (not #208)
+#223 := (or #209 #217)
+#264 := (ite #223 #260 #263)
+#257 := (= #10 0::int)
+#13 := (= #9 0::int)
+#12 := (= #8 0::int)
+#14 := (or #12 #13)
+#265 := (ite #14 #257 #264)
+#759 := (forall (vars (?v0 int) (?v1 int)) (:pat #758) #265)
+#268 := (forall (vars (?v0 int) (?v1 int)) #265)
+#762 := (iff #268 #759)
+#760 := (iff #265 #265)
+#761 := [refl]: #760
+#763 := [quant-intro #761]: #762
+#228 := (ite #223 #21 #76)
+#231 := (ite #14 0::int #228)
+#234 := (= #10 #231)
+#237 := (forall (vars (?v0 int) (?v1 int)) #234)
+#269 := (iff #237 #268)
+#266 := (iff #234 #265)
+#267 := [rewrite]: #266
+#270 := [quant-intro #267]: #269
+#103 := (not #102)
+#96 := (not #95)
+#106 := (and #96 #103)
+#92 := (not #91)
+#99 := (and #92 #96)
+#109 := (or #99 #106)
+#112 := (ite #109 #21 #76)
+#115 := (ite #14 0::int #112)
+#118 := (= #10 #115)
+#121 := (forall (vars (?v0 int) (?v1 int)) #118)
+#238 := (iff #121 #237)
+#235 := (iff #118 #234)
+#232 := (= #115 #231)
+#229 := (= #112 #228)
+#226 := (iff #109 #223)
+#220 := (or #217 #209)
+#224 := (iff #220 #223)
+#225 := [rewrite]: #224
+#221 := (iff #109 #220)
+#218 := (iff #106 #209)
+#219 := [rewrite]: #218
+#206 := (iff #99 #217)
+#207 := [rewrite]: #206
+#222 := [monotonicity #207 #219]: #221
+#227 := [trans #222 #225]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [monotonicity #233]: #235
+#239 := [quant-intro #236]: #238
+#212 := (~ #121 #121)
+#210 := (~ #118 #118)
+#211 := [refl]: #210
+#213 := [nnf-pos #211]: #212
+#23 := (- #9)
+#22 := (- #8)
+#24 := (div #22 #23)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#25 := (ite #20 #21 #24)
+#26 := (ite #14 0::int #25)
+#27 := (= #10 #26)
+#28 := (forall (vars (?v0 int) (?v1 int)) #27)
+#124 := (iff #28 #121)
+#63 := (and #16 #18)
+#66 := (or #17 #63)
+#79 := (ite #66 #21 #76)
+#82 := (ite #14 0::int #79)
+#85 := (= #10 #82)
+#88 := (forall (vars (?v0 int) (?v1 int)) #85)
+#122 := (iff #88 #121)
+#119 := (iff #85 #118)
+#116 := (= #82 #115)
+#113 := (= #79 #112)
+#110 := (iff #66 #109)
+#107 := (iff #63 #106)
+#104 := (iff #18 #103)
+#105 := [rewrite]: #104
+#97 := (iff #16 #96)
+#98 := [rewrite]: #97
+#108 := [monotonicity #98 #105]: #107
+#100 := (iff #17 #99)
+#93 := (iff #15 #92)
+#94 := [rewrite]: #93
+#101 := [monotonicity #94 #98]: #100
+#111 := [monotonicity #101 #108]: #110
+#114 := [monotonicity #111]: #113
+#117 := [monotonicity #114]: #116
+#120 := [monotonicity #117]: #119
+#123 := [quant-intro #120]: #122
+#89 := (iff #28 #88)
+#86 := (iff #27 #85)
+#83 := (= #26 #82)
+#80 := (= #25 #79)
+#77 := (= #24 #76)
+#74 := (= #23 #73)
+#75 := [rewrite]: #74
+#71 := (= #22 #70)
+#72 := [rewrite]: #71
+#78 := [monotonicity #72 #75]: #77
+#67 := (iff #20 #66)
+#64 := (iff #19 #63)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#81 := [monotonicity #68 #78]: #80
+#84 := [monotonicity #81]: #83
+#87 := [monotonicity #84]: #86
+#90 := [quant-intro #87]: #89
+#125 := [trans #90 #123]: #124
+#62 := [asserted]: #28
+#126 := [mp #62 #125]: #121
+#203 := [mp~ #126 #213]: #121
+#240 := [mp #203 #239]: #237
+#271 := [mp #240 #270]: #268
+#764 := [mp #271 #763]: #759
+#672 := (not #759)
+#679 := (or #672 #182)
+#345 := (* -1::int -3::int)
+#429 := (* -1::int -5::int)
+#430 := (div #429 #345)
+#431 := (* -1::int #430)
+#422 := (+ #179 #431)
+#433 := (= #422 0::int)
+#434 := (div -5::int -3::int)
+#435 := (* -1::int #434)
+#432 := (+ #179 #435)
+#436 := (= #432 0::int)
+#415 := (<= -3::int 0::int)
+#750 := (<= -5::int 0::int)
+#752 := (or #750 #415)
+#409 := (not #752)
+#539 := (>= -5::int 0::int)
+#746 := (or #415 #539)
+#420 := (not #746)
+#421 := (or #420 #409)
+#753 := (ite #421 #436 #433)
+#754 := (= #179 0::int)
+#755 := (= -3::int 0::int)
+#756 := (= -5::int 0::int)
+#751 := (or #756 #755)
+#757 := (ite #751 #754 #753)
+#663 := (or #672 #757)
+#666 := (iff #663 #679)
+#668 := (iff #679 #679)
+#669 := [rewrite]: #668
+#677 := (iff #757 #182)
+#685 := (ite false #754 #182)
+#675 := (iff #685 #182)
+#676 := [rewrite]: #675
+#681 := (iff #757 #685)
+#683 := (iff #753 #182)
+#721 := 2::int
+#706 := (= #179 2::int)
+#680 := (ite false #706 #182)
+#671 := (iff #680 #182)
+#673 := [rewrite]: #671
+#682 := (iff #753 #680)
+#689 := (iff #433 #182)
+#591 := (+ -1::int #179)
+#596 := (= #591 0::int)
+#599 := (iff #596 #182)
+#692 := [rewrite]: #599
+#597 := (iff #433 #596)
+#587 := (= #422 #591)
+#688 := (+ #179 -1::int)
+#593 := (= #688 #591)
+#594 := [rewrite]: #593
+#691 := (= #422 #688)
+#592 := (= #431 -1::int)
+#581 := (* -1::int 1::int)
+#542 := (= #581 -1::int)
+#690 := [rewrite]: #542
+#582 := (= #431 #581)
+#696 := (= #430 1::int)
+#541 := (div 5::int 3::int)
+#697 := (= #541 1::int)
+#698 := [rewrite]: #697
+#694 := (= #430 #541)
+#538 := (= #345 3::int)
+#540 := [rewrite]: #538
+#702 := (= #429 5::int)
+#709 := [rewrite]: #702
+#695 := [monotonicity #709 #540]: #694
+#699 := [trans #695 #698]: #696
+#583 := [monotonicity #699]: #582
+#687 := [trans #583 #690]: #592
+#576 := [monotonicity #687]: #691
+#595 := [trans #576 #594]: #587
+#598 := [monotonicity #595]: #597
+#693 := [trans #598 #692]: #689
+#707 := (iff #436 #706)
+#724 := -2::int
+#712 := (+ -2::int #179)
+#703 := (= #712 0::int)
+#700 := (iff #703 #706)
+#701 := [rewrite]: #700
+#704 := (iff #436 #703)
+#560 := (= #432 #712)
+#711 := (+ #179 -2::int)
+#718 := (= #711 #712)
+#559 := [rewrite]: #718
+#716 := (= #432 #711)
+#715 := (= #435 -2::int)
+#719 := (* -1::int 2::int)
+#713 := (= #719 -2::int)
+#714 := [rewrite]: #713
+#723 := (= #435 #719)
+#722 := (= #434 2::int)
+#437 := [rewrite]: #722
+#720 := [monotonicity #437]: #723
+#710 := [trans #720 #714]: #715
+#717 := [monotonicity #710]: #716
+#561 := [trans #717 #559]: #560
+#705 := [monotonicity #561]: #704
+#708 := [trans #705 #701]: #707
+#442 := (iff #421 false)
+#408 := (or false false)
+#733 := (iff #408 false)
+#396 := [rewrite]: #733
+#440 := (iff #421 #408)
+#726 := (iff #409 false)
+#1 := true
+#383 := (not true)
+#742 := (iff #383 false)
+#745 := [rewrite]: #742
+#725 := (iff #409 #383)
+#450 := (iff #752 true)
+#456 := (or true true)
+#727 := (iff #456 true)
+#728 := [rewrite]: #727
+#457 := (iff #752 #456)
+#399 := (iff #415 true)
+#735 := [rewrite]: #399
+#454 := (iff #750 true)
+#455 := [rewrite]: #454
+#351 := [monotonicity #455 #735]: #457
+#451 := [trans #351 #728]: #450
+#729 := [monotonicity #451]: #725
+#730 := [trans #729 #745]: #726
+#731 := (iff #420 false)
+#384 := (iff #420 #383)
+#741 := (iff #746 true)
+#738 := (or true false)
+#740 := (iff #738 true)
+#378 := [rewrite]: #740
+#739 := (iff #746 #738)
+#736 := (iff #539 false)
+#737 := [rewrite]: #736
+#734 := [monotonicity #735 #737]: #739
+#743 := [trans #734 #378]: #741
+#744 := [monotonicity #743]: #384
+#732 := [trans #744 #745]: #731
+#441 := [monotonicity #732 #730]: #440
+#443 := [trans #441 #396]: #442
+#674 := [monotonicity #443 #708 #693]: #682
+#684 := [trans #674 #673]: #683
+#397 := (iff #751 false)
+#749 := (iff #751 #408)
+#412 := (iff #755 false)
+#748 := [rewrite]: #412
+#747 := (iff #756 false)
+#407 := [rewrite]: #747
+#392 := [monotonicity #407 #748]: #749
+#398 := [trans #392 #396]: #397
+#686 := [monotonicity #398 #684]: #681
+#678 := [trans #686 #676]: #677
+#667 := [monotonicity #678]: #666
+#665 := [trans #667 #669]: #666
+#664 := [quant-inst]: #663
+#670 := [mp #664 #665]: #679
+[unit-resolution #670 #764 #200]: false
+unsat
+1a424f78adbf3f5b91865b15057a1edb6fd9f0c7 268 0
+#2 := false
+#11 := 0::int
+decl f4 :: (-> int int int)
+#38 := (f4 0::int 0::int)
+#39 := (= #38 0::int)
+#40 := (not #39)
+#167 := [asserted]: #40
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#743 := (pattern #29)
+#64 := -1::int
+#68 := (* -1::int #9)
+#65 := (* -1::int #8)
+#123 := (mod #65 #68)
+#254 := (+ #29 #123)
+#255 := (= #254 0::int)
+#30 := (mod #8 #9)
+#251 := (* -1::int #30)
+#252 := (+ #29 #251)
+#253 := (= #252 0::int)
+#90 := (<= #9 0::int)
+#86 := (<= #8 0::int)
+#193 := (or #86 #90)
+#194 := (not #193)
+#97 := (>= #8 0::int)
+#185 := (or #90 #97)
+#186 := (not #185)
+#200 := (or #186 #194)
+#256 := (ite #200 #253 #255)
+#250 := (= #29 0::int)
+#12 := (= #8 0::int)
+#257 := (ite #12 #250 #256)
+#249 := (= #8 #29)
+#13 := (= #9 0::int)
+#258 := (ite #13 #249 #257)
+#744 := (forall (vars (?v0 int) (?v1 int)) (:pat #743) #258)
+#261 := (forall (vars (?v0 int) (?v1 int)) #258)
+#747 := (iff #261 #744)
+#745 := (iff #258 #258)
+#746 := [refl]: #745
+#748 := [quant-intro #746]: #747
+#129 := (* -1::int #123)
+#218 := (ite #200 #30 #129)
+#221 := (ite #12 0::int #218)
+#224 := (ite #13 #8 #221)
+#227 := (= #29 #224)
+#230 := (forall (vars (?v0 int) (?v1 int)) #227)
+#262 := (iff #230 #261)
+#259 := (iff #227 #258)
+#260 := [rewrite]: #259
+#263 := [quant-intro #260]: #262
+#98 := (not #97)
+#91 := (not #90)
+#101 := (and #91 #98)
+#87 := (not #86)
+#94 := (and #87 #91)
+#104 := (or #94 #101)
+#149 := (ite #104 #30 #129)
+#152 := (ite #12 0::int #149)
+#155 := (ite #13 #8 #152)
+#158 := (= #29 #155)
+#161 := (forall (vars (?v0 int) (?v1 int)) #158)
+#231 := (iff #161 #230)
+#228 := (iff #158 #227)
+#225 := (= #155 #224)
+#222 := (= #152 #221)
+#219 := (= #149 #218)
+#203 := (iff #104 #200)
+#197 := (or #194 #186)
+#201 := (iff #197 #200)
+#202 := [rewrite]: #201
+#198 := (iff #104 #197)
+#195 := (iff #101 #186)
+#196 := [rewrite]: #195
+#183 := (iff #94 #194)
+#184 := [rewrite]: #183
+#199 := [monotonicity #184 #196]: #198
+#204 := [trans #199 #202]: #203
+#220 := [monotonicity #204]: #219
+#223 := [monotonicity #220]: #222
+#226 := [monotonicity #223]: #225
+#229 := [monotonicity #226]: #228
+#232 := [quant-intro #229]: #231
+#181 := (~ #161 #161)
+#178 := (~ #158 #158)
+#191 := [refl]: #178
+#182 := [nnf-pos #191]: #181
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#164 := (iff #37 #161)
+#58 := (and #16 #18)
+#61 := (or #17 #58)
+#134 := (ite #61 #30 #129)
+#137 := (ite #12 0::int #134)
+#140 := (ite #13 #8 #137)
+#143 := (= #29 #140)
+#146 := (forall (vars (?v0 int) (?v1 int)) #143)
+#162 := (iff #146 #161)
+#159 := (iff #143 #158)
+#156 := (= #140 #155)
+#153 := (= #137 #152)
+#150 := (= #134 #149)
+#105 := (iff #61 #104)
+#102 := (iff #58 #101)
+#99 := (iff #18 #98)
+#100 := [rewrite]: #99
+#92 := (iff #16 #91)
+#93 := [rewrite]: #92
+#103 := [monotonicity #93 #100]: #102
+#95 := (iff #17 #94)
+#88 := (iff #15 #87)
+#89 := [rewrite]: #88
+#96 := [monotonicity #89 #93]: #95
+#106 := [monotonicity #96 #103]: #105
+#151 := [monotonicity #106]: #150
+#154 := [monotonicity #151]: #153
+#157 := [monotonicity #154]: #156
+#160 := [monotonicity #157]: #159
+#163 := [quant-intro #160]: #162
+#147 := (iff #37 #146)
+#144 := (iff #36 #143)
+#141 := (= #35 #140)
+#138 := (= #34 #137)
+#135 := (= #33 #134)
+#132 := (= #32 #129)
+#126 := (- #123)
+#130 := (= #126 #129)
+#131 := [rewrite]: #130
+#127 := (= #32 #126)
+#124 := (= #31 #123)
+#69 := (= #23 #68)
+#70 := [rewrite]: #69
+#66 := (= #22 #65)
+#67 := [rewrite]: #66
+#125 := [monotonicity #67 #70]: #124
+#128 := [monotonicity #125]: #127
+#133 := [trans #128 #131]: #132
+#62 := (iff #20 #61)
+#59 := (iff #19 #58)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#136 := [monotonicity #63 #133]: #135
+#139 := [monotonicity #136]: #138
+#142 := [monotonicity #139]: #141
+#145 := [monotonicity #142]: #144
+#148 := [quant-intro #145]: #147
+#165 := [trans #148 #163]: #164
+#122 := [asserted]: #37
+#166 := [mp #122 #165]: #161
+#192 := [mp~ #166 #182]: #161
+#233 := [mp #192 #232]: #230
+#264 := [mp #233 #263]: #261
+#749 := [mp #264 #748]: #744
+#690 := (not #744)
+#696 := (or #690 #39)
+#322 := (* -1::int 0::int)
+#407 := (mod #322 #322)
+#408 := (+ #38 #407)
+#409 := (= #408 0::int)
+#400 := (mod 0::int 0::int)
+#411 := (* -1::int #400)
+#412 := (+ #38 #411)
+#340 := (= #412 0::int)
+#413 := (<= 0::int 0::int)
+#410 := (or #413 #413)
+#414 := (not #410)
+#393 := (>= 0::int 0::int)
+#728 := (or #413 #393)
+#730 := (not #728)
+#387 := (or #730 #414)
+#517 := (ite #387 #340 #409)
+#724 := (= 0::int 0::int)
+#398 := (ite #724 #39 #517)
+#168 := (= 0::int #38)
+#399 := (ite #724 #168 #398)
+#537 := (or #690 #399)
+#539 := (iff #537 #696)
+#682 := (iff #696 #696)
+#683 := [rewrite]: #682
+#694 := (iff #399 #39)
+#1 := true
+#691 := (ite true #39 #39)
+#688 := (iff #691 #39)
+#689 := [rewrite]: #688
+#692 := (iff #399 #691)
+#698 := (iff #398 #39)
+#328 := (+ #38 #400)
+#428 := (= #328 0::int)
+#699 := (ite true #39 #428)
+#697 := (iff #699 #39)
+#701 := [rewrite]: #697
+#700 := (iff #398 #699)
+#420 := (iff #517 #428)
+#707 := (ite false #340 #428)
+#418 := (iff #707 #428)
+#419 := [rewrite]: #418
+#704 := (iff #517 #707)
+#429 := (iff #409 #428)
+#705 := (= #408 #328)
+#434 := (= #407 #400)
+#432 := (= #322 0::int)
+#433 := [rewrite]: #432
+#435 := [monotonicity #433 #433]: #434
+#706 := [monotonicity #435]: #705
+#703 := [monotonicity #706]: #429
+#709 := (iff #387 false)
+#361 := (or false false)
+#720 := (iff #361 false)
+#723 := [rewrite]: #720
+#362 := (iff #387 #361)
+#719 := (iff #414 false)
+#711 := (not true)
+#376 := (iff #711 false)
+#377 := [rewrite]: #376
+#718 := (iff #414 #711)
+#717 := (iff #410 true)
+#725 := (or true true)
+#726 := (iff #725 true)
+#386 := [rewrite]: #726
+#715 := (iff #410 #725)
+#733 := (iff #413 true)
+#734 := [rewrite]: #733
+#716 := [monotonicity #734 #734]: #715
+#712 := [trans #716 #386]: #717
+#356 := [monotonicity #712]: #718
+#721 := [trans #356 #377]: #719
+#713 := (iff #730 false)
+#374 := (iff #730 #711)
+#727 := (iff #728 true)
+#385 := (iff #728 #725)
+#729 := (iff #393 true)
+#735 := [rewrite]: #729
+#390 := [monotonicity #734 #735]: #385
+#370 := [trans #390 #386]: #727
+#375 := [monotonicity #370]: #374
+#714 := [trans #375 #377]: #713
+#722 := [monotonicity #714 #721]: #362
+#710 := [trans #722 #723]: #709
+#708 := [monotonicity #710 #703]: #704
+#421 := [trans #708 #419]: #420
+#731 := (iff #724 true)
+#732 := [rewrite]: #731
+#415 := [monotonicity #732 #421]: #700
+#702 := [trans #415 #701]: #698
+#174 := (iff #168 #39)
+#175 := [rewrite]: #174
+#693 := [monotonicity #732 #175 #702]: #692
+#695 := [trans #693 #689]: #694
+#681 := [monotonicity #695]: #539
+#684 := [trans #681 #683]: #539
+#538 := [quant-inst]: #537
+#678 := [mp #538 #684]: #696
+[unit-resolution #678 #749 #167]: false
+unsat
+d05667c302799334d71c6767e44df657452bd738 276 0
+#2 := false
+decl f4 :: (-> int int int)
+#11 := 0::int
+decl f5 :: int
+#38 := f5
+#39 := (f4 f5 0::int)
+#169 := (= f5 #39)
+#172 := (not #169)
+#40 := (= #39 f5)
+#41 := (not #40)
+#173 := (iff #41 #172)
+#170 := (iff #40 #169)
+#171 := [rewrite]: #170
+#174 := [monotonicity #171]: #173
+#168 := [asserted]: #41
+#177 := [mp #168 #174]: #172
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#741 := (pattern #29)
+#65 := -1::int
+#69 := (* -1::int #9)
+#66 := (* -1::int #8)
+#124 := (mod #66 #69)
+#252 := (+ #29 #124)
+#253 := (= #252 0::int)
+#30 := (mod #8 #9)
+#249 := (* -1::int #30)
+#250 := (+ #29 #249)
+#251 := (= #250 0::int)
+#91 := (<= #9 0::int)
+#87 := (<= #8 0::int)
+#191 := (or #87 #91)
+#192 := (not #191)
+#98 := (>= #8 0::int)
+#183 := (or #91 #98)
+#184 := (not #183)
+#198 := (or #184 #192)
+#254 := (ite #198 #251 #253)
+#248 := (= #29 0::int)
+#12 := (= #8 0::int)
+#255 := (ite #12 #248 #254)
+#247 := (= #8 #29)
+#13 := (= #9 0::int)
+#256 := (ite #13 #247 #255)
+#742 := (forall (vars (?v0 int) (?v1 int)) (:pat #741) #256)
+#259 := (forall (vars (?v0 int) (?v1 int)) #256)
+#745 := (iff #259 #742)
+#743 := (iff #256 #256)
+#744 := [refl]: #743
+#746 := [quant-intro #744]: #745
+#130 := (* -1::int #124)
+#216 := (ite #198 #30 #130)
+#219 := (ite #12 0::int #216)
+#222 := (ite #13 #8 #219)
+#225 := (= #29 #222)
+#228 := (forall (vars (?v0 int) (?v1 int)) #225)
+#260 := (iff #228 #259)
+#257 := (iff #225 #256)
+#258 := [rewrite]: #257
+#261 := [quant-intro #258]: #260
+#99 := (not #98)
+#92 := (not #91)
+#102 := (and #92 #99)
+#88 := (not #87)
+#95 := (and #88 #92)
+#105 := (or #95 #102)
+#150 := (ite #105 #30 #130)
+#153 := (ite #12 0::int #150)
+#156 := (ite #13 #8 #153)
+#159 := (= #29 #156)
+#162 := (forall (vars (?v0 int) (?v1 int)) #159)
+#229 := (iff #162 #228)
+#226 := (iff #159 #225)
+#223 := (= #156 #222)
+#220 := (= #153 #219)
+#217 := (= #150 #216)
+#201 := (iff #105 #198)
+#195 := (or #192 #184)
+#199 := (iff #195 #198)
+#200 := [rewrite]: #199
+#196 := (iff #105 #195)
+#193 := (iff #102 #184)
+#194 := [rewrite]: #193
+#181 := (iff #95 #192)
+#182 := [rewrite]: #181
+#197 := [monotonicity #182 #194]: #196
+#202 := [trans #197 #200]: #201
+#218 := [monotonicity #202]: #217
+#221 := [monotonicity #218]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [quant-intro #227]: #229
+#179 := (~ #162 #162)
+#175 := (~ #159 #159)
+#189 := [refl]: #175
+#180 := [nnf-pos #189]: #179
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#165 := (iff #37 #162)
+#59 := (and #16 #18)
+#62 := (or #17 #59)
+#135 := (ite #62 #30 #130)
+#138 := (ite #12 0::int #135)
+#141 := (ite #13 #8 #138)
+#144 := (= #29 #141)
+#147 := (forall (vars (?v0 int) (?v1 int)) #144)
+#163 := (iff #147 #162)
+#160 := (iff #144 #159)
+#157 := (= #141 #156)
+#154 := (= #138 #153)
+#151 := (= #135 #150)
+#106 := (iff #62 #105)
+#103 := (iff #59 #102)
+#100 := (iff #18 #99)
+#101 := [rewrite]: #100
+#93 := (iff #16 #92)
+#94 := [rewrite]: #93
+#104 := [monotonicity #94 #101]: #103
+#96 := (iff #17 #95)
+#89 := (iff #15 #88)
+#90 := [rewrite]: #89
+#97 := [monotonicity #90 #94]: #96
+#107 := [monotonicity #97 #104]: #106
+#152 := [monotonicity #107]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [quant-intro #161]: #163
+#148 := (iff #37 #147)
+#145 := (iff #36 #144)
+#142 := (= #35 #141)
+#139 := (= #34 #138)
+#136 := (= #33 #135)
+#133 := (= #32 #130)
+#127 := (- #124)
+#131 := (= #127 #130)
+#132 := [rewrite]: #131
+#128 := (= #32 #127)
+#125 := (= #31 #124)
+#70 := (= #23 #69)
+#71 := [rewrite]: #70
+#67 := (= #22 #66)
+#68 := [rewrite]: #67
+#126 := [monotonicity #68 #71]: #125
+#129 := [monotonicity #126]: #128
+#134 := [trans #129 #132]: #133
+#63 := (iff #20 #62)
+#60 := (iff #19 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#137 := [monotonicity #64 #134]: #136
+#140 := [monotonicity #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [quant-intro #146]: #148
+#166 := [trans #149 #164]: #165
+#123 := [asserted]: #37
+#167 := [mp #123 #166]: #162
+#190 := [mp~ #167 #180]: #162
+#231 := [mp #190 #230]: #228
+#262 := [mp #231 #261]: #259
+#747 := [mp #262 #746]: #742
+#535 := (not #742)
+#536 := (or #535 #169)
+#320 := (* -1::int 0::int)
+#405 := (* -1::int f5)
+#406 := (mod #405 #320)
+#407 := (+ #39 #406)
+#398 := (= #407 0::int)
+#409 := (mod f5 0::int)
+#410 := (* -1::int #409)
+#338 := (+ #39 #410)
+#411 := (= #338 0::int)
+#408 := (<= 0::int 0::int)
+#412 := (<= f5 0::int)
+#391 := (or #412 #408)
+#726 := (not #391)
+#728 := (>= f5 0::int)
+#385 := (or #408 #728)
+#515 := (not #385)
+#722 := (or #515 #726)
+#396 := (ite #722 #411 #398)
+#397 := (= #39 0::int)
+#729 := (= f5 0::int)
+#730 := (ite #729 #397 #396)
+#731 := (= 0::int 0::int)
+#732 := (ite #731 #169 #730)
+#537 := (or #535 #732)
+#680 := (iff #537 #536)
+#682 := (iff #536 #536)
+#676 := [rewrite]: #682
+#688 := (iff #732 #169)
+#426 := (mod #405 0::int)
+#705 := (+ #39 #426)
+#416 := (= #705 0::int)
+#700 := (ite #729 #397 #416)
+#1 := true
+#691 := (ite true #169 #700)
+#692 := (iff #691 #169)
+#693 := [rewrite]: #692
+#686 := (iff #732 #691)
+#689 := (iff #730 #700)
+#699 := (iff #396 #416)
+#419 := (ite false #411 #416)
+#413 := (iff #419 #416)
+#695 := [rewrite]: #413
+#697 := (iff #396 #419)
+#417 := (iff #398 #416)
+#702 := (= #407 #705)
+#427 := (= #406 #426)
+#703 := (= #320 0::int)
+#704 := [rewrite]: #703
+#701 := [monotonicity #704]: #427
+#706 := [monotonicity #701]: #702
+#418 := [monotonicity #706]: #417
+#433 := (iff #722 false)
+#707 := (or false false)
+#431 := (iff #707 false)
+#432 := [rewrite]: #431
+#708 := (iff #722 #707)
+#718 := (iff #726 false)
+#373 := (not true)
+#711 := (iff #373 false)
+#712 := [rewrite]: #711
+#360 := (iff #726 #373)
+#719 := (iff #391 true)
+#715 := (or #412 true)
+#354 := (iff #715 true)
+#717 := [rewrite]: #354
+#710 := (iff #391 #715)
+#723 := (iff #408 true)
+#383 := [rewrite]: #723
+#716 := [monotonicity #383]: #710
+#359 := [trans #716 #717]: #719
+#720 := [monotonicity #359]: #360
+#721 := [trans #720 #712]: #718
+#713 := (iff #515 false)
+#374 := (iff #515 #373)
+#709 := (iff #385 true)
+#388 := (or true #728)
+#725 := (iff #388 true)
+#368 := [rewrite]: #725
+#724 := (iff #385 #388)
+#384 := [monotonicity #383]: #724
+#372 := [trans #384 #368]: #709
+#375 := [monotonicity #372]: #374
+#714 := [trans #375 #712]: #713
+#430 := [monotonicity #714 #721]: #708
+#326 := [trans #430 #432]: #433
+#698 := [monotonicity #326 #418]: #697
+#696 := [trans #698 #695]: #699
+#690 := [monotonicity #696]: #689
+#727 := (iff #731 true)
+#733 := [rewrite]: #727
+#687 := [monotonicity #733 #690]: #686
+#694 := [trans #687 #693]: #688
+#681 := [monotonicity #694]: #680
+#677 := [trans #681 #676]: #680
+#679 := [quant-inst]: #537
+#683 := [mp #679 #677]: #536
+[unit-resolution #683 #747 #177]: false
+unsat
+07a66f14187da887bd1f0f4bb16d6c9a7023aeaf 298 0
+#2 := false
+#11 := 0::int
+decl f4 :: (-> int int int)
+#38 := 1::int
+#39 := (f4 0::int 1::int)
+#40 := (= #39 0::int)
+#41 := (not #40)
+#168 := [asserted]: #41
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#743 := (pattern #29)
+#65 := -1::int
+#69 := (* -1::int #9)
+#66 := (* -1::int #8)
+#124 := (mod #66 #69)
+#255 := (+ #29 #124)
+#256 := (= #255 0::int)
+#30 := (mod #8 #9)
+#252 := (* -1::int #30)
+#253 := (+ #29 #252)
+#254 := (= #253 0::int)
+#91 := (<= #9 0::int)
+#87 := (<= #8 0::int)
+#194 := (or #87 #91)
+#195 := (not #194)
+#98 := (>= #8 0::int)
+#186 := (or #91 #98)
+#187 := (not #186)
+#201 := (or #187 #195)
+#257 := (ite #201 #254 #256)
+#251 := (= #29 0::int)
+#12 := (= #8 0::int)
+#258 := (ite #12 #251 #257)
+#250 := (= #8 #29)
+#13 := (= #9 0::int)
+#259 := (ite #13 #250 #258)
+#744 := (forall (vars (?v0 int) (?v1 int)) (:pat #743) #259)
+#262 := (forall (vars (?v0 int) (?v1 int)) #259)
+#747 := (iff #262 #744)
+#745 := (iff #259 #259)
+#746 := [refl]: #745
+#748 := [quant-intro #746]: #747
+#130 := (* -1::int #124)
+#219 := (ite #201 #30 #130)
+#222 := (ite #12 0::int #219)
+#225 := (ite #13 #8 #222)
+#228 := (= #29 #225)
+#231 := (forall (vars (?v0 int) (?v1 int)) #228)
+#263 := (iff #231 #262)
+#260 := (iff #228 #259)
+#261 := [rewrite]: #260
+#264 := [quant-intro #261]: #263
+#99 := (not #98)
+#92 := (not #91)
+#102 := (and #92 #99)
+#88 := (not #87)
+#95 := (and #88 #92)
+#105 := (or #95 #102)
+#150 := (ite #105 #30 #130)
+#153 := (ite #12 0::int #150)
+#156 := (ite #13 #8 #153)
+#159 := (= #29 #156)
+#162 := (forall (vars (?v0 int) (?v1 int)) #159)
+#232 := (iff #162 #231)
+#229 := (iff #159 #228)
+#226 := (= #156 #225)
+#223 := (= #153 #222)
+#220 := (= #150 #219)
+#204 := (iff #105 #201)
+#198 := (or #195 #187)
+#202 := (iff #198 #201)
+#203 := [rewrite]: #202
+#199 := (iff #105 #198)
+#196 := (iff #102 #187)
+#197 := [rewrite]: #196
+#184 := (iff #95 #195)
+#185 := [rewrite]: #184
+#200 := [monotonicity #185 #197]: #199
+#205 := [trans #200 #203]: #204
+#221 := [monotonicity #205]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [quant-intro #230]: #232
+#182 := (~ #162 #162)
+#179 := (~ #159 #159)
+#192 := [refl]: #179
+#183 := [nnf-pos #192]: #182
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#165 := (iff #37 #162)
+#59 := (and #16 #18)
+#62 := (or #17 #59)
+#135 := (ite #62 #30 #130)
+#138 := (ite #12 0::int #135)
+#141 := (ite #13 #8 #138)
+#144 := (= #29 #141)
+#147 := (forall (vars (?v0 int) (?v1 int)) #144)
+#163 := (iff #147 #162)
+#160 := (iff #144 #159)
+#157 := (= #141 #156)
+#154 := (= #138 #153)
+#151 := (= #135 #150)
+#106 := (iff #62 #105)
+#103 := (iff #59 #102)
+#100 := (iff #18 #99)
+#101 := [rewrite]: #100
+#93 := (iff #16 #92)
+#94 := [rewrite]: #93
+#104 := [monotonicity #94 #101]: #103
+#96 := (iff #17 #95)
+#89 := (iff #15 #88)
+#90 := [rewrite]: #89
+#97 := [monotonicity #90 #94]: #96
+#107 := [monotonicity #97 #104]: #106
+#152 := [monotonicity #107]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [quant-intro #161]: #163
+#148 := (iff #37 #147)
+#145 := (iff #36 #144)
+#142 := (= #35 #141)
+#139 := (= #34 #138)
+#136 := (= #33 #135)
+#133 := (= #32 #130)
+#127 := (- #124)
+#131 := (= #127 #130)
+#132 := [rewrite]: #131
+#128 := (= #32 #127)
+#125 := (= #31 #124)
+#70 := (= #23 #69)
+#71 := [rewrite]: #70
+#67 := (= #22 #66)
+#68 := [rewrite]: #67
+#126 := [monotonicity #68 #71]: #125
+#129 := [monotonicity #126]: #128
+#134 := [trans #129 #132]: #133
+#63 := (iff #20 #62)
+#60 := (iff #19 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#137 := [monotonicity #64 #134]: #136
+#140 := [monotonicity #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [quant-intro #146]: #148
+#166 := [trans #149 #164]: #165
+#123 := [asserted]: #37
+#167 := [mp #123 #166]: #162
+#193 := [mp~ #167 #183]: #162
+#234 := [mp #193 #233]: #231
+#265 := [mp #234 #264]: #262
+#749 := [mp #265 #748]: #744
+#665 := (not #744)
+#666 := (or #665 #40)
+#323 := (* -1::int 1::int)
+#407 := (* -1::int 0::int)
+#408 := (mod #407 #323)
+#409 := (+ #39 #408)
+#400 := (= #409 0::int)
+#411 := (mod 0::int 1::int)
+#412 := (* -1::int #411)
+#413 := (+ #39 #412)
+#410 := (= #413 0::int)
+#414 := (<= 1::int 0::int)
+#393 := (<= 0::int 0::int)
+#728 := (or #393 #414)
+#730 := (not #728)
+#387 := (>= 0::int 0::int)
+#517 := (or #414 #387)
+#724 := (not #517)
+#398 := (or #724 #730)
+#399 := (ite #398 #410 #400)
+#731 := (= 0::int 0::int)
+#732 := (ite #731 #40 #399)
+#169 := (= 0::int #39)
+#733 := (= 1::int 0::int)
+#734 := (ite #733 #169 #732)
+#669 := (or #665 #734)
+#569 := (iff #669 #666)
+#572 := (iff #666 #666)
+#565 := [rewrite]: #572
+#668 := (iff #734 #40)
+#686 := (ite false #40 #40)
+#516 := (iff #686 #40)
+#518 := [rewrite]: #516
+#561 := (iff #734 #686)
+#559 := (iff #732 #40)
+#1 := true
+#673 := (ite true #40 #40)
+#674 := (iff #673 #40)
+#677 := [rewrite]: #674
+#675 := (iff #732 #673)
+#519 := (iff #399 #40)
+#680 := (iff #399 #686)
+#679 := (iff #400 #40)
+#684 := (= #409 #39)
+#415 := (+ #39 0::int)
+#698 := (= #415 #39)
+#702 := [rewrite]: #698
+#682 := (= #409 #415)
+#539 := (= #408 0::int)
+#695 := (mod 0::int -1::int)
+#537 := (= #695 0::int)
+#538 := [rewrite]: #537
+#690 := (= #408 #695)
+#689 := (= #323 -1::int)
+#694 := [rewrite]: #689
+#420 := (= #407 0::int)
+#421 := [rewrite]: #420
+#696 := [monotonicity #421 #694]: #690
+#681 := [trans #696 #538]: #539
+#683 := [monotonicity #681]: #682
+#678 := [trans #683 #702]: #684
+#685 := [monotonicity #678]: #679
+#693 := (iff #410 #40)
+#691 := (= #413 #39)
+#697 := (= #413 #415)
+#699 := (= #412 0::int)
+#418 := (= #412 #407)
+#704 := (= #411 0::int)
+#708 := [rewrite]: #704
+#419 := [monotonicity #708]: #418
+#700 := [trans #419 #421]: #699
+#701 := [monotonicity #700]: #697
+#692 := [trans #701 #702]: #691
+#688 := [monotonicity #692]: #693
+#703 := (iff #398 false)
+#329 := (or false false)
+#428 := (iff #329 false)
+#429 := [rewrite]: #428
+#705 := (iff #398 #329)
+#434 := (iff #730 false)
+#714 := (not true)
+#717 := (iff #714 false)
+#712 := [rewrite]: #717
+#432 := (iff #730 #714)
+#709 := (iff #728 true)
+#361 := (or true false)
+#720 := (iff #361 true)
+#723 := [rewrite]: #720
+#362 := (iff #728 #361)
+#390 := (iff #414 false)
+#726 := [rewrite]: #390
+#719 := (iff #393 true)
+#721 := [rewrite]: #719
+#722 := [monotonicity #721 #726]: #362
+#710 := [trans #722 #723]: #709
+#433 := [monotonicity #710]: #432
+#435 := [trans #433 #712]: #434
+#718 := (iff #724 false)
+#715 := (iff #724 #714)
+#377 := (iff #517 true)
+#370 := (or false true)
+#375 := (iff #370 true)
+#376 := [rewrite]: #375
+#711 := (iff #517 #370)
+#386 := (iff #387 true)
+#727 := [rewrite]: #386
+#374 := [monotonicity #726 #727]: #711
+#713 := [trans #374 #376]: #377
+#716 := [monotonicity #713]: #715
+#356 := [trans #716 #712]: #718
+#706 := [monotonicity #356 #435]: #705
+#707 := [trans #706 #429]: #703
+#687 := [monotonicity #707 #688 #685]: #680
+#672 := [trans #687 #518]: #519
+#725 := (iff #731 true)
+#385 := [rewrite]: #725
+#676 := [monotonicity #385 #672]: #675
+#560 := [trans #676 #677]: #559
+#175 := (iff #169 #40)
+#176 := [rewrite]: #175
+#729 := (iff #733 false)
+#735 := [rewrite]: #729
+#520 := [monotonicity #735 #176 #560]: #561
+#570 := [trans #520 #518]: #668
+#571 := [monotonicity #570]: #569
+#573 := [trans #571 #565]: #569
+#554 := [quant-inst]: #669
+#574 := [mp #554 #573]: #666
+[unit-resolution #574 #749 #168]: false
+unsat
+ed1abab981b05d680a1c92a497bf3305ff9e1f16 296 0
+#2 := false
+#11 := 0::int
+decl f4 :: (-> int int int)
+#38 := 1::int
+#39 := (f4 1::int 1::int)
+#40 := (= #39 0::int)
+#41 := (not #40)
+#168 := [asserted]: #41
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#743 := (pattern #29)
+#65 := -1::int
+#69 := (* -1::int #9)
+#66 := (* -1::int #8)
+#124 := (mod #66 #69)
+#255 := (+ #29 #124)
+#256 := (= #255 0::int)
+#30 := (mod #8 #9)
+#252 := (* -1::int #30)
+#253 := (+ #29 #252)
+#254 := (= #253 0::int)
+#91 := (<= #9 0::int)
+#87 := (<= #8 0::int)
+#194 := (or #87 #91)
+#195 := (not #194)
+#98 := (>= #8 0::int)
+#186 := (or #91 #98)
+#187 := (not #186)
+#201 := (or #187 #195)
+#257 := (ite #201 #254 #256)
+#251 := (= #29 0::int)
+#12 := (= #8 0::int)
+#258 := (ite #12 #251 #257)
+#250 := (= #8 #29)
+#13 := (= #9 0::int)
+#259 := (ite #13 #250 #258)
+#744 := (forall (vars (?v0 int) (?v1 int)) (:pat #743) #259)
+#262 := (forall (vars (?v0 int) (?v1 int)) #259)
+#747 := (iff #262 #744)
+#745 := (iff #259 #259)
+#746 := [refl]: #745
+#748 := [quant-intro #746]: #747
+#130 := (* -1::int #124)
+#219 := (ite #201 #30 #130)
+#222 := (ite #12 0::int #219)
+#225 := (ite #13 #8 #222)
+#228 := (= #29 #225)
+#231 := (forall (vars (?v0 int) (?v1 int)) #228)
+#263 := (iff #231 #262)
+#260 := (iff #228 #259)
+#261 := [rewrite]: #260
+#264 := [quant-intro #261]: #263
+#99 := (not #98)
+#92 := (not #91)
+#102 := (and #92 #99)
+#88 := (not #87)
+#95 := (and #88 #92)
+#105 := (or #95 #102)
+#150 := (ite #105 #30 #130)
+#153 := (ite #12 0::int #150)
+#156 := (ite #13 #8 #153)
+#159 := (= #29 #156)
+#162 := (forall (vars (?v0 int) (?v1 int)) #159)
+#232 := (iff #162 #231)
+#229 := (iff #159 #228)
+#226 := (= #156 #225)
+#223 := (= #153 #222)
+#220 := (= #150 #219)
+#204 := (iff #105 #201)
+#198 := (or #195 #187)
+#202 := (iff #198 #201)
+#203 := [rewrite]: #202
+#199 := (iff #105 #198)
+#196 := (iff #102 #187)
+#197 := [rewrite]: #196
+#184 := (iff #95 #195)
+#185 := [rewrite]: #184
+#200 := [monotonicity #185 #197]: #199
+#205 := [trans #200 #203]: #204
+#221 := [monotonicity #205]: #220
+#224 := [monotonicity #221]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [quant-intro #230]: #232
+#182 := (~ #162 #162)
+#179 := (~ #159 #159)
+#192 := [refl]: #179
+#183 := [nnf-pos #192]: #182
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#165 := (iff #37 #162)
+#59 := (and #16 #18)
+#62 := (or #17 #59)
+#135 := (ite #62 #30 #130)
+#138 := (ite #12 0::int #135)
+#141 := (ite #13 #8 #138)
+#144 := (= #29 #141)
+#147 := (forall (vars (?v0 int) (?v1 int)) #144)
+#163 := (iff #147 #162)
+#160 := (iff #144 #159)
+#157 := (= #141 #156)
+#154 := (= #138 #153)
+#151 := (= #135 #150)
+#106 := (iff #62 #105)
+#103 := (iff #59 #102)
+#100 := (iff #18 #99)
+#101 := [rewrite]: #100
+#93 := (iff #16 #92)
+#94 := [rewrite]: #93
+#104 := [monotonicity #94 #101]: #103
+#96 := (iff #17 #95)
+#89 := (iff #15 #88)
+#90 := [rewrite]: #89
+#97 := [monotonicity #90 #94]: #96
+#107 := [monotonicity #97 #104]: #106
+#152 := [monotonicity #107]: #151
+#155 := [monotonicity #152]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [quant-intro #161]: #163
+#148 := (iff #37 #147)
+#145 := (iff #36 #144)
+#142 := (= #35 #141)
+#139 := (= #34 #138)
+#136 := (= #33 #135)
+#133 := (= #32 #130)
+#127 := (- #124)
+#131 := (= #127 #130)
+#132 := [rewrite]: #131
+#128 := (= #32 #127)
+#125 := (= #31 #124)
+#70 := (= #23 #69)
+#71 := [rewrite]: #70
+#67 := (= #22 #66)
+#68 := [rewrite]: #67
+#126 := [monotonicity #68 #71]: #125
+#129 := [monotonicity #126]: #128
+#134 := [trans #129 #132]: #133
+#63 := (iff #20 #62)
+#60 := (iff #19 #59)
+#61 := [rewrite]: #60
+#64 := [monotonicity #61]: #63
+#137 := [monotonicity #64 #134]: #136
+#140 := [monotonicity #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [quant-intro #146]: #148
+#166 := [trans #149 #164]: #165
+#123 := [asserted]: #37
+#167 := [mp #123 #166]: #162
+#193 := [mp~ #167 #183]: #162
+#234 := [mp #193 #233]: #231
+#265 := [mp #234 #264]: #262
+#749 := [mp #265 #748]: #744
+#666 := (not #744)
+#669 := (or #666 #40)
+#323 := (* -1::int 1::int)
+#407 := (mod #323 #323)
+#408 := (+ #39 #407)
+#409 := (= #408 0::int)
+#400 := (mod 1::int 1::int)
+#411 := (* -1::int #400)
+#412 := (+ #39 #411)
+#413 := (= #412 0::int)
+#410 := (<= 1::int 0::int)
+#414 := (or #410 #410)
+#393 := (not #414)
+#728 := (>= 1::int 0::int)
+#730 := (or #410 #728)
+#387 := (not #730)
+#517 := (or #387 #393)
+#724 := (ite #517 #413 #409)
+#398 := (= 1::int 0::int)
+#399 := (ite #398 #40 #724)
+#731 := (= 1::int #39)
+#732 := (ite #398 #731 #399)
+#554 := (or #666 #732)
+#571 := (iff #554 #669)
+#565 := (iff #669 #669)
+#573 := [rewrite]: #565
+#570 := (iff #732 #40)
+#735 := (= #39 1::int)
+#559 := (ite false #735 #40)
+#520 := (iff #559 #40)
+#668 := [rewrite]: #520
+#560 := (iff #732 #559)
+#674 := (iff #399 #40)
+#519 := (ite false #40 #40)
+#675 := (iff #519 #40)
+#676 := [rewrite]: #675
+#672 := (iff #399 #519)
+#516 := (iff #724 #40)
+#1 := true
+#679 := (ite true #40 #40)
+#680 := (iff #679 #40)
+#687 := [rewrite]: #680
+#685 := (iff #724 #679)
+#684 := (iff #409 #40)
+#682 := (= #408 #39)
+#699 := (+ #39 0::int)
+#697 := (= #699 #39)
+#701 := [rewrite]: #697
+#539 := (= #408 #699)
+#537 := (= #407 0::int)
+#689 := (mod -1::int -1::int)
+#690 := (= #689 0::int)
+#696 := [rewrite]: #690
+#694 := (= #407 #689)
+#693 := (= #323 -1::int)
+#688 := [rewrite]: #693
+#695 := [monotonicity #688 #688]: #694
+#538 := [trans #695 #696]: #537
+#681 := [monotonicity #538]: #539
+#683 := [trans #681 #701]: #682
+#678 := [monotonicity #683]: #684
+#691 := (iff #413 #40)
+#698 := (= #412 #39)
+#700 := (= #412 #699)
+#420 := (= #411 0::int)
+#707 := (* -1::int 0::int)
+#418 := (= #707 0::int)
+#419 := [rewrite]: #418
+#704 := (= #411 #707)
+#429 := (= #400 0::int)
+#703 := [rewrite]: #429
+#708 := [monotonicity #703]: #704
+#421 := [trans #708 #419]: #420
+#415 := [monotonicity #421]: #700
+#702 := [trans #415 #701]: #698
+#692 := [monotonicity #702]: #691
+#706 := (iff #517 true)
+#727 := (or false true)
+#374 := (iff #727 true)
+#375 := [rewrite]: #374
+#329 := (iff #517 #727)
+#434 := (iff #393 true)
+#723 := (not false)
+#432 := (iff #723 true)
+#433 := [rewrite]: #432
+#709 := (iff #393 #723)
+#722 := (iff #414 false)
+#356 := (or false false)
+#361 := (iff #356 false)
+#362 := [rewrite]: #361
+#719 := (iff #414 #356)
+#385 := (iff #410 false)
+#390 := [rewrite]: #385
+#721 := [monotonicity #390 #390]: #719
+#720 := [trans #721 #362]: #722
+#710 := [monotonicity #720]: #709
+#435 := [trans #710 #433]: #434
+#712 := (iff #387 false)
+#713 := (not true)
+#716 := (iff #713 false)
+#717 := [rewrite]: #716
+#714 := (iff #387 #713)
+#376 := (iff #730 true)
+#370 := (iff #730 #727)
+#726 := (iff #728 true)
+#386 := [rewrite]: #726
+#711 := [monotonicity #390 #386]: #370
+#377 := [trans #711 #375]: #376
+#715 := [monotonicity #377]: #714
+#718 := [trans #715 #717]: #712
+#705 := [monotonicity #718 #435]: #329
+#428 := [trans #705 #375]: #706
+#686 := [monotonicity #428 #692 #678]: #685
+#518 := [trans #686 #687]: #516
+#733 := (iff #398 false)
+#734 := [rewrite]: #733
+#673 := [monotonicity #734 #518]: #672
+#677 := [trans #673 #676]: #674
+#729 := (iff #731 #735)
+#725 := [rewrite]: #729
+#561 := [monotonicity #734 #725 #677]: #560
+#665 := [trans #561 #668]: #570
+#572 := [monotonicity #665]: #571
+#574 := [trans #572 #573]: #571
+#569 := [quant-inst]: #554
+#575 := [mp #569 #574]: #669
+[unit-resolution #575 #749 #168]: false
+unsat
+52cf99958a1402707eac2a505ecb8d6adc72de1a 307 0
+#2 := false
+#11 := 0::int
+decl f4 :: (-> int int int)
+#39 := 1::int
+#38 := 3::int
+#40 := (f4 3::int 1::int)
+#41 := (= #40 0::int)
+#42 := (not #41)
+#169 := [asserted]: #42
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#744 := (pattern #29)
+#66 := -1::int
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#125 := (mod #67 #70)
+#256 := (+ #29 #125)
+#257 := (= #256 0::int)
+#30 := (mod #8 #9)
+#253 := (* -1::int #30)
+#254 := (+ #29 #253)
+#255 := (= #254 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#195 := (or #88 #92)
+#196 := (not #195)
+#99 := (>= #8 0::int)
+#187 := (or #92 #99)
+#188 := (not #187)
+#202 := (or #188 #196)
+#258 := (ite #202 #255 #257)
+#252 := (= #29 0::int)
+#12 := (= #8 0::int)
+#259 := (ite #12 #252 #258)
+#251 := (= #8 #29)
+#13 := (= #9 0::int)
+#260 := (ite #13 #251 #259)
+#745 := (forall (vars (?v0 int) (?v1 int)) (:pat #744) #260)
+#263 := (forall (vars (?v0 int) (?v1 int)) #260)
+#748 := (iff #263 #745)
+#746 := (iff #260 #260)
+#747 := [refl]: #746
+#749 := [quant-intro #747]: #748
+#131 := (* -1::int #125)
+#220 := (ite #202 #30 #131)
+#223 := (ite #12 0::int #220)
+#226 := (ite #13 #8 #223)
+#229 := (= #29 #226)
+#232 := (forall (vars (?v0 int) (?v1 int)) #229)
+#264 := (iff #232 #263)
+#261 := (iff #229 #260)
+#262 := [rewrite]: #261
+#265 := [quant-intro #262]: #264
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#151 := (ite #106 #30 #131)
+#154 := (ite #12 0::int #151)
+#157 := (ite #13 #8 #154)
+#160 := (= #29 #157)
+#163 := (forall (vars (?v0 int) (?v1 int)) #160)
+#233 := (iff #163 #232)
+#230 := (iff #160 #229)
+#227 := (= #157 #226)
+#224 := (= #154 #223)
+#221 := (= #151 #220)
+#205 := (iff #106 #202)
+#199 := (or #196 #188)
+#203 := (iff #199 #202)
+#204 := [rewrite]: #203
+#200 := (iff #106 #199)
+#197 := (iff #103 #188)
+#198 := [rewrite]: #197
+#185 := (iff #96 #196)
+#186 := [rewrite]: #185
+#201 := [monotonicity #186 #198]: #200
+#206 := [trans #201 #204]: #205
+#222 := [monotonicity #206]: #221
+#225 := [monotonicity #222]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [quant-intro #231]: #233
+#183 := (~ #163 #163)
+#180 := (~ #160 #160)
+#193 := [refl]: #180
+#184 := [nnf-pos #193]: #183
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#166 := (iff #37 #163)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#136 := (ite #63 #30 #131)
+#139 := (ite #12 0::int #136)
+#142 := (ite #13 #8 #139)
+#145 := (= #29 #142)
+#148 := (forall (vars (?v0 int) (?v1 int)) #145)
+#164 := (iff #148 #163)
+#161 := (iff #145 #160)
+#158 := (= #142 #157)
+#155 := (= #139 #154)
+#152 := (= #136 #151)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#153 := [monotonicity #108]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [quant-intro #162]: #164
+#149 := (iff #37 #148)
+#146 := (iff #36 #145)
+#143 := (= #35 #142)
+#140 := (= #34 #139)
+#137 := (= #33 #136)
+#134 := (= #32 #131)
+#128 := (- #125)
+#132 := (= #128 #131)
+#133 := [rewrite]: #132
+#129 := (= #32 #128)
+#126 := (= #31 #125)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#127 := [monotonicity #69 #72]: #126
+#130 := [monotonicity #127]: #129
+#135 := [trans #130 #133]: #134
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#138 := [monotonicity #65 #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [quant-intro #147]: #149
+#167 := [trans #150 #165]: #166
+#124 := [asserted]: #37
+#168 := [mp #124 #167]: #163
+#194 := [mp~ #168 #184]: #163
+#235 := [mp #194 #234]: #232
+#266 := [mp #235 #265]: #263
+#750 := [mp #266 #749]: #745
+#577 := (not #745)
+#578 := (or #577 #41)
+#324 := (* -1::int 1::int)
+#408 := (* -1::int 3::int)
+#409 := (mod #408 #324)
+#410 := (+ #40 #409)
+#401 := (= #410 0::int)
+#412 := (mod 3::int 1::int)
+#413 := (* -1::int #412)
+#414 := (+ #40 #413)
+#411 := (= #414 0::int)
+#415 := (<= 1::int 0::int)
+#394 := (<= 3::int 0::int)
+#729 := (or #394 #415)
+#731 := (not #729)
+#388 := (>= 3::int 0::int)
+#518 := (or #415 #388)
+#725 := (not #518)
+#399 := (or #725 #731)
+#400 := (ite #399 #411 #401)
+#732 := (= 3::int 0::int)
+#733 := (ite #732 #41 #400)
+#734 := (= 3::int #40)
+#735 := (= 1::int 0::int)
+#730 := (ite #735 #734 #733)
+#671 := (or #577 #730)
+#672 := (iff #671 #578)
+#661 := (iff #578 #578)
+#653 := [rewrite]: #661
+#575 := (iff #730 #41)
+#391 := (= #40 3::int)
+#570 := (ite false #391 #41)
+#566 := (iff #570 #41)
+#574 := [rewrite]: #566
+#572 := (iff #730 #570)
+#670 := (iff #733 #41)
+#521 := (ite false #41 #41)
+#666 := (iff #521 #41)
+#667 := [rewrite]: #666
+#669 := (iff #733 #521)
+#561 := (iff #400 #41)
+#1 := true
+#676 := (ite true #41 #41)
+#678 := (iff #676 #41)
+#560 := [rewrite]: #678
+#677 := (iff #400 #676)
+#673 := (iff #401 #41)
+#519 := (= #410 #40)
+#692 := (+ #40 0::int)
+#689 := (= #692 #40)
+#690 := [rewrite]: #689
+#688 := (= #410 #692)
+#687 := (= #409 0::int)
+#538 := -3::int
+#684 := (mod -3::int -1::int)
+#680 := (= #684 0::int)
+#686 := [rewrite]: #680
+#685 := (= #409 #684)
+#682 := (= #324 -1::int)
+#683 := [rewrite]: #682
+#539 := (= #408 -3::int)
+#540 := [rewrite]: #539
+#679 := [monotonicity #540 #683]: #685
+#681 := [trans #679 #686]: #687
+#517 := [monotonicity #681]: #688
+#520 := [trans #517 #690]: #519
+#674 := [monotonicity #520]: #673
+#691 := (iff #411 #41)
+#695 := (= #414 #40)
+#693 := (= #414 #692)
+#699 := (= #413 0::int)
+#700 := (* -1::int 0::int)
+#698 := (= #700 0::int)
+#702 := [rewrite]: #698
+#701 := (= #413 #700)
+#421 := (= #412 0::int)
+#422 := [rewrite]: #421
+#416 := [monotonicity #422]: #701
+#703 := [trans #416 #702]: #699
+#694 := [monotonicity #703]: #693
+#696 := [trans #694 #690]: #695
+#697 := [monotonicity #696]: #691
+#419 := (iff #399 true)
+#377 := (or false true)
+#715 := (iff #377 true)
+#716 := [rewrite]: #715
+#705 := (iff #399 #377)
+#704 := (iff #731 true)
+#330 := (not false)
+#429 := (iff #330 true)
+#430 := [rewrite]: #429
+#706 := (iff #731 #330)
+#435 := (iff #729 false)
+#724 := (or false false)
+#433 := (iff #724 false)
+#434 := [rewrite]: #433
+#710 := (iff #729 #724)
+#371 := (iff #415 false)
+#712 := [rewrite]: #371
+#723 := (iff #394 false)
+#721 := [rewrite]: #723
+#711 := [monotonicity #721 #712]: #710
+#436 := [trans #711 #434]: #435
+#707 := [monotonicity #436]: #706
+#708 := [trans #707 #430]: #704
+#362 := (iff #725 false)
+#713 := (not true)
+#720 := (iff #713 false)
+#722 := [rewrite]: #720
+#719 := (iff #725 #713)
+#717 := (iff #518 true)
+#378 := (iff #518 #377)
+#375 := (iff #388 true)
+#376 := [rewrite]: #375
+#714 := [monotonicity #712 #376]: #378
+#718 := [trans #714 #716]: #717
+#357 := [monotonicity #718]: #719
+#363 := [trans #357 #722]: #362
+#709 := [monotonicity #363 #708]: #705
+#420 := [trans #709 #716]: #419
+#675 := [monotonicity #420 #697 #674]: #677
+#562 := [trans #675 #560]: #561
+#387 := (iff #732 false)
+#728 := [rewrite]: #387
+#571 := [monotonicity #728 #562]: #669
+#555 := [trans #571 #667]: #670
+#386 := (iff #734 #391)
+#727 := [rewrite]: #386
+#736 := (iff #735 false)
+#726 := [rewrite]: #736
+#573 := [monotonicity #726 #727 #555]: #572
+#576 := [trans #573 #574]: #575
+#659 := [monotonicity #576]: #672
+#650 := [trans #659 #653]: #672
+#668 := [quant-inst]: #671
+#652 := [mp #668 #650]: #578
+[unit-resolution #652 #750 #169]: false
+unsat
+6d75bf2e8df3400e173e94c70d533cd85e2830a4 308 0
+#2 := false
+#11 := 0::int
+decl f5 :: int
+#38 := f5
+#732 := (= f5 0::int)
+#573 := (not #732)
+#394 := (<= f5 0::int)
+#720 := (not #394)
+#388 := (>= f5 0::int)
+#377 := (not #388)
+#688 := (or #377 #720 #732)
+#575 := (not #688)
+#66 := -1::int
+#408 := (* -1::int f5)
+#700 := (mod #408 -1::int)
+decl f4 :: (-> int int int)
+#39 := 1::int
+#40 := (f4 f5 1::int)
+#698 := (+ #40 #700)
+#703 := (= #698 0::int)
+#41 := (= #40 0::int)
+#520 := (ite #688 #41 #703)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#744 := (pattern #29)
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#125 := (mod #67 #70)
+#256 := (+ #29 #125)
+#257 := (= #256 0::int)
+#30 := (mod #8 #9)
+#253 := (* -1::int #30)
+#254 := (+ #29 #253)
+#255 := (= #254 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#195 := (or #88 #92)
+#196 := (not #195)
+#99 := (>= #8 0::int)
+#187 := (or #92 #99)
+#188 := (not #187)
+#202 := (or #188 #196)
+#258 := (ite #202 #255 #257)
+#252 := (= #29 0::int)
+#12 := (= #8 0::int)
+#259 := (ite #12 #252 #258)
+#251 := (= #8 #29)
+#13 := (= #9 0::int)
+#260 := (ite #13 #251 #259)
+#745 := (forall (vars (?v0 int) (?v1 int)) (:pat #744) #260)
+#263 := (forall (vars (?v0 int) (?v1 int)) #260)
+#748 := (iff #263 #745)
+#746 := (iff #260 #260)
+#747 := [refl]: #746
+#749 := [quant-intro #747]: #748
+#131 := (* -1::int #125)
+#220 := (ite #202 #30 #131)
+#223 := (ite #12 0::int #220)
+#226 := (ite #13 #8 #223)
+#229 := (= #29 #226)
+#232 := (forall (vars (?v0 int) (?v1 int)) #229)
+#264 := (iff #232 #263)
+#261 := (iff #229 #260)
+#262 := [rewrite]: #261
+#265 := [quant-intro #262]: #264
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#151 := (ite #106 #30 #131)
+#154 := (ite #12 0::int #151)
+#157 := (ite #13 #8 #154)
+#160 := (= #29 #157)
+#163 := (forall (vars (?v0 int) (?v1 int)) #160)
+#233 := (iff #163 #232)
+#230 := (iff #160 #229)
+#227 := (= #157 #226)
+#224 := (= #154 #223)
+#221 := (= #151 #220)
+#205 := (iff #106 #202)
+#199 := (or #196 #188)
+#203 := (iff #199 #202)
+#204 := [rewrite]: #203
+#200 := (iff #106 #199)
+#197 := (iff #103 #188)
+#198 := [rewrite]: #197
+#185 := (iff #96 #196)
+#186 := [rewrite]: #185
+#201 := [monotonicity #186 #198]: #200
+#206 := [trans #201 #204]: #205
+#222 := [monotonicity #206]: #221
+#225 := [monotonicity #222]: #224
+#228 := [monotonicity #225]: #227
+#231 := [monotonicity #228]: #230
+#234 := [quant-intro #231]: #233
+#183 := (~ #163 #163)
+#180 := (~ #160 #160)
+#193 := [refl]: #180
+#184 := [nnf-pos #193]: #183
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#166 := (iff #37 #163)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#136 := (ite #63 #30 #131)
+#139 := (ite #12 0::int #136)
+#142 := (ite #13 #8 #139)
+#145 := (= #29 #142)
+#148 := (forall (vars (?v0 int) (?v1 int)) #145)
+#164 := (iff #148 #163)
+#161 := (iff #145 #160)
+#158 := (= #142 #157)
+#155 := (= #139 #154)
+#152 := (= #136 #151)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#153 := [monotonicity #108]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [quant-intro #162]: #164
+#149 := (iff #37 #148)
+#146 := (iff #36 #145)
+#143 := (= #35 #142)
+#140 := (= #34 #139)
+#137 := (= #33 #136)
+#134 := (= #32 #131)
+#128 := (- #125)
+#132 := (= #128 #131)
+#133 := [rewrite]: #132
+#129 := (= #32 #128)
+#126 := (= #31 #125)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#127 := [monotonicity #69 #72]: #126
+#130 := [monotonicity #127]: #129
+#135 := [trans #130 #133]: #134
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#138 := [monotonicity #65 #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [quant-intro #147]: #149
+#167 := [trans #150 #165]: #166
+#124 := [asserted]: #37
+#168 := [mp #124 #167]: #163
+#194 := [mp~ #168 #184]: #163
+#235 := [mp #194 #234]: #232
+#266 := [mp #235 #265]: #263
+#750 := [mp #266 #749]: #745
+#675 := (not #745)
+#678 := (or #675 #520)
+#324 := (* -1::int 1::int)
+#409 := (mod #408 #324)
+#410 := (+ #40 #409)
+#401 := (= #410 0::int)
+#412 := (mod f5 1::int)
+#413 := (* -1::int #412)
+#414 := (+ #40 #413)
+#411 := (= #414 0::int)
+#415 := (<= 1::int 0::int)
+#729 := (or #394 #415)
+#731 := (not #729)
+#518 := (or #415 #388)
+#725 := (not #518)
+#399 := (or #725 #731)
+#400 := (ite #399 #411 #401)
+#733 := (ite #732 #41 #400)
+#734 := (= f5 #40)
+#735 := (= 1::int 0::int)
+#730 := (ite #735 #734 #733)
+#560 := (or #675 #730)
+#562 := (iff #560 #678)
+#669 := (iff #678 #678)
+#571 := [rewrite]: #669
+#676 := (iff #730 #520)
+#363 := (or #377 #720)
+#697 := (or #363 #732)
+#538 := (ite #697 #41 #703)
+#673 := (iff #538 #520)
+#517 := (iff #697 #688)
+#519 := [rewrite]: #517
+#674 := [monotonicity #519]: #673
+#687 := (iff #730 #538)
+#684 := (ite false #734 #538)
+#680 := (iff #684 #538)
+#686 := [rewrite]: #680
+#685 := (iff #730 #684)
+#682 := (iff #733 #538)
+#694 := (ite #363 #41 #703)
+#695 := (ite #732 #41 #694)
+#539 := (iff #695 #538)
+#540 := [rewrite]: #539
+#696 := (iff #733 #695)
+#689 := (iff #400 #694)
+#692 := (iff #401 #703)
+#702 := (= #410 #698)
+#701 := (= #409 #700)
+#421 := (= #324 -1::int)
+#422 := [rewrite]: #421
+#416 := [monotonicity #422]: #701
+#699 := [monotonicity #416]: #702
+#693 := [monotonicity #699]: #692
+#419 := (iff #411 #41)
+#705 := (= #414 #40)
+#707 := (+ #40 0::int)
+#704 := (= #707 #40)
+#708 := [rewrite]: #704
+#429 := (= #414 #707)
+#330 := (= #413 0::int)
+#711 := (* -1::int 0::int)
+#435 := (= #711 0::int)
+#436 := [rewrite]: #435
+#433 := (= #413 #711)
+#724 := (= #412 0::int)
+#710 := [rewrite]: #724
+#434 := [monotonicity #710]: #433
+#706 := [trans #434 #436]: #330
+#430 := [monotonicity #706]: #429
+#709 := [trans #430 #708]: #705
+#420 := [monotonicity #709]: #419
+#723 := (iff #399 #363)
+#722 := (iff #731 #720)
+#719 := (iff #729 #394)
+#715 := (or #394 false)
+#718 := (iff #715 #394)
+#713 := [rewrite]: #718
+#716 := (iff #729 #715)
+#386 := (iff #415 false)
+#391 := [rewrite]: #386
+#717 := [monotonicity #391]: #716
+#357 := [trans #717 #713]: #719
+#362 := [monotonicity #357]: #722
+#378 := (iff #725 #377)
+#375 := (iff #518 #388)
+#727 := (or false #388)
+#371 := (iff #727 #388)
+#712 := [rewrite]: #371
+#387 := (iff #518 #727)
+#728 := [monotonicity #391]: #387
+#376 := [trans #728 #712]: #375
+#714 := [monotonicity #376]: #378
+#721 := [monotonicity #714 #362]: #723
+#690 := [monotonicity #721 #420 #693]: #689
+#691 := [monotonicity #690]: #696
+#683 := [trans #691 #540]: #682
+#736 := (iff #735 false)
+#726 := [rewrite]: #736
+#679 := [monotonicity #726 #683]: #685
+#681 := [trans #679 #686]: #687
+#677 := [trans #681 #674]: #676
+#521 := [monotonicity #677]: #562
+#666 := [trans #521 #571]: #562
+#561 := [quant-inst]: #560
+#667 := [mp #561 #666]: #678
+#660 := [unit-resolution #667 #750]: #520
+#668 := (not #520)
+#665 := (or #668 #575)
+#42 := (not #41)
+#169 := [asserted]: #42
+#672 := (or #668 #575 #41)
+#659 := [def-axiom]: #672
+#654 := [unit-resolution #659 #169]: #665
+#655 := [unit-resolution #654 #660]: #575
+#566 := (or #688 #573)
+#574 := [def-axiom]: #566
+#656 := [unit-resolution #574 #655]: #573
+#670 := (or #688 #388)
+#555 := [def-axiom]: #670
+#657 := [unit-resolution #555 #655]: #388
+#570 := (or #688 #394)
+#572 := [def-axiom]: #570
+#651 := [unit-resolution #572 #655]: #394
+#658 := (or #732 #720 #377)
+#642 := [th-lemma]: #658
+[unit-resolution #642 #651 #657 #656]: false
+unsat
+a09ca425a49bbf59a7db8aba4b01dbd7473e9c09 317 0
+#2 := false
+#11 := 0::int
+decl f4 :: (-> int int int)
+#66 := -1::int
+#172 := (f4 0::int -1::int)
+#175 := (= #172 0::int)
+#188 := (not #175)
+#38 := 1::int
+#39 := (- 1::int)
+#40 := (f4 0::int #39)
+#41 := (= #40 0::int)
+#42 := (not #41)
+#191 := (iff #42 #188)
+#178 := (= 0::int #172)
+#183 := (not #178)
+#189 := (iff #183 #188)
+#186 := (iff #178 #175)
+#187 := [rewrite]: #186
+#190 := [monotonicity #187]: #189
+#184 := (iff #42 #183)
+#181 := (iff #41 #178)
+#179 := (iff #175 #178)
+#180 := [rewrite]: #179
+#176 := (iff #41 #175)
+#173 := (= #40 #172)
+#170 := (= #39 -1::int)
+#171 := [rewrite]: #170
+#174 := [monotonicity #171]: #173
+#177 := [monotonicity #174]: #176
+#182 := [trans #177 #180]: #181
+#185 := [monotonicity #182]: #184
+#192 := [trans #185 #190]: #191
+#169 := [asserted]: #42
+#193 := [mp #169 #192]: #188
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#758 := (pattern #29)
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#125 := (mod #67 #70)
+#270 := (+ #29 #125)
+#271 := (= #270 0::int)
+#30 := (mod #8 #9)
+#267 := (* -1::int #30)
+#268 := (+ #29 #267)
+#269 := (= #268 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#209 := (or #88 #92)
+#210 := (not #209)
+#99 := (>= #8 0::int)
+#201 := (or #92 #99)
+#202 := (not #201)
+#216 := (or #202 #210)
+#272 := (ite #216 #269 #271)
+#266 := (= #29 0::int)
+#12 := (= #8 0::int)
+#273 := (ite #12 #266 #272)
+#265 := (= #8 #29)
+#13 := (= #9 0::int)
+#274 := (ite #13 #265 #273)
+#759 := (forall (vars (?v0 int) (?v1 int)) (:pat #758) #274)
+#277 := (forall (vars (?v0 int) (?v1 int)) #274)
+#762 := (iff #277 #759)
+#760 := (iff #274 #274)
+#761 := [refl]: #760
+#763 := [quant-intro #761]: #762
+#131 := (* -1::int #125)
+#234 := (ite #216 #30 #131)
+#237 := (ite #12 0::int #234)
+#240 := (ite #13 #8 #237)
+#243 := (= #29 #240)
+#246 := (forall (vars (?v0 int) (?v1 int)) #243)
+#278 := (iff #246 #277)
+#275 := (iff #243 #274)
+#276 := [rewrite]: #275
+#279 := [quant-intro #276]: #278
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#151 := (ite #106 #30 #131)
+#154 := (ite #12 0::int #151)
+#157 := (ite #13 #8 #154)
+#160 := (= #29 #157)
+#163 := (forall (vars (?v0 int) (?v1 int)) #160)
+#247 := (iff #163 #246)
+#244 := (iff #160 #243)
+#241 := (= #157 #240)
+#238 := (= #154 #237)
+#235 := (= #151 #234)
+#219 := (iff #106 #216)
+#213 := (or #210 #202)
+#217 := (iff #213 #216)
+#218 := [rewrite]: #217
+#214 := (iff #106 #213)
+#211 := (iff #103 #202)
+#212 := [rewrite]: #211
+#199 := (iff #96 #210)
+#200 := [rewrite]: #199
+#215 := [monotonicity #200 #212]: #214
+#220 := [trans #215 #218]: #219
+#236 := [monotonicity #220]: #235
+#239 := [monotonicity #236]: #238
+#242 := [monotonicity #239]: #241
+#245 := [monotonicity #242]: #244
+#248 := [quant-intro #245]: #247
+#197 := (~ #163 #163)
+#194 := (~ #160 #160)
+#207 := [refl]: #194
+#198 := [nnf-pos #207]: #197
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#166 := (iff #37 #163)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#136 := (ite #63 #30 #131)
+#139 := (ite #12 0::int #136)
+#142 := (ite #13 #8 #139)
+#145 := (= #29 #142)
+#148 := (forall (vars (?v0 int) (?v1 int)) #145)
+#164 := (iff #148 #163)
+#161 := (iff #145 #160)
+#158 := (= #142 #157)
+#155 := (= #139 #154)
+#152 := (= #136 #151)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#153 := [monotonicity #108]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [quant-intro #162]: #164
+#149 := (iff #37 #148)
+#146 := (iff #36 #145)
+#143 := (= #35 #142)
+#140 := (= #34 #139)
+#137 := (= #33 #136)
+#134 := (= #32 #131)
+#128 := (- #125)
+#132 := (= #128 #131)
+#133 := [rewrite]: #132
+#129 := (= #32 #128)
+#126 := (= #31 #125)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#127 := [monotonicity #69 #72]: #126
+#130 := [monotonicity #127]: #129
+#135 := [trans #130 #133]: #134
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#138 := [monotonicity #65 #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [quant-intro #147]: #149
+#167 := [trans #150 #165]: #166
+#124 := [asserted]: #37
+#168 := [mp #124 #167]: #163
+#208 := [mp~ #168 #198]: #163
+#249 := [mp #208 #248]: #246
+#280 := [mp #249 #279]: #277
+#764 := [mp #280 #763]: #759
+#535 := (not #759)
+#683 := (or #535 #175)
+#338 := (* -1::int -1::int)
+#422 := (* -1::int 0::int)
+#423 := (mod #422 #338)
+#424 := (+ #172 #423)
+#415 := (= #424 0::int)
+#426 := (mod 0::int -1::int)
+#427 := (* -1::int #426)
+#428 := (+ #172 #427)
+#425 := (= #428 0::int)
+#429 := (<= -1::int 0::int)
+#408 := (<= 0::int 0::int)
+#743 := (or #408 #429)
+#745 := (not #743)
+#402 := (>= 0::int 0::int)
+#532 := (or #429 #402)
+#739 := (not #532)
+#413 := (or #739 #745)
+#414 := (ite #413 #425 #415)
+#746 := (= 0::int 0::int)
+#747 := (ite #746 #175 #414)
+#748 := (= -1::int 0::int)
+#749 := (ite #748 #178 #747)
+#585 := (or #535 #749)
+#681 := (iff #585 #683)
+#569 := (iff #683 #683)
+#584 := [rewrite]: #569
+#575 := (iff #749 #175)
+#693 := (ite false #175 #175)
+#701 := (iff #693 #175)
+#695 := [rewrite]: #701
+#692 := (iff #749 #693)
+#691 := (iff #747 #175)
+#1 := true
+#533 := (ite true #175 #175)
+#688 := (iff #533 #175)
+#690 := [rewrite]: #688
+#534 := (iff #747 #533)
+#702 := (iff #414 #175)
+#694 := (iff #414 #693)
+#698 := (iff #415 #175)
+#696 := (= #424 #172)
+#436 := (+ #172 0::int)
+#430 := (= #436 #172)
+#712 := [rewrite]: #430
+#553 := (= #424 #436)
+#711 := (= #423 0::int)
+#703 := (mod 0::int 1::int)
+#710 := (= #703 0::int)
+#705 := [rewrite]: #710
+#704 := (= #423 #703)
+#707 := (= #338 1::int)
+#708 := [rewrite]: #707
+#723 := (= #422 0::int)
+#433 := [rewrite]: #723
+#709 := [monotonicity #433 #708]: #704
+#552 := [trans #709 #705]: #711
+#554 := [monotonicity #552]: #553
+#697 := [trans #554 #712]: #696
+#699 := [monotonicity #697]: #698
+#717 := (iff #425 #175)
+#716 := (= #428 #172)
+#714 := (= #428 #436)
+#434 := (= #427 0::int)
+#722 := (= #427 #422)
+#444 := (= #426 0::int)
+#718 := [rewrite]: #444
+#719 := [monotonicity #718]: #722
+#435 := [trans #719 #433]: #434
+#715 := [monotonicity #435]: #714
+#713 := [trans #715 #712]: #716
+#706 := [monotonicity #713]: #717
+#721 := (iff #413 false)
+#448 := (or false false)
+#344 := (iff #448 false)
+#720 := [rewrite]: #344
+#449 := (iff #413 #448)
+#725 := (iff #745 false)
+#729 := (not true)
+#732 := (iff #729 false)
+#727 := [rewrite]: #732
+#738 := (iff #745 #729)
+#737 := (iff #743 true)
+#385 := (or true true)
+#390 := (iff #385 true)
+#391 := [rewrite]: #390
+#376 := (iff #743 #385)
+#405 := (iff #429 true)
+#741 := [rewrite]: #405
+#734 := (iff #408 true)
+#736 := [rewrite]: #734
+#377 := [monotonicity #736 #741]: #376
+#735 := [trans #377 #391]: #737
+#724 := [monotonicity #735]: #738
+#447 := [trans #724 #727]: #725
+#733 := (iff #739 false)
+#730 := (iff #739 #729)
+#392 := (iff #532 true)
+#726 := (iff #532 #385)
+#401 := (iff #402 true)
+#742 := [rewrite]: #401
+#389 := [monotonicity #741 #742]: #726
+#728 := [trans #389 #391]: #392
+#731 := [monotonicity #728]: #730
+#371 := [trans #731 #727]: #733
+#450 := [monotonicity #371 #447]: #449
+#443 := [trans #450 #720]: #721
+#700 := [monotonicity #443 #706 #699]: #694
+#531 := [trans #700 #695]: #702
+#740 := (iff #746 true)
+#400 := [rewrite]: #740
+#687 := [monotonicity #400 #531]: #534
+#689 := [trans #687 #690]: #691
+#744 := (iff #748 false)
+#750 := [rewrite]: #744
+#574 := [monotonicity #750 #187 #689]: #692
+#576 := [trans #574 #695]: #575
+#684 := [monotonicity #576]: #681
+#586 := [trans #684 #584]: #681
+#680 := [quant-inst]: #585
+#587 := [mp #680 #586]: #683
+[unit-resolution #587 #764 #193]: false
+unsat
+07f15f3f61db6e3805237fa8c50e95e2181bdd46 327 0
 #2 := false
 #11 := 0::int
 decl f4 :: (-> int int int)
@@ -32351,598 +36973,7 @@
 #673 := [mp #590 #686]: #588
 [unit-resolution #673 #764 #193]: false
 unsat
-b94918a15776ebd094f6867ac20bcae7605bc260 282 0
-#2 := false
-#11 := 0::int
-decl f3 :: (-> int int int)
-#38 := 3::int
-#39 := (f3 0::int 3::int)
-#40 := (= #39 0::int)
-#41 := (not #40)
-#168 := [asserted]: #41
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#737 := (pattern #10)
-#65 := -1::int
-#69 := (* -1::int #9)
-#66 := (* -1::int #8)
-#72 := (div #66 #69)
-#239 := (* -1::int #72)
-#240 := (+ #10 #239)
-#241 := (= #240 0::int)
-#21 := (div #8 #9)
-#236 := (* -1::int #21)
-#237 := (+ #10 #236)
-#238 := (= #237 0::int)
-#91 := (<= #9 0::int)
-#87 := (<= #8 0::int)
-#194 := (or #87 #91)
-#195 := (not #194)
-#98 := (>= #8 0::int)
-#186 := (or #91 #98)
-#187 := (not #186)
-#201 := (or #187 #195)
-#242 := (ite #201 #238 #241)
-#235 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#243 := (ite #14 #235 #242)
-#738 := (forall (vars (?v0 int) (?v1 int)) (:pat #737) #243)
-#246 := (forall (vars (?v0 int) (?v1 int)) #243)
-#741 := (iff #246 #738)
-#739 := (iff #243 #243)
-#740 := [refl]: #739
-#742 := [quant-intro #740]: #741
-#206 := (ite #201 #21 #72)
-#209 := (ite #14 0::int #206)
-#212 := (= #10 #209)
-#215 := (forall (vars (?v0 int) (?v1 int)) #212)
-#247 := (iff #215 #246)
-#244 := (iff #212 #243)
-#245 := [rewrite]: #244
-#248 := [quant-intro #245]: #247
-#99 := (not #98)
-#92 := (not #91)
-#102 := (and #92 #99)
-#88 := (not #87)
-#95 := (and #88 #92)
-#105 := (or #95 #102)
-#108 := (ite #105 #21 #72)
-#111 := (ite #14 0::int #108)
-#114 := (= #10 #111)
-#117 := (forall (vars (?v0 int) (?v1 int)) #114)
-#216 := (iff #117 #215)
-#213 := (iff #114 #212)
-#210 := (= #111 #209)
-#207 := (= #108 #206)
-#204 := (iff #105 #201)
-#198 := (or #195 #187)
-#202 := (iff #198 #201)
-#203 := [rewrite]: #202
-#199 := (iff #105 #198)
-#196 := (iff #102 #187)
-#197 := [rewrite]: #196
-#184 := (iff #95 #195)
-#185 := [rewrite]: #184
-#200 := [monotonicity #185 #197]: #199
-#205 := [trans #200 #203]: #204
-#208 := [monotonicity #205]: #207
-#211 := [monotonicity #208]: #210
-#214 := [monotonicity #211]: #213
-#217 := [quant-intro #214]: #216
-#190 := (~ #117 #117)
-#188 := (~ #114 #114)
-#189 := [refl]: #188
-#191 := [nnf-pos #189]: #190
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#120 := (iff #28 #117)
-#59 := (and #16 #18)
-#62 := (or #17 #59)
-#75 := (ite #62 #21 #72)
-#78 := (ite #14 0::int #75)
-#81 := (= #10 #78)
-#84 := (forall (vars (?v0 int) (?v1 int)) #81)
-#118 := (iff #84 #117)
-#115 := (iff #81 #114)
-#112 := (= #78 #111)
-#109 := (= #75 #108)
-#106 := (iff #62 #105)
-#103 := (iff #59 #102)
-#100 := (iff #18 #99)
-#101 := [rewrite]: #100
-#93 := (iff #16 #92)
-#94 := [rewrite]: #93
-#104 := [monotonicity #94 #101]: #103
-#96 := (iff #17 #95)
-#89 := (iff #15 #88)
-#90 := [rewrite]: #89
-#97 := [monotonicity #90 #94]: #96
-#107 := [monotonicity #97 #104]: #106
-#110 := [monotonicity #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [quant-intro #116]: #118
-#85 := (iff #28 #84)
-#82 := (iff #27 #81)
-#79 := (= #26 #78)
-#76 := (= #25 #75)
-#73 := (= #24 #72)
-#70 := (= #23 #69)
-#71 := [rewrite]: #70
-#67 := (= #22 #66)
-#68 := [rewrite]: #67
-#74 := [monotonicity #68 #71]: #73
-#63 := (iff #20 #62)
-#60 := (iff #19 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#77 := [monotonicity #64 #74]: #76
-#80 := [monotonicity #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [quant-intro #83]: #85
-#121 := [trans #86 #119]: #120
-#58 := [asserted]: #28
-#122 := [mp #58 #121]: #117
-#181 := [mp~ #122 #191]: #117
-#218 := [mp #181 #217]: #215
-#249 := [mp #218 #248]: #246
-#743 := [mp #249 #742]: #738
-#572 := (not #738)
-#573 := (or #572 #40)
-#323 := (* -1::int 3::int)
-#408 := (* -1::int 0::int)
-#409 := (div #408 #323)
-#410 := (* -1::int #409)
-#401 := (+ #39 #410)
-#412 := (= #401 0::int)
-#413 := (div 0::int 3::int)
-#341 := (* -1::int #413)
-#414 := (+ #39 #341)
-#411 := (= #414 0::int)
-#415 := (<= 3::int 0::int)
-#394 := (<= 0::int 0::int)
-#729 := (or #394 #415)
-#731 := (not #729)
-#388 := (>= 0::int 0::int)
-#518 := (or #415 #388)
-#725 := (not #518)
-#399 := (or #725 #731)
-#400 := (ite #399 #411 #412)
-#732 := (= 3::int 0::int)
-#733 := (= 0::int 0::int)
-#734 := (or #733 #732)
-#735 := (ite #734 #40 #400)
-#566 := (or #572 #735)
-#575 := (iff #566 #573)
-#577 := (iff #573 #573)
-#578 := [rewrite]: #577
-#555 := (iff #735 #40)
-#1 := true
-#669 := (ite true #40 #40)
-#667 := (iff #669 #40)
-#670 := [rewrite]: #667
-#571 := (iff #735 #669)
-#562 := (iff #400 #40)
-#677 := (ite false #40 #40)
-#560 := (iff #677 #40)
-#561 := [rewrite]: #560
-#675 := (iff #400 #677)
-#674 := (iff #412 #40)
-#520 := (= #401 #39)
-#703 := (+ #39 0::int)
-#694 := (= #703 #39)
-#689 := [rewrite]: #694
-#517 := (= #401 #703)
-#681 := (= #410 0::int)
-#416 := (= #408 0::int)
-#698 := [rewrite]: #416
-#686 := (= #410 #408)
-#679 := (= #409 0::int)
-#697 := -3::int
-#540 := (div 0::int -3::int)
-#684 := (= #540 0::int)
-#685 := [rewrite]: #684
-#682 := (= #409 #540)
-#538 := (= #323 -3::int)
-#539 := [rewrite]: #538
-#683 := [monotonicity #698 #539]: #682
-#680 := [trans #683 #685]: #679
-#687 := [monotonicity #680]: #686
-#688 := [trans #687 #698]: #681
-#519 := [monotonicity #688]: #517
-#673 := [trans #519 #689]: #520
-#676 := [monotonicity #673]: #674
-#696 := (iff #411 #40)
-#690 := (= #414 #39)
-#692 := (= #414 #703)
-#702 := (= #341 0::int)
-#700 := (= #341 #408)
-#421 := (= #413 0::int)
-#422 := [rewrite]: #421
-#701 := [monotonicity #422]: #700
-#699 := [trans #701 #698]: #702
-#693 := [monotonicity #699]: #692
-#695 := [trans #693 #689]: #690
-#691 := [monotonicity #695]: #696
-#419 := (iff #399 false)
-#430 := (or false false)
-#705 := (iff #430 false)
-#709 := [rewrite]: #705
-#704 := (iff #399 #430)
-#707 := (iff #731 false)
-#720 := (not true)
-#363 := (iff #720 false)
-#723 := [rewrite]: #363
-#329 := (iff #731 #720)
-#435 := (iff #729 true)
-#391 := (or true false)
-#728 := (iff #391 true)
-#371 := [rewrite]: #728
-#433 := (iff #729 #391)
-#376 := (iff #415 false)
-#377 := [rewrite]: #376
-#710 := (iff #394 true)
-#711 := [rewrite]: #710
-#434 := [monotonicity #711 #377]: #433
-#436 := [trans #434 #371]: #435
-#706 := [monotonicity #436]: #329
-#429 := [trans #706 #723]: #707
-#721 := (iff #725 false)
-#722 := (iff #725 #720)
-#719 := (iff #518 true)
-#715 := (or false true)
-#718 := (iff #715 true)
-#713 := [rewrite]: #718
-#716 := (iff #518 #715)
-#378 := (iff #388 true)
-#714 := [rewrite]: #378
-#717 := [monotonicity #377 #714]: #716
-#357 := [trans #717 #713]: #719
-#362 := [monotonicity #357]: #722
-#724 := [trans #362 #723]: #721
-#708 := [monotonicity #724 #429]: #704
-#420 := [trans #708 #709]: #419
-#678 := [monotonicity #420 #691 #676]: #675
-#521 := [trans #678 #561]: #562
-#712 := (iff #734 true)
-#727 := (iff #734 #391)
-#726 := (iff #732 false)
-#386 := [rewrite]: #726
-#730 := (iff #733 true)
-#736 := [rewrite]: #730
-#387 := [monotonicity #736 #386]: #727
-#375 := [trans #387 #371]: #712
-#666 := [monotonicity #375 #521]: #571
-#570 := [trans #666 #670]: #555
-#576 := [monotonicity #570]: #575
-#671 := [trans #576 #578]: #575
-#574 := [quant-inst]: #566
-#668 := [mp #574 #671]: #573
-[unit-resolution #668 #743 #168]: false
-unsat
-f28e01ed5231dd8c14a90a1eb336549610812dce 307 0
-#2 := false
-#11 := 0::int
-decl f3 :: (-> int int int)
-#170 := -3::int
-#173 := (f3 0::int -3::int)
-#176 := (= #173 0::int)
-#189 := (not #176)
-#38 := 3::int
-#39 := (- 3::int)
-#40 := (f3 0::int #39)
-#41 := (= #40 0::int)
-#42 := (not #41)
-#192 := (iff #42 #189)
-#179 := (= 0::int #173)
-#184 := (not #179)
-#190 := (iff #184 #189)
-#187 := (iff #179 #176)
-#188 := [rewrite]: #187
-#191 := [monotonicity #188]: #190
-#185 := (iff #42 #184)
-#182 := (iff #41 #179)
-#180 := (iff #176 #179)
-#181 := [rewrite]: #180
-#177 := (iff #41 #176)
-#174 := (= #40 #173)
-#171 := (= #39 -3::int)
-#172 := [rewrite]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#183 := [trans #178 #181]: #182
-#186 := [monotonicity #183]: #185
-#193 := [trans #186 #191]: #192
-#169 := [asserted]: #42
-#194 := [mp #169 #193]: #189
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#753 := (pattern #10)
-#66 := -1::int
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#73 := (div #67 #70)
-#255 := (* -1::int #73)
-#256 := (+ #10 #255)
-#257 := (= #256 0::int)
-#21 := (div #8 #9)
-#252 := (* -1::int #21)
-#253 := (+ #10 #252)
-#254 := (= #253 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#210 := (or #88 #92)
-#211 := (not #210)
-#99 := (>= #8 0::int)
-#202 := (or #92 #99)
-#203 := (not #202)
-#217 := (or #203 #211)
-#258 := (ite #217 #254 #257)
-#251 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#259 := (ite #14 #251 #258)
-#754 := (forall (vars (?v0 int) (?v1 int)) (:pat #753) #259)
-#262 := (forall (vars (?v0 int) (?v1 int)) #259)
-#757 := (iff #262 #754)
-#755 := (iff #259 #259)
-#756 := [refl]: #755
-#758 := [quant-intro #756]: #757
-#222 := (ite #217 #21 #73)
-#225 := (ite #14 0::int #222)
-#228 := (= #10 #225)
-#231 := (forall (vars (?v0 int) (?v1 int)) #228)
-#263 := (iff #231 #262)
-#260 := (iff #228 #259)
-#261 := [rewrite]: #260
-#264 := [quant-intro #261]: #263
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#109 := (ite #106 #21 #73)
-#112 := (ite #14 0::int #109)
-#115 := (= #10 #112)
-#118 := (forall (vars (?v0 int) (?v1 int)) #115)
-#232 := (iff #118 #231)
-#229 := (iff #115 #228)
-#226 := (= #112 #225)
-#223 := (= #109 #222)
-#220 := (iff #106 #217)
-#214 := (or #211 #203)
-#218 := (iff #214 #217)
-#219 := [rewrite]: #218
-#215 := (iff #106 #214)
-#212 := (iff #103 #203)
-#213 := [rewrite]: #212
-#200 := (iff #96 #211)
-#201 := [rewrite]: #200
-#216 := [monotonicity #201 #213]: #215
-#221 := [trans #216 #219]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [quant-intro #230]: #232
-#206 := (~ #118 #118)
-#204 := (~ #115 #115)
-#205 := [refl]: #204
-#207 := [nnf-pos #205]: #206
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#121 := (iff #28 #118)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#76 := (ite #63 #21 #73)
-#79 := (ite #14 0::int #76)
-#82 := (= #10 #79)
-#85 := (forall (vars (?v0 int) (?v1 int)) #82)
-#119 := (iff #85 #118)
-#116 := (iff #82 #115)
-#113 := (= #79 #112)
-#110 := (= #76 #109)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#111 := [monotonicity #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [quant-intro #117]: #119
-#86 := (iff #28 #85)
-#83 := (iff #27 #82)
-#80 := (= #26 #79)
-#77 := (= #25 #76)
-#74 := (= #24 #73)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#75 := [monotonicity #69 #72]: #74
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#78 := [monotonicity #65 #75]: #77
-#81 := [monotonicity #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [quant-intro #84]: #86
-#122 := [trans #87 #120]: #121
-#59 := [asserted]: #28
-#123 := [mp #59 #122]: #118
-#197 := [mp~ #123 #207]: #118
-#234 := [mp #197 #233]: #231
-#265 := [mp #234 #264]: #262
-#759 := [mp #265 #758]: #754
-#586 := (not #754)
-#588 := (or #586 #176)
-#339 := (* -1::int -3::int)
-#424 := (* -1::int 0::int)
-#425 := (div #424 #339)
-#426 := (* -1::int #425)
-#417 := (+ #173 #426)
-#428 := (= #417 0::int)
-#429 := (div 0::int -3::int)
-#357 := (* -1::int #429)
-#430 := (+ #173 #357)
-#427 := (= #430 0::int)
-#431 := (<= -3::int 0::int)
-#410 := (<= 0::int 0::int)
-#745 := (or #410 #431)
-#747 := (not #745)
-#404 := (>= 0::int 0::int)
-#534 := (or #431 #404)
-#741 := (not #534)
-#415 := (or #741 #747)
-#416 := (ite #415 #427 #428)
-#748 := (= -3::int 0::int)
-#749 := (= 0::int 0::int)
-#750 := (or #749 #748)
-#751 := (ite #750 #176 #416)
-#589 := (or #586 #751)
-#590 := (iff #589 #588)
-#592 := (iff #588 #588)
-#593 := [rewrite]: #592
-#686 := (iff #751 #176)
-#1 := true
-#537 := (ite true #176 #176)
-#682 := (iff #537 #176)
-#683 := [rewrite]: #682
-#685 := (iff #751 #537)
-#577 := (iff #416 #176)
-#692 := (ite false #176 #176)
-#694 := (iff #692 #176)
-#576 := [rewrite]: #694
-#693 := (iff #416 #692)
-#689 := (iff #428 #176)
-#535 := (= #417 #173)
-#719 := (+ #173 0::int)
-#710 := (= #719 #173)
-#705 := [rewrite]: #710
-#704 := (= #417 #719)
-#703 := (= #426 0::int)
-#432 := (= #424 0::int)
-#714 := [rewrite]: #432
-#696 := (= #426 #424)
-#701 := (= #425 0::int)
-#555 := (div 0::int 3::int)
-#699 := (= #555 0::int)
-#700 := [rewrite]: #699
-#556 := (= #425 #555)
-#713 := (= #339 3::int)
-#554 := [rewrite]: #713
-#698 := [monotonicity #714 #554]: #556
-#695 := [trans #698 #700]: #701
-#702 := [monotonicity #695]: #696
-#697 := [trans #702 #714]: #703
-#533 := [monotonicity #697]: #704
-#536 := [trans #533 #705]: #535
-#690 := [monotonicity #536]: #689
-#712 := (iff #427 #176)
-#706 := (= #430 #173)
-#708 := (= #430 #719)
-#718 := (= #357 0::int)
-#716 := (= #357 #424)
-#437 := (= #429 0::int)
-#438 := [rewrite]: #437
-#717 := [monotonicity #438]: #716
-#715 := [trans #717 #714]: #718
-#709 := [monotonicity #715]: #708
-#711 := [trans #709 #705]: #706
-#707 := [monotonicity #711]: #712
-#435 := (iff #415 false)
-#446 := (or false false)
-#721 := (iff #446 false)
-#725 := [rewrite]: #721
-#720 := (iff #415 #446)
-#723 := (iff #747 false)
-#736 := (not true)
-#379 := (iff #736 false)
-#739 := [rewrite]: #379
-#345 := (iff #747 #736)
-#451 := (iff #745 true)
-#731 := (or true true)
-#734 := (iff #731 true)
-#729 := [rewrite]: #734
-#449 := (iff #745 #731)
-#392 := (iff #431 true)
-#393 := [rewrite]: #392
-#726 := (iff #410 true)
-#727 := [rewrite]: #726
-#450 := [monotonicity #727 #393]: #449
-#452 := [trans #450 #729]: #451
-#722 := [monotonicity #452]: #345
-#445 := [trans #722 #739]: #723
-#737 := (iff #741 false)
-#738 := (iff #741 #736)
-#735 := (iff #534 true)
-#732 := (iff #534 #731)
-#394 := (iff #404 true)
-#730 := [rewrite]: #394
-#733 := [monotonicity #393 #730]: #732
-#373 := [trans #733 #729]: #735
-#378 := [monotonicity #373]: #738
-#740 := [trans #378 #739]: #737
-#724 := [monotonicity #740 #445]: #720
-#436 := [trans #724 #725]: #435
-#691 := [monotonicity #436 #707 #690]: #693
-#578 := [trans #691 #576]: #577
-#728 := (iff #750 true)
-#407 := (or true false)
-#744 := (iff #407 true)
-#387 := [rewrite]: #744
-#743 := (iff #750 #407)
-#742 := (iff #748 false)
-#402 := [rewrite]: #742
-#746 := (iff #749 true)
-#752 := [rewrite]: #746
-#403 := [monotonicity #752 #402]: #743
-#391 := [trans #403 #387]: #728
-#587 := [monotonicity #391 #578]: #685
-#571 := [trans #587 #683]: #686
-#591 := [monotonicity #571]: #590
-#594 := [trans #591 #593]: #590
-#582 := [quant-inst]: #589
-#687 := [mp #582 #594]: #588
-[unit-resolution #687 #759 #194]: false
-unsat
-e3ca3cfa3906cd959718a475a745a6d7221ec25b 329 0
+8144b6d093845ae8dee3931af66c9361d99b4453 329 0
 #2 := false
 #11 := 0::int
 decl f4 :: (-> int int int)
@@ -33272,304 +37303,7 @@
 #676 := [mp #592 #674]: #590
 [unit-resolution #676 #765 #194]: false
 unsat
-9c08922893cb633ba38530e84ba0b136e5cd1a81 296 0
-#2 := false
-#11 := 0::int
-decl f3 :: (-> int int int)
-#39 := 3::int
-#38 := 1::int
-#40 := (f3 1::int 3::int)
-#41 := (= #40 0::int)
-#42 := (not #41)
-#169 := [asserted]: #42
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#737 := (pattern #10)
-#66 := -1::int
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#73 := (div #67 #70)
-#240 := (* -1::int #73)
-#241 := (+ #10 #240)
-#242 := (= #241 0::int)
-#21 := (div #8 #9)
-#237 := (* -1::int #21)
-#238 := (+ #10 #237)
-#239 := (= #238 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#195 := (or #88 #92)
-#196 := (not #195)
-#99 := (>= #8 0::int)
-#187 := (or #92 #99)
-#188 := (not #187)
-#202 := (or #188 #196)
-#243 := (ite #202 #239 #242)
-#236 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#244 := (ite #14 #236 #243)
-#738 := (forall (vars (?v0 int) (?v1 int)) (:pat #737) #244)
-#247 := (forall (vars (?v0 int) (?v1 int)) #244)
-#741 := (iff #247 #738)
-#739 := (iff #244 #244)
-#740 := [refl]: #739
-#742 := [quant-intro #740]: #741
-#207 := (ite #202 #21 #73)
-#210 := (ite #14 0::int #207)
-#213 := (= #10 #210)
-#216 := (forall (vars (?v0 int) (?v1 int)) #213)
-#248 := (iff #216 #247)
-#245 := (iff #213 #244)
-#246 := [rewrite]: #245
-#249 := [quant-intro #246]: #248
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#109 := (ite #106 #21 #73)
-#112 := (ite #14 0::int #109)
-#115 := (= #10 #112)
-#118 := (forall (vars (?v0 int) (?v1 int)) #115)
-#217 := (iff #118 #216)
-#214 := (iff #115 #213)
-#211 := (= #112 #210)
-#208 := (= #109 #207)
-#205 := (iff #106 #202)
-#199 := (or #196 #188)
-#203 := (iff #199 #202)
-#204 := [rewrite]: #203
-#200 := (iff #106 #199)
-#197 := (iff #103 #188)
-#198 := [rewrite]: #197
-#185 := (iff #96 #196)
-#186 := [rewrite]: #185
-#201 := [monotonicity #186 #198]: #200
-#206 := [trans #201 #204]: #205
-#209 := [monotonicity #206]: #208
-#212 := [monotonicity #209]: #211
-#215 := [monotonicity #212]: #214
-#218 := [quant-intro #215]: #217
-#191 := (~ #118 #118)
-#189 := (~ #115 #115)
-#190 := [refl]: #189
-#192 := [nnf-pos #190]: #191
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#121 := (iff #28 #118)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#76 := (ite #63 #21 #73)
-#79 := (ite #14 0::int #76)
-#82 := (= #10 #79)
-#85 := (forall (vars (?v0 int) (?v1 int)) #82)
-#119 := (iff #85 #118)
-#116 := (iff #82 #115)
-#113 := (= #79 #112)
-#110 := (= #76 #109)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#111 := [monotonicity #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [quant-intro #117]: #119
-#86 := (iff #28 #85)
-#83 := (iff #27 #82)
-#80 := (= #26 #79)
-#77 := (= #25 #76)
-#74 := (= #24 #73)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#75 := [monotonicity #69 #72]: #74
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#78 := [monotonicity #65 #75]: #77
-#81 := [monotonicity #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [quant-intro #84]: #86
-#122 := [trans #87 #120]: #121
-#59 := [asserted]: #28
-#123 := [mp #59 #122]: #118
-#182 := [mp~ #123 #192]: #118
-#219 := [mp #182 #218]: #216
-#250 := [mp #219 #249]: #247
-#743 := [mp #250 #742]: #738
-#650 := (not #738)
-#652 := (or #650 #41)
-#324 := (* -1::int 3::int)
-#408 := (* -1::int 1::int)
-#409 := (div #408 #324)
-#410 := (* -1::int #409)
-#401 := (+ #40 #410)
-#412 := (= #401 0::int)
-#413 := (div 1::int 3::int)
-#414 := (* -1::int #413)
-#411 := (+ #40 #414)
-#415 := (= #411 0::int)
-#394 := (<= 3::int 0::int)
-#729 := (<= 1::int 0::int)
-#731 := (or #729 #394)
-#388 := (not #731)
-#518 := (>= 1::int 0::int)
-#725 := (or #394 #518)
-#399 := (not #725)
-#400 := (or #399 #388)
-#732 := (ite #400 #415 #412)
-#733 := (= 3::int 0::int)
-#734 := (= 1::int 0::int)
-#735 := (or #734 #733)
-#730 := (ite #735 #41 #732)
-#662 := (or #650 #730)
-#664 := (iff #662 #652)
-#665 := (iff #652 #652)
-#654 := [rewrite]: #665
-#661 := (iff #730 #41)
-#578 := (ite false #41 #41)
-#672 := (iff #578 #41)
-#659 := [rewrite]: #672
-#671 := (iff #730 #578)
-#576 := (iff #732 #41)
-#666 := (= #40 1::int)
-#1 := true
-#572 := (ite true #41 #666)
-#574 := (iff #572 #41)
-#575 := [rewrite]: #574
-#573 := (iff #732 #572)
-#555 := (iff #412 #666)
-#675 := (+ -1::int #40)
-#521 := (= #675 0::int)
-#667 := (iff #521 #666)
-#670 := [rewrite]: #667
-#669 := (iff #412 #521)
-#561 := (= #401 #675)
-#674 := (+ #40 -1::int)
-#678 := (= #674 #675)
-#560 := [rewrite]: #678
-#676 := (= #401 #674)
-#520 := (= #410 -1::int)
-#539 := (= #408 -1::int)
-#540 := [rewrite]: #539
-#517 := (= #410 #408)
-#681 := (= #409 1::int)
-#682 := -3::int
-#685 := (div -1::int -3::int)
-#686 := (= #685 1::int)
-#687 := [rewrite]: #686
-#679 := (= #409 #685)
-#683 := (= #324 -3::int)
-#684 := [rewrite]: #683
-#680 := [monotonicity #540 #684]: #679
-#688 := [trans #680 #687]: #681
-#519 := [monotonicity #688]: #517
-#673 := [trans #519 #540]: #520
-#677 := [monotonicity #673]: #676
-#562 := [trans #677 #560]: #561
-#571 := [monotonicity #562]: #669
-#570 := [trans #571 #670]: #555
-#697 := (iff #415 #41)
-#696 := (= #411 #40)
-#693 := (+ #40 0::int)
-#690 := (= #693 #40)
-#695 := [rewrite]: #690
-#694 := (= #411 #693)
-#703 := (= #414 0::int)
-#701 := (* -1::int 0::int)
-#702 := (= #701 0::int)
-#699 := [rewrite]: #702
-#416 := (= #414 #701)
-#422 := (= #413 0::int)
-#700 := [rewrite]: #422
-#698 := [monotonicity #700]: #416
-#692 := [trans #698 #699]: #703
-#689 := [monotonicity #692]: #694
-#691 := [trans #689 #695]: #696
-#538 := [monotonicity #691]: #697
-#420 := (iff #400 true)
-#716 := (or false true)
-#713 := (iff #716 true)
-#719 := [rewrite]: #713
-#709 := (iff #400 #716)
-#708 := (iff #388 true)
-#706 := (not false)
-#430 := (iff #706 true)
-#704 := [rewrite]: #430
-#707 := (iff #388 #706)
-#436 := (iff #731 false)
-#727 := (or false false)
-#371 := (iff #727 false)
-#712 := [rewrite]: #371
-#434 := (iff #731 #727)
-#377 := (iff #394 false)
-#378 := [rewrite]: #377
-#711 := (iff #729 false)
-#433 := [rewrite]: #711
-#435 := [monotonicity #433 #378]: #434
-#330 := [trans #435 #712]: #436
-#429 := [monotonicity #330]: #707
-#705 := [trans #429 #704]: #708
-#724 := (iff #399 false)
-#722 := (not true)
-#723 := (iff #722 false)
-#721 := [rewrite]: #723
-#362 := (iff #399 #722)
-#357 := (iff #725 true)
-#717 := (iff #725 #716)
-#714 := (iff #518 true)
-#715 := [rewrite]: #714
-#718 := [monotonicity #378 #715]: #717
-#720 := [trans #718 #719]: #357
-#363 := [monotonicity #720]: #362
-#710 := [trans #363 #721]: #724
-#419 := [monotonicity #710 #705]: #709
-#421 := [trans #419 #719]: #420
-#566 := [monotonicity #421 #538 #570]: #573
-#577 := [trans #566 #575]: #576
-#375 := (iff #735 false)
-#387 := (iff #735 #727)
-#386 := (iff #733 false)
-#391 := [rewrite]: #386
-#736 := (iff #734 false)
-#726 := [rewrite]: #736
-#728 := [monotonicity #726 #391]: #387
-#376 := [trans #728 #712]: #375
-#668 := [monotonicity #376 #577]: #671
-#653 := [trans #668 #659]: #661
-#660 := [monotonicity #653]: #664
-#655 := [trans #660 #654]: #664
-#663 := [quant-inst]: #662
-#656 := [mp #663 #655]: #652
-[unit-resolution #656 #743 #169]: false
-unsat
-296b085c95c2238dbf4db3cb90fb09e839ecea3d 306 0
+a20f91759967cf78b23640f832ca57a185975634 306 0
 #2 := false
 #11 := 0::int
 decl f4 :: (-> int int int)
@@ -33876,294 +37610,7 @@
 #693 := [mp #535 #690]: #532
 [unit-resolution #693 #765 #194]: false
 unsat
-4b6a61d48a9a0af02d6fd3725ddd2c3187d77b9e 286 0
-#2 := false
-#40 := 1::int
-decl f3 :: (-> int int int)
-#38 := 3::int
-#39 := (f3 3::int 3::int)
-#41 := (= #39 1::int)
-#42 := (not #41)
-#169 := [asserted]: #42
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#727 := (pattern #10)
-#11 := 0::int
-#66 := -1::int
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#73 := (div #67 #70)
-#230 := (* -1::int #73)
-#231 := (+ #10 #230)
-#232 := (= #231 0::int)
-#21 := (div #8 #9)
-#227 := (* -1::int #21)
-#228 := (+ #10 #227)
-#229 := (= #228 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#185 := (or #88 #92)
-#186 := (not #185)
-#99 := (>= #8 0::int)
-#177 := (or #92 #99)
-#178 := (not #177)
-#192 := (or #178 #186)
-#233 := (ite #192 #229 #232)
-#226 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#234 := (ite #14 #226 #233)
-#728 := (forall (vars (?v0 int) (?v1 int)) (:pat #727) #234)
-#237 := (forall (vars (?v0 int) (?v1 int)) #234)
-#731 := (iff #237 #728)
-#729 := (iff #234 #234)
-#730 := [refl]: #729
-#732 := [quant-intro #730]: #731
-#197 := (ite #192 #21 #73)
-#200 := (ite #14 0::int #197)
-#203 := (= #10 #200)
-#206 := (forall (vars (?v0 int) (?v1 int)) #203)
-#238 := (iff #206 #237)
-#235 := (iff #203 #234)
-#236 := [rewrite]: #235
-#239 := [quant-intro #236]: #238
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#109 := (ite #106 #21 #73)
-#112 := (ite #14 0::int #109)
-#115 := (= #10 #112)
-#118 := (forall (vars (?v0 int) (?v1 int)) #115)
-#207 := (iff #118 #206)
-#204 := (iff #115 #203)
-#201 := (= #112 #200)
-#198 := (= #109 #197)
-#195 := (iff #106 #192)
-#189 := (or #186 #178)
-#193 := (iff #189 #192)
-#194 := [rewrite]: #193
-#190 := (iff #106 #189)
-#187 := (iff #103 #178)
-#188 := [rewrite]: #187
-#175 := (iff #96 #186)
-#176 := [rewrite]: #175
-#191 := [monotonicity #176 #188]: #190
-#196 := [trans #191 #194]: #195
-#199 := [monotonicity #196]: #198
-#202 := [monotonicity #199]: #201
-#205 := [monotonicity #202]: #204
-#208 := [quant-intro #205]: #207
-#181 := (~ #118 #118)
-#179 := (~ #115 #115)
-#180 := [refl]: #179
-#182 := [nnf-pos #180]: #181
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#121 := (iff #28 #118)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#76 := (ite #63 #21 #73)
-#79 := (ite #14 0::int #76)
-#82 := (= #10 #79)
-#85 := (forall (vars (?v0 int) (?v1 int)) #82)
-#119 := (iff #85 #118)
-#116 := (iff #82 #115)
-#113 := (= #79 #112)
-#110 := (= #76 #109)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#111 := [monotonicity #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [quant-intro #117]: #119
-#86 := (iff #28 #85)
-#83 := (iff #27 #82)
-#80 := (= #26 #79)
-#77 := (= #25 #76)
-#74 := (= #24 #73)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#75 := [monotonicity #69 #72]: #74
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#78 := [monotonicity #65 #75]: #77
-#81 := [monotonicity #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [quant-intro #84]: #86
-#122 := [trans #87 #120]: #121
-#59 := [asserted]: #28
-#123 := [mp #59 #122]: #118
-#172 := [mp~ #123 #182]: #118
-#209 := [mp #172 #208]: #206
-#240 := [mp #209 #239]: #237
-#733 := [mp #240 #732]: #728
-#565 := (not #728)
-#566 := (or #565 #41)
-#314 := (* -1::int 3::int)
-#398 := (div #314 #314)
-#399 := (* -1::int #398)
-#400 := (+ #39 #399)
-#391 := (= #400 0::int)
-#402 := (div 3::int 3::int)
-#403 := (* -1::int #402)
-#404 := (+ #39 #403)
-#401 := (= #404 0::int)
-#405 := (<= 3::int 0::int)
-#384 := (or #405 #405)
-#719 := (not #384)
-#721 := (>= 3::int 0::int)
-#378 := (or #405 #721)
-#508 := (not #378)
-#715 := (or #508 #719)
-#389 := (ite #715 #401 #391)
-#390 := (= #39 0::int)
-#722 := (= 3::int 0::int)
-#723 := (or #722 #722)
-#724 := (ite #723 #390 #389)
-#567 := (or #565 #724)
-#661 := (iff #567 #566)
-#662 := (iff #566 #566)
-#649 := [rewrite]: #662
-#556 := (iff #724 #41)
-#660 := (ite false #390 #41)
-#562 := (iff #660 #41)
-#563 := [rewrite]: #562
-#545 := (iff #724 #660)
-#656 := (iff #389 #41)
-#1 := true
-#551 := (ite true #41 #41)
-#659 := (iff #551 #41)
-#561 := [rewrite]: #659
-#552 := (iff #389 #551)
-#668 := (iff #391 #41)
-#689 := (+ -1::int #39)
-#679 := (= #689 0::int)
-#686 := (iff #679 #41)
-#681 := [rewrite]: #686
-#667 := (iff #391 #679)
-#664 := (= #400 #689)
-#406 := (+ #39 -1::int)
-#693 := (= #406 #689)
-#682 := [rewrite]: #693
-#510 := (= #400 #406)
-#507 := (= #399 -1::int)
-#699 := (* -1::int 1::int)
-#411 := (= #699 -1::int)
-#412 := [rewrite]: #411
-#671 := (= #399 #699)
-#676 := (= #398 1::int)
-#529 := -3::int
-#673 := (div -3::int -3::int)
-#669 := (= #673 1::int)
-#670 := [rewrite]: #669
-#674 := (= #398 #673)
-#530 := (= #314 -3::int)
-#672 := [rewrite]: #530
-#675 := [monotonicity #672 #672]: #674
-#677 := [trans #675 #670]: #676
-#678 := [monotonicity #677]: #671
-#509 := [trans #678 #412]: #507
-#663 := [monotonicity #509]: #510
-#666 := [trans #663 #682]: #664
-#665 := [monotonicity #666]: #667
-#550 := [trans #665 #681]: #668
-#687 := (iff #401 #41)
-#680 := (iff #401 #679)
-#683 := (= #404 #689)
-#688 := (= #404 #406)
-#690 := (= #403 -1::int)
-#409 := (= #403 #699)
-#698 := (= #402 1::int)
-#695 := [rewrite]: #698
-#410 := [monotonicity #695]: #409
-#691 := [trans #410 #412]: #690
-#692 := [monotonicity #691]: #688
-#684 := [trans #692 #682]: #683
-#685 := [monotonicity #684]: #680
-#528 := [trans #685 #681]: #687
-#420 := (iff #715 true)
-#367 := (or false true)
-#705 := (iff #367 true)
-#706 := [rewrite]: #705
-#697 := (iff #715 #367)
-#320 := (iff #719 true)
-#701 := (not false)
-#425 := (iff #701 true)
-#426 := [rewrite]: #425
-#423 := (iff #719 #701)
-#714 := (iff #384 false)
-#726 := (or false false)
-#381 := (iff #726 false)
-#717 := [rewrite]: #381
-#713 := (iff #384 #726)
-#361 := (iff #405 false)
-#702 := [rewrite]: #361
-#711 := [monotonicity #702 #702]: #713
-#700 := [trans #711 #717]: #714
-#424 := [monotonicity #700]: #423
-#696 := [trans #424 #426]: #320
-#352 := (iff #508 false)
-#703 := (not true)
-#710 := (iff #703 false)
-#712 := [rewrite]: #710
-#709 := (iff #508 #703)
-#707 := (iff #378 true)
-#368 := (iff #378 #367)
-#365 := (iff #721 true)
-#366 := [rewrite]: #365
-#704 := [monotonicity #702 #366]: #368
-#708 := [trans #704 #706]: #707
-#347 := [monotonicity #708]: #709
-#353 := [trans #347 #712]: #352
-#419 := [monotonicity #353 #696]: #697
-#694 := [trans #419 #706]: #420
-#511 := [monotonicity #694 #528 #550]: #552
-#657 := [trans #511 #561]: #656
-#377 := (iff #723 false)
-#716 := (iff #723 #726)
-#725 := (iff #722 false)
-#720 := [rewrite]: #725
-#376 := [monotonicity #720 #720]: #716
-#718 := [trans #376 #717]: #377
-#560 := [monotonicity #718 #657]: #545
-#564 := [trans #560 #563]: #556
-#658 := [monotonicity #564]: #661
-#651 := [trans #658 #649]: #661
-#568 := [quant-inst]: #567
-#643 := [mp #568 #651]: #566
-[unit-resolution #643 #733 #169]: false
-unsat
-62ada4366d569f6c75cf58cfc0c1710258d4c728 299 0
+450a206c661160bbd83de0094374a847857dd804 299 0
 #2 := false
 #11 := 0::int
 decl f4 :: (-> int int int)
@@ -34463,318 +37910,7 @@
 #575 := [mp #555 #574]: #667
 [unit-resolution #575 #750 #168]: false
 unsat
-a30bbe93d2d8e059cff59983b5c369152f8b4c56 310 0
-#2 := false
-#41 := 1::int
-decl f3 :: (-> int int int)
-#39 := 3::int
-#38 := 5::int
-#40 := (f3 5::int 3::int)
-#42 := (= #40 1::int)
-#43 := (not #42)
-#170 := [asserted]: #43
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#728 := (pattern #10)
-#11 := 0::int
-#67 := -1::int
-#71 := (* -1::int #9)
-#68 := (* -1::int #8)
-#74 := (div #68 #71)
-#231 := (* -1::int #74)
-#232 := (+ #10 #231)
-#233 := (= #232 0::int)
-#21 := (div #8 #9)
-#228 := (* -1::int #21)
-#229 := (+ #10 #228)
-#230 := (= #229 0::int)
-#93 := (<= #9 0::int)
-#89 := (<= #8 0::int)
-#186 := (or #89 #93)
-#187 := (not #186)
-#100 := (>= #8 0::int)
-#178 := (or #93 #100)
-#179 := (not #178)
-#193 := (or #179 #187)
-#234 := (ite #193 #230 #233)
-#227 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#235 := (ite #14 #227 #234)
-#729 := (forall (vars (?v0 int) (?v1 int)) (:pat #728) #235)
-#238 := (forall (vars (?v0 int) (?v1 int)) #235)
-#732 := (iff #238 #729)
-#730 := (iff #235 #235)
-#731 := [refl]: #730
-#733 := [quant-intro #731]: #732
-#198 := (ite #193 #21 #74)
-#201 := (ite #14 0::int #198)
-#204 := (= #10 #201)
-#207 := (forall (vars (?v0 int) (?v1 int)) #204)
-#239 := (iff #207 #238)
-#236 := (iff #204 #235)
-#237 := [rewrite]: #236
-#240 := [quant-intro #237]: #239
-#101 := (not #100)
-#94 := (not #93)
-#104 := (and #94 #101)
-#90 := (not #89)
-#97 := (and #90 #94)
-#107 := (or #97 #104)
-#110 := (ite #107 #21 #74)
-#113 := (ite #14 0::int #110)
-#116 := (= #10 #113)
-#119 := (forall (vars (?v0 int) (?v1 int)) #116)
-#208 := (iff #119 #207)
-#205 := (iff #116 #204)
-#202 := (= #113 #201)
-#199 := (= #110 #198)
-#196 := (iff #107 #193)
-#190 := (or #187 #179)
-#194 := (iff #190 #193)
-#195 := [rewrite]: #194
-#191 := (iff #107 #190)
-#188 := (iff #104 #179)
-#189 := [rewrite]: #188
-#176 := (iff #97 #187)
-#177 := [rewrite]: #176
-#192 := [monotonicity #177 #189]: #191
-#197 := [trans #192 #195]: #196
-#200 := [monotonicity #197]: #199
-#203 := [monotonicity #200]: #202
-#206 := [monotonicity #203]: #205
-#209 := [quant-intro #206]: #208
-#182 := (~ #119 #119)
-#180 := (~ #116 #116)
-#181 := [refl]: #180
-#183 := [nnf-pos #181]: #182
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#122 := (iff #28 #119)
-#61 := (and #16 #18)
-#64 := (or #17 #61)
-#77 := (ite #64 #21 #74)
-#80 := (ite #14 0::int #77)
-#83 := (= #10 #80)
-#86 := (forall (vars (?v0 int) (?v1 int)) #83)
-#120 := (iff #86 #119)
-#117 := (iff #83 #116)
-#114 := (= #80 #113)
-#111 := (= #77 #110)
-#108 := (iff #64 #107)
-#105 := (iff #61 #104)
-#102 := (iff #18 #101)
-#103 := [rewrite]: #102
-#95 := (iff #16 #94)
-#96 := [rewrite]: #95
-#106 := [monotonicity #96 #103]: #105
-#98 := (iff #17 #97)
-#91 := (iff #15 #90)
-#92 := [rewrite]: #91
-#99 := [monotonicity #92 #96]: #98
-#109 := [monotonicity #99 #106]: #108
-#112 := [monotonicity #109]: #111
-#115 := [monotonicity #112]: #114
-#118 := [monotonicity #115]: #117
-#121 := [quant-intro #118]: #120
-#87 := (iff #28 #86)
-#84 := (iff #27 #83)
-#81 := (= #26 #80)
-#78 := (= #25 #77)
-#75 := (= #24 #74)
-#72 := (= #23 #71)
-#73 := [rewrite]: #72
-#69 := (= #22 #68)
-#70 := [rewrite]: #69
-#76 := [monotonicity #70 #73]: #75
-#65 := (iff #20 #64)
-#62 := (iff #19 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#79 := [monotonicity #66 #76]: #78
-#82 := [monotonicity #79]: #81
-#85 := [monotonicity #82]: #84
-#88 := [quant-intro #85]: #87
-#123 := [trans #88 #121]: #122
-#60 := [asserted]: #28
-#124 := [mp #60 #123]: #119
-#173 := [mp~ #124 #183]: #119
-#210 := [mp #173 #209]: #207
-#241 := [mp #210 #240]: #238
-#734 := [mp #241 #733]: #729
-#633 := (not #729)
-#634 := (or #633 #42)
-#315 := (* -1::int 3::int)
-#399 := (* -1::int 5::int)
-#400 := (div #399 #315)
-#401 := (* -1::int #400)
-#392 := (+ #40 #401)
-#403 := (= #392 0::int)
-#404 := (div 5::int 3::int)
-#405 := (* -1::int #404)
-#402 := (+ #40 #405)
-#406 := (= #402 0::int)
-#385 := (<= 3::int 0::int)
-#720 := (<= 5::int 0::int)
-#722 := (or #720 #385)
-#379 := (not #722)
-#509 := (>= 5::int 0::int)
-#716 := (or #385 #509)
-#390 := (not #716)
-#391 := (or #390 #379)
-#723 := (ite #391 #406 #403)
-#724 := (= #40 0::int)
-#725 := (= 3::int 0::int)
-#726 := (= 5::int 0::int)
-#721 := (or #726 #725)
-#727 := (ite #721 #724 #723)
-#636 := (or #633 #727)
-#638 := (iff #636 #634)
-#635 := (iff #634 #634)
-#640 := [rewrite]: #635
-#642 := (iff #727 #42)
-#656 := (ite false #724 #42)
-#647 := (iff #656 #42)
-#648 := [rewrite]: #647
-#645 := (iff #727 #656)
-#655 := (iff #723 #42)
-#665 := 2::int
-#662 := (= #40 2::int)
-#1 := true
-#644 := (ite true #42 #662)
-#653 := (iff #644 #42)
-#654 := [rewrite]: #653
-#641 := (iff #723 #644)
-#650 := (iff #403 #662)
-#512 := -2::int
-#563 := (+ -2::int #40)
-#567 := (= #563 0::int)
-#659 := (iff #567 #662)
-#663 := [rewrite]: #659
-#568 := (iff #403 #567)
-#565 := (= #392 #563)
-#661 := (+ #40 -2::int)
-#564 := (= #661 #563)
-#557 := [rewrite]: #564
-#546 := (= #392 #661)
-#657 := (= #401 -2::int)
-#551 := (* -1::int 2::int)
-#660 := (= #551 -2::int)
-#562 := [rewrite]: #660
-#552 := (= #401 #551)
-#666 := (= #400 2::int)
-#672 := -3::int
-#671 := -5::int
-#510 := (div -5::int -3::int)
-#667 := (= #510 2::int)
-#668 := [rewrite]: #667
-#511 := (= #400 #510)
-#679 := (= #315 -3::int)
-#508 := [rewrite]: #679
-#677 := (= #399 -5::int)
-#678 := [rewrite]: #677
-#664 := [monotonicity #678 #508]: #511
-#669 := [trans #664 #668]: #666
-#553 := [monotonicity #669]: #552
-#658 := [trans #553 #562]: #657
-#561 := [monotonicity #658]: #546
-#566 := [trans #561 #557]: #565
-#569 := [monotonicity #566]: #568
-#652 := [trans #569 #663]: #650
-#676 := (iff #406 #42)
-#686 := (+ -1::int #40)
-#530 := (= #686 0::int)
-#674 := (iff #530 #42)
-#675 := [rewrite]: #674
-#531 := (iff #406 #530)
-#688 := (= #402 #686)
-#685 := (+ #40 -1::int)
-#687 := (= #685 #686)
-#682 := [rewrite]: #687
-#680 := (= #402 #685)
-#683 := (= #405 -1::int)
-#407 := (* -1::int 1::int)
-#690 := (= #407 -1::int)
-#694 := [rewrite]: #690
-#689 := (= #405 #407)
-#691 := (= #404 1::int)
-#692 := [rewrite]: #691
-#693 := [monotonicity #692]: #689
-#684 := [trans #693 #694]: #683
-#681 := [monotonicity #684]: #680
-#529 := [trans #681 #682]: #688
-#673 := [monotonicity #529]: #531
-#670 := [trans #673 #675]: #676
-#412 := (iff #391 true)
-#708 := (or false true)
-#710 := (iff #708 true)
-#348 := [rewrite]: #710
-#410 := (iff #391 #708)
-#696 := (iff #379 true)
-#698 := (not false)
-#695 := (iff #698 true)
-#699 := [rewrite]: #695
-#420 := (iff #379 #698)
-#321 := (iff #722 false)
-#378 := (or false false)
-#703 := (iff #378 false)
-#366 := [rewrite]: #703
-#426 := (iff #722 #378)
-#369 := (iff #385 false)
-#705 := [rewrite]: #369
-#424 := (iff #720 false)
-#425 := [rewrite]: #424
-#427 := [monotonicity #425 #705]: #426
-#697 := [trans #427 #366]: #321
-#421 := [monotonicity #697]: #420
-#700 := [trans #421 #699]: #696
-#701 := (iff #390 false)
-#353 := (not true)
-#712 := (iff #353 false)
-#715 := [rewrite]: #712
-#354 := (iff #390 #353)
-#711 := (iff #716 true)
-#709 := (iff #716 #708)
-#706 := (iff #509 true)
-#707 := [rewrite]: #706
-#704 := [monotonicity #705 #707]: #709
-#713 := [trans #704 #348]: #711
-#714 := [monotonicity #713]: #354
-#702 := [trans #714 #715]: #701
-#411 := [monotonicity #702 #700]: #410
-#413 := [trans #411 #348]: #412
-#643 := [monotonicity #413 #670 #652]: #641
-#651 := [trans #643 #654]: #655
-#367 := (iff #721 false)
-#719 := (iff #721 #378)
-#382 := (iff #725 false)
-#718 := [rewrite]: #382
-#717 := (iff #726 false)
-#377 := [rewrite]: #717
-#362 := [monotonicity #377 #718]: #719
-#368 := [trans #362 #366]: #367
-#646 := [monotonicity #368 #651]: #645
-#649 := [trans #646 #648]: #642
-#639 := [monotonicity #649]: #638
-#626 := [trans #639 #640]: #638
-#637 := [quant-inst]: #636
-#627 := [mp #637 #626]: #634
-[unit-resolution #627 #734 #170]: false
-unsat
-ce00a9a2ac98ee74eda5a6ff3af7cf5e8e01ed5f 318 0
+b8be49aa798ad99c4b186f0fa5e2759eac880cd8 318 0
 #2 := false
 #11 := 0::int
 decl f4 :: (-> int int int)
@@ -35093,656 +38229,7 @@
 #588 := [mp #587 #586]: #537
 [unit-resolution #588 #766 #194]: false
 unsat
-67d1507c84bf5b55736763e84724925e9337b87e 324 0
-#2 := false
-#68 := -1::int
-decl f3 :: (-> int int int)
-#172 := -3::int
-#38 := 1::int
-#175 := (f3 1::int -3::int)
-#180 := (= #175 -1::int)
-#193 := (not #180)
-#42 := (- 1::int)
-#39 := 3::int
-#40 := (- 3::int)
-#41 := (f3 1::int #40)
-#43 := (= #41 #42)
-#44 := (not #43)
-#196 := (iff #44 #193)
-#183 := (= -1::int #175)
-#188 := (not #183)
-#194 := (iff #188 #193)
-#191 := (iff #183 #180)
-#192 := [rewrite]: #191
-#195 := [monotonicity #192]: #194
-#189 := (iff #44 #188)
-#186 := (iff #43 #183)
-#184 := (iff #180 #183)
-#185 := [rewrite]: #184
-#181 := (iff #43 #180)
-#178 := (= #42 -1::int)
-#179 := [rewrite]: #178
-#176 := (= #41 #175)
-#173 := (= #40 -3::int)
-#174 := [rewrite]: #173
-#177 := [monotonicity #174]: #176
-#182 := [monotonicity #177 #179]: #181
-#187 := [trans #182 #185]: #186
-#190 := [monotonicity #187]: #189
-#197 := [trans #190 #195]: #196
-#171 := [asserted]: #44
-#198 := [mp #171 #197]: #193
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#756 := (pattern #10)
-#11 := 0::int
-#72 := (* -1::int #9)
-#69 := (* -1::int #8)
-#75 := (div #69 #72)
-#259 := (* -1::int #75)
-#260 := (+ #10 #259)
-#261 := (= #260 0::int)
-#21 := (div #8 #9)
-#256 := (* -1::int #21)
-#257 := (+ #10 #256)
-#258 := (= #257 0::int)
-#94 := (<= #9 0::int)
-#90 := (<= #8 0::int)
-#214 := (or #90 #94)
-#215 := (not #214)
-#101 := (>= #8 0::int)
-#206 := (or #94 #101)
-#207 := (not #206)
-#221 := (or #207 #215)
-#262 := (ite #221 #258 #261)
-#255 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#263 := (ite #14 #255 #262)
-#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
-#266 := (forall (vars (?v0 int) (?v1 int)) #263)
-#760 := (iff #266 #757)
-#758 := (iff #263 #263)
-#759 := [refl]: #758
-#761 := [quant-intro #759]: #760
-#226 := (ite #221 #21 #75)
-#229 := (ite #14 0::int #226)
-#232 := (= #10 #229)
-#235 := (forall (vars (?v0 int) (?v1 int)) #232)
-#267 := (iff #235 #266)
-#264 := (iff #232 #263)
-#265 := [rewrite]: #264
-#268 := [quant-intro #265]: #267
-#102 := (not #101)
-#95 := (not #94)
-#105 := (and #95 #102)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#111 := (ite #108 #21 #75)
-#114 := (ite #14 0::int #111)
-#117 := (= #10 #114)
-#120 := (forall (vars (?v0 int) (?v1 int)) #117)
-#236 := (iff #120 #235)
-#233 := (iff #117 #232)
-#230 := (= #114 #229)
-#227 := (= #111 #226)
-#224 := (iff #108 #221)
-#218 := (or #215 #207)
-#222 := (iff #218 #221)
-#223 := [rewrite]: #222
-#219 := (iff #108 #218)
-#216 := (iff #105 #207)
-#217 := [rewrite]: #216
-#204 := (iff #98 #215)
-#205 := [rewrite]: #204
-#220 := [monotonicity #205 #217]: #219
-#225 := [trans #220 #223]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [quant-intro #234]: #236
-#210 := (~ #120 #120)
-#208 := (~ #117 #117)
-#209 := [refl]: #208
-#211 := [nnf-pos #209]: #210
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#123 := (iff #28 #120)
-#62 := (and #16 #18)
-#65 := (or #17 #62)
-#78 := (ite #65 #21 #75)
-#81 := (ite #14 0::int #78)
-#84 := (= #10 #81)
-#87 := (forall (vars (?v0 int) (?v1 int)) #84)
-#121 := (iff #87 #120)
-#118 := (iff #84 #117)
-#115 := (= #81 #114)
-#112 := (= #78 #111)
-#109 := (iff #65 #108)
-#106 := (iff #62 #105)
-#103 := (iff #18 #102)
-#104 := [rewrite]: #103
-#96 := (iff #16 #95)
-#97 := [rewrite]: #96
-#107 := [monotonicity #97 #104]: #106
-#99 := (iff #17 #98)
-#92 := (iff #15 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [monotonicity #116]: #118
-#122 := [quant-intro #119]: #121
-#88 := (iff #28 #87)
-#85 := (iff #27 #84)
-#82 := (= #26 #81)
-#79 := (= #25 #78)
-#76 := (= #24 #75)
-#73 := (= #23 #72)
-#74 := [rewrite]: #73
-#70 := (= #22 #69)
-#71 := [rewrite]: #70
-#77 := [monotonicity #71 #74]: #76
-#66 := (iff #20 #65)
-#63 := (iff #19 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#80 := [monotonicity #67 #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [monotonicity #83]: #85
-#89 := [quant-intro #86]: #88
-#124 := [trans #89 #122]: #123
-#61 := [asserted]: #28
-#125 := [mp #61 #124]: #120
-#201 := [mp~ #125 #211]: #120
-#238 := [mp #201 #237]: #235
-#269 := [mp #238 #268]: #266
-#762 := [mp #269 #761]: #757
-#672 := (not #757)
-#669 := (or #672 #180)
-#343 := (* -1::int -3::int)
-#427 := (* -1::int 1::int)
-#428 := (div #427 #343)
-#429 := (* -1::int #428)
-#420 := (+ #175 #429)
-#431 := (= #420 0::int)
-#432 := (div 1::int -3::int)
-#433 := (* -1::int #432)
-#430 := (+ #175 #433)
-#434 := (= #430 0::int)
-#413 := (<= -3::int 0::int)
-#748 := (<= 1::int 0::int)
-#750 := (or #748 #413)
-#407 := (not #750)
-#537 := (>= 1::int 0::int)
-#744 := (or #413 #537)
-#418 := (not #744)
-#419 := (or #418 #407)
-#751 := (ite #419 #434 #431)
-#752 := (= #175 0::int)
-#753 := (= -3::int 0::int)
-#754 := (= 1::int 0::int)
-#749 := (or #754 #753)
-#755 := (ite #749 #752 #751)
-#671 := (or #672 #755)
-#682 := (iff #671 #669)
-#679 := (iff #669 #669)
-#684 := [rewrite]: #679
-#678 := (iff #755 #180)
-#585 := (ite false #752 #180)
-#595 := (iff #585 #180)
-#596 := [rewrite]: #595
-#687 := (iff #755 #585)
-#597 := (iff #751 #180)
-#593 := (iff #751 #585)
-#591 := (iff #431 #180)
-#580 := (+ 1::int #175)
-#685 := (= #580 0::int)
-#574 := (iff #685 #180)
-#589 := [rewrite]: #574
-#686 := (iff #431 #685)
-#688 := (= #420 #580)
-#694 := (+ #175 1::int)
-#581 := (= #694 #580)
-#540 := [rewrite]: #581
-#697 := (= #420 #694)
-#695 := (= #429 1::int)
-#536 := (* -1::int -1::int)
-#692 := (= #536 1::int)
-#693 := [rewrite]: #692
-#538 := (= #429 #536)
-#700 := (= #428 -1::int)
-#704 := (div -1::int 3::int)
-#705 := (= #704 -1::int)
-#706 := [rewrite]: #705
-#698 := (= #428 #704)
-#702 := (= #343 3::int)
-#703 := [rewrite]: #702
-#559 := (= #427 -1::int)
-#701 := [rewrite]: #559
-#699 := [monotonicity #701 #703]: #698
-#707 := [trans #699 #706]: #700
-#539 := [monotonicity #707]: #538
-#696 := [trans #539 #693]: #695
-#579 := [monotonicity #696]: #697
-#590 := [trans #579 #540]: #688
-#689 := [monotonicity #590]: #686
-#592 := [trans #689 #589]: #591
-#557 := (iff #434 #752)
-#710 := (= #430 #175)
-#713 := (+ #175 0::int)
-#714 := (= #713 #175)
-#715 := [rewrite]: #714
-#708 := (= #430 #713)
-#711 := (= #433 0::int)
-#435 := (* -1::int 0::int)
-#718 := (= #435 0::int)
-#722 := [rewrite]: #718
-#717 := (= #433 #435)
-#719 := (= #432 0::int)
-#720 := [rewrite]: #719
-#721 := [monotonicity #720]: #717
-#712 := [trans #721 #722]: #711
-#709 := [monotonicity #712]: #708
-#716 := [trans #709 #715]: #710
-#558 := [monotonicity #716]: #557
-#440 := (iff #419 false)
-#406 := (or false false)
-#731 := (iff #406 false)
-#394 := [rewrite]: #731
-#438 := (iff #419 #406)
-#724 := (iff #407 false)
-#1 := true
-#381 := (not true)
-#740 := (iff #381 false)
-#743 := [rewrite]: #740
-#723 := (iff #407 #381)
-#448 := (iff #750 true)
-#454 := (or false true)
-#725 := (iff #454 true)
-#726 := [rewrite]: #725
-#455 := (iff #750 #454)
-#397 := (iff #413 true)
-#733 := [rewrite]: #397
-#452 := (iff #748 false)
-#453 := [rewrite]: #452
-#349 := [monotonicity #453 #733]: #455
-#449 := [trans #349 #726]: #448
-#727 := [monotonicity #449]: #723
-#728 := [trans #727 #743]: #724
-#729 := (iff #418 false)
-#382 := (iff #418 #381)
-#739 := (iff #744 true)
-#736 := (or true true)
-#738 := (iff #736 true)
-#376 := [rewrite]: #738
-#737 := (iff #744 #736)
-#734 := (iff #537 true)
-#735 := [rewrite]: #734
-#732 := [monotonicity #733 #735]: #737
-#741 := [trans #732 #376]: #739
-#742 := [monotonicity #741]: #382
-#730 := [trans #742 #743]: #729
-#439 := [monotonicity #730 #728]: #438
-#441 := [trans #439 #394]: #440
-#594 := [monotonicity #441 #558 #592]: #593
-#690 := [trans #594 #596]: #597
-#395 := (iff #749 false)
-#747 := (iff #749 #406)
-#410 := (iff #753 false)
-#746 := [rewrite]: #410
-#745 := (iff #754 false)
-#405 := [rewrite]: #745
-#390 := [monotonicity #405 #746]: #747
-#396 := [trans #390 #394]: #395
-#691 := [monotonicity #396 #690]: #687
-#680 := [trans #691 #596]: #678
-#683 := [monotonicity #680]: #682
-#673 := [trans #683 #684]: #682
-#681 := [quant-inst]: #671
-#674 := [mp #681 #673]: #669
-[unit-resolution #674 #762 #198]: false
-unsat
-3ca836a50902cedb9598c64c13667ab84779478c 323 0
-#2 := false
-#68 := -1::int
-decl f3 :: (-> int int int)
-#172 := -3::int
-#38 := 3::int
-#175 := (f3 3::int -3::int)
-#180 := (= #175 -1::int)
-#193 := (not #180)
-#41 := 1::int
-#42 := (- 1::int)
-#39 := (- 3::int)
-#40 := (f3 3::int #39)
-#43 := (= #40 #42)
-#44 := (not #43)
-#196 := (iff #44 #193)
-#183 := (= -1::int #175)
-#188 := (not #183)
-#194 := (iff #188 #193)
-#191 := (iff #183 #180)
-#192 := [rewrite]: #191
-#195 := [monotonicity #192]: #194
-#189 := (iff #44 #188)
-#186 := (iff #43 #183)
-#184 := (iff #180 #183)
-#185 := [rewrite]: #184
-#181 := (iff #43 #180)
-#178 := (= #42 -1::int)
-#179 := [rewrite]: #178
-#176 := (= #40 #175)
-#173 := (= #39 -3::int)
-#174 := [rewrite]: #173
-#177 := [monotonicity #174]: #176
-#182 := [monotonicity #177 #179]: #181
-#187 := [trans #182 #185]: #186
-#190 := [monotonicity #187]: #189
-#197 := [trans #190 #195]: #196
-#171 := [asserted]: #44
-#198 := [mp #171 #197]: #193
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#756 := (pattern #10)
-#11 := 0::int
-#72 := (* -1::int #9)
-#69 := (* -1::int #8)
-#75 := (div #69 #72)
-#259 := (* -1::int #75)
-#260 := (+ #10 #259)
-#261 := (= #260 0::int)
-#21 := (div #8 #9)
-#256 := (* -1::int #21)
-#257 := (+ #10 #256)
-#258 := (= #257 0::int)
-#94 := (<= #9 0::int)
-#90 := (<= #8 0::int)
-#214 := (or #90 #94)
-#215 := (not #214)
-#101 := (>= #8 0::int)
-#206 := (or #94 #101)
-#207 := (not #206)
-#221 := (or #207 #215)
-#262 := (ite #221 #258 #261)
-#255 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#263 := (ite #14 #255 #262)
-#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
-#266 := (forall (vars (?v0 int) (?v1 int)) #263)
-#760 := (iff #266 #757)
-#758 := (iff #263 #263)
-#759 := [refl]: #758
-#761 := [quant-intro #759]: #760
-#226 := (ite #221 #21 #75)
-#229 := (ite #14 0::int #226)
-#232 := (= #10 #229)
-#235 := (forall (vars (?v0 int) (?v1 int)) #232)
-#267 := (iff #235 #266)
-#264 := (iff #232 #263)
-#265 := [rewrite]: #264
-#268 := [quant-intro #265]: #267
-#102 := (not #101)
-#95 := (not #94)
-#105 := (and #95 #102)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#111 := (ite #108 #21 #75)
-#114 := (ite #14 0::int #111)
-#117 := (= #10 #114)
-#120 := (forall (vars (?v0 int) (?v1 int)) #117)
-#236 := (iff #120 #235)
-#233 := (iff #117 #232)
-#230 := (= #114 #229)
-#227 := (= #111 #226)
-#224 := (iff #108 #221)
-#218 := (or #215 #207)
-#222 := (iff #218 #221)
-#223 := [rewrite]: #222
-#219 := (iff #108 #218)
-#216 := (iff #105 #207)
-#217 := [rewrite]: #216
-#204 := (iff #98 #215)
-#205 := [rewrite]: #204
-#220 := [monotonicity #205 #217]: #219
-#225 := [trans #220 #223]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [quant-intro #234]: #236
-#210 := (~ #120 #120)
-#208 := (~ #117 #117)
-#209 := [refl]: #208
-#211 := [nnf-pos #209]: #210
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#123 := (iff #28 #120)
-#62 := (and #16 #18)
-#65 := (or #17 #62)
-#78 := (ite #65 #21 #75)
-#81 := (ite #14 0::int #78)
-#84 := (= #10 #81)
-#87 := (forall (vars (?v0 int) (?v1 int)) #84)
-#121 := (iff #87 #120)
-#118 := (iff #84 #117)
-#115 := (= #81 #114)
-#112 := (= #78 #111)
-#109 := (iff #65 #108)
-#106 := (iff #62 #105)
-#103 := (iff #18 #102)
-#104 := [rewrite]: #103
-#96 := (iff #16 #95)
-#97 := [rewrite]: #96
-#107 := [monotonicity #97 #104]: #106
-#99 := (iff #17 #98)
-#92 := (iff #15 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [monotonicity #116]: #118
-#122 := [quant-intro #119]: #121
-#88 := (iff #28 #87)
-#85 := (iff #27 #84)
-#82 := (= #26 #81)
-#79 := (= #25 #78)
-#76 := (= #24 #75)
-#73 := (= #23 #72)
-#74 := [rewrite]: #73
-#70 := (= #22 #69)
-#71 := [rewrite]: #70
-#77 := [monotonicity #71 #74]: #76
-#66 := (iff #20 #65)
-#63 := (iff #19 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#80 := [monotonicity #67 #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [monotonicity #83]: #85
-#89 := [quant-intro #86]: #88
-#124 := [trans #89 #122]: #123
-#61 := [asserted]: #28
-#125 := [mp #61 #124]: #120
-#201 := [mp~ #125 #211]: #120
-#238 := [mp #201 #237]: #235
-#269 := [mp #238 #268]: #266
-#762 := [mp #269 #761]: #757
-#680 := (not #757)
-#672 := (or #680 #180)
-#343 := (* -1::int -3::int)
-#427 := (* -1::int 3::int)
-#428 := (div #427 #343)
-#429 := (* -1::int #428)
-#420 := (+ #175 #429)
-#431 := (= #420 0::int)
-#432 := (div 3::int -3::int)
-#433 := (* -1::int #432)
-#430 := (+ #175 #433)
-#434 := (= #430 0::int)
-#413 := (<= -3::int 0::int)
-#748 := (<= 3::int 0::int)
-#750 := (or #748 #413)
-#407 := (not #750)
-#537 := (>= 3::int 0::int)
-#744 := (or #413 #537)
-#418 := (not #744)
-#419 := (or #418 #407)
-#751 := (ite #419 #434 #431)
-#752 := (= #175 0::int)
-#753 := (= -3::int 0::int)
-#754 := (= 3::int 0::int)
-#749 := (or #754 #753)
-#755 := (ite #749 #752 #751)
-#669 := (or #680 #755)
-#681 := (iff #669 #672)
-#683 := (iff #672 #672)
-#679 := [rewrite]: #683
-#691 := (iff #755 #180)
-#595 := (ite false #752 #180)
-#690 := (iff #595 #180)
-#687 := [rewrite]: #690
-#596 := (iff #755 #595)
-#593 := (iff #751 #180)
-#574 := (ite false #180 #180)
-#592 := (iff #574 #180)
-#585 := [rewrite]: #592
-#589 := (iff #751 #574)
-#686 := (iff #431 #180)
-#714 := (+ 1::int #175)
-#558 := (= #714 0::int)
-#702 := (iff #558 #180)
-#703 := [rewrite]: #702
-#590 := (iff #431 #558)
-#540 := (= #420 #714)
-#713 := (+ #175 1::int)
-#715 := (= #713 #714)
-#710 := [rewrite]: #715
-#580 := (= #420 #713)
-#697 := (= #429 1::int)
-#435 := (* -1::int -1::int)
-#718 := (= #435 1::int)
-#722 := [rewrite]: #718
-#696 := (= #429 #435)
-#693 := (= #428 -1::int)
-#707 := (div -3::int 3::int)
-#539 := (= #707 -1::int)
-#692 := [rewrite]: #539
-#536 := (= #428 #707)
-#706 := (= #343 3::int)
-#700 := [rewrite]: #706
-#699 := (= #427 -3::int)
-#705 := [rewrite]: #699
-#538 := [monotonicity #705 #700]: #536
-#695 := [trans #538 #692]: #693
-#694 := [monotonicity #695]: #696
-#579 := [trans #694 #722]: #697
-#581 := [monotonicity #579]: #580
-#688 := [trans #581 #710]: #540
-#685 := [monotonicity #688]: #590
-#689 := [trans #685 #703]: #686
-#704 := (iff #434 #180)
-#559 := (iff #434 #558)
-#716 := (= #430 #714)
-#708 := (= #430 #713)
-#711 := (= #433 1::int)
-#717 := (= #433 #435)
-#719 := (= #432 -1::int)
-#720 := [rewrite]: #719
-#721 := [monotonicity #720]: #717
-#712 := [trans #721 #722]: #711
-#709 := [monotonicity #712]: #708
-#557 := [trans #709 #710]: #716
-#701 := [monotonicity #557]: #559
-#698 := [trans #701 #703]: #704
-#440 := (iff #419 false)
-#406 := (or false false)
-#731 := (iff #406 false)
-#394 := [rewrite]: #731
-#438 := (iff #419 #406)
-#724 := (iff #407 false)
-#1 := true
-#381 := (not true)
-#740 := (iff #381 false)
-#743 := [rewrite]: #740
-#723 := (iff #407 #381)
-#448 := (iff #750 true)
-#454 := (or false true)
-#725 := (iff #454 true)
-#726 := [rewrite]: #725
-#455 := (iff #750 #454)
-#397 := (iff #413 true)
-#733 := [rewrite]: #397
-#452 := (iff #748 false)
-#453 := [rewrite]: #452
-#349 := [monotonicity #453 #733]: #455
-#449 := [trans #349 #726]: #448
-#727 := [monotonicity #449]: #723
-#728 := [trans #727 #743]: #724
-#729 := (iff #418 false)
-#382 := (iff #418 #381)
-#739 := (iff #744 true)
-#736 := (or true true)
-#738 := (iff #736 true)
-#376 := [rewrite]: #738
-#737 := (iff #744 #736)
-#734 := (iff #537 true)
-#735 := [rewrite]: #734
-#732 := [monotonicity #733 #735]: #737
-#741 := [trans #732 #376]: #739
-#742 := [monotonicity #741]: #382
-#730 := [trans #742 #743]: #729
-#439 := [monotonicity #730 #728]: #438
-#441 := [trans #439 #394]: #440
-#591 := [monotonicity #441 #698 #689]: #589
-#594 := [trans #591 #585]: #593
-#395 := (iff #749 false)
-#747 := (iff #749 #406)
-#410 := (iff #753 false)
-#746 := [rewrite]: #410
-#745 := (iff #754 false)
-#405 := [rewrite]: #745
-#390 := [monotonicity #405 #746]: #747
-#396 := [trans #390 #394]: #395
-#597 := [monotonicity #396 #594]: #596
-#678 := [trans #597 #687]: #691
-#682 := [monotonicity #678]: #681
-#684 := [trans #682 #679]: #681
-#671 := [quant-inst]: #669
-#673 := [mp #671 #684]: #672
-[unit-resolution #673 #762 #198]: false
-unsat
-7e60c8e870227efa11986e096bca8fb9f1d5067a 322 0
+ed5e3568452fe6600500ab5071290e80a7175922 322 0
 #2 := false
 #38 := 1::int
 decl f4 :: (-> int int int)
@@ -36065,334 +38552,7 @@
 #642 := [mp #654 #658]: #660
 [unit-resolution #642 #750 #169]: false
 unsat
-4e54628370c67b364f92814a1e587bd252e7851a 326 0
-#2 := false
-#179 := -2::int
-decl f3 :: (-> int int int)
-#173 := -3::int
-#38 := 5::int
-#176 := (f3 5::int -3::int)
-#182 := (= #176 -2::int)
-#185 := (not #182)
-#42 := 2::int
-#43 := (- 2::int)
-#39 := 3::int
-#40 := (- 3::int)
-#41 := (f3 5::int #40)
-#44 := (= #41 #43)
-#45 := (not #44)
-#186 := (iff #45 #185)
-#183 := (iff #44 #182)
-#180 := (= #43 -2::int)
-#181 := [rewrite]: #180
-#177 := (= #41 #176)
-#174 := (= #40 -3::int)
-#175 := [rewrite]: #174
-#178 := [monotonicity #175]: #177
-#184 := [monotonicity #178 #181]: #183
-#187 := [monotonicity #184]: #186
-#172 := [asserted]: #45
-#190 := [mp #172 #187]: #185
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#747 := (pattern #10)
-#11 := 0::int
-#69 := -1::int
-#73 := (* -1::int #9)
-#70 := (* -1::int #8)
-#76 := (div #70 #73)
-#249 := (* -1::int #76)
-#250 := (+ #10 #249)
-#251 := (= #250 0::int)
-#21 := (div #8 #9)
-#246 := (* -1::int #21)
-#247 := (+ #10 #246)
-#248 := (= #247 0::int)
-#95 := (<= #9 0::int)
-#91 := (<= #8 0::int)
-#204 := (or #91 #95)
-#205 := (not #204)
-#102 := (>= #8 0::int)
-#196 := (or #95 #102)
-#197 := (not #196)
-#211 := (or #197 #205)
-#252 := (ite #211 #248 #251)
-#245 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#253 := (ite #14 #245 #252)
-#748 := (forall (vars (?v0 int) (?v1 int)) (:pat #747) #253)
-#256 := (forall (vars (?v0 int) (?v1 int)) #253)
-#751 := (iff #256 #748)
-#749 := (iff #253 #253)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#216 := (ite #211 #21 #76)
-#219 := (ite #14 0::int #216)
-#222 := (= #10 #219)
-#225 := (forall (vars (?v0 int) (?v1 int)) #222)
-#257 := (iff #225 #256)
-#254 := (iff #222 #253)
-#255 := [rewrite]: #254
-#258 := [quant-intro #255]: #257
-#103 := (not #102)
-#96 := (not #95)
-#106 := (and #96 #103)
-#92 := (not #91)
-#99 := (and #92 #96)
-#109 := (or #99 #106)
-#112 := (ite #109 #21 #76)
-#115 := (ite #14 0::int #112)
-#118 := (= #10 #115)
-#121 := (forall (vars (?v0 int) (?v1 int)) #118)
-#226 := (iff #121 #225)
-#223 := (iff #118 #222)
-#220 := (= #115 #219)
-#217 := (= #112 #216)
-#214 := (iff #109 #211)
-#208 := (or #205 #197)
-#212 := (iff #208 #211)
-#213 := [rewrite]: #212
-#209 := (iff #109 #208)
-#206 := (iff #106 #197)
-#207 := [rewrite]: #206
-#194 := (iff #99 #205)
-#195 := [rewrite]: #194
-#210 := [monotonicity #195 #207]: #209
-#215 := [trans #210 #213]: #214
-#218 := [monotonicity #215]: #217
-#221 := [monotonicity #218]: #220
-#224 := [monotonicity #221]: #223
-#227 := [quant-intro #224]: #226
-#200 := (~ #121 #121)
-#198 := (~ #118 #118)
-#199 := [refl]: #198
-#201 := [nnf-pos #199]: #200
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#124 := (iff #28 #121)
-#63 := (and #16 #18)
-#66 := (or #17 #63)
-#79 := (ite #66 #21 #76)
-#82 := (ite #14 0::int #79)
-#85 := (= #10 #82)
-#88 := (forall (vars (?v0 int) (?v1 int)) #85)
-#122 := (iff #88 #121)
-#119 := (iff #85 #118)
-#116 := (= #82 #115)
-#113 := (= #79 #112)
-#110 := (iff #66 #109)
-#107 := (iff #63 #106)
-#104 := (iff #18 #103)
-#105 := [rewrite]: #104
-#97 := (iff #16 #96)
-#98 := [rewrite]: #97
-#108 := [monotonicity #98 #105]: #107
-#100 := (iff #17 #99)
-#93 := (iff #15 #92)
-#94 := [rewrite]: #93
-#101 := [monotonicity #94 #98]: #100
-#111 := [monotonicity #101 #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [monotonicity #117]: #119
-#123 := [quant-intro #120]: #122
-#89 := (iff #28 #88)
-#86 := (iff #27 #85)
-#83 := (= #26 #82)
-#80 := (= #25 #79)
-#77 := (= #24 #76)
-#74 := (= #23 #73)
-#75 := [rewrite]: #74
-#71 := (= #22 #70)
-#72 := [rewrite]: #71
-#78 := [monotonicity #72 #75]: #77
-#67 := (iff #20 #66)
-#64 := (iff #19 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#81 := [monotonicity #68 #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [monotonicity #84]: #86
-#90 := [quant-intro #87]: #89
-#125 := [trans #90 #123]: #124
-#62 := [asserted]: #28
-#126 := [mp #62 #125]: #121
-#191 := [mp~ #126 #201]: #121
-#228 := [mp #191 #227]: #225
-#259 := [mp #228 #258]: #256
-#753 := [mp #259 #752]: #748
-#667 := (not #748)
-#661 := (or #667 #182)
-#333 := (* -1::int -3::int)
-#418 := (* -1::int 5::int)
-#419 := (div #418 #333)
-#420 := (* -1::int #419)
-#411 := (+ #176 #420)
-#422 := (= #411 0::int)
-#423 := (div 5::int -3::int)
-#351 := (* -1::int #423)
-#424 := (+ #176 #351)
-#421 := (= #424 0::int)
-#425 := (<= -3::int 0::int)
-#404 := (<= 5::int 0::int)
-#739 := (or #404 #425)
-#741 := (not #739)
-#398 := (>= 5::int 0::int)
-#528 := (or #425 #398)
-#735 := (not #528)
-#409 := (or #735 #741)
-#410 := (ite #409 #421 #422)
-#742 := (= #176 0::int)
-#743 := (= -3::int 0::int)
-#744 := (= 5::int 0::int)
-#745 := (or #744 #743)
-#740 := (ite #745 #742 #410)
-#668 := (or #667 #740)
-#653 := (iff #668 #661)
-#656 := (iff #661 #661)
-#657 := [rewrite]: #656
-#665 := (iff #740 #182)
-#673 := (ite false #742 #182)
-#675 := (iff #673 #182)
-#664 := [rewrite]: #675
-#674 := (iff #740 #673)
-#662 := (iff #410 #182)
-#693 := (= #176 -1::int)
-#682 := (ite false #693 #182)
-#663 := (iff #682 #182)
-#660 := [rewrite]: #663
-#669 := (iff #410 #682)
-#681 := (iff #422 #182)
-#565 := (+ 2::int #176)
-#584 := (= #565 0::int)
-#587 := (iff #584 #182)
-#588 := [rewrite]: #587
-#585 := (iff #422 #584)
-#583 := (= #411 #565)
-#676 := (+ #176 2::int)
-#580 := (= #676 #565)
-#582 := [rewrite]: #580
-#677 := (= #411 #676)
-#679 := (= #420 2::int)
-#688 := (* -1::int -2::int)
-#572 := (= #688 2::int)
-#531 := [rewrite]: #572
-#570 := (= #420 #688)
-#687 := (= #419 -2::int)
-#696 := -5::int
-#529 := (div -5::int 3::int)
-#684 := (= #529 -2::int)
-#686 := [rewrite]: #684
-#530 := (= #419 #529)
-#698 := (= #333 3::int)
-#527 := [rewrite]: #698
-#697 := (= #418 -5::int)
-#691 := [rewrite]: #697
-#683 := [monotonicity #691 #527]: #530
-#685 := [trans #683 #686]: #687
-#571 := [monotonicity #685]: #570
-#581 := [trans #571 #531]: #679
-#680 := [monotonicity #581]: #677
-#576 := [trans #680 #582]: #583
-#586 := [monotonicity #576]: #585
-#678 := [trans #586 #588]: #681
-#689 := (iff #421 #693)
-#712 := 1::int
-#705 := (+ 1::int #176)
-#549 := (= #705 0::int)
-#694 := (iff #549 #693)
-#695 := [rewrite]: #694
-#550 := (iff #421 #549)
-#707 := (= #424 #705)
-#704 := (+ #176 1::int)
-#706 := (= #704 #705)
-#701 := [rewrite]: #706
-#699 := (= #424 #704)
-#702 := (= #351 1::int)
-#711 := (* -1::int -1::int)
-#709 := (= #711 1::int)
-#713 := [rewrite]: #709
-#426 := (= #351 #711)
-#432 := (= #423 -1::int)
-#710 := [rewrite]: #432
-#708 := [monotonicity #710]: #426
-#703 := [trans #708 #713]: #702
-#700 := [monotonicity #703]: #699
-#548 := [trans #700 #701]: #707
-#692 := [monotonicity #548]: #550
-#690 := [trans #692 #695]: #689
-#430 := (iff #409 false)
-#737 := (or false false)
-#381 := (iff #737 false)
-#722 := [rewrite]: #381
-#719 := (iff #409 #737)
-#718 := (iff #741 false)
-#1 := true
-#732 := (not true)
-#733 := (iff #732 false)
-#731 := [rewrite]: #733
-#440 := (iff #741 #732)
-#717 := (iff #739 true)
-#444 := (or false true)
-#339 := (iff #444 true)
-#716 := [rewrite]: #339
-#445 := (iff #739 #444)
-#387 := (iff #425 true)
-#388 := [rewrite]: #387
-#721 := (iff #404 false)
-#443 := [rewrite]: #721
-#446 := [monotonicity #443 #388]: #445
-#439 := [trans #446 #716]: #717
-#714 := [monotonicity #439]: #440
-#715 := [trans #714 #731]: #718
-#734 := (iff #735 false)
-#372 := (iff #735 #732)
-#367 := (iff #528 true)
-#726 := (or true true)
-#723 := (iff #726 true)
-#729 := [rewrite]: #723
-#727 := (iff #528 #726)
-#724 := (iff #398 true)
-#725 := [rewrite]: #724
-#728 := [monotonicity #388 #725]: #727
-#730 := [trans #728 #729]: #367
-#373 := [monotonicity #730]: #372
-#720 := [trans #373 #731]: #734
-#429 := [monotonicity #720 #715]: #719
-#431 := [trans #429 #722]: #430
-#671 := [monotonicity #431 #690 #678]: #669
-#672 := [trans #671 #660]: #662
-#385 := (iff #745 false)
-#397 := (iff #745 #737)
-#396 := (iff #743 false)
-#401 := [rewrite]: #396
-#746 := (iff #744 false)
-#736 := [rewrite]: #746
-#738 := [monotonicity #736 #401]: #397
-#386 := [trans #738 #722]: #385
-#670 := [monotonicity #386 #672]: #674
-#666 := [trans #670 #664]: #665
-#655 := [monotonicity #666]: #653
-#658 := [trans #655 #657]: #653
-#652 := [quant-inst]: #668
-#654 := [mp #652 #658]: #661
-[unit-resolution #654 #753 #190]: false
-unsat
-6560bfd674a12139ed8cf76157a9702921110fe8 297 0
+1897b65589b01a36e8c901ddcdce3eb69e66fd4d 297 0
 #2 := false
 #11 := 0::int
 decl f4 :: (-> int int int)
@@ -36690,329 +38850,7 @@
 #576 := [mp #570 #575]: #670
 [unit-resolution #576 #750 #168]: false
 unsat
-d0a25a18442fdd27e302706e9c8d8ea55968f062 321 0
-#2 := false
-#67 := -1::int
-decl f3 :: (-> int int int)
-#40 := 3::int
-#173 := (f3 -1::int 3::int)
-#176 := (= #173 -1::int)
-#189 := (not #176)
-#38 := 1::int
-#39 := (- 1::int)
-#41 := (f3 #39 3::int)
-#42 := (= #41 #39)
-#43 := (not #42)
-#192 := (iff #43 #189)
-#179 := (= -1::int #173)
-#184 := (not #179)
-#190 := (iff #184 #189)
-#187 := (iff #179 #176)
-#188 := [rewrite]: #187
-#191 := [monotonicity #188]: #190
-#185 := (iff #43 #184)
-#182 := (iff #42 #179)
-#180 := (iff #176 #179)
-#181 := [rewrite]: #180
-#177 := (iff #42 #176)
-#171 := (= #39 -1::int)
-#172 := [rewrite]: #171
-#174 := (= #41 #173)
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175 #172]: #177
-#183 := [trans #178 #181]: #182
-#186 := [monotonicity #183]: #185
-#193 := [trans #186 #191]: #192
-#170 := [asserted]: #43
-#194 := [mp #170 #193]: #189
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#752 := (pattern #10)
-#11 := 0::int
-#71 := (* -1::int #9)
-#68 := (* -1::int #8)
-#74 := (div #68 #71)
-#255 := (* -1::int #74)
-#256 := (+ #10 #255)
-#257 := (= #256 0::int)
-#21 := (div #8 #9)
-#252 := (* -1::int #21)
-#253 := (+ #10 #252)
-#254 := (= #253 0::int)
-#93 := (<= #9 0::int)
-#89 := (<= #8 0::int)
-#210 := (or #89 #93)
-#211 := (not #210)
-#100 := (>= #8 0::int)
-#202 := (or #93 #100)
-#203 := (not #202)
-#217 := (or #203 #211)
-#258 := (ite #217 #254 #257)
-#251 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#259 := (ite #14 #251 #258)
-#753 := (forall (vars (?v0 int) (?v1 int)) (:pat #752) #259)
-#262 := (forall (vars (?v0 int) (?v1 int)) #259)
-#756 := (iff #262 #753)
-#754 := (iff #259 #259)
-#755 := [refl]: #754
-#757 := [quant-intro #755]: #756
-#222 := (ite #217 #21 #74)
-#225 := (ite #14 0::int #222)
-#228 := (= #10 #225)
-#231 := (forall (vars (?v0 int) (?v1 int)) #228)
-#263 := (iff #231 #262)
-#260 := (iff #228 #259)
-#261 := [rewrite]: #260
-#264 := [quant-intro #261]: #263
-#101 := (not #100)
-#94 := (not #93)
-#104 := (and #94 #101)
-#90 := (not #89)
-#97 := (and #90 #94)
-#107 := (or #97 #104)
-#110 := (ite #107 #21 #74)
-#113 := (ite #14 0::int #110)
-#116 := (= #10 #113)
-#119 := (forall (vars (?v0 int) (?v1 int)) #116)
-#232 := (iff #119 #231)
-#229 := (iff #116 #228)
-#226 := (= #113 #225)
-#223 := (= #110 #222)
-#220 := (iff #107 #217)
-#214 := (or #211 #203)
-#218 := (iff #214 #217)
-#219 := [rewrite]: #218
-#215 := (iff #107 #214)
-#212 := (iff #104 #203)
-#213 := [rewrite]: #212
-#200 := (iff #97 #211)
-#201 := [rewrite]: #200
-#216 := [monotonicity #201 #213]: #215
-#221 := [trans #216 #219]: #220
-#224 := [monotonicity #221]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [quant-intro #230]: #232
-#206 := (~ #119 #119)
-#204 := (~ #116 #116)
-#205 := [refl]: #204
-#207 := [nnf-pos #205]: #206
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#122 := (iff #28 #119)
-#61 := (and #16 #18)
-#64 := (or #17 #61)
-#77 := (ite #64 #21 #74)
-#80 := (ite #14 0::int #77)
-#83 := (= #10 #80)
-#86 := (forall (vars (?v0 int) (?v1 int)) #83)
-#120 := (iff #86 #119)
-#117 := (iff #83 #116)
-#114 := (= #80 #113)
-#111 := (= #77 #110)
-#108 := (iff #64 #107)
-#105 := (iff #61 #104)
-#102 := (iff #18 #101)
-#103 := [rewrite]: #102
-#95 := (iff #16 #94)
-#96 := [rewrite]: #95
-#106 := [monotonicity #96 #103]: #105
-#98 := (iff #17 #97)
-#91 := (iff #15 #90)
-#92 := [rewrite]: #91
-#99 := [monotonicity #92 #96]: #98
-#109 := [monotonicity #99 #106]: #108
-#112 := [monotonicity #109]: #111
-#115 := [monotonicity #112]: #114
-#118 := [monotonicity #115]: #117
-#121 := [quant-intro #118]: #120
-#87 := (iff #28 #86)
-#84 := (iff #27 #83)
-#81 := (= #26 #80)
-#78 := (= #25 #77)
-#75 := (= #24 #74)
-#72 := (= #23 #71)
-#73 := [rewrite]: #72
-#69 := (= #22 #68)
-#70 := [rewrite]: #69
-#76 := [monotonicity #70 #73]: #75
-#65 := (iff #20 #64)
-#62 := (iff #19 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#79 := [monotonicity #66 #76]: #78
-#82 := [monotonicity #79]: #81
-#85 := [monotonicity #82]: #84
-#88 := [quant-intro #85]: #87
-#123 := [trans #88 #121]: #122
-#60 := [asserted]: #28
-#124 := [mp #60 #123]: #119
-#197 := [mp~ #124 #207]: #119
-#234 := [mp #197 #233]: #231
-#265 := [mp #234 #264]: #262
-#758 := [mp #265 #757]: #753
-#665 := (not #753)
-#667 := (or #665 #176)
-#339 := (* -1::int 3::int)
-#423 := (* -1::int -1::int)
-#424 := (div #423 #339)
-#425 := (* -1::int #424)
-#416 := (+ #173 #425)
-#427 := (= #416 0::int)
-#428 := (div -1::int 3::int)
-#429 := (* -1::int #428)
-#426 := (+ #173 #429)
-#430 := (= #426 0::int)
-#409 := (<= 3::int 0::int)
-#744 := (<= -1::int 0::int)
-#746 := (or #744 #409)
-#403 := (not #746)
-#533 := (>= -1::int 0::int)
-#740 := (or #409 #533)
-#414 := (not #740)
-#415 := (or #414 #403)
-#747 := (ite #415 #430 #427)
-#748 := (= #173 0::int)
-#749 := (= 3::int 0::int)
-#750 := (= -1::int 0::int)
-#745 := (or #750 #749)
-#751 := (ite #745 #748 #747)
-#677 := (or #665 #751)
-#679 := (iff #677 #667)
-#680 := (iff #667 #667)
-#669 := [rewrite]: #680
-#676 := (iff #751 #176)
-#593 := (ite false #748 #176)
-#687 := (iff #593 #176)
-#674 := [rewrite]: #687
-#686 := (iff #751 #593)
-#591 := (iff #747 #176)
-#1 := true
-#587 := (ite true #176 #748)
-#589 := (iff #587 #176)
-#590 := [rewrite]: #589
-#588 := (iff #747 #587)
-#570 := (iff #427 #748)
-#682 := (= #416 #173)
-#577 := (+ #173 0::int)
-#586 := (= #577 #173)
-#681 := [rewrite]: #586
-#536 := (= #416 #577)
-#575 := (= #425 0::int)
-#689 := (* -1::int 0::int)
-#690 := (= #689 0::int)
-#693 := [rewrite]: #690
-#691 := (= #425 #689)
-#535 := (= #424 0::int)
-#694 := -3::int
-#702 := (div 1::int -3::int)
-#532 := (= #702 0::int)
-#534 := [rewrite]: #532
-#696 := (= #424 #702)
-#695 := (= #339 -3::int)
-#701 := [rewrite]: #695
-#717 := (= #423 1::int)
-#714 := [rewrite]: #717
-#703 := [monotonicity #714 #701]: #696
-#688 := [trans #703 #534]: #535
-#692 := [monotonicity #688]: #691
-#576 := [trans #692 #693]: #575
-#684 := [monotonicity #576]: #536
-#685 := [trans #684 #681]: #682
-#585 := [monotonicity #685]: #570
-#699 := (iff #430 #176)
-#705 := (+ 1::int #173)
-#553 := (= #705 0::int)
-#697 := (iff #553 #176)
-#698 := [rewrite]: #697
-#554 := (iff #430 #553)
-#706 := (= #426 #705)
-#708 := (+ #173 1::int)
-#710 := (= #708 #705)
-#711 := [rewrite]: #710
-#709 := (= #426 #708)
-#718 := (= #429 1::int)
-#431 := (= #429 #423)
-#715 := (= #428 -1::int)
-#716 := [rewrite]: #715
-#713 := [monotonicity #716]: #431
-#707 := [trans #713 #714]: #718
-#704 := [monotonicity #707]: #709
-#712 := [trans #704 #711]: #706
-#555 := [monotonicity #712]: #554
-#700 := [trans #555 #698]: #699
-#436 := (iff #415 true)
-#726 := (or true false)
-#450 := (iff #726 true)
-#451 := [rewrite]: #450
-#434 := (iff #415 #726)
-#720 := (iff #403 false)
-#722 := (not true)
-#719 := (iff #722 false)
-#723 := [rewrite]: #719
-#444 := (iff #403 #722)
-#345 := (iff #746 true)
-#448 := (iff #746 #726)
-#393 := (iff #409 false)
-#729 := [rewrite]: #393
-#739 := (iff #744 true)
-#725 := [rewrite]: #739
-#449 := [monotonicity #725 #729]: #448
-#721 := [trans #449 #451]: #345
-#445 := [monotonicity #721]: #444
-#724 := [trans #445 #723]: #720
-#738 := (iff #414 true)
-#372 := (not false)
-#377 := (iff #372 true)
-#378 := [rewrite]: #377
-#735 := (iff #414 #372)
-#728 := (iff #740 false)
-#402 := (or false false)
-#727 := (iff #402 false)
-#390 := [rewrite]: #727
-#732 := (iff #740 #402)
-#730 := (iff #533 false)
-#731 := [rewrite]: #730
-#733 := [monotonicity #729 #731]: #732
-#734 := [trans #733 #390]: #728
-#737 := [monotonicity #734]: #735
-#736 := [trans #737 #378]: #738
-#435 := [monotonicity #736 #724]: #434
-#437 := [trans #435 #451]: #436
-#581 := [monotonicity #437 #700 #585]: #588
-#592 := [trans #581 #590]: #591
-#391 := (iff #745 false)
-#743 := (iff #745 #402)
-#406 := (iff #749 false)
-#742 := [rewrite]: #406
-#741 := (iff #750 false)
-#401 := [rewrite]: #741
-#386 := [monotonicity #401 #742]: #743
-#392 := [trans #386 #390]: #391
-#683 := [monotonicity #392 #592]: #686
-#668 := [trans #683 #674]: #676
-#675 := [monotonicity #668]: #679
-#670 := [trans #675 #669]: #679
-#678 := [quant-inst]: #677
-#671 := [mp #678 #670]: #667
-[unit-resolution #671 #758 #194]: false
-unsat
-9f593513c6223913ee1444c7c2d179bd416f9b73 328 0
+0950f059c8c59b021ddf8b08664ab965652bd6ab 328 0
 #2 := false
 #41 := 2::int
 decl f4 :: (-> int int int)
@@ -37341,331 +39179,7 @@
 #641 := [mp #635 #636]: #650
 [unit-resolution #641 #742 #170]: false
 unsat
-502812e8687a6ca679f5bc63f75291a9fdb3db70 323 0
-#2 := false
-#68 := -1::int
-decl f3 :: (-> int int int)
-#38 := 3::int
-#172 := -3::int
-#175 := (f3 -3::int 3::int)
-#180 := (= #175 -1::int)
-#193 := (not #180)
-#41 := 1::int
-#42 := (- 1::int)
-#39 := (- 3::int)
-#40 := (f3 #39 3::int)
-#43 := (= #40 #42)
-#44 := (not #43)
-#196 := (iff #44 #193)
-#183 := (= -1::int #175)
-#188 := (not #183)
-#194 := (iff #188 #193)
-#191 := (iff #183 #180)
-#192 := [rewrite]: #191
-#195 := [monotonicity #192]: #194
-#189 := (iff #44 #188)
-#186 := (iff #43 #183)
-#184 := (iff #180 #183)
-#185 := [rewrite]: #184
-#181 := (iff #43 #180)
-#178 := (= #42 -1::int)
-#179 := [rewrite]: #178
-#176 := (= #40 #175)
-#173 := (= #39 -3::int)
-#174 := [rewrite]: #173
-#177 := [monotonicity #174]: #176
-#182 := [monotonicity #177 #179]: #181
-#187 := [trans #182 #185]: #186
-#190 := [monotonicity #187]: #189
-#197 := [trans #190 #195]: #196
-#171 := [asserted]: #44
-#198 := [mp #171 #197]: #193
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#756 := (pattern #10)
-#11 := 0::int
-#72 := (* -1::int #9)
-#69 := (* -1::int #8)
-#75 := (div #69 #72)
-#259 := (* -1::int #75)
-#260 := (+ #10 #259)
-#261 := (= #260 0::int)
-#21 := (div #8 #9)
-#256 := (* -1::int #21)
-#257 := (+ #10 #256)
-#258 := (= #257 0::int)
-#94 := (<= #9 0::int)
-#90 := (<= #8 0::int)
-#214 := (or #90 #94)
-#215 := (not #214)
-#101 := (>= #8 0::int)
-#206 := (or #94 #101)
-#207 := (not #206)
-#221 := (or #207 #215)
-#262 := (ite #221 #258 #261)
-#255 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#263 := (ite #14 #255 #262)
-#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
-#266 := (forall (vars (?v0 int) (?v1 int)) #263)
-#760 := (iff #266 #757)
-#758 := (iff #263 #263)
-#759 := [refl]: #758
-#761 := [quant-intro #759]: #760
-#226 := (ite #221 #21 #75)
-#229 := (ite #14 0::int #226)
-#232 := (= #10 #229)
-#235 := (forall (vars (?v0 int) (?v1 int)) #232)
-#267 := (iff #235 #266)
-#264 := (iff #232 #263)
-#265 := [rewrite]: #264
-#268 := [quant-intro #265]: #267
-#102 := (not #101)
-#95 := (not #94)
-#105 := (and #95 #102)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#111 := (ite #108 #21 #75)
-#114 := (ite #14 0::int #111)
-#117 := (= #10 #114)
-#120 := (forall (vars (?v0 int) (?v1 int)) #117)
-#236 := (iff #120 #235)
-#233 := (iff #117 #232)
-#230 := (= #114 #229)
-#227 := (= #111 #226)
-#224 := (iff #108 #221)
-#218 := (or #215 #207)
-#222 := (iff #218 #221)
-#223 := [rewrite]: #222
-#219 := (iff #108 #218)
-#216 := (iff #105 #207)
-#217 := [rewrite]: #216
-#204 := (iff #98 #215)
-#205 := [rewrite]: #204
-#220 := [monotonicity #205 #217]: #219
-#225 := [trans #220 #223]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [quant-intro #234]: #236
-#210 := (~ #120 #120)
-#208 := (~ #117 #117)
-#209 := [refl]: #208
-#211 := [nnf-pos #209]: #210
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#123 := (iff #28 #120)
-#62 := (and #16 #18)
-#65 := (or #17 #62)
-#78 := (ite #65 #21 #75)
-#81 := (ite #14 0::int #78)
-#84 := (= #10 #81)
-#87 := (forall (vars (?v0 int) (?v1 int)) #84)
-#121 := (iff #87 #120)
-#118 := (iff #84 #117)
-#115 := (= #81 #114)
-#112 := (= #78 #111)
-#109 := (iff #65 #108)
-#106 := (iff #62 #105)
-#103 := (iff #18 #102)
-#104 := [rewrite]: #103
-#96 := (iff #16 #95)
-#97 := [rewrite]: #96
-#107 := [monotonicity #97 #104]: #106
-#99 := (iff #17 #98)
-#92 := (iff #15 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [monotonicity #116]: #118
-#122 := [quant-intro #119]: #121
-#88 := (iff #28 #87)
-#85 := (iff #27 #84)
-#82 := (= #26 #81)
-#79 := (= #25 #78)
-#76 := (= #24 #75)
-#73 := (= #23 #72)
-#74 := [rewrite]: #73
-#70 := (= #22 #69)
-#71 := [rewrite]: #70
-#77 := [monotonicity #71 #74]: #76
-#66 := (iff #20 #65)
-#63 := (iff #19 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#80 := [monotonicity #67 #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [monotonicity #83]: #85
-#89 := [quant-intro #86]: #88
-#124 := [trans #89 #122]: #123
-#61 := [asserted]: #28
-#125 := [mp #61 #124]: #120
-#201 := [mp~ #125 #211]: #120
-#238 := [mp #201 #237]: #235
-#269 := [mp #238 #268]: #266
-#762 := [mp #269 #761]: #757
-#680 := (not #757)
-#672 := (or #680 #180)
-#343 := (* -1::int 3::int)
-#427 := (* -1::int -3::int)
-#428 := (div #427 #343)
-#429 := (* -1::int #428)
-#420 := (+ #175 #429)
-#431 := (= #420 0::int)
-#432 := (div -3::int 3::int)
-#433 := (* -1::int #432)
-#430 := (+ #175 #433)
-#434 := (= #430 0::int)
-#413 := (<= 3::int 0::int)
-#748 := (<= -3::int 0::int)
-#750 := (or #748 #413)
-#407 := (not #750)
-#537 := (>= -3::int 0::int)
-#744 := (or #413 #537)
-#418 := (not #744)
-#419 := (or #418 #407)
-#751 := (ite #419 #434 #431)
-#752 := (= #175 0::int)
-#753 := (= 3::int 0::int)
-#754 := (= -3::int 0::int)
-#749 := (or #754 #753)
-#755 := (ite #749 #752 #751)
-#669 := (or #680 #755)
-#681 := (iff #669 #672)
-#683 := (iff #672 #672)
-#679 := [rewrite]: #683
-#691 := (iff #755 #180)
-#595 := (ite false #752 #180)
-#690 := (iff #595 #180)
-#687 := [rewrite]: #690
-#596 := (iff #755 #595)
-#593 := (iff #751 #180)
-#1 := true
-#574 := (ite true #180 #180)
-#592 := (iff #574 #180)
-#585 := [rewrite]: #592
-#589 := (iff #751 #574)
-#686 := (iff #431 #180)
-#714 := (+ 1::int #175)
-#558 := (= #714 0::int)
-#702 := (iff #558 #180)
-#703 := [rewrite]: #702
-#590 := (iff #431 #558)
-#540 := (= #420 #714)
-#713 := (+ #175 1::int)
-#715 := (= #713 #714)
-#710 := [rewrite]: #715
-#580 := (= #420 #713)
-#697 := (= #429 1::int)
-#435 := (* -1::int -1::int)
-#718 := (= #435 1::int)
-#722 := [rewrite]: #718
-#696 := (= #429 #435)
-#693 := (= #428 -1::int)
-#707 := (div 3::int -3::int)
-#539 := (= #707 -1::int)
-#692 := [rewrite]: #539
-#536 := (= #428 #707)
-#706 := (= #343 -3::int)
-#700 := [rewrite]: #706
-#699 := (= #427 3::int)
-#705 := [rewrite]: #699
-#538 := [monotonicity #705 #700]: #536
-#695 := [trans #538 #692]: #693
-#694 := [monotonicity #695]: #696
-#579 := [trans #694 #722]: #697
-#581 := [monotonicity #579]: #580
-#688 := [trans #581 #710]: #540
-#685 := [monotonicity #688]: #590
-#689 := [trans #685 #703]: #686
-#704 := (iff #434 #180)
-#559 := (iff #434 #558)
-#716 := (= #430 #714)
-#708 := (= #430 #713)
-#711 := (= #433 1::int)
-#717 := (= #433 #435)
-#719 := (= #432 -1::int)
-#720 := [rewrite]: #719
-#721 := [monotonicity #720]: #717
-#712 := [trans #721 #722]: #711
-#709 := [monotonicity #712]: #708
-#557 := [trans #709 #710]: #716
-#701 := [monotonicity #557]: #559
-#698 := [trans #701 #703]: #704
-#440 := (iff #419 true)
-#730 := (or true false)
-#454 := (iff #730 true)
-#455 := [rewrite]: #454
-#438 := (iff #419 #730)
-#724 := (iff #407 false)
-#726 := (not true)
-#723 := (iff #726 false)
-#727 := [rewrite]: #723
-#448 := (iff #407 #726)
-#349 := (iff #750 true)
-#452 := (iff #750 #730)
-#397 := (iff #413 false)
-#733 := [rewrite]: #397
-#743 := (iff #748 true)
-#729 := [rewrite]: #743
-#453 := [monotonicity #729 #733]: #452
-#725 := [trans #453 #455]: #349
-#449 := [monotonicity #725]: #448
-#728 := [trans #449 #727]: #724
-#742 := (iff #418 true)
-#376 := (not false)
-#381 := (iff #376 true)
-#382 := [rewrite]: #381
-#739 := (iff #418 #376)
-#732 := (iff #744 false)
-#406 := (or false false)
-#731 := (iff #406 false)
-#394 := [rewrite]: #731
-#736 := (iff #744 #406)
-#734 := (iff #537 false)
-#735 := [rewrite]: #734
-#737 := [monotonicity #733 #735]: #736
-#738 := [trans #737 #394]: #732
-#741 := [monotonicity #738]: #739
-#740 := [trans #741 #382]: #742
-#439 := [monotonicity #740 #728]: #438
-#441 := [trans #439 #455]: #440
-#591 := [monotonicity #441 #698 #689]: #589
-#594 := [trans #591 #585]: #593
-#395 := (iff #749 false)
-#747 := (iff #749 #406)
-#410 := (iff #753 false)
-#746 := [rewrite]: #410
-#745 := (iff #754 false)
-#405 := [rewrite]: #745
-#390 := [monotonicity #405 #746]: #747
-#396 := [trans #390 #394]: #395
-#597 := [monotonicity #396 #594]: #596
-#678 := [trans #597 #687]: #691
-#682 := [monotonicity #678]: #681
-#684 := [trans #682 #679]: #681
-#671 := [quant-inst]: #669
-#673 := [mp #671 #684]: #672
-[unit-resolution #673 #762 #198]: false
-unsat
-9617f71299996e3e5076f71a16d3a6ef69c7fc1f 335 0
+f77523eb025c744a899f70384fe23771c2e2df49 335 0
 #2 := false
 #179 := -2::int
 decl f4 :: (-> int int int)
@@ -38001,662 +39515,7 @@
 #666 := [mp #673 #665]: #671
 [unit-resolution #666 #759 #190]: false
 unsat
-ca3dae13e761e693f76c918c923ae5c553f3cdb1 326 0
-#2 := false
-#179 := -2::int
-decl f3 :: (-> int int int)
-#40 := 3::int
-#173 := -5::int
-#176 := (f3 -5::int 3::int)
-#182 := (= #176 -2::int)
-#185 := (not #182)
-#42 := 2::int
-#43 := (- 2::int)
-#38 := 5::int
-#39 := (- 5::int)
-#41 := (f3 #39 3::int)
-#44 := (= #41 #43)
-#45 := (not #44)
-#186 := (iff #45 #185)
-#183 := (iff #44 #182)
-#180 := (= #43 -2::int)
-#181 := [rewrite]: #180
-#177 := (= #41 #176)
-#174 := (= #39 -5::int)
-#175 := [rewrite]: #174
-#178 := [monotonicity #175]: #177
-#184 := [monotonicity #178 #181]: #183
-#187 := [monotonicity #184]: #186
-#172 := [asserted]: #45
-#190 := [mp #172 #187]: #185
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#747 := (pattern #10)
-#11 := 0::int
-#69 := -1::int
-#73 := (* -1::int #9)
-#70 := (* -1::int #8)
-#76 := (div #70 #73)
-#249 := (* -1::int #76)
-#250 := (+ #10 #249)
-#251 := (= #250 0::int)
-#21 := (div #8 #9)
-#246 := (* -1::int #21)
-#247 := (+ #10 #246)
-#248 := (= #247 0::int)
-#95 := (<= #9 0::int)
-#91 := (<= #8 0::int)
-#204 := (or #91 #95)
-#205 := (not #204)
-#102 := (>= #8 0::int)
-#196 := (or #95 #102)
-#197 := (not #196)
-#211 := (or #197 #205)
-#252 := (ite #211 #248 #251)
-#245 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#253 := (ite #14 #245 #252)
-#748 := (forall (vars (?v0 int) (?v1 int)) (:pat #747) #253)
-#256 := (forall (vars (?v0 int) (?v1 int)) #253)
-#751 := (iff #256 #748)
-#749 := (iff #253 #253)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#216 := (ite #211 #21 #76)
-#219 := (ite #14 0::int #216)
-#222 := (= #10 #219)
-#225 := (forall (vars (?v0 int) (?v1 int)) #222)
-#257 := (iff #225 #256)
-#254 := (iff #222 #253)
-#255 := [rewrite]: #254
-#258 := [quant-intro #255]: #257
-#103 := (not #102)
-#96 := (not #95)
-#106 := (and #96 #103)
-#92 := (not #91)
-#99 := (and #92 #96)
-#109 := (or #99 #106)
-#112 := (ite #109 #21 #76)
-#115 := (ite #14 0::int #112)
-#118 := (= #10 #115)
-#121 := (forall (vars (?v0 int) (?v1 int)) #118)
-#226 := (iff #121 #225)
-#223 := (iff #118 #222)
-#220 := (= #115 #219)
-#217 := (= #112 #216)
-#214 := (iff #109 #211)
-#208 := (or #205 #197)
-#212 := (iff #208 #211)
-#213 := [rewrite]: #212
-#209 := (iff #109 #208)
-#206 := (iff #106 #197)
-#207 := [rewrite]: #206
-#194 := (iff #99 #205)
-#195 := [rewrite]: #194
-#210 := [monotonicity #195 #207]: #209
-#215 := [trans #210 #213]: #214
-#218 := [monotonicity #215]: #217
-#221 := [monotonicity #218]: #220
-#224 := [monotonicity #221]: #223
-#227 := [quant-intro #224]: #226
-#200 := (~ #121 #121)
-#198 := (~ #118 #118)
-#199 := [refl]: #198
-#201 := [nnf-pos #199]: #200
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#124 := (iff #28 #121)
-#63 := (and #16 #18)
-#66 := (or #17 #63)
-#79 := (ite #66 #21 #76)
-#82 := (ite #14 0::int #79)
-#85 := (= #10 #82)
-#88 := (forall (vars (?v0 int) (?v1 int)) #85)
-#122 := (iff #88 #121)
-#119 := (iff #85 #118)
-#116 := (= #82 #115)
-#113 := (= #79 #112)
-#110 := (iff #66 #109)
-#107 := (iff #63 #106)
-#104 := (iff #18 #103)
-#105 := [rewrite]: #104
-#97 := (iff #16 #96)
-#98 := [rewrite]: #97
-#108 := [monotonicity #98 #105]: #107
-#100 := (iff #17 #99)
-#93 := (iff #15 #92)
-#94 := [rewrite]: #93
-#101 := [monotonicity #94 #98]: #100
-#111 := [monotonicity #101 #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [monotonicity #117]: #119
-#123 := [quant-intro #120]: #122
-#89 := (iff #28 #88)
-#86 := (iff #27 #85)
-#83 := (= #26 #82)
-#80 := (= #25 #79)
-#77 := (= #24 #76)
-#74 := (= #23 #73)
-#75 := [rewrite]: #74
-#71 := (= #22 #70)
-#72 := [rewrite]: #71
-#78 := [monotonicity #72 #75]: #77
-#67 := (iff #20 #66)
-#64 := (iff #19 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#81 := [monotonicity #68 #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [monotonicity #84]: #86
-#90 := [quant-intro #87]: #89
-#125 := [trans #90 #123]: #124
-#62 := [asserted]: #28
-#126 := [mp #62 #125]: #121
-#191 := [mp~ #126 #201]: #121
-#228 := [mp #191 #227]: #225
-#259 := [mp #228 #258]: #256
-#753 := [mp #259 #752]: #748
-#667 := (not #748)
-#661 := (or #667 #182)
-#333 := (* -1::int 3::int)
-#418 := (* -1::int -5::int)
-#419 := (div #418 #333)
-#420 := (* -1::int #419)
-#411 := (+ #176 #420)
-#422 := (= #411 0::int)
-#423 := (div -5::int 3::int)
-#351 := (* -1::int #423)
-#424 := (+ #176 #351)
-#421 := (= #424 0::int)
-#425 := (<= 3::int 0::int)
-#404 := (<= -5::int 0::int)
-#739 := (or #404 #425)
-#741 := (not #739)
-#398 := (>= -5::int 0::int)
-#528 := (or #425 #398)
-#735 := (not #528)
-#409 := (or #735 #741)
-#410 := (ite #409 #421 #422)
-#742 := (= #176 0::int)
-#743 := (= 3::int 0::int)
-#744 := (= -5::int 0::int)
-#745 := (or #744 #743)
-#740 := (ite #745 #742 #410)
-#668 := (or #667 #740)
-#653 := (iff #668 #661)
-#656 := (iff #661 #661)
-#657 := [rewrite]: #656
-#665 := (iff #740 #182)
-#673 := (ite false #742 #182)
-#675 := (iff #673 #182)
-#664 := [rewrite]: #675
-#674 := (iff #740 #673)
-#662 := (iff #410 #182)
-#586 := (= #176 -1::int)
-#1 := true
-#682 := (ite true #182 #586)
-#663 := (iff #682 #182)
-#660 := [rewrite]: #663
-#669 := (iff #410 #682)
-#681 := (iff #422 #586)
-#570 := 1::int
-#680 := (+ 1::int #176)
-#576 := (= #680 0::int)
-#587 := (iff #576 #586)
-#588 := [rewrite]: #587
-#584 := (iff #422 #576)
-#582 := (= #411 #680)
-#581 := (+ #176 1::int)
-#565 := (= #581 #680)
-#580 := [rewrite]: #565
-#676 := (= #411 #581)
-#531 := (= #420 1::int)
-#687 := (* -1::int -1::int)
-#571 := (= #687 1::int)
-#572 := [rewrite]: #571
-#685 := (= #420 #687)
-#684 := (= #419 -1::int)
-#696 := -3::int
-#698 := (div 5::int -3::int)
-#530 := (= #698 -1::int)
-#683 := [rewrite]: #530
-#527 := (= #419 #698)
-#697 := (= #333 -3::int)
-#691 := [rewrite]: #697
-#689 := (= #418 5::int)
-#690 := [rewrite]: #689
-#529 := [monotonicity #690 #691]: #527
-#686 := [trans #529 #683]: #684
-#688 := [monotonicity #686]: #685
-#679 := [trans #688 #572]: #531
-#677 := [monotonicity #679]: #676
-#583 := [trans #677 #580]: #582
-#585 := [monotonicity #583]: #584
-#678 := [trans #585 #588]: #681
-#694 := (iff #421 #182)
-#700 := (+ 2::int #176)
-#548 := (= #700 0::int)
-#692 := (iff #548 #182)
-#693 := [rewrite]: #692
-#549 := (iff #421 #548)
-#701 := (= #424 #700)
-#703 := (+ #176 2::int)
-#705 := (= #703 #700)
-#706 := [rewrite]: #705
-#704 := (= #424 #703)
-#713 := (= #351 2::int)
-#711 := (* -1::int -2::int)
-#712 := (= #711 2::int)
-#709 := [rewrite]: #712
-#426 := (= #351 #711)
-#432 := (= #423 -2::int)
-#710 := [rewrite]: #432
-#708 := [monotonicity #710]: #426
-#702 := [trans #708 #709]: #713
-#699 := [monotonicity #702]: #704
-#707 := [trans #699 #706]: #701
-#550 := [monotonicity #707]: #549
-#695 := [trans #550 #693]: #694
-#430 := (iff #409 true)
-#720 := (or true false)
-#444 := (iff #720 true)
-#445 := [rewrite]: #444
-#719 := (iff #409 #720)
-#718 := (iff #741 false)
-#716 := (not true)
-#440 := (iff #716 false)
-#714 := [rewrite]: #440
-#717 := (iff #741 #716)
-#446 := (iff #739 true)
-#721 := (iff #739 #720)
-#387 := (iff #425 false)
-#388 := [rewrite]: #387
-#731 := (iff #404 true)
-#734 := [rewrite]: #731
-#443 := [monotonicity #734 #388]: #721
-#339 := [trans #443 #445]: #446
-#439 := [monotonicity #339]: #717
-#715 := [trans #439 #714]: #718
-#373 := (iff #735 true)
-#729 := (not false)
-#732 := (iff #729 true)
-#372 := [rewrite]: #732
-#367 := (iff #735 #729)
-#728 := (iff #528 false)
-#737 := (or false false)
-#381 := (iff #737 false)
-#722 := [rewrite]: #381
-#726 := (iff #528 #737)
-#724 := (iff #398 false)
-#725 := [rewrite]: #724
-#727 := [monotonicity #388 #725]: #726
-#723 := [trans #727 #722]: #728
-#730 := [monotonicity #723]: #367
-#733 := [trans #730 #372]: #373
-#429 := [monotonicity #733 #715]: #719
-#431 := [trans #429 #445]: #430
-#671 := [monotonicity #431 #695 #678]: #669
-#672 := [trans #671 #660]: #662
-#385 := (iff #745 false)
-#397 := (iff #745 #737)
-#396 := (iff #743 false)
-#401 := [rewrite]: #396
-#746 := (iff #744 false)
-#736 := [rewrite]: #746
-#738 := [monotonicity #736 #401]: #397
-#386 := [trans #738 #722]: #385
-#670 := [monotonicity #386 #672]: #674
-#666 := [trans #670 #664]: #665
-#655 := [monotonicity #666]: #653
-#658 := [trans #655 #657]: #653
-#652 := [quant-inst]: #668
-#654 := [mp #652 #658]: #661
-[unit-resolution #654 #753 #190]: false
-unsat
-3370d946d5a916a6204a00a35f20bfddd3071fdf 327 0
-#2 := false
-#11 := 0::int
-decl f3 :: (-> int int int)
-#174 := -3::int
-#68 := -1::int
-#177 := (f3 -1::int -3::int)
-#180 := (= #177 0::int)
-#193 := (not #180)
-#40 := 3::int
-#41 := (- 3::int)
-#38 := 1::int
-#39 := (- 1::int)
-#42 := (f3 #39 #41)
-#43 := (= #42 0::int)
-#44 := (not #43)
-#196 := (iff #44 #193)
-#183 := (= 0::int #177)
-#188 := (not #183)
-#194 := (iff #188 #193)
-#191 := (iff #183 #180)
-#192 := [rewrite]: #191
-#195 := [monotonicity #192]: #194
-#189 := (iff #44 #188)
-#186 := (iff #43 #183)
-#184 := (iff #180 #183)
-#185 := [rewrite]: #184
-#181 := (iff #43 #180)
-#178 := (= #42 #177)
-#175 := (= #41 -3::int)
-#176 := [rewrite]: #175
-#172 := (= #39 -1::int)
-#173 := [rewrite]: #172
-#179 := [monotonicity #173 #176]: #178
-#182 := [monotonicity #179]: #181
-#187 := [trans #182 #185]: #186
-#190 := [monotonicity #187]: #189
-#197 := [trans #190 #195]: #196
-#171 := [asserted]: #44
-#198 := [mp #171 #197]: #193
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#756 := (pattern #10)
-#72 := (* -1::int #9)
-#69 := (* -1::int #8)
-#75 := (div #69 #72)
-#259 := (* -1::int #75)
-#260 := (+ #10 #259)
-#261 := (= #260 0::int)
-#21 := (div #8 #9)
-#256 := (* -1::int #21)
-#257 := (+ #10 #256)
-#258 := (= #257 0::int)
-#94 := (<= #9 0::int)
-#90 := (<= #8 0::int)
-#214 := (or #90 #94)
-#215 := (not #214)
-#101 := (>= #8 0::int)
-#206 := (or #94 #101)
-#207 := (not #206)
-#221 := (or #207 #215)
-#262 := (ite #221 #258 #261)
-#255 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#263 := (ite #14 #255 #262)
-#757 := (forall (vars (?v0 int) (?v1 int)) (:pat #756) #263)
-#266 := (forall (vars (?v0 int) (?v1 int)) #263)
-#760 := (iff #266 #757)
-#758 := (iff #263 #263)
-#759 := [refl]: #758
-#761 := [quant-intro #759]: #760
-#226 := (ite #221 #21 #75)
-#229 := (ite #14 0::int #226)
-#232 := (= #10 #229)
-#235 := (forall (vars (?v0 int) (?v1 int)) #232)
-#267 := (iff #235 #266)
-#264 := (iff #232 #263)
-#265 := [rewrite]: #264
-#268 := [quant-intro #265]: #267
-#102 := (not #101)
-#95 := (not #94)
-#105 := (and #95 #102)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#111 := (ite #108 #21 #75)
-#114 := (ite #14 0::int #111)
-#117 := (= #10 #114)
-#120 := (forall (vars (?v0 int) (?v1 int)) #117)
-#236 := (iff #120 #235)
-#233 := (iff #117 #232)
-#230 := (= #114 #229)
-#227 := (= #111 #226)
-#224 := (iff #108 #221)
-#218 := (or #215 #207)
-#222 := (iff #218 #221)
-#223 := [rewrite]: #222
-#219 := (iff #108 #218)
-#216 := (iff #105 #207)
-#217 := [rewrite]: #216
-#204 := (iff #98 #215)
-#205 := [rewrite]: #204
-#220 := [monotonicity #205 #217]: #219
-#225 := [trans #220 #223]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [monotonicity #231]: #233
-#237 := [quant-intro #234]: #236
-#210 := (~ #120 #120)
-#208 := (~ #117 #117)
-#209 := [refl]: #208
-#211 := [nnf-pos #209]: #210
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#123 := (iff #28 #120)
-#62 := (and #16 #18)
-#65 := (or #17 #62)
-#78 := (ite #65 #21 #75)
-#81 := (ite #14 0::int #78)
-#84 := (= #10 #81)
-#87 := (forall (vars (?v0 int) (?v1 int)) #84)
-#121 := (iff #87 #120)
-#118 := (iff #84 #117)
-#115 := (= #81 #114)
-#112 := (= #78 #111)
-#109 := (iff #65 #108)
-#106 := (iff #62 #105)
-#103 := (iff #18 #102)
-#104 := [rewrite]: #103
-#96 := (iff #16 #95)
-#97 := [rewrite]: #96
-#107 := [monotonicity #97 #104]: #106
-#99 := (iff #17 #98)
-#92 := (iff #15 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#113 := [monotonicity #110]: #112
-#116 := [monotonicity #113]: #115
-#119 := [monotonicity #116]: #118
-#122 := [quant-intro #119]: #121
-#88 := (iff #28 #87)
-#85 := (iff #27 #84)
-#82 := (= #26 #81)
-#79 := (= #25 #78)
-#76 := (= #24 #75)
-#73 := (= #23 #72)
-#74 := [rewrite]: #73
-#70 := (= #22 #69)
-#71 := [rewrite]: #70
-#77 := [monotonicity #71 #74]: #76
-#66 := (iff #20 #65)
-#63 := (iff #19 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#80 := [monotonicity #67 #77]: #79
-#83 := [monotonicity #80]: #82
-#86 := [monotonicity #83]: #85
-#89 := [quant-intro #86]: #88
-#124 := [trans #89 #122]: #123
-#61 := [asserted]: #28
-#125 := [mp #61 #124]: #120
-#201 := [mp~ #125 #211]: #120
-#238 := [mp #201 #237]: #235
-#269 := [mp #238 #268]: #266
-#762 := [mp #269 #761]: #757
-#681 := (not #757)
-#682 := (or #681 #180)
-#343 := (* -1::int -3::int)
-#427 := (* -1::int -1::int)
-#428 := (div #427 #343)
-#429 := (* -1::int #428)
-#420 := (+ #177 #429)
-#431 := (= #420 0::int)
-#432 := (div -1::int -3::int)
-#433 := (* -1::int #432)
-#430 := (+ #177 #433)
-#434 := (= #430 0::int)
-#413 := (<= -3::int 0::int)
-#748 := (<= -1::int 0::int)
-#750 := (or #748 #413)
-#407 := (not #750)
-#537 := (>= -1::int 0::int)
-#744 := (or #413 #537)
-#418 := (not #744)
-#419 := (or #418 #407)
-#751 := (ite #419 #434 #431)
-#752 := (= -3::int 0::int)
-#753 := (= -1::int 0::int)
-#754 := (or #753 #752)
-#749 := (ite #754 #180 #751)
-#683 := (or #681 #749)
-#684 := (iff #683 #682)
-#674 := (iff #682 #682)
-#675 := [rewrite]: #674
-#669 := (iff #749 #180)
-#687 := (ite false #180 #180)
-#680 := (iff #687 #180)
-#672 := [rewrite]: #680
-#691 := (iff #749 #687)
-#597 := (iff #751 #180)
-#701 := (= #177 1::int)
-#585 := (ite false #701 #180)
-#595 := (iff #585 #180)
-#596 := [rewrite]: #595
-#593 := (iff #751 #585)
-#591 := (iff #431 #180)
-#574 := (= #420 #177)
-#688 := (+ #177 0::int)
-#686 := (= #688 #177)
-#689 := [rewrite]: #686
-#590 := (= #420 #688)
-#581 := (= #429 0::int)
-#696 := (* -1::int 0::int)
-#579 := (= #696 0::int)
-#580 := [rewrite]: #579
-#694 := (= #429 #696)
-#693 := (= #428 0::int)
-#707 := (div 1::int 3::int)
-#539 := (= #707 0::int)
-#692 := [rewrite]: #539
-#536 := (= #428 #707)
-#706 := (= #343 3::int)
-#700 := [rewrite]: #706
-#699 := (= #427 1::int)
-#705 := [rewrite]: #699
-#538 := [monotonicity #705 #700]: #536
-#695 := [trans #538 #692]: #693
-#697 := [monotonicity #695]: #694
-#540 := [trans #697 #580]: #581
-#685 := [monotonicity #540]: #590
-#589 := [trans #685 #689]: #574
-#592 := [monotonicity #589]: #591
-#704 := (iff #434 #701)
-#709 := (+ -1::int #177)
-#557 := (= #709 0::int)
-#702 := (iff #557 #701)
-#703 := [rewrite]: #702
-#558 := (iff #434 #557)
-#710 := (= #430 #709)
-#712 := (+ #177 -1::int)
-#714 := (= #712 #709)
-#715 := [rewrite]: #714
-#713 := (= #430 #712)
-#722 := (= #433 -1::int)
-#720 := (* -1::int 1::int)
-#721 := (= #720 -1::int)
-#718 := [rewrite]: #721
-#435 := (= #433 #720)
-#441 := (= #432 1::int)
-#719 := [rewrite]: #441
-#717 := [monotonicity #719]: #435
-#711 := [trans #717 #718]: #722
-#708 := [monotonicity #711]: #713
-#716 := [trans #708 #715]: #710
-#559 := [monotonicity #716]: #558
-#698 := [trans #559 #703]: #704
-#439 := (iff #419 false)
-#746 := (or false false)
-#390 := (iff #746 false)
-#731 := [rewrite]: #390
-#728 := (iff #419 #746)
-#727 := (iff #407 false)
-#1 := true
-#741 := (not true)
-#742 := (iff #741 false)
-#740 := [rewrite]: #742
-#449 := (iff #407 #741)
-#726 := (iff #750 true)
-#453 := (or true true)
-#349 := (iff #453 true)
-#725 := [rewrite]: #349
-#454 := (iff #750 #453)
-#396 := (iff #413 true)
-#397 := [rewrite]: #396
-#730 := (iff #748 true)
-#452 := [rewrite]: #730
-#455 := [monotonicity #452 #397]: #454
-#448 := [trans #455 #725]: #726
-#723 := [monotonicity #448]: #449
-#724 := [trans #723 #740]: #727
-#743 := (iff #418 false)
-#381 := (iff #418 #741)
-#376 := (iff #744 true)
-#735 := (or true false)
-#732 := (iff #735 true)
-#738 := [rewrite]: #732
-#736 := (iff #744 #735)
-#733 := (iff #537 false)
-#734 := [rewrite]: #733
-#737 := [monotonicity #397 #734]: #736
-#739 := [trans #737 #738]: #376
-#382 := [monotonicity #739]: #381
-#729 := [trans #382 #740]: #743
-#438 := [monotonicity #729 #724]: #728
-#440 := [trans #438 #731]: #439
-#594 := [monotonicity #440 #698 #592]: #593
-#690 := [trans #594 #596]: #597
-#394 := (iff #754 false)
-#406 := (iff #754 #746)
-#405 := (iff #752 false)
-#410 := [rewrite]: #405
-#755 := (iff #753 false)
-#745 := [rewrite]: #755
-#747 := [monotonicity #745 #410]: #406
-#395 := [trans #747 #731]: #394
-#678 := [monotonicity #395 #690]: #691
-#671 := [trans #678 #672]: #669
-#673 := [monotonicity #671]: #684
-#676 := [trans #673 #675]: #684
-#679 := [quant-inst]: #683
-#670 := [mp #679 #676]: #682
-[unit-resolution #670 #762 #198]: false
-unsat
-e0123afab77616719c99ab38af30fadddb3d3514 328 0
+51326f007e56e93f50afc5ba2d03581cdc697a2d 328 0
 #2 := false
 #11 := 0::int
 decl f4 :: (-> int int int)
@@ -38985,319 +39844,7 @@
 #688 := [mp #591 #684]: #582
 [unit-resolution #688 #766 #194]: false
 unsat
-c88cce63d6e0a186daa8cd66ece19fb97c1244ca 311 0
-#2 := false
-#41 := 1::int
-decl f3 :: (-> int int int)
-#171 := -3::int
-#174 := (f3 -3::int -3::int)
-#177 := (= #174 1::int)
-#190 := (not #177)
-#38 := 3::int
-#39 := (- 3::int)
-#40 := (f3 #39 #39)
-#42 := (= #40 1::int)
-#43 := (not #42)
-#193 := (iff #43 #190)
-#180 := (= 1::int #174)
-#185 := (not #180)
-#191 := (iff #185 #190)
-#188 := (iff #180 #177)
-#189 := [rewrite]: #188
-#192 := [monotonicity #189]: #191
-#186 := (iff #43 #185)
-#183 := (iff #42 #180)
-#181 := (iff #177 #180)
-#182 := [rewrite]: #181
-#178 := (iff #42 #177)
-#175 := (= #40 #174)
-#172 := (= #39 -3::int)
-#173 := [rewrite]: #172
-#176 := [monotonicity #173 #173]: #175
-#179 := [monotonicity #176]: #178
-#184 := [trans #179 #182]: #183
-#187 := [monotonicity #184]: #186
-#194 := [trans #187 #192]: #193
-#170 := [asserted]: #43
-#195 := [mp #170 #194]: #190
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#753 := (pattern #10)
-#11 := 0::int
-#67 := -1::int
-#71 := (* -1::int #9)
-#68 := (* -1::int #8)
-#74 := (div #68 #71)
-#256 := (* -1::int #74)
-#257 := (+ #10 #256)
-#258 := (= #257 0::int)
-#21 := (div #8 #9)
-#253 := (* -1::int #21)
-#254 := (+ #10 #253)
-#255 := (= #254 0::int)
-#93 := (<= #9 0::int)
-#89 := (<= #8 0::int)
-#211 := (or #89 #93)
-#212 := (not #211)
-#100 := (>= #8 0::int)
-#203 := (or #93 #100)
-#204 := (not #203)
-#218 := (or #204 #212)
-#259 := (ite #218 #255 #258)
-#252 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#260 := (ite #14 #252 #259)
-#754 := (forall (vars (?v0 int) (?v1 int)) (:pat #753) #260)
-#263 := (forall (vars (?v0 int) (?v1 int)) #260)
-#757 := (iff #263 #754)
-#755 := (iff #260 #260)
-#756 := [refl]: #755
-#758 := [quant-intro #756]: #757
-#223 := (ite #218 #21 #74)
-#226 := (ite #14 0::int #223)
-#229 := (= #10 #226)
-#232 := (forall (vars (?v0 int) (?v1 int)) #229)
-#264 := (iff #232 #263)
-#261 := (iff #229 #260)
-#262 := [rewrite]: #261
-#265 := [quant-intro #262]: #264
-#101 := (not #100)
-#94 := (not #93)
-#104 := (and #94 #101)
-#90 := (not #89)
-#97 := (and #90 #94)
-#107 := (or #97 #104)
-#110 := (ite #107 #21 #74)
-#113 := (ite #14 0::int #110)
-#116 := (= #10 #113)
-#119 := (forall (vars (?v0 int) (?v1 int)) #116)
-#233 := (iff #119 #232)
-#230 := (iff #116 #229)
-#227 := (= #113 #226)
-#224 := (= #110 #223)
-#221 := (iff #107 #218)
-#215 := (or #212 #204)
-#219 := (iff #215 #218)
-#220 := [rewrite]: #219
-#216 := (iff #107 #215)
-#213 := (iff #104 #204)
-#214 := [rewrite]: #213
-#201 := (iff #97 #212)
-#202 := [rewrite]: #201
-#217 := [monotonicity #202 #214]: #216
-#222 := [trans #217 #220]: #221
-#225 := [monotonicity #222]: #224
-#228 := [monotonicity #225]: #227
-#231 := [monotonicity #228]: #230
-#234 := [quant-intro #231]: #233
-#207 := (~ #119 #119)
-#205 := (~ #116 #116)
-#206 := [refl]: #205
-#208 := [nnf-pos #206]: #207
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#122 := (iff #28 #119)
-#61 := (and #16 #18)
-#64 := (or #17 #61)
-#77 := (ite #64 #21 #74)
-#80 := (ite #14 0::int #77)
-#83 := (= #10 #80)
-#86 := (forall (vars (?v0 int) (?v1 int)) #83)
-#120 := (iff #86 #119)
-#117 := (iff #83 #116)
-#114 := (= #80 #113)
-#111 := (= #77 #110)
-#108 := (iff #64 #107)
-#105 := (iff #61 #104)
-#102 := (iff #18 #101)
-#103 := [rewrite]: #102
-#95 := (iff #16 #94)
-#96 := [rewrite]: #95
-#106 := [monotonicity #96 #103]: #105
-#98 := (iff #17 #97)
-#91 := (iff #15 #90)
-#92 := [rewrite]: #91
-#99 := [monotonicity #92 #96]: #98
-#109 := [monotonicity #99 #106]: #108
-#112 := [monotonicity #109]: #111
-#115 := [monotonicity #112]: #114
-#118 := [monotonicity #115]: #117
-#121 := [quant-intro #118]: #120
-#87 := (iff #28 #86)
-#84 := (iff #27 #83)
-#81 := (= #26 #80)
-#78 := (= #25 #77)
-#75 := (= #24 #74)
-#72 := (= #23 #71)
-#73 := [rewrite]: #72
-#69 := (= #22 #68)
-#70 := [rewrite]: #69
-#76 := [monotonicity #70 #73]: #75
-#65 := (iff #20 #64)
-#62 := (iff #19 #61)
-#63 := [rewrite]: #62
-#66 := [monotonicity #63]: #65
-#79 := [monotonicity #66 #76]: #78
-#82 := [monotonicity #79]: #81
-#85 := [monotonicity #82]: #84
-#88 := [quant-intro #85]: #87
-#123 := [trans #88 #121]: #122
-#60 := [asserted]: #28
-#124 := [mp #60 #123]: #119
-#198 := [mp~ #124 #208]: #119
-#235 := [mp #198 #234]: #232
-#266 := [mp #235 #265]: #263
-#759 := [mp #266 #758]: #754
-#590 := (not #754)
-#591 := (or #590 #177)
-#340 := (* -1::int -3::int)
-#424 := (div #340 #340)
-#425 := (* -1::int #424)
-#426 := (+ #174 #425)
-#417 := (= #426 0::int)
-#428 := (div -3::int -3::int)
-#429 := (* -1::int #428)
-#430 := (+ #174 #429)
-#427 := (= #430 0::int)
-#431 := (<= -3::int 0::int)
-#410 := (or #431 #431)
-#745 := (not #410)
-#747 := (>= -3::int 0::int)
-#404 := (or #431 #747)
-#534 := (not #404)
-#741 := (or #534 #745)
-#415 := (ite #741 #427 #417)
-#416 := (= #174 0::int)
-#748 := (= -3::int 0::int)
-#749 := (or #748 #748)
-#750 := (ite #749 #416 #415)
-#592 := (or #590 #750)
-#594 := (iff #592 #591)
-#684 := (iff #591 #591)
-#688 := [rewrite]: #684
-#589 := (iff #750 #177)
-#683 := (ite false #416 #177)
-#586 := (iff #683 #177)
-#588 := [rewrite]: #586
-#686 := (iff #750 #683)
-#587 := (iff #415 #177)
-#576 := (ite false #177 #177)
-#537 := (iff #576 #177)
-#685 := [rewrite]: #537
-#577 := (iff #415 #576)
-#691 := (iff #417 #177)
-#715 := (+ -1::int #174)
-#705 := (= #715 0::int)
-#712 := (iff #705 #177)
-#707 := [rewrite]: #712
-#692 := (iff #417 #705)
-#689 := (= #426 #715)
-#432 := (+ #174 -1::int)
-#719 := (= #432 #715)
-#708 := [rewrite]: #719
-#535 := (= #426 #432)
-#704 := (= #425 -1::int)
-#725 := (* -1::int 1::int)
-#437 := (= #725 -1::int)
-#438 := [rewrite]: #437
-#703 := (= #425 #725)
-#696 := (= #424 1::int)
-#698 := (div 3::int 3::int)
-#701 := (= #698 1::int)
-#695 := [rewrite]: #701
-#699 := (= #424 #698)
-#555 := (= #340 3::int)
-#556 := [rewrite]: #555
-#700 := [monotonicity #556 #556]: #699
-#702 := [trans #700 #695]: #696
-#697 := [monotonicity #702]: #703
-#533 := [trans #697 #438]: #704
-#536 := [monotonicity #533]: #535
-#690 := [trans #536 #708]: #689
-#693 := [monotonicity #690]: #692
-#694 := [trans #693 #707]: #691
-#713 := (iff #427 #177)
-#706 := (iff #427 #705)
-#709 := (= #430 #715)
-#714 := (= #430 #432)
-#716 := (= #429 -1::int)
-#435 := (= #429 #725)
-#724 := (= #428 1::int)
-#721 := [rewrite]: #724
-#436 := [monotonicity #721]: #435
-#717 := [trans #436 #438]: #716
-#718 := [monotonicity #717]: #714
-#710 := [trans #718 #708]: #709
-#711 := [monotonicity #710]: #706
-#554 := [trans #711 #707]: #713
-#446 := (iff #741 false)
-#752 := (or false false)
-#407 := (iff #752 false)
-#743 := [rewrite]: #407
-#723 := (iff #741 #752)
-#346 := (iff #745 false)
-#1 := true
-#729 := (not true)
-#736 := (iff #729 false)
-#738 := [rewrite]: #736
-#451 := (iff #745 #729)
-#449 := (iff #410 true)
-#739 := (or true true)
-#726 := (iff #739 true)
-#727 := [rewrite]: #726
-#737 := (iff #410 #739)
-#387 := (iff #431 true)
-#728 := [rewrite]: #387
-#740 := [monotonicity #728 #728]: #737
-#450 := [trans #740 #727]: #449
-#452 := [monotonicity #450]: #451
-#722 := [trans #452 #738]: #346
-#378 := (iff #534 false)
-#735 := (iff #534 #729)
-#733 := (iff #404 true)
-#393 := (or true false)
-#731 := (iff #393 true)
-#732 := [rewrite]: #731
-#394 := (iff #404 #393)
-#391 := (iff #747 false)
-#392 := [rewrite]: #391
-#730 := [monotonicity #728 #392]: #394
-#734 := [trans #730 #732]: #733
-#373 := [monotonicity #734]: #735
-#379 := [trans #373 #738]: #378
-#445 := [monotonicity #379 #722]: #723
-#720 := [trans #445 #743]: #446
-#578 := [monotonicity #720 #554 #694]: #577
-#682 := [trans #578 #685]: #587
-#403 := (iff #749 false)
-#742 := (iff #749 #752)
-#751 := (iff #748 false)
-#746 := [rewrite]: #751
-#402 := [monotonicity #746 #746]: #742
-#744 := [trans #402 #743]: #403
-#571 := [monotonicity #744 #682]: #686
-#582 := [trans #571 #588]: #589
-#687 := [monotonicity #582]: #594
-#675 := [trans #687 #688]: #594
-#593 := [quant-inst]: #592
-#677 := [mp #593 #675]: #591
-[unit-resolution #677 #759 #195]: false
-unsat
-9635e0bc08ee97ed1256a38a5dbd874adffbbe2e 356 0
+0f74c41c938e9378ba24d8b61b7a4d0b50210370 356 0
 #2 := false
 #69 := -1::int
 decl f4 :: (-> int int int)
@@ -39654,346 +40201,7 @@
 #669 := [mp #663 #664]: #678
 [unit-resolution #669 #770 #199]: false
 unsat
-d7d527dac30acb7be44977e66eb01c6ffc6a5300 338 0
-#2 := false
-#43 := 1::int
-decl f3 :: (-> int int int)
-#176 := -3::int
-#173 := -5::int
-#179 := (f3 -5::int -3::int)
-#182 := (= #179 1::int)
-#195 := (not #182)
-#40 := 3::int
-#41 := (- 3::int)
-#38 := 5::int
-#39 := (- 5::int)
-#42 := (f3 #39 #41)
-#44 := (= #42 1::int)
-#45 := (not #44)
-#198 := (iff #45 #195)
-#185 := (= 1::int #179)
-#190 := (not #185)
-#196 := (iff #190 #195)
-#193 := (iff #185 #182)
-#194 := [rewrite]: #193
-#197 := [monotonicity #194]: #196
-#191 := (iff #45 #190)
-#188 := (iff #44 #185)
-#186 := (iff #182 #185)
-#187 := [rewrite]: #186
-#183 := (iff #44 #182)
-#180 := (= #42 #179)
-#177 := (= #41 -3::int)
-#178 := [rewrite]: #177
-#174 := (= #39 -5::int)
-#175 := [rewrite]: #174
-#181 := [monotonicity #175 #178]: #180
-#184 := [monotonicity #181]: #183
-#189 := [trans #184 #187]: #188
-#192 := [monotonicity #189]: #191
-#199 := [trans #192 #197]: #198
-#172 := [asserted]: #45
-#200 := [mp #172 #199]: #195
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#10 := (f3 #8 #9)
-#758 := (pattern #10)
-#11 := 0::int
-#69 := -1::int
-#73 := (* -1::int #9)
-#70 := (* -1::int #8)
-#76 := (div #70 #73)
-#261 := (* -1::int #76)
-#262 := (+ #10 #261)
-#263 := (= #262 0::int)
-#21 := (div #8 #9)
-#258 := (* -1::int #21)
-#259 := (+ #10 #258)
-#260 := (= #259 0::int)
-#95 := (<= #9 0::int)
-#91 := (<= #8 0::int)
-#216 := (or #91 #95)
-#217 := (not #216)
-#102 := (>= #8 0::int)
-#208 := (or #95 #102)
-#209 := (not #208)
-#223 := (or #209 #217)
-#264 := (ite #223 #260 #263)
-#257 := (= #10 0::int)
-#13 := (= #9 0::int)
-#12 := (= #8 0::int)
-#14 := (or #12 #13)
-#265 := (ite #14 #257 #264)
-#759 := (forall (vars (?v0 int) (?v1 int)) (:pat #758) #265)
-#268 := (forall (vars (?v0 int) (?v1 int)) #265)
-#762 := (iff #268 #759)
-#760 := (iff #265 #265)
-#761 := [refl]: #760
-#763 := [quant-intro #761]: #762
-#228 := (ite #223 #21 #76)
-#231 := (ite #14 0::int #228)
-#234 := (= #10 #231)
-#237 := (forall (vars (?v0 int) (?v1 int)) #234)
-#269 := (iff #237 #268)
-#266 := (iff #234 #265)
-#267 := [rewrite]: #266
-#270 := [quant-intro #267]: #269
-#103 := (not #102)
-#96 := (not #95)
-#106 := (and #96 #103)
-#92 := (not #91)
-#99 := (and #92 #96)
-#109 := (or #99 #106)
-#112 := (ite #109 #21 #76)
-#115 := (ite #14 0::int #112)
-#118 := (= #10 #115)
-#121 := (forall (vars (?v0 int) (?v1 int)) #118)
-#238 := (iff #121 #237)
-#235 := (iff #118 #234)
-#232 := (= #115 #231)
-#229 := (= #112 #228)
-#226 := (iff #109 #223)
-#220 := (or #217 #209)
-#224 := (iff #220 #223)
-#225 := [rewrite]: #224
-#221 := (iff #109 #220)
-#218 := (iff #106 #209)
-#219 := [rewrite]: #218
-#206 := (iff #99 #217)
-#207 := [rewrite]: #206
-#222 := [monotonicity #207 #219]: #221
-#227 := [trans #222 #225]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [monotonicity #233]: #235
-#239 := [quant-intro #236]: #238
-#212 := (~ #121 #121)
-#210 := (~ #118 #118)
-#211 := [refl]: #210
-#213 := [nnf-pos #211]: #212
-#23 := (- #9)
-#22 := (- #8)
-#24 := (div #22 #23)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#25 := (ite #20 #21 #24)
-#26 := (ite #14 0::int #25)
-#27 := (= #10 #26)
-#28 := (forall (vars (?v0 int) (?v1 int)) #27)
-#124 := (iff #28 #121)
-#63 := (and #16 #18)
-#66 := (or #17 #63)
-#79 := (ite #66 #21 #76)
-#82 := (ite #14 0::int #79)
-#85 := (= #10 #82)
-#88 := (forall (vars (?v0 int) (?v1 int)) #85)
-#122 := (iff #88 #121)
-#119 := (iff #85 #118)
-#116 := (= #82 #115)
-#113 := (= #79 #112)
-#110 := (iff #66 #109)
-#107 := (iff #63 #106)
-#104 := (iff #18 #103)
-#105 := [rewrite]: #104
-#97 := (iff #16 #96)
-#98 := [rewrite]: #97
-#108 := [monotonicity #98 #105]: #107
-#100 := (iff #17 #99)
-#93 := (iff #15 #92)
-#94 := [rewrite]: #93
-#101 := [monotonicity #94 #98]: #100
-#111 := [monotonicity #101 #108]: #110
-#114 := [monotonicity #111]: #113
-#117 := [monotonicity #114]: #116
-#120 := [monotonicity #117]: #119
-#123 := [quant-intro #120]: #122
-#89 := (iff #28 #88)
-#86 := (iff #27 #85)
-#83 := (= #26 #82)
-#80 := (= #25 #79)
-#77 := (= #24 #76)
-#74 := (= #23 #73)
-#75 := [rewrite]: #74
-#71 := (= #22 #70)
-#72 := [rewrite]: #71
-#78 := [monotonicity #72 #75]: #77
-#67 := (iff #20 #66)
-#64 := (iff #19 #63)
-#65 := [rewrite]: #64
-#68 := [monotonicity #65]: #67
-#81 := [monotonicity #68 #78]: #80
-#84 := [monotonicity #81]: #83
-#87 := [monotonicity #84]: #86
-#90 := [quant-intro #87]: #89
-#125 := [trans #90 #123]: #124
-#62 := [asserted]: #28
-#126 := [mp #62 #125]: #121
-#203 := [mp~ #126 #213]: #121
-#240 := [mp #203 #239]: #237
-#271 := [mp #240 #270]: #268
-#764 := [mp #271 #763]: #759
-#672 := (not #759)
-#679 := (or #672 #182)
-#345 := (* -1::int -3::int)
-#429 := (* -1::int -5::int)
-#430 := (div #429 #345)
-#431 := (* -1::int #430)
-#422 := (+ #179 #431)
-#433 := (= #422 0::int)
-#434 := (div -5::int -3::int)
-#435 := (* -1::int #434)
-#432 := (+ #179 #435)
-#436 := (= #432 0::int)
-#415 := (<= -3::int 0::int)
-#750 := (<= -5::int 0::int)
-#752 := (or #750 #415)
-#409 := (not #752)
-#539 := (>= -5::int 0::int)
-#746 := (or #415 #539)
-#420 := (not #746)
-#421 := (or #420 #409)
-#753 := (ite #421 #436 #433)
-#754 := (= #179 0::int)
-#755 := (= -3::int 0::int)
-#756 := (= -5::int 0::int)
-#751 := (or #756 #755)
-#757 := (ite #751 #754 #753)
-#663 := (or #672 #757)
-#666 := (iff #663 #679)
-#668 := (iff #679 #679)
-#669 := [rewrite]: #668
-#677 := (iff #757 #182)
-#685 := (ite false #754 #182)
-#675 := (iff #685 #182)
-#676 := [rewrite]: #675
-#681 := (iff #757 #685)
-#683 := (iff #753 #182)
-#721 := 2::int
-#706 := (= #179 2::int)
-#680 := (ite false #706 #182)
-#671 := (iff #680 #182)
-#673 := [rewrite]: #671
-#682 := (iff #753 #680)
-#689 := (iff #433 #182)
-#591 := (+ -1::int #179)
-#596 := (= #591 0::int)
-#599 := (iff #596 #182)
-#692 := [rewrite]: #599
-#597 := (iff #433 #596)
-#587 := (= #422 #591)
-#688 := (+ #179 -1::int)
-#593 := (= #688 #591)
-#594 := [rewrite]: #593
-#691 := (= #422 #688)
-#592 := (= #431 -1::int)
-#581 := (* -1::int 1::int)
-#542 := (= #581 -1::int)
-#690 := [rewrite]: #542
-#582 := (= #431 #581)
-#696 := (= #430 1::int)
-#541 := (div 5::int 3::int)
-#697 := (= #541 1::int)
-#698 := [rewrite]: #697
-#694 := (= #430 #541)
-#538 := (= #345 3::int)
-#540 := [rewrite]: #538
-#702 := (= #429 5::int)
-#709 := [rewrite]: #702
-#695 := [monotonicity #709 #540]: #694
-#699 := [trans #695 #698]: #696
-#583 := [monotonicity #699]: #582
-#687 := [trans #583 #690]: #592
-#576 := [monotonicity #687]: #691
-#595 := [trans #576 #594]: #587
-#598 := [monotonicity #595]: #597
-#693 := [trans #598 #692]: #689
-#707 := (iff #436 #706)
-#724 := -2::int
-#712 := (+ -2::int #179)
-#703 := (= #712 0::int)
-#700 := (iff #703 #706)
-#701 := [rewrite]: #700
-#704 := (iff #436 #703)
-#560 := (= #432 #712)
-#711 := (+ #179 -2::int)
-#718 := (= #711 #712)
-#559 := [rewrite]: #718
-#716 := (= #432 #711)
-#715 := (= #435 -2::int)
-#719 := (* -1::int 2::int)
-#713 := (= #719 -2::int)
-#714 := [rewrite]: #713
-#723 := (= #435 #719)
-#722 := (= #434 2::int)
-#437 := [rewrite]: #722
-#720 := [monotonicity #437]: #723
-#710 := [trans #720 #714]: #715
-#717 := [monotonicity #710]: #716
-#561 := [trans #717 #559]: #560
-#705 := [monotonicity #561]: #704
-#708 := [trans #705 #701]: #707
-#442 := (iff #421 false)
-#408 := (or false false)
-#733 := (iff #408 false)
-#396 := [rewrite]: #733
-#440 := (iff #421 #408)
-#726 := (iff #409 false)
-#1 := true
-#383 := (not true)
-#742 := (iff #383 false)
-#745 := [rewrite]: #742
-#725 := (iff #409 #383)
-#450 := (iff #752 true)
-#456 := (or true true)
-#727 := (iff #456 true)
-#728 := [rewrite]: #727
-#457 := (iff #752 #456)
-#399 := (iff #415 true)
-#735 := [rewrite]: #399
-#454 := (iff #750 true)
-#455 := [rewrite]: #454
-#351 := [monotonicity #455 #735]: #457
-#451 := [trans #351 #728]: #450
-#729 := [monotonicity #451]: #725
-#730 := [trans #729 #745]: #726
-#731 := (iff #420 false)
-#384 := (iff #420 #383)
-#741 := (iff #746 true)
-#738 := (or true false)
-#740 := (iff #738 true)
-#378 := [rewrite]: #740
-#739 := (iff #746 #738)
-#736 := (iff #539 false)
-#737 := [rewrite]: #736
-#734 := [monotonicity #735 #737]: #739
-#743 := [trans #734 #378]: #741
-#744 := [monotonicity #743]: #384
-#732 := [trans #744 #745]: #731
-#441 := [monotonicity #732 #730]: #440
-#443 := [trans #441 #396]: #442
-#674 := [monotonicity #443 #708 #693]: #682
-#684 := [trans #674 #673]: #683
-#397 := (iff #751 false)
-#749 := (iff #751 #408)
-#412 := (iff #755 false)
-#748 := [rewrite]: #412
-#747 := (iff #756 false)
-#407 := [rewrite]: #747
-#392 := [monotonicity #407 #748]: #749
-#398 := [trans #392 #396]: #397
-#686 := [monotonicity #398 #684]: #681
-#678 := [trans #686 #676]: #677
-#667 := [monotonicity #678]: #666
-#665 := [trans #667 #669]: #666
-#664 := [quant-inst]: #663
-#670 := [mp #664 #665]: #679
-[unit-resolution #670 #764 #200]: false
-unsat
-23ee07330031fda7a649c24c72b346abba5a15ed 350 0
+3c5a12d92626ff8ea2f3e7c2d04bebd45ef00916 350 0
 #2 := false
 #42 := 2::int
 decl f4 :: (-> int int int)
@@ -40344,7 +40552,2386 @@
 #664 := [mp #674 #663]: #673
 [unit-resolution #664 #766 #195]: false
 unsat
-5a36ea40ec6f132383fe7e0f161b9c3e56510423 592 0
+9ee8d0dc4ede7b68c19a265d2c4cda80156ee20b 331 0
+#2 := false
+#11 := 0::int
+decl f4 :: (-> int int int)
+#38 := 3::int
+#170 := -3::int
+#173 := (f4 -3::int 3::int)
+#176 := (= #173 0::int)
+#189 := (not #176)
+#39 := (- 3::int)
+#40 := (f4 #39 3::int)
+#41 := (= #40 0::int)
+#42 := (not #41)
+#192 := (iff #42 #189)
+#179 := (= 0::int #173)
+#184 := (not #179)
+#190 := (iff #184 #189)
+#187 := (iff #179 #176)
+#188 := [rewrite]: #187
+#191 := [monotonicity #188]: #190
+#185 := (iff #42 #184)
+#182 := (iff #41 #179)
+#180 := (iff #176 #179)
+#181 := [rewrite]: #180
+#177 := (iff #41 #176)
+#174 := (= #40 #173)
+#171 := (= #39 -3::int)
+#172 := [rewrite]: #171
+#175 := [monotonicity #172]: #174
+#178 := [monotonicity #175]: #177
+#183 := [trans #178 #181]: #182
+#186 := [monotonicity #183]: #185
+#193 := [trans #186 #191]: #192
+#169 := [asserted]: #42
+#194 := [mp #169 #193]: #189
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#760 := (pattern #29)
+#66 := -1::int
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#125 := (mod #67 #70)
+#271 := (+ #29 #125)
+#272 := (= #271 0::int)
+#30 := (mod #8 #9)
+#268 := (* -1::int #30)
+#269 := (+ #29 #268)
+#270 := (= #269 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#210 := (or #88 #92)
+#211 := (not #210)
+#99 := (>= #8 0::int)
+#202 := (or #92 #99)
+#203 := (not #202)
+#217 := (or #203 #211)
+#273 := (ite #217 #270 #272)
+#267 := (= #29 0::int)
+#12 := (= #8 0::int)
+#274 := (ite #12 #267 #273)
+#266 := (= #8 #29)
+#13 := (= #9 0::int)
+#275 := (ite #13 #266 #274)
+#761 := (forall (vars (?v0 int) (?v1 int)) (:pat #760) #275)
+#278 := (forall (vars (?v0 int) (?v1 int)) #275)
+#764 := (iff #278 #761)
+#762 := (iff #275 #275)
+#763 := [refl]: #762
+#765 := [quant-intro #763]: #764
+#131 := (* -1::int #125)
+#235 := (ite #217 #30 #131)
+#238 := (ite #12 0::int #235)
+#241 := (ite #13 #8 #238)
+#244 := (= #29 #241)
+#247 := (forall (vars (?v0 int) (?v1 int)) #244)
+#279 := (iff #247 #278)
+#276 := (iff #244 #275)
+#277 := [rewrite]: #276
+#280 := [quant-intro #277]: #279
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#151 := (ite #106 #30 #131)
+#154 := (ite #12 0::int #151)
+#157 := (ite #13 #8 #154)
+#160 := (= #29 #157)
+#163 := (forall (vars (?v0 int) (?v1 int)) #160)
+#248 := (iff #163 #247)
+#245 := (iff #160 #244)
+#242 := (= #157 #241)
+#239 := (= #154 #238)
+#236 := (= #151 #235)
+#220 := (iff #106 #217)
+#214 := (or #211 #203)
+#218 := (iff #214 #217)
+#219 := [rewrite]: #218
+#215 := (iff #106 #214)
+#212 := (iff #103 #203)
+#213 := [rewrite]: #212
+#200 := (iff #96 #211)
+#201 := [rewrite]: #200
+#216 := [monotonicity #201 #213]: #215
+#221 := [trans #216 #219]: #220
+#237 := [monotonicity #221]: #236
+#240 := [monotonicity #237]: #239
+#243 := [monotonicity #240]: #242
+#246 := [monotonicity #243]: #245
+#249 := [quant-intro #246]: #248
+#198 := (~ #163 #163)
+#195 := (~ #160 #160)
+#208 := [refl]: #195
+#199 := [nnf-pos #208]: #198
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#166 := (iff #37 #163)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#136 := (ite #63 #30 #131)
+#139 := (ite #12 0::int #136)
+#142 := (ite #13 #8 #139)
+#145 := (= #29 #142)
+#148 := (forall (vars (?v0 int) (?v1 int)) #145)
+#164 := (iff #148 #163)
+#161 := (iff #145 #160)
+#158 := (= #142 #157)
+#155 := (= #139 #154)
+#152 := (= #136 #151)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#153 := [monotonicity #108]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [quant-intro #162]: #164
+#149 := (iff #37 #148)
+#146 := (iff #36 #145)
+#143 := (= #35 #142)
+#140 := (= #34 #139)
+#137 := (= #33 #136)
+#134 := (= #32 #131)
+#128 := (- #125)
+#132 := (= #128 #131)
+#133 := [rewrite]: #132
+#129 := (= #32 #128)
+#126 := (= #31 #125)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#127 := [monotonicity #69 #72]: #126
+#130 := [monotonicity #127]: #129
+#135 := [trans #130 #133]: #134
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#138 := [monotonicity #65 #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [quant-intro #147]: #149
+#167 := [trans #150 #165]: #166
+#124 := [asserted]: #37
+#168 := [mp #124 #167]: #163
+#209 := [mp~ #168 #199]: #163
+#250 := [mp #209 #249]: #247
+#281 := [mp #250 #280]: #278
+#766 := [mp #281 #765]: #761
+#591 := (not #761)
+#592 := (or #591 #176)
+#339 := (* -1::int 3::int)
+#424 := (* -1::int -3::int)
+#425 := (mod #424 #339)
+#426 := (+ #173 #425)
+#417 := (= #426 0::int)
+#428 := (mod -3::int 3::int)
+#429 := (* -1::int #428)
+#357 := (+ #173 #429)
+#430 := (= #357 0::int)
+#427 := (<= 3::int 0::int)
+#431 := (<= -3::int 0::int)
+#410 := (or #431 #427)
+#745 := (not #410)
+#747 := (>= -3::int 0::int)
+#404 := (or #427 #747)
+#534 := (not #404)
+#741 := (or #534 #745)
+#415 := (ite #741 #430 #417)
+#416 := (= -3::int 0::int)
+#748 := (ite #416 #176 #415)
+#749 := (= -3::int #173)
+#750 := (= 3::int 0::int)
+#751 := (ite #750 #749 #748)
+#593 := (or #591 #751)
+#687 := (iff #593 #592)
+#688 := (iff #592 #592)
+#675 := [rewrite]: #688
+#582 := (iff #751 #176)
+#402 := (= #173 -3::int)
+#686 := (ite false #402 #176)
+#588 := (iff #686 #176)
+#589 := [rewrite]: #588
+#571 := (iff #751 #686)
+#682 := (iff #748 #176)
+#577 := (ite false #176 #176)
+#685 := (iff #577 #176)
+#587 := [rewrite]: #685
+#578 := (iff #748 #577)
+#694 := (iff #415 #176)
+#1 := true
+#689 := (ite true #176 #176)
+#693 := (iff #689 #176)
+#691 := [rewrite]: #693
+#690 := (iff #415 #689)
+#535 := (iff #417 #176)
+#704 := (= #426 #173)
+#719 := (+ #173 0::int)
+#710 := (= #719 #173)
+#705 := [rewrite]: #710
+#703 := (= #426 #719)
+#696 := (= #425 0::int)
+#698 := (mod 3::int -3::int)
+#701 := (= #698 0::int)
+#695 := [rewrite]: #701
+#699 := (= #425 #698)
+#555 := (= #339 -3::int)
+#556 := [rewrite]: #555
+#713 := (= #424 3::int)
+#554 := [rewrite]: #713
+#700 := [monotonicity #554 #556]: #699
+#702 := [trans #700 #695]: #696
+#697 := [monotonicity #702]: #703
+#533 := [trans #697 #705]: #704
+#536 := [monotonicity #533]: #535
+#712 := (iff #430 #176)
+#706 := (= #357 #173)
+#708 := (= #357 #719)
+#718 := (= #429 0::int)
+#438 := (* -1::int 0::int)
+#432 := (= #438 0::int)
+#714 := [rewrite]: #432
+#716 := (= #429 #438)
+#436 := (= #428 0::int)
+#437 := [rewrite]: #436
+#717 := [monotonicity #437]: #716
+#715 := [trans #717 #714]: #718
+#709 := [monotonicity #715]: #708
+#711 := [trans #709 #705]: #706
+#707 := [monotonicity #711]: #712
+#725 := (iff #741 true)
+#737 := (or true false)
+#727 := (iff #737 true)
+#449 := [rewrite]: #727
+#724 := (iff #741 #737)
+#446 := (iff #745 false)
+#452 := (not true)
+#723 := (iff #452 false)
+#445 := [rewrite]: #723
+#345 := (iff #745 #452)
+#450 := (iff #410 true)
+#740 := (iff #410 #737)
+#744 := (iff #427 false)
+#387 := [rewrite]: #744
+#379 := (iff #431 true)
+#739 := [rewrite]: #379
+#726 := [monotonicity #739 #387]: #740
+#451 := [trans #726 #449]: #450
+#722 := [monotonicity #451]: #345
+#720 := [trans #722 #445]: #446
+#738 := (iff #534 true)
+#734 := (not false)
+#373 := (iff #734 true)
+#736 := [rewrite]: #373
+#729 := (iff #534 #734)
+#732 := (iff #404 false)
+#392 := (or false false)
+#730 := (iff #392 false)
+#731 := [rewrite]: #730
+#393 := (iff #404 #392)
+#728 := (iff #747 false)
+#391 := [rewrite]: #728
+#394 := [monotonicity #387 #391]: #393
+#733 := [trans #394 #731]: #732
+#735 := [monotonicity #733]: #729
+#378 := [trans #735 #736]: #738
+#721 := [monotonicity #378 #720]: #724
+#435 := [trans #721 #449]: #725
+#692 := [monotonicity #435 #707 #536]: #690
+#576 := [trans #692 #691]: #694
+#743 := (iff #416 false)
+#403 := [rewrite]: #743
+#537 := [monotonicity #403 #576]: #578
+#683 := [trans #537 #587]: #682
+#742 := (iff #749 #402)
+#407 := [rewrite]: #742
+#746 := (iff #750 false)
+#752 := [rewrite]: #746
+#586 := [monotonicity #752 #407 #683]: #571
+#590 := [trans #586 #589]: #582
+#684 := [monotonicity #590]: #687
+#677 := [trans #684 #675]: #687
+#594 := [quant-inst]: #593
+#669 := [mp #594 #677]: #592
+[unit-resolution #669 #766 #194]: false
+unsat
+0dff6836610ad24fd350792fdba18f67fffe78ae 353 0
+#2 := false
+#42 := 1::int
+decl f4 :: (-> int int int)
+#40 := 3::int
+#172 := -5::int
+#175 := (f4 -5::int 3::int)
+#178 := (= #175 1::int)
+#191 := (not #178)
+#38 := 5::int
+#39 := (- 5::int)
+#41 := (f4 #39 3::int)
+#43 := (= #41 1::int)
+#44 := (not #43)
+#194 := (iff #44 #191)
+#181 := (= 1::int #175)
+#186 := (not #181)
+#192 := (iff #186 #191)
+#189 := (iff #181 #178)
+#190 := [rewrite]: #189
+#193 := [monotonicity #190]: #192
+#187 := (iff #44 #186)
+#184 := (iff #43 #181)
+#182 := (iff #178 #181)
+#183 := [rewrite]: #182
+#179 := (iff #43 #178)
+#176 := (= #41 #175)
+#173 := (= #39 -5::int)
+#174 := [rewrite]: #173
+#177 := [monotonicity #174]: #176
+#180 := [monotonicity #177]: #179
+#185 := [trans #180 #183]: #184
+#188 := [monotonicity #185]: #187
+#195 := [trans #188 #193]: #194
+#171 := [asserted]: #44
+#196 := [mp #171 #195]: #191
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#761 := (pattern #29)
+#11 := 0::int
+#68 := -1::int
+#72 := (* -1::int #9)
+#69 := (* -1::int #8)
+#127 := (mod #69 #72)
+#273 := (+ #29 #127)
+#274 := (= #273 0::int)
+#30 := (mod #8 #9)
+#270 := (* -1::int #30)
+#271 := (+ #29 #270)
+#272 := (= #271 0::int)
+#94 := (<= #9 0::int)
+#90 := (<= #8 0::int)
+#212 := (or #90 #94)
+#213 := (not #212)
+#101 := (>= #8 0::int)
+#204 := (or #94 #101)
+#205 := (not #204)
+#219 := (or #205 #213)
+#275 := (ite #219 #272 #274)
+#269 := (= #29 0::int)
+#12 := (= #8 0::int)
+#276 := (ite #12 #269 #275)
+#268 := (= #8 #29)
+#13 := (= #9 0::int)
+#277 := (ite #13 #268 #276)
+#762 := (forall (vars (?v0 int) (?v1 int)) (:pat #761) #277)
+#280 := (forall (vars (?v0 int) (?v1 int)) #277)
+#765 := (iff #280 #762)
+#763 := (iff #277 #277)
+#764 := [refl]: #763
+#766 := [quant-intro #764]: #765
+#133 := (* -1::int #127)
+#237 := (ite #219 #30 #133)
+#240 := (ite #12 0::int #237)
+#243 := (ite #13 #8 #240)
+#246 := (= #29 #243)
+#249 := (forall (vars (?v0 int) (?v1 int)) #246)
+#281 := (iff #249 #280)
+#278 := (iff #246 #277)
+#279 := [rewrite]: #278
+#282 := [quant-intro #279]: #281
+#102 := (not #101)
+#95 := (not #94)
+#105 := (and #95 #102)
+#91 := (not #90)
+#98 := (and #91 #95)
+#108 := (or #98 #105)
+#153 := (ite #108 #30 #133)
+#156 := (ite #12 0::int #153)
+#159 := (ite #13 #8 #156)
+#162 := (= #29 #159)
+#165 := (forall (vars (?v0 int) (?v1 int)) #162)
+#250 := (iff #165 #249)
+#247 := (iff #162 #246)
+#244 := (= #159 #243)
+#241 := (= #156 #240)
+#238 := (= #153 #237)
+#222 := (iff #108 #219)
+#216 := (or #213 #205)
+#220 := (iff #216 #219)
+#221 := [rewrite]: #220
+#217 := (iff #108 #216)
+#214 := (iff #105 #205)
+#215 := [rewrite]: #214
+#202 := (iff #98 #213)
+#203 := [rewrite]: #202
+#218 := [monotonicity #203 #215]: #217
+#223 := [trans #218 #221]: #222
+#239 := [monotonicity #223]: #238
+#242 := [monotonicity #239]: #241
+#245 := [monotonicity #242]: #244
+#248 := [monotonicity #245]: #247
+#251 := [quant-intro #248]: #250
+#200 := (~ #165 #165)
+#197 := (~ #162 #162)
+#210 := [refl]: #197
+#201 := [nnf-pos #210]: #200
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#168 := (iff #37 #165)
+#62 := (and #16 #18)
+#65 := (or #17 #62)
+#138 := (ite #65 #30 #133)
+#141 := (ite #12 0::int #138)
+#144 := (ite #13 #8 #141)
+#147 := (= #29 #144)
+#150 := (forall (vars (?v0 int) (?v1 int)) #147)
+#166 := (iff #150 #165)
+#163 := (iff #147 #162)
+#160 := (= #144 #159)
+#157 := (= #141 #156)
+#154 := (= #138 #153)
+#109 := (iff #65 #108)
+#106 := (iff #62 #105)
+#103 := (iff #18 #102)
+#104 := [rewrite]: #103
+#96 := (iff #16 #95)
+#97 := [rewrite]: #96
+#107 := [monotonicity #97 #104]: #106
+#99 := (iff #17 #98)
+#92 := (iff #15 #91)
+#93 := [rewrite]: #92
+#100 := [monotonicity #93 #97]: #99
+#110 := [monotonicity #100 #107]: #109
+#155 := [monotonicity #110]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [quant-intro #164]: #166
+#151 := (iff #37 #150)
+#148 := (iff #36 #147)
+#145 := (= #35 #144)
+#142 := (= #34 #141)
+#139 := (= #33 #138)
+#136 := (= #32 #133)
+#130 := (- #127)
+#134 := (= #130 #133)
+#135 := [rewrite]: #134
+#131 := (= #32 #130)
+#128 := (= #31 #127)
+#73 := (= #23 #72)
+#74 := [rewrite]: #73
+#70 := (= #22 #69)
+#71 := [rewrite]: #70
+#129 := [monotonicity #71 #74]: #128
+#132 := [monotonicity #129]: #131
+#137 := [trans #132 #135]: #136
+#66 := (iff #20 #65)
+#63 := (iff #19 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#140 := [monotonicity #67 #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [monotonicity #146]: #148
+#152 := [quant-intro #149]: #151
+#169 := [trans #152 #167]: #168
+#126 := [asserted]: #37
+#170 := [mp #126 #169]: #165
+#211 := [mp~ #170 #201]: #165
+#252 := [mp #211 #251]: #249
+#283 := [mp #252 #282]: #280
+#767 := [mp #283 #766]: #762
+#668 := (not #762)
+#675 := (or #668 #178)
+#341 := (* -1::int 3::int)
+#425 := (* -1::int -5::int)
+#426 := (mod #425 #341)
+#427 := (+ #175 #426)
+#418 := (= #427 0::int)
+#429 := (mod -5::int 3::int)
+#430 := (* -1::int #429)
+#431 := (+ #175 #430)
+#428 := (= #431 0::int)
+#432 := (<= 3::int 0::int)
+#411 := (<= -5::int 0::int)
+#746 := (or #411 #432)
+#748 := (not #746)
+#405 := (>= -5::int 0::int)
+#535 := (or #432 #405)
+#742 := (not #535)
+#416 := (or #742 #748)
+#417 := (ite #416 #428 #418)
+#749 := (= #175 0::int)
+#750 := (= -5::int 0::int)
+#751 := (ite #750 #749 #417)
+#752 := (= -5::int #175)
+#747 := (= 3::int 0::int)
+#753 := (ite #747 #752 #751)
+#659 := (or #668 #753)
+#662 := (iff #659 #675)
+#664 := (iff #675 #675)
+#665 := [rewrite]: #664
+#673 := (iff #753 #178)
+#744 := (= #175 -5::int)
+#681 := (ite false #744 #178)
+#671 := (iff #681 #178)
+#672 := [rewrite]: #671
+#677 := (iff #753 #681)
+#679 := (iff #751 #178)
+#676 := (ite false #749 #178)
+#667 := (iff #676 #178)
+#669 := [rewrite]: #667
+#678 := (iff #751 #676)
+#685 := (iff #417 #178)
+#572 := -2::int
+#587 := (= #175 -2::int)
+#1 := true
+#592 := (ite true #178 #587)
+#595 := (iff #592 #178)
+#688 := [rewrite]: #595
+#593 := (iff #417 #592)
+#583 := (iff #418 #587)
+#537 := 2::int
+#578 := (+ 2::int #175)
+#683 := (= #578 0::int)
+#589 := (iff #683 #587)
+#590 := [rewrite]: #589
+#684 := (iff #418 #683)
+#686 := (= #427 #578)
+#692 := (+ #175 2::int)
+#579 := (= #692 #578)
+#538 := [rewrite]: #579
+#695 := (= #427 #692)
+#693 := (= #426 2::int)
+#703 := -3::int
+#705 := (mod 5::int -3::int)
+#690 := (= #705 2::int)
+#691 := [rewrite]: #690
+#534 := (= #426 #705)
+#704 := (= #341 -3::int)
+#698 := [rewrite]: #704
+#696 := (= #425 5::int)
+#697 := [rewrite]: #696
+#536 := [monotonicity #697 #698]: #534
+#694 := [trans #536 #691]: #693
+#577 := [monotonicity #694]: #695
+#588 := [trans #577 #538]: #686
+#687 := [monotonicity #588]: #684
+#591 := [trans #687 #590]: #583
+#701 := (iff #428 #178)
+#707 := (+ -1::int #175)
+#555 := (= #707 0::int)
+#699 := (iff #555 #178)
+#700 := [rewrite]: #699
+#556 := (iff #428 #555)
+#708 := (= #431 #707)
+#710 := (+ #175 -1::int)
+#712 := (= #710 #707)
+#713 := [rewrite]: #712
+#711 := (= #431 #710)
+#720 := (= #430 -1::int)
+#718 := (* -1::int 1::int)
+#719 := (= #718 -1::int)
+#716 := [rewrite]: #719
+#433 := (= #430 #718)
+#439 := (= #429 1::int)
+#717 := [rewrite]: #439
+#715 := [monotonicity #717]: #433
+#709 := [trans #715 #716]: #720
+#706 := [monotonicity #709]: #711
+#714 := [trans #706 #713]: #708
+#557 := [monotonicity #714]: #556
+#702 := [trans #557 #700]: #701
+#437 := (iff #416 true)
+#727 := (or true false)
+#451 := (iff #727 true)
+#452 := [rewrite]: #451
+#726 := (iff #416 #727)
+#725 := (iff #748 false)
+#723 := (not true)
+#447 := (iff #723 false)
+#721 := [rewrite]: #447
+#724 := (iff #748 #723)
+#453 := (iff #746 true)
+#728 := (iff #746 #727)
+#729 := (iff #432 false)
+#392 := [rewrite]: #729
+#738 := (iff #411 true)
+#741 := [rewrite]: #738
+#450 := [monotonicity #741 #392]: #728
+#347 := [trans #450 #452]: #453
+#446 := [monotonicity #347]: #724
+#722 := [trans #446 #721]: #725
+#380 := (iff #742 true)
+#736 := (not false)
+#739 := (iff #736 true)
+#379 := [rewrite]: #739
+#374 := (iff #742 #736)
+#735 := (iff #535 false)
+#395 := (or false false)
+#733 := (iff #395 false)
+#734 := [rewrite]: #733
+#731 := (iff #535 #395)
+#393 := (iff #405 false)
+#394 := [rewrite]: #393
+#732 := [monotonicity #392 #394]: #731
+#730 := [trans #732 #734]: #735
+#737 := [monotonicity #730]: #374
+#740 := [trans #737 #379]: #380
+#436 := [monotonicity #740 #722]: #726
+#438 := [trans #436 #452]: #437
+#594 := [monotonicity #438 #702 #591]: #593
+#689 := [trans #594 #688]: #685
+#745 := (iff #750 false)
+#388 := [rewrite]: #745
+#670 := [monotonicity #388 #689]: #678
+#680 := [trans #670 #669]: #679
+#408 := (iff #752 #744)
+#404 := [rewrite]: #408
+#743 := (iff #747 false)
+#403 := [rewrite]: #743
+#682 := [monotonicity #403 #404 #680]: #677
+#674 := [trans #682 #672]: #673
+#663 := [monotonicity #674]: #662
+#661 := [trans #663 #665]: #662
+#660 := [quant-inst]: #659
+#666 := [mp #660 #661]: #675
+[unit-resolution #666 #767 #196]: false
+unsat
+2131919aacf2b81143bdcdf048ab7c7b571f4dab 350 0
+#2 := false
+#68 := -1::int
+decl f4 :: (-> int int int)
+#174 := -3::int
+#177 := (f4 -1::int -3::int)
+#180 := (= #177 -1::int)
+#193 := (not #180)
+#38 := 1::int
+#39 := (- 1::int)
+#40 := 3::int
+#41 := (- 3::int)
+#42 := (f4 #39 #41)
+#43 := (= #42 #39)
+#44 := (not #43)
+#196 := (iff #44 #193)
+#183 := (= -1::int #177)
+#188 := (not #183)
+#194 := (iff #188 #193)
+#191 := (iff #183 #180)
+#192 := [rewrite]: #191
+#195 := [monotonicity #192]: #194
+#189 := (iff #44 #188)
+#186 := (iff #43 #183)
+#184 := (iff #180 #183)
+#185 := [rewrite]: #184
+#181 := (iff #43 #180)
+#172 := (= #39 -1::int)
+#173 := [rewrite]: #172
+#178 := (= #42 #177)
+#175 := (= #41 -3::int)
+#176 := [rewrite]: #175
+#179 := [monotonicity #173 #176]: #178
+#182 := [monotonicity #179 #173]: #181
+#187 := [trans #182 #185]: #186
+#190 := [monotonicity #187]: #189
+#197 := [trans #190 #195]: #196
+#171 := [asserted]: #44
+#198 := [mp #171 #197]: #193
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#763 := (pattern #29)
+#11 := 0::int
+#72 := (* -1::int #9)
+#69 := (* -1::int #8)
+#127 := (mod #69 #72)
+#275 := (+ #29 #127)
+#276 := (= #275 0::int)
+#30 := (mod #8 #9)
+#272 := (* -1::int #30)
+#273 := (+ #29 #272)
+#274 := (= #273 0::int)
+#94 := (<= #9 0::int)
+#90 := (<= #8 0::int)
+#214 := (or #90 #94)
+#215 := (not #214)
+#101 := (>= #8 0::int)
+#206 := (or #94 #101)
+#207 := (not #206)
+#221 := (or #207 #215)
+#277 := (ite #221 #274 #276)
+#271 := (= #29 0::int)
+#12 := (= #8 0::int)
+#278 := (ite #12 #271 #277)
+#270 := (= #8 #29)
+#13 := (= #9 0::int)
+#279 := (ite #13 #270 #278)
+#764 := (forall (vars (?v0 int) (?v1 int)) (:pat #763) #279)
+#282 := (forall (vars (?v0 int) (?v1 int)) #279)
+#767 := (iff #282 #764)
+#765 := (iff #279 #279)
+#766 := [refl]: #765
+#768 := [quant-intro #766]: #767
+#133 := (* -1::int #127)
+#239 := (ite #221 #30 #133)
+#242 := (ite #12 0::int #239)
+#245 := (ite #13 #8 #242)
+#248 := (= #29 #245)
+#251 := (forall (vars (?v0 int) (?v1 int)) #248)
+#283 := (iff #251 #282)
+#280 := (iff #248 #279)
+#281 := [rewrite]: #280
+#284 := [quant-intro #281]: #283
+#102 := (not #101)
+#95 := (not #94)
+#105 := (and #95 #102)
+#91 := (not #90)
+#98 := (and #91 #95)
+#108 := (or #98 #105)
+#153 := (ite #108 #30 #133)
+#156 := (ite #12 0::int #153)
+#159 := (ite #13 #8 #156)
+#162 := (= #29 #159)
+#165 := (forall (vars (?v0 int) (?v1 int)) #162)
+#252 := (iff #165 #251)
+#249 := (iff #162 #248)
+#246 := (= #159 #245)
+#243 := (= #156 #242)
+#240 := (= #153 #239)
+#224 := (iff #108 #221)
+#218 := (or #215 #207)
+#222 := (iff #218 #221)
+#223 := [rewrite]: #222
+#219 := (iff #108 #218)
+#216 := (iff #105 #207)
+#217 := [rewrite]: #216
+#204 := (iff #98 #215)
+#205 := [rewrite]: #204
+#220 := [monotonicity #205 #217]: #219
+#225 := [trans #220 #223]: #224
+#241 := [monotonicity #225]: #240
+#244 := [monotonicity #241]: #243
+#247 := [monotonicity #244]: #246
+#250 := [monotonicity #247]: #249
+#253 := [quant-intro #250]: #252
+#202 := (~ #165 #165)
+#199 := (~ #162 #162)
+#212 := [refl]: #199
+#203 := [nnf-pos #212]: #202
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#168 := (iff #37 #165)
+#62 := (and #16 #18)
+#65 := (or #17 #62)
+#138 := (ite #65 #30 #133)
+#141 := (ite #12 0::int #138)
+#144 := (ite #13 #8 #141)
+#147 := (= #29 #144)
+#150 := (forall (vars (?v0 int) (?v1 int)) #147)
+#166 := (iff #150 #165)
+#163 := (iff #147 #162)
+#160 := (= #144 #159)
+#157 := (= #141 #156)
+#154 := (= #138 #153)
+#109 := (iff #65 #108)
+#106 := (iff #62 #105)
+#103 := (iff #18 #102)
+#104 := [rewrite]: #103
+#96 := (iff #16 #95)
+#97 := [rewrite]: #96
+#107 := [monotonicity #97 #104]: #106
+#99 := (iff #17 #98)
+#92 := (iff #15 #91)
+#93 := [rewrite]: #92
+#100 := [monotonicity #93 #97]: #99
+#110 := [monotonicity #100 #107]: #109
+#155 := [monotonicity #110]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [quant-intro #164]: #166
+#151 := (iff #37 #150)
+#148 := (iff #36 #147)
+#145 := (= #35 #144)
+#142 := (= #34 #141)
+#139 := (= #33 #138)
+#136 := (= #32 #133)
+#130 := (- #127)
+#134 := (= #130 #133)
+#135 := [rewrite]: #134
+#131 := (= #32 #130)
+#128 := (= #31 #127)
+#73 := (= #23 #72)
+#74 := [rewrite]: #73
+#70 := (= #22 #69)
+#71 := [rewrite]: #70
+#129 := [monotonicity #71 #74]: #128
+#132 := [monotonicity #129]: #131
+#137 := [trans #132 #135]: #136
+#66 := (iff #20 #65)
+#63 := (iff #19 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#140 := [monotonicity #67 #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [monotonicity #146]: #148
+#152 := [quant-intro #149]: #151
+#169 := [trans #152 #167]: #168
+#126 := [asserted]: #37
+#170 := [mp #126 #169]: #165
+#213 := [mp~ #170 #203]: #165
+#254 := [mp #213 #253]: #251
+#285 := [mp #254 #284]: #282
+#769 := [mp #285 #768]: #764
+#684 := (not #764)
+#673 := (or #684 #180)
+#343 := (* -1::int -3::int)
+#427 := (* -1::int -1::int)
+#428 := (mod #427 #343)
+#429 := (+ #177 #428)
+#420 := (= #429 0::int)
+#431 := (mod -1::int -3::int)
+#432 := (* -1::int #431)
+#433 := (+ #177 #432)
+#430 := (= #433 0::int)
+#434 := (<= -3::int 0::int)
+#413 := (<= -1::int 0::int)
+#748 := (or #413 #434)
+#750 := (not #748)
+#407 := (>= -1::int 0::int)
+#537 := (or #434 #407)
+#744 := (not #537)
+#418 := (or #744 #750)
+#419 := (ite #418 #430 #420)
+#751 := (= #177 0::int)
+#752 := (= -1::int 0::int)
+#753 := (ite #752 #751 #419)
+#754 := (= -3::int 0::int)
+#749 := (ite #754 #183 #753)
+#674 := (or #684 #749)
+#676 := (iff #674 #673)
+#677 := (iff #673 #673)
+#661 := [rewrite]: #677
+#683 := (iff #749 #180)
+#672 := (ite false #180 #180)
+#681 := (iff #672 #180)
+#682 := [rewrite]: #681
+#669 := (iff #749 #672)
+#678 := (iff #753 #180)
+#596 := (ite false #751 #180)
+#687 := (iff #596 #180)
+#691 := [rewrite]: #687
+#597 := (iff #753 #596)
+#594 := (iff #419 #180)
+#728 := 2::int
+#558 := (= #177 2::int)
+#589 := (ite false #558 #180)
+#585 := (iff #589 #180)
+#593 := [rewrite]: #585
+#591 := (iff #419 #589)
+#689 := (iff #420 #180)
+#694 := (+ 1::int #177)
+#540 := (= #694 0::int)
+#685 := (iff #540 #180)
+#686 := [rewrite]: #685
+#688 := (iff #420 #540)
+#580 := (= #429 #694)
+#693 := (+ #177 1::int)
+#697 := (= #693 #694)
+#579 := [rewrite]: #697
+#695 := (= #429 #693)
+#539 := (= #428 1::int)
+#706 := (mod 1::int 3::int)
+#536 := (= #706 1::int)
+#538 := [rewrite]: #536
+#700 := (= #428 #706)
+#699 := (= #343 3::int)
+#705 := [rewrite]: #699
+#704 := (= #427 1::int)
+#698 := [rewrite]: #704
+#707 := [monotonicity #698 #705]: #700
+#692 := [trans #707 #538]: #539
+#696 := [monotonicity #692]: #695
+#581 := [trans #696 #579]: #580
+#590 := [monotonicity #581]: #688
+#574 := [trans #590 #686]: #689
+#702 := (iff #430 #558)
+#720 := -2::int
+#713 := (+ -2::int #177)
+#710 := (= #713 0::int)
+#559 := (iff #710 #558)
+#701 := [rewrite]: #559
+#716 := (iff #430 #710)
+#714 := (= #433 #713)
+#722 := (+ #177 -2::int)
+#708 := (= #722 #713)
+#709 := [rewrite]: #708
+#711 := (= #433 #722)
+#721 := (= #432 -2::int)
+#440 := (* -1::int 2::int)
+#435 := (= #440 -2::int)
+#717 := [rewrite]: #435
+#441 := (= #432 #440)
+#438 := (= #431 2::int)
+#439 := [rewrite]: #438
+#719 := [monotonicity #439]: #441
+#718 := [trans #719 #717]: #721
+#712 := [monotonicity #718]: #711
+#715 := [trans #712 #709]: #714
+#557 := [monotonicity #715]: #716
+#703 := [trans #557 #701]: #702
+#727 := (iff #418 false)
+#725 := (or false false)
+#449 := (iff #725 false)
+#723 := [rewrite]: #449
+#726 := (iff #418 #725)
+#455 := (iff #750 false)
+#1 := true
+#735 := (not true)
+#732 := (iff #735 false)
+#738 := [rewrite]: #732
+#453 := (iff #750 #735)
+#730 := (iff #748 true)
+#382 := (or true true)
+#743 := (iff #382 true)
+#729 := [rewrite]: #743
+#742 := (iff #748 #382)
+#746 := (iff #434 true)
+#406 := [rewrite]: #746
+#741 := (iff #413 true)
+#381 := [rewrite]: #741
+#740 := [monotonicity #381 #406]: #742
+#452 := [trans #740 #729]: #730
+#454 := [monotonicity #452]: #453
+#349 := [trans #454 #738]: #455
+#376 := (iff #744 false)
+#736 := (iff #744 #735)
+#733 := (iff #537 true)
+#731 := (or true false)
+#396 := (iff #731 true)
+#397 := [rewrite]: #396
+#394 := (iff #537 #731)
+#747 := (iff #407 false)
+#390 := [rewrite]: #747
+#395 := [monotonicity #406 #390]: #394
+#734 := [trans #395 #397]: #733
+#737 := [monotonicity #734]: #736
+#739 := [trans #737 #738]: #376
+#448 := [monotonicity #739 #349]: #726
+#724 := [trans #448 #723]: #727
+#592 := [monotonicity #724 #703 #574]: #591
+#595 := [trans #592 #593]: #594
+#405 := (iff #752 false)
+#410 := [rewrite]: #405
+#690 := [monotonicity #410 #595]: #597
+#680 := [trans #690 #691]: #678
+#755 := (iff #754 false)
+#745 := [rewrite]: #755
+#671 := [monotonicity #745 #192 #680]: #669
+#679 := [trans #671 #682]: #683
+#670 := [monotonicity #679]: #676
+#662 := [trans #670 #661]: #676
+#675 := [quant-inst]: #674
+#664 := [mp #675 #662]: #673
+[unit-resolution #664 #769 #198]: false
+unsat
+f185b775c0ed207acb3897bf916bd950213b79f9 319 0
+#2 := false
+#11 := 0::int
+decl f4 :: (-> int int int)
+#170 := -3::int
+#173 := (f4 -3::int -3::int)
+#176 := (= #173 0::int)
+#189 := (not #176)
+#38 := 3::int
+#39 := (- 3::int)
+#40 := (f4 #39 #39)
+#41 := (= #40 0::int)
+#42 := (not #41)
+#192 := (iff #42 #189)
+#179 := (= 0::int #173)
+#184 := (not #179)
+#190 := (iff #184 #189)
+#187 := (iff #179 #176)
+#188 := [rewrite]: #187
+#191 := [monotonicity #188]: #190
+#185 := (iff #42 #184)
+#182 := (iff #41 #179)
+#180 := (iff #176 #179)
+#181 := [rewrite]: #180
+#177 := (iff #41 #176)
+#174 := (= #40 #173)
+#171 := (= #39 -3::int)
+#172 := [rewrite]: #171
+#175 := [monotonicity #172 #172]: #174
+#178 := [monotonicity #175]: #177
+#183 := [trans #178 #181]: #182
+#186 := [monotonicity #183]: #185
+#193 := [trans #186 #191]: #192
+#169 := [asserted]: #42
+#194 := [mp #169 #193]: #189
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#760 := (pattern #29)
+#66 := -1::int
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#125 := (mod #67 #70)
+#271 := (+ #29 #125)
+#272 := (= #271 0::int)
+#30 := (mod #8 #9)
+#268 := (* -1::int #30)
+#269 := (+ #29 #268)
+#270 := (= #269 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#210 := (or #88 #92)
+#211 := (not #210)
+#99 := (>= #8 0::int)
+#202 := (or #92 #99)
+#203 := (not #202)
+#217 := (or #203 #211)
+#273 := (ite #217 #270 #272)
+#267 := (= #29 0::int)
+#12 := (= #8 0::int)
+#274 := (ite #12 #267 #273)
+#266 := (= #8 #29)
+#13 := (= #9 0::int)
+#275 := (ite #13 #266 #274)
+#761 := (forall (vars (?v0 int) (?v1 int)) (:pat #760) #275)
+#278 := (forall (vars (?v0 int) (?v1 int)) #275)
+#764 := (iff #278 #761)
+#762 := (iff #275 #275)
+#763 := [refl]: #762
+#765 := [quant-intro #763]: #764
+#131 := (* -1::int #125)
+#235 := (ite #217 #30 #131)
+#238 := (ite #12 0::int #235)
+#241 := (ite #13 #8 #238)
+#244 := (= #29 #241)
+#247 := (forall (vars (?v0 int) (?v1 int)) #244)
+#279 := (iff #247 #278)
+#276 := (iff #244 #275)
+#277 := [rewrite]: #276
+#280 := [quant-intro #277]: #279
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#151 := (ite #106 #30 #131)
+#154 := (ite #12 0::int #151)
+#157 := (ite #13 #8 #154)
+#160 := (= #29 #157)
+#163 := (forall (vars (?v0 int) (?v1 int)) #160)
+#248 := (iff #163 #247)
+#245 := (iff #160 #244)
+#242 := (= #157 #241)
+#239 := (= #154 #238)
+#236 := (= #151 #235)
+#220 := (iff #106 #217)
+#214 := (or #211 #203)
+#218 := (iff #214 #217)
+#219 := [rewrite]: #218
+#215 := (iff #106 #214)
+#212 := (iff #103 #203)
+#213 := [rewrite]: #212
+#200 := (iff #96 #211)
+#201 := [rewrite]: #200
+#216 := [monotonicity #201 #213]: #215
+#221 := [trans #216 #219]: #220
+#237 := [monotonicity #221]: #236
+#240 := [monotonicity #237]: #239
+#243 := [monotonicity #240]: #242
+#246 := [monotonicity #243]: #245
+#249 := [quant-intro #246]: #248
+#198 := (~ #163 #163)
+#195 := (~ #160 #160)
+#208 := [refl]: #195
+#199 := [nnf-pos #208]: #198
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#166 := (iff #37 #163)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#136 := (ite #63 #30 #131)
+#139 := (ite #12 0::int #136)
+#142 := (ite #13 #8 #139)
+#145 := (= #29 #142)
+#148 := (forall (vars (?v0 int) (?v1 int)) #145)
+#164 := (iff #148 #163)
+#161 := (iff #145 #160)
+#158 := (= #142 #157)
+#155 := (= #139 #154)
+#152 := (= #136 #151)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#153 := [monotonicity #108]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [quant-intro #162]: #164
+#149 := (iff #37 #148)
+#146 := (iff #36 #145)
+#143 := (= #35 #142)
+#140 := (= #34 #139)
+#137 := (= #33 #136)
+#134 := (= #32 #131)
+#128 := (- #125)
+#132 := (= #128 #131)
+#133 := [rewrite]: #132
+#129 := (= #32 #128)
+#126 := (= #31 #125)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#127 := [monotonicity #69 #72]: #126
+#130 := [monotonicity #127]: #129
+#135 := [trans #130 #133]: #134
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#138 := [monotonicity #65 #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [quant-intro #147]: #149
+#167 := [trans #150 #165]: #166
+#124 := [asserted]: #37
+#168 := [mp #124 #167]: #163
+#209 := [mp~ #168 #199]: #163
+#250 := [mp #209 #249]: #247
+#281 := [mp #250 #280]: #278
+#766 := [mp #281 #765]: #761
+#537 := (not #761)
+#685 := (or #537 #176)
+#339 := (* -1::int -3::int)
+#424 := (mod #339 #339)
+#425 := (+ #173 #424)
+#426 := (= #425 0::int)
+#417 := (mod -3::int -3::int)
+#428 := (* -1::int #417)
+#429 := (+ #173 #428)
+#357 := (= #429 0::int)
+#430 := (<= -3::int 0::int)
+#427 := (or #430 #430)
+#431 := (not #427)
+#410 := (>= -3::int 0::int)
+#745 := (or #430 #410)
+#747 := (not #745)
+#404 := (or #747 #431)
+#534 := (ite #404 #357 #426)
+#741 := (= -3::int 0::int)
+#415 := (ite #741 #176 #534)
+#416 := (= -3::int #173)
+#748 := (ite #741 #416 #415)
+#587 := (or #537 #748)
+#683 := (iff #587 #685)
+#571 := (iff #685 #685)
+#586 := [rewrite]: #571
+#577 := (iff #748 #176)
+#746 := (= #173 -3::int)
+#692 := (ite false #746 #176)
+#694 := (iff #692 #176)
+#576 := [rewrite]: #694
+#693 := (iff #748 #692)
+#689 := (iff #415 #176)
+#695 := (ite false #176 #176)
+#703 := (iff #695 #176)
+#697 := [rewrite]: #703
+#535 := (iff #415 #695)
+#704 := (iff #534 #176)
+#696 := (iff #534 #695)
+#700 := (iff #426 #176)
+#698 := (= #425 #173)
+#438 := (+ #173 0::int)
+#432 := (= #438 #173)
+#714 := [rewrite]: #432
+#555 := (= #425 #438)
+#713 := (= #424 0::int)
+#705 := (mod 3::int 3::int)
+#712 := (= #705 0::int)
+#707 := [rewrite]: #712
+#706 := (= #424 #705)
+#709 := (= #339 3::int)
+#710 := [rewrite]: #709
+#711 := [monotonicity #710 #710]: #706
+#554 := [trans #711 #707]: #713
+#556 := [monotonicity #554]: #555
+#699 := [trans #556 #714]: #698
+#701 := [monotonicity #699]: #700
+#719 := (iff #357 #176)
+#718 := (= #429 #173)
+#716 := (= #429 #438)
+#436 := (= #428 0::int)
+#720 := (* -1::int 0::int)
+#725 := (= #720 0::int)
+#435 := [rewrite]: #725
+#724 := (= #428 #720)
+#445 := (= #417 0::int)
+#446 := [rewrite]: #445
+#721 := [monotonicity #446]: #724
+#437 := [trans #721 #435]: #436
+#717 := [monotonicity #437]: #716
+#715 := [trans #717 #714]: #718
+#708 := [monotonicity #715]: #719
+#722 := (iff #404 false)
+#449 := (or false false)
+#452 := (iff #449 false)
+#345 := [rewrite]: #452
+#450 := (iff #404 #449)
+#726 := (iff #431 false)
+#1 := true
+#394 := (not true)
+#732 := (iff #394 false)
+#733 := [rewrite]: #732
+#737 := (iff #431 #394)
+#379 := (iff #427 true)
+#735 := (or true true)
+#738 := (iff #735 true)
+#378 := [rewrite]: #738
+#373 := (iff #427 #735)
+#742 := (iff #430 true)
+#402 := [rewrite]: #742
+#736 := [monotonicity #402 #402]: #373
+#739 := [trans #736 #378]: #379
+#740 := [monotonicity #739]: #737
+#727 := [trans #740 #733]: #726
+#734 := (iff #747 false)
+#730 := (iff #747 #394)
+#392 := (iff #745 true)
+#403 := (or true false)
+#728 := (iff #403 true)
+#391 := [rewrite]: #728
+#744 := (iff #745 #403)
+#407 := (iff #410 false)
+#743 := [rewrite]: #407
+#387 := [monotonicity #402 #743]: #744
+#393 := [trans #387 #391]: #392
+#731 := [monotonicity #393]: #730
+#729 := [trans #731 #733]: #734
+#451 := [monotonicity #729 #727]: #450
+#723 := [trans #451 #345]: #722
+#702 := [monotonicity #723 #708 #701]: #696
+#533 := [trans #702 #697]: #704
+#749 := (iff #741 false)
+#750 := [rewrite]: #749
+#536 := [monotonicity #750 #533]: #535
+#690 := [trans #536 #697]: #689
+#751 := (iff #416 #746)
+#752 := [rewrite]: #751
+#691 := [monotonicity #750 #752 #690]: #693
+#578 := [trans #691 #576]: #577
+#686 := [monotonicity #578]: #683
+#588 := [trans #686 #586]: #683
+#682 := [quant-inst]: #587
+#589 := [mp #682 #588]: #685
+[unit-resolution #589 #766 #194]: false
+unsat
+fc9f250b0540aecbc3a008bfe364829a1228d272 347 0
+#2 := false
+#183 := -2::int
+decl f4 :: (-> int int int)
+#177 := -3::int
+#174 := -5::int
+#180 := (f4 -5::int -3::int)
+#186 := (= #180 -2::int)
+#189 := (not #186)
+#43 := 2::int
+#44 := (- 2::int)
+#40 := 3::int
+#41 := (- 3::int)
+#38 := 5::int
+#39 := (- 5::int)
+#42 := (f4 #39 #41)
+#45 := (= #42 #44)
+#46 := (not #45)
+#190 := (iff #46 #189)
+#187 := (iff #45 #186)
+#184 := (= #44 -2::int)
+#185 := [rewrite]: #184
+#181 := (= #42 #180)
+#178 := (= #41 -3::int)
+#179 := [rewrite]: #178
+#175 := (= #39 -5::int)
+#176 := [rewrite]: #175
+#182 := [monotonicity #176 #179]: #181
+#188 := [monotonicity #182 #185]: #187
+#191 := [monotonicity #188]: #190
+#173 := [asserted]: #46
+#194 := [mp #173 #191]: #189
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#758 := (pattern #29)
+#11 := 0::int
+#70 := -1::int
+#74 := (* -1::int #9)
+#71 := (* -1::int #8)
+#129 := (mod #71 #74)
+#269 := (+ #29 #129)
+#270 := (= #269 0::int)
+#30 := (mod #8 #9)
+#266 := (* -1::int #30)
+#267 := (+ #29 #266)
+#268 := (= #267 0::int)
+#96 := (<= #9 0::int)
+#92 := (<= #8 0::int)
+#208 := (or #92 #96)
+#209 := (not #208)
+#103 := (>= #8 0::int)
+#200 := (or #96 #103)
+#201 := (not #200)
+#215 := (or #201 #209)
+#271 := (ite #215 #268 #270)
+#265 := (= #29 0::int)
+#12 := (= #8 0::int)
+#272 := (ite #12 #265 #271)
+#264 := (= #8 #29)
+#13 := (= #9 0::int)
+#273 := (ite #13 #264 #272)
+#759 := (forall (vars (?v0 int) (?v1 int)) (:pat #758) #273)
+#276 := (forall (vars (?v0 int) (?v1 int)) #273)
+#762 := (iff #276 #759)
+#760 := (iff #273 #273)
+#761 := [refl]: #760
+#763 := [quant-intro #761]: #762
+#135 := (* -1::int #129)
+#233 := (ite #215 #30 #135)
+#236 := (ite #12 0::int #233)
+#239 := (ite #13 #8 #236)
+#242 := (= #29 #239)
+#245 := (forall (vars (?v0 int) (?v1 int)) #242)
+#277 := (iff #245 #276)
+#274 := (iff #242 #273)
+#275 := [rewrite]: #274
+#278 := [quant-intro #275]: #277
+#104 := (not #103)
+#97 := (not #96)
+#107 := (and #97 #104)
+#93 := (not #92)
+#100 := (and #93 #97)
+#110 := (or #100 #107)
+#155 := (ite #110 #30 #135)
+#158 := (ite #12 0::int #155)
+#161 := (ite #13 #8 #158)
+#164 := (= #29 #161)
+#167 := (forall (vars (?v0 int) (?v1 int)) #164)
+#246 := (iff #167 #245)
+#243 := (iff #164 #242)
+#240 := (= #161 #239)
+#237 := (= #158 #236)
+#234 := (= #155 #233)
+#218 := (iff #110 #215)
+#212 := (or #209 #201)
+#216 := (iff #212 #215)
+#217 := [rewrite]: #216
+#213 := (iff #110 #212)
+#210 := (iff #107 #201)
+#211 := [rewrite]: #210
+#198 := (iff #100 #209)
+#199 := [rewrite]: #198
+#214 := [monotonicity #199 #211]: #213
+#219 := [trans #214 #217]: #218
+#235 := [monotonicity #219]: #234
+#238 := [monotonicity #235]: #237
+#241 := [monotonicity #238]: #240
+#244 := [monotonicity #241]: #243
+#247 := [quant-intro #244]: #246
+#196 := (~ #167 #167)
+#192 := (~ #164 #164)
+#206 := [refl]: #192
+#197 := [nnf-pos #206]: #196
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#170 := (iff #37 #167)
+#64 := (and #16 #18)
+#67 := (or #17 #64)
+#140 := (ite #67 #30 #135)
+#143 := (ite #12 0::int #140)
+#146 := (ite #13 #8 #143)
+#149 := (= #29 #146)
+#152 := (forall (vars (?v0 int) (?v1 int)) #149)
+#168 := (iff #152 #167)
+#165 := (iff #149 #164)
+#162 := (= #146 #161)
+#159 := (= #143 #158)
+#156 := (= #140 #155)
+#111 := (iff #67 #110)
+#108 := (iff #64 #107)
+#105 := (iff #18 #104)
+#106 := [rewrite]: #105
+#98 := (iff #16 #97)
+#99 := [rewrite]: #98
+#109 := [monotonicity #99 #106]: #108
+#101 := (iff #17 #100)
+#94 := (iff #15 #93)
+#95 := [rewrite]: #94
+#102 := [monotonicity #95 #99]: #101
+#112 := [monotonicity #102 #109]: #111
+#157 := [monotonicity #112]: #156
+#160 := [monotonicity #157]: #159
+#163 := [monotonicity #160]: #162
+#166 := [monotonicity #163]: #165
+#169 := [quant-intro #166]: #168
+#153 := (iff #37 #152)
+#150 := (iff #36 #149)
+#147 := (= #35 #146)
+#144 := (= #34 #143)
+#141 := (= #33 #140)
+#138 := (= #32 #135)
+#132 := (- #129)
+#136 := (= #132 #135)
+#137 := [rewrite]: #136
+#133 := (= #32 #132)
+#130 := (= #31 #129)
+#75 := (= #23 #74)
+#76 := [rewrite]: #75
+#72 := (= #22 #71)
+#73 := [rewrite]: #72
+#131 := [monotonicity #73 #76]: #130
+#134 := [monotonicity #131]: #133
+#139 := [trans #134 #137]: #138
+#68 := (iff #20 #67)
+#65 := (iff #19 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#142 := [monotonicity #69 #139]: #141
+#145 := [monotonicity #142]: #144
+#148 := [monotonicity #145]: #147
+#151 := [monotonicity #148]: #150
+#154 := [quant-intro #151]: #153
+#171 := [trans #154 #169]: #170
+#128 := [asserted]: #37
+#172 := [mp #128 #171]: #167
+#207 := [mp~ #172 #197]: #167
+#248 := [mp #207 #247]: #245
+#279 := [mp #248 #278]: #276
+#764 := [mp #279 #763]: #759
+#669 := (not #759)
+#670 := (or #669 #186)
+#337 := (* -1::int -3::int)
+#422 := (* -1::int -5::int)
+#423 := (mod #422 #337)
+#424 := (+ #180 #423)
+#415 := (= #424 0::int)
+#426 := (mod -5::int -3::int)
+#427 := (* -1::int #426)
+#355 := (+ #180 #427)
+#428 := (= #355 0::int)
+#425 := (<= -3::int 0::int)
+#429 := (<= -5::int 0::int)
+#408 := (or #429 #425)
+#743 := (not #408)
+#745 := (>= -5::int 0::int)
+#402 := (or #425 #745)
+#532 := (not #402)
+#739 := (or #532 #743)
+#413 := (ite #739 #428 #415)
+#414 := (= #180 0::int)
+#746 := (= -5::int 0::int)
+#747 := (ite #746 #414 #413)
+#748 := (= -5::int #180)
+#749 := (= -3::int 0::int)
+#744 := (ite #749 #748 #747)
+#671 := (or #669 #744)
+#672 := (iff #671 #670)
+#657 := (iff #670 #670)
+#659 := [rewrite]: #657
+#679 := (iff #744 #186)
+#405 := (= #180 -5::int)
+#666 := (ite false #405 #186)
+#678 := (iff #666 #186)
+#674 := [rewrite]: #678
+#676 := (iff #744 #666)
+#667 := (iff #747 #186)
+#685 := (ite false #414 #186)
+#673 := (iff #685 #186)
+#675 := [rewrite]: #673
+#682 := (iff #747 #685)
+#591 := (iff #413 #186)
+#435 := 1::int
+#696 := (= #180 1::int)
+#587 := (ite false #696 #186)
+#589 := (iff #587 #186)
+#590 := [rewrite]: #589
+#580 := (iff #413 #587)
+#584 := (iff #415 #186)
+#574 := (+ 2::int #180)
+#585 := (= #574 0::int)
+#684 := (iff #585 #186)
+#569 := [rewrite]: #684
+#680 := (iff #415 #585)
+#535 := (= #424 #574)
+#691 := (+ #180 2::int)
+#575 := (= #691 #574)
+#576 := [rewrite]: #575
+#689 := (= #424 #691)
+#688 := (= #423 2::int)
+#702 := (mod 5::int 3::int)
+#534 := (= #702 2::int)
+#687 := [rewrite]: #534
+#531 := (= #423 #702)
+#701 := (= #337 3::int)
+#695 := [rewrite]: #701
+#694 := (= #422 5::int)
+#700 := [rewrite]: #694
+#533 := [monotonicity #700 #695]: #531
+#690 := [trans #533 #687]: #688
+#692 := [monotonicity #690]: #689
+#683 := [trans #692 #576]: #535
+#681 := [monotonicity #683]: #680
+#586 := [trans #681 #569]: #584
+#699 := (iff #428 #696)
+#704 := (+ -1::int #180)
+#552 := (= #704 0::int)
+#697 := (iff #552 #696)
+#698 := [rewrite]: #697
+#553 := (iff #428 #552)
+#705 := (= #355 #704)
+#707 := (+ #180 -1::int)
+#709 := (= #707 #704)
+#710 := [rewrite]: #709
+#708 := (= #355 #707)
+#717 := (= #427 -1::int)
+#715 := (* -1::int 1::int)
+#716 := (= #715 -1::int)
+#713 := [rewrite]: #716
+#430 := (= #427 #715)
+#436 := (= #426 1::int)
+#714 := [rewrite]: #436
+#712 := [monotonicity #714]: #430
+#706 := [trans #712 #713]: #717
+#703 := [monotonicity #706]: #708
+#711 := [trans #703 #710]: #705
+#554 := [monotonicity #711]: #553
+#693 := [trans #554 #698]: #699
+#433 := (iff #739 false)
+#444 := (or false false)
+#719 := (iff #444 false)
+#723 := [rewrite]: #719
+#718 := (iff #739 #444)
+#721 := (iff #743 false)
+#1 := true
+#727 := (not true)
+#734 := (iff #727 false)
+#736 := [rewrite]: #734
+#343 := (iff #743 #727)
+#449 := (iff #408 true)
+#738 := (or true true)
+#447 := (iff #738 true)
+#448 := [rewrite]: #447
+#724 := (iff #408 #738)
+#385 := (iff #425 true)
+#726 := [rewrite]: #385
+#737 := (iff #429 true)
+#735 := [rewrite]: #737
+#725 := [monotonicity #735 #726]: #724
+#450 := [trans #725 #448]: #449
+#720 := [monotonicity #450]: #343
+#443 := [trans #720 #736]: #721
+#376 := (iff #532 false)
+#733 := (iff #532 #727)
+#731 := (iff #402 true)
+#391 := (or true false)
+#729 := (iff #391 true)
+#730 := [rewrite]: #729
+#392 := (iff #402 #391)
+#389 := (iff #745 false)
+#390 := [rewrite]: #389
+#728 := [monotonicity #726 #390]: #392
+#732 := [trans #728 #730]: #731
+#371 := [monotonicity #732]: #733
+#377 := [trans #371 #736]: #376
+#722 := [monotonicity #377 #443]: #718
+#434 := [trans #722 #723]: #433
+#588 := [monotonicity #434 #693 #586]: #580
+#592 := [trans #588 #590]: #591
+#401 := (iff #746 false)
+#742 := [rewrite]: #401
+#686 := [monotonicity #742 #592]: #682
+#664 := [trans #686 #675]: #667
+#400 := (iff #748 #405)
+#741 := [rewrite]: #400
+#750 := (iff #749 false)
+#740 := [rewrite]: #750
+#677 := [monotonicity #740 #741 #664]: #676
+#668 := [trans #677 #674]: #679
+#656 := [monotonicity #668]: #672
+#660 := [trans #656 #659]: #672
+#665 := [quant-inst]: #671
+#661 := [mp #665 #660]: #670
+[unit-resolution #661 #764 #194]: false
+unsat
+66247d826364718443f0bc07b82495d982768eb5 327 0
+#2 := false
+#11 := 0::int
+decl f5 :: int
+#38 := f5
+#418 := (<= f5 0::int)
+#734 := (>= f5 0::int)
+#380 := (not #734)
+#723 := (not #418)
+#727 := (or #723 #380)
+#690 := (not #727)
+#39 := 3::int
+#415 := (mod f5 3::int)
+#66 := -1::int
+#416 := (* -1::int #415)
+decl f4 :: (-> int int int)
+#40 := (f4 f5 3::int)
+#344 := (+ #40 #416)
+#417 := (= #344 0::int)
+#563 := (not #417)
+#520 := (<= #344 0::int)
+#623 := (not #520)
+#631 := (>= #415 3::int)
+#632 := (not #631)
+#1 := true
+#57 := [true-axiom]: true
+#619 := (or false #632)
+#620 := [th-lemma]: #619
+#621 := [unit-resolution #620 #57]: #632
+#622 := [hypothesis]: #520
+#173 := (>= #40 3::int)
+#41 := (< #40 3::int)
+#42 := (not #41)
+#181 := (iff #42 #173)
+#172 := (not #173)
+#176 := (not #172)
+#179 := (iff #176 #173)
+#180 := [rewrite]: #179
+#177 := (iff #42 #176)
+#174 := (iff #41 #172)
+#175 := [rewrite]: #174
+#178 := [monotonicity #175]: #177
+#182 := [trans #178 #180]: #181
+#169 := [asserted]: #42
+#183 := [mp #169 #182]: #173
+#617 := [th-lemma #183 #622 #621]: false
+#609 := [lemma #617]: #623
+#626 := (or #563 #520)
+#637 := [th-lemma]: #626
+#615 := [unit-resolution #637 #609]: #563
+#614 := (or #690 #417)
+#438 := -3::int
+#411 := (* -1::int f5)
+#709 := (mod #411 -3::int)
+#433 := (+ #40 #709)
+#708 := (= #433 0::int)
+#423 := (ite #727 #417 #708)
+#403 := (= #40 0::int)
+#735 := (= f5 0::int)
+#703 := (ite #735 #403 #423)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#747 := (pattern #29)
+#70 := (* -1::int #9)
+#67 := (* -1::int #8)
+#125 := (mod #67 #70)
+#258 := (+ #29 #125)
+#259 := (= #258 0::int)
+#30 := (mod #8 #9)
+#255 := (* -1::int #30)
+#256 := (+ #29 #255)
+#257 := (= #256 0::int)
+#92 := (<= #9 0::int)
+#88 := (<= #8 0::int)
+#197 := (or #88 #92)
+#198 := (not #197)
+#99 := (>= #8 0::int)
+#189 := (or #92 #99)
+#190 := (not #189)
+#204 := (or #190 #198)
+#260 := (ite #204 #257 #259)
+#254 := (= #29 0::int)
+#12 := (= #8 0::int)
+#261 := (ite #12 #254 #260)
+#253 := (= #8 #29)
+#13 := (= #9 0::int)
+#262 := (ite #13 #253 #261)
+#748 := (forall (vars (?v0 int) (?v1 int)) (:pat #747) #262)
+#265 := (forall (vars (?v0 int) (?v1 int)) #262)
+#751 := (iff #265 #748)
+#749 := (iff #262 #262)
+#750 := [refl]: #749
+#752 := [quant-intro #750]: #751
+#131 := (* -1::int #125)
+#222 := (ite #204 #30 #131)
+#225 := (ite #12 0::int #222)
+#228 := (ite #13 #8 #225)
+#231 := (= #29 #228)
+#234 := (forall (vars (?v0 int) (?v1 int)) #231)
+#266 := (iff #234 #265)
+#263 := (iff #231 #262)
+#264 := [rewrite]: #263
+#267 := [quant-intro #264]: #266
+#100 := (not #99)
+#93 := (not #92)
+#103 := (and #93 #100)
+#89 := (not #88)
+#96 := (and #89 #93)
+#106 := (or #96 #103)
+#151 := (ite #106 #30 #131)
+#154 := (ite #12 0::int #151)
+#157 := (ite #13 #8 #154)
+#160 := (= #29 #157)
+#163 := (forall (vars (?v0 int) (?v1 int)) #160)
+#235 := (iff #163 #234)
+#232 := (iff #160 #231)
+#229 := (= #157 #228)
+#226 := (= #154 #225)
+#223 := (= #151 #222)
+#207 := (iff #106 #204)
+#201 := (or #198 #190)
+#205 := (iff #201 #204)
+#206 := [rewrite]: #205
+#202 := (iff #106 #201)
+#199 := (iff #103 #190)
+#200 := [rewrite]: #199
+#187 := (iff #96 #198)
+#188 := [rewrite]: #187
+#203 := [monotonicity #188 #200]: #202
+#208 := [trans #203 #206]: #207
+#224 := [monotonicity #208]: #223
+#227 := [monotonicity #224]: #226
+#230 := [monotonicity #227]: #229
+#233 := [monotonicity #230]: #232
+#236 := [quant-intro #233]: #235
+#185 := (~ #163 #163)
+#170 := (~ #160 #160)
+#195 := [refl]: #170
+#186 := [nnf-pos #195]: #185
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#166 := (iff #37 #163)
+#60 := (and #16 #18)
+#63 := (or #17 #60)
+#136 := (ite #63 #30 #131)
+#139 := (ite #12 0::int #136)
+#142 := (ite #13 #8 #139)
+#145 := (= #29 #142)
+#148 := (forall (vars (?v0 int) (?v1 int)) #145)
+#164 := (iff #148 #163)
+#161 := (iff #145 #160)
+#158 := (= #142 #157)
+#155 := (= #139 #154)
+#152 := (= #136 #151)
+#107 := (iff #63 #106)
+#104 := (iff #60 #103)
+#101 := (iff #18 #100)
+#102 := [rewrite]: #101
+#94 := (iff #16 #93)
+#95 := [rewrite]: #94
+#105 := [monotonicity #95 #102]: #104
+#97 := (iff #17 #96)
+#90 := (iff #15 #89)
+#91 := [rewrite]: #90
+#98 := [monotonicity #91 #95]: #97
+#108 := [monotonicity #98 #105]: #107
+#153 := [monotonicity #108]: #152
+#156 := [monotonicity #153]: #155
+#159 := [monotonicity #156]: #158
+#162 := [monotonicity #159]: #161
+#165 := [quant-intro #162]: #164
+#149 := (iff #37 #148)
+#146 := (iff #36 #145)
+#143 := (= #35 #142)
+#140 := (= #34 #139)
+#137 := (= #33 #136)
+#134 := (= #32 #131)
+#128 := (- #125)
+#132 := (= #128 #131)
+#133 := [rewrite]: #132
+#129 := (= #32 #128)
+#126 := (= #31 #125)
+#71 := (= #23 #70)
+#72 := [rewrite]: #71
+#68 := (= #22 #67)
+#69 := [rewrite]: #68
+#127 := [monotonicity #69 #72]: #126
+#130 := [monotonicity #127]: #129
+#135 := [trans #130 #133]: #134
+#64 := (iff #20 #63)
+#61 := (iff #19 #60)
+#62 := [rewrite]: #61
+#65 := [monotonicity #62]: #64
+#138 := [monotonicity #65 #135]: #137
+#141 := [monotonicity #138]: #140
+#144 := [monotonicity #141]: #143
+#147 := [monotonicity #144]: #146
+#150 := [quant-intro #147]: #149
+#167 := [trans #150 #165]: #166
+#124 := [asserted]: #37
+#168 := [mp #124 #167]: #163
+#196 := [mp~ #168 #186]: #163
+#237 := [mp #196 #236]: #234
+#268 := [mp #237 #267]: #265
+#753 := [mp #268 #752]: #748
+#692 := (not #748)
+#693 := (or #692 #703)
+#326 := (* -1::int 3::int)
+#412 := (mod #411 #326)
+#413 := (+ #40 #412)
+#404 := (= #413 0::int)
+#414 := (<= 3::int 0::int)
+#397 := (or #418 #414)
+#732 := (not #397)
+#391 := (or #414 #734)
+#521 := (not #391)
+#728 := (or #521 #732)
+#402 := (ite #728 #417 #404)
+#736 := (ite #735 #403 #402)
+#737 := (= f5 #40)
+#738 := (= 3::int 0::int)
+#733 := (ite #738 #737 #736)
+#698 := (or #692 #733)
+#694 := (iff #698 #693)
+#541 := (iff #693 #693)
+#542 := [rewrite]: #541
+#696 := (iff #733 #703)
+#701 := (ite false #737 #703)
+#706 := (iff #701 #703)
+#695 := [rewrite]: #706
+#705 := (iff #733 #701)
+#704 := (iff #736 #703)
+#424 := (iff #402 #423)
+#712 := (iff #404 #708)
+#707 := (= #413 #433)
+#710 := (= #412 #709)
+#439 := (= #326 -3::int)
+#332 := [rewrite]: #439
+#432 := [monotonicity #332]: #710
+#711 := [monotonicity #432]: #707
+#422 := [monotonicity #711]: #712
+#436 := (iff #728 #727)
+#366 := (or #380 #723)
+#713 := (iff #366 #727)
+#714 := [rewrite]: #713
+#726 := (iff #728 #366)
+#725 := (iff #732 #723)
+#722 := (iff #397 #418)
+#718 := (or #418 false)
+#721 := (iff #718 #418)
+#716 := [rewrite]: #721
+#719 := (iff #397 #718)
+#389 := (iff #414 false)
+#394 := [rewrite]: #389
+#720 := [monotonicity #394]: #719
+#360 := [trans #720 #716]: #722
+#365 := [monotonicity #360]: #725
+#381 := (iff #521 #380)
+#378 := (iff #391 #734)
+#730 := (or false #734)
+#374 := (iff #730 #734)
+#715 := [rewrite]: #374
+#390 := (iff #391 #730)
+#731 := [monotonicity #394]: #390
+#379 := [trans #731 #715]: #378
+#717 := [monotonicity #379]: #381
+#724 := [monotonicity #717 #365]: #726
+#437 := [trans #724 #714]: #436
+#425 := [monotonicity #437 #422]: #424
+#419 := [monotonicity #425]: #704
+#739 := (iff #738 false)
+#729 := [rewrite]: #739
+#702 := [monotonicity #729 #419]: #705
+#697 := [trans #702 #695]: #696
+#700 := [monotonicity #697]: #694
+#543 := [trans #700 #542]: #694
+#699 := [quant-inst]: #698
+#685 := [mp #699 #543]: #693
+#616 := [unit-resolution #685 #753]: #703
+#670 := (not #735)
+#669 := (not #703)
+#611 := (or #669 #670)
+#576 := (not #403)
+#686 := (<= #40 0::int)
+#618 := (not #686)
+#648 := (or #618 #172)
+#649 := [th-lemma]: #648
+#605 := [unit-resolution #649 #183]: #618
+#606 := (or #576 #686)
+#607 := [th-lemma]: #606
+#610 := [unit-resolution #607 #605]: #576
+#673 := (or #669 #670 #403)
+#558 := [def-axiom]: #673
+#612 := [unit-resolution #558 #610]: #611
+#613 := [unit-resolution #612 #616]: #670
+#573 := (or #669 #735 #423)
+#575 := [def-axiom]: #573
+#608 := [unit-resolution #575 #613 #616]: #423
+#677 := (not #423)
+#679 := (or #677 #690 #417)
+#680 := [def-axiom]: #679
+#587 := [unit-resolution #680 #608]: #614
+#588 := [unit-resolution #587 #615]: #690
+#688 := (or #727 #418)
+#682 := [def-axiom]: #688
+#589 := [unit-resolution #682 #588]: #418
+#683 := (or #727 #734)
+#689 := [def-axiom]: #683
+#482 := [unit-resolution #689 #588]: #734
+#593 := (or #735 #723 #380)
+#594 := [th-lemma]: #593
+#595 := [unit-resolution #594 #613]: #727
+[unit-resolution #595 #482 #589]: false
+unsat
+e48a7e8698a7ec4071541fd4399337a2b0f4fdb6 345 0
+#2 := false
+#39 := 3::int
+decl f4 :: (-> int int int)
+decl f5 :: int
+#38 := f5
+#40 := (f4 f5 3::int)
+#441 := (mod #40 3::int)
+#657 := (>= #441 3::int)
+#658 := (not #657)
+#1 := true
+#59 := [true-axiom]: true
+#647 := (or false #658)
+#642 := [th-lemma]: #647
+#648 := [unit-resolution #642 #59]: #658
+#11 := 0::int
+#68 := -1::int
+#436 := (* -1::int #40)
+#600 := (+ f5 #436)
+#601 := (<= #600 0::int)
+#172 := (= f5 #40)
+#188 := (>= f5 3::int)
+#187 := (not #188)
+#178 := (not #172)
+#194 := (or #178 #187)
+#199 := (not #194)
+#42 := (< f5 3::int)
+#41 := (= #40 f5)
+#43 := (implies #41 #42)
+#44 := (not #43)
+#202 := (iff #44 #199)
+#179 := (or #42 #178)
+#184 := (not #179)
+#200 := (iff #184 #199)
+#197 := (iff #179 #194)
+#191 := (or #187 #178)
+#195 := (iff #191 #194)
+#196 := [rewrite]: #195
+#192 := (iff #179 #191)
+#189 := (iff #42 #187)
+#190 := [rewrite]: #189
+#193 := [monotonicity #190]: #192
+#198 := [trans #193 #196]: #197
+#201 := [monotonicity #198]: #200
+#185 := (iff #44 #184)
+#182 := (iff #43 #179)
+#175 := (implies #172 #42)
+#180 := (iff #175 #179)
+#181 := [rewrite]: #180
+#176 := (iff #43 #175)
+#173 := (iff #41 #172)
+#174 := [rewrite]: #173
+#177 := [monotonicity #174]: #176
+#183 := [trans #177 #181]: #182
+#186 := [monotonicity #183]: #185
+#203 := [trans #186 #201]: #202
+#171 := [asserted]: #44
+#204 := [mp #171 #203]: #199
+#205 := [not-or-elim #204]: #172
+#634 := (or #178 #601)
+#630 := [th-lemma]: #634
+#631 := [unit-resolution #630 #205]: #601
+#206 := [not-or-elim #204]: #188
+#438 := (f4 #40 3::int)
+#602 := (* -1::int #438)
+#603 := (+ #40 #602)
+#604 := (<= #603 0::int)
+#763 := (= #40 #438)
+#635 := (= #438 #40)
+#632 := [symm #205]: #41
+#636 := [monotonicity #632]: #635
+#637 := [symm #636]: #763
+#638 := (not #763)
+#633 := (or #638 #604)
+#639 := [th-lemma]: #633
+#612 := [unit-resolution #639 #637]: #604
+#369 := (* -1::int #441)
+#442 := (+ #438 #369)
+#707 := (<= #442 0::int)
+#439 := (= #442 0::int)
+#738 := -3::int
+#462 := (mod #436 -3::int)
+#357 := (+ #438 #462)
+#457 := (= #357 0::int)
+#422 := (<= #40 0::int)
+#750 := (not #422)
+#416 := (>= #40 0::int)
+#406 := (not #416)
+#751 := (or #406 #750)
+#736 := (ite #751 #439 #457)
+#760 := (= #438 0::int)
+#761 := (= #40 0::int)
+#447 := (ite #761 #760 #736)
+#9 := (:var 0 int)
+#8 := (:var 1 int)
+#29 := (f4 #8 #9)
+#772 := (pattern #29)
+#72 := (* -1::int #9)
+#69 := (* -1::int #8)
+#127 := (mod #69 #72)
+#283 := (+ #29 #127)
+#284 := (= #283 0::int)
+#30 := (mod #8 #9)
+#280 := (* -1::int #30)
+#281 := (+ #29 #280)
+#282 := (= #281 0::int)
+#94 := (<= #9 0::int)
+#90 := (<= #8 0::int)
+#224 := (or #90 #94)
+#225 := (not #224)
+#101 := (>= #8 0::int)
+#216 := (or #94 #101)
+#217 := (not #216)
+#229 := (or #217 #225)
+#285 := (ite #229 #282 #284)
+#279 := (= #29 0::int)
+#12 := (= #8 0::int)
+#286 := (ite #12 #279 #285)
+#278 := (= #8 #29)
+#13 := (= #9 0::int)
+#287 := (ite #13 #278 #286)
+#773 := (forall (vars (?v0 int) (?v1 int)) (:pat #772) #287)
+#290 := (forall (vars (?v0 int) (?v1 int)) #287)
+#776 := (iff #290 #773)
+#774 := (iff #287 #287)
+#775 := [refl]: #774
+#777 := [quant-intro #775]: #776
+#133 := (* -1::int #127)
+#247 := (ite #229 #30 #133)
+#250 := (ite #12 0::int #247)
+#253 := (ite #13 #8 #250)
+#256 := (= #29 #253)
+#259 := (forall (vars (?v0 int) (?v1 int)) #256)
+#291 := (iff #259 #290)
+#288 := (iff #256 #287)
+#289 := [rewrite]: #288
+#292 := [quant-intro #289]: #291
+#102 := (not #101)
+#95 := (not #94)
+#105 := (and #95 #102)
+#91 := (not #90)
+#98 := (and #91 #95)
+#108 := (or #98 #105)
+#153 := (ite #108 #30 #133)
+#156 := (ite #12 0::int #153)
+#159 := (ite #13 #8 #156)
+#162 := (= #29 #159)
+#165 := (forall (vars (?v0 int) (?v1 int)) #162)
+#260 := (iff #165 #259)
+#257 := (iff #162 #256)
+#254 := (= #159 #253)
+#251 := (= #156 #250)
+#248 := (= #153 #247)
+#232 := (iff #108 #229)
+#226 := (or #225 #217)
+#230 := (iff #226 #229)
+#231 := [rewrite]: #230
+#227 := (iff #108 #226)
+#214 := (iff #105 #217)
+#215 := [rewrite]: #214
+#212 := (iff #98 #225)
+#213 := [rewrite]: #212
+#228 := [monotonicity #213 #215]: #227
+#233 := [trans #228 #231]: #232
+#249 := [monotonicity #233]: #248
+#252 := [monotonicity #249]: #251
+#255 := [monotonicity #252]: #254
+#258 := [monotonicity #255]: #257
+#261 := [quant-intro #258]: #260
+#210 := (~ #165 #165)
+#207 := (~ #162 #162)
+#222 := [refl]: #207
+#211 := [nnf-pos #222]: #210
+#23 := (- #9)
+#22 := (- #8)
+#31 := (mod #22 #23)
+#32 := (- #31)
+#16 := (< 0::int #9)
+#18 := (< #8 0::int)
+#19 := (and #18 #16)
+#15 := (< 0::int #8)
+#17 := (and #15 #16)
+#20 := (or #17 #19)
+#33 := (ite #20 #30 #32)
+#34 := (ite #12 0::int #33)
+#35 := (ite #13 #8 #34)
+#36 := (= #29 #35)
+#37 := (forall (vars (?v0 int) (?v1 int)) #36)
+#168 := (iff #37 #165)
+#62 := (and #16 #18)
+#65 := (or #17 #62)
+#138 := (ite #65 #30 #133)
+#141 := (ite #12 0::int #138)
+#144 := (ite #13 #8 #141)
+#147 := (= #29 #144)
+#150 := (forall (vars (?v0 int) (?v1 int)) #147)
+#166 := (iff #150 #165)
+#163 := (iff #147 #162)
+#160 := (= #144 #159)
+#157 := (= #141 #156)
+#154 := (= #138 #153)
+#109 := (iff #65 #108)
+#106 := (iff #62 #105)
+#103 := (iff #18 #102)
+#104 := [rewrite]: #103
+#96 := (iff #16 #95)
+#97 := [rewrite]: #96
+#107 := [monotonicity #97 #104]: #106
+#99 := (iff #17 #98)
+#92 := (iff #15 #91)
+#93 := [rewrite]: #92
+#100 := [monotonicity #93 #97]: #99
+#110 := [monotonicity #100 #107]: #109
+#155 := [monotonicity #110]: #154
+#158 := [monotonicity #155]: #157
+#161 := [monotonicity #158]: #160
+#164 := [monotonicity #161]: #163
+#167 := [quant-intro #164]: #166
+#151 := (iff #37 #150)
+#148 := (iff #36 #147)
+#145 := (= #35 #144)
+#142 := (= #34 #141)
+#139 := (= #33 #138)
+#136 := (= #32 #133)
+#130 := (- #127)
+#134 := (= #130 #133)
+#135 := [rewrite]: #134
+#131 := (= #32 #130)
+#128 := (= #31 #127)
+#73 := (= #23 #72)
+#74 := [rewrite]: #73
+#70 := (= #22 #69)
+#71 := [rewrite]: #70
+#129 := [monotonicity #71 #74]: #128
+#132 := [monotonicity #129]: #131
+#137 := [trans #132 #135]: #136
+#66 := (iff #20 #65)
+#63 := (iff #19 #62)
+#64 := [rewrite]: #63
+#67 := [monotonicity #64]: #66
+#140 := [monotonicity #67 #137]: #139
+#143 := [monotonicity #140]: #142
+#146 := [monotonicity #143]: #145
+#149 := [monotonicity #146]: #148
+#152 := [quant-intro #149]: #151
+#169 := [trans #152 #167]: #168
+#126 := [asserted]: #37
+#170 := [mp #126 #169]: #165
+#223 := [mp~ #170 #211]: #165
+#262 := [mp #223 #261]: #259
+#293 := [mp #262 #292]: #290
+#778 := [mp #293 #777]: #773
+#731 := (not #773)
+#720 := (or #731 #447)
+#351 := (* -1::int 3::int)
+#437 := (mod #436 #351)
+#429 := (+ #438 #437)
+#440 := (= #429 0::int)
+#443 := (<= 3::int 0::int)
+#757 := (or #422 #443)
+#759 := (not #757)
+#546 := (or #443 #416)
+#753 := (not #546)
+#427 := (or #753 #759)
+#428 := (ite #427 #439 #440)
+#762 := (ite #761 #760 #428)
+#758 := (= 3::int 0::int)
+#764 := (ite #758 #763 #762)
+#721 := (or #731 #764)
+#717 := (iff #721 #720)
+#723 := (iff #720 #720)
+#724 := [rewrite]: #723
+#730 := (iff #764 #447)
+#450 := (ite false #763 #447)
+#444 := (iff #450 #447)
+#726 := [rewrite]: #444
+#728 := (iff #764 #450)
+#448 := (iff #762 #447)
+#733 := (iff #428 #736)
+#458 := (iff #440 #457)
+#734 := (= #429 #357)
+#463 := (= #437 #462)
+#739 := (= #351 -3::int)
+#461 := [rewrite]: #739
+#464 := [monotonicity #461]: #463
+#735 := [monotonicity #464]: #734
+#732 := [monotonicity #735]: #458
+#749 := (iff #427 #751)
+#390 := (iff #759 #750)
+#385 := (iff #757 #422)
+#744 := (or #422 false)
+#741 := (iff #744 #422)
+#747 := [rewrite]: #741
+#745 := (iff #757 #744)
+#419 := (iff #443 false)
+#755 := [rewrite]: #419
+#746 := [monotonicity #755]: #745
+#748 := [trans #746 #747]: #385
+#391 := [monotonicity #748]: #390
+#742 := (iff #753 #406)
+#404 := (iff #546 #416)
+#415 := (or false #416)
+#740 := (iff #415 #416)
+#403 := [rewrite]: #740
+#756 := (iff #546 #415)
+#399 := [monotonicity #755]: #756
+#405 := [trans #399 #403]: #404
+#743 := [monotonicity #405]: #742
+#752 := [monotonicity #743 #391]: #749
+#737 := [monotonicity #752 #732]: #733
+#449 := [monotonicity #737]: #448
+#754 := (iff #758 false)
+#414 := [rewrite]: #754
+#729 := [monotonicity #414 #449]: #728
+#727 := [trans #729 #726]: #730
+#718 := [monotonicity #727]: #717
+#719 := [trans #718 #724]: #717
+#722 := [quant-inst]: #721
+#725 := [mp #722 #719]: #720
+#613 := [unit-resolution #725 #778]: #447
+#589 := (not #761)
+#614 := (not #601)
+#507 := (or #750 #187 #614)
+#618 := [th-lemma]: #507
+#619 := [unit-resolution #618 #206 #631]: #750
+#620 := (or #589 #422)
+#625 := [th-lemma]: #620
+#621 := [unit-resolution #625 #619]: #589
+#588 := (not #447)
+#697 := (or #588 #761 #736)
+#599 := [def-axiom]: #697
+#622 := [unit-resolution #599 #621 #613]: #736
+#568 := (or #751 #422)
+#710 := [def-axiom]: #568
+#623 := [unit-resolution #710 #619]: #751
+#711 := (not #751)
+#709 := (not #736)
+#716 := (or #709 #711 #439)
+#545 := [def-axiom]: #716
+#626 := [unit-resolution #545 #623 #622]: #439
+#701 := (not #439)
+#627 := (or #701 #707)
+#628 := [th-lemma]: #627
+#624 := [unit-resolution #628 #626]: #707
+[th-lemma #624 #612 #206 #631 #648]: false
+unsat
+ab1c3c43720ded895d2a82ffbaf56e6367dbc9b8 592 0
 #2 := false
 #11 := 0::int
 decl f3 :: (-> int int int)
@@ -40937,693 +43524,7 @@
 #362 := [unit-resolution #397 #361]: #600
 [th-lemma #362 #415 #382 #378]: false
 unsat
-faecfb2bed668dee6da551d02f1c23504bfe42c5 331 0
-#2 := false
-#11 := 0::int
-decl f4 :: (-> int int int)
-#38 := 3::int
-#170 := -3::int
-#173 := (f4 -3::int 3::int)
-#176 := (= #173 0::int)
-#189 := (not #176)
-#39 := (- 3::int)
-#40 := (f4 #39 3::int)
-#41 := (= #40 0::int)
-#42 := (not #41)
-#192 := (iff #42 #189)
-#179 := (= 0::int #173)
-#184 := (not #179)
-#190 := (iff #184 #189)
-#187 := (iff #179 #176)
-#188 := [rewrite]: #187
-#191 := [monotonicity #188]: #190
-#185 := (iff #42 #184)
-#182 := (iff #41 #179)
-#180 := (iff #176 #179)
-#181 := [rewrite]: #180
-#177 := (iff #41 #176)
-#174 := (= #40 #173)
-#171 := (= #39 -3::int)
-#172 := [rewrite]: #171
-#175 := [monotonicity #172]: #174
-#178 := [monotonicity #175]: #177
-#183 := [trans #178 #181]: #182
-#186 := [monotonicity #183]: #185
-#193 := [trans #186 #191]: #192
-#169 := [asserted]: #42
-#194 := [mp #169 #193]: #189
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#760 := (pattern #29)
-#66 := -1::int
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#125 := (mod #67 #70)
-#271 := (+ #29 #125)
-#272 := (= #271 0::int)
-#30 := (mod #8 #9)
-#268 := (* -1::int #30)
-#269 := (+ #29 #268)
-#270 := (= #269 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#210 := (or #88 #92)
-#211 := (not #210)
-#99 := (>= #8 0::int)
-#202 := (or #92 #99)
-#203 := (not #202)
-#217 := (or #203 #211)
-#273 := (ite #217 #270 #272)
-#267 := (= #29 0::int)
-#12 := (= #8 0::int)
-#274 := (ite #12 #267 #273)
-#266 := (= #8 #29)
-#13 := (= #9 0::int)
-#275 := (ite #13 #266 #274)
-#761 := (forall (vars (?v0 int) (?v1 int)) (:pat #760) #275)
-#278 := (forall (vars (?v0 int) (?v1 int)) #275)
-#764 := (iff #278 #761)
-#762 := (iff #275 #275)
-#763 := [refl]: #762
-#765 := [quant-intro #763]: #764
-#131 := (* -1::int #125)
-#235 := (ite #217 #30 #131)
-#238 := (ite #12 0::int #235)
-#241 := (ite #13 #8 #238)
-#244 := (= #29 #241)
-#247 := (forall (vars (?v0 int) (?v1 int)) #244)
-#279 := (iff #247 #278)
-#276 := (iff #244 #275)
-#277 := [rewrite]: #276
-#280 := [quant-intro #277]: #279
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#151 := (ite #106 #30 #131)
-#154 := (ite #12 0::int #151)
-#157 := (ite #13 #8 #154)
-#160 := (= #29 #157)
-#163 := (forall (vars (?v0 int) (?v1 int)) #160)
-#248 := (iff #163 #247)
-#245 := (iff #160 #244)
-#242 := (= #157 #241)
-#239 := (= #154 #238)
-#236 := (= #151 #235)
-#220 := (iff #106 #217)
-#214 := (or #211 #203)
-#218 := (iff #214 #217)
-#219 := [rewrite]: #218
-#215 := (iff #106 #214)
-#212 := (iff #103 #203)
-#213 := [rewrite]: #212
-#200 := (iff #96 #211)
-#201 := [rewrite]: #200
-#216 := [monotonicity #201 #213]: #215
-#221 := [trans #216 #219]: #220
-#237 := [monotonicity #221]: #236
-#240 := [monotonicity #237]: #239
-#243 := [monotonicity #240]: #242
-#246 := [monotonicity #243]: #245
-#249 := [quant-intro #246]: #248
-#198 := (~ #163 #163)
-#195 := (~ #160 #160)
-#208 := [refl]: #195
-#199 := [nnf-pos #208]: #198
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#166 := (iff #37 #163)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#136 := (ite #63 #30 #131)
-#139 := (ite #12 0::int #136)
-#142 := (ite #13 #8 #139)
-#145 := (= #29 #142)
-#148 := (forall (vars (?v0 int) (?v1 int)) #145)
-#164 := (iff #148 #163)
-#161 := (iff #145 #160)
-#158 := (= #142 #157)
-#155 := (= #139 #154)
-#152 := (= #136 #151)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#153 := [monotonicity #108]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#149 := (iff #37 #148)
-#146 := (iff #36 #145)
-#143 := (= #35 #142)
-#140 := (= #34 #139)
-#137 := (= #33 #136)
-#134 := (= #32 #131)
-#128 := (- #125)
-#132 := (= #128 #131)
-#133 := [rewrite]: #132
-#129 := (= #32 #128)
-#126 := (= #31 #125)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#127 := [monotonicity #69 #72]: #126
-#130 := [monotonicity #127]: #129
-#135 := [trans #130 #133]: #134
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#138 := [monotonicity #65 #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [quant-intro #147]: #149
-#167 := [trans #150 #165]: #166
-#124 := [asserted]: #37
-#168 := [mp #124 #167]: #163
-#209 := [mp~ #168 #199]: #163
-#250 := [mp #209 #249]: #247
-#281 := [mp #250 #280]: #278
-#766 := [mp #281 #765]: #761
-#591 := (not #761)
-#592 := (or #591 #176)
-#339 := (* -1::int 3::int)
-#424 := (* -1::int -3::int)
-#425 := (mod #424 #339)
-#426 := (+ #173 #425)
-#417 := (= #426 0::int)
-#428 := (mod -3::int 3::int)
-#429 := (* -1::int #428)
-#357 := (+ #173 #429)
-#430 := (= #357 0::int)
-#427 := (<= 3::int 0::int)
-#431 := (<= -3::int 0::int)
-#410 := (or #431 #427)
-#745 := (not #410)
-#747 := (>= -3::int 0::int)
-#404 := (or #427 #747)
-#534 := (not #404)
-#741 := (or #534 #745)
-#415 := (ite #741 #430 #417)
-#416 := (= -3::int 0::int)
-#748 := (ite #416 #176 #415)
-#749 := (= -3::int #173)
-#750 := (= 3::int 0::int)
-#751 := (ite #750 #749 #748)
-#593 := (or #591 #751)
-#687 := (iff #593 #592)
-#688 := (iff #592 #592)
-#675 := [rewrite]: #688
-#582 := (iff #751 #176)
-#402 := (= #173 -3::int)
-#686 := (ite false #402 #176)
-#588 := (iff #686 #176)
-#589 := [rewrite]: #588
-#571 := (iff #751 #686)
-#682 := (iff #748 #176)
-#577 := (ite false #176 #176)
-#685 := (iff #577 #176)
-#587 := [rewrite]: #685
-#578 := (iff #748 #577)
-#694 := (iff #415 #176)
-#1 := true
-#689 := (ite true #176 #176)
-#693 := (iff #689 #176)
-#691 := [rewrite]: #693
-#690 := (iff #415 #689)
-#535 := (iff #417 #176)
-#704 := (= #426 #173)
-#719 := (+ #173 0::int)
-#710 := (= #719 #173)
-#705 := [rewrite]: #710
-#703 := (= #426 #719)
-#696 := (= #425 0::int)
-#698 := (mod 3::int -3::int)
-#701 := (= #698 0::int)
-#695 := [rewrite]: #701
-#699 := (= #425 #698)
-#555 := (= #339 -3::int)
-#556 := [rewrite]: #555
-#713 := (= #424 3::int)
-#554 := [rewrite]: #713
-#700 := [monotonicity #554 #556]: #699
-#702 := [trans #700 #695]: #696
-#697 := [monotonicity #702]: #703
-#533 := [trans #697 #705]: #704
-#536 := [monotonicity #533]: #535
-#712 := (iff #430 #176)
-#706 := (= #357 #173)
-#708 := (= #357 #719)
-#718 := (= #429 0::int)
-#438 := (* -1::int 0::int)
-#432 := (= #438 0::int)
-#714 := [rewrite]: #432
-#716 := (= #429 #438)
-#436 := (= #428 0::int)
-#437 := [rewrite]: #436
-#717 := [monotonicity #437]: #716
-#715 := [trans #717 #714]: #718
-#709 := [monotonicity #715]: #708
-#711 := [trans #709 #705]: #706
-#707 := [monotonicity #711]: #712
-#725 := (iff #741 true)
-#737 := (or true false)
-#727 := (iff #737 true)
-#449 := [rewrite]: #727
-#724 := (iff #741 #737)
-#446 := (iff #745 false)
-#452 := (not true)
-#723 := (iff #452 false)
-#445 := [rewrite]: #723
-#345 := (iff #745 #452)
-#450 := (iff #410 true)
-#740 := (iff #410 #737)
-#744 := (iff #427 false)
-#387 := [rewrite]: #744
-#379 := (iff #431 true)
-#739 := [rewrite]: #379
-#726 := [monotonicity #739 #387]: #740
-#451 := [trans #726 #449]: #450
-#722 := [monotonicity #451]: #345
-#720 := [trans #722 #445]: #446
-#738 := (iff #534 true)
-#734 := (not false)
-#373 := (iff #734 true)
-#736 := [rewrite]: #373
-#729 := (iff #534 #734)
-#732 := (iff #404 false)
-#392 := (or false false)
-#730 := (iff #392 false)
-#731 := [rewrite]: #730
-#393 := (iff #404 #392)
-#728 := (iff #747 false)
-#391 := [rewrite]: #728
-#394 := [monotonicity #387 #391]: #393
-#733 := [trans #394 #731]: #732
-#735 := [monotonicity #733]: #729
-#378 := [trans #735 #736]: #738
-#721 := [monotonicity #378 #720]: #724
-#435 := [trans #721 #449]: #725
-#692 := [monotonicity #435 #707 #536]: #690
-#576 := [trans #692 #691]: #694
-#743 := (iff #416 false)
-#403 := [rewrite]: #743
-#537 := [monotonicity #403 #576]: #578
-#683 := [trans #537 #587]: #682
-#742 := (iff #749 #402)
-#407 := [rewrite]: #742
-#746 := (iff #750 false)
-#752 := [rewrite]: #746
-#586 := [monotonicity #752 #407 #683]: #571
-#590 := [trans #586 #589]: #582
-#684 := [monotonicity #590]: #687
-#677 := [trans #684 #675]: #687
-#594 := [quant-inst]: #593
-#669 := [mp #594 #677]: #592
-[unit-resolution #669 #766 #194]: false
-unsat
-1cc348013db3bd37921bfa60ffc6651c1d4acce9 353 0
-#2 := false
-#42 := 1::int
-decl f4 :: (-> int int int)
-#40 := 3::int
-#172 := -5::int
-#175 := (f4 -5::int 3::int)
-#178 := (= #175 1::int)
-#191 := (not #178)
-#38 := 5::int
-#39 := (- 5::int)
-#41 := (f4 #39 3::int)
-#43 := (= #41 1::int)
-#44 := (not #43)
-#194 := (iff #44 #191)
-#181 := (= 1::int #175)
-#186 := (not #181)
-#192 := (iff #186 #191)
-#189 := (iff #181 #178)
-#190 := [rewrite]: #189
-#193 := [monotonicity #190]: #192
-#187 := (iff #44 #186)
-#184 := (iff #43 #181)
-#182 := (iff #178 #181)
-#183 := [rewrite]: #182
-#179 := (iff #43 #178)
-#176 := (= #41 #175)
-#173 := (= #39 -5::int)
-#174 := [rewrite]: #173
-#177 := [monotonicity #174]: #176
-#180 := [monotonicity #177]: #179
-#185 := [trans #180 #183]: #184
-#188 := [monotonicity #185]: #187
-#195 := [trans #188 #193]: #194
-#171 := [asserted]: #44
-#196 := [mp #171 #195]: #191
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#761 := (pattern #29)
-#11 := 0::int
-#68 := -1::int
-#72 := (* -1::int #9)
-#69 := (* -1::int #8)
-#127 := (mod #69 #72)
-#273 := (+ #29 #127)
-#274 := (= #273 0::int)
-#30 := (mod #8 #9)
-#270 := (* -1::int #30)
-#271 := (+ #29 #270)
-#272 := (= #271 0::int)
-#94 := (<= #9 0::int)
-#90 := (<= #8 0::int)
-#212 := (or #90 #94)
-#213 := (not #212)
-#101 := (>= #8 0::int)
-#204 := (or #94 #101)
-#205 := (not #204)
-#219 := (or #205 #213)
-#275 := (ite #219 #272 #274)
-#269 := (= #29 0::int)
-#12 := (= #8 0::int)
-#276 := (ite #12 #269 #275)
-#268 := (= #8 #29)
-#13 := (= #9 0::int)
-#277 := (ite #13 #268 #276)
-#762 := (forall (vars (?v0 int) (?v1 int)) (:pat #761) #277)
-#280 := (forall (vars (?v0 int) (?v1 int)) #277)
-#765 := (iff #280 #762)
-#763 := (iff #277 #277)
-#764 := [refl]: #763
-#766 := [quant-intro #764]: #765
-#133 := (* -1::int #127)
-#237 := (ite #219 #30 #133)
-#240 := (ite #12 0::int #237)
-#243 := (ite #13 #8 #240)
-#246 := (= #29 #243)
-#249 := (forall (vars (?v0 int) (?v1 int)) #246)
-#281 := (iff #249 #280)
-#278 := (iff #246 #277)
-#279 := [rewrite]: #278
-#282 := [quant-intro #279]: #281
-#102 := (not #101)
-#95 := (not #94)
-#105 := (and #95 #102)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#153 := (ite #108 #30 #133)
-#156 := (ite #12 0::int #153)
-#159 := (ite #13 #8 #156)
-#162 := (= #29 #159)
-#165 := (forall (vars (?v0 int) (?v1 int)) #162)
-#250 := (iff #165 #249)
-#247 := (iff #162 #246)
-#244 := (= #159 #243)
-#241 := (= #156 #240)
-#238 := (= #153 #237)
-#222 := (iff #108 #219)
-#216 := (or #213 #205)
-#220 := (iff #216 #219)
-#221 := [rewrite]: #220
-#217 := (iff #108 #216)
-#214 := (iff #105 #205)
-#215 := [rewrite]: #214
-#202 := (iff #98 #213)
-#203 := [rewrite]: #202
-#218 := [monotonicity #203 #215]: #217
-#223 := [trans #218 #221]: #222
-#239 := [monotonicity #223]: #238
-#242 := [monotonicity #239]: #241
-#245 := [monotonicity #242]: #244
-#248 := [monotonicity #245]: #247
-#251 := [quant-intro #248]: #250
-#200 := (~ #165 #165)
-#197 := (~ #162 #162)
-#210 := [refl]: #197
-#201 := [nnf-pos #210]: #200
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#168 := (iff #37 #165)
-#62 := (and #16 #18)
-#65 := (or #17 #62)
-#138 := (ite #65 #30 #133)
-#141 := (ite #12 0::int #138)
-#144 := (ite #13 #8 #141)
-#147 := (= #29 #144)
-#150 := (forall (vars (?v0 int) (?v1 int)) #147)
-#166 := (iff #150 #165)
-#163 := (iff #147 #162)
-#160 := (= #144 #159)
-#157 := (= #141 #156)
-#154 := (= #138 #153)
-#109 := (iff #65 #108)
-#106 := (iff #62 #105)
-#103 := (iff #18 #102)
-#104 := [rewrite]: #103
-#96 := (iff #16 #95)
-#97 := [rewrite]: #96
-#107 := [monotonicity #97 #104]: #106
-#99 := (iff #17 #98)
-#92 := (iff #15 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#155 := [monotonicity #110]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [quant-intro #164]: #166
-#151 := (iff #37 #150)
-#148 := (iff #36 #147)
-#145 := (= #35 #144)
-#142 := (= #34 #141)
-#139 := (= #33 #138)
-#136 := (= #32 #133)
-#130 := (- #127)
-#134 := (= #130 #133)
-#135 := [rewrite]: #134
-#131 := (= #32 #130)
-#128 := (= #31 #127)
-#73 := (= #23 #72)
-#74 := [rewrite]: #73
-#70 := (= #22 #69)
-#71 := [rewrite]: #70
-#129 := [monotonicity #71 #74]: #128
-#132 := [monotonicity #129]: #131
-#137 := [trans #132 #135]: #136
-#66 := (iff #20 #65)
-#63 := (iff #19 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#140 := [monotonicity #67 #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [quant-intro #149]: #151
-#169 := [trans #152 #167]: #168
-#126 := [asserted]: #37
-#170 := [mp #126 #169]: #165
-#211 := [mp~ #170 #201]: #165
-#252 := [mp #211 #251]: #249
-#283 := [mp #252 #282]: #280
-#767 := [mp #283 #766]: #762
-#668 := (not #762)
-#675 := (or #668 #178)
-#341 := (* -1::int 3::int)
-#425 := (* -1::int -5::int)
-#426 := (mod #425 #341)
-#427 := (+ #175 #426)
-#418 := (= #427 0::int)
-#429 := (mod -5::int 3::int)
-#430 := (* -1::int #429)
-#431 := (+ #175 #430)
-#428 := (= #431 0::int)
-#432 := (<= 3::int 0::int)
-#411 := (<= -5::int 0::int)
-#746 := (or #411 #432)
-#748 := (not #746)
-#405 := (>= -5::int 0::int)
-#535 := (or #432 #405)
-#742 := (not #535)
-#416 := (or #742 #748)
-#417 := (ite #416 #428 #418)
-#749 := (= #175 0::int)
-#750 := (= -5::int 0::int)
-#751 := (ite #750 #749 #417)
-#752 := (= -5::int #175)
-#747 := (= 3::int 0::int)
-#753 := (ite #747 #752 #751)
-#659 := (or #668 #753)
-#662 := (iff #659 #675)
-#664 := (iff #675 #675)
-#665 := [rewrite]: #664
-#673 := (iff #753 #178)
-#744 := (= #175 -5::int)
-#681 := (ite false #744 #178)
-#671 := (iff #681 #178)
-#672 := [rewrite]: #671
-#677 := (iff #753 #681)
-#679 := (iff #751 #178)
-#676 := (ite false #749 #178)
-#667 := (iff #676 #178)
-#669 := [rewrite]: #667
-#678 := (iff #751 #676)
-#685 := (iff #417 #178)
-#572 := -2::int
-#587 := (= #175 -2::int)
-#1 := true
-#592 := (ite true #178 #587)
-#595 := (iff #592 #178)
-#688 := [rewrite]: #595
-#593 := (iff #417 #592)
-#583 := (iff #418 #587)
-#537 := 2::int
-#578 := (+ 2::int #175)
-#683 := (= #578 0::int)
-#589 := (iff #683 #587)
-#590 := [rewrite]: #589
-#684 := (iff #418 #683)
-#686 := (= #427 #578)
-#692 := (+ #175 2::int)
-#579 := (= #692 #578)
-#538 := [rewrite]: #579
-#695 := (= #427 #692)
-#693 := (= #426 2::int)
-#703 := -3::int
-#705 := (mod 5::int -3::int)
-#690 := (= #705 2::int)
-#691 := [rewrite]: #690
-#534 := (= #426 #705)
-#704 := (= #341 -3::int)
-#698 := [rewrite]: #704
-#696 := (= #425 5::int)
-#697 := [rewrite]: #696
-#536 := [monotonicity #697 #698]: #534
-#694 := [trans #536 #691]: #693
-#577 := [monotonicity #694]: #695
-#588 := [trans #577 #538]: #686
-#687 := [monotonicity #588]: #684
-#591 := [trans #687 #590]: #583
-#701 := (iff #428 #178)
-#707 := (+ -1::int #175)
-#555 := (= #707 0::int)
-#699 := (iff #555 #178)
-#700 := [rewrite]: #699
-#556 := (iff #428 #555)
-#708 := (= #431 #707)
-#710 := (+ #175 -1::int)
-#712 := (= #710 #707)
-#713 := [rewrite]: #712
-#711 := (= #431 #710)
-#720 := (= #430 -1::int)
-#718 := (* -1::int 1::int)
-#719 := (= #718 -1::int)
-#716 := [rewrite]: #719
-#433 := (= #430 #718)
-#439 := (= #429 1::int)
-#717 := [rewrite]: #439
-#715 := [monotonicity #717]: #433
-#709 := [trans #715 #716]: #720
-#706 := [monotonicity #709]: #711
-#714 := [trans #706 #713]: #708
-#557 := [monotonicity #714]: #556
-#702 := [trans #557 #700]: #701
-#437 := (iff #416 true)
-#727 := (or true false)
-#451 := (iff #727 true)
-#452 := [rewrite]: #451
-#726 := (iff #416 #727)
-#725 := (iff #748 false)
-#723 := (not true)
-#447 := (iff #723 false)
-#721 := [rewrite]: #447
-#724 := (iff #748 #723)
-#453 := (iff #746 true)
-#728 := (iff #746 #727)
-#729 := (iff #432 false)
-#392 := [rewrite]: #729
-#738 := (iff #411 true)
-#741 := [rewrite]: #738
-#450 := [monotonicity #741 #392]: #728
-#347 := [trans #450 #452]: #453
-#446 := [monotonicity #347]: #724
-#722 := [trans #446 #721]: #725
-#380 := (iff #742 true)
-#736 := (not false)
-#739 := (iff #736 true)
-#379 := [rewrite]: #739
-#374 := (iff #742 #736)
-#735 := (iff #535 false)
-#395 := (or false false)
-#733 := (iff #395 false)
-#734 := [rewrite]: #733
-#731 := (iff #535 #395)
-#393 := (iff #405 false)
-#394 := [rewrite]: #393
-#732 := [monotonicity #392 #394]: #731
-#730 := [trans #732 #734]: #735
-#737 := [monotonicity #730]: #374
-#740 := [trans #737 #379]: #380
-#436 := [monotonicity #740 #722]: #726
-#438 := [trans #436 #452]: #437
-#594 := [monotonicity #438 #702 #591]: #593
-#689 := [trans #594 #688]: #685
-#745 := (iff #750 false)
-#388 := [rewrite]: #745
-#670 := [monotonicity #388 #689]: #678
-#680 := [trans #670 #669]: #679
-#408 := (iff #752 #744)
-#404 := [rewrite]: #408
-#743 := (iff #747 false)
-#403 := [rewrite]: #743
-#682 := [monotonicity #403 #404 #680]: #677
-#674 := [trans #682 #672]: #673
-#663 := [monotonicity #674]: #662
-#661 := [trans #663 #665]: #662
-#660 := [quant-inst]: #659
-#666 := [mp #660 #661]: #675
-[unit-resolution #666 #767 #196]: false
-unsat
-0cfeb0d355451ec30e86083321e953491e3cc226 549 0
+f7d21861165159375bc45e6364e84fc0183b7f2c 549 0
 #2 := false
 #11 := 0::int
 decl f3 :: (-> int int int)
@@ -42173,358 +44074,7 @@
 #478 := [unit-resolution #470 #507]: #751
 [th-lemma #478 #476 #486 #472]: false
 unsat
-2a90f79ab6d055bafcbc76d83737ad593ffdc667 350 0
-#2 := false
-#68 := -1::int
-decl f4 :: (-> int int int)
-#174 := -3::int
-#177 := (f4 -1::int -3::int)
-#180 := (= #177 -1::int)
-#193 := (not #180)
-#38 := 1::int
-#39 := (- 1::int)
-#40 := 3::int
-#41 := (- 3::int)
-#42 := (f4 #39 #41)
-#43 := (= #42 #39)
-#44 := (not #43)
-#196 := (iff #44 #193)
-#183 := (= -1::int #177)
-#188 := (not #183)
-#194 := (iff #188 #193)
-#191 := (iff #183 #180)
-#192 := [rewrite]: #191
-#195 := [monotonicity #192]: #194
-#189 := (iff #44 #188)
-#186 := (iff #43 #183)
-#184 := (iff #180 #183)
-#185 := [rewrite]: #184
-#181 := (iff #43 #180)
-#172 := (= #39 -1::int)
-#173 := [rewrite]: #172
-#178 := (= #42 #177)
-#175 := (= #41 -3::int)
-#176 := [rewrite]: #175
-#179 := [monotonicity #173 #176]: #178
-#182 := [monotonicity #179 #173]: #181
-#187 := [trans #182 #185]: #186
-#190 := [monotonicity #187]: #189
-#197 := [trans #190 #195]: #196
-#171 := [asserted]: #44
-#198 := [mp #171 #197]: #193
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#763 := (pattern #29)
-#11 := 0::int
-#72 := (* -1::int #9)
-#69 := (* -1::int #8)
-#127 := (mod #69 #72)
-#275 := (+ #29 #127)
-#276 := (= #275 0::int)
-#30 := (mod #8 #9)
-#272 := (* -1::int #30)
-#273 := (+ #29 #272)
-#274 := (= #273 0::int)
-#94 := (<= #9 0::int)
-#90 := (<= #8 0::int)
-#214 := (or #90 #94)
-#215 := (not #214)
-#101 := (>= #8 0::int)
-#206 := (or #94 #101)
-#207 := (not #206)
-#221 := (or #207 #215)
-#277 := (ite #221 #274 #276)
-#271 := (= #29 0::int)
-#12 := (= #8 0::int)
-#278 := (ite #12 #271 #277)
-#270 := (= #8 #29)
-#13 := (= #9 0::int)
-#279 := (ite #13 #270 #278)
-#764 := (forall (vars (?v0 int) (?v1 int)) (:pat #763) #279)
-#282 := (forall (vars (?v0 int) (?v1 int)) #279)
-#767 := (iff #282 #764)
-#765 := (iff #279 #279)
-#766 := [refl]: #765
-#768 := [quant-intro #766]: #767
-#133 := (* -1::int #127)
-#239 := (ite #221 #30 #133)
-#242 := (ite #12 0::int #239)
-#245 := (ite #13 #8 #242)
-#248 := (= #29 #245)
-#251 := (forall (vars (?v0 int) (?v1 int)) #248)
-#283 := (iff #251 #282)
-#280 := (iff #248 #279)
-#281 := [rewrite]: #280
-#284 := [quant-intro #281]: #283
-#102 := (not #101)
-#95 := (not #94)
-#105 := (and #95 #102)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#153 := (ite #108 #30 #133)
-#156 := (ite #12 0::int #153)
-#159 := (ite #13 #8 #156)
-#162 := (= #29 #159)
-#165 := (forall (vars (?v0 int) (?v1 int)) #162)
-#252 := (iff #165 #251)
-#249 := (iff #162 #248)
-#246 := (= #159 #245)
-#243 := (= #156 #242)
-#240 := (= #153 #239)
-#224 := (iff #108 #221)
-#218 := (or #215 #207)
-#222 := (iff #218 #221)
-#223 := [rewrite]: #222
-#219 := (iff #108 #218)
-#216 := (iff #105 #207)
-#217 := [rewrite]: #216
-#204 := (iff #98 #215)
-#205 := [rewrite]: #204
-#220 := [monotonicity #205 #217]: #219
-#225 := [trans #220 #223]: #224
-#241 := [monotonicity #225]: #240
-#244 := [monotonicity #241]: #243
-#247 := [monotonicity #244]: #246
-#250 := [monotonicity #247]: #249
-#253 := [quant-intro #250]: #252
-#202 := (~ #165 #165)
-#199 := (~ #162 #162)
-#212 := [refl]: #199
-#203 := [nnf-pos #212]: #202
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#168 := (iff #37 #165)
-#62 := (and #16 #18)
-#65 := (or #17 #62)
-#138 := (ite #65 #30 #133)
-#141 := (ite #12 0::int #138)
-#144 := (ite #13 #8 #141)
-#147 := (= #29 #144)
-#150 := (forall (vars (?v0 int) (?v1 int)) #147)
-#166 := (iff #150 #165)
-#163 := (iff #147 #162)
-#160 := (= #144 #159)
-#157 := (= #141 #156)
-#154 := (= #138 #153)
-#109 := (iff #65 #108)
-#106 := (iff #62 #105)
-#103 := (iff #18 #102)
-#104 := [rewrite]: #103
-#96 := (iff #16 #95)
-#97 := [rewrite]: #96
-#107 := [monotonicity #97 #104]: #106
-#99 := (iff #17 #98)
-#92 := (iff #15 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#155 := [monotonicity #110]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [quant-intro #164]: #166
-#151 := (iff #37 #150)
-#148 := (iff #36 #147)
-#145 := (= #35 #144)
-#142 := (= #34 #141)
-#139 := (= #33 #138)
-#136 := (= #32 #133)
-#130 := (- #127)
-#134 := (= #130 #133)
-#135 := [rewrite]: #134
-#131 := (= #32 #130)
-#128 := (= #31 #127)
-#73 := (= #23 #72)
-#74 := [rewrite]: #73
-#70 := (= #22 #69)
-#71 := [rewrite]: #70
-#129 := [monotonicity #71 #74]: #128
-#132 := [monotonicity #129]: #131
-#137 := [trans #132 #135]: #136
-#66 := (iff #20 #65)
-#63 := (iff #19 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#140 := [monotonicity #67 #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [quant-intro #149]: #151
-#169 := [trans #152 #167]: #168
-#126 := [asserted]: #37
-#170 := [mp #126 #169]: #165
-#213 := [mp~ #170 #203]: #165
-#254 := [mp #213 #253]: #251
-#285 := [mp #254 #284]: #282
-#769 := [mp #285 #768]: #764
-#684 := (not #764)
-#673 := (or #684 #180)
-#343 := (* -1::int -3::int)
-#427 := (* -1::int -1::int)
-#428 := (mod #427 #343)
-#429 := (+ #177 #428)
-#420 := (= #429 0::int)
-#431 := (mod -1::int -3::int)
-#432 := (* -1::int #431)
-#433 := (+ #177 #432)
-#430 := (= #433 0::int)
-#434 := (<= -3::int 0::int)
-#413 := (<= -1::int 0::int)
-#748 := (or #413 #434)
-#750 := (not #748)
-#407 := (>= -1::int 0::int)
-#537 := (or #434 #407)
-#744 := (not #537)
-#418 := (or #744 #750)
-#419 := (ite #418 #430 #420)
-#751 := (= #177 0::int)
-#752 := (= -1::int 0::int)
-#753 := (ite #752 #751 #419)
-#754 := (= -3::int 0::int)
-#749 := (ite #754 #183 #753)
-#674 := (or #684 #749)
-#676 := (iff #674 #673)
-#677 := (iff #673 #673)
-#661 := [rewrite]: #677
-#683 := (iff #749 #180)
-#672 := (ite false #180 #180)
-#681 := (iff #672 #180)
-#682 := [rewrite]: #681
-#669 := (iff #749 #672)
-#678 := (iff #753 #180)
-#596 := (ite false #751 #180)
-#687 := (iff #596 #180)
-#691 := [rewrite]: #687
-#597 := (iff #753 #596)
-#594 := (iff #419 #180)
-#728 := 2::int
-#558 := (= #177 2::int)
-#589 := (ite false #558 #180)
-#585 := (iff #589 #180)
-#593 := [rewrite]: #585
-#591 := (iff #419 #589)
-#689 := (iff #420 #180)
-#694 := (+ 1::int #177)
-#540 := (= #694 0::int)
-#685 := (iff #540 #180)
-#686 := [rewrite]: #685
-#688 := (iff #420 #540)
-#580 := (= #429 #694)
-#693 := (+ #177 1::int)
-#697 := (= #693 #694)
-#579 := [rewrite]: #697
-#695 := (= #429 #693)
-#539 := (= #428 1::int)
-#706 := (mod 1::int 3::int)
-#536 := (= #706 1::int)
-#538 := [rewrite]: #536
-#700 := (= #428 #706)
-#699 := (= #343 3::int)
-#705 := [rewrite]: #699
-#704 := (= #427 1::int)
-#698 := [rewrite]: #704
-#707 := [monotonicity #698 #705]: #700
-#692 := [trans #707 #538]: #539
-#696 := [monotonicity #692]: #695
-#581 := [trans #696 #579]: #580
-#590 := [monotonicity #581]: #688
-#574 := [trans #590 #686]: #689
-#702 := (iff #430 #558)
-#720 := -2::int
-#713 := (+ -2::int #177)
-#710 := (= #713 0::int)
-#559 := (iff #710 #558)
-#701 := [rewrite]: #559
-#716 := (iff #430 #710)
-#714 := (= #433 #713)
-#722 := (+ #177 -2::int)
-#708 := (= #722 #713)
-#709 := [rewrite]: #708
-#711 := (= #433 #722)
-#721 := (= #432 -2::int)
-#440 := (* -1::int 2::int)
-#435 := (= #440 -2::int)
-#717 := [rewrite]: #435
-#441 := (= #432 #440)
-#438 := (= #431 2::int)
-#439 := [rewrite]: #438
-#719 := [monotonicity #439]: #441
-#718 := [trans #719 #717]: #721
-#712 := [monotonicity #718]: #711
-#715 := [trans #712 #709]: #714
-#557 := [monotonicity #715]: #716
-#703 := [trans #557 #701]: #702
-#727 := (iff #418 false)
-#725 := (or false false)
-#449 := (iff #725 false)
-#723 := [rewrite]: #449
-#726 := (iff #418 #725)
-#455 := (iff #750 false)
-#1 := true
-#735 := (not true)
-#732 := (iff #735 false)
-#738 := [rewrite]: #732
-#453 := (iff #750 #735)
-#730 := (iff #748 true)
-#382 := (or true true)
-#743 := (iff #382 true)
-#729 := [rewrite]: #743
-#742 := (iff #748 #382)
-#746 := (iff #434 true)
-#406 := [rewrite]: #746
-#741 := (iff #413 true)
-#381 := [rewrite]: #741
-#740 := [monotonicity #381 #406]: #742
-#452 := [trans #740 #729]: #730
-#454 := [monotonicity #452]: #453
-#349 := [trans #454 #738]: #455
-#376 := (iff #744 false)
-#736 := (iff #744 #735)
-#733 := (iff #537 true)
-#731 := (or true false)
-#396 := (iff #731 true)
-#397 := [rewrite]: #396
-#394 := (iff #537 #731)
-#747 := (iff #407 false)
-#390 := [rewrite]: #747
-#395 := [monotonicity #406 #390]: #394
-#734 := [trans #395 #397]: #733
-#737 := [monotonicity #734]: #736
-#739 := [trans #737 #738]: #376
-#448 := [monotonicity #739 #349]: #726
-#724 := [trans #448 #723]: #727
-#592 := [monotonicity #724 #703 #574]: #591
-#595 := [trans #592 #593]: #594
-#405 := (iff #752 false)
-#410 := [rewrite]: #405
-#690 := [monotonicity #410 #595]: #597
-#680 := [trans #690 #691]: #678
-#755 := (iff #754 false)
-#745 := [rewrite]: #755
-#671 := [monotonicity #745 #192 #680]: #669
-#679 := [trans #671 #682]: #683
-#670 := [monotonicity #679]: #676
-#662 := [trans #670 #661]: #676
-#675 := [quant-inst]: #674
-#664 := [mp #675 #662]: #673
-[unit-resolution #664 #769 #198]: false
-unsat
-15bd1be394385145d20cb6ec18ac38668f075cbe 75 0
+b8a677f41acfea6ca1bd28f53fd89f2c10758abc 75 0
 #2 := false
 #8 := 0::int
 decl f3 :: int
@@ -42600,327 +44150,7 @@
 #96 := [unit-resolution #95 #92]: #90
 [th-lemma #89 #70 #96]: false
 unsat
-7f8f90a6f1c8936c3bb2040faca497f7f7f61ec8 319 0
-#2 := false
-#11 := 0::int
-decl f4 :: (-> int int int)
-#170 := -3::int
-#173 := (f4 -3::int -3::int)
-#176 := (= #173 0::int)
-#189 := (not #176)
-#38 := 3::int
-#39 := (- 3::int)
-#40 := (f4 #39 #39)
-#41 := (= #40 0::int)
-#42 := (not #41)
-#192 := (iff #42 #189)
-#179 := (= 0::int #173)
-#184 := (not #179)
-#190 := (iff #184 #189)
-#187 := (iff #179 #176)
-#188 := [rewrite]: #187
-#191 := [monotonicity #188]: #190
-#185 := (iff #42 #184)
-#182 := (iff #41 #179)
-#180 := (iff #176 #179)
-#181 := [rewrite]: #180
-#177 := (iff #41 #176)
-#174 := (= #40 #173)
-#171 := (= #39 -3::int)
-#172 := [rewrite]: #171
-#175 := [monotonicity #172 #172]: #174
-#178 := [monotonicity #175]: #177
-#183 := [trans #178 #181]: #182
-#186 := [monotonicity #183]: #185
-#193 := [trans #186 #191]: #192
-#169 := [asserted]: #42
-#194 := [mp #169 #193]: #189
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#760 := (pattern #29)
-#66 := -1::int
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#125 := (mod #67 #70)
-#271 := (+ #29 #125)
-#272 := (= #271 0::int)
-#30 := (mod #8 #9)
-#268 := (* -1::int #30)
-#269 := (+ #29 #268)
-#270 := (= #269 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#210 := (or #88 #92)
-#211 := (not #210)
-#99 := (>= #8 0::int)
-#202 := (or #92 #99)
-#203 := (not #202)
-#217 := (or #203 #211)
-#273 := (ite #217 #270 #272)
-#267 := (= #29 0::int)
-#12 := (= #8 0::int)
-#274 := (ite #12 #267 #273)
-#266 := (= #8 #29)
-#13 := (= #9 0::int)
-#275 := (ite #13 #266 #274)
-#761 := (forall (vars (?v0 int) (?v1 int)) (:pat #760) #275)
-#278 := (forall (vars (?v0 int) (?v1 int)) #275)
-#764 := (iff #278 #761)
-#762 := (iff #275 #275)
-#763 := [refl]: #762
-#765 := [quant-intro #763]: #764
-#131 := (* -1::int #125)
-#235 := (ite #217 #30 #131)
-#238 := (ite #12 0::int #235)
-#241 := (ite #13 #8 #238)
-#244 := (= #29 #241)
-#247 := (forall (vars (?v0 int) (?v1 int)) #244)
-#279 := (iff #247 #278)
-#276 := (iff #244 #275)
-#277 := [rewrite]: #276
-#280 := [quant-intro #277]: #279
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#151 := (ite #106 #30 #131)
-#154 := (ite #12 0::int #151)
-#157 := (ite #13 #8 #154)
-#160 := (= #29 #157)
-#163 := (forall (vars (?v0 int) (?v1 int)) #160)
-#248 := (iff #163 #247)
-#245 := (iff #160 #244)
-#242 := (= #157 #241)
-#239 := (= #154 #238)
-#236 := (= #151 #235)
-#220 := (iff #106 #217)
-#214 := (or #211 #203)
-#218 := (iff #214 #217)
-#219 := [rewrite]: #218
-#215 := (iff #106 #214)
-#212 := (iff #103 #203)
-#213 := [rewrite]: #212
-#200 := (iff #96 #211)
-#201 := [rewrite]: #200
-#216 := [monotonicity #201 #213]: #215
-#221 := [trans #216 #219]: #220
-#237 := [monotonicity #221]: #236
-#240 := [monotonicity #237]: #239
-#243 := [monotonicity #240]: #242
-#246 := [monotonicity #243]: #245
-#249 := [quant-intro #246]: #248
-#198 := (~ #163 #163)
-#195 := (~ #160 #160)
-#208 := [refl]: #195
-#199 := [nnf-pos #208]: #198
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#166 := (iff #37 #163)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#136 := (ite #63 #30 #131)
-#139 := (ite #12 0::int #136)
-#142 := (ite #13 #8 #139)
-#145 := (= #29 #142)
-#148 := (forall (vars (?v0 int) (?v1 int)) #145)
-#164 := (iff #148 #163)
-#161 := (iff #145 #160)
-#158 := (= #142 #157)
-#155 := (= #139 #154)
-#152 := (= #136 #151)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#153 := [monotonicity #108]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#149 := (iff #37 #148)
-#146 := (iff #36 #145)
-#143 := (= #35 #142)
-#140 := (= #34 #139)
-#137 := (= #33 #136)
-#134 := (= #32 #131)
-#128 := (- #125)
-#132 := (= #128 #131)
-#133 := [rewrite]: #132
-#129 := (= #32 #128)
-#126 := (= #31 #125)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#127 := [monotonicity #69 #72]: #126
-#130 := [monotonicity #127]: #129
-#135 := [trans #130 #133]: #134
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#138 := [monotonicity #65 #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [quant-intro #147]: #149
-#167 := [trans #150 #165]: #166
-#124 := [asserted]: #37
-#168 := [mp #124 #167]: #163
-#209 := [mp~ #168 #199]: #163
-#250 := [mp #209 #249]: #247
-#281 := [mp #250 #280]: #278
-#766 := [mp #281 #765]: #761
-#537 := (not #761)
-#685 := (or #537 #176)
-#339 := (* -1::int -3::int)
-#424 := (mod #339 #339)
-#425 := (+ #173 #424)
-#426 := (= #425 0::int)
-#417 := (mod -3::int -3::int)
-#428 := (* -1::int #417)
-#429 := (+ #173 #428)
-#357 := (= #429 0::int)
-#430 := (<= -3::int 0::int)
-#427 := (or #430 #430)
-#431 := (not #427)
-#410 := (>= -3::int 0::int)
-#745 := (or #430 #410)
-#747 := (not #745)
-#404 := (or #747 #431)
-#534 := (ite #404 #357 #426)
-#741 := (= -3::int 0::int)
-#415 := (ite #741 #176 #534)
-#416 := (= -3::int #173)
-#748 := (ite #741 #416 #415)
-#587 := (or #537 #748)
-#683 := (iff #587 #685)
-#571 := (iff #685 #685)
-#586 := [rewrite]: #571
-#577 := (iff #748 #176)
-#746 := (= #173 -3::int)
-#692 := (ite false #746 #176)
-#694 := (iff #692 #176)
-#576 := [rewrite]: #694
-#693 := (iff #748 #692)
-#689 := (iff #415 #176)
-#695 := (ite false #176 #176)
-#703 := (iff #695 #176)
-#697 := [rewrite]: #703
-#535 := (iff #415 #695)
-#704 := (iff #534 #176)
-#696 := (iff #534 #695)
-#700 := (iff #426 #176)
-#698 := (= #425 #173)
-#438 := (+ #173 0::int)
-#432 := (= #438 #173)
-#714 := [rewrite]: #432
-#555 := (= #425 #438)
-#713 := (= #424 0::int)
-#705 := (mod 3::int 3::int)
-#712 := (= #705 0::int)
-#707 := [rewrite]: #712
-#706 := (= #424 #705)
-#709 := (= #339 3::int)
-#710 := [rewrite]: #709
-#711 := [monotonicity #710 #710]: #706
-#554 := [trans #711 #707]: #713
-#556 := [monotonicity #554]: #555
-#699 := [trans #556 #714]: #698
-#701 := [monotonicity #699]: #700
-#719 := (iff #357 #176)
-#718 := (= #429 #173)
-#716 := (= #429 #438)
-#436 := (= #428 0::int)
-#720 := (* -1::int 0::int)
-#725 := (= #720 0::int)
-#435 := [rewrite]: #725
-#724 := (= #428 #720)
-#445 := (= #417 0::int)
-#446 := [rewrite]: #445
-#721 := [monotonicity #446]: #724
-#437 := [trans #721 #435]: #436
-#717 := [monotonicity #437]: #716
-#715 := [trans #717 #714]: #718
-#708 := [monotonicity #715]: #719
-#722 := (iff #404 false)
-#449 := (or false false)
-#452 := (iff #449 false)
-#345 := [rewrite]: #452
-#450 := (iff #404 #449)
-#726 := (iff #431 false)
-#1 := true
-#394 := (not true)
-#732 := (iff #394 false)
-#733 := [rewrite]: #732
-#737 := (iff #431 #394)
-#379 := (iff #427 true)
-#735 := (or true true)
-#738 := (iff #735 true)
-#378 := [rewrite]: #738
-#373 := (iff #427 #735)
-#742 := (iff #430 true)
-#402 := [rewrite]: #742
-#736 := [monotonicity #402 #402]: #373
-#739 := [trans #736 #378]: #379
-#740 := [monotonicity #739]: #737
-#727 := [trans #740 #733]: #726
-#734 := (iff #747 false)
-#730 := (iff #747 #394)
-#392 := (iff #745 true)
-#403 := (or true false)
-#728 := (iff #403 true)
-#391 := [rewrite]: #728
-#744 := (iff #745 #403)
-#407 := (iff #410 false)
-#743 := [rewrite]: #407
-#387 := [monotonicity #402 #743]: #744
-#393 := [trans #387 #391]: #392
-#731 := [monotonicity #393]: #730
-#729 := [trans #731 #733]: #734
-#451 := [monotonicity #729 #727]: #450
-#723 := [trans #451 #345]: #722
-#702 := [monotonicity #723 #708 #701]: #696
-#533 := [trans #702 #697]: #704
-#749 := (iff #741 false)
-#750 := [rewrite]: #749
-#536 := [monotonicity #750 #533]: #535
-#690 := [trans #536 #697]: #689
-#751 := (iff #416 #746)
-#752 := [rewrite]: #751
-#691 := [monotonicity #750 #752 #690]: #693
-#578 := [trans #691 #576]: #577
-#686 := [monotonicity #578]: #683
-#588 := [trans #686 #586]: #683
-#682 := [quant-inst]: #587
-#589 := [mp #682 #588]: #685
-[unit-resolution #589 #766 #194]: false
-unsat
-98ce2e7fe8c73154e060ef0707079589f8062204 132 0
+957272aa2f77e61687a16c7aa490ba2664908958 132 0
 #2 := false
 #9 := 0::int
 decl f3 :: int
@@ -43053,7 +44283,7 @@
 #162 := [th-lemma]: #161
 [unit-resolution #162 #160 #143]: false
 unsat
-11cbd971427456e31403121d2898ec25b367a8f3 103 0
+9485d306079aa8cdc08952543a8ac86391d45fc0 103 0
 #2 := false
 #8 := 0::int
 decl f3 :: int
@@ -43157,7 +44387,7 @@
 #124 := [unit-resolution #123 #120]: #115
 [th-lemma #110 #124]: false
 unsat
-08b44e1a6f35749f6a110c211434791c0d3e5dd5 149 0
+443d726f158e992756000aa2462469d5494d62ee 149 0
 #2 := false
 #9 := 0::int
 decl f3 :: int
@@ -43307,7 +44537,7 @@
 #170 := [unit-resolution #169 #155]: #97
 [th-lemma #159 #170 #167]: false
 unsat
-603464f42ca695d3e1441697b9257ae6111df711 114 0
+5d75c12dca04a93af891e80a12133cb48b0e8ce3 114 0
 #2 := false
 #9 := 0::int
 decl f3 :: int
@@ -43422,355 +44652,7 @@
 #143 := [unit-resolution #142 #139]: #137
 [th-lemma #136 #134 #143]: false
 unsat
-6b1006b88fea0865d9f28ce9c2aca40c518bab7b 347 0
-#2 := false
-#183 := -2::int
-decl f4 :: (-> int int int)
-#177 := -3::int
-#174 := -5::int
-#180 := (f4 -5::int -3::int)
-#186 := (= #180 -2::int)
-#189 := (not #186)
-#43 := 2::int
-#44 := (- 2::int)
-#40 := 3::int
-#41 := (- 3::int)
-#38 := 5::int
-#39 := (- 5::int)
-#42 := (f4 #39 #41)
-#45 := (= #42 #44)
-#46 := (not #45)
-#190 := (iff #46 #189)
-#187 := (iff #45 #186)
-#184 := (= #44 -2::int)
-#185 := [rewrite]: #184
-#181 := (= #42 #180)
-#178 := (= #41 -3::int)
-#179 := [rewrite]: #178
-#175 := (= #39 -5::int)
-#176 := [rewrite]: #175
-#182 := [monotonicity #176 #179]: #181
-#188 := [monotonicity #182 #185]: #187
-#191 := [monotonicity #188]: #190
-#173 := [asserted]: #46
-#194 := [mp #173 #191]: #189
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#758 := (pattern #29)
-#11 := 0::int
-#70 := -1::int
-#74 := (* -1::int #9)
-#71 := (* -1::int #8)
-#129 := (mod #71 #74)
-#269 := (+ #29 #129)
-#270 := (= #269 0::int)
-#30 := (mod #8 #9)
-#266 := (* -1::int #30)
-#267 := (+ #29 #266)
-#268 := (= #267 0::int)
-#96 := (<= #9 0::int)
-#92 := (<= #8 0::int)
-#208 := (or #92 #96)
-#209 := (not #208)
-#103 := (>= #8 0::int)
-#200 := (or #96 #103)
-#201 := (not #200)
-#215 := (or #201 #209)
-#271 := (ite #215 #268 #270)
-#265 := (= #29 0::int)
-#12 := (= #8 0::int)
-#272 := (ite #12 #265 #271)
-#264 := (= #8 #29)
-#13 := (= #9 0::int)
-#273 := (ite #13 #264 #272)
-#759 := (forall (vars (?v0 int) (?v1 int)) (:pat #758) #273)
-#276 := (forall (vars (?v0 int) (?v1 int)) #273)
-#762 := (iff #276 #759)
-#760 := (iff #273 #273)
-#761 := [refl]: #760
-#763 := [quant-intro #761]: #762
-#135 := (* -1::int #129)
-#233 := (ite #215 #30 #135)
-#236 := (ite #12 0::int #233)
-#239 := (ite #13 #8 #236)
-#242 := (= #29 #239)
-#245 := (forall (vars (?v0 int) (?v1 int)) #242)
-#277 := (iff #245 #276)
-#274 := (iff #242 #273)
-#275 := [rewrite]: #274
-#278 := [quant-intro #275]: #277
-#104 := (not #103)
-#97 := (not #96)
-#107 := (and #97 #104)
-#93 := (not #92)
-#100 := (and #93 #97)
-#110 := (or #100 #107)
-#155 := (ite #110 #30 #135)
-#158 := (ite #12 0::int #155)
-#161 := (ite #13 #8 #158)
-#164 := (= #29 #161)
-#167 := (forall (vars (?v0 int) (?v1 int)) #164)
-#246 := (iff #167 #245)
-#243 := (iff #164 #242)
-#240 := (= #161 #239)
-#237 := (= #158 #236)
-#234 := (= #155 #233)
-#218 := (iff #110 #215)
-#212 := (or #209 #201)
-#216 := (iff #212 #215)
-#217 := [rewrite]: #216
-#213 := (iff #110 #212)
-#210 := (iff #107 #201)
-#211 := [rewrite]: #210
-#198 := (iff #100 #209)
-#199 := [rewrite]: #198
-#214 := [monotonicity #199 #211]: #213
-#219 := [trans #214 #217]: #218
-#235 := [monotonicity #219]: #234
-#238 := [monotonicity #235]: #237
-#241 := [monotonicity #238]: #240
-#244 := [monotonicity #241]: #243
-#247 := [quant-intro #244]: #246
-#196 := (~ #167 #167)
-#192 := (~ #164 #164)
-#206 := [refl]: #192
-#197 := [nnf-pos #206]: #196
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#170 := (iff #37 #167)
-#64 := (and #16 #18)
-#67 := (or #17 #64)
-#140 := (ite #67 #30 #135)
-#143 := (ite #12 0::int #140)
-#146 := (ite #13 #8 #143)
-#149 := (= #29 #146)
-#152 := (forall (vars (?v0 int) (?v1 int)) #149)
-#168 := (iff #152 #167)
-#165 := (iff #149 #164)
-#162 := (= #146 #161)
-#159 := (= #143 #158)
-#156 := (= #140 #155)
-#111 := (iff #67 #110)
-#108 := (iff #64 #107)
-#105 := (iff #18 #104)
-#106 := [rewrite]: #105
-#98 := (iff #16 #97)
-#99 := [rewrite]: #98
-#109 := [monotonicity #99 #106]: #108
-#101 := (iff #17 #100)
-#94 := (iff #15 #93)
-#95 := [rewrite]: #94
-#102 := [monotonicity #95 #99]: #101
-#112 := [monotonicity #102 #109]: #111
-#157 := [monotonicity #112]: #156
-#160 := [monotonicity #157]: #159
-#163 := [monotonicity #160]: #162
-#166 := [monotonicity #163]: #165
-#169 := [quant-intro #166]: #168
-#153 := (iff #37 #152)
-#150 := (iff #36 #149)
-#147 := (= #35 #146)
-#144 := (= #34 #143)
-#141 := (= #33 #140)
-#138 := (= #32 #135)
-#132 := (- #129)
-#136 := (= #132 #135)
-#137 := [rewrite]: #136
-#133 := (= #32 #132)
-#130 := (= #31 #129)
-#75 := (= #23 #74)
-#76 := [rewrite]: #75
-#72 := (= #22 #71)
-#73 := [rewrite]: #72
-#131 := [monotonicity #73 #76]: #130
-#134 := [monotonicity #131]: #133
-#139 := [trans #134 #137]: #138
-#68 := (iff #20 #67)
-#65 := (iff #19 #64)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#142 := [monotonicity #69 #139]: #141
-#145 := [monotonicity #142]: #144
-#148 := [monotonicity #145]: #147
-#151 := [monotonicity #148]: #150
-#154 := [quant-intro #151]: #153
-#171 := [trans #154 #169]: #170
-#128 := [asserted]: #37
-#172 := [mp #128 #171]: #167
-#207 := [mp~ #172 #197]: #167
-#248 := [mp #207 #247]: #245
-#279 := [mp #248 #278]: #276
-#764 := [mp #279 #763]: #759
-#669 := (not #759)
-#670 := (or #669 #186)
-#337 := (* -1::int -3::int)
-#422 := (* -1::int -5::int)
-#423 := (mod #422 #337)
-#424 := (+ #180 #423)
-#415 := (= #424 0::int)
-#426 := (mod -5::int -3::int)
-#427 := (* -1::int #426)
-#355 := (+ #180 #427)
-#428 := (= #355 0::int)
-#425 := (<= -3::int 0::int)
-#429 := (<= -5::int 0::int)
-#408 := (or #429 #425)
-#743 := (not #408)
-#745 := (>= -5::int 0::int)
-#402 := (or #425 #745)
-#532 := (not #402)
-#739 := (or #532 #743)
-#413 := (ite #739 #428 #415)
-#414 := (= #180 0::int)
-#746 := (= -5::int 0::int)
-#747 := (ite #746 #414 #413)
-#748 := (= -5::int #180)
-#749 := (= -3::int 0::int)
-#744 := (ite #749 #748 #747)
-#671 := (or #669 #744)
-#672 := (iff #671 #670)
-#657 := (iff #670 #670)
-#659 := [rewrite]: #657
-#679 := (iff #744 #186)
-#405 := (= #180 -5::int)
-#666 := (ite false #405 #186)
-#678 := (iff #666 #186)
-#674 := [rewrite]: #678
-#676 := (iff #744 #666)
-#667 := (iff #747 #186)
-#685 := (ite false #414 #186)
-#673 := (iff #685 #186)
-#675 := [rewrite]: #673
-#682 := (iff #747 #685)
-#591 := (iff #413 #186)
-#435 := 1::int
-#696 := (= #180 1::int)
-#587 := (ite false #696 #186)
-#589 := (iff #587 #186)
-#590 := [rewrite]: #589
-#580 := (iff #413 #587)
-#584 := (iff #415 #186)
-#574 := (+ 2::int #180)
-#585 := (= #574 0::int)
-#684 := (iff #585 #186)
-#569 := [rewrite]: #684
-#680 := (iff #415 #585)
-#535 := (= #424 #574)
-#691 := (+ #180 2::int)
-#575 := (= #691 #574)
-#576 := [rewrite]: #575
-#689 := (= #424 #691)
-#688 := (= #423 2::int)
-#702 := (mod 5::int 3::int)
-#534 := (= #702 2::int)
-#687 := [rewrite]: #534
-#531 := (= #423 #702)
-#701 := (= #337 3::int)
-#695 := [rewrite]: #701
-#694 := (= #422 5::int)
-#700 := [rewrite]: #694
-#533 := [monotonicity #700 #695]: #531
-#690 := [trans #533 #687]: #688
-#692 := [monotonicity #690]: #689
-#683 := [trans #692 #576]: #535
-#681 := [monotonicity #683]: #680
-#586 := [trans #681 #569]: #584
-#699 := (iff #428 #696)
-#704 := (+ -1::int #180)
-#552 := (= #704 0::int)
-#697 := (iff #552 #696)
-#698 := [rewrite]: #697
-#553 := (iff #428 #552)
-#705 := (= #355 #704)
-#707 := (+ #180 -1::int)
-#709 := (= #707 #704)
-#710 := [rewrite]: #709
-#708 := (= #355 #707)
-#717 := (= #427 -1::int)
-#715 := (* -1::int 1::int)
-#716 := (= #715 -1::int)
-#713 := [rewrite]: #716
-#430 := (= #427 #715)
-#436 := (= #426 1::int)
-#714 := [rewrite]: #436
-#712 := [monotonicity #714]: #430
-#706 := [trans #712 #713]: #717
-#703 := [monotonicity #706]: #708
-#711 := [trans #703 #710]: #705
-#554 := [monotonicity #711]: #553
-#693 := [trans #554 #698]: #699
-#433 := (iff #739 false)
-#444 := (or false false)
-#719 := (iff #444 false)
-#723 := [rewrite]: #719
-#718 := (iff #739 #444)
-#721 := (iff #743 false)
-#1 := true
-#727 := (not true)
-#734 := (iff #727 false)
-#736 := [rewrite]: #734
-#343 := (iff #743 #727)
-#449 := (iff #408 true)
-#738 := (or true true)
-#447 := (iff #738 true)
-#448 := [rewrite]: #447
-#724 := (iff #408 #738)
-#385 := (iff #425 true)
-#726 := [rewrite]: #385
-#737 := (iff #429 true)
-#735 := [rewrite]: #737
-#725 := [monotonicity #735 #726]: #724
-#450 := [trans #725 #448]: #449
-#720 := [monotonicity #450]: #343
-#443 := [trans #720 #736]: #721
-#376 := (iff #532 false)
-#733 := (iff #532 #727)
-#731 := (iff #402 true)
-#391 := (or true false)
-#729 := (iff #391 true)
-#730 := [rewrite]: #729
-#392 := (iff #402 #391)
-#389 := (iff #745 false)
-#390 := [rewrite]: #389
-#728 := [monotonicity #726 #390]: #392
-#732 := [trans #728 #730]: #731
-#371 := [monotonicity #732]: #733
-#377 := [trans #371 #736]: #376
-#722 := [monotonicity #377 #443]: #718
-#434 := [trans #722 #723]: #433
-#588 := [monotonicity #434 #693 #586]: #580
-#592 := [trans #588 #590]: #591
-#401 := (iff #746 false)
-#742 := [rewrite]: #401
-#686 := [monotonicity #742 #592]: #682
-#664 := [trans #686 #675]: #667
-#400 := (iff #748 #405)
-#741 := [rewrite]: #400
-#750 := (iff #749 false)
-#740 := [rewrite]: #750
-#677 := [monotonicity #740 #741 #664]: #676
-#668 := [trans #677 #674]: #679
-#656 := [monotonicity #668]: #672
-#660 := [trans #656 #659]: #672
-#665 := [quant-inst]: #671
-#661 := [mp #665 #660]: #670
-[unit-resolution #661 #764 #194]: false
-unsat
-dce856f3e21ae2f97ea031dc9fe8a9a3d8bcd965 57 0
+1c29e683939b29daf6c0c39d6dc5211f90494d2b 57 0
 #2 := false
 #36 := 0::int
 decl f4 :: int
@@ -43828,7 +44710,7 @@
 #77 := [th-lemma]: #76
 [unit-resolution #77 #74 #56]: false
 unsat
-1c2c19656480fea9eac0d64b2d7713bbaf1ce18e 57 0
+f5bdd04ade0ff62ddedb44ca71a4ab32cea43ed1 57 0
 #2 := false
 #36 := 0::int
 decl f4 :: int
@@ -43886,7 +44768,7 @@
 #77 := [unit-resolution #76 #73]: #71
 [th-lemma #77 #56 #72]: false
 unsat
-dcce7f1c4cfeb0855ad108c9c837348dc081133f 103 0
+db7c87847633d861c99b1fec84d68fb0617d9c27 103 0
 #2 := false
 #45 := 0::int
 decl f5 :: int
@@ -43990,335 +44872,7 @@
 #122 := [unit-resolution #121 #118]: #115
 [th-lemma #122 #92 #93]: false
 unsat
-cc54796722d31f22331ee38cd4d2e526cb5b071c 327 0
-#2 := false
-#11 := 0::int
-decl f5 :: int
-#38 := f5
-#418 := (<= f5 0::int)
-#734 := (>= f5 0::int)
-#380 := (not #734)
-#723 := (not #418)
-#727 := (or #723 #380)
-#690 := (not #727)
-#39 := 3::int
-#415 := (mod f5 3::int)
-#66 := -1::int
-#416 := (* -1::int #415)
-decl f4 :: (-> int int int)
-#40 := (f4 f5 3::int)
-#344 := (+ #40 #416)
-#417 := (= #344 0::int)
-#563 := (not #417)
-#520 := (<= #344 0::int)
-#623 := (not #520)
-#631 := (>= #415 3::int)
-#632 := (not #631)
-#1 := true
-#57 := [true-axiom]: true
-#619 := (or false #632)
-#620 := [th-lemma]: #619
-#621 := [unit-resolution #620 #57]: #632
-#622 := [hypothesis]: #520
-#173 := (>= #40 3::int)
-#41 := (< #40 3::int)
-#42 := (not #41)
-#181 := (iff #42 #173)
-#172 := (not #173)
-#176 := (not #172)
-#179 := (iff #176 #173)
-#180 := [rewrite]: #179
-#177 := (iff #42 #176)
-#174 := (iff #41 #172)
-#175 := [rewrite]: #174
-#178 := [monotonicity #175]: #177
-#182 := [trans #178 #180]: #181
-#169 := [asserted]: #42
-#183 := [mp #169 #182]: #173
-#617 := [th-lemma #183 #622 #621]: false
-#609 := [lemma #617]: #623
-#626 := (or #563 #520)
-#637 := [th-lemma]: #626
-#615 := [unit-resolution #637 #609]: #563
-#614 := (or #690 #417)
-#438 := -3::int
-#411 := (* -1::int f5)
-#709 := (mod #411 -3::int)
-#433 := (+ #40 #709)
-#708 := (= #433 0::int)
-#423 := (ite #727 #417 #708)
-#403 := (= #40 0::int)
-#735 := (= f5 0::int)
-#703 := (ite #735 #403 #423)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#747 := (pattern #29)
-#70 := (* -1::int #9)
-#67 := (* -1::int #8)
-#125 := (mod #67 #70)
-#258 := (+ #29 #125)
-#259 := (= #258 0::int)
-#30 := (mod #8 #9)
-#255 := (* -1::int #30)
-#256 := (+ #29 #255)
-#257 := (= #256 0::int)
-#92 := (<= #9 0::int)
-#88 := (<= #8 0::int)
-#197 := (or #88 #92)
-#198 := (not #197)
-#99 := (>= #8 0::int)
-#189 := (or #92 #99)
-#190 := (not #189)
-#204 := (or #190 #198)
-#260 := (ite #204 #257 #259)
-#254 := (= #29 0::int)
-#12 := (= #8 0::int)
-#261 := (ite #12 #254 #260)
-#253 := (= #8 #29)
-#13 := (= #9 0::int)
-#262 := (ite #13 #253 #261)
-#748 := (forall (vars (?v0 int) (?v1 int)) (:pat #747) #262)
-#265 := (forall (vars (?v0 int) (?v1 int)) #262)
-#751 := (iff #265 #748)
-#749 := (iff #262 #262)
-#750 := [refl]: #749
-#752 := [quant-intro #750]: #751
-#131 := (* -1::int #125)
-#222 := (ite #204 #30 #131)
-#225 := (ite #12 0::int #222)
-#228 := (ite #13 #8 #225)
-#231 := (= #29 #228)
-#234 := (forall (vars (?v0 int) (?v1 int)) #231)
-#266 := (iff #234 #265)
-#263 := (iff #231 #262)
-#264 := [rewrite]: #263
-#267 := [quant-intro #264]: #266
-#100 := (not #99)
-#93 := (not #92)
-#103 := (and #93 #100)
-#89 := (not #88)
-#96 := (and #89 #93)
-#106 := (or #96 #103)
-#151 := (ite #106 #30 #131)
-#154 := (ite #12 0::int #151)
-#157 := (ite #13 #8 #154)
-#160 := (= #29 #157)
-#163 := (forall (vars (?v0 int) (?v1 int)) #160)
-#235 := (iff #163 #234)
-#232 := (iff #160 #231)
-#229 := (= #157 #228)
-#226 := (= #154 #225)
-#223 := (= #151 #222)
-#207 := (iff #106 #204)
-#201 := (or #198 #190)
-#205 := (iff #201 #204)
-#206 := [rewrite]: #205
-#202 := (iff #106 #201)
-#199 := (iff #103 #190)
-#200 := [rewrite]: #199
-#187 := (iff #96 #198)
-#188 := [rewrite]: #187
-#203 := [monotonicity #188 #200]: #202
-#208 := [trans #203 #206]: #207
-#224 := [monotonicity #208]: #223
-#227 := [monotonicity #224]: #226
-#230 := [monotonicity #227]: #229
-#233 := [monotonicity #230]: #232
-#236 := [quant-intro #233]: #235
-#185 := (~ #163 #163)
-#170 := (~ #160 #160)
-#195 := [refl]: #170
-#186 := [nnf-pos #195]: #185
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#166 := (iff #37 #163)
-#60 := (and #16 #18)
-#63 := (or #17 #60)
-#136 := (ite #63 #30 #131)
-#139 := (ite #12 0::int #136)
-#142 := (ite #13 #8 #139)
-#145 := (= #29 #142)
-#148 := (forall (vars (?v0 int) (?v1 int)) #145)
-#164 := (iff #148 #163)
-#161 := (iff #145 #160)
-#158 := (= #142 #157)
-#155 := (= #139 #154)
-#152 := (= #136 #151)
-#107 := (iff #63 #106)
-#104 := (iff #60 #103)
-#101 := (iff #18 #100)
-#102 := [rewrite]: #101
-#94 := (iff #16 #93)
-#95 := [rewrite]: #94
-#105 := [monotonicity #95 #102]: #104
-#97 := (iff #17 #96)
-#90 := (iff #15 #89)
-#91 := [rewrite]: #90
-#98 := [monotonicity #91 #95]: #97
-#108 := [monotonicity #98 #105]: #107
-#153 := [monotonicity #108]: #152
-#156 := [monotonicity #153]: #155
-#159 := [monotonicity #156]: #158
-#162 := [monotonicity #159]: #161
-#165 := [quant-intro #162]: #164
-#149 := (iff #37 #148)
-#146 := (iff #36 #145)
-#143 := (= #35 #142)
-#140 := (= #34 #139)
-#137 := (= #33 #136)
-#134 := (= #32 #131)
-#128 := (- #125)
-#132 := (= #128 #131)
-#133 := [rewrite]: #132
-#129 := (= #32 #128)
-#126 := (= #31 #125)
-#71 := (= #23 #70)
-#72 := [rewrite]: #71
-#68 := (= #22 #67)
-#69 := [rewrite]: #68
-#127 := [monotonicity #69 #72]: #126
-#130 := [monotonicity #127]: #129
-#135 := [trans #130 #133]: #134
-#64 := (iff #20 #63)
-#61 := (iff #19 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#138 := [monotonicity #65 #135]: #137
-#141 := [monotonicity #138]: #140
-#144 := [monotonicity #141]: #143
-#147 := [monotonicity #144]: #146
-#150 := [quant-intro #147]: #149
-#167 := [trans #150 #165]: #166
-#124 := [asserted]: #37
-#168 := [mp #124 #167]: #163
-#196 := [mp~ #168 #186]: #163
-#237 := [mp #196 #236]: #234
-#268 := [mp #237 #267]: #265
-#753 := [mp #268 #752]: #748
-#692 := (not #748)
-#693 := (or #692 #703)
-#326 := (* -1::int 3::int)
-#412 := (mod #411 #326)
-#413 := (+ #40 #412)
-#404 := (= #413 0::int)
-#414 := (<= 3::int 0::int)
-#397 := (or #418 #414)
-#732 := (not #397)
-#391 := (or #414 #734)
-#521 := (not #391)
-#728 := (or #521 #732)
-#402 := (ite #728 #417 #404)
-#736 := (ite #735 #403 #402)
-#737 := (= f5 #40)
-#738 := (= 3::int 0::int)
-#733 := (ite #738 #737 #736)
-#698 := (or #692 #733)
-#694 := (iff #698 #693)
-#541 := (iff #693 #693)
-#542 := [rewrite]: #541
-#696 := (iff #733 #703)
-#701 := (ite false #737 #703)
-#706 := (iff #701 #703)
-#695 := [rewrite]: #706
-#705 := (iff #733 #701)
-#704 := (iff #736 #703)
-#424 := (iff #402 #423)
-#712 := (iff #404 #708)
-#707 := (= #413 #433)
-#710 := (= #412 #709)
-#439 := (= #326 -3::int)
-#332 := [rewrite]: #439
-#432 := [monotonicity #332]: #710
-#711 := [monotonicity #432]: #707
-#422 := [monotonicity #711]: #712
-#436 := (iff #728 #727)
-#366 := (or #380 #723)
-#713 := (iff #366 #727)
-#714 := [rewrite]: #713
-#726 := (iff #728 #366)
-#725 := (iff #732 #723)
-#722 := (iff #397 #418)
-#718 := (or #418 false)
-#721 := (iff #718 #418)
-#716 := [rewrite]: #721
-#719 := (iff #397 #718)
-#389 := (iff #414 false)
-#394 := [rewrite]: #389
-#720 := [monotonicity #394]: #719
-#360 := [trans #720 #716]: #722
-#365 := [monotonicity #360]: #725
-#381 := (iff #521 #380)
-#378 := (iff #391 #734)
-#730 := (or false #734)
-#374 := (iff #730 #734)
-#715 := [rewrite]: #374
-#390 := (iff #391 #730)
-#731 := [monotonicity #394]: #390
-#379 := [trans #731 #715]: #378
-#717 := [monotonicity #379]: #381
-#724 := [monotonicity #717 #365]: #726
-#437 := [trans #724 #714]: #436
-#425 := [monotonicity #437 #422]: #424
-#419 := [monotonicity #425]: #704
-#739 := (iff #738 false)
-#729 := [rewrite]: #739
-#702 := [monotonicity #729 #419]: #705
-#697 := [trans #702 #695]: #696
-#700 := [monotonicity #697]: #694
-#543 := [trans #700 #542]: #694
-#699 := [quant-inst]: #698
-#685 := [mp #699 #543]: #693
-#616 := [unit-resolution #685 #753]: #703
-#670 := (not #735)
-#669 := (not #703)
-#611 := (or #669 #670)
-#576 := (not #403)
-#686 := (<= #40 0::int)
-#618 := (not #686)
-#648 := (or #618 #172)
-#649 := [th-lemma]: #648
-#605 := [unit-resolution #649 #183]: #618
-#606 := (or #576 #686)
-#607 := [th-lemma]: #606
-#610 := [unit-resolution #607 #605]: #576
-#673 := (or #669 #670 #403)
-#558 := [def-axiom]: #673
-#612 := [unit-resolution #558 #610]: #611
-#613 := [unit-resolution #612 #616]: #670
-#573 := (or #669 #735 #423)
-#575 := [def-axiom]: #573
-#608 := [unit-resolution #575 #613 #616]: #423
-#677 := (not #423)
-#679 := (or #677 #690 #417)
-#680 := [def-axiom]: #679
-#587 := [unit-resolution #680 #608]: #614
-#588 := [unit-resolution #587 #615]: #690
-#688 := (or #727 #418)
-#682 := [def-axiom]: #688
-#589 := [unit-resolution #682 #588]: #418
-#683 := (or #727 #734)
-#689 := [def-axiom]: #683
-#482 := [unit-resolution #689 #588]: #734
-#593 := (or #735 #723 #380)
-#594 := [th-lemma]: #593
-#595 := [unit-resolution #594 #613]: #727
-[unit-resolution #595 #482 #589]: false
-unsat
-ce21500c8b03b5e1a394643a4c361d6ebb12e85f 86 0
+30ec056750b76c9c44be73825eb8959f04eaf2af 86 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -44405,7 +44959,7 @@
 #105 := [trans #104 #83]: #51
 [unit-resolution #57 #105]: false
 unsat
-22be385fa1e47d4d76e059f3bfa8188c80f22cdd 68 0
+87cffe59a43ecd3ffcda40df06578c44d2a9feac 68 0
 #2 := false
 #8 := 0::int
 decl f3 :: int
@@ -44474,7 +45028,7 @@
 #88 := [trans #87 #84]: #13
 [unit-resolution #71 #88]: false
 unsat
-2253342327dba5f019f3a86fda5fc5ff24024127 124 0
+90c0dd925b0006ab13047c20a6f0e8d277ec4cdf 124 0
 #2 := false
 #13 := 0::int
 decl f4 :: int
@@ -44599,7 +45153,7 @@
 #145 := [unit-resolution #117 #144]: #106
 [th-lemma #131 #143 #141 #85 #145]: false
 unsat
-8a7449660323be981d8338388af366ba304fb872 57 0
+de67b37b9c3eba477099ff5d9b09e840de376762 57 0
 #2 := false
 #36 := 0::int
 decl f4 :: int
@@ -44657,353 +45211,7 @@
 #77 := [unit-resolution #76 #73]: #70
 [th-lemma #77 #56 #72]: false
 unsat
-1c20abf656adf6300dff05d39209b84754f973b9 345 0
-#2 := false
-#39 := 3::int
-decl f4 :: (-> int int int)
-decl f5 :: int
-#38 := f5
-#40 := (f4 f5 3::int)
-#441 := (mod #40 3::int)
-#657 := (>= #441 3::int)
-#658 := (not #657)
-#1 := true
-#59 := [true-axiom]: true
-#647 := (or false #658)
-#642 := [th-lemma]: #647
-#648 := [unit-resolution #642 #59]: #658
-#11 := 0::int
-#68 := -1::int
-#436 := (* -1::int #40)
-#600 := (+ f5 #436)
-#601 := (<= #600 0::int)
-#172 := (= f5 #40)
-#188 := (>= f5 3::int)
-#187 := (not #188)
-#178 := (not #172)
-#194 := (or #178 #187)
-#199 := (not #194)
-#42 := (< f5 3::int)
-#41 := (= #40 f5)
-#43 := (implies #41 #42)
-#44 := (not #43)
-#202 := (iff #44 #199)
-#179 := (or #42 #178)
-#184 := (not #179)
-#200 := (iff #184 #199)
-#197 := (iff #179 #194)
-#191 := (or #187 #178)
-#195 := (iff #191 #194)
-#196 := [rewrite]: #195
-#192 := (iff #179 #191)
-#189 := (iff #42 #187)
-#190 := [rewrite]: #189
-#193 := [monotonicity #190]: #192
-#198 := [trans #193 #196]: #197
-#201 := [monotonicity #198]: #200
-#185 := (iff #44 #184)
-#182 := (iff #43 #179)
-#175 := (implies #172 #42)
-#180 := (iff #175 #179)
-#181 := [rewrite]: #180
-#176 := (iff #43 #175)
-#173 := (iff #41 #172)
-#174 := [rewrite]: #173
-#177 := [monotonicity #174]: #176
-#183 := [trans #177 #181]: #182
-#186 := [monotonicity #183]: #185
-#203 := [trans #186 #201]: #202
-#171 := [asserted]: #44
-#204 := [mp #171 #203]: #199
-#205 := [not-or-elim #204]: #172
-#634 := (or #178 #601)
-#630 := [th-lemma]: #634
-#631 := [unit-resolution #630 #205]: #601
-#206 := [not-or-elim #204]: #188
-#438 := (f4 #40 3::int)
-#602 := (* -1::int #438)
-#603 := (+ #40 #602)
-#604 := (<= #603 0::int)
-#763 := (= #40 #438)
-#635 := (= #438 #40)
-#632 := [symm #205]: #41
-#636 := [monotonicity #632]: #635
-#637 := [symm #636]: #763
-#638 := (not #763)
-#633 := (or #638 #604)
-#639 := [th-lemma]: #633
-#612 := [unit-resolution #639 #637]: #604
-#369 := (* -1::int #441)
-#442 := (+ #438 #369)
-#707 := (<= #442 0::int)
-#439 := (= #442 0::int)
-#738 := -3::int
-#462 := (mod #436 -3::int)
-#357 := (+ #438 #462)
-#457 := (= #357 0::int)
-#422 := (<= #40 0::int)
-#750 := (not #422)
-#416 := (>= #40 0::int)
-#406 := (not #416)
-#751 := (or #406 #750)
-#736 := (ite #751 #439 #457)
-#760 := (= #438 0::int)
-#761 := (= #40 0::int)
-#447 := (ite #761 #760 #736)
-#9 := (:var 0 int)
-#8 := (:var 1 int)
-#29 := (f4 #8 #9)
-#772 := (pattern #29)
-#72 := (* -1::int #9)
-#69 := (* -1::int #8)
-#127 := (mod #69 #72)
-#283 := (+ #29 #127)
-#284 := (= #283 0::int)
-#30 := (mod #8 #9)
-#280 := (* -1::int #30)
-#281 := (+ #29 #280)
-#282 := (= #281 0::int)
-#94 := (<= #9 0::int)
-#90 := (<= #8 0::int)
-#224 := (or #90 #94)
-#225 := (not #224)
-#101 := (>= #8 0::int)
-#216 := (or #94 #101)
-#217 := (not #216)
-#229 := (or #217 #225)
-#285 := (ite #229 #282 #284)
-#279 := (= #29 0::int)
-#12 := (= #8 0::int)
-#286 := (ite #12 #279 #285)
-#278 := (= #8 #29)
-#13 := (= #9 0::int)
-#287 := (ite #13 #278 #286)
-#773 := (forall (vars (?v0 int) (?v1 int)) (:pat #772) #287)
-#290 := (forall (vars (?v0 int) (?v1 int)) #287)
-#776 := (iff #290 #773)
-#774 := (iff #287 #287)
-#775 := [refl]: #774
-#777 := [quant-intro #775]: #776
-#133 := (* -1::int #127)
-#247 := (ite #229 #30 #133)
-#250 := (ite #12 0::int #247)
-#253 := (ite #13 #8 #250)
-#256 := (= #29 #253)
-#259 := (forall (vars (?v0 int) (?v1 int)) #256)
-#291 := (iff #259 #290)
-#288 := (iff #256 #287)
-#289 := [rewrite]: #288
-#292 := [quant-intro #289]: #291
-#102 := (not #101)
-#95 := (not #94)
-#105 := (and #95 #102)
-#91 := (not #90)
-#98 := (and #91 #95)
-#108 := (or #98 #105)
-#153 := (ite #108 #30 #133)
-#156 := (ite #12 0::int #153)
-#159 := (ite #13 #8 #156)
-#162 := (= #29 #159)
-#165 := (forall (vars (?v0 int) (?v1 int)) #162)
-#260 := (iff #165 #259)
-#257 := (iff #162 #256)
-#254 := (= #159 #253)
-#251 := (= #156 #250)
-#248 := (= #153 #247)
-#232 := (iff #108 #229)
-#226 := (or #225 #217)
-#230 := (iff #226 #229)
-#231 := [rewrite]: #230
-#227 := (iff #108 #226)
-#214 := (iff #105 #217)
-#215 := [rewrite]: #214
-#212 := (iff #98 #225)
-#213 := [rewrite]: #212
-#228 := [monotonicity #213 #215]: #227
-#233 := [trans #228 #231]: #232
-#249 := [monotonicity #233]: #248
-#252 := [monotonicity #249]: #251
-#255 := [monotonicity #252]: #254
-#258 := [monotonicity #255]: #257
-#261 := [quant-intro #258]: #260
-#210 := (~ #165 #165)
-#207 := (~ #162 #162)
-#222 := [refl]: #207
-#211 := [nnf-pos #222]: #210
-#23 := (- #9)
-#22 := (- #8)
-#31 := (mod #22 #23)
-#32 := (- #31)
-#16 := (< 0::int #9)
-#18 := (< #8 0::int)
-#19 := (and #18 #16)
-#15 := (< 0::int #8)
-#17 := (and #15 #16)
-#20 := (or #17 #19)
-#33 := (ite #20 #30 #32)
-#34 := (ite #12 0::int #33)
-#35 := (ite #13 #8 #34)
-#36 := (= #29 #35)
-#37 := (forall (vars (?v0 int) (?v1 int)) #36)
-#168 := (iff #37 #165)
-#62 := (and #16 #18)
-#65 := (or #17 #62)
-#138 := (ite #65 #30 #133)
-#141 := (ite #12 0::int #138)
-#144 := (ite #13 #8 #141)
-#147 := (= #29 #144)
-#150 := (forall (vars (?v0 int) (?v1 int)) #147)
-#166 := (iff #150 #165)
-#163 := (iff #147 #162)
-#160 := (= #144 #159)
-#157 := (= #141 #156)
-#154 := (= #138 #153)
-#109 := (iff #65 #108)
-#106 := (iff #62 #105)
-#103 := (iff #18 #102)
-#104 := [rewrite]: #103
-#96 := (iff #16 #95)
-#97 := [rewrite]: #96
-#107 := [monotonicity #97 #104]: #106
-#99 := (iff #17 #98)
-#92 := (iff #15 #91)
-#93 := [rewrite]: #92
-#100 := [monotonicity #93 #97]: #99
-#110 := [monotonicity #100 #107]: #109
-#155 := [monotonicity #110]: #154
-#158 := [monotonicity #155]: #157
-#161 := [monotonicity #158]: #160
-#164 := [monotonicity #161]: #163
-#167 := [quant-intro #164]: #166
-#151 := (iff #37 #150)
-#148 := (iff #36 #147)
-#145 := (= #35 #144)
-#142 := (= #34 #141)
-#139 := (= #33 #138)
-#136 := (= #32 #133)
-#130 := (- #127)
-#134 := (= #130 #133)
-#135 := [rewrite]: #134
-#131 := (= #32 #130)
-#128 := (= #31 #127)
-#73 := (= #23 #72)
-#74 := [rewrite]: #73
-#70 := (= #22 #69)
-#71 := [rewrite]: #70
-#129 := [monotonicity #71 #74]: #128
-#132 := [monotonicity #129]: #131
-#137 := [trans #132 #135]: #136
-#66 := (iff #20 #65)
-#63 := (iff #19 #62)
-#64 := [rewrite]: #63
-#67 := [monotonicity #64]: #66
-#140 := [monotonicity #67 #137]: #139
-#143 := [monotonicity #140]: #142
-#146 := [monotonicity #143]: #145
-#149 := [monotonicity #146]: #148
-#152 := [quant-intro #149]: #151
-#169 := [trans #152 #167]: #168
-#126 := [asserted]: #37
-#170 := [mp #126 #169]: #165
-#223 := [mp~ #170 #211]: #165
-#262 := [mp #223 #261]: #259
-#293 := [mp #262 #292]: #290
-#778 := [mp #293 #777]: #773
-#731 := (not #773)
-#720 := (or #731 #447)
-#351 := (* -1::int 3::int)
-#437 := (mod #436 #351)
-#429 := (+ #438 #437)
-#440 := (= #429 0::int)
-#443 := (<= 3::int 0::int)
-#757 := (or #422 #443)
-#759 := (not #757)
-#546 := (or #443 #416)
-#753 := (not #546)
-#427 := (or #753 #759)
-#428 := (ite #427 #439 #440)
-#762 := (ite #761 #760 #428)
-#758 := (= 3::int 0::int)
-#764 := (ite #758 #763 #762)
-#721 := (or #731 #764)
-#717 := (iff #721 #720)
-#723 := (iff #720 #720)
-#724 := [rewrite]: #723
-#730 := (iff #764 #447)
-#450 := (ite false #763 #447)
-#444 := (iff #450 #447)
-#726 := [rewrite]: #444
-#728 := (iff #764 #450)
-#448 := (iff #762 #447)
-#733 := (iff #428 #736)
-#458 := (iff #440 #457)
-#734 := (= #429 #357)
-#463 := (= #437 #462)
-#739 := (= #351 -3::int)
-#461 := [rewrite]: #739
-#464 := [monotonicity #461]: #463
-#735 := [monotonicity #464]: #734
-#732 := [monotonicity #735]: #458
-#749 := (iff #427 #751)
-#390 := (iff #759 #750)
-#385 := (iff #757 #422)
-#744 := (or #422 false)
-#741 := (iff #744 #422)
-#747 := [rewrite]: #741
-#745 := (iff #757 #744)
-#419 := (iff #443 false)
-#755 := [rewrite]: #419
-#746 := [monotonicity #755]: #745
-#748 := [trans #746 #747]: #385
-#391 := [monotonicity #748]: #390
-#742 := (iff #753 #406)
-#404 := (iff #546 #416)
-#415 := (or false #416)
-#740 := (iff #415 #416)
-#403 := [rewrite]: #740
-#756 := (iff #546 #415)
-#399 := [monotonicity #755]: #756
-#405 := [trans #399 #403]: #404
-#743 := [monotonicity #405]: #742
-#752 := [monotonicity #743 #391]: #749
-#737 := [monotonicity #752 #732]: #733
-#449 := [monotonicity #737]: #448
-#754 := (iff #758 false)
-#414 := [rewrite]: #754
-#729 := [monotonicity #414 #449]: #728
-#727 := [trans #729 #726]: #730
-#718 := [monotonicity #727]: #717
-#719 := [trans #718 #724]: #717
-#722 := [quant-inst]: #721
-#725 := [mp #722 #719]: #720
-#613 := [unit-resolution #725 #778]: #447
-#589 := (not #761)
-#614 := (not #601)
-#507 := (or #750 #187 #614)
-#618 := [th-lemma]: #507
-#619 := [unit-resolution #618 #206 #631]: #750
-#620 := (or #589 #422)
-#625 := [th-lemma]: #620
-#621 := [unit-resolution #625 #619]: #589
-#588 := (not #447)
-#697 := (or #588 #761 #736)
-#599 := [def-axiom]: #697
-#622 := [unit-resolution #599 #621 #613]: #736
-#568 := (or #751 #422)
-#710 := [def-axiom]: #568
-#623 := [unit-resolution #710 #619]: #751
-#711 := (not #751)
-#709 := (not #736)
-#716 := (or #709 #711 #439)
-#545 := [def-axiom]: #716
-#626 := [unit-resolution #545 #623 #622]: #439
-#701 := (not #439)
-#627 := (or #701 #707)
-#628 := [th-lemma]: #627
-#624 := [unit-resolution #628 #626]: #707
-[th-lemma #624 #612 #206 #631 #648]: false
-unsat
-4dce9532aca5ad04bb32a324214a8d6e10933595 57 0
+8f0b2c755e25c9b0ef5750035ec56d21d3c6b32f 57 0
 #2 := false
 #35 := 0::int
 decl f4 :: int
@@ -45061,7 +45269,7 @@
 #77 := [th-lemma]: #76
 [unit-resolution #77 #74 #56]: false
 unsat
-4c651ded3b3a1d80978c76e6d7d096efa4221c9f 103 0
+ba050e782d9473f46d4f759400e69d34d257264e 103 0
 #2 := false
 #45 := 0::int
 decl f3 :: int
@@ -45165,7 +45373,7 @@
 #122 := [unit-resolution #121 #118]: #116
 [th-lemma #122 #91 #93]: false
 unsat
-4dcddda0c75e28e85f0009ab3200f08d892d02c4 88 0
+9c2cfdc304fee997e8f612dd9123abd86a877f29 88 0
 #2 := false
 decl f4 :: int
 #9 := f4
@@ -45254,7 +45462,7 @@
 #109 := [trans #108 #83]: #51
 [unit-resolution #57 #109]: false
 unsat
-600697e3c100a020914718001e57a63394741230 66 0
+66ca5933e35ee3faa0336268f65c331335330f57 66 0
 #2 := false
 decl f3 :: int
 #9 := f3
@@ -45321,7 +45529,7 @@
 #86 := [trans #83 #85]: #33
 [unit-resolution #69 #86]: false
 unsat
-45b4f832b01805ab14c570832adc97242b473045 228 0
+a176c257f1c89ffea971e08639242e005fb1222f 228 0
 #2 := false
 #9 := 0::int
 decl f4 :: int
@@ -45550,7 +45758,7 @@
 #250 := [unit-resolution #196 #249]: #190
 [th-lemma #236 #250 #131 #234 #248 #238]: false
 unsat
-49cc983d173a58df0ca800b897e7609030c1adbd 56 0
+efdfb7635dd41e99f117d8463d9d75f3897207dd 56 0
 #2 := false
 #11 := 1::int
 decl f3 :: int
@@ -45607,7 +45815,7 @@
 #71 := [not-or-elim #69]: #70
 [unit-resolution #71 #85]: false
 unsat
-838b399a3a6da31b0c058aef87c3e393bc9c198f 18 0
+6a196ac012aba8c7b41b1d8437b14fc3fb23e5a4 18 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -45626,25 +45834,7 @@
 #27 := [asserted]: #10
 [mp #27 #38]: false
 unsat
-f401bbb35719168186be7c7fdc36b726ddad542e 17 0
-#2 := false
-#8 := 0::real
-#9 := (= 0::real 0::real)
-#10 := (not #9)
-#35 := (iff #10 false)
-#1 := true
-#30 := (not true)
-#33 := (iff #30 false)
-#34 := [rewrite]: #33
-#31 := (iff #10 #30)
-#28 := (iff #9 true)
-#29 := [rewrite]: #28
-#32 := [monotonicity #29]: #31
-#36 := [trans #32 #34]: #35
-#27 := [asserted]: #10
-[mp #27 #36]: false
-unsat
-acd9efc2e486913895049a85d947303a715afaf4 51 0
+4afe860c901fd901bf34dc83b799fd986f9e4155 51 0
 #2 := false
 decl f4 :: int
 #9 := f4
@@ -45696,7 +45886,7 @@
 #33 := [asserted]: #16
 [mp #33 #68]: false
 unsat
-876d4808395b1353460558d27a1ff7e23ea1a045 56 0
+5551b99ea77d386f007b1b1979a0b6b379c3a347 56 0
 #2 := false
 decl f4 :: int
 #9 := f4
@@ -45753,51 +45943,7 @@
 #33 := [asserted]: #16
 [mp #33 #73]: false
 unsat
-2c7d006b46aef7c76688a4b4a4964ad07b6656a1 25 0
-#2 := false
-#8 := 0::real
-#9 := (- 0::real)
-#10 := (= 0::real #9)
-#11 := (not #10)
-#43 := (iff #11 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #11 #38)
-#36 := (iff #10 true)
-#31 := (= 0::real 0::real)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #10 #31)
-#29 := (= #9 0::real)
-#30 := [rewrite]: #29
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#28 := [asserted]: #11
-[mp #28 #44]: false
-unsat
-70737154521415199c9b18902d90c0ff2d6966da 17 0
-#2 := false
-#8 := 1::real
-#9 := (= 1::real 1::real)
-#10 := (not #9)
-#35 := (iff #10 false)
-#1 := true
-#30 := (not true)
-#33 := (iff #30 false)
-#34 := [rewrite]: #33
-#31 := (iff #10 #30)
-#28 := (iff #9 true)
-#29 := [rewrite]: #28
-#32 := [monotonicity #29]: #31
-#36 := [trans #32 #34]: #35
-#27 := [asserted]: #10
-[mp #27 #36]: false
-unsat
-e1c4625af215a329500d17ad89e6dc8f577b02b1 52 0
+76fdd03dce324fb45070b1e1983f0a282cda6fa6 52 0
 #2 := false
 #40 := 0::int
 decl f4 :: int
@@ -45850,42 +45996,7 @@
 #77 := [unit-resolution #76 #65]: #53
 [unit-resolution #77 #67]: false
 unsat
-079e8a190b645549c5a2d16ab104adb956315901 34 0
-#2 := false
-#8 := 1::real
-#9 := (- 1::real)
-#10 := (= #9 1::real)
-#11 := (not #10)
-#12 := (not #11)
-#52 := (iff #12 false)
-#1 := true
-#47 := (not true)
-#50 := (iff #47 false)
-#51 := [rewrite]: #50
-#48 := (iff #12 #47)
-#45 := (iff #11 true)
-#40 := (not false)
-#43 := (iff #40 true)
-#44 := [rewrite]: #43
-#41 := (iff #11 #40)
-#38 := (iff #10 false)
-#30 := -1::real
-#33 := (= -1::real 1::real)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #10 #33)
-#31 := (= #9 -1::real)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#29 := [asserted]: #12
-[mp #29 #53]: false
-unsat
-2eb8b7f54e63226cb1a9ab4c59e18e9b90fe4ed0 73 0
+550f7d68b0836924510ab12e5b3c4ed9f6c794bb 73 0
 #2 := false
 #58 := 0::int
 decl f4 :: int
@@ -45959,26 +46070,7 @@
 #78 := [unit-resolution #82 #74]: #83
 [unit-resolution #78 #92 #89]: false
 unsat
-a2184c17e30d6d1fdfb1b99141d590277924af4f 18 0
-#2 := false
-#9 := 1::real
-#8 := 0::real
-#10 := (< 0::real 1::real)
-#11 := (not #10)
-#38 := (iff #11 false)
-#1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #11 #33)
-#31 := (iff #10 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#28 := [asserted]: #11
-[mp #28 #39]: false
-unsat
-56d5fed825ed136d8c662448f5f823a6b191adf2 15 0
+65c77124096528f9cb7c1cb6b89625b62f5eeb2a 15 0
 #2 := false
 decl f3 :: int
 #8 := f3
@@ -45994,26 +46086,7 @@
 #28 := [asserted]: #11
 [mp #28 #34]: false
 unsat
-ed3ca239863adeeb7925561fb018b520b18a23a9 18 0
-#2 := false
-#9 := 1::real
-#8 := 0::real
-#10 := (<= 0::real 1::real)
-#11 := (not #10)
-#38 := (iff #11 false)
-#1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #11 #33)
-#31 := (iff #10 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#28 := [asserted]: #11
-[mp #28 #39]: false
-unsat
-1969eccfcb8fcfbee552d3423834a8c5c81b7a3e 75 0
+8aa9d7db6e905a29f4a4232a6a82f51c63e2641b 75 0
 #2 := false
 #53 := 0::int
 decl f4 :: int
@@ -46089,67 +46162,7 @@
 #89 := [not-or-elim #88]: #54
 [th-lemma #89 #91 #92]: false
 unsat
-88a6a03ef194abfd27e9e9c71cd5d14dc85a3e0c 40 0
-#2 := false
-#12 := 567::real
-#10 := 345::real
-#8 := 123::real
-#9 := (- 123::real)
-#11 := (+ #9 345::real)
-#13 := (< #11 567::real)
-#14 := (not #13)
-#58 := (iff #14 false)
-#38 := 222::real
-#43 := (< 222::real 567::real)
-#46 := (not #43)
-#56 := (iff #46 false)
-#1 := true
-#51 := (not true)
-#54 := (iff #51 false)
-#55 := [rewrite]: #54
-#52 := (iff #46 #51)
-#49 := (iff #43 true)
-#50 := [rewrite]: #49
-#53 := [monotonicity #50]: #52
-#57 := [trans #53 #55]: #56
-#47 := (iff #14 #46)
-#44 := (iff #13 #43)
-#41 := (= #11 222::real)
-#32 := -123::real
-#35 := (+ -123::real 345::real)
-#39 := (= #35 222::real)
-#40 := [rewrite]: #39
-#36 := (= #11 #35)
-#33 := (= #9 -123::real)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#42 := [trans #37 #40]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#59 := [trans #48 #57]: #58
-#31 := [asserted]: #14
-[mp #31 #59]: false
-unsat
-15b2b70e02e33b3fd62ad125d3d090b78e843ef0 18 0
-#2 := false
-#9 := 2345678901::real
-#8 := 123456789::real
-#10 := (< 123456789::real 2345678901::real)
-#11 := (not #10)
-#38 := (iff #11 false)
-#1 := true
-#33 := (not true)
-#36 := (iff #33 false)
-#37 := [rewrite]: #36
-#34 := (iff #11 #33)
-#31 := (iff #10 true)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#28 := [asserted]: #11
-[mp #28 #39]: false
-unsat
-1f807fc1d963d1157d011baf2bc15be87a543e47 80 0
+625ca444862ba21a1fa0a52470751952d4f5acee 80 0
 #2 := false
 #53 := 0::int
 decl f4 :: int
@@ -46230,38 +46243,7 @@
 #94 := [not-or-elim #93]: #54
 [th-lemma #94 #96 #97]: false
 unsat
-99d44ac5b1eabf28408c90ba22548007cb115846 30 0
-#2 := false
-#10 := 2345678901::real
-#8 := 123456789::real
-#9 := (- 123456789::real)
-#11 := (< #9 2345678901::real)
-#12 := (not #11)
-#48 := (iff #12 false)
-#30 := -123456789::real
-#33 := (< -123456789::real 2345678901::real)
-#36 := (not #33)
-#46 := (iff #36 false)
-#1 := true
-#41 := (not true)
-#44 := (iff #41 false)
-#45 := [rewrite]: #44
-#42 := (iff #36 #41)
-#39 := (iff #33 true)
-#40 := [rewrite]: #39
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#37 := (iff #12 #36)
-#34 := (iff #11 #33)
-#31 := (= #9 -123456789::real)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#38 := [monotonicity #35]: #37
-#49 := [trans #38 #47]: #48
-#29 := [asserted]: #12
-[mp #29 #49]: false
-unsat
-285e04b09127df030f3fb9fc56707e4ac5536d20 80 0
+59582f385e59c3a49a302bb1b9701c92bb368fac 80 0
 #2 := false
 #52 := 0::int
 decl f4 :: int
@@ -46342,61 +46324,7 @@
 #96 := [not-or-elim #93]: #95
 [th-lemma #96 #94 #97]: false
 unsat
-1e2efa99a6b6da8267e97fbabfbfc4ad6d75e298 26 0
-#2 := false
-decl f3 :: real
-#8 := f3
-#9 := 0::real
-#10 := (+ f3 0::real)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-db8ff96061c803374c98cc69bff61f209e6704b2 26 0
-#2 := false
-decl f3 :: real
-#9 := f3
-#8 := 0::real
-#10 := (+ 0::real f3)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-ef932f399da076ed00e03e4da73316a7d197a3fc 85 0
+6dfe89c45e68ba796109229b1c54d23603c64ded 85 0
 #2 := false
 #52 := 0::int
 decl f4 :: int
@@ -46482,37 +46410,7 @@
 #101 := [not-or-elim #99]: #66
 [th-lemma #101 #100 #102]: false
 unsat
-0e8698b45bf05888a03321a1f80727dbab79ce92 29 0
-#2 := false
-decl f3 :: real
-#8 := f3
-decl f4 :: real
-#9 := f4
-#11 := (+ f4 f3)
-#10 := (+ f3 f4)
-#12 := (= #10 #11)
-#13 := (not #12)
-#45 := (iff #13 false)
-#1 := true
-#40 := (not true)
-#43 := (iff #40 false)
-#44 := [rewrite]: #43
-#41 := (iff #13 #40)
-#38 := (iff #12 true)
-#33 := (= #10 #10)
-#36 := (iff #33 true)
-#37 := [rewrite]: #36
-#34 := (iff #12 #33)
-#31 := (= #11 #10)
-#32 := [rewrite]: #31
-#35 := [monotonicity #32]: #34
-#39 := [trans #35 #37]: #38
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#30 := [asserted]: #13
-[mp #30 #46]: false
-unsat
-fa0e4c03539b13ece5f7ecd99f1cc759989c1bcf 69 0
+650b9ceb8c2cf801e6ceee5375af886f013abe2c 69 0
 #2 := false
 #44 := 0::int
 decl f5 :: int
@@ -46582,7 +46480,317 @@
 #85 := [and-elim #83]: #53
 [th-lemma #85 #84 #86]: false
 unsat
-38433e3faa18ccf7e7f7256e4aa4dd42dcf43860 33 0
+0eeabd2aea1625cea2b9a9ade1eee621e6dfb534 17 0
+#2 := false
+#8 := 0::real
+#9 := (= 0::real 0::real)
+#10 := (not #9)
+#35 := (iff #10 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #10 #30)
+#28 := (iff #9 true)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#27 := [asserted]: #10
+[mp #27 #36]: false
+unsat
+582ef11d89a67dd029d6b29272ca6688d8312bd7 25 0
+#2 := false
+#8 := 0::real
+#9 := (- 0::real)
+#10 := (= 0::real #9)
+#11 := (not #10)
+#43 := (iff #11 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #11 #38)
+#36 := (iff #10 true)
+#31 := (= 0::real 0::real)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #10 #31)
+#29 := (= #9 0::real)
+#30 := [rewrite]: #29
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#28 := [asserted]: #11
+[mp #28 #44]: false
+unsat
+4de73c1caf8d03027271f9dfec62b23debf65d9b 17 0
+#2 := false
+#8 := 1::real
+#9 := (= 1::real 1::real)
+#10 := (not #9)
+#35 := (iff #10 false)
+#1 := true
+#30 := (not true)
+#33 := (iff #30 false)
+#34 := [rewrite]: #33
+#31 := (iff #10 #30)
+#28 := (iff #9 true)
+#29 := [rewrite]: #28
+#32 := [monotonicity #29]: #31
+#36 := [trans #32 #34]: #35
+#27 := [asserted]: #10
+[mp #27 #36]: false
+unsat
+793c5962cbb9973917b8d8c66a2d2a3d94594803 34 0
+#2 := false
+#8 := 1::real
+#9 := (- 1::real)
+#10 := (= #9 1::real)
+#11 := (not #10)
+#12 := (not #11)
+#52 := (iff #12 false)
+#1 := true
+#47 := (not true)
+#50 := (iff #47 false)
+#51 := [rewrite]: #50
+#48 := (iff #12 #47)
+#45 := (iff #11 true)
+#40 := (not false)
+#43 := (iff #40 true)
+#44 := [rewrite]: #43
+#41 := (iff #11 #40)
+#38 := (iff #10 false)
+#30 := -1::real
+#33 := (= -1::real 1::real)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #10 #33)
+#31 := (= #9 -1::real)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#49 := [monotonicity #46]: #48
+#53 := [trans #49 #51]: #52
+#29 := [asserted]: #12
+[mp #29 #53]: false
+unsat
+8f6bb26e23c49df219a9fc6920a8bbad56872cba 18 0
+#2 := false
+#9 := 1::real
+#8 := 0::real
+#10 := (< 0::real 1::real)
+#11 := (not #10)
+#38 := (iff #11 false)
+#1 := true
+#33 := (not true)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (iff #10 true)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#28 := [asserted]: #11
+[mp #28 #39]: false
+unsat
+6edbad6a7b2935c8d856f03c54b56bf43891a380 18 0
+#2 := false
+#9 := 1::real
+#8 := 0::real
+#10 := (<= 0::real 1::real)
+#11 := (not #10)
+#38 := (iff #11 false)
+#1 := true
+#33 := (not true)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (iff #10 true)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#28 := [asserted]: #11
+[mp #28 #39]: false
+unsat
+a64bea89744a3af0ed560a5c871536de3fcb2ecf 40 0
+#2 := false
+#12 := 567::real
+#10 := 345::real
+#8 := 123::real
+#9 := (- 123::real)
+#11 := (+ #9 345::real)
+#13 := (< #11 567::real)
+#14 := (not #13)
+#58 := (iff #14 false)
+#38 := 222::real
+#43 := (< 222::real 567::real)
+#46 := (not #43)
+#56 := (iff #46 false)
+#1 := true
+#51 := (not true)
+#54 := (iff #51 false)
+#55 := [rewrite]: #54
+#52 := (iff #46 #51)
+#49 := (iff #43 true)
+#50 := [rewrite]: #49
+#53 := [monotonicity #50]: #52
+#57 := [trans #53 #55]: #56
+#47 := (iff #14 #46)
+#44 := (iff #13 #43)
+#41 := (= #11 222::real)
+#32 := -123::real
+#35 := (+ -123::real 345::real)
+#39 := (= #35 222::real)
+#40 := [rewrite]: #39
+#36 := (= #11 #35)
+#33 := (= #9 -123::real)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#42 := [trans #37 #40]: #41
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#59 := [trans #48 #57]: #58
+#31 := [asserted]: #14
+[mp #31 #59]: false
+unsat
+a79ee55daec933b360adb88ed0db37156e2f7821 18 0
+#2 := false
+#9 := 2345678901::real
+#8 := 123456789::real
+#10 := (< 123456789::real 2345678901::real)
+#11 := (not #10)
+#38 := (iff #11 false)
+#1 := true
+#33 := (not true)
+#36 := (iff #33 false)
+#37 := [rewrite]: #36
+#34 := (iff #11 #33)
+#31 := (iff #10 true)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#28 := [asserted]: #11
+[mp #28 #39]: false
+unsat
+4b51b4eed1dc4e4e6099fbf906b70822230d5e3f 30 0
+#2 := false
+#10 := 2345678901::real
+#8 := 123456789::real
+#9 := (- 123456789::real)
+#11 := (< #9 2345678901::real)
+#12 := (not #11)
+#48 := (iff #12 false)
+#30 := -123456789::real
+#33 := (< -123456789::real 2345678901::real)
+#36 := (not #33)
+#46 := (iff #36 false)
+#1 := true
+#41 := (not true)
+#44 := (iff #41 false)
+#45 := [rewrite]: #44
+#42 := (iff #36 #41)
+#39 := (iff #33 true)
+#40 := [rewrite]: #39
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#37 := (iff #12 #36)
+#34 := (iff #11 #33)
+#31 := (= #9 -123456789::real)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#38 := [monotonicity #35]: #37
+#49 := [trans #38 #47]: #48
+#29 := [asserted]: #12
+[mp #29 #49]: false
+unsat
+209cf5d4457acae6abf17187fd6e89c259187362 26 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := 0::real
+#10 := (+ f3 0::real)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+97dafa0bba507529233c05cc33dd1519b4e28e4b 26 0
+#2 := false
+decl f3 :: real
+#9 := f3
+#8 := 0::real
+#10 := (+ 0::real f3)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+393f5dbb0db04527f22218d40363df111099baf5 29 0
+#2 := false
+decl f3 :: real
+#8 := f3
+decl f4 :: real
+#9 := f4
+#11 := (+ f4 f3)
+#10 := (+ f3 f4)
+#12 := (= #10 #11)
+#13 := (not #12)
+#45 := (iff #13 false)
+#1 := true
+#40 := (not true)
+#43 := (iff #40 false)
+#44 := [rewrite]: #43
+#41 := (iff #13 #40)
+#38 := (iff #12 true)
+#33 := (= #10 #10)
+#36 := (iff #33 true)
+#37 := [rewrite]: #36
+#34 := (iff #12 #33)
+#31 := (= #11 #10)
+#32 := [rewrite]: #31
+#35 := [monotonicity #32]: #34
+#39 := [trans #35 #37]: #38
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#30 := [asserted]: #13
+[mp #30 #46]: false
+unsat
+08018537eda07e4214b99470b7aa75706e7cd28c 33 0
 #2 := false
 decl f5 :: real
 #10 := f5
@@ -46616,7 +46824,7 @@
 #33 := [asserted]: #16
 [mp #33 #49]: false
 unsat
-1fdb35a1399271a8f0f610e1f353642ad440e0a5 45 0
+afbfb539cd215cee99e6f9076de9621f41db722f 45 0
 #2 := false
 decl f4 :: real
 #9 := f4
@@ -46662,7 +46870,7 @@
 #33 := [asserted]: #16
 [mp #33 #63]: false
 unsat
-1dd629fda226d261e70599846e7cb0aed5bce0e4 58 0
+4a497c9573e0d4cf02c29e65ea385ac694a5d2a9 58 0
 #2 := false
 decl f3 :: real
 #8 := f3
@@ -46721,34 +46929,7 @@
 #31 := [asserted]: #14
 [mp #31 #77]: false
 unsat
-f05f2d2d486f345aec8eda31ab857db74ae27876 26 0
-#2 := false
-decl f3 :: real
-#8 := f3
-#9 := 0::real
-#10 := (- f3 0::real)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-56d5d1ebf2a3e86b0eef89fb438ab0199a14cb1f 61 0
+5310d952762e8bd0d9db1c0127d9100532f42cf4 61 0
 #2 := false
 #8 := 0::real
 decl f3 :: real
@@ -46810,7 +46991,96 @@
 #31 := [asserted]: #14
 [mp #31 #79]: false
 unsat
-790f41c10a6a91834ac605d1e5a736ba38cac6ca 32 0
+aed50da01a066fa4f6c8e7af4a461d101bc09de0 61 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#11 := (- f3)
+#9 := 0::real
+#12 := (< 0::real #11)
+#10 := (< f3 0::real)
+#13 := (implies #10 #12)
+#14 := (not #13)
+#78 := (iff #14 false)
+#32 := -1::real
+#33 := (* -1::real f3)
+#36 := (< 0::real #33)
+#42 := (not #10)
+#43 := (or #42 #36)
+#48 := (not #43)
+#76 := (iff #48 false)
+#1 := true
+#71 := (not true)
+#74 := (iff #71 false)
+#75 := [rewrite]: #74
+#72 := (iff #48 #71)
+#69 := (iff #43 true)
+#51 := (>= f3 0::real)
+#52 := (not #51)
+#64 := (or #51 #52)
+#67 := (iff #64 true)
+#68 := [rewrite]: #67
+#65 := (iff #43 #64)
+#62 := (iff #36 #52)
+#63 := [rewrite]: #62
+#60 := (iff #42 #51)
+#55 := (not #52)
+#58 := (iff #55 #51)
+#59 := [rewrite]: #58
+#56 := (iff #42 #55)
+#53 := (iff #10 #52)
+#54 := [rewrite]: #53
+#57 := [monotonicity #54]: #56
+#61 := [trans #57 #59]: #60
+#66 := [monotonicity #61 #63]: #65
+#70 := [trans #66 #68]: #69
+#73 := [monotonicity #70]: #72
+#77 := [trans #73 #75]: #76
+#49 := (iff #14 #48)
+#46 := (iff #13 #43)
+#39 := (implies #10 #36)
+#44 := (iff #39 #43)
+#45 := [rewrite]: #44
+#40 := (iff #13 #39)
+#37 := (iff #12 #36)
+#34 := (= #11 #33)
+#35 := [rewrite]: #34
+#38 := [monotonicity #35]: #37
+#41 := [monotonicity #38]: #40
+#47 := [trans #41 #45]: #46
+#50 := [monotonicity #47]: #49
+#79 := [trans #50 #77]: #78
+#31 := [asserted]: #14
+[mp #31 #79]: false
+unsat
+4c33a6158d9a09229cc4bfd8f383004f3cebc48a 26 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := 0::real
+#10 := (- f3 0::real)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+5fa448e93a50f684d9003c71f7eb6c60b8908f77 32 0
 #2 := false
 decl f3 :: real
 #9 := f3
@@ -46843,7 +47113,7 @@
 #30 := [asserted]: #13
 [mp #30 #50]: false
 unsat
-45b60930fea61c4a8f7b103e68e903e1ceab7852 64 0
+abc85cf86b0b1c8a34cd74d5da49e570c77ddea0 64 0
 #2 := false
 #12 := 0::real
 decl f4 :: real
@@ -46908,69 +47178,7 @@
 #32 := [asserted]: #15
 [mp #32 #81]: false
 unsat
-60ae5a86685e4f3dd9f231aaafe937bfd9ceb4bc 61 0
-#2 := false
-decl f3 :: real
-#8 := f3
-#11 := (- f3)
-#9 := 0::real
-#12 := (< 0::real #11)
-#10 := (< f3 0::real)
-#13 := (implies #10 #12)
-#14 := (not #13)
-#78 := (iff #14 false)
-#32 := -1::real
-#33 := (* -1::real f3)
-#36 := (< 0::real #33)
-#42 := (not #10)
-#43 := (or #42 #36)
-#48 := (not #43)
-#76 := (iff #48 false)
-#1 := true
-#71 := (not true)
-#74 := (iff #71 false)
-#75 := [rewrite]: #74
-#72 := (iff #48 #71)
-#69 := (iff #43 true)
-#51 := (>= f3 0::real)
-#52 := (not #51)
-#64 := (or #51 #52)
-#67 := (iff #64 true)
-#68 := [rewrite]: #67
-#65 := (iff #43 #64)
-#62 := (iff #36 #52)
-#63 := [rewrite]: #62
-#60 := (iff #42 #51)
-#55 := (not #52)
-#58 := (iff #55 #51)
-#59 := [rewrite]: #58
-#56 := (iff #42 #55)
-#53 := (iff #10 #52)
-#54 := [rewrite]: #53
-#57 := [monotonicity #54]: #56
-#61 := [trans #57 #59]: #60
-#66 := [monotonicity #61 #63]: #65
-#70 := [trans #66 #68]: #69
-#73 := [monotonicity #70]: #72
-#77 := [trans #73 #75]: #76
-#49 := (iff #14 #48)
-#46 := (iff #13 #43)
-#39 := (implies #10 #36)
-#44 := (iff #39 #43)
-#45 := [rewrite]: #44
-#40 := (iff #13 #39)
-#37 := (iff #12 #36)
-#34 := (= #11 #33)
-#35 := [rewrite]: #34
-#38 := [monotonicity #35]: #37
-#41 := [monotonicity #38]: #40
-#47 := [trans #41 #45]: #46
-#50 := [monotonicity #47]: #49
-#79 := [trans #50 #77]: #78
-#31 := [asserted]: #14
-[mp #31 #79]: false
-unsat
-390f065bbd860ad0bb40feb02d88be98544fabc4 44 0
+8084abd03f885814b6c145eb3fdc41f5a2cc85f8 44 0
 #2 := false
 decl f3 :: real
 #8 := f3
@@ -47015,7 +47223,7 @@
 #31 := [asserted]: #14
 [mp #31 #61]: false
 unsat
-ff168f63f9897fde96bfb7de5db7da56a8ec5202 42 0
+9afe5717b3e2c9027579ba3e8d9d66db44c6cbda 42 0
 #2 := false
 decl f3 :: real
 #8 := f3
@@ -47058,7 +47266,7 @@
 #31 := [asserted]: #14
 [mp #31 #59]: false
 unsat
-fbdc4cb05a56d63893610ccb3b08ec35be0de896 48 0
+a1710b56b11072c592931adbf944a5bd3bc6efc2 48 0
 #2 := false
 decl f5 :: real
 #11 := f5
@@ -47107,7 +47315,7 @@
 #33 := [asserted]: #16
 [mp #33 #64]: false
 unsat
-35cb5c6f18d527568affbd6fa3b8106b1a97d4c5 30 0
+4611c2bccf9693379d8f36635022f4216eaaa919 30 0
 #2 := false
 #8 := 1::real
 #9 := 2::real
@@ -47138,44 +47346,7 @@
 #29 := [asserted]: #12
 [mp #29 #49]: false
 unsat
-a66448e31ec3061bc2656a02b5d410722684294d 36 0
-#2 := false
-decl f3 :: real
-#9 := f3
-#8 := 3::real
-#10 := (/ f3 3::real)
-#11 := (* 3::real #10)
-#12 := (= #11 f3)
-#13 := (not #12)
-#53 := (iff #13 false)
-#1 := true
-#48 := (not true)
-#51 := (iff #48 false)
-#52 := [rewrite]: #51
-#49 := (iff #13 #48)
-#46 := (iff #12 true)
-#41 := (= f3 f3)
-#44 := (iff #41 true)
-#45 := [rewrite]: #44
-#42 := (iff #12 #41)
-#31 := 1/3::real
-#32 := (* 1/3::real f3)
-#35 := (* 3::real #32)
-#38 := (= #35 f3)
-#39 := [rewrite]: #38
-#36 := (= #11 #35)
-#33 := (= #10 #32)
-#34 := [rewrite]: #33
-#37 := [monotonicity #34]: #36
-#40 := [trans #37 #39]: #12
-#43 := [monotonicity #40]: #42
-#47 := [trans #43 #45]: #46
-#50 := [monotonicity #47]: #49
-#54 := [trans #50 #52]: #53
-#30 := [asserted]: #13
-[mp #30 #54]: false
-unsat
-3037834a6c55cfbe96598ac3d4b462835eeaed7d 27 0
+300cf7e266e08d39c05d69e60b19d0ac09a08a2e 27 0
 #2 := false
 #9 := 3::real
 #8 := 1::real
@@ -47203,43 +47374,7 @@
 #29 := [asserted]: #12
 [mp #29 #46]: false
 unsat
-0c0a26d5b20997d02798707aedc1fa07591ae1bf 35 0
-#2 := false
-decl f3 :: real
-#8 := f3
-#9 := 3::real
-#10 := (* f3 3::real)
-#11 := (/ #10 3::real)
-#12 := (= #11 f3)
-#13 := (not #12)
-#52 := (iff #13 false)
-#1 := true
-#47 := (not true)
-#50 := (iff #47 false)
-#51 := [rewrite]: #50
-#48 := (iff #13 #47)
-#45 := (iff #12 true)
-#40 := (= f3 f3)
-#43 := (iff #40 true)
-#44 := [rewrite]: #43
-#41 := (iff #12 #40)
-#31 := (* 3::real f3)
-#34 := (/ #31 3::real)
-#37 := (= #34 f3)
-#38 := [rewrite]: #37
-#35 := (= #11 #34)
-#32 := (= #10 #31)
-#33 := [rewrite]: #32
-#36 := [monotonicity #33]: #35
-#39 := [trans #36 #38]: #12
-#42 := [monotonicity #39]: #41
-#46 := [trans #42 #44]: #45
-#49 := [monotonicity #46]: #48
-#53 := [trans #49 #51]: #52
-#30 := [asserted]: #13
-[mp #30 #53]: false
-unsat
-c0ca03e227f816842315b007cba7acf006e07203 48 0
+b59d35169428d1cd490a83e17435ecfc93225870 48 0
 #2 := false
 #9 := 3::real
 #8 := 1::real
@@ -47288,7 +47423,310 @@
 #32 := [asserted]: #15
 [mp #32 #67]: false
 unsat
-167b73607533e079718467537de3ca170ac6b4fc 62 0
+1c222157f628411945e7e47ef57130c5ba4ad155 36 0
+#2 := false
+#10 := 3::real
+#8 := 1::real
+#9 := (- 1::real)
+#11 := (/ #9 3::real)
+#12 := (= #11 #11)
+#13 := (not #12)
+#54 := (iff #13 false)
+#1 := true
+#49 := (not true)
+#52 := (iff #49 false)
+#53 := [rewrite]: #52
+#50 := (iff #13 #49)
+#47 := (iff #12 true)
+#37 := -1/3::real
+#42 := (= -1/3::real -1/3::real)
+#45 := (iff #42 true)
+#46 := [rewrite]: #45
+#43 := (iff #12 #42)
+#40 := (= #11 -1/3::real)
+#31 := -1::real
+#34 := (/ -1::real 3::real)
+#38 := (= #34 -1/3::real)
+#39 := [rewrite]: #38
+#35 := (= #11 #34)
+#32 := (= #9 -1::real)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#41 := [trans #36 #39]: #40
+#44 := [monotonicity #41 #41]: #43
+#48 := [trans #44 #46]: #47
+#51 := [monotonicity #48]: #50
+#55 := [trans #51 #53]: #54
+#30 := [asserted]: #13
+[mp #30 #55]: false
+unsat
+e4a7188c884c4cc69972b6b4c9f7bcbb1cd3ef93 43 0
+#2 := false
+#10 := 3::real
+#8 := 1::real
+#13 := (/ 1::real 3::real)
+#11 := (- 3::real)
+#9 := (- 1::real)
+#12 := (/ #9 #11)
+#14 := (= #12 #13)
+#15 := (not #14)
+#61 := (iff #15 false)
+#1 := true
+#56 := (not true)
+#59 := (iff #56 false)
+#60 := [rewrite]: #59
+#57 := (iff #15 #56)
+#54 := (iff #14 true)
+#42 := 1/3::real
+#49 := (= 1/3::real 1/3::real)
+#52 := (iff #49 true)
+#53 := [rewrite]: #52
+#50 := (iff #14 #49)
+#47 := (= #13 1/3::real)
+#48 := [rewrite]: #47
+#45 := (= #12 1/3::real)
+#36 := -3::real
+#33 := -1::real
+#39 := (/ -1::real -3::real)
+#43 := (= #39 1/3::real)
+#44 := [rewrite]: #43
+#40 := (= #12 #39)
+#37 := (= #11 -3::real)
+#38 := [rewrite]: #37
+#34 := (= #9 -1::real)
+#35 := [rewrite]: #34
+#41 := [monotonicity #35 #38]: #40
+#46 := [trans #41 #44]: #45
+#51 := [monotonicity #46 #48]: #50
+#55 := [trans #51 #53]: #54
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#32 := [asserted]: #15
+[mp #32 #62]: false
+unsat
+b7bd87b08d1cd38b7e0db00083a20eb0fa944982 26 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := 1::real
+#10 := (/ f3 1::real)
+#11 := (= #10 f3)
+#12 := (not #11)
+#43 := (iff #12 false)
+#1 := true
+#38 := (not true)
+#41 := (iff #38 false)
+#42 := [rewrite]: #41
+#39 := (iff #12 #38)
+#36 := (iff #11 true)
+#31 := (= f3 f3)
+#34 := (iff #31 true)
+#35 := [rewrite]: #34
+#32 := (iff #11 #31)
+#30 := [rewrite]: #11
+#33 := [monotonicity #30]: #32
+#37 := [trans #33 #35]: #36
+#40 := [monotonicity #37]: #39
+#44 := [trans #40 #42]: #43
+#29 := [asserted]: #12
+[mp #29 #44]: false
+unsat
+c3e8ed15657d66fdc6a77370b7e3994d0741653a 60 0
+#2 := false
+#8 := 0::real
+decl f3 :: real
+#9 := f3
+#65 := 2/3::real
+#66 := (* 2/3::real f3)
+#67 := (<= #66 0::real)
+#63 := (not #67)
+#52 := (<= f3 0::real)
+#69 := (or #52 #63)
+#72 := (not #69)
+#11 := 3::real
+#12 := (/ f3 3::real)
+#13 := (< #12 f3)
+#10 := (< 0::real f3)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#75 := (iff #15 #72)
+#33 := 1/3::real
+#34 := (* 1/3::real f3)
+#37 := (< #34 f3)
+#43 := (not #10)
+#44 := (or #43 #37)
+#49 := (not #44)
+#73 := (iff #49 #72)
+#70 := (iff #44 #69)
+#64 := (iff #37 #63)
+#68 := [rewrite]: #64
+#61 := (iff #43 #52)
+#53 := (not #52)
+#56 := (not #53)
+#59 := (iff #56 #52)
+#60 := [rewrite]: #59
+#57 := (iff #43 #56)
+#54 := (iff #10 #53)
+#55 := [rewrite]: #54
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#71 := [monotonicity #62 #68]: #70
+#74 := [monotonicity #71]: #73
+#50 := (iff #15 #49)
+#47 := (iff #14 #44)
+#40 := (implies #10 #37)
+#45 := (iff #40 #44)
+#46 := [rewrite]: #45
+#41 := (iff #14 #40)
+#38 := (iff #13 #37)
+#35 := (= #12 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#42 := [monotonicity #39]: #41
+#48 := [trans #42 #46]: #47
+#51 := [monotonicity #48]: #50
+#76 := [trans #51 #74]: #75
+#32 := [asserted]: #15
+#77 := [mp #32 #76]: #72
+#79 := [not-or-elim #77]: #67
+#78 := [not-or-elim #77]: #53
+[th-lemma #78 #79]: false
+unsat
+05dd4ddb8672ca6d3f31acc3ffa7f7986078b232 60 0
+#2 := false
+#9 := 0::real
+decl f3 :: real
+#8 := f3
+#67 := 2/3::real
+#68 := (* 2/3::real f3)
+#65 := (>= #68 0::real)
+#63 := (not #65)
+#54 := (>= f3 0::real)
+#69 := (or #54 #63)
+#72 := (not #69)
+#11 := 3::real
+#12 := (/ f3 3::real)
+#13 := (< f3 #12)
+#10 := (< f3 0::real)
+#14 := (implies #10 #13)
+#15 := (not #14)
+#75 := (iff #15 #72)
+#33 := 1/3::real
+#34 := (* 1/3::real f3)
+#37 := (< f3 #34)
+#43 := (not #10)
+#44 := (or #43 #37)
+#49 := (not #44)
+#73 := (iff #49 #72)
+#70 := (iff #44 #69)
+#64 := (iff #37 #63)
+#66 := [rewrite]: #64
+#61 := (iff #43 #54)
+#52 := (not #54)
+#56 := (not #52)
+#59 := (iff #56 #54)
+#60 := [rewrite]: #59
+#57 := (iff #43 #56)
+#53 := (iff #10 #52)
+#55 := [rewrite]: #53
+#58 := [monotonicity #55]: #57
+#62 := [trans #58 #60]: #61
+#71 := [monotonicity #62 #66]: #70
+#74 := [monotonicity #71]: #73
+#50 := (iff #15 #49)
+#47 := (iff #14 #44)
+#40 := (implies #10 #37)
+#45 := (iff #40 #44)
+#46 := [rewrite]: #45
+#41 := (iff #14 #40)
+#38 := (iff #13 #37)
+#35 := (= #12 #34)
+#36 := [rewrite]: #35
+#39 := [monotonicity #36]: #38
+#42 := [monotonicity #39]: #41
+#48 := [trans #42 #46]: #47
+#51 := [monotonicity #48]: #50
+#76 := [trans #51 #74]: #75
+#32 := [asserted]: #15
+#77 := [mp #32 #76]: #72
+#79 := [not-or-elim #77]: #65
+#78 := [not-or-elim #77]: #52
+[th-lemma #78 #79]: false
+unsat
+b7a066feb9f43bcc3b0373cd9c9287361b54eff6 36 0
+#2 := false
+decl f3 :: real
+#9 := f3
+#8 := 3::real
+#10 := (/ f3 3::real)
+#11 := (* 3::real #10)
+#12 := (= #11 f3)
+#13 := (not #12)
+#53 := (iff #13 false)
+#1 := true
+#48 := (not true)
+#51 := (iff #48 false)
+#52 := [rewrite]: #51
+#49 := (iff #13 #48)
+#46 := (iff #12 true)
+#41 := (= f3 f3)
+#44 := (iff #41 true)
+#45 := [rewrite]: #44
+#42 := (iff #12 #41)
+#31 := 1/3::real
+#32 := (* 1/3::real f3)
+#35 := (* 3::real #32)
+#38 := (= #35 f3)
+#39 := [rewrite]: #38
+#36 := (= #11 #35)
+#33 := (= #10 #32)
+#34 := [rewrite]: #33
+#37 := [monotonicity #34]: #36
+#40 := [trans #37 #39]: #12
+#43 := [monotonicity #40]: #42
+#47 := [trans #43 #45]: #46
+#50 := [monotonicity #47]: #49
+#54 := [trans #50 #52]: #53
+#30 := [asserted]: #13
+[mp #30 #54]: false
+unsat
+60b8185463f5b2ce142483f90c095e9accf8989c 35 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := 3::real
+#10 := (* f3 3::real)
+#11 := (/ #10 3::real)
+#12 := (= #11 f3)
+#13 := (not #12)
+#52 := (iff #13 false)
+#1 := true
+#47 := (not true)
+#50 := (iff #47 false)
+#51 := [rewrite]: #50
+#48 := (iff #13 #47)
+#45 := (iff #12 true)
+#40 := (= f3 f3)
+#43 := (iff #40 true)
+#44 := [rewrite]: #43
+#41 := (iff #12 #40)
+#31 := (* 3::real f3)
+#34 := (/ #31 3::real)
+#37 := (= #34 f3)
+#38 := [rewrite]: #37
+#35 := (= #11 #34)
+#32 := (= #10 #31)
+#33 := [rewrite]: #32
+#36 := [monotonicity #33]: #35
+#39 := [trans #36 #38]: #12
+#42 := [monotonicity #39]: #41
+#46 := [trans #42 #44]: #45
+#49 := [monotonicity #46]: #48
+#53 := [trans #49 #51]: #52
+#30 := [asserted]: #13
+[mp #30 #53]: false
+unsat
+8140105cc276b32acd77e4f2cd380fea1f24efd8 62 0
 #2 := false
 #8 := 0::real
 decl f3 :: real
@@ -47351,88 +47789,7 @@
 #80 := [not-or-elim #79]: #55
 [th-lemma #80 #81]: false
 unsat
-407d897cdd96a77ccd0a5e9af3ea8310eebe935c 36 0
-#2 := false
-#10 := 3::real
-#8 := 1::real
-#9 := (- 1::real)
-#11 := (/ #9 3::real)
-#12 := (= #11 #11)
-#13 := (not #12)
-#54 := (iff #13 false)
-#1 := true
-#49 := (not true)
-#52 := (iff #49 false)
-#53 := [rewrite]: #52
-#50 := (iff #13 #49)
-#47 := (iff #12 true)
-#37 := -1/3::real
-#42 := (= -1/3::real -1/3::real)
-#45 := (iff #42 true)
-#46 := [rewrite]: #45
-#43 := (iff #12 #42)
-#40 := (= #11 -1/3::real)
-#31 := -1::real
-#34 := (/ -1::real 3::real)
-#38 := (= #34 -1/3::real)
-#39 := [rewrite]: #38
-#35 := (= #11 #34)
-#32 := (= #9 -1::real)
-#33 := [rewrite]: #32
-#36 := [monotonicity #33]: #35
-#41 := [trans #36 #39]: #40
-#44 := [monotonicity #41 #41]: #43
-#48 := [trans #44 #46]: #47
-#51 := [monotonicity #48]: #50
-#55 := [trans #51 #53]: #54
-#30 := [asserted]: #13
-[mp #30 #55]: false
-unsat
-dae8653f4906be077917c7741a65becd7fc6baa9 43 0
-#2 := false
-#10 := 3::real
-#8 := 1::real
-#13 := (/ 1::real 3::real)
-#11 := (- 3::real)
-#9 := (- 1::real)
-#12 := (/ #9 #11)
-#14 := (= #12 #13)
-#15 := (not #14)
-#61 := (iff #15 false)
-#1 := true
-#56 := (not true)
-#59 := (iff #56 false)
-#60 := [rewrite]: #59
-#57 := (iff #15 #56)
-#54 := (iff #14 true)
-#42 := 1/3::real
-#49 := (= 1/3::real 1/3::real)
-#52 := (iff #49 true)
-#53 := [rewrite]: #52
-#50 := (iff #14 #49)
-#47 := (= #13 1/3::real)
-#48 := [rewrite]: #47
-#45 := (= #12 1/3::real)
-#36 := -3::real
-#33 := -1::real
-#39 := (/ -1::real -3::real)
-#43 := (= #39 1/3::real)
-#44 := [rewrite]: #43
-#40 := (= #12 #39)
-#37 := (= #11 -3::real)
-#38 := [rewrite]: #37
-#34 := (= #9 -1::real)
-#35 := [rewrite]: #34
-#41 := [monotonicity #35 #38]: #40
-#46 := [trans #41 #44]: #45
-#51 := [monotonicity #46 #48]: #50
-#55 := [trans #51 #53]: #54
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#32 := [asserted]: #15
-[mp #32 #62]: false
-unsat
-5f5bc75d0e15785a03976c15c11ed28c9527a9c1 62 0
+9a571f31a85693be816acc5c7b7aa7362cb820bb 62 0
 #2 := false
 #9 := 0::real
 decl f3 :: real
@@ -47495,34 +47852,7 @@
 #80 := [not-or-elim #79]: #54
 [th-lemma #80 #81]: false
 unsat
-760d3be0f602d4f12e9c082b34c9607286d80e81 26 0
-#2 := false
-decl f3 :: real
-#8 := f3
-#9 := 1::real
-#10 := (/ f3 1::real)
-#11 := (= #10 f3)
-#12 := (not #11)
-#43 := (iff #12 false)
-#1 := true
-#38 := (not true)
-#41 := (iff #38 false)
-#42 := [rewrite]: #41
-#39 := (iff #12 #38)
-#36 := (iff #11 true)
-#31 := (= f3 f3)
-#34 := (iff #31 true)
-#35 := [rewrite]: #34
-#32 := (iff #11 #31)
-#30 := [rewrite]: #11
-#33 := [monotonicity #30]: #32
-#37 := [trans #33 #35]: #36
-#40 := [monotonicity #37]: #39
-#44 := [trans #40 #42]: #43
-#29 := [asserted]: #12
-[mp #29 #44]: false
-unsat
-490baa52b7aa34ed9cb90263f1ecd055bf5a7ff6 75 0
+2f685a966903afb267e7499dd8ad6b2b43caca93 75 0
 #2 := false
 #8 := 0::real
 decl f3 :: real
@@ -47598,68 +47928,7 @@
 #96 := [unit-resolution #95 #92]: #90
 [th-lemma #89 #70 #96]: false
 unsat
-9c25469b6a76ae1f1d1ef57b133f6ba4622084dd 60 0
-#2 := false
-#8 := 0::real
-decl f3 :: real
-#9 := f3
-#65 := 2/3::real
-#66 := (* 2/3::real f3)
-#67 := (<= #66 0::real)
-#63 := (not #67)
-#52 := (<= f3 0::real)
-#69 := (or #52 #63)
-#72 := (not #69)
-#11 := 3::real
-#12 := (/ f3 3::real)
-#13 := (< #12 f3)
-#10 := (< 0::real f3)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#75 := (iff #15 #72)
-#33 := 1/3::real
-#34 := (* 1/3::real f3)
-#37 := (< #34 f3)
-#43 := (not #10)
-#44 := (or #43 #37)
-#49 := (not #44)
-#73 := (iff #49 #72)
-#70 := (iff #44 #69)
-#64 := (iff #37 #63)
-#68 := [rewrite]: #64
-#61 := (iff #43 #52)
-#53 := (not #52)
-#56 := (not #53)
-#59 := (iff #56 #52)
-#60 := [rewrite]: #59
-#57 := (iff #43 #56)
-#54 := (iff #10 #53)
-#55 := [rewrite]: #54
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#71 := [monotonicity #62 #68]: #70
-#74 := [monotonicity #71]: #73
-#50 := (iff #15 #49)
-#47 := (iff #14 #44)
-#40 := (implies #10 #37)
-#45 := (iff #40 #44)
-#46 := [rewrite]: #45
-#41 := (iff #14 #40)
-#38 := (iff #13 #37)
-#35 := (= #12 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#42 := [monotonicity #39]: #41
-#48 := [trans #42 #46]: #47
-#51 := [monotonicity #48]: #50
-#76 := [trans #51 #74]: #75
-#32 := [asserted]: #15
-#77 := [mp #32 #76]: #72
-#79 := [not-or-elim #77]: #67
-#78 := [not-or-elim #77]: #53
-[th-lemma #78 #79]: false
-unsat
-2dc606b7a7bd26f5089ecfacf1617fe8ce130325 132 0
+4a38ab99c62d0654d0c5bc149db3e769cf921224 132 0
 #2 := false
 #9 := 0::real
 decl f3 :: real
@@ -47792,68 +48061,7 @@
 #162 := [th-lemma]: #161
 [unit-resolution #162 #160 #143]: false
 unsat
-0eac487a9514449bb01231188977421b8bb134df 60 0
-#2 := false
-#9 := 0::real
-decl f3 :: real
-#8 := f3
-#67 := 2/3::real
-#68 := (* 2/3::real f3)
-#65 := (>= #68 0::real)
-#63 := (not #65)
-#54 := (>= f3 0::real)
-#69 := (or #54 #63)
-#72 := (not #69)
-#11 := 3::real
-#12 := (/ f3 3::real)
-#13 := (< f3 #12)
-#10 := (< f3 0::real)
-#14 := (implies #10 #13)
-#15 := (not #14)
-#75 := (iff #15 #72)
-#33 := 1/3::real
-#34 := (* 1/3::real f3)
-#37 := (< f3 #34)
-#43 := (not #10)
-#44 := (or #43 #37)
-#49 := (not #44)
-#73 := (iff #49 #72)
-#70 := (iff #44 #69)
-#64 := (iff #37 #63)
-#66 := [rewrite]: #64
-#61 := (iff #43 #54)
-#52 := (not #54)
-#56 := (not #52)
-#59 := (iff #56 #54)
-#60 := [rewrite]: #59
-#57 := (iff #43 #56)
-#53 := (iff #10 #52)
-#55 := [rewrite]: #53
-#58 := [monotonicity #55]: #57
-#62 := [trans #58 #60]: #61
-#71 := [monotonicity #62 #66]: #70
-#74 := [monotonicity #71]: #73
-#50 := (iff #15 #49)
-#47 := (iff #14 #44)
-#40 := (implies #10 #37)
-#45 := (iff #40 #44)
-#46 := [rewrite]: #45
-#41 := (iff #14 #40)
-#38 := (iff #13 #37)
-#35 := (= #12 #34)
-#36 := [rewrite]: #35
-#39 := [monotonicity #36]: #38
-#42 := [monotonicity #39]: #41
-#48 := [trans #42 #46]: #47
-#51 := [monotonicity #48]: #50
-#76 := [trans #51 #74]: #75
-#32 := [asserted]: #15
-#77 := [mp #32 #76]: #72
-#79 := [not-or-elim #77]: #65
-#78 := [not-or-elim #77]: #52
-[th-lemma #78 #79]: false
-unsat
-9db23a49c890fc2c240ef900b9554e7cff9b9382 103 0
+704113f68324742364e301291c46543b32d30adc 103 0
 #2 := false
 #8 := 0::real
 decl f3 :: real
@@ -47957,7 +48165,7 @@
 #124 := [unit-resolution #123 #120]: #115
 [th-lemma #110 #124]: false
 unsat
-949e408b2eea8c150227b26f7ecc3f591066ebd6 149 0
+099809f4b951e6c4b8dd87d068c12977d185ca9a 149 0
 #2 := false
 #9 := 0::real
 decl f3 :: real
@@ -48107,123 +48315,7 @@
 #170 := [unit-resolution #169 #155]: #97
 [th-lemma #159 #170 #167]: false
 unsat
-9e92ed579ec028b4688be273656268ff0a3d0850 57 0
-#2 := false
-#36 := 0::real
-decl f4 :: real
-#9 := f4
-decl f3 :: real
-#8 := f3
-#33 := -1::real
-#34 := (* -1::real f4)
-#35 := (+ f3 #34)
-#37 := (<= #35 0::real)
-#40 := (ite #37 f3 f4)
-#48 := (* -1::real #40)
-#49 := (+ f3 #48)
-#47 := (>= #49 0::real)
-#53 := (not #47)
-#10 := (<= f3 f4)
-#11 := (ite #10 f3 f4)
-#12 := (<= #11 f3)
-#13 := (not #12)
-#54 := (iff #13 #53)
-#51 := (iff #12 #47)
-#43 := (<= #40 f3)
-#46 := (iff #43 #47)
-#50 := [rewrite]: #46
-#44 := (iff #12 #43)
-#41 := (= #11 #40)
-#38 := (iff #10 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#52 := [trans #45 #50]: #51
-#55 := [monotonicity #52]: #54
-#30 := [asserted]: #13
-#56 := [mp #30 #55]: #53
-#60 := (= f3 #40)
-#31 := (+ f4 #48)
-#65 := (>= #31 0::real)
-#61 := (= f4 #40)
-#62 := (not #37)
-#66 := [hypothesis]: #62
-#59 := (or #37 #61)
-#57 := [def-axiom]: #59
-#67 := [unit-resolution #57 #66]: #61
-#68 := (not #61)
-#69 := (or #68 #65)
-#70 := [th-lemma]: #69
-#71 := [unit-resolution #70 #67]: #65
-#72 := [th-lemma #56 #66 #71]: false
-#73 := [lemma #72]: #37
-#63 := (or #62 #60)
-#58 := [def-axiom]: #63
-#74 := [unit-resolution #58 #73]: #60
-#75 := (not #60)
-#76 := (or #75 #47)
-#77 := [th-lemma]: #76
-[unit-resolution #77 #74 #56]: false
-unsat
-49128a64794a78bd051fb157e2f6db1aa53acbe7 57 0
-#2 := false
-#36 := 0::real
-decl f4 :: real
-#9 := f4
-#33 := -1::real
-#34 := (* -1::real f4)
-decl f3 :: real
-#8 := f3
-#35 := (+ f3 #34)
-#37 := (<= #35 0::real)
-#40 := (ite #37 f3 f4)
-#61 := (= f4 #40)
-#65 := (not #61)
-#47 := (* -1::real #40)
-#48 := (+ f4 #47)
-#46 := (>= #48 0::real)
-#53 := (not #46)
-#10 := (<= f3 f4)
-#11 := (ite #10 f3 f4)
-#12 := (<= #11 f4)
-#13 := (not #12)
-#54 := (iff #13 #53)
-#51 := (iff #12 #46)
-#43 := (<= #40 f4)
-#49 := (iff #43 #46)
-#50 := [rewrite]: #49
-#44 := (iff #12 #43)
-#41 := (= #11 #40)
-#38 := (iff #10 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#52 := [trans #45 #50]: #51
-#55 := [monotonicity #52]: #54
-#30 := [asserted]: #13
-#56 := [mp #30 #55]: #53
-#64 := [hypothesis]: #61
-#66 := (or #65 #46)
-#67 := [th-lemma]: #66
-#68 := [unit-resolution #67 #64 #56]: false
-#69 := [lemma #68]: #65
-#59 := (or #37 #61)
-#57 := [def-axiom]: #59
-#72 := [unit-resolution #57 #69]: #37
-#31 := (+ f3 #47)
-#71 := (>= #31 0::real)
-#60 := (= f3 #40)
-#62 := (not #37)
-#63 := (or #62 #60)
-#58 := [def-axiom]: #63
-#73 := [unit-resolution #58 #72]: #60
-#74 := (not #60)
-#75 := (or #74 #71)
-#76 := [th-lemma]: #75
-#77 := [unit-resolution #76 #73]: #71
-[th-lemma #77 #56 #72]: false
-unsat
-ba68972e04b6d39e23213630ff5fcde9dcaca230 114 0
+29b8934bcf2c51c8a551e0b17bf814bf8deedd61 114 0
 #2 := false
 #9 := 0::real
 decl f3 :: real
@@ -48338,7 +48430,123 @@
 #143 := [unit-resolution #142 #139]: #137
 [th-lemma #136 #134 #143]: false
 unsat
-a19015a56beb41efa267de75df62459c522bbc0a 103 0
+c7322eea663ce724ffdf3e5de8e20e490ab8caf6 57 0
+#2 := false
+#36 := 0::real
+decl f4 :: real
+#9 := f4
+decl f3 :: real
+#8 := f3
+#33 := -1::real
+#34 := (* -1::real f4)
+#35 := (+ f3 #34)
+#37 := (<= #35 0::real)
+#40 := (ite #37 f3 f4)
+#48 := (* -1::real #40)
+#49 := (+ f3 #48)
+#47 := (>= #49 0::real)
+#53 := (not #47)
+#10 := (<= f3 f4)
+#11 := (ite #10 f3 f4)
+#12 := (<= #11 f3)
+#13 := (not #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #47)
+#43 := (<= #40 f3)
+#46 := (iff #43 #47)
+#50 := [rewrite]: #46
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#52 := [trans #45 #50]: #51
+#55 := [monotonicity #52]: #54
+#30 := [asserted]: #13
+#56 := [mp #30 #55]: #53
+#60 := (= f3 #40)
+#31 := (+ f4 #48)
+#65 := (>= #31 0::real)
+#61 := (= f4 #40)
+#62 := (not #37)
+#66 := [hypothesis]: #62
+#59 := (or #37 #61)
+#57 := [def-axiom]: #59
+#67 := [unit-resolution #57 #66]: #61
+#68 := (not #61)
+#69 := (or #68 #65)
+#70 := [th-lemma]: #69
+#71 := [unit-resolution #70 #67]: #65
+#72 := [th-lemma #56 #66 #71]: false
+#73 := [lemma #72]: #37
+#63 := (or #62 #60)
+#58 := [def-axiom]: #63
+#74 := [unit-resolution #58 #73]: #60
+#75 := (not #60)
+#76 := (or #75 #47)
+#77 := [th-lemma]: #76
+[unit-resolution #77 #74 #56]: false
+unsat
+f580fbf74c17d6b6fb5afde9912701d1c54bba4d 57 0
+#2 := false
+#36 := 0::real
+decl f4 :: real
+#9 := f4
+#33 := -1::real
+#34 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#35 := (+ f3 #34)
+#37 := (<= #35 0::real)
+#40 := (ite #37 f3 f4)
+#61 := (= f4 #40)
+#65 := (not #61)
+#47 := (* -1::real #40)
+#48 := (+ f4 #47)
+#46 := (>= #48 0::real)
+#53 := (not #46)
+#10 := (<= f3 f4)
+#11 := (ite #10 f3 f4)
+#12 := (<= #11 f4)
+#13 := (not #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #46)
+#43 := (<= #40 f4)
+#49 := (iff #43 #46)
+#50 := [rewrite]: #49
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#52 := [trans #45 #50]: #51
+#55 := [monotonicity #52]: #54
+#30 := [asserted]: #13
+#56 := [mp #30 #55]: #53
+#64 := [hypothesis]: #61
+#66 := (or #65 #46)
+#67 := [th-lemma]: #66
+#68 := [unit-resolution #67 #64 #56]: false
+#69 := [lemma #68]: #65
+#59 := (or #37 #61)
+#57 := [def-axiom]: #59
+#72 := [unit-resolution #57 #69]: #37
+#31 := (+ f3 #47)
+#71 := (>= #31 0::real)
+#60 := (= f3 #40)
+#62 := (not #37)
+#63 := (or #62 #60)
+#58 := [def-axiom]: #63
+#73 := [unit-resolution #58 #72]: #60
+#74 := (not #60)
+#75 := (or #74 #71)
+#76 := [th-lemma]: #75
+#77 := [unit-resolution #76 #73]: #71
+[th-lemma #77 #56 #72]: false
+unsat
+cc7a80da13c82cc207500cb8afbaae97318e63e2 103 0
 #2 := false
 #45 := 0::real
 decl f5 :: real
@@ -48442,123 +48650,7 @@
 #122 := [unit-resolution #121 #118]: #115
 [th-lemma #122 #92 #93]: false
 unsat
-385a845ab61bebe2a2caff1fe491e1a60a61d0b8 57 0
-#2 := false
-#36 := 0::real
-decl f4 :: real
-#9 := f4
-#33 := -1::real
-#34 := (* -1::real f4)
-decl f3 :: real
-#8 := f3
-#35 := (+ f3 #34)
-#37 := (<= #35 0::real)
-#40 := (ite #37 f4 f3)
-#61 := (= f3 #40)
-#65 := (not #61)
-#46 := (* -1::real #40)
-#47 := (+ f3 #46)
-#48 := (<= #47 0::real)
-#53 := (not #48)
-#10 := (<= f3 f4)
-#11 := (ite #10 f4 f3)
-#12 := (<= f3 #11)
-#13 := (not #12)
-#54 := (iff #13 #53)
-#51 := (iff #12 #48)
-#43 := (<= f3 #40)
-#49 := (iff #43 #48)
-#50 := [rewrite]: #49
-#44 := (iff #12 #43)
-#41 := (= #11 #40)
-#38 := (iff #10 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#52 := [trans #45 #50]: #51
-#55 := [monotonicity #52]: #54
-#30 := [asserted]: #13
-#56 := [mp #30 #55]: #53
-#64 := [hypothesis]: #61
-#66 := (or #65 #48)
-#67 := [th-lemma]: #66
-#68 := [unit-resolution #67 #64 #56]: false
-#69 := [lemma #68]: #65
-#59 := (or #37 #61)
-#57 := [def-axiom]: #59
-#72 := [unit-resolution #57 #69]: #37
-#31 := (+ f4 #46)
-#70 := (<= #31 0::real)
-#60 := (= f4 #40)
-#62 := (not #37)
-#63 := (or #62 #60)
-#58 := [def-axiom]: #63
-#73 := [unit-resolution #58 #72]: #60
-#74 := (not #60)
-#75 := (or #74 #70)
-#76 := [th-lemma]: #75
-#77 := [unit-resolution #76 #73]: #70
-[th-lemma #77 #56 #72]: false
-unsat
-3bf0824ed026ba333e5bb1b1e54ccba54d70d87f 57 0
-#2 := false
-#35 := 0::real
-decl f4 :: real
-#9 := f4
-decl f3 :: real
-#8 := f3
-#33 := -1::real
-#37 := (* -1::real f4)
-#38 := (+ f3 #37)
-#36 := (>= #38 0::real)
-#40 := (ite #36 f3 f4)
-#46 := (* -1::real #40)
-#47 := (+ f3 #46)
-#48 := (<= #47 0::real)
-#53 := (not #48)
-#10 := (<= f4 f3)
-#11 := (ite #10 f3 f4)
-#12 := (<= f3 #11)
-#13 := (not #12)
-#54 := (iff #13 #53)
-#51 := (iff #12 #48)
-#43 := (<= f3 #40)
-#49 := (iff #43 #48)
-#50 := [rewrite]: #49
-#44 := (iff #12 #43)
-#41 := (= #11 #40)
-#34 := (iff #10 #36)
-#39 := [rewrite]: #34
-#42 := [monotonicity #39]: #41
-#45 := [monotonicity #42]: #44
-#52 := [trans #45 #50]: #51
-#55 := [monotonicity #52]: #54
-#30 := [asserted]: #13
-#56 := [mp #30 #55]: #53
-#60 := (= f3 #40)
-#31 := (+ f4 #46)
-#64 := (<= #31 0::real)
-#61 := (= f4 #40)
-#62 := (not #36)
-#66 := [hypothesis]: #62
-#59 := (or #36 #61)
-#57 := [def-axiom]: #59
-#67 := [unit-resolution #57 #66]: #61
-#68 := (not #61)
-#69 := (or #68 #64)
-#70 := [th-lemma]: #69
-#71 := [unit-resolution #70 #67]: #64
-#72 := [th-lemma #56 #66 #71]: false
-#73 := [lemma #72]: #36
-#63 := (or #62 #60)
-#58 := [def-axiom]: #63
-#74 := [unit-resolution #58 #73]: #60
-#75 := (not #60)
-#76 := (or #75 #48)
-#77 := [th-lemma]: #76
-[unit-resolution #77 #74 #56]: false
-unsat
-37f421aa1e81128329d966841b0fde5f3cd8d944 86 0
+23d9458c2d94638d741588b7f5f53da3b743fc4b 86 0
 #2 := false
 decl f3 :: real
 #8 := f3
@@ -48645,7 +48737,7 @@
 #105 := [trans #104 #83]: #51
 [unit-resolution #57 #105]: false
 unsat
-3b84d41e468d1d259c36f6a458b1bdd65a2c38ee 68 0
+ca3670773dec1aa185941c6109c12ef74c091595 68 0
 #2 := false
 #8 := 0::real
 decl f3 :: real
@@ -48714,111 +48806,7 @@
 #88 := [trans #87 #84]: #13
 [unit-resolution #71 #88]: false
 unsat
-56cfe43fc596233456f5d5ed3a41821e49f560df 103 0
-#2 := false
-#45 := 0::real
-decl f3 :: real
-#8 := f3
-decl f5 :: real
-#11 := f5
-#43 := -1::real
-#51 := (* -1::real f5)
-#63 := (+ f3 #51)
-#64 := (<= #63 0::real)
-#67 := (ite #64 f5 f3)
-#73 := (* -1::real #67)
-decl f4 :: real
-#9 := f4
-#74 := (+ f4 #73)
-#75 := (<= #74 0::real)
-#76 := (not #75)
-#52 := (+ f4 #51)
-#53 := (<= #52 0::real)
-#54 := (not #53)
-#47 := (* -1::real f4)
-#48 := (+ f3 #47)
-#46 := (>= #48 0::real)
-#44 := (not #46)
-#57 := (and #44 #54)
-#60 := (not #57)
-#81 := (or #60 #76)
-#84 := (not #81)
-#14 := (<= f3 f5)
-#15 := (ite #14 f5 f3)
-#16 := (< #15 f4)
-#12 := (< f5 f4)
-#10 := (< f3 f4)
-#13 := (and #10 #12)
-#17 := (implies #13 #16)
-#18 := (not #17)
-#87 := (iff #18 #84)
-#36 := (not #13)
-#37 := (or #36 #16)
-#40 := (not #37)
-#85 := (iff #40 #84)
-#82 := (iff #37 #81)
-#79 := (iff #16 #76)
-#70 := (< #67 f4)
-#77 := (iff #70 #76)
-#78 := [rewrite]: #77
-#71 := (iff #16 #70)
-#68 := (= #15 #67)
-#65 := (iff #14 #64)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#80 := [trans #72 #78]: #79
-#61 := (iff #36 #60)
-#58 := (iff #13 #57)
-#55 := (iff #12 #54)
-#56 := [rewrite]: #55
-#49 := (iff #10 #44)
-#50 := [rewrite]: #49
-#59 := [monotonicity #50 #56]: #58
-#62 := [monotonicity #59]: #61
-#83 := [monotonicity #62 #80]: #82
-#86 := [monotonicity #83]: #85
-#41 := (iff #18 #40)
-#38 := (iff #17 #37)
-#39 := [rewrite]: #38
-#42 := [monotonicity #39]: #41
-#88 := [trans #42 #86]: #87
-#35 := [asserted]: #18
-#89 := [mp #35 #88]: #84
-#93 := [not-or-elim #89]: #75
-#90 := [not-or-elim #89]: #57
-#91 := [and-elim #90]: #44
-#97 := (+ f3 #73)
-#116 := (>= #97 0::real)
-#104 := (= f3 #67)
-#105 := (not #64)
-#103 := (= f5 #67)
-#110 := (not #103)
-#100 := (+ f5 #73)
-#98 := (>= #100 0::real)
-#107 := (not #98)
-#92 := [and-elim #90]: #54
-#96 := [hypothesis]: #98
-#94 := [th-lemma #96 #92 #93]: false
-#108 := [lemma #94]: #107
-#109 := [hypothesis]: #103
-#111 := (or #110 #98)
-#112 := [th-lemma]: #111
-#113 := [unit-resolution #112 #109 #108]: false
-#114 := [lemma #113]: #110
-#106 := (or #105 #103)
-#101 := [def-axiom]: #106
-#117 := [unit-resolution #101 #114]: #105
-#102 := (or #64 #104)
-#99 := [def-axiom]: #102
-#118 := [unit-resolution #99 #117]: #104
-#119 := (not #104)
-#120 := (or #119 #116)
-#121 := [th-lemma]: #120
-#122 := [unit-resolution #121 #118]: #116
-[th-lemma #122 #91 #93]: false
-unsat
-7c5cf575f0888dae85c506d289c48f18d6429f5a 124 0
+a5005d5e2177d7e219c0762e500aaee9c6b18ed1 124 0
 #2 := false
 #13 := 0::real
 decl f4 :: real
@@ -48943,7 +48931,227 @@
 #145 := [unit-resolution #117 #144]: #106
 [th-lemma #131 #143 #141 #85 #145]: false
 unsat
-d61ccd78ced6caee45a422d1f20159081681ab1d 88 0
+dcaa54c51c4b138dac6c0178c67a0d52f05b3002 57 0
+#2 := false
+#36 := 0::real
+decl f4 :: real
+#9 := f4
+#33 := -1::real
+#34 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#35 := (+ f3 #34)
+#37 := (<= #35 0::real)
+#40 := (ite #37 f4 f3)
+#61 := (= f3 #40)
+#65 := (not #61)
+#46 := (* -1::real #40)
+#47 := (+ f3 #46)
+#48 := (<= #47 0::real)
+#53 := (not #48)
+#10 := (<= f3 f4)
+#11 := (ite #10 f4 f3)
+#12 := (<= f3 #11)
+#13 := (not #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #48)
+#43 := (<= f3 #40)
+#49 := (iff #43 #48)
+#50 := [rewrite]: #49
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#52 := [trans #45 #50]: #51
+#55 := [monotonicity #52]: #54
+#30 := [asserted]: #13
+#56 := [mp #30 #55]: #53
+#64 := [hypothesis]: #61
+#66 := (or #65 #48)
+#67 := [th-lemma]: #66
+#68 := [unit-resolution #67 #64 #56]: false
+#69 := [lemma #68]: #65
+#59 := (or #37 #61)
+#57 := [def-axiom]: #59
+#72 := [unit-resolution #57 #69]: #37
+#31 := (+ f4 #46)
+#70 := (<= #31 0::real)
+#60 := (= f4 #40)
+#62 := (not #37)
+#63 := (or #62 #60)
+#58 := [def-axiom]: #63
+#73 := [unit-resolution #58 #72]: #60
+#74 := (not #60)
+#75 := (or #74 #70)
+#76 := [th-lemma]: #75
+#77 := [unit-resolution #76 #73]: #70
+[th-lemma #77 #56 #72]: false
+unsat
+ef39e4f5f84c012d1a7afd1eb9ae7787355eb901 57 0
+#2 := false
+#35 := 0::real
+decl f4 :: real
+#9 := f4
+decl f3 :: real
+#8 := f3
+#33 := -1::real
+#37 := (* -1::real f4)
+#38 := (+ f3 #37)
+#36 := (>= #38 0::real)
+#40 := (ite #36 f3 f4)
+#46 := (* -1::real #40)
+#47 := (+ f3 #46)
+#48 := (<= #47 0::real)
+#53 := (not #48)
+#10 := (<= f4 f3)
+#11 := (ite #10 f3 f4)
+#12 := (<= f3 #11)
+#13 := (not #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #48)
+#43 := (<= f3 #40)
+#49 := (iff #43 #48)
+#50 := [rewrite]: #49
+#44 := (iff #12 #43)
+#41 := (= #11 #40)
+#34 := (iff #10 #36)
+#39 := [rewrite]: #34
+#42 := [monotonicity #39]: #41
+#45 := [monotonicity #42]: #44
+#52 := [trans #45 #50]: #51
+#55 := [monotonicity #52]: #54
+#30 := [asserted]: #13
+#56 := [mp #30 #55]: #53
+#60 := (= f3 #40)
+#31 := (+ f4 #46)
+#64 := (<= #31 0::real)
+#61 := (= f4 #40)
+#62 := (not #36)
+#66 := [hypothesis]: #62
+#59 := (or #36 #61)
+#57 := [def-axiom]: #59
+#67 := [unit-resolution #57 #66]: #61
+#68 := (not #61)
+#69 := (or #68 #64)
+#70 := [th-lemma]: #69
+#71 := [unit-resolution #70 #67]: #64
+#72 := [th-lemma #56 #66 #71]: false
+#73 := [lemma #72]: #36
+#63 := (or #62 #60)
+#58 := [def-axiom]: #63
+#74 := [unit-resolution #58 #73]: #60
+#75 := (not #60)
+#76 := (or #75 #48)
+#77 := [th-lemma]: #76
+[unit-resolution #77 #74 #56]: false
+unsat
+7eae59ca8b45a027fbc591665e655f191dd6bbc4 103 0
+#2 := false
+#45 := 0::real
+decl f3 :: real
+#8 := f3
+decl f5 :: real
+#11 := f5
+#43 := -1::real
+#51 := (* -1::real f5)
+#63 := (+ f3 #51)
+#64 := (<= #63 0::real)
+#67 := (ite #64 f5 f3)
+#73 := (* -1::real #67)
+decl f4 :: real
+#9 := f4
+#74 := (+ f4 #73)
+#75 := (<= #74 0::real)
+#76 := (not #75)
+#52 := (+ f4 #51)
+#53 := (<= #52 0::real)
+#54 := (not #53)
+#47 := (* -1::real f4)
+#48 := (+ f3 #47)
+#46 := (>= #48 0::real)
+#44 := (not #46)
+#57 := (and #44 #54)
+#60 := (not #57)
+#81 := (or #60 #76)
+#84 := (not #81)
+#14 := (<= f3 f5)
+#15 := (ite #14 f5 f3)
+#16 := (< #15 f4)
+#12 := (< f5 f4)
+#10 := (< f3 f4)
+#13 := (and #10 #12)
+#17 := (implies #13 #16)
+#18 := (not #17)
+#87 := (iff #18 #84)
+#36 := (not #13)
+#37 := (or #36 #16)
+#40 := (not #37)
+#85 := (iff #40 #84)
+#82 := (iff #37 #81)
+#79 := (iff #16 #76)
+#70 := (< #67 f4)
+#77 := (iff #70 #76)
+#78 := [rewrite]: #77
+#71 := (iff #16 #70)
+#68 := (= #15 #67)
+#65 := (iff #14 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#72 := [monotonicity #69]: #71
+#80 := [trans #72 #78]: #79
+#61 := (iff #36 #60)
+#58 := (iff #13 #57)
+#55 := (iff #12 #54)
+#56 := [rewrite]: #55
+#49 := (iff #10 #44)
+#50 := [rewrite]: #49
+#59 := [monotonicity #50 #56]: #58
+#62 := [monotonicity #59]: #61
+#83 := [monotonicity #62 #80]: #82
+#86 := [monotonicity #83]: #85
+#41 := (iff #18 #40)
+#38 := (iff #17 #37)
+#39 := [rewrite]: #38
+#42 := [monotonicity #39]: #41
+#88 := [trans #42 #86]: #87
+#35 := [asserted]: #18
+#89 := [mp #35 #88]: #84
+#93 := [not-or-elim #89]: #75
+#90 := [not-or-elim #89]: #57
+#91 := [and-elim #90]: #44
+#97 := (+ f3 #73)
+#116 := (>= #97 0::real)
+#104 := (= f3 #67)
+#105 := (not #64)
+#103 := (= f5 #67)
+#110 := (not #103)
+#100 := (+ f5 #73)
+#98 := (>= #100 0::real)
+#107 := (not #98)
+#92 := [and-elim #90]: #54
+#96 := [hypothesis]: #98
+#94 := [th-lemma #96 #92 #93]: false
+#108 := [lemma #94]: #107
+#109 := [hypothesis]: #103
+#111 := (or #110 #98)
+#112 := [th-lemma]: #111
+#113 := [unit-resolution #112 #109 #108]: false
+#114 := [lemma #113]: #110
+#106 := (or #105 #103)
+#101 := [def-axiom]: #106
+#117 := [unit-resolution #101 #114]: #105
+#102 := (or #64 #104)
+#99 := [def-axiom]: #102
+#118 := [unit-resolution #99 #117]: #104
+#119 := (not #104)
+#120 := (or #119 #116)
+#121 := [th-lemma]: #120
+#122 := [unit-resolution #121 #118]: #116
+[th-lemma #122 #91 #93]: false
+unsat
+f8a9afea5f80c13265f7efc519efee9034d86aaa 88 0
 #2 := false
 decl f4 :: real
 #9 := f4
@@ -49032,7 +49240,7 @@
 #109 := [trans #108 #83]: #51
 [unit-resolution #57 #109]: false
 unsat
-ca09892ea7a85486f9b03ea9c10592c837c45810 66 0
+c008fb0a346a13df61c397707ef86eadaaaaf028 66 0
 #2 := false
 decl f3 :: real
 #9 := f3
@@ -49099,26 +49307,7 @@
 #86 := [trans #83 #85]: #33
 [unit-resolution #69 #86]: false
 unsat
-43eaef47fadbc62036dedee99a53f5627c2aea2d 18 0
-#2 := false
-decl f3 :: real
-#8 := f3
-#9 := (<= f3 f3)
-#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)
-#31 := [rewrite]: #30
-#34 := [monotonicity #31]: #33
-#38 := [trans #34 #36]: #37
-#27 := [asserted]: #10
-[mp #27 #38]: false
-unsat
-2a53f1e9691b42c6b60d21a29f4be1df277b5c0e 228 0
+3ea0cce22deeb1cf0a91c70b01f38d938cbfca2b 228 0
 #2 := false
 #9 := 0::real
 decl f4 :: real
@@ -49347,7 +49536,26 @@
 #250 := [unit-resolution #196 #249]: #190
 [th-lemma #236 #250 #131 #234 #248 #238]: false
 unsat
-f4ae26a6b5fd11d6cc627389a122029146dcae87 50 0
+6fa8c48985ebc99327aefe25360343fbef04699f 18 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := (<= f3 f3)
+#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)
+#31 := [rewrite]: #30
+#34 := [monotonicity #31]: #33
+#38 := [trans #34 #36]: #37
+#27 := [asserted]: #10
+[mp #27 #38]: false
+unsat
+6246909589ff44c53af5060ab09e0fb241168550 50 0
 #2 := false
 #44 := 0::real
 decl f4 :: real
@@ -49398,7 +49606,7 @@
 #68 := [not-or-elim #65]: #67
 [th-lemma #68 #66]: false
 unsat
-3c98043342d67c384e77c1b1c5755900a361dac4 55 0
+9a368b708e53fe0140c26e7ca790639aa465ac37 55 0
 #2 := false
 #43 := 0::real
 decl f4 :: real
@@ -49454,7 +49662,7 @@
 #72 := [not-or-elim #71]: #42
 [th-lemma #72 #73]: false
 unsat
-fe03b23c1657b4573ded6dbd4e82c4b99ddfa3be 52 0
+9d1b38a4c0ecf43766b852c7e4d288a3e46da901 52 0
 #2 := false
 #40 := 0::real
 decl f4 :: real
@@ -49507,7 +49715,417 @@
 #77 := [unit-resolution #76 #65]: #53
 [unit-resolution #77 #67]: false
 unsat
-d1bc3a4e60e3c1d280eca79821081b4e3318341f 43 0
+5631a67f2c650efd9761a68c96a2b28d9ed4cdd0 15 0
+#2 := false
+decl f3 :: real
+#8 := f3
+#9 := (< f3 f3)
+#10 := (not #9)
+#11 := (not #10)
+#33 := (iff #11 false)
+#31 := (iff #9 false)
+#32 := [rewrite]: #31
+#29 := (iff #11 #9)
+#30 := [rewrite]: #29
+#34 := [trans #30 #32]: #33
+#28 := [asserted]: #11
+[mp #28 #34]: false
+unsat
+c41bf12f912d9026a2697f2c615b98bf21c74fe7 75 0
+#2 := false
+#53 := 0::real
+decl f4 :: real
+#9 := f4
+#50 := -1::real
+#64 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#65 := (+ f3 #64)
+#66 := (<= #65 0::real)
+#69 := (not #66)
+decl f5 :: real
+#11 := f5
+#51 := (* -1::real f5)
+#60 := (+ f3 #51)
+#61 := (<= #60 0::real)
+#52 := (+ f4 #51)
+#54 := (<= #52 0::real)
+#57 := (not #54)
+#78 := (or #57 #61 #69)
+#83 := (not #78)
+#13 := (<= f3 f5)
+#12 := (<= f4 f5)
+#14 := (implies #12 #13)
+#10 := (<= f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#86 := (iff #16 #83)
+#34 := (not #12)
+#35 := (or #34 #13)
+#41 := (not #10)
+#42 := (or #41 #35)
+#47 := (not #42)
+#84 := (iff #47 #83)
+#81 := (iff #42 #78)
+#72 := (or #57 #61)
+#75 := (or #69 #72)
+#79 := (iff #75 #78)
+#80 := [rewrite]: #79
+#76 := (iff #42 #75)
+#73 := (iff #35 #72)
+#62 := (iff #13 #61)
+#63 := [rewrite]: #62
+#58 := (iff #34 #57)
+#55 := (iff #12 #54)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#74 := [monotonicity #59 #63]: #73
+#70 := (iff #41 #69)
+#67 := (iff #10 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#77 := [monotonicity #71 #74]: #76
+#82 := [trans #77 #80]: #81
+#85 := [monotonicity #82]: #84
+#48 := (iff #16 #47)
+#45 := (iff #15 #42)
+#38 := (implies #10 #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #15 #38)
+#36 := (iff #14 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #46]: #48
+#87 := [trans #49 #85]: #86
+#33 := [asserted]: #16
+#88 := [mp #33 #87]: #83
+#92 := [not-or-elim #88]: #66
+#90 := (not #61)
+#91 := [not-or-elim #88]: #90
+#89 := [not-or-elim #88]: #54
+[th-lemma #89 #91 #92]: false
+unsat
+9f5fa7c760db14a67656e2a38b69825c2338f5ee 80 0
+#2 := false
+#53 := 0::real
+decl f4 :: real
+#9 := f4
+#50 := -1::real
+#66 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#67 := (+ f3 #66)
+#65 := (>= #67 0::real)
+#64 := (not #65)
+decl f5 :: real
+#11 := f5
+#51 := (* -1::real f5)
+#60 := (+ f3 #51)
+#61 := (<= #60 0::real)
+#52 := (+ f4 #51)
+#54 := (<= #52 0::real)
+#57 := (not #54)
+#83 := (or #57 #61 #65)
+#88 := (not #83)
+#13 := (<= f3 f5)
+#12 := (<= f4 f5)
+#14 := (implies #12 #13)
+#10 := (< f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#91 := (iff #16 #88)
+#34 := (not #12)
+#35 := (or #34 #13)
+#41 := (not #10)
+#42 := (or #41 #35)
+#47 := (not #42)
+#89 := (iff #47 #88)
+#86 := (iff #42 #83)
+#77 := (or #57 #61)
+#80 := (or #65 #77)
+#84 := (iff #80 #83)
+#85 := [rewrite]: #84
+#81 := (iff #42 #80)
+#78 := (iff #35 #77)
+#62 := (iff #13 #61)
+#63 := [rewrite]: #62
+#58 := (iff #34 #57)
+#55 := (iff #12 #54)
+#56 := [rewrite]: #55
+#59 := [monotonicity #56]: #58
+#79 := [monotonicity #59 #63]: #78
+#75 := (iff #41 #65)
+#70 := (not #64)
+#73 := (iff #70 #65)
+#74 := [rewrite]: #73
+#71 := (iff #41 #70)
+#68 := (iff #10 #64)
+#69 := [rewrite]: #68
+#72 := [monotonicity #69]: #71
+#76 := [trans #72 #74]: #75
+#82 := [monotonicity #76 #79]: #81
+#87 := [trans #82 #85]: #86
+#90 := [monotonicity #87]: #89
+#48 := (iff #16 #47)
+#45 := (iff #15 #42)
+#38 := (implies #10 #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #15 #38)
+#36 := (iff #14 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #46]: #48
+#92 := [trans #49 #90]: #91
+#33 := [asserted]: #16
+#93 := [mp #33 #92]: #88
+#97 := [not-or-elim #93]: #64
+#95 := (not #61)
+#96 := [not-or-elim #93]: #95
+#94 := [not-or-elim #93]: #54
+[th-lemma #94 #96 #97]: false
+unsat
+ef54c95730a86f29e142ca8c0703d6c3a6105c5e 80 0
+#2 := false
+#52 := 0::real
+decl f4 :: real
+#9 := f4
+#50 := -1::real
+#69 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#70 := (+ f3 #69)
+#71 := (<= #70 0::real)
+#74 := (not #71)
+decl f5 :: real
+#11 := f5
+#54 := (* -1::real f5)
+#65 := (+ f3 #54)
+#66 := (<= #65 0::real)
+#55 := (+ f4 #54)
+#53 := (>= #55 0::real)
+#83 := (or #53 #66 #74)
+#88 := (not #83)
+#13 := (<= f3 f5)
+#12 := (< f4 f5)
+#14 := (implies #12 #13)
+#10 := (<= f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#91 := (iff #16 #88)
+#34 := (not #12)
+#35 := (or #34 #13)
+#41 := (not #10)
+#42 := (or #41 #35)
+#47 := (not #42)
+#89 := (iff #47 #88)
+#86 := (iff #42 #83)
+#77 := (or #53 #66)
+#80 := (or #74 #77)
+#84 := (iff #80 #83)
+#85 := [rewrite]: #84
+#81 := (iff #42 #80)
+#78 := (iff #35 #77)
+#67 := (iff #13 #66)
+#68 := [rewrite]: #67
+#63 := (iff #34 #53)
+#51 := (not #53)
+#58 := (not #51)
+#61 := (iff #58 #53)
+#62 := [rewrite]: #61
+#59 := (iff #34 #58)
+#56 := (iff #12 #51)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#79 := [monotonicity #64 #68]: #78
+#75 := (iff #41 #74)
+#72 := (iff #10 #71)
+#73 := [rewrite]: #72
+#76 := [monotonicity #73]: #75
+#82 := [monotonicity #76 #79]: #81
+#87 := [trans #82 #85]: #86
+#90 := [monotonicity #87]: #89
+#48 := (iff #16 #47)
+#45 := (iff #15 #42)
+#38 := (implies #10 #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #15 #38)
+#36 := (iff #14 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #46]: #48
+#92 := [trans #49 #90]: #91
+#33 := [asserted]: #16
+#93 := [mp #33 #92]: #88
+#97 := [not-or-elim #93]: #71
+#94 := [not-or-elim #93]: #51
+#95 := (not #66)
+#96 := [not-or-elim #93]: #95
+[th-lemma #96 #94 #97]: false
+unsat
+0c5d7dbb8aa2814977e1a9556d08eabbc11dd00b 85 0
+#2 := false
+#52 := 0::real
+decl f4 :: real
+#9 := f4
+#50 := -1::real
+#72 := (* -1::real f4)
+decl f3 :: real
+#8 := f3
+#73 := (+ f3 #72)
+#71 := (>= #73 0::real)
+#70 := (not #71)
+decl f5 :: real
+#11 := f5
+#54 := (* -1::real f5)
+#67 := (+ f3 #54)
+#66 := (>= #67 0::real)
+#65 := (not #66)
+#55 := (+ f4 #54)
+#53 := (>= #55 0::real)
+#89 := (or #53 #65 #71)
+#94 := (not #89)
+#13 := (< f3 f5)
+#12 := (< f4 f5)
+#14 := (implies #12 #13)
+#10 := (< f3 f4)
+#15 := (implies #10 #14)
+#16 := (not #15)
+#97 := (iff #16 #94)
+#34 := (not #12)
+#35 := (or #34 #13)
+#41 := (not #10)
+#42 := (or #41 #35)
+#47 := (not #42)
+#95 := (iff #47 #94)
+#92 := (iff #42 #89)
+#83 := (or #53 #65)
+#86 := (or #71 #83)
+#90 := (iff #86 #89)
+#91 := [rewrite]: #90
+#87 := (iff #42 #86)
+#84 := (iff #35 #83)
+#68 := (iff #13 #65)
+#69 := [rewrite]: #68
+#63 := (iff #34 #53)
+#51 := (not #53)
+#58 := (not #51)
+#61 := (iff #58 #53)
+#62 := [rewrite]: #61
+#59 := (iff #34 #58)
+#56 := (iff #12 #51)
+#57 := [rewrite]: #56
+#60 := [monotonicity #57]: #59
+#64 := [trans #60 #62]: #63
+#85 := [monotonicity #64 #69]: #84
+#81 := (iff #41 #71)
+#76 := (not #70)
+#79 := (iff #76 #71)
+#80 := [rewrite]: #79
+#77 := (iff #41 #76)
+#74 := (iff #10 #70)
+#75 := [rewrite]: #74
+#78 := [monotonicity #75]: #77
+#82 := [trans #78 #80]: #81
+#88 := [monotonicity #82 #85]: #87
+#93 := [trans #88 #91]: #92
+#96 := [monotonicity #93]: #95
+#48 := (iff #16 #47)
+#45 := (iff #15 #42)
+#38 := (implies #10 #35)
+#43 := (iff #38 #42)
+#44 := [rewrite]: #43
+#39 := (iff #15 #38)
+#36 := (iff #14 #35)
+#37 := [rewrite]: #36
+#40 := [monotonicity #37]: #39
+#46 := [trans #40 #44]: #45
+#49 := [monotonicity #46]: #48
+#98 := [trans #49 #96]: #97
+#33 := [asserted]: #16
+#99 := [mp #33 #98]: #94
+#102 := [not-or-elim #99]: #70
+#100 := [not-or-elim #99]: #51
+#101 := [not-or-elim #99]: #66
+[th-lemma #101 #100 #102]: false
+unsat
+ad850a4d677f642c1e98f0e5f3b7d3f84b6c874a 69 0
+#2 := false
+#44 := 0::real
+decl f5 :: real
+#11 := f5
+#42 := -1::real
+#51 := (* -1::real f5)
+decl f3 :: real
+#8 := f3
+#62 := (+ f3 #51)
+#63 := (<= #62 0::real)
+#64 := (not #63)
+decl f4 :: real
+#9 := f4
+#52 := (+ f4 #51)
+#50 := (>= #52 0::real)
+#53 := (not #50)
+#46 := (* -1::real f4)
+#47 := (+ f3 #46)
+#45 := (>= #47 0::real)
+#43 := (not #45)
+#56 := (and #43 #53)
+#59 := (not #56)
+#74 := (or #59 #63)
+#77 := (not #74)
+#14 := (< f5 f3)
+#15 := (not #14)
+#12 := (< f4 f5)
+#10 := (< f3 f4)
+#13 := (and #10 #12)
+#16 := (implies #13 #15)
+#17 := (not #16)
+#80 := (iff #17 #77)
+#35 := (not #13)
+#36 := (or #35 #15)
+#39 := (not #36)
+#78 := (iff #39 #77)
+#75 := (iff #36 #74)
+#72 := (iff #15 #63)
+#67 := (not #64)
+#70 := (iff #67 #63)
+#71 := [rewrite]: #70
+#68 := (iff #15 #67)
+#65 := (iff #14 #64)
+#66 := [rewrite]: #65
+#69 := [monotonicity #66]: #68
+#73 := [trans #69 #71]: #72
+#60 := (iff #35 #59)
+#57 := (iff #13 #56)
+#54 := (iff #12 #53)
+#55 := [rewrite]: #54
+#48 := (iff #10 #43)
+#49 := [rewrite]: #48
+#58 := [monotonicity #49 #55]: #57
+#61 := [monotonicity #58]: #60
+#76 := [monotonicity #61 #73]: #75
+#79 := [monotonicity #76]: #78
+#40 := (iff #17 #39)
+#37 := (iff #16 #36)
+#38 := [rewrite]: #37
+#41 := [monotonicity #38]: #40
+#81 := [trans #41 #79]: #80
+#34 := [asserted]: #17
+#82 := [mp #34 #81]: #77
+#86 := [not-or-elim #82]: #64
+#83 := [not-or-elim #82]: #56
+#84 := [and-elim #83]: #43
+#85 := [and-elim #83]: #53
+[th-lemma #85 #84 #86]: false
+unsat
+7db3ee0924a4cb1b14a4cebbf1c598c0b8dbec57 43 0
 #2 := false
 decl f5 :: (-> S2 S2 S3)
 #15 := (:var 0 S2)
@@ -49551,7 +50169,7 @@
 #145 := [quant-inst]: #231
 [unit-resolution #145 #45 #567]: false
 unsat
-2fee6903df28c3fb9fdfe41b68f30e20ac97873f 43 0
+8502f9cde674da83d9cbc8a977644ab6e85265ed 43 0
 #2 := false
 decl f5 :: (-> S2 S2 S3)
 #15 := (:var 0 S2)
@@ -49595,23 +50213,7 @@
 #163 := [quant-inst]: #235
 [unit-resolution #163 #45 #573]: false
 unsat
-9e985a47bba5857a10e800553a31e2def569aae1 15 0
-#2 := false
-decl f3 :: real
-#8 := f3
-#9 := (< f3 f3)
-#10 := (not #9)
-#11 := (not #10)
-#33 := (iff #11 false)
-#31 := (iff #9 false)
-#32 := [rewrite]: #31
-#29 := (iff #11 #9)
-#30 := [rewrite]: #29
-#34 := [trans #30 #32]: #33
-#28 := [asserted]: #11
-[mp #28 #34]: false
-unsat
-27ecb5fef2d88b43d79e314c4934972296e27d35 85 0
+7028fd42bf273f5da876a633b9b2fac12fd44679 85 0
 #2 := false
 decl f5 :: S2
 #9 := f5
@@ -49697,83 +50299,7 @@
 #206 := [unit-resolution #170 #205]: #239
 [unit-resolution #206 #186]: false
 unsat
-06bb2cc4f48d1ee0c5893ec218e691f0f9b659a2 75 0
-#2 := false
-#53 := 0::real
-decl f4 :: real
-#9 := f4
-#50 := -1::real
-#64 := (* -1::real f4)
-decl f3 :: real
-#8 := f3
-#65 := (+ f3 #64)
-#66 := (<= #65 0::real)
-#69 := (not #66)
-decl f5 :: real
-#11 := f5
-#51 := (* -1::real f5)
-#60 := (+ f3 #51)
-#61 := (<= #60 0::real)
-#52 := (+ f4 #51)
-#54 := (<= #52 0::real)
-#57 := (not #54)
-#78 := (or #57 #61 #69)
-#83 := (not #78)
-#13 := (<= f3 f5)
-#12 := (<= f4 f5)
-#14 := (implies #12 #13)
-#10 := (<= f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#86 := (iff #16 #83)
-#34 := (not #12)
-#35 := (or #34 #13)
-#41 := (not #10)
-#42 := (or #41 #35)
-#47 := (not #42)
-#84 := (iff #47 #83)
-#81 := (iff #42 #78)
-#72 := (or #57 #61)
-#75 := (or #69 #72)
-#79 := (iff #75 #78)
-#80 := [rewrite]: #79
-#76 := (iff #42 #75)
-#73 := (iff #35 #72)
-#62 := (iff #13 #61)
-#63 := [rewrite]: #62
-#58 := (iff #34 #57)
-#55 := (iff #12 #54)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#74 := [monotonicity #59 #63]: #73
-#70 := (iff #41 #69)
-#67 := (iff #10 #66)
-#68 := [rewrite]: #67
-#71 := [monotonicity #68]: #70
-#77 := [monotonicity #71 #74]: #76
-#82 := [trans #77 #80]: #81
-#85 := [monotonicity #82]: #84
-#48 := (iff #16 #47)
-#45 := (iff #15 #42)
-#38 := (implies #10 #35)
-#43 := (iff #38 #42)
-#44 := [rewrite]: #43
-#39 := (iff #15 #38)
-#36 := (iff #14 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#46 := [trans #40 #44]: #45
-#49 := [monotonicity #46]: #48
-#87 := [trans #49 #85]: #86
-#33 := [asserted]: #16
-#88 := [mp #33 #87]: #83
-#92 := [not-or-elim #88]: #66
-#90 := (not #61)
-#91 := [not-or-elim #88]: #90
-#89 := [not-or-elim #88]: #54
-[th-lemma #89 #91 #92]: false
-unsat
-8078fea9528cc0af35f2ba128aaa4ddff79359bb 155 0
+ab91d7002afe61891f92aa68c03a93dbeac150bb 155 0
 #2 := false
 decl f7 :: S2
 #12 := f7
@@ -49929,88 +50455,7 @@
 #263 := [def-axiom]: #176
 [unit-resolution #263 #289 #215 #569]: false
 unsat
-783cc208ed65b94bffd8eeb1bb636056967f88c2 80 0
-#2 := false
-#53 := 0::real
-decl f4 :: real
-#9 := f4
-#50 := -1::real
-#66 := (* -1::real f4)
-decl f3 :: real
-#8 := f3
-#67 := (+ f3 #66)
-#65 := (>= #67 0::real)
-#64 := (not #65)
-decl f5 :: real
-#11 := f5
-#51 := (* -1::real f5)
-#60 := (+ f3 #51)
-#61 := (<= #60 0::real)
-#52 := (+ f4 #51)
-#54 := (<= #52 0::real)
-#57 := (not #54)
-#83 := (or #57 #61 #65)
-#88 := (not #83)
-#13 := (<= f3 f5)
-#12 := (<= f4 f5)
-#14 := (implies #12 #13)
-#10 := (< f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#91 := (iff #16 #88)
-#34 := (not #12)
-#35 := (or #34 #13)
-#41 := (not #10)
-#42 := (or #41 #35)
-#47 := (not #42)
-#89 := (iff #47 #88)
-#86 := (iff #42 #83)
-#77 := (or #57 #61)
-#80 := (or #65 #77)
-#84 := (iff #80 #83)
-#85 := [rewrite]: #84
-#81 := (iff #42 #80)
-#78 := (iff #35 #77)
-#62 := (iff #13 #61)
-#63 := [rewrite]: #62
-#58 := (iff #34 #57)
-#55 := (iff #12 #54)
-#56 := [rewrite]: #55
-#59 := [monotonicity #56]: #58
-#79 := [monotonicity #59 #63]: #78
-#75 := (iff #41 #65)
-#70 := (not #64)
-#73 := (iff #70 #65)
-#74 := [rewrite]: #73
-#71 := (iff #41 #70)
-#68 := (iff #10 #64)
-#69 := [rewrite]: #68
-#72 := [monotonicity #69]: #71
-#76 := [trans #72 #74]: #75
-#82 := [monotonicity #76 #79]: #81
-#87 := [trans #82 #85]: #86
-#90 := [monotonicity #87]: #89
-#48 := (iff #16 #47)
-#45 := (iff #15 #42)
-#38 := (implies #10 #35)
-#43 := (iff #38 #42)
-#44 := [rewrite]: #43
-#39 := (iff #15 #38)
-#36 := (iff #14 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#46 := [trans #40 #44]: #45
-#49 := [monotonicity #46]: #48
-#92 := [trans #49 #90]: #91
-#33 := [asserted]: #16
-#93 := [mp #33 #92]: #88
-#97 := [not-or-elim #93]: #64
-#95 := (not #61)
-#96 := [not-or-elim #93]: #95
-#94 := [not-or-elim #93]: #54
-[th-lemma #94 #96 #97]: false
-unsat
-94dd01d5ce8a66038a4fafc28cc8fc9a3d392fba 91 0
+c53da5ad16e14d4123258f05451b97645b05e47b 91 0
 #2 := false
 decl f9 :: S3
 #14 := f9
@@ -50102,88 +50547,7 @@
 #320 := [unit-resolution #230 #598]: #299
 [unit-resolution #320 #321]: false
 unsat
-8618512b77e4b49096ff35dd0be727f2675c21ad 80 0
-#2 := false
-#52 := 0::real
-decl f4 :: real
-#9 := f4
-#50 := -1::real
-#69 := (* -1::real f4)
-decl f3 :: real
-#8 := f3
-#70 := (+ f3 #69)
-#71 := (<= #70 0::real)
-#74 := (not #71)
-decl f5 :: real
-#11 := f5
-#54 := (* -1::real f5)
-#65 := (+ f3 #54)
-#66 := (<= #65 0::real)
-#55 := (+ f4 #54)
-#53 := (>= #55 0::real)
-#83 := (or #53 #66 #74)
-#88 := (not #83)
-#13 := (<= f3 f5)
-#12 := (< f4 f5)
-#14 := (implies #12 #13)
-#10 := (<= f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#91 := (iff #16 #88)
-#34 := (not #12)
-#35 := (or #34 #13)
-#41 := (not #10)
-#42 := (or #41 #35)
-#47 := (not #42)
-#89 := (iff #47 #88)
-#86 := (iff #42 #83)
-#77 := (or #53 #66)
-#80 := (or #74 #77)
-#84 := (iff #80 #83)
-#85 := [rewrite]: #84
-#81 := (iff #42 #80)
-#78 := (iff #35 #77)
-#67 := (iff #13 #66)
-#68 := [rewrite]: #67
-#63 := (iff #34 #53)
-#51 := (not #53)
-#58 := (not #51)
-#61 := (iff #58 #53)
-#62 := [rewrite]: #61
-#59 := (iff #34 #58)
-#56 := (iff #12 #51)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#79 := [monotonicity #64 #68]: #78
-#75 := (iff #41 #74)
-#72 := (iff #10 #71)
-#73 := [rewrite]: #72
-#76 := [monotonicity #73]: #75
-#82 := [monotonicity #76 #79]: #81
-#87 := [trans #82 #85]: #86
-#90 := [monotonicity #87]: #89
-#48 := (iff #16 #47)
-#45 := (iff #15 #42)
-#38 := (implies #10 #35)
-#43 := (iff #38 #42)
-#44 := [rewrite]: #43
-#39 := (iff #15 #38)
-#36 := (iff #14 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#46 := [trans #40 #44]: #45
-#49 := [monotonicity #46]: #48
-#92 := [trans #49 #90]: #91
-#33 := [asserted]: #16
-#93 := [mp #33 #92]: #88
-#97 := [not-or-elim #93]: #71
-#94 := [not-or-elim #93]: #51
-#95 := (not #66)
-#96 := [not-or-elim #93]: #95
-[th-lemma #96 #94 #97]: false
-unsat
-f1064899dd3b2b344c829f77d7843d7c713a00e1 210 0
+4d6ae030a899d6a058af8429edba2402745a216b 210 0
 #2 := false
 decl f11 :: S5
 #16 := f11
@@ -50394,93 +50758,7 @@
 #321 := [def-axiom]: #234
 [unit-resolution #321 #597 #608 #332]: false
 unsat
-eb502ccd121bb8afc79076bd6ce9fee84004caac 85 0
-#2 := false
-#52 := 0::real
-decl f4 :: real
-#9 := f4
-#50 := -1::real
-#72 := (* -1::real f4)
-decl f3 :: real
-#8 := f3
-#73 := (+ f3 #72)
-#71 := (>= #73 0::real)
-#70 := (not #71)
-decl f5 :: real
-#11 := f5
-#54 := (* -1::real f5)
-#67 := (+ f3 #54)
-#66 := (>= #67 0::real)
-#65 := (not #66)
-#55 := (+ f4 #54)
-#53 := (>= #55 0::real)
-#89 := (or #53 #65 #71)
-#94 := (not #89)
-#13 := (< f3 f5)
-#12 := (< f4 f5)
-#14 := (implies #12 #13)
-#10 := (< f3 f4)
-#15 := (implies #10 #14)
-#16 := (not #15)
-#97 := (iff #16 #94)
-#34 := (not #12)
-#35 := (or #34 #13)
-#41 := (not #10)
-#42 := (or #41 #35)
-#47 := (not #42)
-#95 := (iff #47 #94)
-#92 := (iff #42 #89)
-#83 := (or #53 #65)
-#86 := (or #71 #83)
-#90 := (iff #86 #89)
-#91 := [rewrite]: #90
-#87 := (iff #42 #86)
-#84 := (iff #35 #83)
-#68 := (iff #13 #65)
-#69 := [rewrite]: #68
-#63 := (iff #34 #53)
-#51 := (not #53)
-#58 := (not #51)
-#61 := (iff #58 #53)
-#62 := [rewrite]: #61
-#59 := (iff #34 #58)
-#56 := (iff #12 #51)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#64 := [trans #60 #62]: #63
-#85 := [monotonicity #64 #69]: #84
-#81 := (iff #41 #71)
-#76 := (not #70)
-#79 := (iff #76 #71)
-#80 := [rewrite]: #79
-#77 := (iff #41 #76)
-#74 := (iff #10 #70)
-#75 := [rewrite]: #74
-#78 := [monotonicity #75]: #77
-#82 := [trans #78 #80]: #81
-#88 := [monotonicity #82 #85]: #87
-#93 := [trans #88 #91]: #92
-#96 := [monotonicity #93]: #95
-#48 := (iff #16 #47)
-#45 := (iff #15 #42)
-#38 := (implies #10 #35)
-#43 := (iff #38 #42)
-#44 := [rewrite]: #43
-#39 := (iff #15 #38)
-#36 := (iff #14 #35)
-#37 := [rewrite]: #36
-#40 := [monotonicity #37]: #39
-#46 := [trans #40 #44]: #45
-#49 := [monotonicity #46]: #48
-#98 := [trans #49 #96]: #97
-#33 := [asserted]: #16
-#99 := [mp #33 #98]: #94
-#102 := [not-or-elim #99]: #70
-#100 := [not-or-elim #99]: #51
-#101 := [not-or-elim #99]: #66
-[th-lemma #101 #100 #102]: false
-unsat
-53a01e2ecfe5fcdece4d167dc97ab57afbf5b665 144 0
+003bb45597da3e4b1800d61bab0b4e1d95dbdf99 144 0
 #2 := false
 decl f11 :: S3
 #16 := f11
@@ -50625,77 +50903,7 @@
 #432 := [unit-resolution #232 #431]: #301
 [unit-resolution #432 #433]: false
 unsat
-e52bb6d4fc18c5b1c7dd7b024810982ae6751f44 69 0
-#2 := false
-#44 := 0::real
-decl f5 :: real
-#11 := f5
-#42 := -1::real
-#51 := (* -1::real f5)
-decl f3 :: real
-#8 := f3
-#62 := (+ f3 #51)
-#63 := (<= #62 0::real)
-#64 := (not #63)
-decl f4 :: real
-#9 := f4
-#52 := (+ f4 #51)
-#50 := (>= #52 0::real)
-#53 := (not #50)
-#46 := (* -1::real f4)
-#47 := (+ f3 #46)
-#45 := (>= #47 0::real)
-#43 := (not #45)
-#56 := (and #43 #53)
-#59 := (not #56)
-#74 := (or #59 #63)
-#77 := (not #74)
-#14 := (< f5 f3)
-#15 := (not #14)
-#12 := (< f4 f5)
-#10 := (< f3 f4)
-#13 := (and #10 #12)
-#16 := (implies #13 #15)
-#17 := (not #16)
-#80 := (iff #17 #77)
-#35 := (not #13)
-#36 := (or #35 #15)
-#39 := (not #36)
-#78 := (iff #39 #77)
-#75 := (iff #36 #74)
-#72 := (iff #15 #63)
-#67 := (not #64)
-#70 := (iff #67 #63)
-#71 := [rewrite]: #70
-#68 := (iff #15 #67)
-#65 := (iff #14 #64)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#73 := [trans #69 #71]: #72
-#60 := (iff #35 #59)
-#57 := (iff #13 #56)
-#54 := (iff #12 #53)
-#55 := [rewrite]: #54
-#48 := (iff #10 #43)
-#49 := [rewrite]: #48
-#58 := [monotonicity #49 #55]: #57
-#61 := [monotonicity #58]: #60
-#76 := [monotonicity #61 #73]: #75
-#79 := [monotonicity #76]: #78
-#40 := (iff #17 #39)
-#37 := (iff #16 #36)
-#38 := [rewrite]: #37
-#41 := [monotonicity #38]: #40
-#81 := [trans #41 #79]: #80
-#34 := [asserted]: #17
-#82 := [mp #34 #81]: #77
-#86 := [not-or-elim #82]: #64
-#83 := [not-or-elim #82]: #56
-#84 := [and-elim #83]: #43
-#85 := [and-elim #83]: #53
-[th-lemma #85 #84 #86]: false
-unsat
-64328afb82eb17196ff1275de441cf37fad9bf4a 144 0
+31b5dadcaa7e7a3e69848f4809b04b844a6e8b56 144 0
 #2 := false
 decl f12 :: S3
 #17 := f12
@@ -50840,7 +51048,7 @@
 #432 := [unit-resolution #232 #431]: #301
 [unit-resolution #432 #433]: false
 unsat
-ca6daa73749cee4dc8b11e40a0201ba82325b005 103 0
+87752431ac232f724f4719a9dd746411dc8e0334 103 0
 #2 := false
 decl f6 :: S3
 #9 := f6
@@ -50944,7 +51152,7 @@
 #205 := [unit-resolution #171 #544]: #240
 [unit-resolution #205 #206]: false
 unsat
-0273cec9a3b2d721f13b81a5f7cb9a26c53610a3 111 0
+de0be68d62a4eef58cc08ca9b43494f9219ad474 111 0
 #2 := false
 decl f9 :: (-> S2 S3)
 decl f7 :: S2
@@ -51056,7 +51264,7 @@
 #66 := [not-or-elim #63]: #65
 [unit-resolution #66 #563]: false
 unsat
-59ef7a0dffeb5563b747aceef193a9e3d4f5d32d 117 0
+c992b1f07c8690f317843ec597ee745825b8d2b2 117 0
 #2 := false
 decl f6 :: (-> S3 S3 S2)
 decl f3 :: (-> S2 S3)
@@ -51174,7 +51382,7 @@
 #545 := [unit-resolution #170 #207]: #239
 [unit-resolution #545 #551]: false
 unsat
-13c013ce9b60f948f65ac05c9f64640c23a178bb 50 0
+6cc8ed53fe294f253a561b590f79ef0e0271d1c2 50 0
 #2 := false
 decl f3 :: (-> S2 S3 S4 S3 S4)
 #15 := (:var 1 S3)
@@ -51225,7 +51433,7 @@
 #155 := [quant-inst]: #241
 [unit-resolution #155 #55 #577]: false
 unsat
-1359b66e79f681fc73d3d69747fa44ddaf8fc00b 85 0
+d2a264ef3e43d9b7d009fa11ec172212f0bd6279 85 0
 #2 := false
 decl f8 :: (-> S3 S2 S4)
 decl f4 :: S2
@@ -51311,7 +51519,7 @@
 #241 := [quant-inst]: #250
 [unit-resolution #241 #592 #162]: false
 unsat
-85295dd87d7cebdd794ace783556d1b1d280619a 158 0
+13cd2a6082f8fe0947641619628aa7b793fa5eb0 158 0
 #2 := false
 decl f5 :: (-> S3 S2 S4)
 decl f3 :: S2
@@ -51470,7 +51678,7 @@
 #73 := [not-or-elim #72]: #71
 [unit-resolution #73 #578]: false
 unsat
-c0ecafa6d8b41ce5e1c9ab26d4838fdbd8c57d3d 72 0
+c3052f64b6a04dd1c8c5afaf04fa56dc411bc19c 72 0
 #2 := false
 decl f6 :: (-> S3 S2 S4 S3)
 #23 := (:var 0 S4)
@@ -51543,7 +51751,7 @@
 #265 := [quant-inst]: #264
 [unit-resolution #265 #73 #598]: false
 unsat
-dc41ee203ffc081fb445ff0000ddb4be9134fe60 81 0
+2dd7e2139c57ac13e3558d5a7c2ee7d6b5a8a254 81 0
 #2 := false
 decl f5 :: (-> S3 S2 S4)
 decl f3 :: S2
@@ -51625,7 +51833,7 @@
 #73 := [not-or-elim #72]: #71
 [unit-resolution #73 #230]: false
 unsat
-ae5be72196cf39e4c9692c5e427b5fb33965ed8f 187 0
+d43a3750252b86094159a0508ea79def7392e6da 187 0
 #2 := false
 decl f6 :: (-> S3 S2 S4)
 decl f5 :: S2
@@ -51813,7 +52021,7 @@
 #67 := [not-or-elim #66]: #65
 [unit-resolution #67 #496]: false
 unsat
-2f659b6a47ef547b90b00946538367bd9efdeee0 31 0
+d9c2fc1edc378ccb88037e9ae16a84f1542acb6f 31 0
 #2 := false
 decl f1 :: S1
 #4 := f1
@@ -51845,7 +52053,7 @@
 #62 := [asserted]: #12
 [mp #62 #79]: false
 unsat
-3329505aa680c82f608d61377279461a25778b94 58 0
+3df517f77a8847ec580730167b0937b5bdc9f32c 58 0
 #2 := false
 decl f3 :: (-> S2 S1)
 #13 := (:var 0 S2)
@@ -51904,7 +52112,7 @@
 #247 := [quant-inst]: #333
 [unit-resolution #247 #78 #667]: false
 unsat
-f68aac6d5243061ae9a95773075ebafc014b27eb 46 0
+1b877eab526e97351cb862fc0b9910541c0a7e4b 46 0
 #2 := false
 decl f3 :: (-> S2 S1)
 #17 := (:var 0 S2)
@@ -51951,7 +52159,7 @@
 #239 := [quant-inst]: #325
 [unit-resolution #239 #70 #666]: false
 unsat
-fca05a20824fb9ae1ae5b948aca1cdacb4ec3a3d 119 0
+9cf9419534c29ea2783ed62db9d7dac14034c845 119 0
 #2 := false
 decl f3 :: (-> S2 S2 S3 S1)
 decl f6 :: S3
@@ -52071,7 +52279,7 @@
 #320 := [unit-resolution #678 #329]: #319
 [unit-resolution #320 #318 #317]: false
 unsat
-3c528fd543bec1b0abe827803d678f1293dd7fb0 154 0
+db4d005483a981015636afecf4abdbe3eecdc540 154 0
 #2 := false
 decl f7 :: (-> S2 S3 S1)
 decl f6 :: S3
@@ -52226,7 +52434,7 @@
 #289 := [quant-inst]: #651
 [unit-resolution #289 #675 #294]: false
 unsat
-156b5bbccd88bf00c5d19d456c8d5c95867a3e79 128 0
+01e84163a16924ffd8e379badcb76f97c88eb8e1 128 0
 #2 := false
 decl f8 :: (-> S2 S3 S1)
 decl f6 :: S3
@@ -52355,7 +52563,7 @@
 #630 := [quant-inst]: #635
 [unit-resolution #630 #667 #637]: false
 unsat
-e9501ad699b29b1a0c65a378dbd0d68cdbadce66 146 0
+db25ac5ac3d60bebb553d3f6b343562b94a56253 146 0
 #2 := false
 decl f3 :: (-> S2 S2 S3 S1)
 decl f6 :: S3
@@ -52502,7 +52710,7 @@
 #632 := [unit-resolution #661 #642]: #635
 [unit-resolution #632 #631 #633]: false
 unsat
-60cdff9edbb9caaee078a8376311922be886cc87 121 0
+9033d495190da4d9088c43145881d91ed9687495 121 0
 #2 := false
 decl f3 :: (-> S2 S2 S3 S1)
 decl f5 :: S3
@@ -52624,7 +52832,7 @@
 #650 := [unit-resolution #323 #308]: #649
 [unit-resolution #650 #648 #647]: false
 unsat
-e7ec03d0541acce6c328f68f87047aa506800ef8 258 0
+d24feed52b94afbe0c3926c41e67eb725f57798d 258 0
 #2 := false
 decl f3 :: (-> S2 S3 S1)
 decl f8 :: S3
@@ -52883,7 +53091,7 @@
 #585 := [def-axiom]: #575
 [unit-resolution #585 #539 #546 #581]: false
 unsat
-0ff3bde207876a1e2bbf9f523fbb88a3af58b75b 153 0
+5b1f4025c8afe3b7c1a0fb50a6e0140ed51756ba 153 0
 #2 := false
 decl f7 :: (-> S2 S3 S1)
 decl f6 :: S3
@@ -53037,7 +53245,7 @@
 #339 := [unit-resolution #692 #689]: #338
 [unit-resolution #339 #337 #674]: false
 unsat
-af9d88d34e35638de5cad45a5fcb0943b421dc7f 141 0
+14e5476f4f3857f931521140926538df69a7900f 141 0
 #2 := false
 decl f7 :: (-> S2 S3 S1)
 decl f6 :: S3
@@ -53179,7 +53387,7 @@
 #312 := [quant-inst]: #652
 [unit-resolution #312 #668 #637]: false
 unsat
-1fe992aa332936da32d8835a880128a83f76f965 165 0
+17d0e6f19e122ea3db2aaeed6f9623f5ae4eb5b6 165 0
 #2 := false
 decl f7 :: (-> S2 S3 S1)
 decl f6 :: S3
@@ -53345,7 +53553,7 @@
 #665 := [def-axiom]: #664
 [unit-resolution #665 #655 #654]: false
 unsat
-71f085d2a9c00dbd0a999021926a678b17395642 164 0
+8c5227e6af822f9c7c2a140803c4af49bcf24bcb 164 0
 #2 := false
 decl f3 :: (-> S2 S2 S3 S1)
 decl f6 :: S3
@@ -53510,7 +53718,7 @@
 #626 := [unit-resolution #290 #354]: #625
 [unit-resolution #626 #636 #631]: false
 unsat
-4a2ec1009e57974d1e4c4125b313542f141f334f 142 0
+8156155a61a8ea554dc6bef7e96703a3d13ceb5f 142 0
 #2 := false
 decl f3 :: (-> S2 S2 S3 S1)
 decl f5 :: S3
@@ -53653,7 +53861,7 @@
 #655 := [unit-resolution #309 #645]: #295
 [unit-resolution #655 #294 #654]: false
 unsat
-9a719bb56314c3b4bab4bac5b0adde4b491a8497 279 0
+f0bdfff0ca207ce8dcf7aafa0f5fd49080a4003e 279 0
 #2 := false
 decl f3 :: (-> S2 S3 S1)
 decl f8 :: S3
@@ -53933,7 +54141,7 @@
 #580 := [def-axiom]: #579
 [unit-resolution #580 #526 #543 #572]: false
 unsat
-d1f4c7d9bd1f639df15a28175017a4537fb9637f 18 0
+0166ab8a0d2c326b9fbcb4a04b09f2f360525618 18 0
 #2 := false
 decl f3 :: S2
 #8 := f3
@@ -53952,211 +54160,3 @@
 #60 := [asserted]: #10
 [mp #60 #69]: false
 unsat
-c08976b5943421000363d731a8009a5d8459d100 93 0
-#2 := false
-decl f5 :: (-> S2 S1)
-decl f6 :: S2
-#16 := f6
-#20 := (f5 f6)
-decl f1 :: S1
-#4 := f1
-#65 := (= f1 #20)
-#84 := (not #65)
-decl f3 :: (-> S2 S3 S1)
-decl f4 :: S3
-#9 := f4
-#17 := (f3 f6 f4)
-#59 := (= f1 #17)
-#8 := (:var 0 S2)
-#12 := (f5 #8)
-#44 := (= f1 #12)
-#10 := (f3 #8 f4)
-#41 := (= f1 #10)
-#50 := (not #41)
-#51 := (or #50 #44)
-#56 := (forall (vars (?v0 S2)) #51)
-#62 := (and #56 #59)
-#71 := (not #62)
-#72 := (or #71 #65)
-#77 := (not #72)
-#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)
-#78 := (iff #23 #77)
-#75 := (iff #22 #72)
-#68 := (implies #62 #65)
-#73 := (iff #68 #72)
-#74 := [rewrite]: #73
-#69 := (iff #22 #68)
-#66 := (iff #21 #65)
-#67 := [rewrite]: #66
-#63 := (iff #19 #62)
-#60 := (iff #18 #59)
-#61 := [rewrite]: #60
-#57 := (iff #15 #56)
-#54 := (iff #14 #51)
-#47 := (implies #41 #44)
-#52 := (iff #47 #51)
-#53 := [rewrite]: #52
-#48 := (iff #14 #47)
-#45 := (iff #13 #44)
-#46 := [rewrite]: #45
-#42 := (iff #11 #41)
-#43 := [rewrite]: #42
-#49 := [monotonicity #43 #46]: #48
-#55 := [trans #49 #53]: #54
-#58 := [quant-intro #55]: #57
-#64 := [monotonicity #58 #61]: #63
-#70 := [monotonicity #64 #67]: #69
-#76 := [trans #70 #74]: #75
-#79 := [monotonicity #76]: #78
-#40 := [asserted]: #23
-#82 := [mp #40 #79]: #77
-#85 := [not-or-elim #82]: #84
-#80 := [not-or-elim #82]: #62
-#83 := [and-elim #80]: #59
-#572 := (pattern #12)
-#571 := (pattern #10)
-#573 := (forall (vars (?v0 S2)) (:pat #571 #572) #51)
-#576 := (iff #56 #573)
-#574 := (iff #51 #51)
-#575 := [refl]: #574
-#577 := [quant-intro #575]: #576
-#97 := (~ #56 #56)
-#95 := (~ #51 #51)
-#96 := [refl]: #95
-#98 := [nnf-pos #96]: #97
-#81 := [and-elim #80]: #56
-#87 := [mp~ #81 #98]: #56
-#578 := [mp #87 #577]: #573
-#155 := (not #59)
-#157 := (not #573)
-#244 := (or #157 #155 #65)
-#242 := (or #155 #65)
-#235 := (or #157 #242)
-#247 := (iff #235 #244)
-#175 := [rewrite]: #247
-#246 := [quant-inst]: #235
-#248 := [mp #246 #175]: #244
-[unit-resolution #248 #578 #83 #85]: false
-unsat
-9970f178c30353ca679caf02fa917fbf2a5e19ef 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
-#57 := (= f1 #19)
-decl f5 :: (-> S2 S1)
-#17 := (f5 f6)
-#54 := (= f1 #17)
-#60 := (and #54 #57)
-#63 := (not #60)
-#8 := (:var 0 S2)
-#12 := (f5 #8)
-#45 := (= f1 #12)
-#10 := (f3 #8 f4)
-#42 := (= f1 #10)
-#48 := (and #42 #45)
-#51 := (exists (vars (?v0 S2)) #48)
-#66 := (or #51 #63)
-#69 := (not #66)
-#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)
-#70 := (iff #24 #69)
-#67 := (iff #23 #66)
-#64 := (iff #22 #63)
-#61 := (iff #21 #60)
-#58 := (iff #20 #57)
-#59 := [rewrite]: #58
-#55 := (iff #18 #54)
-#56 := [rewrite]: #55
-#62 := [monotonicity #56 #59]: #61
-#65 := [monotonicity #62]: #64
-#52 := (iff #15 #51)
-#49 := (iff #14 #48)
-#46 := (iff #13 #45)
-#47 := [rewrite]: #46
-#43 := (iff #11 #42)
-#44 := [rewrite]: #43
-#50 := [monotonicity #44 #47]: #49
-#53 := [quant-intro #50]: #52
-#68 := [monotonicity #53 #65]: #67
-#71 := [monotonicity #68]: #70
-#41 := [asserted]: #24
-#74 := [mp #41 #71]: #69
-#75 := [not-or-elim #74]: #60
-#77 := [and-elim #75]: #57
-#76 := [and-elim #75]: #54
-#585 := (pattern #12)
-#584 := (pattern #10)
-#93 := (not #45)
-#92 := (not #42)
-#94 := (or #92 #93)
-#586 := (forall (vars (?v0 S2)) (:pat #584 #585) #94)
-#101 := (forall (vars (?v0 S2)) #94)
-#589 := (iff #101 #586)
-#587 := (iff #94 #94)
-#588 := [refl]: #587
-#590 := [quant-intro #588]: #589
-#87 := (not #48)
-#90 := (forall (vars (?v0 S2)) #87)
-#102 := (iff #90 #101)
-#99 := (iff #87 #94)
-#95 := (not #94)
-#83 := (not #95)
-#97 := (iff #83 #94)
-#98 := [rewrite]: #97
-#84 := (iff #87 #83)
-#85 := (iff #48 #95)
-#86 := [rewrite]: #85
-#96 := [monotonicity #86]: #84
-#100 := [trans #96 #98]: #99
-#103 := [quant-intro #100]: #102
-#72 := (not #51)
-#79 := (~ #72 #90)
-#88 := (~ #87 #87)
-#89 := [refl]: #88
-#80 := [nnf-neg #89]: #79
-#73 := [not-or-elim #74]: #72
-#91 := [mp~ #73 #80]: #90
-#104 := [mp #91 #103]: #101
-#591 := [mp #104 #590]: #586
-#255 := (not #57)
-#168 := (not #54)
-#248 := (not #586)
-#259 := (or #248 #168 #255)
-#169 := (or #255 #168)
-#260 := (or #248 #169)
-#578 := (iff #260 #259)
-#256 := (or #168 #255)
-#261 := (or #248 #256)
-#241 := (iff #261 #259)
-#576 := [rewrite]: #241
-#258 := (iff #260 #261)
-#170 := (iff #169 #256)
-#257 := [rewrite]: #170
-#262 := [monotonicity #257]: #258
-#235 := [trans #262 #576]: #578
-#188 := [quant-inst]: #260
-#365 := [mp #188 #235]: #259
-[unit-resolution #365 #591 #76 #77]: false
-unsat
diff -r 7f58a9a843c2 -r a462d5207aa6 src/HOL/SMT_Examples/SMT_Tests.thy
--- a/src/HOL/SMT_Examples/SMT_Tests.thy	Tue Oct 26 11:45:12 2010 +0200
+++ b/src/HOL/SMT_Examples/SMT_Tests.thy	Tue Oct 26 11:46:19 2010 +0200
@@ -8,7 +8,7 @@
 imports Complex_Main
 begin
 
-declare [[smt_solver=z3, z3_proofs=true]]
+declare [[smt_solver=z3, smt_oracle=false]]
 declare [[smt_certificates="~~/src/HOL/SMT_Examples/SMT_Tests.certs"]]
 declare [[smt_fixed=true]]
 
@@ -145,7 +145,7 @@
   "\<exists>x. P x \<longrightarrow> P a \<and> P b"
   "\<exists>x. (\<exists>y. P y) \<longrightarrow> P x" 
   "(\<exists>x. Q \<longrightarrow> P x) \<longleftrightarrow> (Q \<longrightarrow> (\<exists>x. P x))"
-  using [[z3_proofs=false, z3_options="AUTO_CONFIG=false SATURATE=true"]]
+  using [[smt_oracle=true, z3_options="AUTO_CONFIG=false SATURATE=true"]]
   by smt+
 
 lemma
@@ -165,7 +165,7 @@
   "(\<exists>x. \<forall>y. P x \<longleftrightarrow> P y) \<longrightarrow> ((\<exists>x. P x) \<longleftrightarrow> (\<forall>y. P y))"
   "\<exists>z. P z \<longrightarrow> (\<forall>x. P x)"
   "(\<exists>y. \<forall>x. R x y) \<longrightarrow> (\<forall>x. \<exists>y. R x y)"
-  using [[z3_proofs=false]]
+  using [[smt_oracle=true]]
   by smt+
 
 lemma
@@ -622,6 +622,7 @@
   "p1 = (x, y) \<and> p2 = (y, x) \<longrightarrow> fst p1 = snd p2"
   "(fst (x, y) = snd (x, y)) = (x = y)"
   "(fst p = snd p) = (p = (snd p, fst p))"
+  using [[smt_trace=true]]
   by smt+
 
 
diff -r 7f58a9a843c2 -r a462d5207aa6 src/HOL/SMT_Examples/SMT_Word_Examples.certs
--- a/src/HOL/SMT_Examples/SMT_Word_Examples.certs	Tue Oct 26 11:45:12 2010 +0200
+++ b/src/HOL/SMT_Examples/SMT_Word_Examples.certs	Tue Oct 26 11:46:19 2010 +0200
@@ -44,7 +44,7 @@
 unsat
 833f259a7dd52b3dddfc285b647a432c0daf13c1 1 0
 unsat
-234d4999f188127d090de762711164119fba49e9 1 0
+7d5a71ba893f865044699426792a024fe1612235 1 0
 unsat
 6adbd17723088c30f1d1f0f07e1e4df2076a51b2 1 0
 unsat
diff -r 7f58a9a843c2 -r a462d5207aa6 src/HOL/SMT_Examples/SMT_Word_Examples.thy
--- a/src/HOL/SMT_Examples/SMT_Word_Examples.thy	Tue Oct 26 11:45:12 2010 +0200
+++ b/src/HOL/SMT_Examples/SMT_Word_Examples.thy	Tue Oct 26 11:46:19 2010 +0200
@@ -8,7 +8,7 @@
 imports Word
 begin
 
-declare [[smt_solver=z3, z3_proofs=false]]
+declare [[smt_solver=z3, smt_oracle=true]]
 declare [[smt_certificates="~~/src/HOL/SMT_Examples/SMT_Word_Examples.certs"]]
 declare [[smt_fixed=true]]